Performance of Reynolds-Averaged Turbulence Models for Unsteady Separated Flows with
Periodic Blowing and Suction
Fluid Mechanics Laboratory, Department of Aeronautics and Astronautics,
INTRODUCTION
Control
of a turbulent flow by an oscillatory perturbation is well known to be
effective and practically useful in a wide range of flow fields[1][2]. An
example may be a separation control on an aircraft wing by means of a solid
vortex generator or a small jet. Such an oscillatory flow control is
particularly effective when it is introduced two-dimensionally because large
spanwise structures generated in the flow are responsible for the momentum
transfer across whole the boundary layer.
To
investigate these phenomena, computational fluid dynamics (CFD) is a promising
way. However, there still remain several difficulties to predict such complex
phenomena accurately. Needless to say, one great concern is turbulence
modeling. Although many research groups have tried to develop turbulence models
for complex flow-field predictions, no complete set of turbulence models have
been proposed to give accurate results for such an unsteady turbulence with
oscillatory blowing/suction.
Based on these backgrounds,
the final goal of this study aims to construct an advanced turbulence model
applicable to complex turbulence. For this purpose, the performance of several
RANS models is investigated by
application to an unsteady separated flow over a hump with/without flow
blowing/suction. From the obtained results, the present study discusses the
characteristics of the model performance in detail and some strategies are
tested for further improvement of the prediction accuracy.
TEST CASE
In this
study, all the results are compared with the experimental data of NASA Workshop
Case3[2][3][4]. Experiments were conducted by
l
No flow control (no flow through the
23-inch-span slot; slot left open with no suction or blowing through it)
l
Steady suction (suction rate of 0.01518
kg/s through the slot)
l
Zero-net-mass-flux oscillatory
suction/blowing (frequency (
) = 138.5 Hz and peak velocity out of slot (
) during blowing part of cycle = 26.6 m/s)
According to the experiment[3][4], phase-averaged turbulent statistics
also indicate flow two-dimensionality. Despite the large instantaneous
structures present in the flow, 
is virtually
uncorrelated with either 
or 
. This might serve as a justification for modeling the flow
using a two-dimensional unsteady RANS (URANS) approach. Table 1 shows the experimental
conditions. The hump is a wall-mounted Glauert-Goldschmied type body, whose geometry
is similar to that employed by Seifert & Pack[5]. It has a control slot at
approximately the 65% chord station on the model and a flow control is supplied
two-dimensionally across the span.
Table 1. Experimental conditions.
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COMPUTATIONAL CONDITIONS
Computational
conditions are the same as the previous study[6]. The geometry of the flow
simulated is shown in Fig.1. The inlet flow, at 
(based on the free-stream velocity 
and the chord
length 
), is turbulent. The grid system around the hump is shown in
Fig.2. In a similar manner to the experiment[3][4], it has a cavity inside the
slot. To realize the slot condition sufficiently, grid points are concentrated
in the vicinity of the slot. The computational domain is covered with a
body-fitted grid of 
nodes.
Fig. 1. Overview of flow field.
Fig.2. Grid system.
Conditions at the upper boundary (
) were slip conditions and wall conditions were used at the
lower boundary (
). At the outlet boundary, x/c=4.0, zero streamwise gradients
were prescribed and the inlet boundary conditions were specified based on the
experimental data. In all the test cases, no-slip conditions were specified at
the wall surfaces.
To investigate the performance of
turbulence models, five RANS models were tested: two linear k-
models (LS model[7], AKN model[8]), a linear k-
model (SST model[9]), a non-linear k- k- model ( AJL- model[10]) and a non-linear k- model ( AJL- model[10]). The aforementioned three flow conditions were
considered, among which the velocity of blowing/suction at the slot for the
oscillatory-control case is defined as
(1)
So far, the effect of periodic perturbation on the turbulent separated
flow has been investigated in various types of flows. One of their common
results is that the reattachment length is remarkably reduced when the
frequency of the imposed perturbation falls in a certain range[1]. In this test
case, such an effective excitation (
Hz, 
) was chosen after detailed examinations on its
frequency[3][4].
Calculations were performed
with the finite-volume procedure STREAM of Lien and Leschziner[11], followed by
several improvements and substantially upgraded by Apsley and Leschziner[12].
