UFR 308 Test Case
3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation
Underlying Flow Regime 308 © copyright ERCOFTAC 2004
Test Case
Brief description of the study test case
The flow around an inclined spheroid represents an interesting test case for purpose of validation of numerical methodologies. This test case, in fact, involves complex flow phenomena and a simple geometry. Therefore, the issues coming from the physical modelling should be easily separated from the ones due to the computational grid complexity and clearly identified.
A 6:1 model of a prolate spheroid has been tested in the DLR low speed wind tunnel NWG in Göttingen. The model shape is defined analytically and the main dimensions are the following:
 Major axis = 2a = 2.4 m.
 Minor axis = 2b = 0.4 m.
A sketch of the geometry is presented in Figure 1.
Several combinations of incidences and Reynolds numbers have been tested. Between the test cases available, emphasis can be placed on the following flow conditions :



 
1 









Measured data consist of surface pressures and skin friction, mean velocity in the boundary layer and in the flow field. Data about transition, development of the boundary layers, separation and flow field in the separated flow region have also been obtained.
The flow around an inclined spheroid has been simulated during the E.C. funded project ECARP [8] with the main purpose of validation of the turbulence models. The flow conditions chosen are the ones reported in Table 1. The measured data consist of :
 Pressure coefficients at various cross sections
 Friction coefficients at various cross sections
 Wall shear stress angle distributions at various cross sections
 Velocity profiles at x/2a = 0.73
The data of the inclined spheroid are available on the CDROM of the ECARP book [8], and is Test Case 74 in the ERCOFTAC database.
Test Case Experiments
Experiments on a prolate spheroid, for the flow conditions reported in Table 1, have been performed at the NWG DLR wind tunnel and, at higher Reynolds numbers, at the F1 ONERA wind tunnel.
The NWG DLR is a low speed wind tunnel with an open jet test section and the following main characteristics :
 Maximum speed :65 m/s
 Test section dimensions : width 3m, height 3m, length 6m
Since the tunnel has an open jet test section, the reference static pressure is assumed to be the atmospheric pressure. The total pressure is determined from the wall pressure in the settling chamber, and the dynamic pressure is computed from the pressure in the settling chamber using a correction factor coming from the tunnel calibration. A sketch of the spheroid in the NWG DLR wind tunnel is presented in Figure 2.
The ONERA F1 is a pressurised (maximum pressure is 4 bar) low speed wind tunnel with closed test section. The main characteristics are the following :
 Maximum speed : 125 m/s at a pressure of 1 bar
 Test section dimensions : width 4.5 m, height 3.5 m, length 10 m
The reference static, total and dynamic pressures are determined by using several Prandtl antennas in the upstream part of the test section, wall pressure taps at the end of the contraction section and a Pitot probe in the settling chamber.
Pressures on the model have been measured by 42 pressure taps of 0.3 mm diameter positioned on one meridian in non equidistant distances. Mean velocity in the boundary layer were obtained at a model incidence of 10° applying pressure probes traversed normal to the model surface and a threeholedirection probe to measure the longitudinal and spanwise velocity. Mean velocities in the flow field around the model were measured by a 10hole probe in the NWG and by a 5hole probe in the F1.
The measured data are not corrected, and the blockage effects are estimated as follows :
 DLR NWG
ΔU_{∞}/ U_{∞}= 0.003 at α =10° and ΔU_{∞}/ U_{∞}= 0.01 at α =30°
Δα negligible at α =10° and Δα = 0.3° at α =30°
 F1 ONERA
ΔU_{∞}/ U_{∞}= 0.018 at α =30°
Δα negligible at α =10° and Δα = 0.2° at α =30°
The accuracy of the data are estimated as follows :
 ΔC_{P}= ± 0.01 at NWG DLR and ΔC_{P}= ± 0.005 at F1 ONERA
 ΔC_{f}= ± 0.1
 ΔU = ± 0.01
More details on the experiments can be found in Meier et al. (1984) [18] and (1986) [19], in Kreplin et al. (1995) [11], in the CDROM of the ECARP book [8], and in Test Case 74 of the ERCOFTAC database.
CFD Methods
The flow around an inclined spheroid has been investigated numerically, with the main objective of assessment of turbulence models, during the E.U. funded project ECARP [8] and is Test Case 74 in the ERCOFTAC database. Discussion of this test case can also be found in Lien (1996) [13], in Lien and Durbin (1996) [16], and in Lien and Leschziner (1996) [17].
In the project ECARP, two flow conditions, one mandatory (α = 10°) and an other one optional (α = 30°), as reported in Table 1, were simulated. The numerical methods, the boundary conditions and the turbulence models used by the partners are reported in Table 2 .























LL in RNG formulation 
A common mandatory mesh, with 98x64x80 cells for 5 grid levels, has been used. The height of the first cells adjacent to the wall has allowed to achieve y^{+} values in the order of magnitude of 1 or even less. CFDNorway used the mandatory mesh for the α =10° case and an own mesh including the sting of the wind tunnel model for the α =30° case. Donier/DASALM employed a closetomandatory 137x65x81 grid with the sting for the α =10° case. UMIST has used a closetomandatory 98x82x66 grid for both test cases. FFA and KTH used the mandatory mesh for the mandatory flow condition.
Lien (1996) [10] has applied a non linear eddy viscosity turbulence model with second and third order constitutive relation [15] to simulate flow condition 2 by employing a 65^{3} and a 128^{3} nodes grids. Lien and Durbin (1996) [16] simulated flow condition 2 with a 65^{3} grid by using the low Reynolds κε model by Lien and Leschziner (1993) [14] and a κεv^{2}model [5] with the Launder and Kato's modification for the production of the turbulent kinetic energy [12]. A more detailed discussion of the results achieved by UMIST during the ECARP project is reported in Lien and Leschziner (1996) [17].
© copyright ERCOFTAC 2004
Contributors: Pietro Catalano  CIRA