Abstract

A comprehensive study was carried out to understand the effects of roughness on the turbulence characteristics of flow in an open channel and would be presented in this chapter. Tests were conducted with four different types of bed surface conditions (an impermeable smooth bed, impermeable rough bed, permeable sand bed and an impermeable bed with distributed roughness) and at two different Reynolds number (Re = 47,500 and 31,000). The variables of interest include the mean velocity, turbulence intensity, Reynolds shear stress, shear stress correlation and higher-order moments. Quadrant decomposition was also used to extract the magnitude of the Reynolds shear stress from the turbulent bursting events. The effect of bed roughness on the turbulence characteristics can be seen throughout the depth of flow and thus dispute the 'wall similarity hypothesis'. In comparison to other roughness, distributed roughness shows the greatest effect on both streamwise and vertical turbulence intensities. Velocity triple products that reflects the transportation of turbulent kinetic energy is also seen to be affected by roughness of the channel bed with a variation of 200–300% compared to the flow over smooth bed. To analyze the turbulent bursting events, quadrant decomposition tools were used and found that the roughness affected heavily in the production of extreme turbulent events. The increases of the intensity and frequency of this turbulent burst causes the increase of instantaneous Reynolds shear stress. Transport of the sediment, pollutant suspension from the channel bed, changing the composition of the nutrient in the flow, sustainability of the benthic organisms, entrainment and exchange of energy and momentum are all influenced by this change of Reynolds shear stress. The sand used to form the various bed roughness conditions is same but found that the effect on different turbulence characteristics are different for different roughness. This is a strong indication that the geometric formation of the roughness is the cause of the differences in turbulence characteristics for different roughness formed by the same sand grain.

Keywords: turbulence, open channel flow, roughness, Reynolds shear stress, quadrant analysis, higher-order moment

### 1. Introduction

#### 1.1 Open channel flow: general

Open channel flow comprises a sheared boundary layer like flow [1]. It is in utmost interest for the engineers and researchers to understand the structure and dynamics of the open channel flow. Numerical modeling and laboratory experiments are two tools used by the researchers to explain the sediment transport, resuspension, formation of channel bed, entrainment in the flow and the exchange of energy and momentum in an open channel flow. Turbulence affects the horizontal and vertical transfer of energy and momentum and causes disruption to nutrition/oxygen utilization rates of some benthic organisms. Turbulent mixing increases with the increment of current speed and enhances the transport of phytoplankton. There were lot of studies with the explanation of mechanism of the above-mentioned phenomena but there are still a lot of unanswered questions and dispute. As indicated by [2] that a significant modulation of turbulence can be the result of average bed particle volume fractions as low as 10<sup>4</sup> . The other contribution factors to the modulation of turbulence are the shape, size and arrangement of bed particles. The research in open channel turbulent flow is much less comparing the vast amount of research done on turbulent boundary layer and pipe flow. Although there are significance in engineering application for the flow over rough surfaces but research study on turbulent flow over smooth surfaces [3–9] in both form of experimental and numerical since 1970 superseded the research on flow over rough surfaces. As research grows on the flows over rough surfaces but remains to be the Achilles heel of turbulent research [10]. There are basic differences between the flow in open channel and boundary layer due to the presence of the free surface and channel aspect ratio in an open channel flow and always debatable among researchers to use turbulent boundary layer data for modeling open channel flow [11]. Formation and enhancement of secondary currents occur due to the presence of the free surface and the side walls of the open channel. Free surface also dampens the vertical velocity fluctuations.

similar to the smooth-wall distributions. In Ref. [13] noted that roughness enhances the levels of the Reynolds shear stress over most of the flow. The specific geometry of the roughness elements causes significant enhancement to the levels of the Reynolds stresses as stated by [18]. The enhancement to the levels of the Reynolds stresses does not contain near the bed only but progresses over most of the flow creating a stronger interaction between the regions of flow (inner and outer) than

In case of the three-dimensional flow (when b/d ≤ 5) [7] predicted a reversal of the sign of the Reynolds shear stress (�uv) from positive to negative at the location closer to the free surface. Correlation coefficient of the Reynolds shear stress is

The turbulence intensity in streamwise direction (u) and normal to the bed (v) is used to non-dimensionalize the Reynolds shear stress (�uv). The correlation coefficient of the Reynolds stress only required the turbulence in streamwise and normal to the bed direction and [7] emphasized that the correlation coefficient of the Reynolds stress is very important because the estimation of the friction velocity is not required. The variation of R as stated by [7] is that after monotonous increment with respect to y/d in the region closer to the bed (y/d < 0.1) decreases as one moves away from near bed to the free-surface region. R attains a near constant value in the range of 0.4–0.5 for the middle portion of the flow depth (0.1 ≤ y/d ≤ 0.6). Properties of the mean flow in an open channel and the bed roughness have no effect on the value of R as noted by [7] and called the distribution of R universal.

