Study of flow over permeable bed

1. Study of flow over permeable bed
Presented by:
Narendra Kumar Patel
Advisors:
Junke Guo and David Admiraal
Department of Civil Engineering

2. Introduction
• Usually permeable bed is treated as solid surface and classical
logarithmic profile is generated with no-slip condition. However, at
porous bed surface, velocity is non-zero.
Porous Medium
Open Channel
Flow
Y
X
h
𝛅
uB

3. Introduction
• Research Objectives
• Determination of velocity profile
• Determination of transitional layer thickness
• To study the effect on flow capacity of channel with porous bed for different
types of flow

4. Approaches
• Theoretical
• Numerical
• Experimental

5. Theoretical Approach
• Steady, uniform flow above the bed can be solved using Navier-Stokes
equation and Darcy’s equation can be used for flow through the bed.
µ
𝑑2 𝑈
𝑑𝑦2 =
𝑑𝑝
𝑑𝑥
…. N-S equation
−
µ
𝑘
𝑈 =
𝑑 𝑝
𝑑𝑥
…. Darcy’s laws
• N-S is second order ODE and Darcy’s eq. is first order which makes
impossible to formulate rational boundary conditions.

6. Theoretical Approach
• Navier-Stocks Forchheimer Equation
• Laminar flow: In Bed =>
cn is Jacobi elliptic cosine function, F is elliptic integral of first kind
Above the bed=>
• Turbulent Flow: In Bed ->
Above the bed=>

7. Numerical Approach
• All governing equations are solved numerically in Ansys Fluent
software
• Equations are solved by computational fluid dynamics (CFD)
techniques

8. Numerical Approach
• Volume of fluid (VOF) result

9. Numerical Approach
• Velocity profile above bed at different porosity
Slope=3°, grain size=2mm, Bed thickness= 10cm
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0 0.2 0.4 0.6 0.8 1 1.2
Depth,m
Velocity, m/s
Velocity Profile
P=0.2
P=0.4
P =0.6
Bed Level

10. Experimental Approach
• Flume is 48 ft long, 40cm wide and 50cm deep.
• Slope, flow rate, depth can be varied and velocity, discharge can be
measured

11. Experimental Approach
• Flow velocity above the bed is measured using Acoustic Doppler
Velocimetry (ADV).

12. Experimental Approach
• A fiber optics based sensor is developed to measure flow velocity in
sand bed
• Tracer is injected and Refractive index is measured to determine the
at two locations to determine velocity

13. Conclusions
• Theoretically, velocity profile over porous bed can be represented by
Jacobi elliptic function
• Slip velocity increases as porosity increases and maximum velocity
decreases.
• Flow capacity of channel decreases as bed porosity increases

14. Thank You
Questions ?
waterforfood.nebraska.edu