**Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes**

Stanisław Łopata and Paweł Ocłoń *Cracow University of Technology, Cracow Poland* 

#### **1. Introduction**

326 Fluid Dynamics, Computational Modeling and Applications

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High performance heat exchangers are widely used in many industries such as petrochemical industry, automotive industry, energetic industry and many others. The name of this kind of heat exchangers is in consistency with their structure. Large heat transfer area leads to high thermal efficiency of the device. Its working principle is to cool rapidly large amount of gaseous or liquid medium. Because of its compact size, it is possible to use it for easy installation in various systems, like the heating, drying, air conditioning and the other systems.

High thermal performance of this type of heat exchangers (Nagatha, 2004; Ibrahim & Gomaa, 2009) is achieved due to large packed rectangular fins on tube surface, as well as the shape of the tubes. The elliptical shape ensures better distribution of velocity along the tube circumference during the flow, as well as lower pressure drop in comparison to the circular shape (Matos et al, 2004; Jang & Yang, 1998; Li et al, 2006; Nishiyama et al, 1988; Khan et al, 2004; Saboya & Saboya, 1981; Saboya & Sparrow, 1974; Bordallo & Saboya, 1999). Consequently, the coefficient of heat transfer in the elliptical shape is larger when compared to the circular shape (Idem et al, 1990; Rocha et al, 1997; Taler, 2009). It brings about that the heat exchange process is more efficient in elliptical than in circular tubes.

To use all the aforementioned advantages, it is necessary to ensure uniform distribution of velocity in all the tubes. Failing that, it leads to large differences in mean temperature in the tubes. Consequently, excessive thermal stress occurs, that may cause the heat exchanger to break down. Small volume of collectors of the heat exchangers implicates possibility of improper flow condition inside the tubes, causing unsuitable inner distribution of thermal and mechanical loads. Damages to a tube, Fig. 1, as well as a tube bundle prone to buckling, Fig. 2, prove, that such a failure is possible (Łopata & Ocłon, 2010; Ocłon & Łopata, 2011).

Compressible stresses are undesirable (Łopata & Ocłon, 2010; Łopata & Ocłon, 2011) in this type of construction, because the allowable compressible load (allowable buckling stress) for a slender tube is significantly lower than the safe tensile load.

The simplified method to assess failure of a high performance heat exchanger with finned elliptical tubes is presented in the paper. The diagram, shown on Fig. 3, presents the method. The geometrical representation of construction – a CAD model is prepared at first. Next, on the basis of prepared geometry, numerical representation of the model is created. Afterwards, the flow computation - CFD (Ferziger & Peric 1999; Anderson, 1995; Gresho &

Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 329

This commercial tool computes displacement and stresses for the numerical model of the heat exchanger using the Finite Element Method (Reddy, 1993; Logan, 2011; Smith & Griffiths, 2004; Zienkiewicz & Taylor, 2000; Hutton, 2003). Structural analysis allows finding the zones and locations where allowable stresses are exceeded. When it happens, the computational flow loops back to the CFD analysis and the other geometrical parameters of the collector are set. The loop continues until allowable stresses in the construction are exceeded. If the maximum stress is lower than the critical stress, the construction is safe to

The methodology presented in the paper may help to assess structural safety. The computations described in this chapter were successfully applied in analysis of two failures of a high performance heat exchanger that happened in an industrial company in Poland.

The proper operating conditions of the high performance heat exchanger improve its thermal efficiency and lead to significantly smaller pressure exerted on tube material. The operating conditions depend strongly on flow distribution inside the tubes of the high performance heat exchanger. The main task of hydraulic computation is to confirm, that liquid flowing inside the tubes is distributed properly in all the tubes. It is ideally, when the mass flow rate ݉ሶ in each tube equals to the mass flow at the inlet ݉ሶ divided by the number of tubes ݊ in a single pass of the heat exchanger. Nevertheless, it is impossible in fact to obtain the uniform flow distribution in all the tubes. The improper flow distribution has an influence on heat transfer process in each pass of the heat exchanger, causing high temperature differences in the adjacent tubes that can cause the stress limit of the tube

**2. Hydraulic and thermal performance of heat exchanger** 

Fig. 3. Calculation methodology

use, and the computations stop.

material to be exceeded.

Sani, 2000; Chung, 2010) is carried out using the commercial tool ANSYS CFX (ANSYS, 2008). It is desirable to obtain the uniform mass flow rates in all the tubes of the heat exchanger, because it ensures the appropriate heat transfer conditions for the device. When the mean velocities in tubes differ significantly (Łopata & Ocłon, 2010), new modified collectors are applied to improve flow distribution inside the device (Ocłon & Łopata, 2011). If the liquid distribution among all the tubes ensures safe heat transfer conditions, the CFD computation is stopped. The results obtained with the CFD analysis as the bulk temperatures *Tbulk* and the heat transfer coefficients *h* are transferred next to a code, that calculates temperature distribution inside the elliptical tube, using the Control Volume Method (Chung, 2010; Taler & Duda, 2006) as the mixed type boundary conditions (Incopera, 2001). The obtained temperature and pressure values are used as thermal loads for structural analysis, using the ANSYS Structural (ANSYS ADPL, 2009) software.