For an open channel flow [19] noted that the value of Reynolds shear stress increases to a maximum at the location closer to the bed and decreases after that. The researchers [19] explained that for the flow over smooth wall, the above mentioned variation of Reynolds shear stress is the effect of viscosity, whereas for the flow over rough bed, the emerging mechanisms for momentum extraction in the existing roughness sublayer is responsible. They blamed the lower value of aspect ratio that created secondary currents for the contradiction in the characteristics of the Reynolds stress with respect to the Reynolds number variation. In Ref. [17] reported that the relative contributions of sweep and ejection events within the sublayer showed that sweep events provide the dominant contribution to the Reynolds shear stress within this region. In Ref. [13] noted that triple correlations and turbulence diffusion were strongly modified by the surface roughness. In Ref. [18] noted that surface roughness significantly enhances the levels of the turbulence kinetic energy, and turbulence diffusion in a way that depends on the specific geometry of the roughness elements. In Ref. [8] showed that the wall condition affects the variation of the triple products and the effects are not restrained to the near wall but extended to the full depth of flow. Ejection events shown clear dominance over other events for the full depth of the flow as noted by [8] and they also noted significant variation of ejection events with respect to bed roughness. To compare the effect of rough wall with smooth wall on the magnitude of the extreme events, they did the quadrant decomposition of the instantaneous velocity and found much higher magnitude for the flow over rough bed compared to the smooth wall flow. This is an indication of the effect of roughness propagating into the full depth of flow and not constraint to the region closer to the bed. Quadrant analysis is also done by [11] to compare the turbulent structures of open channel flow with the same in boundary layer flow. They found that the turbulent structures are very similar if all turbulent events are included in the analysis but found very significant difference if only the extreme events are

and is an indicator of the degree of similarity of turbulence-uv.

would be implied by the wall similarity hypothesis.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

defined as <sup>R</sup> <sup>¼</sup> �uv

used in analysis.

51

u � v

DOI: http://dx.doi.org/10.5772/intechopen.85990

### 1.2 Open channel flow: effect of roughness

The flow progression from a developing state to a fully developed condition was studied by [12]. They have observed that for the case of a section with fully developed flow and the aspect ratio b/d ≥ 3, the boundary layer extends to the surface of the water. At the channel centerline and near free surface, the velocity profile does not dip even for channel aspect ratio as low as b/d = 3. As discussed earlier about the differences between the flow in open channel and turbulent boundary due to the existence of free surface, [13] observed similarity on the velocity field due to the effect of roughness in a zero-pressure gradient turbulent boundary layer. The formation of secondary currents in an open channel flow is related to the aspect ratio (width/depth ratio of flow, b/d) and [7] noted the velocity-dip phenomenon for b/ d < 5 where the measurement of maximum velocity on the centerline of a flume are seen to be below the free surface. In Ref. [14] indicated that the streamwise mean velocity profiles follow the well-known logarithmic law for the smooth surface, and with an appropriate shift, for the rough surface. In Ref. [15] observed that wall roughness led to higher turbulence levels in the outer region of the boundary layer. In Ref. [13] noted that roughness enhances the levels of the turbulence intensities over most of the flow.

Particle motion near a solid boundary causing sediment deposition and entrainment is influenced by the coherent structures near the wall as noted by [16] in their study of the particle behavior in the turbulent boundary layer. The generation of high-speed regions by vortices in the viscous layer sweeping along the wall causes particles pushing out of the way [16]. In Ref. [17] reported that for locations above the roughness sublayer, the distributions of the second-order turbulent stresses are

#### Roughness Effects on Turbulence Characteristics in an Open Channel Flow DOI: http://dx.doi.org/10.5772/intechopen.85990

similar to the smooth-wall distributions. In Ref. [13] noted that roughness enhances the levels of the Reynolds shear stress over most of the flow. The specific geometry of the roughness elements causes significant enhancement to the levels of the Reynolds stresses as stated by [18]. The enhancement to the levels of the Reynolds stresses does not contain near the bed only but progresses over most of the flow creating a stronger interaction between the regions of flow (inner and outer) than would be implied by the wall similarity hypothesis.

In case of the three-dimensional flow (when b/d ≤ 5) [7] predicted a reversal of the sign of the Reynolds shear stress (�uv) from positive to negative at the location closer to the free surface. Correlation coefficient of the Reynolds shear stress is defined as <sup>R</sup> <sup>¼</sup> �uv u � v and is an indicator of the degree of similarity of turbulence-uv. The turbulence intensity in streamwise direction (u) and normal to the bed (v) is used to non-dimensionalize the Reynolds shear stress (�uv). The correlation coefficient of the Reynolds stress only required the turbulence in streamwise and normal to the bed direction and [7] emphasized that the correlation coefficient of the Reynolds stress is very important because the estimation of the friction velocity is not required. The variation of R as stated by [7] is that after monotonous increment with respect to y/d in the region closer to the bed (y/d < 0.1) decreases as one moves away from near bed to the free-surface region. R attains a near constant value in the range of 0.4–0.5 for the middle portion of the flow depth (0.1 ≤ y/d ≤ 0.6). Properties of the mean flow in an open channel and the bed roughness have no effect on the value of R as noted by [7] and called the distribution of R universal. For an open channel flow [19] noted that the value of Reynolds shear stress increases to a maximum at the location closer to the bed and decreases after that. The researchers [19] explained that for the flow over smooth wall, the above mentioned variation of Reynolds shear stress is the effect of viscosity, whereas for the flow over rough bed, the emerging mechanisms for momentum extraction in the existing roughness sublayer is responsible. They blamed the lower value of aspect ratio that created secondary currents for the contradiction in the characteristics of the Reynolds stress with respect to the Reynolds number variation.

