3.7 Quadrant analysis

is shown in Figure 12 in outer variables for the flow over both smooth and rough beds. The LDA used to measure the velocity component is two-dimensional and not possible to measure the third component of turbulent intensity. An approximate method as proposed by [30] is used to overcome this shortcoming and the coefficient is changed from 0.75 to 0.5. The effect of roughness is very evident for the transport of the turbulent kinetic energy in the vertical direction as one can see from Figure 12. The effect of roughness is not only confined for near bed but can be seen throughout the depth of flow. This observation is in direct conflict with the observation of [8] who in their tests with large-bottomed roughness did not visualize notable differences in profile for the vertical flux of the turbulent kinetic energy when comparing

open channel flow over smooth bed and rough bed conditions.

Boundary Layer Flows - Theory, Applications and Numerical Methods

Distribution of vertical flux of the turbulent kinetic energy for flow over different bed condition.

Figure 12.

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In order to extract the magnitude of the Reynolds shear stress related to turbulent bursting events researchers often use quadrant decomposition as a convenient tool. A hydro dynamically unstable low-speed fluid particle lifted up from the surface because of the turbulent flow over a fixed bed can be swept away by comparatively high-speed fluid from the outer layer moving towards the bed surface. All different type of turbulent flow events that eventually contributed in the four different very important turbulent characteristics closer to the wall can be described by coupling streamwise and vertical fluctuating velocity components u and v based on their sign. Four different quadrants formed by using u and v with proper sign are related to four very important turbulent bursting events. Quadrant 1 represents the bursting effect called as outward interaction where the value of u is >0 and the value of v is >0. Quadrant 2 represents the bursting effect called as ejection where the value of u is <0 and the value of v is >0. Quadrant 3 represents the bursting effect called as inward interaction where the value of u is <0 and the value of v is <0. Quadrant 4 represents the bursting effect called as sweep where the value of u is >0 and the value of v is <0.

The contributions from Q2 and Q4 events for different threshold values to the Reynolds shear stress are shown in Figure 13 with higher Reynolds number (Re = 47,500). For the flow over rough walls and inclusive of all turbulent events, it was noted higher magnitude of Q2 and Q4 contributions as shown in Figure 13a and b compared to the flow over smooth wall for H = 0. The effect of roughness is not limited to the near-bed region but well progressed into the outer layer (y/d ≈ 0.7). A local peak can be seen at y/d = 0.1–0.2 for the Q2 and Q4 contributions as one progresses from the bed towards the free surface for the flow over all rough beds. The peak magnitudes of both of the events eventually reduced

bed conditions show different deviation from smooth wall with distributed roughness showing the highest deviation. The maximum deviation comparing the flow over smooth wall with the flow over rough bed occurs at a depth of around 0.2d from the bed with distributed roughness shows the highest deviation and continuous roughness and sand bed show almost equal deviation. In Ref. [31] found significantly higher magnitude of Q2 and Q4 events in the region very close to the bed but found very similar distribution for the flow over smooth bed and rough beds for

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

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

In order to investigate the contribution of the extreme turbulent events quad-

rant analysis at different threshold levels (H = 2–5) was also carried out. The respective approach was taken to take care of the contribution of the more energetic eddies and filtering out the small random turbulent fluctuations. The contributions from the extreme events whose amplitude exceeds the threshold value of H = 2 are shown in Figure 13c and d. Although due to the change of threshold value from 0 to 2, the number of events occurring corresponding to Q2 and Q4 reduce quite sharply but the events corresponding to H = 2 produced very large instantaneous Reynolds shear stress >5 ð Þ :5 uv , which can potentially influence the sediment transport in the stream, causing resuspension of pollutant from the bed, bed formation/changes, downstream transportation of nutrients, entrainment and the exchange of energy and momentum in the flow. The trend of the data at H = 2 is very close to H = 0, however, the region of the flow depth affected for Q4 events reduces compared to H = 0. The contributions related to other threshold levels of H = 2.5–5 are shown in Figure 13e–i and one can observe that the region affected over the depth of flow for Q4 events reduces with respect to the increase of the threshold level of H but the affected region goes deep into the outer layer (y � 0.7d)