Fig. 1. View of damaged tube

Fig. 2. Buckled tubes of a high performance heat exchanger

Fig. 3. Calculation methodology

Sani, 2000; Chung, 2010) is carried out using the commercial tool ANSYS CFX (ANSYS, 2008). It is desirable to obtain the uniform mass flow rates in all the tubes of the heat exchanger, because it ensures the appropriate heat transfer conditions for the device. When the mean velocities in tubes differ significantly (Łopata & Ocłon, 2010), new modified collectors are applied to improve flow distribution inside the device (Ocłon & Łopata, 2011). If the liquid distribution among all the tubes ensures safe heat transfer conditions, the CFD computation is stopped. The results obtained with the CFD analysis as the bulk temperatures *Tbulk* and the heat transfer coefficients *h* are transferred next to a code, that calculates temperature distribution inside the elliptical tube, using the Control Volume Method (Chung, 2010; Taler & Duda, 2006) as the mixed type boundary conditions (Incopera, 2001). The obtained temperature and pressure values are used as thermal loads

for structural analysis, using the ANSYS Structural (ANSYS ADPL, 2009) software.

Fig. 1. View of damaged tube

Fig. 2. Buckled tubes of a high performance heat exchanger

This commercial tool computes displacement and stresses for the numerical model of the heat exchanger using the Finite Element Method (Reddy, 1993; Logan, 2011; Smith & Griffiths, 2004; Zienkiewicz & Taylor, 2000; Hutton, 2003). Structural analysis allows finding the zones and locations where allowable stresses are exceeded. When it happens, the computational flow loops back to the CFD analysis and the other geometrical parameters of the collector are set. The loop continues until allowable stresses in the construction are exceeded. If the maximum stress is lower than the critical stress, the construction is safe to use, and the computations stop.

The methodology presented in the paper may help to assess structural safety. The computations described in this chapter were successfully applied in analysis of two failures of a high performance heat exchanger that happened in an industrial company in Poland.

#### **2. Hydraulic and thermal performance of heat exchanger**

The proper operating conditions of the high performance heat exchanger improve its thermal efficiency and lead to significantly smaller pressure exerted on tube material.

The operating conditions depend strongly on flow distribution inside the tubes of the high performance heat exchanger. The main task of hydraulic computation is to confirm, that liquid flowing inside the tubes is distributed properly in all the tubes. It is ideally, when the mass flow rate ݉ሶ in each tube equals to the mass flow at the inlet ݉ሶ divided by the number of tubes ݊ in a single pass of the heat exchanger. Nevertheless, it is impossible in fact to obtain the uniform flow distribution in all the tubes. The improper flow distribution has an influence on heat transfer process in each pass of the heat exchanger, causing high temperature differences in the adjacent tubes that can cause the stress limit of the tube material to be exceeded.


$$
\overrightarrow{\mathbf{w}\_{wat}} = \frac{m\_{wat}}{n \cdot A\_{tuba'} \rho\_{wat}} \,\tag{1}
$$

$$\mathrm{Nu}\_{\mathrm{wat}} = \frac{\frac{1}{\mathfrak{p}} f \cdot (\mathrm{Re}\_{\mathrm{wat}} - \mathrm{1000}) \cdot \mathrm{Pr}\_{\mathrm{wat}}}{1 + 12.7 \cdot \left(\frac{1}{\mathfrak{p}} f\right)^{\frac{1}{\mathfrak{T}}} \cdot (\mathrm{Pr}\_{\mathrm{wat}}^{\frac{2}{3}} - 1)}. \tag{2}$$

$$\text{Pr}\_{\text{wat}} = \frac{c\_{p-\text{wat}} \cdot \eta\_{\text{wat}}}{k\_{\text{wat}}} \tag{3}$$

$$f = (0.79ln \cdot \text{Re}\_{\text{wat}} - 1.64)^{-2}.\tag{4}$$

$$h\_{\text{wat}} = \frac{\text{Nu}\_{\text{wat}} \cdot k\_{\text{wat}}}{d\_h}.\tag{5}$$

$$d\_h = \frac{{}^{4 \cdot A\_{tube}}}{{}^{P\_{tube}}},\tag{6}$$


$$\dot{q}\_{lnt} = \frac{\sum\_{f=1}^{n\_{el}} q\_f \cdot A\_f}{\sum\_{f=1}^{n\_{el}} A\_f}. \tag{7}$$

