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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: [email protected].
2, Associate Professor, Department of Civil Engineering, NIT Rourkela, Odisha 769008, India.
Email: [email protected]
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.
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