Three-Dimensional Boundary Layer and Flow Field Data of an Inclined Prolate Spheroid

The wind tunnel model consists of a 6:1 prolate spheroid, as shown in figure 1 and figure 2.

Several incidence/Reynolds number combinations have been investigated, and data about transition in the 3d boundary layer, development of the boundary layers, 3d boundary layer separation and the separated flow field have been obtained. Measured data are surface pressures, skin friction, and mean velocities in the boundary layer and in the flow field.

Wind tunnel arrangement Fig. 1: Prolate spheroid model in th DLR 3x3m low speed wind tunnel. (Dimensions in mm)

Spheroid geometry Fig. 2: Prolate spheroid geometry and typical surface pressure distributions

Details of Model

The experimental investigations on the flow around the inclined prolate spheroid were carried out in the 3 m Low Speed Wind Tunnel NWG at DLR Göttingen and in the pressurised low speed tunnel F1 of ONERA. Both prolate spheroid models were made using the same mould, thus shape and size of the models was identical.

Reynolds numbers and angle of inclination \(\alpha\) are given in the table below.

Angle \(\alpha\) Re
NWG-10 \(10^o\) \(7.7\times 10^6\)
NWD-30 \(30^o\) \(6.5\times 10^6\)
F1-30 \(30^o\) \(40\times 10^6\)

General Geometric Arrangement: Body of Revolution

  • Body data: 6:1 prolate spheroid with a length of \(L= 2.4\) m and major half axes of 0.2 m.
  • Geometric definition: The model shape is described analytically. The co-ordinates are design values. Contour deviations are less than 0.25% of the maximum diameter.
  • Model support: The model was mounted on a central rear sting. The outer diameter of the sting was 110 mm. The model could be turned around its longitudinal axis through \(\phi = 0^o\) to \(360^o\), thus allowing the flow in one cross-section to be measured with one probe/sensor fixed to the model.

General Tunnel Information

Measurements with the prolate spheroid models at angle of incidence have been performed in two different wind tunnels. These are the 3 m Low Speed Wind Tunnel of DLR,Göttingen (A) and the F1 Wind Tunnel of ONERA, Le Fauga (B).

Tunnel A

  • Tunnel designation: 3 m Low Speed Wind Tunnel, Göttingen (NWG).
  • Tunnel characteristics: Low speed wind tunnel, Göttingen type with closed return and open test section, nozzle contraction 5.4, Speed range: 0 - 65 m/s, continuously running.
  • Test section: Test section dimensions: 3 m wide, 3 m high and 6 m long, open jet.
Free stream conditions
  • Determination of free stream conditions: The total pressure is determined from the wall pressure in the settling chamber. As the tunnel has an open (free jet) test section the ambient, atmospheric pressure is taken as the static pressure. The dynamic pressure in the test section is calculated from the settling chamber pressure using a correction factor determined from a tunnel calibration. The (total) temperature is measured in the collector and assumed to be constant in the tunnel.
  • Tunnel calibration: Spot checks of calibrations have been performed from time to time.
Flow quality
  • Flow uniformity: The deviations of the dynamic pressure are less than +/-0.5% at the standard position of the models. At distances from the nozzle exit between 1 m and 4 m the maximum deviation of the static pressure is +/-1.5% of the dynamic pressure. The flow angularity on the test section centreline is constant within +/-0.25o in the vertical plane, as measured by a multihole pressure probe.
  • Temperature variation: As the tunnel has no cooler, the temperature cannot be controlled. This means that the temperature in the tunnel increases during each run. The temperature increase with time is dependent on the velocity and on the ambient temperature. It was tried to keep the Reynolds number constant by manual control of the fan speed. Temperature variations in the tunnel circuit are assumed to be small and therefore are neglected.
  • Flow unsteadiness: The overall turbulence level is rather high compared to other wind tunnels. Values of 0.33% to 0.4% for the streamwise velocity fluctuations and about 0.8% for the vertical and spanwise components have been measured.

