LARGE-EDDY SIMULATION OF A SINUOUS OPEN CHANNEL

FLOW Ashutosh Priyadarsan1, K.K. Khatua2

1, M.Tech Scholar, Department of Civil Engineering, NIT Rourkela, Odisha 769008, India.

Email: ashutosh.biku@gmail.com.

2, Associate Professor, Department of Civil Engineering, NIT Rourkela, Odisha 769008, India.

Email: kkkhatua@yahoo.com

ABSTRACT

Large eddy simulation was carried out on a mild sinuous flume for a comparative study

between the experiment focusing on streamwise, transverse and vertical velocities along

with secondary flows. The peak velocity occurred in the convex bank and a center cell

region was present alongside a weak outer cell in the concave bank. Keywords: LES, ANSYS-Fluent, velocity contours, secondary flow vectors

1. INTRODUCTION

Most of the river streams tend to have some sinuosity factor in their geometry. This chain of curves,

bends or loops play a major role in the sediment erosion of the outer bank. An experimental study

can be very exhaustive in a real scale. So, schematization in the form of periodic bend flume is more

practical. Numerical modelling is quite economical if we want to gain an insight of the physics of

flow due unavailability of proper experimental setups. Turbulent forces are agents of chaos and a

phenomenon naturally occurring in river streams. Large Eddy simulation (LES) being an

intermediate CFD method between Direct numerical simulation (DNS) and Reynolds-averaged

Navier–Stokes equations (RANS) is optimal for turbulent studies.

The smaller eddies are nearly isotropic and have a universal behaviour (for turbulent flows at

sufficiently high Reynolds numbers at least). On the other hand, the larger eddies, which interact

with and extract energy from the mean flow, are more anisotropic and their behaviour is dictated

by the geometry of the problem domain, the boundary conditions and body forces. When

Reynolds-averaged equations are used the collective behaviour of all eddies must be described by

a single turbulence model, but the problem dependence of the largest eddies complicates the search

for widely applicable models. A different approach to the computation of turbulent flows accepts

that the larger eddies need to be computed for each problem with a time-dependent simulation. The

universal behaviour of the smaller eddies, on the other hand, should hopefully be easier to capture

with a compact model. This is the essence of the large eddy simulation, LES uses spatial filtering

operation to separate the eddies instead of time averaging.

(Demuren and Rodi, 1984) have stated that the secondary flows of prandl’s second kind cannot be

produced by RANs simulation because of their dissipative nature. (Van Balen, Uijetewal and

Blanckert, 2009) have done LES simulation on a mildly curved 60 bend flume. They observed

complex bicellular pattern of secondary flows due to turbulence anisotropy and centrifugal effects.

2. METHODOLOGY

This article deals exclusively on Large Eddy Simulation providing a comparision between the

experimental work done using micro-ADVs focusing on longitudinal velocity and secondary flow

pattern. The fluent module in ANSYS-Academic-19R3 is used for the numerical modelling.

Governing equations

The filtering process effectively filters out the eddies whose scales are smaller than the filter width

or grid spacing used in the computations. A filtered variable is denoted as,

ϕ̅(x) = ∫ ϕ(x′)G(x, x′) ⅆx′D

(1)

Where D is the domain of fluid and G is the filter function.

Ansys fluent uses the Top-Hat filter for LES simulations, the filtering operation can be stated as:

ϕ̅(x) =1

V∫ ϕ(x′) ⅆx′

v, x′ ∈ v (2)

Where v is the computational cell volume. The filter function, G(x, x′) here can be represented in its

commonest form as:

G(x, x′) = {1 ∕ v, x′ ∈ v

0, otherwise (3)

After filtering the Navier-Stokes equation can be stated as:

∂ρ

∂t+

∂(ρu̅i)

∂xi= 0 (4)

∂(ρu̅i)

∂t+

∂(ρu̅iu̅j)

∂xj=

∂(σij)

∂xj−

∂p̅

∂xi−

∂τij

∂xj (5)

Where σij is the stress tensor due to molecular viscosity and is defined by the equation:

σij ≡ [μ (∂u̅i

∂xj+

∂u̅j

∂xi)] −

2

3μ

∂u̅l

∂xlδij (6)

and τij is the subgrid-scale stress defined by

τij ≡ ρui̇uj̅̅ ̅̅ ̅ − ρui̅uj̅ (7)

The subgrid-scale viscosity vsgs, needed for the modelling of the subgrid-scale stress tensor arising

from the filtering operation, is modelled using Smagorinsky’s model (Smagorinsky 1963) :

νsgs = Cs2Δ2|Sij̃|

where Cs is Smagorinsky’s constant and is the filterlength, defined as Δ = (ΔxΔyΔz)1∕3, and Sij̃ is

the rate of strain tensor based on the filtered velocities. In this paper, the value for Smagorinsky’s

constant Cs is taken =0.1.