$$T\_{\omegaall} = \frac{\Sigma\_{f=1}^{n\_{\text{eff}}} \tau\_{f^\*} \mathbf{a}\_f}{\Sigma\_{f=1}^{n\_{\text{eff}}} \mathbf{A}\_f}. \tag{8}$$

$$T\_{cg-bulk} = \frac{\Sigma\_{f=1}^{n\_{al}} T\_f \cdot m\_f}{\Sigma\_{f=1}^{n\_{al}} m\_f} \,. \tag{9}$$

$$h\_{cg}(\mathbf{y}) = \frac{q\_{\text{Int}}}{(T\_{cg-bulk} - T\_{wall})} \tag{10}$$

Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 337

The boundary layer is modelled using the hexahedral elements and the flow core is discretized using the tetrahedral elements. The boundary conditions set for ݉ሶ ௪௧ = 19 kg/s

Fig. 13. Boundary condition for analysis of water flow - ݉ሶ ௪௧ = 19 kg/s

As mentioned in section 1, it is difficult to ensure the uniform flow distribution to all the tubes, due to limited space in the collectors. The zones of the tubes where the velocity is

௪௧ തതതത are marked on red, see Fig. 14.

Fig. 14. Velocity distribution in high performance heat exchanger - ݉ሶ ௪௧ = 19 kg/s

is presented on Fig. 13.

significantly lower than the തݓതത

On Fig. 11 the *hcg* and *Tcg-bulk* distribution along *y* direction for *ts* is presented

Fig. 11. Heat transfer coefficient and bulk temperature distribution for combustion gas - ݐ௦ = 0 mm, ݐ௦ = 1 mm and ݐ௦ = 1.5 mm

Heat transfer coefficient from combustion gas to the tube is larger when boiler scale thickness increases. Rapid growth of *Tcg-bulk* combined with isolative behaviour of scale, causes high temperature increase of the tube. Therefore, operating condition of the device worsens significantly, because the normal stresses acting on the tube grow up with increase in temperature, too.

#### **2.2 Flow distribution inside collectors and tubes of high performance heat exchanger**

Analysis of flow distribution inside the high performance heat exchanger is carried out using the mass, momentum and energy balance equations (Bird, 2001; Incopera & De Witt, 2001). The turbulence model SST is applied to flow behaviour simulation. The numerical model of the flow is presented on Fig. 12.

Fig. 12. Numerical model used for analysis of flow distribution inside heat exchanger

Fig. 11. Heat transfer coefficient and bulk temperature distribution for combustion gas - ݐ௦ =

Heat transfer coefficient from combustion gas to the tube is larger when boiler scale thickness increases. Rapid growth of *Tcg-bulk* combined with isolative behaviour of scale, causes high temperature increase of the tube. Therefore, operating condition of the device worsens significantly, because the normal stresses acting on the tube grow up with increase

**2.2 Flow distribution inside collectors and tubes of high performance heat exchanger**  Analysis of flow distribution inside the high performance heat exchanger is carried out using the mass, momentum and energy balance equations (Bird, 2001; Incopera & De Witt, 2001). The turbulence model SST is applied to flow behaviour simulation. The numerical

Fig. 12. Numerical model used for analysis of flow distribution inside heat exchanger

0 mm, ݐ௦ = 1 mm and ݐ௦ = 1.5 mm

model of the flow is presented on Fig. 12.

in temperature, too.

On Fig. 11 the *hcg* and *Tcg-bulk* distribution along *y* direction for *ts* is presented

The boundary layer is modelled using the hexahedral elements and the flow core is discretized using the tetrahedral elements. The boundary conditions set for ݉ሶ ௪௧ = 19 kg/s is presented on Fig. 13.

Fig. 13. Boundary condition for analysis of water flow - ݉ሶ ௪௧ = 19 kg/s

As mentioned in section 1, it is difficult to ensure the uniform flow distribution to all the tubes, due to limited space in the collectors. The zones of the tubes where the velocity is significantly lower than the തݓതത ௪௧ തതതത are marked on red, see Fig. 14.

Fig. 14. Velocity distribution in high performance heat exchanger - ݉ሶ ௪௧ = 19 kg/s

Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 339

can lead to fracture of the first tube near the axis of symmetry (2nd pass), because temperature increases and stress level exceeds the allowable limits. Therefore the

௪௧ തതതത, that

௪௧ തതതത*,* for the 1st and

௪௧ തതതത for ݉ሶ ௪௧ = 9.5 kg/s, 14

kg/s in the 2nd pass of the heat exchanger, *w* can be even 50 times smaller than ݓതതത

construction of the collector should be modified to improve the ratios ݓȀݓതതത

Fig. 16. Ratios of mean velocity in tube *w* to estimated velocity തݓതത

simplicity and low costs of manufacturing.