for the Q2 events even for the value of H as high as 5. The incorporation of roughness is clearly visible in the increase in both Q2 and Q4 contribution to the Reynolds shear stress, irrespective of the affected region of the depth. Much stronger Q2 events were observed by [31–32] on a flow over a smooth wall when compared to the flow over a rough wall for the location close to the bed and they relate the phenomena for the smooth wall to the contributions of strongly favored Reynolds stress from ejection (Q2 events). The differences in observation between the turbulent boundary layer flow and open channel flow can confirm that turbulent bursting and eventual production of Reynolds shear stress due to ejection (Q2 events) and sweep (Q4 events) is different for the flow in open channel. Significant ejection and sweep components were noted by [8] with ejection events being dominant throughout the depth of flow and they also noted that different types of rib roughness result significant variations. One can notice in the present study that Q2 and Q4 events are dependent on the bed roughness accompanied by significant drop near the free surface for both events, signifies the important role the bed roughness type possesses on Q2 and Q4 events. At the location near bed, generation of turbulent activity varies with the type of bed roughness. Low momentum slow moving fluid from the near-bed is ejected and travels towards the outer layer/free surface and the same will happen for the fluid between the interstices of the roughness. In contrast, high momentum fast moving fluid from the outer layer travels towards bed, sweeping away the low momentum slow moving fluid parcels ejected earlier. The extent of depth of flow affected by the existence of universal intermittent sweep and ejection events is dependent on the type of bed and the flow condition. Figure 14 shows the variation of the contributions from Q2 and Q4 events for different threshold values to the Reynolds shear stress with lower Reynolds number (Re = 31,000). The profile characteristics are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher

Reynolds number for the threshold values of H = 0–5.

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the outer layer.

Figure 13.

Contribution of different quadrant events to the Reynolds shear stress for flow over different bed condition with higher Reynolds number.

to a near-zero constant value as flow moves towards the free surface. The location where the contributions from Q2 and Q4 events attains a near-zero constant value is not the same but varied with bed conditions. For the smooth bed condition the distance of the attainment of near-zero constant value is 0.5d from the bed, for the continuous roughness and sand bed condition the distance is 0.6d from the bed and for the distributed roughness the distance is 0.75d from the bed. Different rough

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

bed conditions show different deviation from smooth wall with distributed roughness showing the highest deviation. The maximum deviation comparing the flow over smooth wall with the flow over rough bed occurs at a depth of around 0.2d from the bed with distributed roughness shows the highest deviation and continuous roughness and sand bed show almost equal deviation. In Ref. [31] found significantly higher magnitude of Q2 and Q4 events in the region very close to the bed but found very similar distribution for the flow over smooth bed and rough beds for the outer layer.

