Section 3 Special Topics

[116] Lu T, Law CK, Ju Y. Some aspects of chemical kinetics in chapman-Jouguet detonation: Induction length analysis. Journal of Propulsion and Power. 2003;**19**(5):901-907

*Direct Numerical Simulations - An Introduction and Applications*

[124] Burr JR, Yu KH. Shock in reactive cross-flow under partial confinement. In: International Colloquium on the Dynamics of Explosions and Reactive

[125] Burr JR, Yu K. Detonation wave propagation in cross-flow of discretely spaced reactant jets. In: 53rd AIAA/SAE/ ASEE Joint Propulsion Conference.

[126] Burr JR, Yu KH. Blast wave propagation in cross-flow of detonable mixture. In: 50th AIAA/ASME/SAE/ ASEE Joint Propulsion Conference.

Systems. 2015. pp. 1-6

2017. p. 4908

2014. p. 3984

[117] Westbrook CK. Hydrogen oxidation kinetics in gaseous

2017. p. 374

2006. p. 7956

**136**

detonations. Combustion Science and Technology. 1982;**29**(1–2):67-81

[118] Masselot D, Fiévet R, Raman V. Effect of equivalence ratio and turbulence fluctuations on the propagation of detonations. In: 55th AIAA Aerospace Sciences Meeting.

[119] Roy A, Strakey P, Sidwell T, Ferguson DH. Unsteady heat transfer analysis to predict combustor wall temperature in rotating detonation engine. In: 51st AIAA/SAE/ASEE Joint Propulsion Conference. 2015. p. 902

[120] Strakey P, Ferguson D, Sisler A, Nix A. Computationally quantifying loss mechanisms in a rotating detonation engine. In: 54th AIAA Aerospace Sciences Meeting. 2016. p. 900

[121] Falempin F, Daniau E, Getin N, Bykovskii F, Zhdan S. Toward a continuous detonation wave rocket engine demonstrator. In: 14th AIAA/ AHI Space Planes and Hypersonic Systems and Technologies Conference.

[122] Asahara M, Tsuboi N, Hayashi AK, Yamada E. Two-dimensional simulation on propagation mechanism of H2/O2 cylindrical detonation with a detailed reaction model: Influence of initial energy and propagation mechanism. Combustion Science and Technology.

[123] Pope S. PDF methods for turbulent reactive flows. Progress in Energy and Combustion Science. 1985;**11**(2):119-192

2010;**182**(11–12):1884-1900

**Chapter 8**

**Abstract**

as cathodes.

**1. Introduction**

**139**

particles, electrochemical current noise

Cr, acting as preferential sites for oxygen reduction.

laminar flow (0.1 ms<sup>1</sup>

in Seawater

Effect of Laminar Flow on the

Corrosion Activity of AA6061-T6

*Gloria Acosta, Lucien Veleva, Luis Chávez and Juan L. López*

The electrochemical behaviour and surface changes on AA6061-T6 alloy exposed to Caribbean seawater from the Cozumel Channel for 30 days under

**Keywords:** aluminium alloy 6061-T6, seawater, laminar flow, intermetallic

Aluminium alloy (AA) 6061-T6 is popular as a nonferrous material for structures in seawater [1] and is characterised by various properties, such as strength-toweight ratio, extrudability—particularly for the manufacture of profiles with complex geometry, low thermal expansion coefficient, good wear resistance and corrosion resistance [2]. The alloy presents good corrosion resistance in many environments having neutral pH, because of the formation of protective amorphous aluminium oxide film on its surface of approximately 2–3 nm thickness and is insoluble in water [3, 4]. The addition of alloying elements to aluminium increases its mechanical properties [5]; however, the precipitated intermetallic particles (IMPs) have a harmful effect on the corrosion resistance of the Al alloys [4, 6–10]. IMPs present electrochemical behaviour different from the alloy matrix, and they may be classified in two types: cathodic and anodic [7, 9–12]. The electrochemically active anodic particles are rich in Mg, Si and Al, with Mg preferential dissolution, leaving a cavity in the oxide layer, while the cathodic particles are rich in Fe, Si and

ditions. Open circuit potential monitoring and electrochemical current fluctuations, considered as electrochemical noise (EN), were employed as two nondestructive methods. The calculated corrosion current, based on Rn, was one order higher in laminar flow. The fluctuations of current were transformed in the frequency domain. Their power spectral density (PSD) plots were obtained in order to gain information concerning the dynamic of the spontaneous release of energy during the corrosion process. The value of the exponent *β* in PSD graphs suggested that the localised corrosion on AA6061-T6 surface occurs as a persistent stationary process, which dynamic is controlled by oxygen diffusion. The changes in the morphology and elemental composition of the formed layers revealed that the localised attacks occurred in the vicinity of intermetallic particles rich in Fe and Cu, which act

) were studied, these contrasting then with stationary con-

#### **Chapter 8**

## Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater

*Gloria Acosta, Lucien Veleva, Luis Chávez and Juan L. López*

#### **Abstract**

The electrochemical behaviour and surface changes on AA6061-T6 alloy exposed to Caribbean seawater from the Cozumel Channel for 30 days under laminar flow (0.1 ms<sup>1</sup> ) were studied, these contrasting then with stationary conditions. Open circuit potential monitoring and electrochemical current fluctuations, considered as electrochemical noise (EN), were employed as two nondestructive methods. The calculated corrosion current, based on Rn, was one order higher in laminar flow. The fluctuations of current were transformed in the frequency domain. Their power spectral density (PSD) plots were obtained in order to gain information concerning the dynamic of the spontaneous release of energy during the corrosion process. The value of the exponent *β* in PSD graphs suggested that the localised corrosion on AA6061-T6 surface occurs as a persistent stationary process, which dynamic is controlled by oxygen diffusion. The changes in the morphology and elemental composition of the formed layers revealed that the localised attacks occurred in the vicinity of intermetallic particles rich in Fe and Cu, which act as cathodes.

**Keywords:** aluminium alloy 6061-T6, seawater, laminar flow, intermetallic particles, electrochemical current noise

#### **1. Introduction**

Aluminium alloy (AA) 6061-T6 is popular as a nonferrous material for structures in seawater [1] and is characterised by various properties, such as strength-toweight ratio, extrudability—particularly for the manufacture of profiles with complex geometry, low thermal expansion coefficient, good wear resistance and corrosion resistance [2]. The alloy presents good corrosion resistance in many environments having neutral pH, because of the formation of protective amorphous aluminium oxide film on its surface of approximately 2–3 nm thickness and is insoluble in water [3, 4]. The addition of alloying elements to aluminium increases its mechanical properties [5]; however, the precipitated intermetallic particles (IMPs) have a harmful effect on the corrosion resistance of the Al alloys [4, 6–10]. IMPs present electrochemical behaviour different from the alloy matrix, and they may be classified in two types: cathodic and anodic [7, 9–12]. The electrochemically active anodic particles are rich in Mg, Si and Al, with Mg preferential dissolution, leaving a cavity in the oxide layer, while the cathodic particles are rich in Fe, Si and Cr, acting as preferential sites for oxygen reduction.

The localised corrosion becomes greater in the presence of aggressive ions, such as chlorides [4, 13–15], and corrosion pits initiate in oxide film sites, weakened by chloride attack. Moreover, the heterogeneity of the surface could result in favourable nucleation sites.

seawater composition and physicochemical properties were as follows: salinity

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

0.18 μmol/L, ammonia 0.99 μmol/L, pH 7.3, dissolved oxygen 5.8 mg L�<sup>1</sup> and

Samples of 1 cm2 were embedded in Epofix resin as working electrodes for electrochemical tests. In addition, samples of 1 cm<sup>2</sup> were cleaned with ethanol and immersed in 100 mL of seawater (triplicated) under flow conditions, for 0, 5, 15 and 30 days, respectively. Before exposure, the specimens were ground with silicon carbide paper to 4000 grit, using distilled water as lubricant. They were washed

, sulphates 2.82 g L�<sup>1</sup>

The speed range found in the Cozumel Channel indicates that the ocean current

peristaltic pump (LAMBDA Laboratory Instrument) with the electrochemical cell has a diameter of 6 mm, and using the lower limit of the flow speed (0.1 m s�<sup>1</sup>

calculated Reynolds number was 622.97, which corresponds to laminar hydrodynamic flow [31]. The dimensionless NRe characterises the diffusion-dependent system and is governed by the ratio of the inertial forces acting on the fluid to the

> *NRe* <sup>¼</sup> *<sup>ρ</sup>ud μ*

), *d* is the tubing diameter (6 mm) and *μ* is the seawater viscosity

AA6061-T6 samples were characterised before and after exposure in seawater by SEM-EDS (Philips-XL and ESEM-JEOL JSM-7600F), in order to observe the microstructure and elemental changes on their surface. Corrosion products formed on AA6061-T6 sample surfaces were identified through X-ray photoelectron spectroscopy (XPS, K-alpha, Thermo Scientific, Waltham, MA, USA). In addition, corrosion products were removed in accordance with ASTM G1-90 standard [32],

A multiport electrochemical cell kit (Gamry Instruments, 1 L total volume) and a Gamry PCI4G750-52103 potentiostat were used for all electrochemical measurements. The experimental setup employed was according to ASTM G199-09 standard [33]: two identical AA6061-T6 working electrodes (WEs) connected to a zero resistance ammeter (ZRA) and a saturated calomel electrode (SCE, Hg2+/Hg2Cl2 = 0.244 V) as reference electrode. The electrodes were immersed in an electrochemical cell with seawater, employed as test electrolyte. All tests were carried out in laminar and stationary flow conditions up to 30 days. EN data were collected at different times during 3 h, initial, 1, 5, 15 and 30 days in OCP, with a sampling frequency of 10 Hz. The obtained data of current and potential fluctuations were plotted vs. time. The current fluctuations were considered as EN and processed in the frequency domain by fast FFT to graph PSD. The PSD as a function of low

). All experiments were carried out at 21°C.

where *ρ* is the fluid density (seawater, 997.8 kg m�<sup>3</sup>

. The tubing employed to connect the

), *u* is the flow speed

, nitrates 0.48 μmol/L, nitrites

), the

(1)

36.4 g L�<sup>1</sup>

viscous forces:

(0.1 m s�<sup>1</sup>

**141**

(0.961 � <sup>10</sup>�<sup>3</sup> Nsm�<sup>2</sup>

**2.3 Surface analysis**

conductivity 51.6 mS.

, chlorides 20.12 g L�<sup>1</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

with distillated water and dried in air.

speed oscillates between 0.1 and 1 m s�<sup>1</sup>

and the alloy surfaces were reexamined.

**2.4 Electrochemical tests**

**2.2 Laminar flow of seawater**

Seawater is a complex electrolyte of different ions, with a high salinity (3.5%, density 1.023 g/cm3 at 25°C), which causes damage to metals in a short time [16, 17]. The principal parameters that affect the corrosion behaviour of metals immersed in this electrolyte are oxygen content, dissolved mineral salts, pH, temperature, specific contaminants and flow velocity [16, 18].

The characterisation of the corrosion process requires electrochemical nondestructive techniques, and the preferred methods are those that do not apply external polarisation. The monitoring of the open circuit potential (φcorr, free corrosion potential) or corrosion current is one of these and is easy to handle. Fluctuations may be interpreted as electrochemical noise (EN), which is useful for the purposes of corrosion mechanism characterisation. Electrochemical noise is presented by random fluctuations of corrosion potential or current, typically with frequencies below 10 Hz and low amplitude [19]. This technique can provide information concerning the nature of the corrosion process and the rate thereof. The main sources of EN observed in corrosion systems are attributed to microscopic and macroscopic events [19–21]. EN measurements can be performed under corrosion potential or any constant potential/current, depending on the research objective, to analyse the corrosion mechanism and obtain the corrosion rate [20].

EN measurements can be analysed transforming the data in the frequency domain by fast Fourier transform (FFT) to obtain power spectral density (PSD) [22, 23]. PSD plots display a slope, *β* exponent, which enables the differentiation between series with fractional Gaussian noise (*fGn*, *β* from 1 to 1) and fractional Brownian motion (fBm, *β* from 1 to 3). The *fGn* is a stationary process, and the fBm is nonstationary [24, 25]. The *β* exponent is a parameter correlated with the strength of persistence in a process [26]. In our previous studies, EN technique was carried out to characterise the first stages of corrosion in stationary seawater of copper [27], aluminium [28] and aluminium alloys [29], as well as the initial stages of AZ31B Mg alloy in simulated body fluid [30].

The object of this study is to investigate the electrochemical behaviour and surface changes on AA6061-T6 alloy, exposed to Caribbean seawater (Cozumel Channel) under laminar flow, contrasting these with stationary flow. Two nondestructive electrochemical methods were used to test the corrosion resistance of the alloy. The corrosion current and φcorr were considered as EN and transformed in the frequency domain, in order to gain information on the dynamics of the spontaneous release of energy during the corrosion process. X-ray photoelectron spectroscopy (XPS) measurement was employed to analyse the composition of the formed corrosion layers, as well as SEM-EDS surface analysis. To the best of own knowledge, there is still no study on the initial stages of localised corrosion of AA6061-T6 alloy in laminar flow conditions.

#### **2. Experimental**

#### **2.1 Materials**

The nominal composition of AA6061-T6 (Metal Plastic Mexicali) was (wt%) 1.10% Mg, 0.5% Fe, 0.4% Si, 0.31% Cu, 0.19% Cr, 0.07% Zn and 0.05% Ti and the remainder Al. The seawater was extracted from the Caribbean Cozumel Channel, at 10 km offshore, to minimise the effect of human pollution, and a depth of 10 m. The *Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

seawater composition and physicochemical properties were as follows: salinity 36.4 g L�<sup>1</sup> , chlorides 20.12 g L�<sup>1</sup> , sulphates 2.82 g L�<sup>1</sup> , nitrates 0.48 μmol/L, nitrites 0.18 μmol/L, ammonia 0.99 μmol/L, pH 7.3, dissolved oxygen 5.8 mg L�<sup>1</sup> and conductivity 51.6 mS.

Samples of 1 cm2 were embedded in Epofix resin as working electrodes for electrochemical tests. In addition, samples of 1 cm<sup>2</sup> were cleaned with ethanol and immersed in 100 mL of seawater (triplicated) under flow conditions, for 0, 5, 15 and 30 days, respectively. Before exposure, the specimens were ground with silicon carbide paper to 4000 grit, using distilled water as lubricant. They were washed with distillated water and dried in air.

#### **2.2 Laminar flow of seawater**

The localised corrosion becomes greater in the presence of aggressive ions, such as chlorides [4, 13–15], and corrosion pits initiate in oxide film sites, weakened by

Seawater is a complex electrolyte of different ions, with a high salinity (3.5%,

The characterisation of the corrosion process requires electrochemical nondestructive techniques, and the preferred methods are those that do not apply external polarisation. The monitoring of the open circuit potential (φcorr, free corrosion potential) or corrosion current is one of these and is easy to handle. Fluctuations may be interpreted as electrochemical noise (EN), which is useful for the purposes of corrosion mechanism characterisation. Electrochemical noise is presented by random fluctuations of corrosion potential or current, typically with frequencies below 10 Hz and low amplitude [19]. This technique can provide information concerning the nature of the corrosion process and the rate thereof. The main sources of EN observed in corrosion systems are attributed to microscopic and macroscopic events [19–21]. EN measurements can be performed under corrosion potential or any constant potential/current, depending on the research objective, to

chloride attack. Moreover, the heterogeneity of the surface could result in

density 1.023 g/cm3 at 25°C), which causes damage to metals in a short time [16, 17]. The principal parameters that affect the corrosion behaviour of metals immersed in this electrolyte are oxygen content, dissolved mineral salts, pH, tem-

perature, specific contaminants and flow velocity [16, 18].

*Direct Numerical Simulations - An Introduction and Applications*

analyse the corrosion mechanism and obtain the corrosion rate [20].

EN measurements can be analysed transforming the data in the frequency domain by fast Fourier transform (FFT) to obtain power spectral density (PSD) [22, 23]. PSD plots display a slope, *β* exponent, which enables the differentiation between series with fractional Gaussian noise (*fGn*, *β* from 1 to 1) and fractional Brownian motion (fBm, *β* from 1 to 3). The *fGn* is a stationary process, and the fBm is nonstationary [24, 25]. The *β* exponent is a parameter correlated with the strength of persistence in a process [26]. In our previous studies, EN technique was carried out to characterise the first stages of corrosion in stationary seawater of copper [27], aluminium [28] and aluminium alloys [29], as well as the initial stages of AZ31B Mg

The object of this study is to investigate the electrochemical behaviour and surface changes on AA6061-T6 alloy, exposed to Caribbean seawater (Cozumel Channel) under laminar flow, contrasting these with stationary flow. Two nondestructive electrochemical methods were used to test the corrosion resistance of the alloy. The corrosion current and φcorr were considered as EN and transformed in the frequency domain, in order to gain information on the dynamics of the spontaneous release of energy during the corrosion process. X-ray photoelectron spectroscopy (XPS) measurement was employed to analyse the composition of the formed corrosion layers, as well as SEM-EDS surface analysis. To the best of own knowledge, there is still no study on the initial stages of localised corrosion of AA6061-T6 alloy

The nominal composition of AA6061-T6 (Metal Plastic Mexicali) was (wt%) 1.10% Mg, 0.5% Fe, 0.4% Si, 0.31% Cu, 0.19% Cr, 0.07% Zn and 0.05% Ti and the remainder Al. The seawater was extracted from the Caribbean Cozumel Channel, at 10 km offshore, to minimise the effect of human pollution, and a depth of 10 m. The

favourable nucleation sites.

alloy in simulated body fluid [30].

in laminar flow conditions.

**2. Experimental**

**2.1 Materials**

**140**

The speed range found in the Cozumel Channel indicates that the ocean current speed oscillates between 0.1 and 1 m s�<sup>1</sup> . The tubing employed to connect the peristaltic pump (LAMBDA Laboratory Instrument) with the electrochemical cell has a diameter of 6 mm, and using the lower limit of the flow speed (0.1 m s�<sup>1</sup> ), the calculated Reynolds number was 622.97, which corresponds to laminar hydrodynamic flow [31]. The dimensionless NRe characterises the diffusion-dependent system and is governed by the ratio of the inertial forces acting on the fluid to the viscous forces:

$$N\_{Re} = \frac{\rho \overline{u}d}{\mu} \tag{1}$$

where *ρ* is the fluid density (seawater, 997.8 kg m�<sup>3</sup> ), *u* is the flow speed (0.1 m s�<sup>1</sup> ), *d* is the tubing diameter (6 mm) and *μ* is the seawater viscosity (0.961 � <sup>10</sup>�<sup>3</sup> Nsm�<sup>2</sup> ). All experiments were carried out at 21°C.

#### **2.3 Surface analysis**

AA6061-T6 samples were characterised before and after exposure in seawater by SEM-EDS (Philips-XL and ESEM-JEOL JSM-7600F), in order to observe the microstructure and elemental changes on their surface. Corrosion products formed on AA6061-T6 sample surfaces were identified through X-ray photoelectron spectroscopy (XPS, K-alpha, Thermo Scientific, Waltham, MA, USA). In addition, corrosion products were removed in accordance with ASTM G1-90 standard [32], and the alloy surfaces were reexamined.

#### **2.4 Electrochemical tests**

A multiport electrochemical cell kit (Gamry Instruments, 1 L total volume) and a Gamry PCI4G750-52103 potentiostat were used for all electrochemical measurements. The experimental setup employed was according to ASTM G199-09 standard [33]: two identical AA6061-T6 working electrodes (WEs) connected to a zero resistance ammeter (ZRA) and a saturated calomel electrode (SCE, Hg2+/Hg2Cl2 = 0.244 V) as reference electrode. The electrodes were immersed in an electrochemical cell with seawater, employed as test electrolyte. All tests were carried out in laminar and stationary flow conditions up to 30 days. EN data were collected at different times during 3 h, initial, 1, 5, 15 and 30 days in OCP, with a sampling frequency of 10 Hz. The obtained data of current and potential fluctuations were plotted vs. time. The current fluctuations were considered as EN and processed in the frequency domain by fast FFT to graph PSD. The PSD as a function of low

frequencies was analysed on bi-logarithmic scale (10�<sup>3</sup> ‒1 Hz) of power per unit frequency (A2 /Hz) vs. frequency (Hz). These procedures allowed the fitting of a straight line and obtention of the *β* slope. The *β* value characterises the corrosion mechanism on AA6061-T6 surface. The processing of data was realised with Electrochemical Signal Analyser V.7.0.1 software (Gamry Instruments, Philadelphia, PA, USA). All measurements were checked in triplicate.

#### *2.4.1 Energy spectral density*

The energy spectral density expresses how the energy of a time series is dispersed with a frequency; it can reflect the change in system dynamic. For a signal X(t) the energy EE is [34]

$$E = \int\_{-\infty}^{\infty} |\varkappa(t)|^2 dt \tag{2}$$

**Figure 1.**

*(2000).*

**Table 1.**

**Figure 2.**

**Table 2.**

**143**

*(a) and (b) after removal of corrosion layer.*

*(a) SEM images (500) of AA6061-T6 surface before immersion in Caribbean seawater and (b) zoom zone*

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

**Element C O Mg Al Si Cr Mn Fe Cu** A 2.4 3.3 — 60.3 6.5 1.3 1.6 23.7 0.9 B 2.3 2.7 — 59.3 7.4 1.3 1.5 24.2 1.3 C 2.2 4.5 — 71.7 4.8 0.6 0.9 14.6 0.7 D 2.0 2.1 1.7 93.7 0.5 —— ——

*SEM images of AA6061-T6 surface after exposure in Caribbean seawater under laminar flow for 5 days*

**Element C O Mg Al Si Cr Mn Fe Cu** D 10.9 4.7 0.4 58.0 5.8 0.6 1.2 17.6 0.8

*under laminar flow at 21°C and (b) after removal of corrosion products.*

*(a) EDS analysis (wt.%) of aluminium alloy 6061-T6 surface after 5 days of exposure in Caribbean seawater*

**(a) Element C O Na Mg Al Si S Cl K Ca** A — 47.4 0.7 1.2 25.1 — 1.8 23.3 — 0.5 B 6.4 56.6 1.9 1.0 29.2 — 0.4 0.5 0.5 3.5 C 4.4 11.5 — 0.8 81.2 0.4 0.4 0.3 0.8 0.2 **(b)**

*EDS analysis (wt%) of reference aluminium alloy 6061-T6 surface.*

For signals with a finite total energy, an equivalent expression for the energy is expressed as

$$E = \int\_{-\infty}^{\infty} \left| \mathbf{x}(t) \right|^2 dt = \int\_{-\infty}^{\infty} \left| \hat{\mathbf{x}}(f) \right|^2 df \tag{3}$$

And using the Fourier transform of the signal:

$$
\hat{\mathfrak{x}}(f) = \int\_{-\infty}^{\infty} e^{-2\pi \circ \mathfrak{f}t} \mathfrak{x}(t) df \tag{4}
$$

where *f* is the frequency in Hz.

The integral on the right-hand side of Eq. (3) is the energy of the signal, and the integrand j j *x f* ^ð Þ <sup>2</sup> describes the energy per unit frequency contained in the signal (ESD).

#### **3. Results and discussion**

#### **3.1 Surface analysis**

**Figure 1** shows SEM images of the as-received specimen of 6061-T6 aluminium alloy surface. Small precipitates (labelled as A, B, C) may be seen (**Figure 1b**). In accordance with EDS, presented in **Table 1**, these precipitates correspond to particles rich in Fe and could be considered as elements of the following phases: Al3Fe, Al▬Si▬Mn▬Fe and α-Al(Fe, Mn, Cu) [9, 10, 35]. The elemental composition of the surface layer is indicated by zone D.

**Figure 2a** presents the SEM image of the film formed on the surface of the sample after 5 days of immersion in seawater from the Cozumel Channel under laminar flow. It can be clearly seen that the passive layer begins to break down around the alloying elements (**Figure 2b**). Probably, this layer is less protective in the vicinity of the intermetallic particles, causing the formation of local electrochemical cells with the Al matrix. EDS analysis, **Table 2**, confirmed the presence of particles mentioned above. According to EDS (**Table 2**), zone A is characterised by its higher content of Al, O and Cl, which could relate to corrosion products. According to previous studies, at pH > 8.5, Al(H2O)6 3+ cations appear, while in the range of pH 4.5–8.5, Al(OH)3 predominates [36, 37]. In chloride solutions,

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

#### **Figure 1.**

frequencies was analysed on bi-logarithmic scale (10�<sup>3</sup> ‒1 Hz) of power per unit

straight line and obtention of the *β* slope. The *β* value characterises the corrosion mechanism on AA6061-T6 surface. The processing of data was realised with Electrochemical Signal Analyser V.7.0.1 software (Gamry Instruments, Philadelphia,

The energy spectral density expresses how the energy of a time series is dispersed with a frequency; it can reflect the change in system dynamic. For a signal

j j *x t*ð Þ <sup>2</sup>

ð<sup>∞</sup> �∞

j j *x f* ^ð Þ <sup>2</sup>

For signals with a finite total energy, an equivalent expression for the energy is

*dt* ¼

*dt* (2)

�2*<sup>π</sup>iftx t*ð Þ*df* (4)

*df* (3)

3+ cations appear, while in the

*E* ¼ ð<sup>∞</sup> �∞

j j *x t*ð Þ <sup>2</sup>

ð<sup>∞</sup> �∞ *e*

The integral on the right-hand side of Eq. (3) is the energy of the signal, and the integrand j j *x f* ^ð Þ <sup>2</sup> describes the energy per unit frequency contained in the

**Figure 1** shows SEM images of the as-received specimen of 6061-T6 aluminium alloy surface. Small precipitates (labelled as A, B, C) may be seen (**Figure 1b**). In accordance with EDS, presented in **Table 1**, these precipitates correspond to particles rich in Fe and could be considered as elements of the following phases: Al3Fe, Al▬Si▬Mn▬Fe and α-Al(Fe, Mn, Cu) [9, 10, 35]. The elemental composition of the

**Figure 2a** presents the SEM image of the film formed on the surface of the sample after 5 days of immersion in seawater from the Cozumel Channel under laminar flow. It can be clearly seen that the passive layer begins to break down around the alloying elements (**Figure 2b**). Probably, this layer is less protective in the vicinity of the intermetallic particles, causing the formation of local electrochemical cells with the Al matrix. EDS analysis, **Table 2**, confirmed the presence of particles mentioned above. According to EDS (**Table 2**), zone A is characterised by

its higher content of Al, O and Cl, which could relate to corrosion products.

range of pH 4.5–8.5, Al(OH)3 predominates [36, 37]. In chloride solutions,

According to previous studies, at pH > 8.5, Al(H2O)6

*x f* ^ð Þ¼

PA, USA). All measurements were checked in triplicate.

*Direct Numerical Simulations - An Introduction and Applications*

*E* ¼ ð<sup>∞</sup> �∞

And using the Fourier transform of the signal:

where *f* is the frequency in Hz.

**3. Results and discussion**

surface layer is indicated by zone D.