The modified version of the collector is presented in the next subchapter.

**2.3 Analysis of flow distribution inside modified collector of high performance heat** 

As mentioned before, difficulties in ensuring uniform flow velocity inside all the tubes of the high performance heat exchangers have forced us to find a new shape of the collector that improves flow distribution inside the tubes of the 1st and the 2nd pass. The shape of the collector, presented on Fig. 17, is being proposed. The greatest advantages of using it are its

kg/s and 19 kg/s

**exchanger** 

the 2nd pass of the high performance heat exchanger.

These zones are formed because pressure changes occur (see Fig. 15) in the direction parallel to the perforated bottom of the collector.

Fig. 15. Pressure and temperature distribution inside high performance heat exchanger - ݉ሶ ௪௧ = 19 kg/s

The pressure is lower in the tubes with velocity bellow ݓതതത ௪௧ തതതത than in the others. Therefore, the driving force of the flow falls down and liquid doesn't come into this segment of the tubes. E.g., in the first pass of the heat exchanger, liquid flows into the tubes of the heat exchanger, those are located directly under the inlet nozzle pipe. Velocity of liquid in these tubes is larger than തݓതത ௪௧ തതതത . Amount of liquid flowing into the other tubes in this pass is much lower so are velocities. For the second pass of the heat exchanger, the component of velocity vector, parallel to the perforated bottom of the collector, is significantly larger than the other components. Therefore, due to the large inertia forces, water encounters difficulties when changing the flow direction by 90 degrees especially when entering the first tubes of the 2nd pass of the heat exchanger. The mean velocity in tube ݓ) calculated as area averaged velocity) is the smallest there. It is even 20 times lower than the mean value (see Fig. 16).

Low flow velocities inside the tubes cause temperature of water to increase significantly. The zones and the locations where saturation temperature is exceeded are marked in red on Fig 15., the vapour bubbles starts to form there. When saturated steam flows inside the tube, the value *hwat* increases rapidly. As a result, heat transfer conditions in the device change considerably and differ from the design predictions.

The ratio of average velocity in tube *w*, computed from numerical simulation, to mean velocity of water തݓതത ௪௧ തതതത, presented on Fig. 16, shows that difficulties with improper flow distribution inside the heat exchanger exist in all the computational cases. For ݉ሶ ௪௧ = 14

These zones are formed because pressure changes occur (see Fig. 15) in the direction parallel

Fig. 15. Pressure and temperature distribution inside high performance heat exchanger -

the driving force of the flow falls down and liquid doesn't come into this segment of the tubes. E.g., in the first pass of the heat exchanger, liquid flows into the tubes of the heat exchanger, those are located directly under the inlet nozzle pipe. Velocity of liquid in these

lower so are velocities. For the second pass of the heat exchanger, the component of velocity vector, parallel to the perforated bottom of the collector, is significantly larger than the other components. Therefore, due to the large inertia forces, water encounters difficulties when changing the flow direction by 90 degrees especially when entering the first tubes of the 2nd pass of the heat exchanger. The mean velocity in tube ݓ) calculated as area averaged velocity) is the smallest there. It is even 20 times lower than the mean value (see Fig. 16). Low flow velocities inside the tubes cause temperature of water to increase significantly. The zones and the locations where saturation temperature is exceeded are marked in red on Fig 15., the vapour bubbles starts to form there. When saturated steam flows inside the tube, the value *hwat* increases rapidly. As a result, heat transfer conditions in the device change

The ratio of average velocity in tube *w*, computed from numerical simulation, to mean

distribution inside the heat exchanger exist in all the computational cases. For ݉ሶ ௪௧ = 14

௪௧

തതതത . Amount of liquid flowing into the other tubes in this pass is much

തതതത, presented on Fig. 16, shows that difficulties with improper flow

തതതത than in the others. Therefore,

The pressure is lower in the tubes with velocity bellow ݓതതത

௪௧

considerably and differ from the design predictions.

௪௧

to the perforated bottom of the collector.

݉ሶ ௪௧ = 19 kg/s

tubes is larger than തݓതത

velocity of water തݓതത

kg/s in the 2nd pass of the heat exchanger, *w* can be even 50 times smaller than ݓതതത ௪௧ തതതത, that can lead to fracture of the first tube near the axis of symmetry (2nd pass), because temperature increases and stress level exceeds the allowable limits. Therefore the construction of the collector should be modified to improve the ratios ݓȀݓതതത ௪௧ തതതത*,* for the 1st and the 2nd pass of the high performance heat exchanger.

Fig. 16. Ratios of mean velocity in tube *w* to estimated velocity തݓതത ௪௧ തതതത for ݉ሶ ௪௧ = 9.5 kg/s, 14 kg/s and 19 kg/s

The modified version of the collector is presented in the next subchapter.

