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Localized Flow Heating for Wave-Drag Reduction at Supersonic Speeds

Background

It is well known that external localized flow heating upstream of supersonic blunt bodies can help to reduce their wave drag and to save the thrust required for a supersonic flight. Regardless of numerous investigations published in the last decades to this topic, an unambiguous statement about the real potential of the thermal effect of energy addition (EA) is missing up to now. Impressive quantitative discrepancies in the effects indicated experimentally and numerically are the reason for that. In the framework of the investigations running at the department this question should be addressed experimentally and numerically.

Results

Fig. 1: Effect of localized flow heating upstream of the 45°-cone model at Mach 5 (Schülein & Zheltovodov (2011)), cases without EA (shadowgram left) and with a 2.3kW DC-arc discharge (shadowgram right) (1 - bow shock wave, 2 - heated wake, 3 - oblique shock wave induced, 4 - recirculation bubble)

Experiments with the localized flow heating by a low-voltage DC-arc discharge were conducted in the Ludwieg Tube Facility at DLR Göttingen at Mach numbers of 3 and 5. Simple hemisphere- and cone-cylinder models were used in the experimental and numerical tests. The cone half-angle was varied between 35° and 65° in order to quantify the effect of the shock intensity at a given heating rate. Additionally, the electric power, introduced by DC-arc for flow heating at an upstream distance of 3.7 model diameters, was varied in the order to indicate the heating power effect at constant shock-wave intensity. To determine the pure heating power added to the flow by the arc-discharge the steady DC-arc theory was applied.
Numerical computations were carried out using the DLR TAU Code, which is a hybrid grid finite volume compressible RANS solver developing at DLR. The test cases with and without EA were simulated as 2-D axisymmetric viscous real-gas flows using the Menter SST (Shear Stress Transport) turbulence model.
Numerical and experimental results demonstrate in good agreement that a distinct wave-drag reduction could be achieved when an overcritical total-pressure deficit in the thin heated wake behind the energy deposition zone is existent. This deficit leads to the emergency of a free recirculation bubble in the front of the blunt body (so-called „thermal-spike“ effect) and thus to the favourable transformation of the bow-shock structure and to wave-drag reduction. The maximal effectiveness of EA appears at the heating power amount minimal needed for the full-scale recirculation bubble in the front of the body. In this case the saved thrust power, e.g. for the 55°-cone at Mach 3, was found to be about a 180-fold added heating power (lossless calculation) or 38-fold introduced electrically in the experiments by the DC-arc discharge. The optimal (critical) heating power is dependent on the bow-shock intensity and lies for blunt bodies investigated between 30% and 60% of the energy flux in the incoming flow through the cross-sectional area of the energy source (DC-arc). The further increase of the heating power leads to a lower effectiveness of energy addition.

Publications on this topic

• Schülein E. , Zheltovodov A.A. (2009) “Effects of Localized Flow Heating by DC-Arc Discharge Ahead of Non-Slender Bodies”, AIAA Paper 2009-7346, 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference,  19 – 22 October 2009, Bremen (Germany), 15p
• Schülein E., Zheltovodov A.A., Pimonov E.A. and Loginov M.S. (2010) “Experimental and Numerical Modeling of the Bow Shock Interaction with Pulse-Heated Air Bubbles“, International Journal of Aerospace Innovations, Vol. 2 (3), pp.165-187. Multi-Science Publishing Co., UK. ISSN 1757-2258
• Schülein E. , Zheltovodov A.A. (2011) “Effects of Localized Flow Heating by DC-Arc Discharge Upstream of Non-Slender Bodies”, Shock Waves, DOI 10.1007/s00193-011-0307-1 (Published online at http://www.springerlink.com), 15p
• Schülein E. , Bornhöft E. (2011) “Potential of Localized Flow Heating“, ISSW28, 28th International Symposium on Shock Waves, 17. - 22. July 2011, Manchester (UK)