Vitaly Soudakov

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

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.

Direct numerical simulation of supersonic boundary-layer stabilization by porous coatings

Two-dimensional direct numerical simulation (DNS) of the porous coating stabilization effect is carried out for near-wall flows over a flat plate, sharp cone and compression corner at freestream Mach numbers 5-6. Numerical data obtained for disturbances propagating in the boundary layer on a flat plate agree satisfactory with the linear stability theory (LST). The coating end effects, which are associated with discontinuity of boundary conditions at the juncture between solid and porous walls, are considered. It is found that the end effects are localized over 2-3 disturbance wavelength and can be neglected in calculations of the integral performance of porous coatings. Receptivity of supersonic boundary layer to fast and slow acoustic waves is modeled. It is shown that the porous coating weakly affects acoustic disturbances and initial amplitudes of the boundary-layer modes, while it strongly suppresses the second-mode amplification. For the compression corner flow, DNS shows that the porous coating weakly affects high-frequency disturbances in the separation region and strongly stabilizes them in the reattached boundary layer downstream from the separation bubble. These numerical studies confirm robustness of the porous coating stabilization concept.

Direct Numerical Simulations of Supersonic Boundary Layer Receptivity to Acoustic Disturbances

Two-dimensional direct numerical simulation of receptivity to acoustic disturbances radiating a flat plate in 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 conducted for acoustic waves of the angles of incidence ± reveal new features of the disturbance field in the leading-edge vicinity, which may play important role in the receptivity process. It is shown that the shock wave, which is formed near the plate leading edge due to viscous-inviscid interaction, produces a profound effect on acoustic near field and receptivity. 45°

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

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.

Supersonic scattering of a wing-induced incident shock by a slender body of revolution

The lift force acting on a slender body of revolution that separates from a thin wing in supersonic flow is analysed using Prandtl-Glauert linearized theory, scattering theory and asymptotic methods. It is shown that this lift is associated with multi-scattering of the wing-induced shock wave by the body surface. The local and global lift coefficients are obtained in simple analytical forms. It is shown that the total lift is mainly induced by the first scattering. Contributions from second, third and higher scatterings are zero in the leading-order approximation. This greatly simplifies calculations of the lift force. The theoretical solution for the flow field is compared with numerical solutions of three-dimensional Euler equations and experimental data at free-stream Mach number 2. There is agreement between the theory and the computations for a wide range of shock-wave strength, demonstrating high elasticity of the leading-order asymptotic approximation. Theoretical and experimental distributions of the cross-sectional normal force coefficient agree satisfactorily, showing robustness of the analytical solution. This solution can be applied to the moderate supersonic (Mach numbers from 1.2 to 3) multi-body interaction problem for crosschecking with other computational or engineering methods.

Stability Analysis of High-Speed Boundary-Layer Flow with Gas Injection

Abstract : Stability analyses of high-speed boundary-layer flow past a 5 deg half angle sharp cone with the wall-normal injection of air through a porous strip are performed using Navier-Stokes solutions for the mean flow and linear stability theory. The configuration and free-stream parameters are chosen to be similar to the experiments, which were carried out at Caltechs T5 shock tunnel to investigate the effect of CO2 injection on laminar-turbulent transition. The analysis is focused on pure aerodynamic effects in the framework of perfect gas model. It is shown that the injection leads to destabilization of the Mack second mode in the nearfield relaxation region and its stabilization in the far-field relaxation region. To reduce the destabilization effect it was suggested to decrease the injector surface slope or use suction blowing of zero net injection. However, the eN computations showed that these modifications did not improve the injector performance in the near-filed region in general. For special cases of low injection rates in which the N-factors in the near field region are below the critical level, shaping can produce a significant stabilization in the mid- and far-field regions.

Investigations of laminar-turbulent transition on a sharp cone with localized heating or cooling in high-spee d flow

A localized heating or cooling effect on stability and transition of the boundary layer flow on a sharp cone at zero angle of attack at the free -stream Mach number 6 is analyzed using the linear stability theory. Three different locati ons of the heating/cooling strip are considered. The steady-state laminar flow solution is calculated using the axisymmetric Navier-Stokes equations to provide the mean flow fi eld. The spatial stability analysis is performed for two-dimensional disturbances associated with the Mack first and second modes. The transition onset points are estimated us ing the e N method. In this framework, the heating/cooling effect on the transition onset is i nconclusive. The heater (or cooler) may cause earlier or later transition depending on the choice of critical N-factor. Direct numerical simulations and experiments are needed to clarify this situation.

Numerical and theoretical modeling of supersonic boundary-layer receptivity to temperature spottiness

A two-dimensional direct numerical simulation (DNS) of receptivity of a flat-plate boundary layer to temperature spottiness in Mach 6 free stream is carried out. The influence of spottiness parameters to the receptivity process is studied. It is shown that the temperature spots propagating near the upper boundary-layer edge generate mode F. Further downstream mode F is synchronized with unstable mode S (Mack second mode) and excites the latter via the inter-modal exchange mechanism. A theoretical model describing the excitation of mode F by the temperature spots is developed 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 shows that this mechanism provides the instability amplitudes an order of magnitude higher than in the case of receptivity to the temperature spots themselves.

Theoretical Modeling of Two-Body Interaction in Supersonic Flow

Atmospheric and space launch stage separation depends on the aerodynamic interference between separating bodies. Quick means of estimating and controlling repulsion or attraction lift associated with this interaction are an important enabling technology to achieve the best compromise between launch separation rocket motor weight and safe staging. Asymptotic methods, scattering, and slender-body theories are used to obtain systematic approximation schemes that advantageously couple with computational methods. Theoretical solutions for the lift interference between two bodies in supersonic flow agree well with numerical solutions. The theory sheds light on important scattering phenomena not previously recognized as relevant to this problem. The analysis helps to identify lumped dimensionless parameters and provides scaling laws as well as closed-form expressions for the interference not accessible solely from computations. These results can be used for interpolation and extrapolation of computational fluid dynamics solutions as well as efficient testing and design of flight vehicles.

Modeling of plasma flow control over a high-speed delta wing

†‡ Numerical modeling of vortex flow over a delta wing with sharp leading edges of 60 ο sweep angle has been performed at free-stream Mach number 1.5 and angles of attack from 0 ο to 30 ο . The flow field contains two strong vortices generated by the rollup of the shear layer emanating from the wing leading edges. Large radial and axial velocities of these primary vortices reduce pressure on the leeside wing surface that may affect the wing aerodynamic performance. Numerical solutions of 3-D Navier-Stokes equations are consistent with available experimental and numerical data. Detailed parametric study has been performed to estimate feasibility of the vortex flow control using the surface barrier discharge (SBD) actuators: the wing-apex SBD, the leading-edge SBD and the multi-element SBD. Heat and momentum forcing produced by these actuators is modeled by analytical approximations of volumetric force and heat distributions. It was shown that the vortex breakdown locus can be controlled by the aforementioned SBD actuators. However this weakly affects the integral aerodynamic forces (lift and drag). Numerical simulations of unsteady flow field indicate that the vortex breakdown evolves with time. This unsteady behavior is sensitive to the SBD forcing. Nevertheless, appreciable migrations of the vortex burst produce small effect on the lift coefficient.