Boundary conditions

A mass flow inlet and outlet which has been obtained from experiments is provided with the flow

rate being in the x-direction vector at the inflow face.

To specify the wall roughness needed for turbulent flow calculations, FLUENT accepts only sand

grain roughness, so the Manning coefficient roughness should be converted by using the equation

below (Marriott & Jayaratne, 2010)

n =ⅆ1∕6

6.7√g

The free surface is a horizontal rigid lid which has been conditioned as a free slip surface with zero

shear stress acting in all direction as the water level slopes are negligible (Pan and Banerjee 1995).

Flume geometry

Figure 1. Plan view of Flume

Table 1. Geometry parameters of the Flume

Parameter Value

Sinuosity of main channel, s 1.35

Valley slope, So 0.00165

Main channel width, b 0.33 m

Bankfull depth, h 0.125 m

Meander belt width, Bmw 2.35 m

Width of channel, B 3.95 m

Wavelength, λ 1.25 m

Figure 2. Computational domain

3. RESULTS

Contour plots of streamwise, transverse and vertical velocities with secondary flow vectors at each

plane are compared.

Figure 4. Streamwise velocitiy contour at SEC-1 using FLUENT

Figure 5. Streamwise velocitiy contour at SEC-1 using microADV

Figure 6. Transverse velocitiy contour at SEC-1 using FLUENT

Figure 7. Transverse velocitiy contour at SEC-1 using microADV

Figure 8. Vertical velocitiy contour at SEC-1 using FLUENT

Figure 9. Vertical velocitiy contour at SEC-1 using microADV

Figure 10. Streamwise velocitiy contour at SEC-2 using FLUENT

Figure 11. Streamwise velocitiy contour at SEC-2 using microADV

Figure 12. Transverse velocitiy contour at SEC-2 using FLUENT

Figure 13. Transverse velocitiy contour at SEC-2 using microADV

Figure 14. Vertical velocitiy contour at SEC-2 using FLUENT

Figure 15. Vertical velocitiy contour at SEC-2 using microADV

Figure 17. Secondary Flow vectors at SEC-1 using FLUENT

Figure 18. Secondary Flow vectors at SEC-1 using microADV

Figure 19. Secondary Flow vectors at SEC-2 using FLUENT

Figure 20. Secondary Flow vectors at SEC-1 using microADV

4. CONCLUSIONS

Lower resolution meshes do not generate precise data, mesh quality plays an important role in the

computation. A balance between quality and computational costs should be maintained. Since the

modelling has been performed with a limit of 512,000 cells/nodes the velocity was over predicted at

certain zones. Streamwise velocity were at peak at inner bank as per expectations. The study showed the existence of a center

cell vague presence of an outer cell at the concave region and velocity was higher at the convex bank of the

flume domain.

REFERENCES:

Demuren AO, Rodi W (1984) Calculation of turbulence-driven secondary motion in non-circular

ducts. Journal of Fluid Mechanics 140: 189-222: DOI: https://doi.org/10.1017/S0022112084000574

Marriott M, Jayaratne R (2010) Hydraulic roughness–links between Manning’s coefficient,

Nikuradse’s equivalent sand roughness and bed grain size. Advances in Computing and Technology

2010: 27-32: DOI: https://doi.org/10.1142/S0578563416400179

Pan, Y, Banerjee S (1995) A numerical study of free‐surface turbulence in channel flow. Physics of

Fluids, 7(7): 1649-1664: DOI: https://doi.org/10.1063/1.868483

Sagaut P (2006) Large eddy simulation for incompressible flows: an introduction. Springer Science

& Business Media: DOI: https://doi.org/10.1007/b137536

Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic

experiment. Monthly weather review 91(3): 99-164.: DOI: https://doi.org/10.1175/1520-

0493(1963)091<0099:GCEWTP>2.3.CO;2 Van Balen W, Uijttewaal WSJ, Blanckaert K (2009) Large-eddy simulation of a mildly curved open-

channel flow. Journal of Fluid Mechanics 630: 413-442: DOI:

https://doi.org/10.1017/S0022112009007277 Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite

volume method. Pearson education: