3.1.1 Outer coordinates

Figure 4 shows the variation of streamwise component of the velocity with respect to the depth of flow in outer coordinates. The mean velocity (U) is nondimensionalize by the maximum velocity (Ue) and the wall normal distance (y) is non-dimensionalize by the maximum flow depth (d). As one can see in the inset in Figure 4 that the velocity profiles of every flow conditions show a slight dip in the outer region where the location of maximum velocity happened to be occurred below the free surface with dU/d∂y is negative in the location close to the free surface. Velocity dip is different with different rough bed conditions with flow over natural sand bed showing the biggest dip followed by distributed roughness and continuous roughness bed. However, the flow over smooth surface shows the dip higher than the flow over distributed roughness and continuous roughness bed. Effect of bed roughness is very evident at the location close to the bed with velocity profile for the flow over smooth wall is fuller compared the flow over different rough beds. The same phenomenon was also observed by [15] and blamed it to the increment of surface drug due to the effect bed roughness. Comparing the effect of various type of bed roughness on the streamwise velocity component as one can see from Figure 4a that distributed roughness profile has the biggest deviation from smooth bed profile with continuous roughness and natural sand bed shows identical deviation. The variation of streamwise component of the velocity with respect to the depth of flow in outer coordinates with respect to the lower Reynolds number is shown in Figure 4b. The velocity profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with the exception of flow over natural sand bed, which shows much higher deviation than flow over the bed of continuous roughness. One can correlate this with the interchange of fluid and momentum across the boundary, which is permeable like the flow over the bed of natural sand. The subsequent momentum/energy loss due to the effect of infiltration and corresponding differences on mean velocity reduces with the increment of Reynolds stress.

#### 3.1.2 Inner coordinates

Figure 5 shows the variation of streamwise component of the velocity with respect to the depth of flow in inner coordinates. The Clauser method was used to calculate the friction velocity for flow over smooth and rough bed conditions by

Figure 4. Streamwise mean velocity profile for flow over different bed condition.

fitting the respective mean velocity profiles of different bed conditions with the classical log law, U<sup>+</sup> = κ<sup>1</sup> ln y<sup>+</sup> + B – ΔU<sup>+</sup> . Log-law constants used here are U<sup>+</sup> = U/Uτ, y<sup>+</sup> = yUτ/ν, κ = 0.41, B = 5 and the downward shift of the velocity profile represented by the roughness function ΔU+ with ΔU<sup>+</sup> = 0 for the flow over the bed which is smooth. The present test data over the smooth bed has better agreement with the standard log-law represented by the solid line. For the flow over rough beds there are downward shift of the profile compared to the smooth bed which is fully expected and clearly visible. The effect of roughness can be measured by the downward shift of the profile and one can note from Figure 5a that the distributed roughness shows the highest deviation from the smooth bed with flow over natural sand bed shows the least deviation and flow over continuous roughness fall inbetween. The variation of streamwise component of the velocity with respect to the depth of flow in inner coordinates with respect to the lower Reynolds number is shown in Figure 5b. The velocity profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number.

dent on the type of bed roughness with distributed roughness has the highest value followed by the flow over the continuous roughness bed surface and the sand bed. The magnitude of friction coefficient is also found to be dependent on the Reynolds number with the reduction of the magnitude of friction coefficient with the increment of the Reynolds number. The magnitude of Cf is seen to be smaller for the flow over a permeable bed (natural sand bed) compared to the flow over an impermeable bed (distributed and continuous roughness bed). One can correlate this with the development of finite slip velocity across the permeable boundary layer causing the reduction of the magnitude of friction compared to the flow over impermeable layer. In contrary, [24] discovered that for the boundaries with similar rugosity the

2

) is found to be depen-

The magnitude of friction coefficient Cf (Cf = 2(Uτ/Ue)

Mean velocity profile in inner coordinates for flow over different bed condition.

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

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

Figure 5.

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

Figure 5. Mean velocity profile in inner coordinates for flow over different bed condition.

depth of flow in inner coordinates with respect to the lower Reynolds number is shown in Figure 5b. The velocity profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number.