**3.1 Surface analysis**

/Hz) vs. frequency (Hz). These procedures allowed the fitting of a

frequency (A2

expressed as

signal (ESD).

**142**

*2.4.1 Energy spectral density*

X(t) the energy EE is [34]

*(a) SEM images (500) of AA6061-T6 surface before immersion in Caribbean seawater and (b) zoom zone (2000).*


#### **Table 1.**

*EDS analysis (wt%) of reference aluminium alloy 6061-T6 surface.*

#### **Figure 2.**

*SEM images of AA6061-T6 surface after exposure in Caribbean seawater under laminar flow for 5 days (a) and (b) after removal of corrosion layer.*


#### **Table 2.**

*(a) EDS analysis (wt.%) of aluminium alloy 6061-T6 surface after 5 days of exposure in Caribbean seawater under laminar flow at 21°C and (b) after removal of corrosion products.*

aluminium metal ionises rapidly to the Al3+ ion, which also hydrolyses very rapidly (owing to the negative potential value) [38]. Both of these Al cations can react with chloride ions and form AlCl3 soluble in water (31.77 wt%) [39]; this is converted later to a relatively stable species of basic aluminium chloride (AlCl3∙H2O), transformed slowly to Al(OH)3 and finally to Al2O3∙H2O, an important corrosion product for the repassivation process of the aluminium surface [38].

Based on EDS analysis, in zone B in addition to oxygen and aluminium, elements of calcium and carbon were present, both possibly as a part of a CaCO3 precipitate, originating from seawater. Meanwhile, the layer in zone C maintained a composition similar to that of the alloy, which indicates that the corrosion process was still beginning on the surfaces of similar areas.

After removal of the layer of corrosion products (**Figure 2b**), area damaged by pitting and cracking was observed on the alloy surface. However, some precipitates remained on the surface of AA6061-T6, which according to EDS (**Table 2**) correspond to cathodic particles rich in Fe, α-Al(Fe,Mn,Cu)Si, which promoted the preferential dissolution of the aluminium matrix (local alkalisation) [10].

> which could be attributed to the following phases, Al▬Si▬Mn▬Fe and Al▬Mg▬Si, reported for aluminium alloy series 6xxx [35]. Zone C of the layer formed under stationary flow (**Figure 3b**) presented a similar composition of the alloy (**Table 3**), however, with the oxide layer of Al2O3∙H2O on the alloy surface 6061-T6, as a transformation product of basic aluminium (AlCl3∙H2O) in the presence of NaCl [38]. This layer is part of the entire surface (**Figure 3a**), since the three zones (A, B

> *EDS analysis (wt%) of aluminium alloy 6061-T6 surfaces: (a) after 30 days of exposure in seawater under*

**(a) Element C O Na Mg Al Si Cr Mn Cl Ca Fe Cu** A 3.3 22.3 2.2 3.3 10.2 0.7 — — 1.0 0.3 1.0 55.7 B 4.2 31.3 1.7 1.8 39.6 3.9 0.5 0.8 0.8 0.5 14.2 0.7 C 12.7 44.9 0.5 3.0 37.8 0.1 — — 0.5 0.5 — — **(b)** D 4.1 — —— 63.3 6.0 1.0 1.2 1.5 — 21.8 1.1 E 5.7 4.4 — 0.5 84.6 3.2 0.7 0.9 —— — — F 5.7 1.5 — — 69.6 5.1 1.3 1.0 — — 15.0 0.8 G 5.8 4.6 — 0.7 88.2 0.4 0.2 ——— — —

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

**Figure 3c** corresponds to the SEM image of the aluminium alloy 6061-T6 exposed in seawater at 30 days with flow, after removal of the layer of corrosion products. An area on the surface damaged by cracking and fissures can be observed, while the surface exposed to seawater without flow (**Figure 3d**) shows less damage, with pitting holes of several diameters. In contrast, on the surface exposed to laminar flow for this same time period, the pits are not clearly observable, but localised corrosion damage appeared in the form of cracks and fissures. This effect is due to the seawater flow, which accelerates the corrosion process, causing detachment of the destroyed passive layer and the appearance of new "fresh" areas, where the oxygen diffuses and is the oxidising agent in the cathodic corrosion reaction. It is also observed that on both surfaces (**Figure 3c** and **d**), some particles remained (named as D and F), and according to EDS (**Table 3**), they correspond to cathodic rich in Fe [7], reported in the reference sample as α-Al(Fe,Mn,Cu)Si [35]; these intermetallic particles promoted the preferential dissolution of the aluminium

**Figure 4** compares the φcorr fluctuations of AA6061-T6 specimens exposed for

different periods of times (0, 5 and 30 days) under laminar flow conditions (**Figure 4a**) and without flow (**Figure 4b**). The average values are summarised in **Table 4**. The trends in the changes, towards more or less negative values, are a response to the transformations that have occurred on the surface of the aluminium alloy with the advance of the corrosion process. These are in the morphology, elemental composition of the layers formed, as well as the type of localised corrosion attack discussed previously. It can be seen (**Table 4**) that the initial values of φcorr are relatively similar, being 30 mV nobler in respect of the exposed surface in laminar flow. At 5 days, which implies the initial destruction of the passive layer (**Figure 2a**), the φcorr is 100 mV more negative with laminar flow than under

and C) have a high oxygen content (**Table 3**) [4].

*laminar flow and (b) after removal the layer of corrosion products.*

**3.2 OCP (free corrosion potential, φcorr) measurements**

matrix [40, 41].

**145**

**Table 3.**

**Figure 3** compares SEM images of the aluminium alloy 6061-T6 after exposure at 30 days in laminar flow (**Figure 3a** and **c**) and stationary flow (**Figure 3b** and **d**). In these micrographs, the products formed on the surfaces of the alloy (**Figure 3a** and **b**) can be seen and compared, whose EDS analysis is summarised in **Table 3**. In laminar flow (**Figure 3a**), the segregation of particles rich in Cu (particles A) with the presence of O and Al could be considered as the phases of Al2Cu, AlMgSiCu (Q-phase) and Al7Cu2Fe; both relatively resistant to corrosion, because they are nobler than the aluminium matrix [4, 12]. Q-phase acts as a cathode and does not contribute to intergranular corrosion when it is not connected to any other Cu particle. Otherwise, the Q-phase as cathode promotes the development of intergranular corrosion, initiated in the presence of chloride ions (NaCl). In the corrosion layer, particles without Cu appeared (particles B), rich in Fe, Al and Mg,

#### **Figure 3.**

*SEM images of AA6061-T6 surface after 30 days of exposure in Caribbean seawater, (a) laminar and (b) stationary flow conditions; after removal of corrosion products, (c) laminar and (d) stationary flow conditions.*

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*


#### **Table 3.**

aluminium metal ionises rapidly to the Al3+ ion, which also hydrolyses very rapidly (owing to the negative potential value) [38]. Both of these Al cations can react with chloride ions and form AlCl3 soluble in water (31.77 wt%) [39]; this is converted later to a relatively stable species of basic aluminium chloride (AlCl3∙H2O), transformed slowly to Al(OH)3 and finally to Al2O3∙H2O, an important corrosion

Based on EDS analysis, in zone B in addition to oxygen and aluminium, elements of calcium and carbon were present, both possibly as a part of a CaCO3 precipitate, originating from seawater. Meanwhile, the layer in zone C maintained a composition similar to that of the alloy, which indicates that the corrosion process was still

After removal of the layer of corrosion products (**Figure 2b**), area damaged by pitting and cracking was observed on the alloy surface. However, some precipitates

**Figure 3** compares SEM images of the aluminium alloy 6061-T6 after exposure at 30 days in laminar flow (**Figure 3a** and **c**) and stationary flow (**Figure 3b** and **d**). In these micrographs, the products formed on the surfaces of the alloy (**Figure 3a** and **b**) can be seen and compared, whose EDS analysis is summarised in **Table 3**. In laminar flow (**Figure 3a**), the segregation of particles rich in Cu (particles A) with the presence of O and Al could be considered as the phases of Al2Cu, AlMgSiCu (Q-phase) and Al7Cu2Fe; both relatively resistant to corrosion, because they are nobler than the aluminium matrix [4, 12]. Q-phase acts as a cathode and does not contribute to intergranular corrosion when it is not connected to any other Cu particle. Otherwise, the Q-phase as cathode promotes the development of intergranular corrosion, initiated in the presence of chloride ions (NaCl). In the corrosion layer, particles without Cu appeared (particles B), rich in Fe, Al and Mg,

remained on the surface of AA6061-T6, which according to EDS (**Table 2**) correspond to cathodic particles rich in Fe, α-Al(Fe,Mn,Cu)Si, which promoted the preferential dissolution of the aluminium matrix (local alkalisation) [10].

*SEM images of AA6061-T6 surface after 30 days of exposure in Caribbean seawater, (a) laminar and (b) stationary flow conditions; after removal of corrosion products, (c) laminar and (d) stationary flow conditions.*

product for the repassivation process of the aluminium surface [38].

*Direct Numerical Simulations - An Introduction and Applications*

beginning on the surfaces of similar areas.

**Figure 3.**

**144**

*EDS analysis (wt%) of aluminium alloy 6061-T6 surfaces: (a) after 30 days of exposure in seawater under laminar flow and (b) after removal the layer of corrosion products.*

which could be attributed to the following phases, Al▬Si▬Mn▬Fe and Al▬Mg▬Si, reported for aluminium alloy series 6xxx [35]. Zone C of the layer formed under stationary flow (**Figure 3b**) presented a similar composition of the alloy (**Table 3**), however, with the oxide layer of Al2O3∙H2O on the alloy surface 6061-T6, as a transformation product of basic aluminium (AlCl3∙H2O) in the presence of NaCl [38]. This layer is part of the entire surface (**Figure 3a**), since the three zones (A, B and C) have a high oxygen content (**Table 3**) [4].

**Figure 3c** corresponds to the SEM image of the aluminium alloy 6061-T6 exposed in seawater at 30 days with flow, after removal of the layer of corrosion products. An area on the surface damaged by cracking and fissures can be observed, while the surface exposed to seawater without flow (**Figure 3d**) shows less damage, with pitting holes of several diameters. In contrast, on the surface exposed to laminar flow for this same time period, the pits are not clearly observable, but localised corrosion damage appeared in the form of cracks and fissures. This effect is due to the seawater flow, which accelerates the corrosion process, causing detachment of the destroyed passive layer and the appearance of new "fresh" areas, where the oxygen diffuses and is the oxidising agent in the cathodic corrosion reaction. It is also observed that on both surfaces (**Figure 3c** and **d**), some particles remained (named as D and F), and according to EDS (**Table 3**), they correspond to cathodic rich in Fe [7], reported in the reference sample as α-Al(Fe,Mn,Cu)Si [35]; these intermetallic particles promoted the preferential dissolution of the aluminium matrix [40, 41].

#### **3.2 OCP (free corrosion potential, φcorr) measurements**

**Figure 4** compares the φcorr fluctuations of AA6061-T6 specimens exposed for different periods of times (0, 5 and 30 days) under laminar flow conditions (**Figure 4a**) and without flow (**Figure 4b**). The average values are summarised in **Table 4**. The trends in the changes, towards more or less negative values, are a response to the transformations that have occurred on the surface of the aluminium alloy with the advance of the corrosion process. These are in the morphology, elemental composition of the layers formed, as well as the type of localised corrosion attack discussed previously. It can be seen (**Table 4**) that the initial values of φcorr are relatively similar, being 30 mV nobler in respect of the exposed surface in laminar flow. At 5 days, which implies the initial destruction of the passive layer (**Figure 2a**), the φcorr is 100 mV more negative with laminar flow than under

**Figure 4.**

*Free corrosion potential (φcorr) values of AA6061-T6 samples in Caribbean seawater during 30 days: (a) with laminar and (b) stationary flows.*


#### **Table 4.**

*Average of free corrosion potential (φcorr) values for AA6061-T6 in Caribbean seawater under laminar and stationary flows at different times.*

stationary flow. At 30 days, the φcorr values in both seawater conditions (with and without laminar flow) are very similar (**Table 4**). However, when the product layer was removed (**Figure 3c** and **d**), the SEM images revealed a greater localised attack on the aluminium surface under laminar flow (**Figure 3c**), while in the absence of flow, this attack has been less aggressive, presenting shallow pits. Free corrosion potential (φcorr) tendency towards more or less negative values indicates periods of corrosion activation or repassivation of the surface, both facts related to the characteristics of the layers formed [4, 42].

#### **3.3 Surface characterisation by XPS**

In order to identify the composition of the corrosion product layer created on the alloy surface after 30 days of exposure in laminar flow, XPS analysis was carried out on the specimen immersed, taking into account that aluminium corrosion products were not provided by XRD analysis as crystalline phases and are possibly amorphous.

laminar flow of seawater is higher in ≈50 μA cm<sup>2</sup> than that current in stationary flow. This suggested that the corrosion of the aluminium alloy 6061-T6 surface in laminar flow initiates faster, when the oxide layer on the alloy begins to break down. However, at the end of the experiment (30 days), the current value diminished suddenly, compared with the initial values. However, in stationary flow the current shifted to one order higher values than those in laminar flow, suggesting an acceleration of the corrosion process at that period of time [44]. Conversely, the current oscillations in stationary conditions (**Figure 6b**) presented slow variations, while for flow conditions (**Figure 6a**), intense current fluctuations were acquired with greater amplitude, which suggest greater corrosion [45]. The observed current

*Current density fluctuation for AA6061-T3 immersed in Caribbean seawater up to 30 days under (a) laminar*

*Overview XPS spectra acquired from AA6061-T6 after 30 days of immersion in Caribbean seawater with*

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

The corrosion current density was calculated from the value of polarisation resistance *Rp* (on the assumption that *Rp* is equivalent to polarisation resistance

free corrosion potential (φcorr) values in several mV (**Figure 4**).

) (**Figure 6**) correspond to the variation of the

oscillations registered in (μA cm<sup>2</sup>

**Figure 5.**

**Figure 6.**

**147**

*and (b) stationary flows.*

*laminar flow.*

**Figure 5** shows the full XPS spectrum of the corrosion products formed on the aluminium alloy surface of 6061-T6. The XPS spectrum revealed signals of Mg, Na, O, Cl, C, Si and Al, which accord with EDS analysis. The high-resolution peak for Al2p, situated at 74.38 eV, has been associated with the presence of aluminium hydroxide [Al(OH)3] [43], possibly derived from the transformation of basic aluminium chloride (AlCl3∙H2O) [38]. On the other hand, the signal of O1s centred in 531.88 eV could be attributed to aluminium oxide (Al2O3), an important product of the repassivation process of the aluminium surface.

#### **3.4 Electrochemical noise measurement**

**Figure 6** shows the current oscillations, and it can be seen that at the beginning of the experiment (0 days), the current density of AA6061-T6 surface immersed in *Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

**Figure 5.**

stationary flow. At 30 days, the φcorr values in both seawater conditions (with and without laminar flow) are very similar (**Table 4**). However, when the product layer was removed (**Figure 3c** and **d**), the SEM images revealed a greater localised attack on the aluminium surface under laminar flow (**Figure 3c**), while in the absence of flow, this attack has been less aggressive, presenting shallow pits. Free corrosion potential (φcorr) tendency towards more or less negative values indicates periods of corrosion activation or repassivation of the surface, both facts related to the

*Average of free corrosion potential (φcorr) values for AA6061-T6 in Caribbean seawater under laminar and*

*Free corrosion potential (φcorr) values of AA6061-T6 samples in Caribbean seawater during 30 days: (a) with*

**Exposure time/days φcorr vs. SCE/mV (laminar flow) φcorr vs. SCE/mV (stationary flow)**

0 713 2.80 741 16.40 5 729 2.70 619 0.95 30 618 1.00 614 0.28

*Direct Numerical Simulations - An Introduction and Applications*

In order to identify the composition of the corrosion product layer created on the alloy surface after 30 days of exposure in laminar flow, XPS analysis was carried out on the specimen immersed, taking into account that aluminium corrosion products were not provided by XRD analysis as crystalline phases and are possibly

**Figure 5** shows the full XPS spectrum of the corrosion products formed on the aluminium alloy surface of 6061-T6. The XPS spectrum revealed signals of Mg, Na, O, Cl, C, Si and Al, which accord with EDS analysis. The high-resolution peak for Al2p, situated at 74.38 eV, has been associated with the presence of aluminium hydroxide [Al(OH)3] [43], possibly derived from the transformation of basic aluminium chloride (AlCl3∙H2O) [38]. On the other hand, the signal of O1s centred in 531.88 eV could be attributed to aluminium oxide (Al2O3), an important product

**Figure 6** shows the current oscillations, and it can be seen that at the beginning of the experiment (0 days), the current density of AA6061-T6 surface immersed in

characteristics of the layers formed [4, 42].

of the repassivation process of the aluminium surface.

**3.4 Electrochemical noise measurement**

**3.3 Surface characterisation by XPS**

amorphous.

**146**

**Figure 4.**

**Table 4.**

*laminar and (b) stationary flows.*

*stationary flows at different times.*

*Overview XPS spectra acquired from AA6061-T6 after 30 days of immersion in Caribbean seawater with laminar flow.*

#### **Figure 6.**

*Current density fluctuation for AA6061-T3 immersed in Caribbean seawater up to 30 days under (a) laminar and (b) stationary flows.*

laminar flow of seawater is higher in ≈50 μA cm<sup>2</sup> than that current in stationary flow. This suggested that the corrosion of the aluminium alloy 6061-T6 surface in laminar flow initiates faster, when the oxide layer on the alloy begins to break down. However, at the end of the experiment (30 days), the current value diminished suddenly, compared with the initial values. However, in stationary flow the current shifted to one order higher values than those in laminar flow, suggesting an acceleration of the corrosion process at that period of time [44]. Conversely, the current oscillations in stationary conditions (**Figure 6b**) presented slow variations, while for flow conditions (**Figure 6a**), intense current fluctuations were acquired with greater amplitude, which suggest greater corrosion [45]. The observed current oscillations registered in (μA cm<sup>2</sup> ) (**Figure 6**) correspond to the variation of the free corrosion potential (φcorr) values in several mV (**Figure 4**).

The corrosion current density was calculated from the value of polarisation resistance *Rp* (on the assumption that *Rp* is equivalent to polarisation resistance


where σ<sup>i</sup> is the standard deviation and *irms* the main square root of current noise. Values of PI above 0.1 may indicate localised corrosion [20, 49]. The pitting indexes are shown in **Table 7**. Thus, the calculated PI value suggests that at the end of the experiment (30 days), for both flow cases, AA606-T6 showed pitting corrosion, approximately four times higher in flow conditions, reaching PI = 0.96. These facts agree with the SEM images (**Figure 3**) comparing the corrosion attacks on

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

The current fluctuations, considered as EN, were transformed into the frequency domain to estimate PSD slopes (*β* exponent). **Figure 7** compares the PSD plots in bi-logarithmic scale, corresponding to AA6061-T6 surfaces after 30 days of exposure in seawater under laminar and stationary flows. In each case, the *β* exponent decreases as the frequency increases, and this fact could be associated with the advance of the localised corrosion attacks on the alloy surface [34]. At 30 days, *β* values are similar in laminar and stationary flows (1.0 and 0.94, respectively) and may be attributed to the fractional Gaussian noise (*fGn*), associated with a persistent process [26]. This type of noise (*fGn*) is considered also as a stationary process [24]. **Figure 8** shows the spontaneous energy E during the corrosion process. At the beginning, after 5 days the energy was of an order of magnitude higher in laminar

which showed the accelerated corrosion process causing severe damage to the alloy

However, at the end of the experiment (30 days), the energy diminished in

characteristics that act as a physical barrier on the alloy surfaces, slowing down

**Time/days Laminar Stationary Laminar Stationary Laminar Stationary** 772 639 5462 5255 0.14 0.12 1279 1146 4252 2866 0.30 0.40 639 1471 666 6733 0.96 0.22

*Pitting index of AA6061-T6 immersed for 30 days in Caribbean seawater (Cozumel Channel) under laminar*

*Released energy (E) from AA6061-T6 surface after immersion in seawater under laminar flow, (a) at 5 days and (b) after 30 days of exposure; stationary flow, (c) at 5 days and (d) after 30 days of exposure.*

account of the formation of layers of corrosion products with different

). This fact is consistent with the SEM image presented in **Figure 2**,

**σi/nA irms/nA Pitting index**

, for both flows, probably on

AA6061-T6 exposed to both flow conditions.

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

flow (1.1 <sup>10</sup><sup>4</sup>

the corrosion attack.

**Table 7.**

**Figure 7.**

**149**

*and stationary flows.*

surface exposed to laminar flow.

magnitude, being very similar in the order of 10<sup>7</sup>

**Table 5.**

*Polarisation resistance (*Rp*) and corrosion current density values for AA6061-T6 immersed up to 30 days in Caribbean seawater with laminar and stationary flows.*


**Table 6.**

*Corrosion rate of AA6061-T6 in Caribbean seawater from the Cozumel Channel under laminar and stationary flows.*

noise *Rn*) obtained by ECN tests, according to the Stern-Geary equation (Eq. (5)). *Rn* is calculated by dividing the standard deviation of potential by standard deviation of current (the potential noise can be modelled as the action of the current noise on the metal-solution impedance):

$$i\_{corr} = \frac{B}{R\_p} = \frac{1}{R\_p} \propto \frac{b\_a b\_c}{2.303 \ (b\_a + b\_c)}\tag{5}$$

where *Rp* is the polarisation resistance and *ba* and *bc* are the Tafel coefficients. In this research, the *B* value employed was 0.26 V, taking common values for *ba* and *b*<sup>c</sup> of aluminium alloys [46, 47]. The calculated values (**Table 5**) show that the corrosion current of AA6061-T6 increases with the time of exposure, being more than one order higher when the alloy is exposed under laminar flow of seawater, while in stationary conditions, it maintains almost similar values up to 30 days.

Subsequently, Faraday's law was applied to calculate the corrosion rate (CR, **Table 6**) in the following form:

$$CR = \frac{i\_{corr} KE\_w}{\rho A} \tag{6}$$

where *Ew* stands for the equivalent mass of AA6061-T6, Icorr is the corrosion density (A cm�<sup>2</sup> ), *ρ* is the metal density, *K* is a constant (3272 mm/A cm year) and *A* is the exposed specimen area (1 cm<sup>2</sup> ) [48].

The corrosion rate values presented in **Table 6** indicate that under laminar flow, the values varied 0.08 and 0.20 mm per year, while in stationary conditions, they were between 0.012 and 0.162 mm per year.

With the statistical data obtained from the corrosion current, the pitting index (PI) [19] was calculated in order to reveal AA606-T6 susceptibility to localised corrosion for the laminar and stationary:

$$PI = \sigma\_i(i\_{rm})^{-1} = (639.17 \, nA)(666.42 \, nA)^{-1} = 0.96\tag{7}$$

#### *Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

where σ<sup>i</sup> is the standard deviation and *irms* the main square root of current noise.

Values of PI above 0.1 may indicate localised corrosion [20, 49]. The pitting indexes are shown in **Table 7**. Thus, the calculated PI value suggests that at the end of the experiment (30 days), for both flow cases, AA606-T6 showed pitting corrosion, approximately four times higher in flow conditions, reaching PI = 0.96. These facts agree with the SEM images (**Figure 3**) comparing the corrosion attacks on AA6061-T6 exposed to both flow conditions.

The current fluctuations, considered as EN, were transformed into the frequency domain to estimate PSD slopes (*β* exponent). **Figure 7** compares the PSD plots in bi-logarithmic scale, corresponding to AA6061-T6 surfaces after 30 days of exposure in seawater under laminar and stationary flows. In each case, the *β* exponent decreases as the frequency increases, and this fact could be associated with the advance of the localised corrosion attacks on the alloy surface [34]. At 30 days, *β* values are similar in laminar and stationary flows (1.0 and 0.94, respectively) and may be attributed to the fractional Gaussian noise (*fGn*), associated with a persistent process [26]. This type of noise (*fGn*) is considered also as a stationary process [24].

**Figure 8** shows the spontaneous energy E during the corrosion process. At the beginning, after 5 days the energy was of an order of magnitude higher in laminar flow (1.1 <sup>10</sup><sup>4</sup> ). This fact is consistent with the SEM image presented in **Figure 2**, which showed the accelerated corrosion process causing severe damage to the alloy surface exposed to laminar flow.

However, at the end of the experiment (30 days), the energy diminished in magnitude, being very similar in the order of 10<sup>7</sup> , for both flows, probably on account of the formation of layers of corrosion products with different characteristics that act as a physical barrier on the alloy surfaces, slowing down the corrosion attack.


#### **Table 7.**

noise *Rn*) obtained by ECN tests, according to the Stern-Geary equation (Eq. (5)). *Rn* is calculated by dividing the standard deviation of potential by standard deviation of current (the potential noise can be modelled as the action of the current

*Corrosion rate of AA6061-T6 in Caribbean seawater from the Cozumel Channel under laminar and*

where *Rp* is the polarisation resistance and *ba* and *bc* are the Tafel coefficients. In this research, the *B* value employed was 0.26 V, taking common values for *ba* and *b*<sup>c</sup> of aluminium alloys [46, 47]. The calculated values (**Table 5**) show that the corrosion current of AA6061-T6 increases with the time of exposure, being more than one order higher when the alloy is exposed under laminar flow of seawater, while in

Subsequently, Faraday's law was applied to calculate the corrosion rate (CR,

*CR* <sup>¼</sup> *icorrKEw*

where *Ew* stands for the equivalent mass of AA6061-T6, Icorr is the corrosion

) [48]. The corrosion rate values presented in **Table 6** indicate that under laminar flow, the values varied 0.08 and 0.20 mm per year, while in stationary conditions, they

With the statistical data obtained from the corrosion current, the pitting index (PI) [19] was calculated in order to reveal AA606-T6 susceptibility to localised

), *ρ* is the metal density, *K* is a constant (3272 mm/A cm year) and

*PI* <sup>¼</sup> *<sup>σ</sup><sup>i</sup> <sup>i</sup>*ð Þ *rms* �<sup>1</sup> <sup>¼</sup> ð Þ <sup>639</sup>*:*<sup>17</sup> *nA* ð Þ <sup>666</sup>*:*<sup>42</sup> *nA* �<sup>1</sup> <sup>¼</sup> <sup>0</sup>*:*96 (7)

*babc* 2*:*303 ð Þ *ba* þ *bc*

**CR/mm year**�**<sup>1</sup>**

**Rp/kΩ cm2 icorr /μA cm**�**<sup>2</sup>**

**Time/d Laminar flow Stationary flow Laminar flow Stationary flow** 3.65 23.46 7.12 1.11 2.24 17.5 11.60 1.49 1.44 19.3 18.08 1.35

*Polarisation resistance (*Rp*) and corrosion current density values for AA6061-T6 immersed up to 30 days in*

**Time/d Laminar flow Stationary flow** 0.08 0.012 0.13 0.016 0.20 0.014

*<sup>ρ</sup><sup>A</sup>* (6)

(5)

noise on the metal-solution impedance):

*Caribbean seawater with laminar and stationary flows.*

*Direct Numerical Simulations - An Introduction and Applications*

**Table 6**) in the following form:

*A* is the exposed specimen area (1 cm<sup>2</sup>

were between 0.012 and 0.162 mm per year.

corrosion for the laminar and stationary:

density (A cm�<sup>2</sup>

**148**

**Table 5.**

**Table 6.**

*stationary flows.*

*icorr* <sup>¼</sup> *<sup>B</sup> Rp* ¼ 1 *Rp x*

stationary conditions, it maintains almost similar values up to 30 days.

