Finite Element Method - Application using Fastflo
Turbulent flow in an axisymmetric narrowing bend
Contact personnel: X.L.
Luo
This was a benchmark problem investigated at the 1994 annual meeting of
the World User Association in Applied Computational Fluid Dynamics. One
major question is whether experimentally-observed flow separation after
the axisymmetric bend can be predicted by a k-epsilon model.
Numerical turbulence modeling can always predict a recirculation behind
sharp corners, such as a step, and the concern in such cases is how large
the recirculation should be. Here, however, a balance between pressure,
inertia, viscous and turbulent stresses determines whether there is a flow
separation and where it occurs. The high normal pressure gradient and the
curvature of the walls make some universal wall functions totally
unsuitable in this problem.
The figures show the streamfunction, pressure, turbulent energy and
turbulent viscosity for a Reynolds number of 286,000, based on the inlet
pipe diameter and a uniform inlet velocity.
Streamfunction
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Pressure
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Turbulent energy
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Turbulent viscosity
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Computations
The mesh used contained 5,054 nodes with a higher node concentration
near both inner and outer walls. This mesh was created using the 'meshmap'
capability in Fastflo.
Three k-epsilon based turbulence models have been incorporated
in the Fastflo module: the standard linear model, the RNG model and
the non-linear model proposed by Speziale [1]. All three models have been
applied to this benchmark problem and, provided proper wall functions were
used, all gave good results in terms of numerical convergence, flow
separation prediction, and comparison with experimental data on wall
pressure distribution.
Logarithmic velocity profile wall functions were unsuitable for this
problem because of the strong normal pressure gradient and wall curvature
[2]. Instead, the van Driest mixing length wall functions were used. The
exponential damping function in van Driest mixing length progressively
suppresses the mixing length as y+ diminishes.
Results
Flow separation after the bend was predicted by all three models, with
the RNG model predicting the shortest recirculation, followed by linear
and non-linear k-epsilon models. There is very little difference
between linear and nonlinear k-epsilon models in terms of predicted
velocity fields, and the non-linearities mainly affect the distribution of
turbulent normal stress and pressure.
The pressure distributions on the inner and outer walls compare very
well against experimental data provided by Daimler-Benz and against the
results of Engelman [4].
References
[1] C.G. Speziale, On nonlinear k-l and k-epsilon models of
turbulence, Journal of Fluid Mechanics, 178, 459-475 (1986).
[2] X.-L. Luo, Operator splitting computation of turbulent flow in
an axisymmetric 180o narrowing bend using several k-epsilon
models and wall functions, International Journal of Numerical Methods
in Fluids, 22, 1189-1205 (1996).
[3] R. Glowinski and O. Pironneau, Finite element method for Navier-Stokes
equations, Annual Review of Fluid Mechanics, 24,
167-204 (1992).
[4] M. Engelman, Axi-symmetric isothermal turbulent flow in a
narrowing bend, Report to WUA-CFD annual meeting, Basel, May (1994).
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