High-speed Boundary-layer Flows Research Articles

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.

LES wall modeling for heat transfer at high speeds

Temperature transformation does not collapse data, but the resulting wall model accurately predicts temperatures in high-speed boundary layer flows. Here we explain why this is so. The insights gained lead to a new turbulent Prandtl number formulation and more accurate wall models.

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans- or supercritical with respect to the pseudo-critical temperature, $T_{pc}$. When transitioning from sub- to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub- and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to $T_{pc}$ and the higher the Eckert number. In the transcritical case, when the temperature profile crosses $T_{pc}$, the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack’s second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans- and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.

Secondary instabilities of Görtler vortices in high-speed boundary layer flows

Görtler vortices developed in laminar boundary layer experience remarkable changes when the flow is subjected to compressibility effects. In the present study, five $\mathit{Ma}$ numbers, covering incompressible to hypersonic flows, at $\mathit{Ma}=0.015$, 1.5, 3.0, 4.5 and 6.0 are specified to illustrate these effects. Görtler vortices in subsonic and moderate supersonic flows ($\mathit{Ma}=0.015$, 1.5 and 3.0) are governed by the conventional wall-layer mode (mode W). In hypersonic flows ($\mathit{Ma}=4.5$, 6.0), the trapped-layer mode (mode T) becomes dominant. This difference is maintained and intensifies downstream leading to different scenarios of secondary instabilities. The linear and nonlinear development of Görtler vortices which are governed by dominant modal disturbances are investigated with direct marching of the nonlinear parabolic equations. The secondary instabilities of Görtler vortices set in when the resulting streaks are adequately developed. They are studied with Floquet theory at multiple streamwise locations. The secondary perturbations become unstable downstream following the sequence of sinuous mode type I, varicose mode and sinuous mode type II, indicating an increasing threshold amplitude. Onset conditions are determined for these modes. The above three modes can each have the largest growth rate under the right conditions. In the hypersonic cases, the threshold amplitude $A(u)$ is dramatically reduced, showing the significant impact of the thermal streaks. To investigate the parametric effect of the spanwise wavenumber, three global wavenumbers ($B=0.5$, 1.0 and $2.0\times 10^{-3}$) are specified. The relationship between the dominant mode (sinuous or varicose) and the spanwise wavenumber of Görtler vortices found in incompressible flows (Li &amp; Malik, J. Fluid Mech., vol. 297, 1995, pp. 77–100) is shown to be not fully applicable in high-speed cases. The sinuous mode becomes the most dangerous, regardless of the spanwise wavelength when $\mathit{Ma}&gt;3.0$. The subharmonic type can be the most dangerous mode while the detuned type can be neglected, although some of the sub-dominant secondary modes reach their peak growth rates under detuned states.

Prediction and Control of Laminar-turbulent Transition in High-speed Boundary-Layer Flows

Issues related to prediction of laminar-turbulent transition on hypersonic configurations in high-altitude flight are discussed. The laminar flow control strategy and appropriate laminarization methods for high-speed vehicles are reviewed. The paper is aimed to motivate the transition study groups to integrate their knowledge and tools in the rational framework of the amplitude method. This may help to coordinate efforts focused on different aspects of the transition problem and improve our transition-prediction and laminar-flow-control capabilities on a solid physics-based foundation.

Flow Structures and Heating Augmentation Around Finite-Width Cavity in Hypersonic Flow

Cavities significantly affect the heating of bodies in hypersonic flows. Previous studies have shown that boundary-layer flows can enter the interior of shallow cavities and augment heating. In this study, the three-dimensional flow structure induced by a finite-width rectangular cavity was revealed in compressible Navier–Stokes simulations. A finite-width rectangular cavity was found to encourage downwash into the cavity, and a pair of counter-rotating longitudinal vortices was established in the wake region of the cavity. The downwash draws high-speed boundary-layer flow into the cavity and augments the heating on the cavity floor. The high-speed flow impinges on the cavity endwall and causes local peak heating. Slowly dissipating longitudinal vortices are produced that generate long streaky hot regions in the wake. The heating augmentation induced by deep or narrow cavities is less than in shallow and wide cavities owing to the insignificant amount of high-speed flow entering the cavity.