#### **2.3 Analysis of flow distribution inside modified collector of high performance heat exchanger**

As mentioned before, difficulties in ensuring uniform flow velocity inside all the tubes of the high performance heat exchangers have forced us to find a new shape of the collector that improves flow distribution inside the tubes of the 1st and the 2nd pass. The shape of the collector, presented on Fig. 17, is being proposed. The greatest advantages of using it are its simplicity and low costs of manufacturing.

$$\begin{aligned} \Phi\_1^e &= \frac{1}{4} \cdot (1 - \xi) \cdot (1 - \eta) \\ \Phi\_2^e &= \frac{1}{4} \cdot (1 + \xi) \cdot (1 - \eta) \\ \Phi\_3^e &= \frac{1}{4} \cdot (1 + \xi) \cdot (1 + \eta) \\ \Phi\_4^e &= \frac{1}{4} \cdot (1 - \xi) \cdot (1 + \eta) \end{aligned} \tag{11}$$

$$T(\xi, \eta) = \Sigma\_{l=1}^4 T\_l \cdot \Phi\_l^e \tag{12}$$

$$\begin{aligned} \chi &= \sum\_{l=1 \atop \emptyset}^{4} \chi\_l \cdot \Phi\_l^e \\ \chi &= \sum\_{l=1}^{4} \chi\_l \cdot \Phi\_l^e \end{aligned} \tag{13}$$

$$\begin{aligned} k\_A \cdot \sum\_{\text{Cs2,3}} (\frac{dT}{dx} \cdot n\_\text{x} + \frac{dT}{dy} \cdot n\_\text{y}) \cdot \overrightarrow{\Delta \Gamma} + k\_B \cdot \sum\_{\text{Cs3,4}} (\frac{dT}{dx} \cdot n\_\text{x} + \frac{dT}{dy} \cdot n\_\text{y}) \cdot \overrightarrow{\Delta \Gamma} + \text{y} &= \sum\_{l=1}^4 \text{y}\_l \cdot \Phi\_l^e \\ k\_c \cdot \sum\_{\text{Cs4,1}} (\frac{dT}{dx} \cdot n\_\text{x} + \frac{dT}{dy} \cdot n\_\text{y}) \cdot \overrightarrow{\Delta \Gamma} + k\_D \cdot \sum\_{\text{Cs1,2}} (\frac{dT}{dx} \cdot n\_\text{x} + \frac{dT}{dy} \cdot n\_\text{y}) \cdot \overrightarrow{\Delta \Gamma} &= 0 \end{aligned} \tag{14}$$

$$Q\_A = k\_A \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_2 + \frac{d\tau}{dy} \cdot \sin\theta\_2\right) \cdot \overrightarrow{\Delta\Gamma}\_2 + k\_A \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_3 + \frac{d\tau}{dy} \cdot \sin\theta\_3\right) \cdot \overrightarrow{\Delta\Gamma}\_3 \tag{15}$$

$$Q\_B = k\_B \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_3 + \frac{d\tau}{dy} \cdot \sin\theta\_3\right) \cdot \overrightarrow{\Delta\Gamma\_3} + k\_B \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_4 + \frac{d\tau}{dy} \cdot \sin\theta\_4\right) \cdot \overrightarrow{\Delta\Gamma\_4} \tag{16}$$

$$Q\_{\mathbb{C}} = k\_{\mathbb{C}} \cdot \left( \frac{d\mathbb{T}}{dx} \cdot \cos \theta\_{\mathbb{4}} + \frac{d\mathbb{T}}{dy} \cdot \sin \theta\_{\mathbb{4}} \right) \cdot \overrightarrow{\Delta \Gamma}\_{\mathbb{4}} + k\_{\mathbb{C}} \cdot \left( \frac{d\mathbb{T}}{dx} \cdot \cos \theta\_{\mathbb{1}} + \frac{d\mathbb{T}}{dy} \cdot \sin \theta\_{\mathbb{1}} \right) \cdot \overrightarrow{\Delta \Gamma}\_{\mathbb{1}} \tag{17}$$

$$Q\_D = k\_D \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_1 + \frac{d\tau}{dy} \cdot \sin\theta\_1\right) \cdot \overrightarrow{\Delta\Gamma\_4} + k\_D \cdot \left(\frac{d\tau}{dx} \cdot \cos\theta\_2 + \frac{d\tau}{dy} \cdot \sin\theta\_2\right) \cdot \overrightarrow{\Delta\Gamma\_2} \tag{18}$$