The magnitude of friction coefficient Cf (Cf = 2(Uτ/Ue) 2 ) is found to be dependent on the type of bed roughness with distributed roughness has the highest value followed by the flow over the continuous roughness bed surface and the sand bed. The magnitude of friction coefficient is also found to be dependent on the Reynolds number with the reduction of the magnitude of friction coefficient with the increment of the Reynolds number. The magnitude of Cf is seen to be smaller for the flow over a permeable bed (natural sand bed) compared to the flow over an impermeable bed (distributed and continuous roughness bed). One can correlate this with the development of finite slip velocity across the permeable boundary layer causing the reduction of the magnitude of friction compared to the flow over impermeable layer. In contrary, [24] discovered that for the boundaries with similar rugosity the

fitting the respective mean velocity profiles of different bed conditions with the

U<sup>+</sup> = U/Uτ, y<sup>+</sup> = yUτ/ν, κ = 0.41, B = 5 and the downward shift of the velocity profile represented by the roughness function ΔU+ with ΔU<sup>+</sup> = 0 for the flow over the bed which is smooth. The present test data over the smooth bed has better agreement with the standard log-law represented by the solid line. For the flow over rough beds there are downward shift of the profile compared to the smooth bed which is fully expected and clearly visible. The effect of roughness can be measured by the downward shift of the profile and one can note from Figure 5a that the distributed roughness shows the highest deviation from the smooth bed with flow over natural sand bed shows the least deviation and flow over continuous roughness fall inbetween. The variation of streamwise component of the velocity with respect to the

. Log-law constants used here are

classical log law, U<sup>+</sup> = κ<sup>1</sup> ln y<sup>+</sup> + B – ΔU<sup>+</sup>

Streamwise mean velocity profile for flow over different bed condition.

Boundary Layer Flows - Theory, Applications and Numerical Methods

Figure 4.

56

magnitude of friction resistance is seen to be higher for the flow over a permeable bed compared to the flow over an impermeable bed. Dissipation of energy happened in the transition zone of the porous permeable medium with added loss of energy due to interchange of fluid and momentum across the permeable boundary translated back into the main flow. They commented that the net effect of combined energy loss might be responsible for the higher resistance.

can bring additional uncertainties in relation to the scaling parameters and to avoid

any additional uncertainties, the streamwise turbulent intensity (u) is nondimensionalize by the maximum velocity (Ue) and the wall normal distance (y) is non-dimensionalize by the maximum flow depth (d). Magnitude of the streamwise component of the turbulence intensity reaches to the maximum at the location very close to the bed irrespective of the bed condition as one can note from Figure 6a. The location of maximum streamwise component of the turbulence intensity is different with different bed conditions. The location of the peak for the flow over smooth bed is very close to the bed at y/d 0, whereas the peak for the flow over rough surfaces varies with the different type of roughness. As one can note from Figure 6a that the distributed roughness shows the highest peak compared to the flow over continuous roughness and flow over natural sand bed. The location of the peak for the flow over rough beds are also varied depending on the type of roughness. The location of the peak for the flow over distributed roughness is at around y/d 0.08 whereas the location of the peak for the flow over continuous roughness and natural sand bed have occurred at the same location of y/d 0.04 which is a distance closer to the bed compared to the flow over distributed roughness. Immediately after reaching the peak the streamwise component of the turbulence intensity for flow over both smooth and rough beds reduces but the trend of reduction is very different for the flow over smooth bed compared to the flow over rough surfaces. There is a sharp drop of the magnitude of the streamwise component of the turbulence intensity for the smooth bed before a more constant drop towards the free surface and reaching a near constant value at y/d 0.5. For the flow over rough surfaces the drop of the value towards the free surface after the peak is linear and attains a near constant value but the location and magnitude of constant value is different for different rough surfaces (distributed roughness does not attain constant value but variation near free surface is minimal). The location of a near constant value for the flow over continuous roughness and natural sand bed is at the same level of y/d 0.62. The streamwise component of the turbulence intensity near the free surface also shows the effect of roughness with natural sand bed shows the highest intensity followed by the distributed roughness with flow over continuous roughness is the lowest. The effect of roughness on the distribution of the streamwise component of the turbulence intensity is very evident throughout the flow depth with distributed roughness shows the highest deviation followed by natural sand bed and continuous roughness compared to the smooth surfaces with the exception at the location very close to the bed. Although the sand grain used to create all three bed roughness is of the same gradation characteristics but the geometry of the roughness formation is different causing the differences in the

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

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

distribution of the streamwise component of the turbulence intensity.

natural sand bed is negligible.

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3.2.2 Vertical turbulence intensity

The variation of streamwise component of the turbulence intensity with respect to the depth of flow for the flow conditions to the lower Reynolds number is shown in Figure 6b. The streamwise component of the turbulence intensity profile characteristics are very similar for the lower Reynolds number flow compared to the flow for higher Reynolds number with the exception of flow over distributed roughness bed, which shows much higher deviation than flow over the smooth bed at the lower Reynolds number. In lower Reynolds number flow, the differences in streamwise component of the turbulence intensity for continuous roughness and

The distribution of the vertical component of the turbulence intensity for flow

over both smooth and rough beds is shown in Figure 7. Significant effect of