In Ref. [17] reported that the relative contributions of sweep and ejection events within the sublayer showed that sweep events provide the dominant contribution to the Reynolds shear stress within this region. In Ref. [13] noted that triple correlations and turbulence diffusion were strongly modified by the surface roughness. In Ref. [18] noted that surface roughness significantly enhances the levels of the turbulence kinetic energy, and turbulence diffusion in a way that depends on the specific geometry of the roughness elements. In Ref. [8] showed that the wall condition affects the variation of the triple products and the effects are not restrained to the near wall but extended to the full depth of flow. Ejection events shown clear dominance over other events for the full depth of the flow as noted by [8] and they also noted significant variation of ejection events with respect to bed roughness. To compare the effect of rough wall with smooth wall on the magnitude of the extreme events, they did the quadrant decomposition of the instantaneous velocity and found much higher magnitude for the flow over rough bed compared to the smooth wall flow. This is an indication of the effect of roughness propagating into the full depth of flow and not constraint to the region closer to the bed. Quadrant analysis is also done by [11] to compare the turbulent structures of open channel flow with the same in boundary layer flow. They found that the turbulent structures are very similar if all turbulent events are included in the analysis but found very significant difference if only the extreme events are used in analysis.

dynamics of the open channel flow. Numerical modeling and laboratory experiments are two tools used by the researchers to explain the sediment transport, resuspension, formation of channel bed, entrainment in the flow and the exchange of energy and momentum in an open channel flow. Turbulence affects the horizontal and vertical transfer of energy and momentum and causes disruption to nutrition/oxygen utilization rates of some benthic organisms. Turbulent mixing increases with the increment of current speed and enhances the transport of phytoplankton. There were lot of studies with the explanation of mechanism of the above-mentioned phenomena but there are still a lot of unanswered questions and dispute. As indicated by [2] that a significant modulation of turbulence can be

. The other

the result of average bed particle volume fractions as low as 10<sup>4</sup>

Boundary Layer Flows - Theory, Applications and Numerical Methods

1.2 Open channel flow: effect of roughness

over most of the flow.

50

contribution factors to the modulation of turbulence are the shape, size and arrangement of bed particles. The research in open channel turbulent flow is much less comparing the vast amount of research done on turbulent boundary layer and pipe flow. Although there are significance in engineering application for the flow over rough surfaces but research study on turbulent flow over smooth surfaces [3–9] in both form of experimental and numerical since 1970 superseded the research on flow over rough surfaces. As research grows on the flows over rough surfaces but remains to be the Achilles heel of turbulent research [10]. There are basic differences between the flow in open channel and boundary layer due to the presence of the free surface and channel aspect ratio in an open channel flow and always debatable among researchers to use turbulent boundary layer data for modeling open channel flow [11]. Formation and enhancement of secondary currents occur due to the presence of the free surface and the side walls of the open channel. Free surface also dampens the vertical velocity fluctuations.

The flow progression from a developing state to a fully developed condition was studied by [12]. They have observed that for the case of a section with fully developed flow and the aspect ratio b/d ≥ 3, the boundary layer extends to the surface of the water. At the channel centerline and near free surface, the velocity profile does not dip even for channel aspect ratio as low as b/d = 3. As discussed earlier about the differences between the flow in open channel and turbulent boundary due to the existence of free surface, [13] observed similarity on the velocity field due to the effect of roughness in a zero-pressure gradient turbulent boundary layer. The formation of secondary currents in an open channel flow is related to the aspect ratio (width/depth ratio of flow, b/d) and [7] noted the velocity-dip phenomenon for b/ d < 5 where the measurement of maximum velocity on the centerline of a flume are seen to be below the free surface. In Ref. [14] indicated that the streamwise mean velocity profiles follow the well-known logarithmic law for the smooth surface, and with an appropriate shift, for the rough surface. In Ref. [15] observed that wall roughness led to higher turbulence levels in the outer region of the boundary layer. In Ref. [13] noted that roughness enhances the levels of the turbulence intensities

Particle motion near a solid boundary causing sediment deposition and entrainment is influenced by the coherent structures near the wall as noted by [16] in their study of the particle behavior in the turbulent boundary layer. The generation of high-speed regions by vortices in the viscous layer sweeping along the wall causes particles pushing out of the way [16]. In Ref. [17] reported that for locations above the roughness sublayer, the distributions of the second-order turbulent stresses are