$$Q\_A + Q\_B + Q\_C + Q\_D = 0\tag{19}$$

$$\begin{array}{l} \frac{dT}{d\boldsymbol{x}} = \frac{1}{|\boldsymbol{l}|} \cdot \left( \frac{dT}{d\xi} \cdot \frac{d\boldsymbol{y}}{d\eta} - \frac{dT}{d\eta} \cdot \frac{d\boldsymbol{y}}{d\xi} \right) \\\frac{dT}{d\boldsymbol{y}} = \frac{1}{|\boldsymbol{J}|} \cdot \left( \frac{dT}{d\eta} \cdot \frac{d\boldsymbol{x}}{d\xi} - \frac{dT}{d\xi} \cdot \frac{d\boldsymbol{x}}{d\eta} \right) \end{array} \tag{20}$$

$$\|f\| = \frac{dx}{d\xi} \cdot \frac{dy}{d\eta} - \frac{dy}{d\xi} \cdot \frac{dx}{d\eta} \tag{21}$$


Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 347

of finite elements. Each part of the construction consists of elements with different thickness,

**Component** *tshell* **[mm]**  tube 2 flat bar 15 perforated bottom 12 nozzle pipe 2.5 frame 20 collector 6 shell 8

The midsurface is geometrical representation of the element. The maximal stress value is

*tshell*, (see Tab. 4). Thickness of heat exchanger components are listed on Table 4.

Fig. 27. Construction and support conditions for heat exchanger

Table 4. Thickness of heat exchanger components

Fig. 28. Isoparametric shell element for structural calculations

computed at the outer fibbers of the element.

Fig. 25. Temperature distribution for ℎ���=5000 W/(m2 K), ���������=120 ºC, �� = 1 mm

It is possible to observe, on Fig. 25, that when boiler scale exists inside the tube, e.g. Fig. 26, temperature increases significantly.

Fig. 26. Boiler scale observed in tubes of heat exchanger

The large increase of temperature brings about considerable thermal stresses inside all the tubes that may lead to fracture of the tube; see Fig. 1 & Fig. 2.

#### **4. Analysis of stress state inside construction of high performance heat exchanger**

As mentioned before, structural analysis is carried out on basis of the Finite Element Method using the commercial code ANSYS. The manner in which the construction is supported is illustrated on Fig. 27. As it can be observed, the heat exchanger consists of two collectors with perforated bottoms to which all the tubes are welded. A shell connects the collectors and flat bars welded to the shell stiffen its structure. The frame increases the stiffness of the perforated bottom.

The other components of construction (a conffuser and a diffuser), not shown on Fig. 27 are welded to the shell. These parts constrain structure movement in the *y* direction. The heat exchanger is also clamped at the distance *z* = 525 mm from the upper perforated bottom. The isoparametric linear shell element, SHELL 181 (ANSYS, 2009), used for the structural analysis is presented on Fig. 28. The CAD model of the heat exchanger is divided into a set

Fig. 25. Temperature distribution for ℎ���=5000 W/(m2 K), ���������=120 ºC, �� = 1 mm

temperature increases significantly.

**exchanger** 

perforated bottom.

Fig. 26. Boiler scale observed in tubes of heat exchanger

tubes that may lead to fracture of the tube; see Fig. 1 & Fig. 2.

It is possible to observe, on Fig. 25, that when boiler scale exists inside the tube, e.g. Fig. 26,

The large increase of temperature brings about considerable thermal stresses inside all the

As mentioned before, structural analysis is carried out on basis of the Finite Element Method using the commercial code ANSYS. The manner in which the construction is supported is illustrated on Fig. 27. As it can be observed, the heat exchanger consists of two collectors with perforated bottoms to which all the tubes are welded. A shell connects the collectors and flat bars welded to the shell stiffen its structure. The frame increases the stiffness of the

The other components of construction (a conffuser and a diffuser), not shown on Fig. 27 are welded to the shell. These parts constrain structure movement in the *y* direction. The heat exchanger is also clamped at the distance *z* = 525 mm from the upper perforated bottom. The isoparametric linear shell element, SHELL 181 (ANSYS, 2009), used for the structural analysis is presented on Fig. 28. The CAD model of the heat exchanger is divided into a set

**4. Analysis of stress state inside construction of high performance heat** 

of finite elements. Each part of the construction consists of elements with different thickness, *tshell*, (see Tab. 4). Thickness of heat exchanger components are listed on Table 4.

Fig. 27. Construction and support conditions for heat exchanger


Table 4. Thickness of heat exchanger components

The midsurface is geometrical representation of the element. The maximal stress value is computed at the outer fibbers of the element.