Tunnel B

  • Tunnel designation: F1 Wind Tunnel (F1).
  • Tunnel characteristics: Pressurised low speed wind tunnel, closed test section, nozzle contraction ratio 7.2, Maximum pressure: 4 bar, Maximum speed: 125 m/s at 1 bar, 80 m/s at 4 bar, continuously running.
  • Test section: Closed test section, Test section dimensions: 4.5 m wide, 3.5 m high and 10 m long. A slight divergence of the two vertical test section walls compensates the boundary layers along the walls to ensure a flow without longitudinal gradients.
Free stream conditions
  • Determination of free stream conditions: Several Prandtl antennas placed in the upstream part of the test section, wall pressure taps at the end of the contraction and a Pitot probe in the settling chamber are used for the determination of the reference static, total and dynamic pressures. The (total) temperature is measured in the settling chamber and assumed to be constant in the tunnel.
  • Tunnel calibration: The tunnel has been calibrated after construction.
Flow quality
  • Flow uniformity: The longitudinal gradient of static pressure or Mach number is negligible. The flow angularity in the test section is zero, with an inaccuracy of +/-0.2o. The stagnation pressure shows almost perfect uniformity. The wind tunnel is supplied with compressed air generated by a centrifugal compressor through a buffer tank. The tank is used in combination with a servocontrol for regulating the pressure around an assigned value. The relative deviations of the stagnation pressure are smaller than +/-10-3.
  • Temperature variation: A water cooler is used to stabilise the stagnation temperature around an assigned value between atmospheric temperature and 40oC. A servo-control maintains this temperature around the assigned value within better than 1oC.
  • Flow unsteadiness: Hot wire measurements in the test section showed a low streamwise turbulence level smaller than 0.1%. For Mach numbers above 0.2 the noise level is less than 0.01 in terms of \(c_p\)-RMS if the RMS pressure fluctuations are normalised by the dynamic pressure in the free stream.

Model Pressure Measurements

The prolate spheroid model is equipped with 42 pressure taps of 0.3 mm diameter positioned on one meridian in non-equidistant distances. Due to the fact that the model could be rotated around its longitudinal axis the wall pressures could be measured at the 42 cross sections with a high resolution in the circumferential direction.

Boundary Layer Measurements

Mean velocity profiles in the three-dimensional boundary layers have been measured for a model angle of incidence \(\alpha =10^o\) applying pressure probes. The probe, with its traversing mechanism inside the model, could be positioned in four cross sections. The probe was traversed normal to the model surface. A three-hole-direction-probe was used to determine the longitudinal and spanwise velocity components \(U\) and \(V\). The static pressure used in the data reduction was measured at the wall and assumed to be constant through the entire boundary layer thickness. Errors could have been introduced here, if thick boundary layers close to separation were investigated.

Flow Field Measurements

Mean velocities in the flow field around the model were measured with pressure probes in both wind tunnels. A 10-hole probe was used in the NWG tunnel, and a five-hole probe in the F1 tunnel.

The ONERA five-hole probe, with a diameter of 3 mm, was also traversed on rays perpendicular to the model surface.

Estimated accuracy of Free stream conditions:
Flow velocity +/-0.25% NWG
Dynamic pressure +/-0.3% F1
Model incidence +/-0.1o
Measured data:
Pressure coefficients: \(\Delta c_p = \pm 0.01\) (NWG, \(U_{\infty} = 55\) m/s)
\(\Delta c_p = \pm 0.005\) (F1, \(U_{\infty} = 75\) m/s, \(p_o = 4\) bar)
Wall shear stress: \(\Delta c_f/c_f = \pm 0.1\)
\(\Delta \gamma_w/\gamma_w = \pm 0.1\)
Velocity: \(\Delta U_{\gamma}/U_{\gamma\beta} = \pm 0.01\)
\(\Delta \gamma < 1^o\)

The data available includes:

  • Skin friction coefficient distribution around the body at several different streamwise \(x\) locations
  • Surface pressure coefficient distribution along the length of the body at a number of circumferential angles
  • Profiles of mean \(U\) and \(V\) velocities at a number of streamwise locations and circumferential angles.