*Pitting index of AA6061-T6 immersed for 30 days in Caribbean seawater (Cozumel Channel) under laminar and stationary flows.*

#### **Figure 7.**

*Released energy (E) from AA6061-T6 surface after immersion in seawater under laminar flow, (a) at 5 days and (b) after 30 days of exposure; stationary flow, (c) at 5 days and (d) after 30 days of exposure.*

in the composition of the formed corrosion layers. The presented surface SEM-EDS and XPS analysis agree positively with the results obtained with both

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

The authors acknowledge LANNBIO for permitting the use of their facilities, as well as to M. Sci. Dora Huerta and W. J. Cauich-Ruiz for their technical assistance in

This research was funded by Centro Mexicano de Inovación en Energía del Océano (CEMIE) grant number [00249795]. Luis Chávez gratefully thanks CONACYT for his scholarship as M.Sci. student at CINVESTAV-IPN.

nondestructive electrochemical methods.

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

**Acknowledgements**

data acquisition.

**Funding sources**

**Author details**

**151**

Gloria Acosta, Lucien Veleva\*, Luis Chávez and Juan L. López Applied Physics Department, Research Center for Advanced Study

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

(CINVESTAV-IPN), Mérida, Yucatán, México

provided the original work is properly cited.

\*Address all correspondence to: veleva@cinvestav.mx

**Figure 8.**

*Energy (E) from AA6061-T6 surface after immersion in seawater under laminar flow, (a) at 5 days and (b) after 30 days of exposure; stationary flow, (c) at 5 days and (d) after 30 days of exposure.*

#### **4. Conclusions**


*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

in the composition of the formed corrosion layers. The presented surface SEM-EDS and XPS analysis agree positively with the results obtained with both nondestructive electrochemical methods.

### **Acknowledgements**

The authors acknowledge LANNBIO for permitting the use of their facilities, as well as to M. Sci. Dora Huerta and W. J. Cauich-Ruiz for their technical assistance in data acquisition.

### **Funding sources**

**4. Conclusions**

**Figure 8.**

(0.1 m s<sup>1</sup>

1.The initial electrochemical activity of 6061-T6 aluminium alloy surface,

*Energy (E) from AA6061-T6 surface after immersion in seawater under laminar flow, (a) at 5 days and (b)*

*after 30 days of exposure; stationary flow, (c) at 5 days and (d) after 30 days of exposure.*

*Direct Numerical Simulations - An Introduction and Applications*

of the formed layers have revealed localised corrosion (fissures and deep cracks) in the vicinity of intermetallic particles rich in Fe and Cu, which act as cathodes. The attack was less aggressive in stationary seawater, with shallow

2.The calculated values showed that the corrosion current (icorr) of AA6061-T6 increases with the time of exposure more than one order higher when the alloy

stationary conditions, it maintains almost similar values (17.51–19.32 μA cm<sup>2</sup>

With the statistical data obtained from the corrosion current, the calculated pitting index (PI) revealed that AA606-T6 is four times more susceptible to localised corrosion in seawater under laminar flow (PI = 0.96), compared to that in stationary conditions (PI = 0.22). The estimated PSD slopes (β exponent) of the current fluctuations transformed into the frequency domain revealed that in

electrochemical corrosion may be attributed to the fractional Gaussian noise

(30 days), the energy diminished in magnitude, being very similar in an order

4.The observed effect of the laminar seawater flow on the AA6061-T6 corrosion process should be considered as a consequence of the facilitated diffusion of the oxygen at the metal-seawater interface, resulting in specific transformation

, for both flows, probably on account of the formation of layers of corrosion products with different characteristic, which act as a physical barrier

). However, at the end of the experiment

3.The spontaneous energy release in the initial stages is one order higher in

pits occurring on the surface at 30 days of exposure.

is exposed under laminar flow of seawater (7.12–18.08 μA cm<sup>2</sup>

laminar and stationary flows (β = 1.0 and 0.94, respectively), the

(fGn), associated with a persistent stationary process.

on the alloy surfaces, slowing down the corrosion attack.

laminar flow (ΔE = 1.1 <sup>10</sup><sup>4</sup>

of 10<sup>7</sup>

**150**

immersed in Caribbean seawater, was studied for 30 days under laminar flow

, 21°C). The changes in the morphology and elemental composition

), while in

).

This research was funded by Centro Mexicano de Inovación en Energía del Océano (CEMIE) grant number [00249795]. Luis Chávez gratefully thanks CONACYT for his scholarship as M.Sci. student at CINVESTAV-IPN.

### **Author details**

Gloria Acosta, Lucien Veleva\*, Luis Chávez and Juan L. López Applied Physics Department, Research Center for Advanced Study (CINVESTAV-IPN), Mérida, Yucatán, México

\*Address all correspondence to: veleva@cinvestav.mx

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

[1] Davis JR. Understanding the Basics. Ohio: ASM International; 2001. 351 p. DOI: 10.1361/autb2001p351

[2] Altenpohl DG. Aluminum Viewed from Within: An Introduction into the Metallurgy of Aluminum Fabrication. Düsseldorf: Aluminum-Verlag; 1982

[3] Pourbaix M. Atlas of Electrochemical Equilibria in Aqueous Solutions. Huston, TX: NACE International; 1974

[4] Szklarska-Smialowska Z. Pitting corrosion of aluminum. Corrosion Science. 1999;**41**:1743-1767. DOI: 10.1016/S0010-938X(99)00012-8

[5] Tiryakioğlu M, Staley J. Physical metallurgy and the effect of alloying additions in aluminum alloys. In: Totten GE, MacKenzie DS, editors. Handbook of Aluminum. New York: Marcel Dekker, Inc; 2003. pp. 81-210

[6] Reboul MC, Baroux B. Metallurgical aspects of corrosion resistance of aluminium alloys. Materials and Corrosion. 2011;**62**:215-233. DOI: 10.1002/maco.201005650

[7] Mutombo K. Intermetallic particlesinduced pitting corrosion in 6061-T651 aluminium alloy. Materials Science Forum. 2011;**690**:389-392. DOI: 10.4028/www.scientific.net/ MSF.690.389

[8] Guillaumin V, Mankowski G. Localized corrosion of 2024 T351 aluminium alloy in chloride media. Corrosion Science. 1999;**41**:421-438. DOI: 10.1016/S0010-938X(98)00116-4

[9] Gharavi F, Matori K, Yunus R, Othman NK, Fadaeifard F. Corrosion evaluation of friction stir welded lap joints of AA6061-T6 aluminum alloy. Transactions of Nonferrous Metals Society of China. 2016;**26**:684-696. DOI: 10.1016/S1003-6326(16)64159-6

[10] Zheng Y, Luo B, Bai Z, Wang J, Yin Y. Study of the precipitation hardening behavior and intergranular corrosion of Al-Mg-Si alloy with differing Si contents. Meta. 2017;**7**: 387-399. DOI: 10.3390/met7100387

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*DOI: http://dx.doi.org/10.5772/intechopen.91026*

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

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2006.07.004

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j.jmp.2006.07.004

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2019;**29**:34-42

2.0291811jes

McGraw Hill; 1985

Lemoine L, Torre K, Fortes M, Ninot G. Fractal analyses for 'short' time series: A re-assessment of classical methods. Journal of Mathematical Psychology. 2006;**50**:525-544. DOI: 10.1016/j.jmp.

Characterization of corrosion processes by current noise wavelet-based fractal and correlation analysis. Electrochimica Acta. 2008;**53**:5206-5214. DOI: 10.1016/

[27] López JL, Veleva L, López-Sauri DA. Multifractal detrended analysis of the corrosion potential fluctuations during copper patina formation on its first stages in sea water. International Journal of Electrochemical Science. 2014;**9**:

[28] Acosta G, Veleva L, López JL. Power spectral density analysis of the corrosion potential fluctuation of aluminium in early stages of exposure to Caribbean sea water. International Journal of Electrochemical Science. 2014;**9**:

[29] Acosta G, Veleva L, López JL, López-Sauri DA. Contrasting initial events of localized corrosion on surfaces of 2219-T42 and 6061-T6 aluminum alloys exposed in Caribbean seawater. Transactions of Nonferrous Metals Society of China.

[30] Mena-Morcillo E, Veleva LP, Wipf DO. Multi-scale monitoring the first stages of electrochemical behavior of AZ31B magnesium alloy in simulated body fluid. Journal of the Electrochemical Society. 2018; **165**:C749-C755. DOI: 10.1149/

[31] McCabe WL, Smith JC, Harriott P.

Unit Operations of Chemical Engineering. 4th ed. New York:

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[20] Xia DH, Song SZ, Behnamian Y. Detection of corrosion degradation using electrochemical noise (EN): Review of signal processing methods for identifying corrosion forms. Corrosion Engineering, Science and Technology. 2016;**51**:527-544. DOI: 10.1179/1743278215Y.0000000057

Electrochemical noise analysis of the corrosion of high-purity Mg–Al alloys. Corrosion Science. 2015;**94**:316-326.

[22] Lee CC, Mansfeld F. Analysis of electrochemical noise data for a passive system in the frequency domain. Corrosion Science. 1998;**40**:956-962. DOI: 10.1016/j.arabjc.2012.02.018

[23] Roberge PR. Quantifying the stochastic behavior of electrochemical noise measurement during the corrosion of aluminum. In: Kearns JR, Scully JR, Roberge PR, Reichert DL, Dawson JL,

editors. Electrochemical Noise Measurement for Corrosion

10.1520/STP37957S

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[24] Eke A, Hermán P,

Applications. West Conshohocken, PA: ASTM STP 1277; 1996. pp. 142-156. DOI:

Bassingthwaighte JB, Raymond GM, Percival DB, Cannon M, et al.

Physiological time series: Distinguishing fractal noises from motions. European Journal of Physiology. 2000;**439**: 403-415. DOI: 10.1007/s004249900135

[21] Casajús P, Winzer N.

DOI: 10.20964/2018.01.86

2000

[11] F-l Z, Z-l W, Li J-f, Li C-x, Tan X, Zhang Z, et al. Corrosion mechanism associated with Mg2Si and Si particles in AlMgSi alloys. Transactions of Nonferrous Metals Society of China. 2011;**21**:2559-2567. DOI: 10.1016/S1003- 6326(11)61092-3

[12] Birbilis N, Buchheit RG. Electrochemical characteristics of intermetallic phases in aluminum alloys an experimental survey and discussion. Journal of the Electrochemical Society. 2005;**152**:B140-B151. DOI: 10.1149/ 1.1869984

[13] McCafferty E. Sequence of steps in the pitting of aluminum by chloride ions. Corrosion Science. 2003;**5**: 1421-1438. DOI: 10.1016/S0010-938X (02)00231-7

[14] Burstein GT, Liu C, Souto RM, Vines SP. Origins of pitting corrosion. Corrosion Engineering, Science and Technology. 2004;**39**:25-30. DOI: 10.1179/147842204225016859

[15] Liang M, Melchers R, Chaves I. Corrosion and pitting of 6060 series aluminium after 2 years exposure in seawater splash, tidal and immersion zones. Corrosion Science. 2018;**140**: 286-296. DOI: 10.1016/j.corsci.2018. 05.036

[16] LaQue FL. Marine Corrosion: Causes and Prevention. New York: John Wiley & Sons; 1975

[17] Al-Fozan SA, Malik AU. Effect of seawater level on corrosion behavior of different alloys. Desalination. 2008;**228**: 61-67. DOI: 10.1016/j.desal.2007.08.007 *Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

[18] Roberge PR. Handbook of Corrosion Engineering. New York: McGraw-Hill; 2000

**References**

[1] Davis JR. Understanding the Basics. Ohio: ASM International; 2001. 351 p.

*Direct Numerical Simulations - An Introduction and Applications*

[10] Zheng Y, Luo B, Bai Z, Wang J, Yin Y. Study of the precipitation hardening behavior and intergranular corrosion of Al-Mg-Si alloy with differing Si contents. Meta. 2017;**7**: 387-399. DOI: 10.3390/met7100387

[11] F-l Z, Z-l W, Li J-f, Li C-x, Tan X, Zhang Z, et al. Corrosion mechanism associated with Mg2Si and Si particles in AlMgSi alloys. Transactions of Nonferrous Metals Society of China. 2011;**21**:2559-2567. DOI: 10.1016/S1003-

[13] McCafferty E. Sequence of steps in the pitting of aluminum by chloride ions. Corrosion Science. 2003;**5**: 1421-1438. DOI: 10.1016/S0010-938X

[14] Burstein GT, Liu C, Souto RM, Vines SP. Origins of pitting corrosion. Corrosion Engineering, Science and Technology. 2004;**39**:25-30. DOI: 10.1179/147842204225016859

[15] Liang M, Melchers R, Chaves I. Corrosion and pitting of 6060 series aluminium after 2 years exposure in seawater splash, tidal and immersion zones. Corrosion Science. 2018;**140**: 286-296. DOI: 10.1016/j.corsci.2018.