Fig. 28. Isoparametric shell element for structural calculations

$$\{K\_e\} \cdot \{u\} - \{F\_e^{th}\} = \{M\_e\} \cdot \{\ddot{u}\} + \{F\_e^{pr}\},\tag{22}$$

$$
\lfloor K\_e \rfloor = \int\_{\nu} \, \lbrack B \rceil^T \cdot \lbrack D \rceil \cdot \lbrack B \rbrack dV,\tag{23}
$$

$$\left[F\_e^{th}\right] = \int\_{\mathcal{V}} \left[B\right]^T \cdot \left[D\right] \cdot \left\{\varepsilon\_{th}\right\} d\mathcal{V},\tag{24}$$

$$\{\varepsilon\_e^{th}\} = \mathfrak{a} \cdot (T - T\_{ref}) \,\tag{25}$$

$$\lfloor M\_e \rfloor = \rho \cdot \int\_{\nu} \lfloor N \rfloor^T \cdot \lfloor N \rfloor \cdot \lfloor D \rfloor dV,\tag{26}$$

$$\left\{ F\_e^{pr} \right\} = \int\_A \left[ N\_n \right]^T \cdot \left\{ P \right\} dA,\tag{27}$$


$$
\sigma\_e = \frac{1}{2} \cdot \sqrt{(\sigma\_1 - \sigma\_2)^2 + (\sigma\_2 - \sigma\_3)^2 + + (\sigma\_3 - \sigma\_1)^2},
\tag{28}
$$

$$L\_e = K \cdot L,\tag{29}$$

$$\mathbf{S} = \frac{\mathbf{s}\_a}{\sqrt{\frac{l\_{\text{m}\text{in}}}{\mathbf{A}}}} \mathbf{ } \tag{30}$$

$$\mathbf{s}\_{cr} = \pi \cdot \sqrt{\frac{E}{Y\_s}}.\tag{31}$$


$$
\sigma\_{crit} = \frac{\pi^2 \cdot E}{s^2}.\tag{32}
$$

Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 353

Fig. 36. Equivalent stress acc. to von Mises – heat exchanger with modified collector

Fig. 37. Compressible stresses – heat exchanger with modified collector

Improper liquid distribution in the tubes of the presented heat exchanger causes the mass flow rates of medium flowing inside all the tubes being far from uniform. This implicates that heat transfer conditions inside the tubes differ significantly. Consequently, the temperatures as well as the thermal stresses inside all the tubes are different, often

Reasons of high performance heat exchanger failure, on the basis of the real model applied in the industry, were investigated. The zones and the locations where the allowable stresses are exceeded were presented in the paper. Presented analysis may be applied not only in analysing the stress state in the high performance heat exchanger, but also in accessing safety of boilers, pressure vessels, shell and tube heat exchangers and many other devices

Furthermore, the new and easy in manufacturing model of collectors is presented. On the basis of numerical computation it was proven that application of the new collectors ensures

**5. Conclusions** 

exceeding the allowable stress limits.

applied in the thermal power engineering.

Fig. 34. Thermal loading for construction of high performance heat exchanger – modified collectors

Fig. 35. Nodal displacement – high performance heat exchanger with modified collectors

It is possible to observe that, for the proposed construction of the collector, displacements are significantly lower than for the typical one. The maximum displacement is over 20 times lower – compare Fig. 35 and Fig. 30.

For the modified construction, distribution of equivalent stress acc. to von Mises is presented on Fig. 36. The �� value obtained from computations does not exceed ���, therefore the construction is safe to use. Moreover the compressible stresses �� in the tubes, Fig. 37, do not exceed 22 MPa and are significantly lower than �����.

The modified construction of the collectors improves flow distribution inside the tubes through the heat exchanger. Consequently, thermal load acting on the tubes is lower than in the case of the traditional construction of the collectors. Comparing the maps of nodal displacements {*u*}, effective stresses �� according to von Mises and compressible stresses �� for the traditional and the modified construction of the collectors, it is evident that the proposed construction carries thermal loads better than the one actually available in manufacturing.

Fig. 36. Equivalent stress acc. to von Mises – heat exchanger with modified collector

Fig. 37. Compressible stresses – heat exchanger with modified collector

#### **5. Conclusions**

352 Fluid Dynamics, Computational Modeling and Applications

Fig. 34. Thermal loading for construction of high performance heat exchanger – modified

Fig. 35. Nodal displacement – high performance heat exchanger with modified collectors

It is possible to observe that, for the proposed construction of the collector, displacements are significantly lower than for the typical one. The maximum displacement is over 20 times

For the modified construction, distribution of equivalent stress acc. to von Mises is presented on Fig. 36. The �� value obtained from computations does not exceed ���, therefore the construction is safe to use. Moreover the compressible stresses �� in the tubes,

The modified construction of the collectors improves flow distribution inside the tubes through the heat exchanger. Consequently, thermal load acting on the tubes is lower than in the case of the traditional construction of the collectors. Comparing the maps of nodal displacements {*u*}, effective stresses �� according to von Mises and compressible stresses �� for the traditional and the modified construction of the collectors, it is evident that the proposed construction carries thermal loads better than the one actually available in

Fig. 37, do not exceed 22 MPa and are significantly lower than �����.

collectors

lower – compare Fig. 35 and Fig. 30.

manufacturing.

