Three dimensional experimental investigation of a
hypersonic double-ramp flow
F.F.J. Schrijer, R. Caljouw, F. Scarano, and B.W. van Oudheusden Delft University of Technology, Faculty of Aerospace Engineering
Kluyverweg 1, 2629 HS Delft (The Netherlands)
Summary. The flow over a 15◦-45◦ double compression ramp was studied at Mach 7.5. CFD computations are compared to 2 component PIV (particle image velocimetry) measurements. Furthermore stereoscopic PIV was used to measure the three component velocity vector, enabling to perform a 3D flow survey. The overall flow topology is assessed and special attention is devoted to the separated region. Finally the effect of a sharp leading edge on the separation region is investigated.
1 Introduction
The flow over a double compression ramp is studied experimentally in a short duration Ludwieg-tube facility at Mach 7.5 [5]. The large second ramp angle introduces a shock detachment accompanied by an Edney type V interaction. A schlieren image of the flow is given in figure 1. From previous studies using high-speed schlieren imaging it was found that the flow field shows unsteady behavior [6] which is typical for these type of flows [8]. Movement of the separation shock was detected as well as the movement of the curved shock. The unsteady phenomena occurring at separation were ascribed to transition in the separated shear layer. The movement of the curved shock is believed to be caused by a shock hysteresis phenomena as described by Ben-dor et al. [2]. This in combination with the relatively large separated region and the possible occurrence of transition in the shear layer are the reason that flow simulation by means of CFD is non-trivial [3]. In the current study the flow is investigated more in detail. Two component velocity measurements at the center of the model described in detail in [6] are compared to a turbulent CFD computation. Following the results from this comparison, a three component flow survey is performed using stereoscopic PIV.
2 Experimental setup
The model used in the experiments is a double compression ramp featuring a 15◦first and 45◦second ramp angle. The total model length is 15 cm where the first ramp is 10 cm length and the model width is 11 cm. The setup used for the 2C PIV measurements can be found in Schrijer et al. [6]. The model leading edge radius was increased to 1 mm by adding a piece of tape to the model nose to obtain a uniform geometry.
To measure the three component velocity field, stereo PIV was applied. The illumi-nation was performed by a Quantel laser having 200 mJ per pulse. The typical time separation between the pulses was 1μs. The laser sheet had a thickness of 1.5 mm. The particle images were recorded using two PCO sensicam QE frame-straddling CCD cam-eras having a resolution of 1376× 1040 pixels corresponding to a field of view of 6 × 4.5
Model U Laser 0.5 mm 4 mm 8 mm 20 mm
Fig. 1. Stereo PIV setup and measurement location
The 4 planes that are investigated are oriented parallel to the first ramp, they are located at 0.5, 4, 8 and 20 mm from the model surface. In figure 1 the schematic overview of the setup is given including an insert of a schlieren image showing the exact location of the laser sheet with respect to the model and flow features. The measured velocity components are linked to the orientation of the laser sheet; U , V and W are respectively the in-plane horizontal, spanwise and out-of-plane components. The obtained velocity fields are averages of typical 10 recordings.
3 CFD comparison to 2C-PIV study
A two dimensional CFD computation was performed using a Navier Stokes second order finite volume flow solver (LORE) [7]. The inflow conditions were equal to the wind tunnel free stream conditions. The computational mesh featured 2.1 million cells. Only a fully turbulent calculation converged to a stable solution where Menter’s shear stress transport model was used as turbulence model. In figure 2 the computational results are shown in combination with experimental results which are discussed in detail in Schrijer et al. [6]. It was found that the flow field showed good qualitative agreement. However the separation region in the CFD computations was considerably larger compared to the experiments causing the shock interaction to occur further away from the model surface. This was primarily ascribed to the three dimensionality of the flow field that empties the separation bubble thus making it smaller. To assess the amount of three dimensionality of the flow, it was investigated using stereo PIV.