[16] LaQue FL. Marine Corrosion: Causes and Prevention. New York: John

[17] Al-Fozan SA, Malik AU. Effect of seawater level on corrosion behavior of different alloys. Desalination. 2008;**228**: 61-67. DOI: 10.1016/j.desal.2007.08.007

Wiley & Sons; 1975

6326(11)61092-3

1.1869984

(02)00231-7

05.036

[12] Birbilis N, Buchheit RG. Electrochemical characteristics of intermetallic phases in aluminum alloys an experimental survey and discussion. Journal of the Electrochemical Society. 2005;**152**:B140-B151. DOI: 10.1149/

[2] Altenpohl DG. Aluminum Viewed from Within: An Introduction into the Metallurgy of Aluminum Fabrication. Düsseldorf: Aluminum-Verlag; 1982

[3] Pourbaix M. Atlas of Electrochemical

Equilibria in Aqueous Solutions. Huston, TX: NACE International; 1974

[4] Szklarska-Smialowska Z. Pitting corrosion of aluminum. Corrosion Science. 1999;**41**:1743-1767. DOI: 10.1016/S0010-938X(99)00012-8

[5] Tiryakioğlu M, Staley J. Physical metallurgy and the effect of alloying additions in aluminum alloys. In: Totten GE, MacKenzie DS, editors. Handbook of Aluminum. New York: Marcel Dekker, Inc; 2003. pp. 81-210

[6] Reboul MC, Baroux B. Metallurgical aspects of corrosion resistance of aluminium alloys. Materials and Corrosion. 2011;**62**:215-233. DOI: 10.1002/maco.201005650

[7] Mutombo K. Intermetallic particlesinduced pitting corrosion in 6061-T651 aluminium alloy. Materials Science Forum. 2011;**690**:389-392. DOI: 10.4028/www.scientific.net/

[8] Guillaumin V, Mankowski G. Localized corrosion of 2024 T351 aluminium alloy in chloride media. Corrosion Science. 1999;**41**:421-438. DOI: 10.1016/S0010-938X(98)00116-4

[9] Gharavi F, Matori K, Yunus R, Othman NK, Fadaeifard F. Corrosion evaluation of friction stir welded lap joints of AA6061-T6 aluminum alloy. Transactions of Nonferrous Metals Society of China. 2016;**26**:684-696. DOI:

10.1016/S1003-6326(16)64159-6

MSF.690.389

**152**

DOI: 10.1361/autb2001p351

[19] Dawson JL. Electrochemical noise measurement: The definitive in-situ technique for corrosion applications. In: Kearns J, Scully J, Roberge P, Reichert D, Dawson JL, editors. Electrochemical Noise Measurement for Corrosion Applications. West Conshohocken, PA: ASTM STP 1277; 1996. pp. 3-35. DOI: 10.1520/STP37949S

[20] Xia DH, Song SZ, Behnamian Y. Detection of corrosion degradation using electrochemical noise (EN): Review of signal processing methods for identifying corrosion forms. Corrosion Engineering, Science and Technology. 2016;**51**:527-544. DOI: 10.1179/1743278215Y.0000000057

[21] Casajús P, Winzer N. Electrochemical noise analysis of the corrosion of high-purity Mg–Al alloys. Corrosion Science. 2015;**94**:316-326. DOI: 10.20964/2018.01.86

[22] Lee CC, Mansfeld F. Analysis of electrochemical noise data for a passive system in the frequency domain. Corrosion Science. 1998;**40**:956-962. DOI: 10.1016/j.arabjc.2012.02.018

[23] Roberge PR. Quantifying the stochastic behavior of electrochemical noise measurement during the corrosion of aluminum. In: Kearns JR, Scully JR, Roberge PR, Reichert DL, Dawson JL, editors. Electrochemical Noise Measurement for Corrosion Applications. West Conshohocken, PA: ASTM STP 1277; 1996. pp. 142-156. DOI: 10.1520/STP37957S

[24] Eke A, Hermán P, Bassingthwaighte JB, Raymond GM, Percival DB, Cannon M, et al. Physiological time series: Distinguishing fractal noises from motions. European Journal of Physiology. 2000;**439**: 403-415. DOI: 10.1007/s004249900135

[25] Delignieres D, Ramdani S, Lemoine L, Torre K, Fortes M, Ninot G. Fractal analyses for 'short' time series: A re-assessment of classical methods. Journal of Mathematical Psychology. 2006;**50**:525-544. DOI: 10.1016/j.jmp. 2006.07.004

[26] Planinšič P, Petek A. Characterization of corrosion processes by current noise wavelet-based fractal and correlation analysis. Electrochimica Acta. 2008;**53**:5206-5214. DOI: 10.1016/

j.jmp.2006.07.004

[27] López JL, Veleva L, López-Sauri DA. Multifractal detrended analysis of the corrosion potential fluctuations during copper patina formation on its first stages in sea water. International Journal of Electrochemical Science. 2014;**9**: 1637-1649

[28] Acosta G, Veleva L, López JL. Power spectral density analysis of the corrosion potential fluctuation of aluminium in early stages of exposure to Caribbean sea water. International Journal of Electrochemical Science. 2014;**9**: 6464-6474

[29] Acosta G, Veleva L, López JL, López-Sauri DA. Contrasting initial events of localized corrosion on surfaces of 2219-T42 and 6061-T6 aluminum alloys exposed in Caribbean seawater. Transactions of Nonferrous Metals Society of China. 2019;**29**:34-42

[30] Mena-Morcillo E, Veleva LP, Wipf DO. Multi-scale monitoring the first stages of electrochemical behavior of AZ31B magnesium alloy in simulated body fluid. Journal of the Electrochemical Society. 2018; **165**:C749-C755. DOI: 10.1149/ 2.0291811jes

[31] McCabe WL, Smith JC, Harriott P. Unit Operations of Chemical Engineering. 4th ed. New York: McGraw Hill; 1985

[32] ASTM G190. Standard practice for preparing, cleaning, and evaluation corrosion test specimens

[33] ASTM G199-09. Standard guide for electrochemical noise measurement

[34] Stein JY. Digital Signal Processing: A Computer Science Perspective. 2nd ed. New York: John Wiley & Sons; 2000

[35] Yasakau KA, Zheludkevich ML, Ferreira MGS. Role of intermetallics in corrosion of aluminum alloys. In: Mitra R, editor. Smart Corrosion Protection. Aveiro, Portugal: Woodhead Publishing; 2018. 425 p. DOI: 10.1016/ B978-0-85709-346-2.00015-7

[36] Ender VV, Wetzel C. Gross-Kraftwerkbret: VGB Tech. Ver; 1998, R 6/1-R6/20

[37] Afzal SN, Shaikh MA, Mustafa CM, Nabi M, Ehsan MQ, Khan AH. Study of aluminum corrosion in chloride and nitrate media and its inhibition by nitrite. Journal of Nepal Chemical Society. 2006;**22**:26-33. DOI: 10.3126/ jncs.v22i0.519

[38] Foley RT, Nguyen TH. The chemical nature in aluminum corrosion, V. energy transfer in aluminum dissolution. Journal of the Electrochemical Society. 1982;**129**: 464-467. DOI: 10.1149/1.2123881

[39] Brown RR, Daut GE, Mrazek RV, Gokcen NA. Solubility and Activity of Aluminum Chloride in Aqueous Hydrochloric Acid Solutions. Washington, DC: U.S. Department of the Interior, Bureau of Mines; 1979

[40] Nikseresht Z, Karimzadeh F, Golozar MA, Heidarbeigy M. Effect of heat treatment on microstructure and corrosion behavior of Al6061 alloy weldment. Materials and Design. 2010; **31**:2643-2648. DOI: 10.1016/j. matdes.2009.12.001

[41] Zhu Y, Sun K, Frankel GS. Intermetallic phases in aluminum alloys and their roles in localized corrosion. Journal of the Electrochemical Society. 2018;**165**:C807. DOI: 10.1149/ 2.0931811jes

[48] G102-89. Standard practice for calculation of corrosion rates and related information from electrochemical

*DOI: http://dx.doi.org/10.5772/intechopen.91026*

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater*

[49] Eden DA, John DG, Dawson JL. Corrosion monitoring: WIPO Patent, 1987, 19871107022. 1987. pp. 11–19

measurements

**155**

[42] Ghali E. General, galvanic, and localized corrosion of aluminum and its alloys. In: Winston Revie R, editor. Corrosion Resistance of Aluminum and Magnesium Alloys: Understanding, Performance, and Testing. Hoboken, New Jersey: John Wiley & Sons; 2010. 176 p. DOI: 10.1002/ 9780470531778.ch5

[43] John FM, William FS, Peter ES, Kenneth DB. In: Chastain J, editor. Handbook of X-ray Photoelectron Spectroscopy. Minnesota: Physical Electronics; 1992. pp. 44-55

[44] Loto CA. Electrochemical noise measurement technique in corrosion research. International Journal of Electrochemical Science. 2012;**7**: 9248-9270

[45] Malo JM, Velazco O. Elecrochemical noise response of steel under hydrodynamic conditions. In: Kearns JR, Scully JR, Roberge PR, Reichert DL, Dawson JL, editors. Electrochemical Noise Measurement for Corrosion Applications. West Conshohocken, PA: ASTM STP 1277; 1996. pp. 387-397. DOI: 10.1520/STP37972S

[46] Sanchez-Amaya JM, Cottis RA, Botana FJ. Shot noise and statistical parameters for the estimation of corrosion mechanisms. Corrosion Science. 2005;**47**:3280-3299. DOI: 10.1016/j.corsci.2005.05.047

[47] Curioni M, Cottis RA, Thompson GE. Application of electrochemical noise analysis to corroding aluminium alloys. Surface and Interface Analysis. 2013;**45**:1564-1569. DOI: 10.1002/sia.5173

*Effect of Laminar Flow on the Corrosion Activity of AA6061-T6 in Seawater DOI: http://dx.doi.org/10.5772/intechopen.91026*

[48] G102-89. Standard practice for calculation of corrosion rates and related information from electrochemical measurements

[32] ASTM G190. Standard practice for preparing, cleaning, and evaluation

*Direct Numerical Simulations - An Introduction and Applications*

[41] Zhu Y, Sun K, Frankel GS.

2018;**165**:C807. DOI: 10.1149/

[42] Ghali E. General, galvanic, and localized corrosion of aluminum and its alloys. In: Winston Revie R, editor. Corrosion Resistance of Aluminum and Magnesium Alloys: Understanding, Performance, and Testing. Hoboken, New Jersey: John Wiley & Sons; 2010. 176 p. DOI: 10.1002/

[43] John FM, William FS, Peter ES, Kenneth DB. In: Chastain J, editor. Handbook of X-ray Photoelectron Spectroscopy. Minnesota: Physical Electronics; 1992. pp. 44-55

[44] Loto CA. Electrochemical noise measurement technique in corrosion research. International Journal of Electrochemical Science. 2012;**7**:

[45] Malo JM, Velazco O. Elecrochemical

hydrodynamic conditions. In: Kearns JR, Scully JR, Roberge PR, Reichert DL, Dawson JL, editors. Electrochemical Noise Measurement for Corrosion Applications. West Conshohocken, PA: ASTM STP 1277; 1996. pp. 387-397. DOI:

[46] Sanchez-Amaya JM, Cottis RA, Botana FJ. Shot noise and statistical parameters for the estimation of corrosion mechanisms. Corrosion Science. 2005;**47**:3280-3299. DOI: 10.1016/j.corsci.2005.05.047

corroding aluminium alloys. Surface and Interface Analysis. 2013;**45**:1564-1569.

noise response of steel under

10.1520/STP37972S

[47] Curioni M, Cottis RA, Thompson GE. Application of electrochemical noise analysis to

DOI: 10.1002/sia.5173

2.0931811jes

9780470531778.ch5

9248-9270

Intermetallic phases in aluminum alloys and their roles in localized corrosion. Journal of the Electrochemical Society.

[33] ASTM G199-09. Standard guide for electrochemical noise measurement

[34] Stein JY. Digital Signal Processing: A Computer Science Perspective. 2nd ed. New York: John Wiley & Sons; 2000

[35] Yasakau KA, Zheludkevich ML, Ferreira MGS. Role of intermetallics in corrosion of aluminum alloys. In: Mitra R, editor. Smart Corrosion

Protection. Aveiro, Portugal: Woodhead Publishing; 2018. 425 p. DOI: 10.1016/

[37] Afzal SN, Shaikh MA, Mustafa CM, Nabi M, Ehsan MQ, Khan AH. Study of aluminum corrosion in chloride and nitrate media and its inhibition by nitrite. Journal of Nepal Chemical Society. 2006;**22**:26-33. DOI: 10.3126/

[38] Foley RT, Nguyen TH. The chemical nature in aluminum corrosion, V. energy transfer in aluminum dissolution. Journal of the

Electrochemical Society. 1982;**129**: 464-467. DOI: 10.1149/1.2123881

[39] Brown RR, Daut GE, Mrazek RV, Gokcen NA. Solubility and Activity of Aluminum Chloride in Aqueous Hydrochloric Acid Solutions.

Washington, DC: U.S. Department of the Interior, Bureau of Mines; 1979

[40] Nikseresht Z, Karimzadeh F, Golozar MA, Heidarbeigy M. Effect of heat treatment on microstructure and corrosion behavior of Al6061 alloy weldment. Materials and Design. 2010;

**31**:2643-2648. DOI: 10.1016/j.

matdes.2009.12.001

**154**

B978-0-85709-346-2.00015-7

R 6/1-R6/20

jncs.v22i0.519

[36] Ender VV, Wetzel C. Gross-Kraftwerkbret: VGB Tech. Ver; 1998,

corrosion test specimens

[49] Eden DA, John DG, Dawson JL. Corrosion monitoring: WIPO Patent, 1987, 19871107022. 1987. pp. 11–19

**157**

**Chapter 9**

**Abstract**

a robust model setup.

**1. Introduction**

DNS [12].

