AIAA Paper 2004-0199
Numerical Study on Flow Separation of A TransonicCascade
Zongjun Hu and Ge-Cheng Zha
Dept. of Mechanical EngineeringUniversity of Miami
Coral Gables, Florida 33124E-mail: [email protected]
Jan Lepicovsky
QSS Group, Inc.NASA Glenn Research Center
21000 Brookpark RoadMS 500/QSS
Cleveland, Ohio 44135
Objective:
� Numerical prediction of the boundary layer separation for atransonic cascadeBackground:
� Flow separation is one of the unsteady aerodynamic forcingsources exciting blade flutter
Motivation:
� Develop a CFD solver to predict the steady and unsteady flowseparation for compressor
Governing Equations
3D Reynolds averaged NS equations:
������ � ������ � ���� � ����� � ������ � ����� � ����� (1)where � � ������ ������� ����� � ��!�"#� ����$&%('� � �)�������*�+ � ��,���-&� �����.�� � �����/�"0�21 ��3�$ � �+546��7% ' � ��������� �����8�� �*�+ � �����*-9� �����!�"0�:1 ��;�$ � �+�4
Numerical Algorithms
� Implicit Gauss-Seidel Relaxation Time Marching
� Roe and Van Leer Schemes for inviscid fluxes, 3rd OrderMUSCL-type differencing
� 2nd order central differencing for viscous terms
� Baldwin-Lomax Turbulence model
0
5
10
15
20
25
0.1 1 10 100 1000
u+
y+
law of the wallcomputation
Figure 1: Computed velocity profile comparison with the law of the wall
Figure 2: The transonic inlet-diffuser mesh
0.44584
0.44584
1.03984
1.11409 0.74284 0.668590.52009
Figure 3: Mach number contours of the transonic inlet-diffuser
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-4 -2 0 2 4 6 8
p/pt
x/h
computationexperiment
Figure 4: Upper wall pressure distribution of the transonic inlet-diffuser
inlet flow
Figure 5: NASA transonic flutter cascade tunnel
Figure 6: Cascade 3D mesh
Figure 7: Cascade 3D mesh
Figure 8: Flow pattern of the inlet-diffuser at incidence
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
x/l
Experimental Pressure SideComputational Pressure Side
Experimental Suction SideComputational Suction Side
Figure 9: Mid-span static pressure distribution at Mach number 0.5
(a) Ma=0.5 (b) Ma=0.8 (c) Ma=1.18
Figure 10: Mid-span flow pattern under different inlet Mach numbers
(a) Computed flow pattern (b) Experiment visualization
Figure 11: Suction surface flow pattern at Mach number 0.5
(a) Computed flow pattern (b) Experiment visualization
Figure 12: Suction surface flow pattern at Mach number 0.8
(a) Computed flow pattern (b) Experiment visualization
Figure 13: Suction surface flow pattern at Mach number 1.18
-0.4
-0.2
0
0.2
0.4
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
x/l
Experimental Pressure SideComputational Pressure Side
Experimental Suction SideComputational Suction Side
Figure 14: Mid-span static pressure distribution at Mach number 0.5
-0.4
-0.2
0
0.2
0.4
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cp
x/l
Experimental Pressure SideComputational Pressure Side
Experimental Suction SideComputational Suction Side
Figure 15: Mid-span static pressure distribution at Mach number 0.8
lip shock
Inflow
bow shocktrailing shock
Figure 16: Experimental shock structure of the NASA transonic cascade at Mach number1.18
Conclusions:
� NASA GRD flutter compressor cascade calculated at inci-dence of E�� and D E�� , inlet M=0.5, 0.8, 1.0
� The surface pressure distribution agrees well with the exper-iment with no flow separation.
� At high incidence and subsonic, flow separation starts at lead-ing edge.
� The separation bubble length predicted agree well with theexperiment.
� The computed surface pressure with separation rises moresteeply than that at experiment, overall agreement is reason-able.
� At supersonic, the flow is attached-separated-reattached. Theseparation is due to the shock wave/boundary layer interaction.
� With Baldwin-Lomax turbulence model, the Van Leer schemepredicts the separation region agreeing better than the Roe scheme.