Fig. 2. Comparison between CFD simulation and experimental results; synthetic schlieren
ver-sus experiments (left) and computed vertical flow component verver-sus PIV vertical flow component (right)
4 Flow field overview
First the overall flow field will be discussed using the results obtained from the 4, 8 and 20 mm planes. In figure 3 the particle image recording is shown in combination with the velocity field for the plane at 4 mm from the surface.
Fig. 3. Results for the plane at 4 mm, particle image recording (left) and flow field (right),
contour represents out-of-plane velocity component
Progressing downstream toward the second ramp, an increase is found in the particle density caused by the thermodynamic density increase across the separation shock. This is also observed from the velocity field where the vertical flow component increases when separation occurs. Further downstream the plane crosses the reattachment region (not yet a shock) which is again is associated to an increase in particle density and out-of-plane velocity component. Finally approaching the model surface, streaks are visible in the reattachment region. These streaks are conceived to be caused by the presence of
Fig. 4. Results for the plane at 8 mm, particle image recording (left) and flow field (right).
Finally the flow field at 20 mm above the first ramp surface is shown in figure 5. Clearly visible is the increase in particle density due to the curved shock. After the uniform region of increased particle density, empty blobs are observed that mark the presence of the shear layer. These empty blobs were also observed in the 2C particle image recordings, see [6]. Crossing the shear layer the presence of the wall jet is visualized by an increase of non-uniform particle seeding density. The same is visualized from the
velocity contours, clearly showing the increase in out-of-plane component when crossing the curved shock and an even further increase when entering the wall jet region.
Considering the macroscopic shape of the shock wave pattern established over the model it can be concluded that wave are essentially 2D over a relatively large portion of the center of the model.
5 Surface flow
To investigate the flow in the separated region, a plane at 0.5 mm from the model surface was investigated. Here the largest 3D effects are expected to occur. Again the particle image recording and velocity field are depicted in figure 6. As can be seen from the recorded images, again the particle density increase is observed when crossing the separation shock. Subsequently in the separated region traces of longitudinal streaks can be observed, these are believed to be caused by the emergence of the G¨ortler vortices, similar to the ones observed for the plane at 4 mm. The velocity fields show a large span-wise velocity gradient in the separated region causing an emptying of the separation bubble. Because of this the separation bubble is reduced in size compared to a two dimensional bubble.
Fig. 6. Results for the plane at 0.5 mm, particle image recording (left) and flow field (right).
6 Influence of leading edge shape
Additionally the separation region was also investigated for a sharp leading edge where the nose radius was 0.1 mm. The results are shown in figure 7, comparing this to the results for the rounded leading edge (figure 6) it can be seen that the compression and separation region is dramatically altered. The extent of the compression and separated region is reduced and at some location the separation region is completely absent. Looking at the particle image recording it can be seen that at this location streaks can be observed emanating from the leading edge which destroy the separated region. From literature it is known that the leading edge has a big influence on the wavelength and presence of G¨ortler vortices [1] however it appears that small irregularities can also have a significant influence on the extent of the separated region.
7 Conclusions
The flow over 15◦-45◦ ramp was studied at Mach 7.5. A turbulent CFD simulation on a two dimensional computational grid was made. Comparison with experimental results obtained using 2C PIV and schlieren showed a qualitatively good agreement. However the separation region was found to be considerably larger in the computations. This was ascribed to the three dimensionality of the flow field. Stereo PIV measurements yielding all three velocity components were performed at several planes at 0.5, 4, 8, and 20 mm above the model surface. It was found that the overall shock topology was largely two dimensional over the greater part of the model. Focussing the attention to the plane crossing the separation region showed that here the flow was highly three dimensional. Furthermore it was found that the shape of the model leading edge has a dramatic effect on the extent of the separation region.
Acknowledgement. The authors would like to acknowledge Dr.L.Walpot and D.Sileri for provid-ing the CFD data.
References
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