In order to investigate the contribution of the extreme turbulent events quadrant analysis at different threshold levels (H = 2–5) was also carried out. The respective approach was taken to take care of the contribution of the more energetic eddies and filtering out the small random turbulent fluctuations. The contributions from the extreme events whose amplitude exceeds the threshold value of H = 2 are shown in Figure 13c and d. Although due to the change of threshold value from 0 to 2, the number of events occurring corresponding to Q2 and Q4 reduce quite sharply but the events corresponding to H = 2 produced very large instantaneous Reynolds shear stress >5 ð Þ :5 uv , which can potentially influence the sediment transport in the stream, causing resuspension of pollutant from the bed, bed formation/changes, downstream transportation of nutrients, entrainment and the exchange of energy and momentum in the flow. The trend of the data at H = 2 is very close to H = 0, however, the region of the flow depth affected for Q4 events reduces compared to H = 0. The contributions related to other threshold levels of H = 2.5–5 are shown in Figure 13e–i and one can observe that the region affected over the depth of flow for Q4 events reduces with respect to the increase of the threshold level of H but the affected region goes deep into the outer layer (y � 0.7d) for the Q2 events even for the value of H as high as 5. The incorporation of roughness is clearly visible in the increase in both Q2 and Q4 contribution to the Reynolds shear stress, irrespective of the affected region of the depth. Much stronger Q2 events were observed by [31–32] on a flow over a smooth wall when compared to the flow over a rough wall for the location close to the bed and they relate the phenomena for the smooth wall to the contributions of strongly favored Reynolds stress from ejection (Q2 events). The differences in observation between the turbulent boundary layer flow and open channel flow can confirm that turbulent bursting and eventual production of Reynolds shear stress due to ejection (Q2 events) and sweep (Q4 events) is different for the flow in open channel. Significant ejection and sweep components were noted by [8] with ejection events being dominant throughout the depth of flow and they also noted that different types of rib roughness result significant variations. One can notice in the present study that Q2 and Q4 events are dependent on the bed roughness accompanied by significant drop near the free surface for both events, signifies the important role the bed roughness type possesses on Q2 and Q4 events. At the location near bed, generation of turbulent activity varies with the type of bed roughness. Low momentum slow moving fluid from the near-bed is ejected and travels towards the outer layer/free surface and the same will happen for the fluid between the interstices of the roughness. In contrast, high momentum fast moving fluid from the outer layer travels towards bed, sweeping away the low momentum slow moving fluid parcels ejected earlier. The extent of depth of flow affected by the existence of universal intermittent sweep and ejection events is dependent on the type of bed and the flow condition. Figure 14 shows the variation of the contributions from Q2 and Q4 events for different threshold values to the Reynolds shear stress with lower Reynolds number (Re = 31,000). The profile characteristics are very similar for flow with respect to lower Reynolds number compared to the flow with respect to higher Reynolds number for the threshold values of H = 0–5.

to a near-zero constant value as flow moves towards the free surface. The location where the contributions from Q2 and Q4 events attains a near-zero constant value is not the same but varied with bed conditions. For the smooth bed condition the distance of the attainment of near-zero constant value is 0.5d from the bed, for the continuous roughness and sand bed condition the distance is 0.6d from the bed and for the distributed roughness the distance is 0.75d from the bed. Different rough

Contribution of different quadrant events to the Reynolds shear stress for flow over different bed condition with

Boundary Layer Flows - Theory, Applications and Numerical Methods

Figure 13.

70

higher Reynolds number.

Figure 14.

Contribution of different quadrant events to the Reynolds shear stress for flow over different bed condition with lower Reynolds number.

ejection events compared to the sweep events. The corresponding strength of the ejection events increases in comparison to sweep events with respect to increasing H and as one can note from the Figure 15 that there is a 100 over fold increase for the threshold value of H = 5 compared to H = 0. As one can also note from Figure 15 that there is little dependency on bed conditions of smooth and rough for H = 0 on the ratio of Reynolds shear stress in Q2 and Q4 but for the same value of H = 0 there

Ratio of different quadrant events to the Reynolds shear stress 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

are some effect of roughness for y > 0.5d.

Figure 15.

73

Figure 15 shows the ratio to the Reynolds shear stress contributions of Q2/Q4 for H=0–5 and for two different Reynolds numbers. The Q2/Q4 ratio is near unity at the location very close to the bed indicating identical strength of sweep and ejection event as one can note from Figure 15. The Q2/Q4 ratio increases from near unity to maximum at around mid-depth of the flow (y/d 0.5) as one progress from the bed and towards the free surface which is an indication of relatively stronger

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

Figure 15. Ratio of different quadrant events to the Reynolds shear stress for flow over different bed condition.

ejection events compared to the sweep events. The corresponding strength of the ejection events increases in comparison to sweep events with respect to increasing H and as one can note from the Figure 15 that there is a 100 over fold increase for the threshold value of H = 5 compared to H = 0. As one can also note from Figure 15 that there is little dependency on bed conditions of smooth and rough for H = 0 on the ratio of Reynolds shear stress in Q2 and Q4 but for the same value of H = 0 there are some effect of roughness for y > 0.5d.