A Unique Volume Balance

*Hussein A.M. Al-Zubaidi and Scott A. Wells*

Three-Dimensional

Approach for Verifying the

Hydrodynamic Numerical Models

in Surface Waterbody Simulation

The hydrodynamic numerical modeling is increasingly becoming a widely used tool for simulating the surface waterbodies including rivers, lakes, and reservoirs. A challenging step in any model development is the verification tests, especially at the early stage of development. In this study, a unique approach was developed by implementing the volume balance principle in order to verify the three-dimensional hydrodynamic models for surface waterbody simulation. A developed and verified three-dimensional hydrodynamic and water quality model, called W3, was employed by setting a case study model to be verified using the volume balance technique. The model was qualified by calculating the error in the accumulated water volume within the domain every time step. Results showed that the volume balance reached a constant error over the simulation period, indicating

**Keywords:** hydrodynamic model, lakes and reservoirs, model verification, model simulation, numerical model, volume balance, water quality modeling, W3 model

Many 3D hydrodynamic and water quality models have been developed since the 1960s, and different numerical solution techniques have been used to solve the governing equations. The most popular numerical models and the basis that other models has been built based on are POM [1, 2], ECOM [1, 3], NCOM [4, 5], FVCOM [6, 7], EFDC [8], TRIM-3D [9], UnTRIM [10], GLLVHT [11], and

During the development stage of any numerical model, verification tests need to be performed to ensure that model foundations are valid. The 3D simulation models available in market have been tested either by comparing the predictions with the analytical solution, field data, or both. As a result, each verification approach has its advantages and disadvantages depending on the model complexity (governing equations used to develop the model and assumptions used to simplify the problem).

#### **Chapter 9**

## A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic Numerical Models in Surface Waterbody Simulation

*Hussein A.M. Al-Zubaidi and Scott A. Wells*

### **Abstract**

The hydrodynamic numerical modeling is increasingly becoming a widely used tool for simulating the surface waterbodies including rivers, lakes, and reservoirs. A challenging step in any model development is the verification tests, especially at the early stage of development. In this study, a unique approach was developed by implementing the volume balance principle in order to verify the three-dimensional hydrodynamic models for surface waterbody simulation. A developed and verified three-dimensional hydrodynamic and water quality model, called W3, was employed by setting a case study model to be verified using the volume balance technique. The model was qualified by calculating the error in the accumulated water volume within the domain every time step. Results showed that the volume balance reached a constant error over the simulation period, indicating a robust model setup.

**Keywords:** hydrodynamic model, lakes and reservoirs, model verification, model simulation, numerical model, volume balance, water quality modeling, W3 model

#### **1. Introduction**

Many 3D hydrodynamic and water quality models have been developed since the 1960s, and different numerical solution techniques have been used to solve the governing equations. The most popular numerical models and the basis that other models has been built based on are POM [1, 2], ECOM [1, 3], NCOM [4, 5], FVCOM [6, 7], EFDC [8], TRIM-3D [9], UnTRIM [10], GLLVHT [11], and DNS [12].

During the development stage of any numerical model, verification tests need to be performed to ensure that model foundations are valid. The 3D simulation models available in market have been tested either by comparing the predictions with the analytical solution, field data, or both. As a result, each verification approach has its advantages and disadvantages depending on the model complexity (governing equations used to develop the model and assumptions used to simplify the problem).

All three-dimensional models available to simulate surface waterbodies do not have outputs related to the model of volume balance performance (see the user manuals of the above popular models). Therefore, the user does not know the model preserves volume or not during the simulation period even though the model gives results. In addition, most 3D users run the simulation for a very short time (even for seconds), thinking the model is stable, since the 3D numerical models require long computation time to run. Thus, the need to develop a new volume balance tool arises based on these issues related to 3D hydrodynamic numerical models used in practice for surface waterbodies.

In this work, the volume balance approach was used as a tool to measure how a model preserves volume during the simulation time by calculating the accumulated error over time as a percent. Therefore, the modeler can monitor the model performance over time and decide whether the model is robust or not while running the model rather than waiting until the end of simulation.

#### **2. Methods**

To implement the volume balance approach, the three-dimensional model W3 developed by [13] for modeling hydrodynamics, temperature, and water quality in surface waterbodies was employed. Using the finite differences, the model solves the governing equations of continuity, free surface, momentums, and mass transport. Comparisons with analytical solutions and field data were carried out for verifying and validating the W3 model [13–17].

The model of volume balance was performed by comparing the water volume in the model domain during a time period with the water volume entering and leaving the same domain during the same period of time.

Let Vol be the accumulated water volume in the model domain over time. Then,

$$\text{Vol} = \text{Vol}\_{\text{initial}} + \text{Vol}\_{\text{in}} - \text{Vol}\_{\text{out}} \tag{1}$$

**159**

**Figure 3.**

*Air temperature input data.*

**Figure 1.**

**Figure 2.**

*Wind direction input data.*

*Wind speed input data.*

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic…*

*DOI: http://dx.doi.org/10.5772/intechopen.89691*

where Volinitial = the initial water volume within the domain; Volin = the accumulated water volume entering the domain; and Volout = the accumulated water volume leaving the domain.

Thus, the error over time can be calculated as follows:

$$\text{\%\#Error} = \left(\text{abs}(\text{\%\text{ol}} - \text{\%ol}\_{\text{internal}})\right) / \text{\%\text{ol}}\_{\text{internal}} \times 100\tag{2}$$

where Volinternal is the water volume within the domain at any time during the simulation period.

A subroutine was added to the model to check the volume preservation by calculating % error at every time step. A lower % error represents more accurate model predictions. The error should reach a constant value with time and should not grow with time. If % error grows with time exponentially, this implies that the model goes unstable (blows up). Two tests implementing the volume balance check were performed. One of these tests examined the volume balance over a rectangular domain, and the other tests evaluated the volume balance over an irregular domain. Both tests were performed over a period of 100 days based on the same real meteorological data, calculated solar short radiation, and constant inflow and outflow. The meteorological data are shown in **Figures 1–5**.

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic… DOI: http://dx.doi.org/10.5772/intechopen.89691*

**Figure 1.** *Wind speed input data.*

*Direct Numerical Simulations - An Introduction and Applications*

model rather than waiting until the end of simulation.

verifying and validating the W3 model [13–17].

leaving the same domain during the same period of time.

Thus, the error over time can be calculated as follows:

The meteorological data are shown in **Figures 1–5**.

used in practice for surface waterbodies.

**2. Methods**

leaving the domain.

simulation period.

All three-dimensional models available to simulate surface waterbodies do not have outputs related to the model of volume balance performance (see the user manuals of the above popular models). Therefore, the user does not know the model preserves volume or not during the simulation period even though the model gives results. In addition, most 3D users run the simulation for a very short time (even for seconds), thinking the model is stable, since the 3D numerical models require long computation time to run. Thus, the need to develop a new volume balance tool arises based on these issues related to 3D hydrodynamic numerical models

In this work, the volume balance approach was used as a tool to measure how a model preserves volume during the simulation time by calculating the accumulated error over time as a percent. Therefore, the modeler can monitor the model performance over time and decide whether the model is robust or not while running the

To implement the volume balance approach, the three-dimensional model W3 developed by [13] for modeling hydrodynamics, temperature, and water quality in surface waterbodies was employed. Using the finite differences, the model solves the governing equations of continuity, free surface, momentums, and mass transport. Comparisons with analytical solutions and field data were carried out for

The model of volume balance was performed by comparing the water volume in the model domain during a time period with the water volume entering and

Let Vol be the accumulated water volume in the model domain over time. Then,

where Volinitial = the initial water volume within the domain; Volin = the accumulated water volume entering the domain; and Volout = the accumulated water volume

where Volinternal is the water volume within the domain at any time during the

A subroutine was added to the model to check the volume preservation by calculating % error at every time step. A lower % error represents more accurate model predictions. The error should reach a constant value with time and should not grow with time. If % error grows with time exponentially, this implies that the model goes unstable (blows up). Two tests implementing the volume balance check were performed. One of these tests examined the volume balance over a rectangular domain, and the other tests evaluated the volume balance over an irregular domain. Both tests were performed over a period of 100 days based on the same real meteorological data, calculated solar short radiation, and constant inflow and outflow.

Vol = Volinitial + Volin − Volout (1)

% = (( − ))/ × 100 (2)

**158**

**Figure 2.** *Wind direction input data.*

**Figure 3.** *Air temperature input data.*

**Figure 5.** *Cloud cover input data.*

#### **3. Results and discussion**

The physical domain was divided into computational cells of 1000 × 500 × 1 (*x*,*y*,*z*) m and oriented perpendicular to the north direction as shown in **Figure 6**, in which there are bends at the boundaries to check how the model catches the flow field variability. The code was run without assuming a frictionless fluid, with the Coriolis force, with wind variable in magnitude and direction at 10 m height above


**161**

**Figure 8.**

**Figure 7.**

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic…*

water temperature over time by solving the heat transport equation. Additionally, the adding/subtracting layers algorithm (see [18]) was turned on to examine the

Using a time step of 35 s and a degree of implicitness (θ) of 1, the code was run for the simulation period. **Figure 7** presents the model predictions of the surface velocity field at Julian day 100. The model results showed good performance in following the bends at the boundaries. Furthermore, the volume balance error gave a good agreement in preserving volume in which the percent error reached a constant low value over time as shown in **Figure 8**, which is a semilog plot of the percent error with time. The corresponding water levels at three locations over time were shown in **Figure 9**, denoting a very small change (≅0.005 m) in the surface layer

Since the W3 model uses the degree of implicitness to switch between the fully implicit numerical scheme and the fully explicit scheme, the effect of the degree of implicitness on the accumulated error was evaluated by running the code using θ = 0.5 with the same inputs that were used with θ = 1. The results showed that using the semiimplicit scheme of θ = 0.5 produces less percent error than using θ = 1. **Figure 10** shows the percent error after running the code for day 100 using two degrees of implicitness

In addition and in order to make sure that the numerical answers do not depend on the grid resolution, a grid refinement was performed, and the associated volume

/s, and with variable

the water surface, with a constant inflow and outflow of 0.8 m3

*DOI: http://dx.doi.org/10.5772/intechopen.89691*

surface layer thickness over the simulation period.

thickness resulting from the free water surface waves.

*Surface velocity field for the irregular domain at Julian day 100.*

*Volume balance for the irregular domain using θ = 1.*

(θ = 1 and θ = 0.5).

**Figure 6.** *Irregular physical domain and the input bathymetry.*

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic… DOI: http://dx.doi.org/10.5772/intechopen.89691*

the water surface, with a constant inflow and outflow of 0.8 m3 /s, and with variable water temperature over time by solving the heat transport equation. Additionally, the adding/subtracting layers algorithm (see [18]) was turned on to examine the surface layer thickness over the simulation period.

Using a time step of 35 s and a degree of implicitness (θ) of 1, the code was run for the simulation period. **Figure 7** presents the model predictions of the surface velocity field at Julian day 100. The model results showed good performance in following the bends at the boundaries. Furthermore, the volume balance error gave a good agreement in preserving volume in which the percent error reached a constant low value over time as shown in **Figure 8**, which is a semilog plot of the percent error with time. The corresponding water levels at three locations over time were shown in **Figure 9**, denoting a very small change (≅0.005 m) in the surface layer thickness resulting from the free water surface waves.

Since the W3 model uses the degree of implicitness to switch between the fully implicit numerical scheme and the fully explicit scheme, the effect of the degree of implicitness on the accumulated error was evaluated by running the code using θ = 0.5 with the same inputs that were used with θ = 1. The results showed that using the semiimplicit scheme of θ = 0.5 produces less percent error than using θ = 1. **Figure 10** shows the percent error after running the code for day 100 using two degrees of implicitness (θ = 1 and θ = 0.5).

In addition and in order to make sure that the numerical answers do not depend on the grid resolution, a grid refinement was performed, and the associated volume

**Figure 7.** *Surface velocity field for the irregular domain at Julian day 100.*

**Figure 8.** *Volume balance for the irregular domain using θ = 1.*

*Direct Numerical Simulations - An Introduction and Applications*

**160**

**Figure 6.**

**Figure 4.**

**Figure 5.**

*Cloud cover input data.*

**3. Results and discussion**

*Irregular physical domain and the input bathymetry.*

The physical domain was divided into computational cells of 1000 × 500 × 1 (*x*,*y*,*z*) m and oriented perpendicular to the north direction as shown in **Figure 6**, in which there are bends at the boundaries to check how the model catches the flow field variability. The code was run without assuming a frictionless fluid, with the Coriolis force, with wind variable in magnitude and direction at 10 m height above

*Dew point input data.*

**Figure 9.**

*Surface layer thickness over time for the irregular domain using θ = 1.*

**Figure 10.** *The volume balance for the irregular domain using θ = 1 and θ = 0.5.*

**Figure 11.** *The effect of grid refinement.*

error was assessed. The code was run using θ = 0.5 with three horizontal grid resolutions 1000 × 500, 500 × 500, and 500 × 125 (*x*,*y*) m in which the model was stable numerically. To maintain the stability, three different time steps were chosen to run the code because the refinement lowers the time step (∆t). All resolutions were applied on the same initial water volume in **Figure 6**. Therefore, the initial water volume of the waterbody was fixed, while the grid resolution was varied.