No corrections were applied to the data. As the boundary conditions are known (free jet in NWG, straight solid wall in F1), conventional corrections are possible. Solid blockage effects are estimated to be \(\Delta U_{\infty}/U_{\infty} = -0.003\) at \(\alpha =10^o\) and \(-0.01\) at \(\alpha= 30^o\) for the NWG tunnel and to be \(\Delta U_{\infty}/U_{\infty} = 0.018\) at \(\alpha = 30^o\) for the F1 one. Lift interference effects are estimated to be \(\Delta \alpha = 0.3^o\) in NWG and \(0.2^o\) in Fl at \(\alpha = 30^o\). They are negligible at \(\alpha = 10^o\).

Sample plots of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as individual files.

The file readme.txt contains some description of the files and cases.

Pressure Coefficients

F1-30 NWG-10 NWG-30
f1_30_cp.dat nwg10_cp.dat nwg30_cp.dat

Skin Friction Coefficients

Velocity Profiles

NWG-30 Case
\(\phi\) [o] \(x/(2a)=0.4839\) \(x/(2a)=0.5272\) \(x/(2a)=0.5701\) \(x/(2a)=0.6136\) \(x/(2a)=0.6571\) \(x/(2a)=0.6996\)
0 nwg30uff_001.dat nwg30uff_020.dat nwg30uff_039.dat nwg30uff_058.dat nwg30uff_077.dat nwg30uff_096.dat
30 nwg30uff_002.dat nwg30uff_001.dat nwg30uff_040.dat nwg30uff_059.dat nwg30uff_078.dat nwg30uff_097.dat
60 nwg30uff_003.dat nwg30uff_022.dat nwg30uff_041.dat nwg30uff_060.dat nwg30uff_079.dat nwg30uff_098.dat
90 nwg30uff_004.dat nwg30uff_023.dat nwg30uff_042.dat nwg30uff_061.dat nwg30uff_080.dat nwg30uff_099.dat
100 nwg30uff_005.dat nwg30uff_024.dat nwg30uff_043.dat nwg30uff_062.dat nwg30uff_081.dat nwg30uff_100.dat
110 nwg30uff_006.dat nwg30uff_025.dat nwg30uff_044.dat nwg30uff_063.dat nwg30uff_082.dat nwg30uff_101.dat
120 nwg30uff_007.dat nwg30uff_026.dat nwg30uff_045.dat nwg30uff_064.dat nwg30uff_083.dat nwg30uff_102.dat
130 nwg30uff_008.dat nwg30uff_027.dat nwg30uff_046.dat nwg30uff_065.dat nwg30uff_084.dat nwg30uff_103.dat
135 nwg30uff_009.dat nwg30uff_028.dat nwg30uff_047.dat nwg30uff_066.dat nwg30uff_085.dat nwg30uff_104.dat
140 nwg30uff_010.dat nwg30uff_029.dat nwg30uff_048.dat nwg30uff_067.dat nwg30uff_086.dat nwg30uff_105.dat
145 nwg30uff_011.dat nwg30uff_030.dat nwg30uff_049.dat nwg30uff_068.dat nwg30uff_087.dat nwg30uff_106.dat
150 nwg30uff_012.dat nwg30uff_031.dat nwg30uff_050.dat nwg30uff_069.dat nwg30uff_088.dat nwg30uff_107.dat
155 nwg30uff_013.dat nwg30uff_032.dat nwg30uff_051.dat nwg30uff_070.dat nwg30uff_089.dat nwg30uff_108.dat
160 nwg30uff_014.dat nwg30uff_033.dat nwg30uff_052.dat nwg30uff_071.dat nwg30uff_090.dat nwg30uff_109.dat
165 nwg30uff_015.dat nwg30uff_034.dat nwg30uff_053.dat nwg30uff_072.dat nwg30uff_091.dat nwg30uff_110.dat
