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Hypersonic Laminar Flow Control

A typical challenge for re-entry vehicles during flight is an effective control of hypersonic transition and the laminar/turbulent state of the boundary layer. The state of the boundary layer is of high importance since skin friction drag and heat transfer rates in a turbulent boundary layer can be several times higher than those of a laminar one. A lot of different strategies are used to delay or prevent the transition process. One possibility to manipulate the transition is the use of porous surfaces to influence the growth of the second mode in a passive way. The second mode or so called Mack mode is the dominant mode for the transition process at hypersonic Mach numbers [1].

Figure 1 shows the first practical result on this working field: A wind tunnel experiment of a 5° sharp cone of Rasheed [2]. The figure in the top on the right side shows transition over a smooth wall while over a porous surface a laminar flow can be seen (right side).

Figure 1: Hypersonic transition at a Mach 5 conical flow [2]

The DLR uses two simulation techniques to investigate this effect numerically: Direct numerical simulation, which is performed DLR FLOWer 4th order code that provides complete solutions for flow over and in the pores, and a stability code, called NOLOT, which is a low-cost method to predict the growth rates of the Mack Modes. Figure 2 shows a boundary layer flow at Mach 6: On the left the normal velocity over a smooth wall can be seen while the right figure shows the reduction of the Mack mode amplitude due to the pore effect by absorbing a part of the disturbance energy. This is visible by comparing the legends of both figures: The values for calculations with pores are one order of magnitude smaller.

Figure 2: DNS (contours of the normal velocity): (a) Mack mode developing above a smooth wall and (b) a porous surface with a porosity of 0.25 (16 pores) at the same time step.

For these cases (smooth wall / porous wall with 16 pores) figure 3 shows the eigenfunction shape of the perturbation calculated with DNS in comparison with the stability code NOLOT. In both cases a good agreement is visible.

Figure 3: Eigenfunction shape of the wall normal disturbance velocity: (a) smooth wall and (b) porous wall with 16 pores.

To illustrate the whole porous wall effect a movie of the boundary layer flow at Mach 6 over a porous wall with 8 pores is generated: The Mack modes are moving over the porous wall. The pores absorb a part of the disturbance energy and thus the growth of the modes can be reduced.

Figure 4

Current Activities

Within the DLR IMENS-3C project wind tunnel tests of blunt cones with and without pores are performed in two different wind tunnel facilities (the DLR HEG and H2K).

¹ Mack, L.M. : "Boundary layer linear stability theory". AGARD Special course on stability and transition of laminar flow, 1984.
² Rasheed, A., Hornung, H.G., Fedorov, A.V., Malmuth, N.D.: "Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface". AIAA Journal, Vol. 40, No. 3, pp. 481-489, 2002.

Publication and Conferences:

• Sandham, N.D., Lüdeke, H.: "A numerical study of Mach 6 boundary layer stabilization by means of a porous surface," AIAA-Journal Vol. 47, No. 9, September 2009
• Wartemann, V., Lüdeke, H., Sandham, N.D.: "Stability analysis of hypersonic boundary layer flow over microporous surfaces", 16th AIAA / DLR / DGLR International Space Planes and Hypersonic Systems and Technologies Conference, Bremen, Germany, 19-22 October 2009
• Lüdeke, H.; Wartemann, V.; Sandham, N.: "Investigation of Transition Control by Porous surfaces in Hypersonic Boundary Layers", New Results in Numerical and Experimental Fluid Mechanics VII, Vol. 112, Springer-Verlag, 2010
• Wartemann, V.; Lüdeke, H.: "Investigation of Slip Boundary Conditions of Hypersonic Flow over microporous Surfaces", V European Conference on Computational Fluid Dynamics, ECCOMAS CFD, Lisbon, Portugal, 2010
• Wartemann, V.; Lüdeke, H.; Willems, S.; Gülhan, A.: "Stability analyses and validation of a porous surface boundary condition by hypersonic experiments on a cone model", 7th Aerothermodynamics Symposium, Brugge, Belgium, 9 - 12 May, 2011