Numerical Simulation of Hypersonic Flows

The following special section is based on a series of invited papers that were presented at the AIAA 21st Computational Fluid Dynamics Conference held in June 2013 at San Diego, California. The session included a variety of papers on the subject of simulation of hypersonic flows, ranging from more fundamental papers on numerical methods and physical models to applied papers showing recent results in hypersonic flowprediction.From thosepapers, a subsetwas chosen for inclusion in this special issue. In addition, two other papers have been added that extend and expand the scope of the special section. It is hoped that these papers will serve to show where challenges in adequately simulating hypersonic flow exist and where progress is being made. Understanding these numerical challenges requires knowing the key issues and characteristics of hypersonic flow, including the five characteristics where hypersonic flow is differentiated from supersonic flow [1]: 1) thin shock layers, 2) entropy layers, 3) viscous–inviscid interactions, 4) high-temperature effects and extreme heat transfer, and 5) low-density flows. Each of these characteristics leads to challenging numerical issues, such as appropriate methods, inclusion of nonequilibrium flow chemistry, transition modeling, grid generation, and many others. In fact, you only need to look at the typical assumptions made when deriving the equations of fluid motion to understand why hypersonic flow prediction has beenmore difficult than lower speed simulations. Typically, the equations solved by computational fluid dynamics (CFD) programs are based on the assumptions that the fluid is a continuum, that the perfect gas law applies, and that the only forces are due to pressure, viscous effects, and (typically neglected) body forces. Although the continuum assumption can invalidate the equations for rarefied gas flows at high altitudes when the mean free path of the fluid molecules is on the order of the length of the vehicle, the other assumptions can lead to additional difficulties. These problem areas are due to the complex flow features that can occur in hypersonic flow, as listed herein and also discussed in greater detail in [2–4]. Figure 1 shows many of these fluid dynamic challenges in a computation for the Hyper-X vehicle at M∞ 7: The shock layer coming from the forebody remains very close to the vehicle surface for a large distance down the body length; various shock–shock and shock–boundary-layer interactions occur in the vicinity of the ramp inlet; flow interactions with the engine exhaust and lower surface body contouring create a complex flowfield under the back half of the vehicle; all of this could take place at flight conditions where chemical reactions are important to the results. Many other researchers have outlined the various challenges in accurately predicting hypersonic flow. For example, Cheng, expanding on the difficulties inpredicting viscous/inviscid interactions, stated that [5], “the fluid dynamics of hypersonic flows is complicated by the interaction of the boundary layer and the shear layer with shockwaves, leading to flow separation and instability not amenable to straightforward analysis.” Longo believes that the key issues for CFD related to hypersonic aerodynamic design, such as real gas effects, heating, turbulence, and viscous interactions, have been poorly (or at best moderately) modeled by CFD [6]. From a simulation perspective, Longo et al. showed that at least five factors affect the accuracy of flow predictions for reentry vehicles [7]: 1) adequate grid density, 2) modeling equilibrium or nonequilibrium flows, 3) modeling transition, 4) modeling turbulence, and 5) accurately modeling the vehicle geometry (especially in regions of shock interactions). They believed that, although it was possible for CFD to accurately predict the aerodynamic environment of hypersonic vehicles (including surface pressures and forces/moments), CFD has been severely limited in accurately predicting the aerothermodynamic environment of these vehicles. Finally, Weiland et al. added to the list of challenges with local aerothermodynamic flows (such as flows in deflected flaps and rudders or in gaps between tiles), high-enthalpy flows (including radiation cooling), wall catalycity, turbulence modeling, and jet/ airflow interaction [8]. In spite of all these challenging issues, Mehta believes that CFDwill be as important as ground and flight testing in the development of future hypersonic flight vehicles [9]. However, to achieve this goal, a great deal of work remains to be done to improve computational simulations of high-speed flows, which is the motivation for this special section of the Journal of Spacecraft and Rockets. The special section begins with three papers that discuss various numerical and modeling issues key to hypersonic flow prediction. The first paper, by Graham Candler and Pramod Subbareddy of the University of Minnesota, is titled “Advances in CFD Methods for Hypersonic Flows.” This paper discusses the state of the art in numerical methods and flow modeling, including various upwind and low-dissipation schemes, higher ordermethods, time integration, and equilibrium and nonequilibrium chemistry modeling. The next paper is “Hypersonic Stability and Transition Prediction” by Helen Reed et al. of Texas AM accepted for publication 1 May 2014; published online 19 January 2015. *Professor andHead,Department of Aeronautics. Associate FellowAIAA.