A new modeling approach has been developed that explicitly accounts for expected turbulent eddy length scales in cavity zones. It uses a hybrid approach with Poisson and Hamilton–Jacobi differential equations. These are used to set turbulent length scales to sensible expected values. For complex rim-seal and shroud cavity designs, the method sets an expected length scale based on local cavity width which accurately accounts for the large-scale wakelike flow structures that have been observed in these zones. The method is used to generate length scale fields for three complex rim-seal geometries. Good convergence properties are found, and a smooth transition of length scale between zones is observed. The approach is integrated with the popular Menter shear stress transport (SST) Reynolds-averaged Navier–Stokes (RANS) turbulence model and reduces to the standard Menter model in the mainstream flow. For validation of the model, a transonic deep cavity simulation is performed. Overall, the Poisson–Hamilton–Jacobi model shows significant quantitative and qualitative improvement over the standard Menter and k–ε two-equation turbulence models. In some instances, it is comparable or more accurate than high-fidelity large eddy simulation (LES). In its current development, the approach has been extended through the use of an initial stage of length scale estimation using a Poisson equation. This essentially reduces the need for user objectivity. A key aspect of the approach is that the length scale is automatically set by the model. Notably, the current method is readily implementable in an unstructured, parallel processing computational framework.

References

References
1.
Cherry
,
D.
,
Wadia
,
A.
, and
Beacock
,
R.
,
2005
, “
Analytical Investigation of Low Pressure Turbine With and Without Endwall Gaps Seals and Clearance Features
,”
ASME
Paper No. GT2005-68492.
2.
Wellbourn
,
S. R.
, and
Okiishi
,
T. H.
,
1998
, “
The Influence of Shrouded Stator Cavity Flows on Multistage Compressor Performance
,”
ASME
Paper No. 98-GT-12.
3.
Rosic
,
B.
,
Denton
,
J. D.
, and
Pullan
,
G.
,
2005
, “
The Importance of Shroud Leakage Modelling in Multistage Turbine Flow Calculations
,”
ASME
Paper No. GT2005-68459.
4.
Gangwar
,
A.
,
Lukovic
,
B.
,
Orkwis
,
P.
, and
Sekar
,
B.
,
2001
, “
Modeling Unsteadiness in Steady Cavity Simulations. I—Parametric Solutions
,”
AIAA
Paper No. 2001-0153.
5.
Lukovic
,
B.
,
2002
, “
Modeling Unsteadiness in Steady Simulations With Neural Network Generated Lumped Deterministic Source Terms
,” Ph.D. thesis, Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH.
6.
Gangwar
,
A.
,
2001
, “
Source Term Modeling of Rectangular Flow Cavities
,” M.S. thesis, Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH.
7.
Lukovic
,
B.
,
Gangwar
,
A.
,
Orkwis
,
P.
, and
Sekar
,
B.
,
2001
, “
Modeling Unsteadiness in Steady Cavity Simulations. II—Neural Network Modeling
,”
AIAA
Paper No. 2001-0154.
8.
Lukovic
,
B.
,
Orkwis
,
P.
,
Turner
,
P.
, and
Sekar
,
B.
,
2002
, “
Effect of Cavity L/D Variations on Neural Network-Based Deterministic Unsteadiness Source Terms
,”
AIAA
Paper No. 2002-0857.
9.
Lukovic
,
B.
,
Orkwis
,
P.
,
Turner
,
P.
, and
Sekar
,
B.
,
2002
, “
Modeling Unsteady Cavity Flows With Translating Walls
,”
AIAA
Paper No. 2002-3288.
10.
Jefferson-Loveday
,
R. J.
,
Tucker
,
P. G.
,
Northall
,
J. D.
, and
Rao
,
V. N.
,
2013
, “
Differential Equation Specification of Integral Turbulence Length Scales
,”
ASME J. Turbomach.
,
135
(
3
), p.
031013
.
11.
Fares
,
E.
, and
Schroder
,
W.
,
2002
, “
A Differential Equation to Determine the Wall Distance
,”
Int. J. Numer. Methods Fluids
,
39
(
8
), pp.
743
762
.
12.
Spalding
,
D. B.
,
1972
, “
A Novel Finite Difference Formulation for Differential Expressions Involving Both First and Second Derivatives
,”
Int. J. Numer. Methods Eng.
,
4
(
4
), pp.
551
561
.
13.
Spalding
,
D. B.
,
2013
, “
Trends, Tricks, and Try-ons in CFD/CHT
,”
Adv. Heat Transfer
,
45
, pp.
45
47
.
14.
Visbal
,
M. R.
, and
Gaitonde
,
D. V.
,
2002
, “
On the Use of Higher-Order Finite-Difference Schemes on Curvilinear and Deforming Meshes
,”
J. Comput. Phys.
,
181
, pp.
155
185
.
15.
Tucker
,
P. G.
,
1998
, “
Assessment of Geometric Multilevel Convergence and a Wall Distance Method for Flows With Multiple Internal Boundaries
,”
Appl. Math. Modell.
,
22
, pp.
293
311
.
16.
ANSYS
,
2013
, “
ANSYS Fluent Theory Guide
,” ANSYS, Inc., Canonsburg, PA.
17.
Menter
,
F. R.
,
1993
, “
Zonal Two Equation k–ω Turbulence Models for Aerodynamic Flows
,”
AIAA
Paper No. 93-2906.
18.
Secundov
,
N.
,
Strelets
,
M. K.
, and
Travin
,
A. K.
,
2001
, “
Generalization of vt-92 Turbulence Model for Shear-Free and Stagnation Point Flows
,”
ASME J. Fluids Eng.
,
123
, pp.
111
115
.
19.
Strelets
,
M.
,
2001
, “
Detached Eddy Simulation of Massively Separated Flows
,”
AIAA
Paper No. 2001-0879.
20.
Suponitsky
,
V.
,
Avital
,
E.
, and
Gaster
,
M.
,
2005
, “
On Three-Dimensionality and Control of Incompressible Cavity Flow
,”
Phys. Fluids
,
17
(
10
), p.
104103
.
21.
Tyacke
,
J. C.
,
Tucker
,
P. G.
,
Jefferson-Loveday
,
R. J.
,
Rao
,
V. N.
,
Watson
,
R.
, and
Naqavi
,
I.
,
2013
, “
LES for Turbines: Methodologies, Cost and Future Outlooks
,”
ASME
Paper No. GT2013-94416.
22.
Spalart
,
P. R.
, and
Allmaras
,
S. R.
,
1993
, “
A One-Equation Turbulence Model for Aerodynamic Flows
,”
La Rech. Aerosp.
,
1
(
1
), pp.
5
21
.
23.
Forestier
,
N.
,
Jacquin
,
L.
, and
Geffroy
,
P.
,
2003
, “
The Mixing Layer Over a Deep Cavity at High-Subsonic Speed
,”
J. Fluid Mech.
,
475
, pp.
101
144
.
24.
Menter
,
F. R.
,
1992
, “
Influence of Freestream Values on k–ω Turbulence Model Predictions
,”
AIAA J.
,
30
(
6
), pp.
1657
1659
.
25.
Thornber
,
B.
, and
Drikakis
,
D.
,
2008
, “
Implicit Large-Eddy Simulation of a Deep Cavity Using High-Resolution Methods
,”
AIAA J.
,
46
(
10
), pp.
2634
2645
.
You do not currently have access to this content.