Transition and Stability of High-Speed Boundary Layers

This article reviews stability and laminar-turbulent transition in high-speed boundary-layer flows, emphasizing qualitative features of the disturbance spectrum leading to new mechanisms of receptivity and instability. It is shown that the extension of subsonic and low-supersonic stability concepts and transition prediction methods to hypersonic speeds is not straightforward. The discussion focuses on theoretical models providing insights into the physics of instability and helping make proper decisions on transition control strategies.

On simulation and analysis of instability and transition in high-speed boundary-layer flows

The simulation of instabilities and laminar-trubulent transition in high-speed boundary-layer flows represents one of the major computational challenges of the decade. By taking advantage of recent advances in computational science and instability theory for compressible flows, we have formulated an approach to this problem that combines parabolized stability equation (PSE) methodology with spatial direct numerical simulation (DNS). The relatively inexpensive PSE method is used to explore the parameter space, to compute the early (weakly and moderately nonlinear) stages of laminar breakdown, and to provide inflow conditions for the spatial DNS, which is then used to compute the highly nonlinear laminar-breakdown stage. The approach is made feasible by an accurate and efficient DNS algorithm, which has been implemented in parallel on a CRAY C90 supercomputer. The design of the DNS algorithm is discussed in detail, with emphasis on factors that affect both accuracy and efficiency. The method is applied to the investigation of the laminar breakdown of the boundary layer on an axisymmetric sharp cone in Mach 8 flow. Techniques for analysis of the resulting data are also addressed, including novel computational flow imaging procedures.

Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow

The laminar breakdown of the boundary-layer flow of an axisymmetric sharp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial direct numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinear interactions generate strong streamwise vorticity, which leads in turn to severe spanwise variations in the flow and eventual laminar breakdown. The PSE method is used to compute the weakly and moderately nonlinear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlinear and laminar-breakdown stages of transition are then computed by well-resolved DNS, with a highly accurate algorithm that exploits spectral collocation and high-order compact-difference methods. Evolution of the flow is presented in terms of modal energies, mean quantities (e.g., skin friction), Reynolds stresses, turbulent kinetic energy, and flow visualization. The numerical test case is an approximate computational analog of one of the few stability experiments performed for hypersonic boundary-layer flows. Comparisons and contrasts are drawn between the experimental and the computational results. “Rope-like” waves similar to those observed in schlieren images of high-speed transitional flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.

Spatial direct numerical simulation of high-speed boundary-layer flows part I: Algorithmic considerations and validation

A highly accurate algorithm for the direct numerical simulation (DNS) of spatially evolving high-speed boundary-layer flows is described in detail and is carefully validated. To represent the evolution of instability waves faithfully, the fully explicit scheme relies on non-dissipative high-order compact-difference and spectral collocation methods. Several physical, mathematical, and practical issues relevant to the simulation of high-speed transitional flows are discussed. In particular, careful attention is paid to the implementation of inflow, outflow, and far-field boundary conditions. Four validation cases are presented, in which comparisons are made between DNS results and results obtained from either compressible linear stability theory or from the parabolized stability equation (PSE) method, the latter of which is valid for nonparallel flows and moderately nonlinear disturbance amplitudes. The first three test cases consider the propagation of two-dimensional second-mode disturbances in Mach 4.5 flat-plate boundary-layer flows. The final test case considers the evolution of a pair of oblique second-mode disturbances in a Mach 6.8 flow along a sharp cone. The agreement between the fundamentally different PSE and DNS approaches is remarkable for the test cases presented.

Direct numerical simulation and data analysis of a Mach 4.5 transitional boundary-layer flow

This paper describes the creation by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations of a high quality data set that represents the laminar–turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang [Theoret. Comput. Fluid Dyn. 3, 345 (1992)], and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along the exterior of a hollow cylinder is simulated numerically. From a perturbed laminar initial state, the well-resolved simulation proceeds through laminar breakdown to the beginning of a turbulent flow regime. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy ‘‘budgets’’ are also constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production, dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure–dilatation term is of the same order of magnitude as the compressible dissipation rate. The authors hope that both the data set and the analysis presented will benefit those who attempt to model high-speed transitional flow.