Figure 15 shows the ratio to the Reynolds shear stress contributions of Q2/Q4 for H=0–5 and for two different Reynolds numbers. The Q2/Q4 ratio is near unity at the location very close to the bed indicating identical strength of sweep and ejection event as one can note from Figure 15. The Q2/Q4 ratio increases from near unity to maximum at around mid-depth of the flow (y/d 0.5) as one progress from the bed and towards the free surface which is an indication of relatively stronger

Contribution of different quadrant events to the Reynolds shear stress for flow over different bed condition with

Boundary Layer Flows - Theory, Applications and Numerical Methods

Figure 14.

72

lower Reynolds number.

Figure 16 shows the ratio to the number of events occurring/contributing in Q2 and Q4 for H = 0–3 and for two different Reynolds numbers. The ratio to the number of events occurring/contributing to Q2 and Q4 shows different trends for the threshold value of H = 0 (Figure 16a and b) compared to the threshold value of H=2–3 (Figure 16c–h). This is very unlike to the ratio of the Reynolds shear stress contributions of Q2/Q4 as shown in Figure 15. The NQ2/NQ4 ratio is near unity at the location very close to the bed indicating almost equal occurrence of ejection and sweep events as one can note from Figure 16a and b. The NQ2/NQ4 ratio decreases from near unity to minimum at around mid-depth of the flow (y/d 0.5) as one progress from the bed and towards the free surface which is an indication of relatively reduced ejection events compared to the sweep events. Moving farther away from bed (y > 0.5d) and towards the free surface, the ratio of NQ2/NQ4 ratio is keep on increasing again and reaches to near unity indicating almost equal occurrence of ejection and sweep events. Figure 16c–h show a trend different from Figure 16a and b. As one progress from the bed towards the free surface, there is an increment of 30 over fold for the value of NQ2/NQ4 at around y 0.5d, indicating substantial increase of ejection events. As one can also note from Figure 16 that there is little dependency on bed conditions of smooth and rough for H = 0 on the ratio of number of events in Q2 and Q4.

4. Conclusions

roughness.

roughness bed).

structure.

75

findings are summarized as follows:

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

The purpose of the present study [1] is to explain how the roughness and Reynolds number affect flow characteristics in an open channel flow (OCF). Tests were conducted with four different types of bed surface conditions and at two different Reynolds number for each and every bed surface. Instantaneous velocity components are used to analyze the streamwise mean velocity, turbulence intensity in both streamwise and vertical direction, Reynolds shear stress including shear stress correlation and higher-order moments including vertical flux of the turbulent kinetic energy. In order to extract the magnitude of the Reynolds shear stress related to turbulent bursting events quadrant decomposition was used. The main

Roughness Effects on Turbulence Characteristics in an Open Channel Flow

1.Surface drug increases due to surface roughness making the mean streamwise velocity profile to be more fuller for the smooth bed compared to the rough beds. It is very much evident throughout the depth of the flow that the mean velocity profile is very much affected by the different type of bed roughness. Comparing the effect of various type of bed roughness on the streamwise velocity component and flow with higher flow Reynolds number, distributed roughness profile has the biggest deviation from smooth bed profile with continuous roughness and natural sand bed shows identical deviation. For the flow with lower flow Reynolds number, it was found that the flow over natural sand bed shows much higher deviation than flow over the bed of continuous

2.The magnitude of friction coefficient is found to be dependent on the type of bed roughness with distributed roughness has the highest value followed by 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 friction coefficient 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

flow over the continuous roughness bed surface and the sand bed. The

3.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. Comparing the effect of various type of bed conditions on the vertical component of the turbulence intensity, it was seen that distributed roughness profile has the biggest deviation from smooth bed profile with continuous roughness and natural sand bed shows identical deviation for most the depth of the flow. At locations very close to the bed and due to the introduction of roughness, streamwise turbulence intensity reduces but vertical turbulence intensity increases. Although the sand grain used to create all three bed roughness is of the same gradation characteristics but the specific geometry of the roughness formation is different causing the differences in the formation of turbulence

4.Wall similarity hypothesis is disputed by the present experimental results where the researchers suggested that in the location of outside the roughness

Figure 16. Ratio of number of different quadrant events 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
