The key issues hindering the prediction and control of hypersonic transition are (a) insufficient understanding of the underlying instability mechanisms and their interactions, (b) poorly characterized receptivity and initial conditions, and (c) lack of fundamental validation data. We address these issues with a three-pronged research approach that (1) extends the theoretical framework to include relevant hypersonic phenomena, (2) provides needed validation data and (3) builds methodologies for prediction and control.
Objective 1: Framework Enhancement. We will seek to extend the existing analytical framework to include relevant hypersonic flow physics, including nonequilibrium thermochemistry, thin shock layers, entropy layer, surface chemistry and ablation. These effects modify Mack’s (1984) original formulation of linear stability theory for hypersonic flow, and must be included in physics-based transition models. The enhanced framework will include relevant computational tools from the linear stability theory (LST) to linear and nonlinear parabolized stability (PSE/NPSE) equations to direct numerical simulation (DNS). The outcome will be the identification of dominant instability mechanisms in all regions of the hypersonicflight parameter space and the competition and interaction between these mechanisms.
Objective 2: Foundational Experiments. Coordinating with theoretical and simulation development needs, we will perform a comprehensive set of hypersonic stability experiments to map the hypersonic transition parameter space. We will establish a comprehensive database of mechanisms and growth rates as functions of body geometry, angle of attack, edge Mach number, Reynolds number, surface temperature and surface roughness in quiet flow. The outcome will be the first comprehensive experimental database aimed at validating the broad theoretical framework, a description of the parameter-space boundaries between transition regimes, and the identification of regions with significant interactions between competing mechanisms. With this foundation established, experimental work will proceed in parallel with theory and simulation to consider receptivity, linear and nonlinear mode interactions and breakdown to turbulence. Nonequilibrium effects on all these processes will be considered.
Objective 3: Control Strategies. Using the enhanced theoretical framework, we will seek to develop effective transition control strategies for hypersonic flight. Because of the harsh environment and high frequencies associated with hypersonic flows, the emphasis will be on passive control concepts that could be flight tested in the near term. Possibilities include ultrasonic absorptive coatings for the second mode, distributed roughness elements for crossflow, and passively stable configurations. The outcomes will be advances in these passive control strategies and an assessment of the model fidelity required for control application design.
Figure 1: Hypersonic transition schematic: process (middle), modifiers (bottom), research tools, and lead PI (top).
The research tools and team personnel that will achieve these objectives are shown above in Fig. 1. This figure depicts the transition process from receptivity to linear and nonlinear growth to breakdown and turbulence along a notional hypersonic cone. Physical processes that can potentially modify transition plus the possibility for transition control are indicated along the bottom of the figure. Current knowledge about hypersonic stability and transition is mostly confined to the “Linear Growth” block. The work proposed here will use the methodologies employed by personnel identified along the top of the figure to expand current knowledge across the transition process from receptivity to breakdown along with the identified stability modifiers for both axisymmetric configurations and at angle of attack. There is intentionally significant overlap between the various computational and experimental tools. Areas of overlap will foster synergistic efforts between theory, experiments and simulations and will lead to a comprehensive understanding of hypersonic transition process and methods for hypersonic transition control.
Considerable uncertainty exists regarding hypersonic flow transition due to the dearth of reliable experiments. The paper by Mack (1984) regarding the linear stability of compressible boundary layers remains the most complete description available. Mack’s analysis of ideal-gas high-speed flows considers the “Linear Growth” region of Fig. 1. Mack’s model describes three major differences between supersonic and subsonic flow: the presence of a generalized inflection-point, the dominance of 3-D viscous disturbances, and the presence of high-frequency acoustic modes now named Mack modes. The dominance of 3-D viscous disturbances refers to the fact that at supersonic speeds, the 2-D viscous disturbances called Tollmien–Schlichting (TS) waves at lower speeds are not the most unstable viscous disturbances. Instead, oblique disturbances of the same general family are most amplified. These are called first-mode disturbances.
The acoustic instability discovered by Mack arises when the edge velocity is sufficiently fast that disturbances can propagate downstream at a subsonic speed relative to the boundary-layer edge velocity but supersonic relative to the wall. Such disturbances are inviscid acoustic waves that reflect between the solid wall and the relative sonic line. The lowest-frequency Mack mode, the so-called “second mode” becomes more unstable than the first mode for freestream Mach numbers above about 4. Whereas the first mode is stabilized by wall cooling, the second mode is destabilized via a decrease in the local sound speed and associated increase of the local relative Mach number. Accordingly, factors affecting the thermal boundary layer are critical to understanding the second-mode. The second mode is found in the experiments of Kendall (1975), Demetriades (1977), and Stetson et al. (1984). Beyond these experiments, there has never been a systematic effort to validate Mack’s predictions or to investigate the conditions (roughness, bluntness, angle of attack, wall cooling, chemistry effects etc.) at which the first mode, second mode, transient growth or crossflow dominate transition.
Beyond the additional Mack modes, hypersonic stability analyses are complicated for other reasons. (1) At hypersonic speeds, the ideal-gas assumption is invalid because certain molecular species dissociate due to aerodynamic heating and, in some instances, too few intermolecular collisions occur to support local chemical equilibrium. Additionally, earlier work by Stuckert and Reed 1994 and Lyttle and Reed (2005) shows that equilibrium and various nonequilibrium stability solutions can differ significantly, because of their influence on the thermal boundary layer. (2) The bow shock is close to the edge of the boundary layer and affects transition via the production of an entropy layer. Additionally, the finite shock thickness can be important and this suggests a PSE or DNS simulation approach is required. (3) Surface ablation can have a significant effect on stability via the introduction of roughness, varying surface properties, and localized blowing, all of which affect the thermal and/or momentum boundary layers. (4) The flow is highly 3-D in the neighborhood of drag flaps or fins, or when at angle of attack. 3-D boundary layers are susceptible to crossflow which must be included in determining the appropriate transition physics. Crossflow is ultra sensitive to roughness and freestream disturbances, and leads to important nonlinear effects across much of the transition zone.
It is clear that further theoretical, computational and experimental work on hypersonic transition must be a joint effort that properly identifies and validates flow and chemistry models and the fundamental transition mechanisms. Careful, well documented validation experiments at flight conditions are very much needed. Quiet wind tunnels are needed because conventional facilities can suggest trends opposite to flight and available flight data are sparse and uncertain.
In light of this, our approach derives from the NASA Transition Study Group guidelines (Reshotko 1975). Reshotko describes the need for foundational transition research that couples theoretical understanding to experiments using simple geometries in multiple facilities (preferably quiet wind tunnels) with overlapping parameter ranges. It is our intent that the work proposed here be a culmination of the research vision articulated by the Transition Study Group in 1975 with appropriate updates for current knowledge and computational tools.