Improper liquid distribution in the tubes of the presented heat exchanger causes the mass flow rates of medium flowing inside all the tubes being far from uniform. This implicates that heat transfer conditions inside the tubes differ significantly. Consequently, the temperatures as well as the thermal stresses inside all the tubes are different, often exceeding the allowable stress limits.

Reasons of high performance heat exchanger failure, on the basis of the real model applied in the industry, were investigated. The zones and the locations where the allowable stresses are exceeded were presented in the paper. Presented analysis may be applied not only in analysing the stress state in the high performance heat exchanger, but also in accessing safety of boilers, pressure vessels, shell and tube heat exchangers and many other devices applied in the thermal power engineering.

Furthermore, the new and easy in manufacturing model of collectors is presented. On the basis of numerical computation it was proven that application of the new collectors ensures

Modelling and Optimizing Operating Conditions of Heat Exchanger with Finned Elliptical Tubes 355

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proper flow distribution inside all the tubes that consequently reduces significantly thermal stresses inside the construction.

With continuous increase in computational power it will be possible to investigate in more detail the flow behaviour and heat transfer conditions inside the high performance heat exchanger, including e.g. the phase change effect. If liquid evaporates, the heat transfer coefficient increases significantly and due to the local pressure drop, the cavitation may occur inside the tube that leads to erosion of the tube wall. Consequently, material of the tube is damaged and less resistible on acting stresses. Therefore, the real values of ߪୣ and ߪଷ may be larger than the presented in the paper. This effect should be encountered into calculations in the future.

Wall temperature increases significantly in the tubes where the mass flow rates are low. If water is not prepared properly, boiler scale formation is more intensive than in the other tubes. Influence of boiler scale thickness and its thermal conductivity on the stress state in the high performance heat exchanger should be investigated in the future.

#### **6. References**

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Wall temperature increases significantly in the tubes where the mass flow rates are low. If water is not prepared properly, boiler scale formation is more intensive than in the other tubes. Influence of boiler scale thickness and its thermal conductivity on the stress state in

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the high performance heat exchanger should be investigated in the future.

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stresses inside the construction.

calculations in the future.

**6. References** 


**15** 

*Japan* 

**Simulation of H2-Air Non-Premixed Flame Using Combustion Simulation Technique** 

Combustion simulation that uses computational fluid dynamics (CFD) has been widely adopted as the design tool for combustion equipment. Because flow inside such equipment is generally turbulent, turbulence and combustion models are needed to simulate combustion; many combustion simulations have been performed to verify a system's internal state, such as

Combustion simulation of a confined impinging jet reactor has been performed by the large eddy simulation (LES) model serving as the turbulence model and the presumed probability density function (PDF) serving as the combustion model (Daniele, 2009). The analysis shows that a confined impinging jet reactor is indeed an interesting device because of its high

Under the condition of moderate or intense low-oxygen dilution (MILD), the effect of H2 on H2-CH4 turbulent non-premixed flames was investigated with the improved standard *k* model as the turbulence model and with the eddy dissipation concept (EDC) model (Amir et al., 2010). Simulation results show that H2 addition to CH4 leads to improved mixing, increase in turbulent kinetic energy decay along the flame axis, increase in flame entrainment, higher

Although combustion simulation was considered to be an efficient designing tool, considerable computational time was needed to calculate the chemical reaction. Combustion models that detail chemical mechanisms require reaction calculations involving *n*dimensional ordinary differential equations (ODEs) that are solved according to the number of chemical species involved. Therefore, reducing computation time for the combustion simulation is a significant problem. If computation time could be easily reduced according to the required prediction accuracy, we would be able to obtain the results more quickly. For example, O is a significant species whose mass fraction is necessary to compute the amount of NO present; therefore, the accuracy of the mass fraction of O cannot be neglected. To determine this mass fraction with sufficient accuracy, it is necessary to build a reduced mechanism including O. Generally, a quasi-steady state or partial equilibrium is assumed

The chemical equilibrium method (Nagai et al., 2002) does not use reaction equations; instead, the equilibrium composition of a chemical system is determined by minimizing the

velocity, pressure, mole fractions of chemical species, and temperature.

mixing efficiency and absence of stagnant and recirculation zones.

when the reduced mechanism is built (Warrants et al., 2006).

reaction intensities, and increase in mixture ignitability and rate of heat release.

**1. Introduction** 

**to Reduce Chemical Mechanisms** 

*Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga* 

Kazui Fukumoto and Yoshifumi Ogami