**163**

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic…*

**Figure 11** shows the percent error over time for the three considered grid resolutions, indicating that the error in volume has the same order of magnitude for the

Model verification is the first step after building any new hydrodynamic numerical model for surface waterbody simulation. In this chapter, a new volume balance approach was introduced for verifying the three-dimensional hydrodynamic numerical models in surface waterbody simulation. This technique provides information about whether the code preserves fluid mass or not by calculating the volume balance percent error over time during a model simulation. The model results indicated that the model is considered numerically stable if the volume balance error reaches a constant value over time. In addition, even though the model degree of implicitness had a reasonable volume balance error (less than 0.1%), the semi-implicit numerical scheme had slightly better volume balance error than the

The authors thank the Department of Civil and Environmental Engineering, Portland State University, Portland, OR, USA, for their help in doing this research in association with the Iraqi Ministry of Higher Education and Scientific Research,

1 Department of Environmental Engineering, College of Engineering, University of

2 Department of Civil and Environmental Engineering, Portland State University,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: alzubaidih10@gmail.com; hmahdi@pdx.edu

*DOI: http://dx.doi.org/10.5772/intechopen.89691*

three resolutions.

**4. Conclusions**

fully implicit scheme.

**Acknowledgements**

University of Babylon.

**Author details**

Babylon, Babylon, Iraq

Portland, OR, USA

Hussein A.M. Al-Zubaidi1,2\* and Scott A. Wells2

provided the original work is properly cited.

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic… DOI: http://dx.doi.org/10.5772/intechopen.89691*

**Figure 11** shows the percent error over time for the three considered grid resolutions, indicating that the error in volume has the same order of magnitude for the three resolutions.

#### **4. Conclusions**

*Direct Numerical Simulations - An Introduction and Applications*

*Surface layer thickness over time for the irregular domain using θ = 1.*

*The volume balance for the irregular domain using θ = 1 and θ = 0.5.*

error was assessed. The code was run using θ = 0.5 with three horizontal grid resolutions 1000 × 500, 500 × 500, and 500 × 125 (*x*,*y*) m in which the model was stable numerically. To maintain the stability, three different time steps were chosen to run the code because the refinement lowers the time step (∆t). All resolutions were applied on the same initial water volume in **Figure 6**. Therefore, the initial water volume of the waterbody was fixed, while the grid resolution was varied.

**162**

**Figure 11.**

*The effect of grid refinement.*

**Figure 9.**

**Figure 10.**

Model verification is the first step after building any new hydrodynamic numerical model for surface waterbody simulation. In this chapter, a new volume balance approach was introduced for verifying the three-dimensional hydrodynamic numerical models in surface waterbody simulation. This technique provides information about whether the code preserves fluid mass or not by calculating the volume balance percent error over time during a model simulation. The model results indicated that the model is considered numerically stable if the volume balance error reaches a constant value over time. In addition, even though the model degree of implicitness had a reasonable volume balance error (less than 0.1%), the semi-implicit numerical scheme had slightly better volume balance error than the fully implicit scheme.

#### **Acknowledgements**

The authors thank the Department of Civil and Environmental Engineering, Portland State University, Portland, OR, USA, for their help in doing this research in association with the Iraqi Ministry of Higher Education and Scientific Research, University of Babylon.

#### **Author details**

Hussein A.M. Al-Zubaidi1,2\* and Scott A. Wells2

1 Department of Environmental Engineering, College of Engineering, University of Babylon, Babylon, Iraq

2 Department of Civil and Environmental Engineering, Portland State University, Portland, OR, USA

\*Address all correspondence to: alzubaidih10@gmail.com; hmahdi@pdx.edu

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **References**

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[2] Mellor GL. Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model (October 2002 Version). Princeton, NJ: Program in Atmospheric and Oceanic Sciences, Princeton University; 2002

[3] Blumberg AF. A coastal ocean numerical model. In: Mellor GL, editor. Proceedings of International Symposium on Mathematical Modelling of Estuarine Physics. Berlin: Springer; 1980. pp. 202-219

[4] Barron CN, Kara AB, Martin PJ, Rhodes RC, Smedstad LF. Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM). Ocean Modelling. 2006;**11**(3-4):347-375. DOI: 10.1016/j.ocemod.2005.01.004

[5] Martin PJ, Barron CN, Smedstad LF, Campbell AJ, Rhodes RC, Rowley C, et al. User's Manual for the Navy Coastal Ocean Model (NCOM) Version 4.0. MS: Naval Research Laboratory, Oceanography Division, Stennis Space Center; 2009. Report No. NRL/ MR/7320-08-9151

[6] Chen C, Beardsley RC, Cowles G, Qi J, Lai Z, Gao G, et al. An Unstructured-Grid, Finite-Volume Community Ocean Model FVCOM User Manual. 3rd ed. Cambridge, MA: Massachusetts Institute of Technology; 2011. Report No. 11-1101

[7] Chen C, Liu H, Beardsley RC. An unstructured grid, finite-volume, threedimensional, primitive equations ocean model: Application to coastal ocean and estuaries. Journal of Atmospheric and

Oceanic Technology. 2003;**20**:159-186. DOI: 10.1175/1520-0426(2003) 020<0159:AUGFVT>2.0.CO;2

[8] Hamrick JM. A three-dimensional environmental fluid dynamics computer code: Theoretical and computational aspects. In: Special Report 317 in Applied Marine Science and Ocean Engineering. VA: Virginia Institute of Marine Science, School of Marine Science, College of William and Mary; 1992

[9] Casulli V, Cheng RT. Semi-implicit finite difference methods for threedimensional shallow water flow. International Journal for Numerical Methods in Fluids. 1992;**15**(6):629-648. DOI: 10.1002/fld.1650150602

[10] Casulli V, Walters RA. An unstructured grid, three dimensional model based on the shallow water equations. International Journal for Numerical Methods in Fluids. 2000;**32**:331-348. DOI: 10.1002/(SICI) 10970363(20000215)32:3<331::AID-FLD941>3.0.CO;2-C

[11] Edinger JE. Waterbody Hydrodynamic and Water Quality Modeling: An Introductory Workbook and CD-ROM on Three-Dimensional Waterbody Modeling. VA: ASCE; 2001

[12] Moin P, Mahesh K. Direct numerical simulation: A tool in turbulence research. Annual Review of Fluid Mechanics. 1998;**30**(1):539-578. DOI: 10.1146/annurev.fluid.30.1.539

[13] Al-Zubaidi HAM, Wells SA. Analytical and field verification of a 3D hydrodynamic and water quality numerical scheme based on the 2D formulation in CE-QUAL-W2. Journal of Hydraulic Research. 2018. DOI: 10.1080/00221686.2018.1499051. https://www.tandfonline.com/doi/full/1 0.1080/00221686.2018.1499051

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[14] Al-Zubaidi HAM, Wells SA. 3D numerical temperature model development and calibration for lakes and reservoirs: A case study. In: Proceedings of the World

Environmental and Water Resources Congress 2017. Sacramento, CA: ASCE; 2017. DOI: 10.1061/9780784480601.051

[15] Al-Zubaidi HAM, Wells SA. 2D and 3D numerical modeling of water level and temperature in lakes and reservoirs based on the numerical scheme in CE-QUAL-W2: A case study. In: Proceedings, the 37th International Symposium of the North American Lakes Management Society. Westminster, Colorado: NALMS; 2017

[16] Al-Zubaidi HAM, Wells SA. Comparison of a 2D and 3D hydrodynamic and water quality model for lake systems. In: Proceedings, World Environmental and Water Resources Congress 2018. Minneapolis,

Minnesota: ASCE; 2018. DOI: 10.1061/9780784481400.007

Colorado: iEMSs; 2018

pdx.edu/w2/

[17] Al-Zubaidi HAM, Wells SA. Water level, temperature, and water quality numerical predictions of a 3D semiimplicit scheme for lakes and reservoirs: An analytical and field case study. In: Proceedings, the 9th International Congress on Environmental Modelling and Software (iEMSs 2018). Ft. Collins,

[18] Cole T, Wells SA. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model (Version 4.1). Portland, OR: Department of Civil and Environmental Engineering, Portland State University; 2017. Available from: http://www.cee.

*A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic… DOI: http://dx.doi.org/10.5772/intechopen.89691*

[14] Al-Zubaidi HAM, Wells SA. 3D numerical temperature model development and calibration for lakes and reservoirs: A case study. In: Proceedings of the World Environmental and Water Resources Congress 2017. Sacramento, CA: ASCE; 2017. DOI: 10.1061/9780784480601.051

[15] Al-Zubaidi HAM, Wells SA. 2D and 3D numerical modeling of water level and temperature in lakes and reservoirs based on the numerical scheme in CE-QUAL-W2: A case study. In: Proceedings, the 37th International Symposium of the North American Lakes Management Society. Westminster, Colorado: NALMS; 2017

[16] Al-Zubaidi HAM, Wells SA. Comparison of a 2D and 3D hydrodynamic and water quality model for lake systems. In: Proceedings, World Environmental and Water Resources Congress 2018. Minneapolis, Minnesota: ASCE; 2018. DOI: 10.1061/9780784481400.007

[17] Al-Zubaidi HAM, Wells SA. Water level, temperature, and water quality numerical predictions of a 3D semiimplicit scheme for lakes and reservoirs: An analytical and field case study. In: Proceedings, the 9th International Congress on Environmental Modelling and Software (iEMSs 2018). Ft. Collins, Colorado: iEMSs; 2018

[18] Cole T, Wells SA. CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model (Version 4.1). Portland, OR: Department of Civil and Environmental Engineering, Portland State University; 2017. Available from: http://www.cee. pdx.edu/w2/

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*Direct Numerical Simulations - An Introduction and Applications*

Oceanic Technology. 2003;**20**:159-186.

[8] Hamrick JM. A three-dimensional environmental fluid dynamics computer code: Theoretical and computational aspects. In: Special Report 317 in Applied Marine Science and Ocean Engineering. VA: Virginia Institute of Marine Science, School of Marine Science, College of

[9] Casulli V, Cheng RT. Semi-implicit finite difference methods for threedimensional shallow water flow. International Journal for Numerical Methods in Fluids. 1992;**15**(6):629-648.

DOI: 10.1175/1520-0426(2003) 020<0159:AUGFVT>2.0.CO;2

William and Mary; 1992

DOI: 10.1002/fld.1650150602

[10] Casulli V, Walters RA. An

FLD941>3.0.CO;2-C

[11] Edinger JE. Waterbody Hydrodynamic and Water Quality Modeling: An Introductory Workbook and CD-ROM on Three-Dimensional Waterbody Modeling. VA: ASCE; 2001

unstructured grid, three dimensional model based on the shallow water equations. International Journal for Numerical Methods in Fluids. 2000;**32**:331-348. DOI: 10.1002/(SICI) 10970363(20000215)32:3<331::AID-

[12] Moin P, Mahesh K. Direct numerical

simulation: A tool in turbulence research. Annual Review of Fluid Mechanics. 1998;**30**(1):539-578. DOI: 10.1146/annurev.fluid.30.1.539

[13] Al-Zubaidi HAM, Wells SA. Analytical and field verification of a 3D hydrodynamic and water quality numerical scheme based on the 2D formulation in CE-QUAL-W2. Journal of Hydraulic Research. 2018. DOI: 10.1080/00221686.2018.1499051. https://www.tandfonline.com/doi/full/1

0.1080/00221686.2018.1499051

[1] Blumberg AF, Mellor GL. A description of a three-dimensional coastal ocean circulation model. In: Heaps NS, editor. Three-Dimensional Coastal Ocean Models. Washington, DC: American Geophysical Union; 1987. pp. 1-16. DOI: 10.1029/co004p0001

**References**

[2] Mellor GL. Users Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model (October 2002 Version). Princeton, NJ: Program in Atmospheric and Oceanic Sciences,

Princeton University; 2002

1980. pp. 202-219

MR/7320-08-9151

[3] Blumberg AF. A coastal ocean numerical model. In: Mellor GL, editor. Proceedings of International Symposium on Mathematical Modelling of Estuarine Physics. Berlin: Springer;

[4] Barron CN, Kara AB, Martin PJ, Rhodes RC, Smedstad LF. Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM). Ocean Modelling. 2006;**11**(3-4):347-375. DOI: 10.1016/j.ocemod.2005.01.004

[5] Martin PJ, Barron CN, Smedstad LF, Campbell AJ, Rhodes RC, Rowley C, et al. User's Manual for the Navy Coastal Ocean Model (NCOM) Version 4.0. MS: Naval Research Laboratory, Oceanography Division, Stennis Space Center; 2009. Report No. NRL/

[6] Chen C, Beardsley RC, Cowles G, Qi J, Lai Z, Gao G, et al. An Unstructured-Grid, Finite-Volume Community Ocean Model FVCOM User Manual. 3rd ed. Cambridge, MA: Massachusetts Institute of Technology; 2011. Report No. 11-1101

[7] Chen C, Liu H, Beardsley RC. An unstructured grid, finite-volume, threedimensional, primitive equations ocean model: Application to coastal ocean and estuaries. Journal of Atmospheric and

### *Edited by Srinivasa Rao*

To understand and model the turbulent behavior of flowing fluids is one of the most fascinating, intriguing, annoying, and most important problems of engineering and physics. Admittedly most of the fluid flows are turbulent. In the known universe, turbulence is evident at the macroscopic scale and the microscopic scale in identical proportions. Turbulence is manifested in many places, such as: a plethora of technological devices, atmospheres and ocean currents, astronomical or galactic motions, and biological systems like circulation or respiration. With the continuum as an assumption, the equations that define the physics of fluid flow are the Navier-Stokes equations modeled during the mid-19th Century by Claude-Louis Navier and Sir George Gabriel Stokes. These equations define all flows, even turbulent flows, yet there is no analytical solution to even the simplest turbulent flow possible. However, the numerical solution of the Navier-Stokes equation is able to describe the flow variable as a function of space and time. It is called direct numerical simulations (DNS), which is the subject matter of this book.

Published in London, UK © 2021 IntechOpen © MikeMcFarlane / iStock

Direct Numerical Simulations - An Introduction and Applications

Direct Numerical Simulations

An Introduction and Applications

*Edited by Srinivasa Rao*