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.

Transition and Stability of High-Speed Boundary Layers

The prediction of the laminar-turbulent transition of boundary layers is critically important to the development of hypersonic vehicles because the transition has a first-order impact on aerodynamic heating, drag, and vehicle operation. The success of transition prediction relies on a fundamental understanding of the relevant physical mechanisms. In the 20 years since the review by Kleiser & Zang (1991) on the direct numerical simulation (DNS) of the boundary-layer transition, significant progress has been made on DNS in the hypersonic flow regime and in the spatial DNS approach. Many high-order shock-capturing and shock-fitting finite-difference methods have been developed and extensively applied to numerical simulations of the hypersonic boundary-layer transition. DNS has become a powerful research tool and has led to discoveries of new transition mechanisms. This article reviews the recent progress of DNS on hypersonic boundary-layer receptivity, instability, and transition. The current status and future directions are also presented.

http://cfdhost.seas.ucla.edu/papers/2012/Zhong-X-2012-annurev-fluid-120710-101208.pdf

Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers

The discrete spectrum of disturbances in high-speed boundary layers is discussed with emphasis on singularities caused by synchronization of the normal modes. Numerical examples illustrate different spectral structures and jumps from one structure to another with small variations of basic flow parameters. It is shown that this singular behavior is due to branching of the dispersion curves in the synchronization region. Depending on the locations of the branch points, the spectrum contains an unstable mode or two. In connection with this, the terminology used for instability of high-speed boundary layers is clarified. It is emphasized that the spectrum branching may cause difficulties in stability analyses based on traditional linear stability theory and parabolized stability equations methods. Multiple-mode considerations and direct numerical simulations are needed to clarify this issue.

High-Speed Boundary-Layer Instability: Old Terminology and a New Framework

Three-dimensional spatially growing perturbations in a two-dimensional compressible boundary layer are considered within the scope of linearized Navier{Stokes equations. The Cauchy problem is solved under the assumption of a flnite growth rate of the disturbances. It is shown that the solution can be presented as an expansion into a biorthogonal eigenfunction system. The result can be utilized for decomposition of ∞ow flelds derived from computational studies when pressure, temperature, and all the velocity components, together with some of their derivatives, are available. The method can be used also if partial data are available when a priori information may be utilized in the decomposition alogorithm. Properties of the discrete spectrum for a boundary layer over a cone with an adiabatic wall at the edge Mach number 5.6 is explored. It is shown that the synchronism of the slow discrete mode with acoustic waves at a low frequency or a low Reynolds number is primarily two-dimensional. At high angles of disturbance propagation, the fast discrete mode is no longer synchronized with entropy and vorticity modes.

Three-dimensional spatial normal modes in compressible boundary layers

Developing mechanism-based methods for estimating hypersonic boundary-layer transition in flight: The role of quiet tunnels

Two-dimensional direct numerical simulation (DNS) of receptivity to acoustic disturbances radiating onto a flat plate with a sharp leading edge in the Mach 6 free stream is carried out. Numerical data obtained for fast and slow acoustic waves of zero angle of incidence are consistent with the asymptotic theory. Numerical experiments with acoustic waves of non-zero angles of incidence reveal new features of the disturbance field near the plate leading edge. The shock wave, which is formed near the leading edge owing to viscous–inviscid interaction, produces a profound effect on the acoustic near field and excitation of boundary-layer modes. DNS of the porous coating effect on stability and receptivity of the hypersonic boundary layer is carried out. A porous coating of regular porosity (equally spaced cylindrical blind micro-holes) effectively diminishes the second-mode growth rate in accordance with the predictions of linear stability theory, while weakly affecting acoustic waves. The coating end effects, associated with junctures between solid and porous surfaces, are investigated.

Receptivity of a hypersonic boundary layer over a flat plate with a porous coating

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

Ultrasonically absorptive coatings (UAC) can suppress the second-mode instability in hypersonic boundary layer and thereby delay laminar-turbulent transition. Theory and numerical simulations indicate that this stabilization effect essentially depends on the UAC thickness. It is expected that optimal coatings may be several times thinner than it was assumed before. To validate these findings, the UAC thickness effect is investigated on a sharp cone in the Mach=6 wind tunnel. The coatings comprise several layers of a stainless still wire mesh. Their microstructure mimics textile materials frequently used for thermal protection. The wall-pressure disturbances are measured upstream and downstream from the coated region. It is shown that the coatings stabilize the second mode and its higher harmonics in accord with the UAC laminarization concept. The experimental growth rates are compared with predictions of the linear stability theory and direct numerical simulations of 2D disturbances. It is found that an optimal coating is approximately five times thinner than UAC tested in previous experiments. This may facilitate manufacturing and integration of UAC into actual thermal protection systems.

Stabilization of High-Speed Boundary Layer Using Porous Coatings of Various Thicknesses

Abstract Two-dimensional direct numerical simulation (DNS) of the receptivity of a flat-plate boundary layer to temperature spottiness in the Mach 6 free stream is carried out. The influence of spottiness parameters on the receptivity process is studied. It is shown that the temperature spots propagating near the upper boundary-layer edge generate mode F inside the boundary layer. Further downstream mode F is synchronized with unstable mode S (Mack second mode) and excites the latter via the inter-modal exchange mechanism. Theoretical assessments of the mode F amplitude are made using the biorthogonal eigenfunction decomposition method. The DNS results agree with the theoretical predictions. If the temperature spots are initiated in the free stream and pass through the bow shock, the dominant receptivity mechanism is different. The spot–shock interaction leads to excitation of acoustic waves, which penetrate into the boundary layer and excite mode S. Numerical simulations show that this mechanism provides the instability amplitudes an order of magnitude higher than in the case of receptivity to the temperature spots themselves.

/pdf/receptivity-of-a-high-speed-boundary-layer-to-temperature-3u1mel7muc.pdf

Receptivity of a high-speed boundary layer to temperature spottiness

A localized heating or cooling effect on stability of the boundary-layer flow on a sharp cone at zero angle of attack and freestream Mach number 6 is analyzed. Experiments were carried out in the Transit-M wind tunnel of the Institute of Theoretical and Applied Mechanics (Novosibirsk, Russia) for different heating/cooling intensities and freestream Reynolds numbers. The mean flows with localized heating/cooling are calculated using axisymmetric Navier–Stokes equations. These solutions are used for the spatial linear stability analysis to estimate the transition onset points using the eN method. Direct numerical simulations of two-dimensional disturbances propagating in the boundary layer through the cooled/heated region are performed. The experiment and computations showed similar qualitative trends. The localized cooling decreases the second-mode amplitude and delays transition. The heating produced an opposite effect, which is less pronounced.

Vitaly Soudakov

Papers

Receptivity of a hypersonic boundary layer over a flat plate with a porous coating

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

Stabilization of High-Speed Boundary Layer Using Porous Coatings of Various Thicknesses

Receptivity of a high-speed boundary layer to temperature spottiness

High-Speed Boundary-Layer Stability on a Cone with Localized Wall Heating or Cooling