170 nwg30uff_016.dat nwg30uff_035.dat nwg30uff_054.dat nwg30uff_073.dat nwg30uff_092.dat nwg30uff_111.dat
175 nwg30uff_017.dat nwg30uff_036.dat nwg30uff_055.dat nwg30uff_074.dat nwg30uff_093.dat nwg30uff_112.dat
180 nwg30uff_018.dat nwg30uff_037.dat nwg30uff_056.dat nwg30uff_075.dat nwg30uff_094.dat nwg30uff_113.dat
185 nwg30uff_019.dat nwg30uff_038.dat nwg30uff_057.dat nwg30uff_076.dat nwg30uff_095.dat nwg30uff_114.dat
\(\phi\) [o] \(x/(2a)=0.7420\) \(x/(2a)=0.7856\) \(x/(2a)=0.8279\) \(x/(2a)=0.8758\) \(x/(2a)=0.9167\)
0 nwg30uff_115.dat nwg30uff_134.dat nwg30uff_153.dat nwg30uff_190.dat
30 nwg30uff_116.dat nwg30uff_135.dat nwg30uff_154.dat nwg30uff_172.dat nwg30uff_191.dat
60 nwg30uff_117.dat nwg30uff_136.dat nwg30uff_155.dat nwg30uff_173.dat nwg30uff_192.dat
90 nwg30uff_118.dat nwg30uff_137.dat nwg30uff_156.dat nwg30uff_174.dat nwg30uff_193.dat
100 nwg30uff_119.dat nwg30uff_138.dat nwg30uff_157.dat nwg30uff_175.dat nwg30uff_194.dat
110 nwg30uff_120.dat nwg30uff_139.dat nwg30uff_158.dat nwg30uff_176.dat nwg30uff_195.dat
120 nwg30uff_121.dat nwg30uff_140.dat nwg30uff_159.dat nwg30uff_177.dat nwg30uff_196.dat
130 nwg30uff_122.dat nwg30uff_141.dat nwg30uff_160.dat nwg30uff_178.dat nwg30uff_197.dat
135 nwg30uff_123.dat nwg30uff_142.dat nwg30uff_161.dat nwg30uff_179.dat nwg30uff_198.dat
140 nwg30uff_124.dat nwg30uff_143.dat nwg30uff_162.dat nwg30uff_180.dat nwg30uff_199.dat
145 nwg30uff_125.dat nwg30uff_144.dat nwg30uff_163.dat nwg30uff_181.dat nwg30uff_200.dat
150 nwg30uff_126.dat nwg30uff_145.dat nwg30uff_164.dat nwg30uff_182.dat nwg30uff_201.dat
155 nwg30uff_127.dat nwg30uff_146.dat nwg30uff_165.dat nwg30uff_183.dat nwg30uff_202.dat
160 nwg30uff_128.dat nwg30uff_147.dat nwg30uff_166.dat nwg30uff_184.dat nwg30uff_203.dat
165 nwg30uff_129.dat nwg30uff_148.dat nwg30uff_167.dat nwg30uff_185.dat nwg30uff_204.dat
170 nwg30uff_130.dat nwg30uff_149.dat nwg30uff_168.dat nwg30uff_186.dat nwg30uff_205.dat
175 nwg30uff_131.dat nwg30uff_150.dat nwg30uff_169.dat nwg30uff_187.dat nwg30uff_206.dat
180 nwg30uff_132.dat nwg30uff_151.dat nwg30uff_170.dat nwg30uff_188.dat nwg30uff_207.dat
185 nwg30uff_133.dat nwg30uff_152.dat nwg30uff_171.dat nwg30uff_189.dat nwg30uff_208.dat

- Kreplin, H.P. (1995). Three-dimensional boundary layer and flow field data of an inclined prolate spheroid. AGARD FDP WG-14 Experimental test cases for CFD validation, Test Case ID: GE-20.

Indexed data:

case074 (dbcase, flow_around_body)
titleFlow around inclined prolate spheroid
flow_tag3d, separated, bluff_body