This method uses collocated storage on a non-orthogonal grid and all variables
are approximated on cell faces by the UMIST scheme[13], a TVD implementation of
the QUICK scheme. The solution algorithm is SIMPLE, with a Rhie-Chow
interpolation for pressure.
SAMPLE RESULTS
Reattachment length and streamlines
The obtained reattachment lengths are
summarized in Table 2 and representative streamlines are illustrated in Fig. 3.
Table 2 Reattachment points.
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Model |
Baseline |
Steady suction |
Osc.control |
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Exp. |
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LS |
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SST |
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AKN |
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AJL- |
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AJL- |
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(a)
(b)
(c)
Fig.3. Streamlines (AJL- model): Baseline; (b) Steady suction; (c)
Oscillatory control.
Pressure coefficients
Figures
4-6 show time-mean pressure coefficients 
for the baseline
and suction cases as well as time-mean and rms surface pressure coefficients 
for the oscillatory control case. All the
models return generally reasonable results, though the values of just behind the
slot did not correspond to the experimental data. Note that it is reported that
almost all the participants of the NASA workshop using RANS approach obtained
this trend[2]. As shown in Table 2, AJL- model gives the largest reattachment length among all the
tested models and its effect is also seen in the pressure-field prediction.
(a)
(b)
Fig.4.
Pressure coefficients for baseline case.
(a)
(b)
Fig. 5. Pressure coefficients for
steady-suction case.
(a)
(b)
Fig. 6. Comparison of mean and
fluctuating pressure coefficients for oscillatory control case.
More detailed descriptions are given in the
reference paper[14].
REFERENCES
[1] Syuya Yoshioka, Shinnosuke Obi, Shigeaki Masuda,
"Organized vortex motion in periodically perturbed turbulent separated
flow over a backward-facing step," Int. J. Heat and Fluid Flow 22, 301-307
(2001).
[2] T.B. Gatski and C. Rumsey,
[3] David Greenblatt, Keith B. Paschal, Chung-Sheng Yao,
Jerome Harris, Norman W. Schaeffler, Anthony E. Washburn, "A Separation
Control CFD Validation Test Case, Part 1: Baseline and Steady Suction,"
AIAA 2004-2220, June-July (2004).
[4] David Greenblatt, Keith B. Paschal, Chung-Sheng Yao,
Jerome Harris, "A Separation Control CFD Validation Test Case, Part 2:
Zero Efflux Oscillatory Blowing," AIAA 2005-0485, January (2005).
[5] Avi Seifert, LaTunia G. Pack, "Active Flow
Separation Control on Wall-Mounted Hump at High Reynolds Numbers," AIAA
Journal, Vol. 40, No. 7, 1363-1372 (2002).
[6] Masashi Yoshio, Ken-ichi Abe, "An investigation of
Reynolds-averaged turbulence models for unsteady separation flows with periodic
blowing and suction," 17th
International Symposium on Transport Phenomena, September (2006).
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Flows -
[9] F.R. Menter, "Two-Equation Eddy-Viscosity
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[10] K. Abe, Y.-J. Jang, M.A.Leschziner, "An investigation
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eddy-viscosity models," Int. J. Heat and Fluid Flow 24, 181-198 (2003).
[11] F.S. Lien, M.A. Leschziner, "A general
non-orthogonal collocated finite volume algorithm for turbulent flow at all
speeds incorporating second-moment turbulence-transport closure, Part1:
computational implementation," Comput. Methods Appl. Mech. Eng. 114,
123-148 (1994).
[12] D.D. Apsley, M.A. Leschziner, "Advanced turbulence
modelling of separated flow in a diffuser," Flow Turbulence Combust. 63,
81-112 (2000).
[13] F.S. Lien, M.A. Leschziner, "Upstream monotonic
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flows," Int. J. Num. Methods Fluids 19, 527-548 (1994).
[14] Masashi
YOSHIO and Ken-ichi ABE,
¡°Performance of Reynolds-Averaged
Turbulence Models for Unsteady Separated Flows with Periodic
Blowing and Suction,¡±
Proceedings of 18th International
Symposium on Transport Phenomena, Daejeon, pp. 1359-1366, 2007.
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Copyright(C) 2008, Fluid Mechanics Laboratory,
Department of Aeronautics
and Astronautics,