Institute of Theoretical and Applied Mechanics

The three-dimensional resonant interaction of a plane Tollmien-Schlichting wave, having a frequency f 1 , with a pair of oblique waves having frequencies ½ f 1 , was observed and studied experimentally. In the initial stages, the interaction proved to be a parametric resonance, resulting in the amplification of small random priming (background) oscillations of frequency ½ f 1 , and of a packet of low-frequency oscillations. The resonant interaction of waves in a boundary layer was investigated also by introducing a priming oscillation with frequency f ’ = ½ f 1 + Δ f for different values of the frequency detuning Δ f . The importance of the discovered wave interaction in boundary-layer transition is demonstrated. Causes of realization of different types of laminar-flow breakdown are discussed.

The modification of the mean and fluctuating characteristics of a flat-plate boundary layer subjected to nearly isotropic free stream turbulence (FST) is studied experimentally using hot-wire anemometry. The study is focussed on the region upstream of the transition onset, where the fluctuations inside the boundary layer are dominated by elongated flow structures which grow downstream both in amplitude and length. Their downstream development and scaling are investigated and the results are compared with those obtained by previous authors. This allows some conclusions about the parameters which are relevant for the modelling of the transition process. The mechanisms underlying the transition process and the relative importance of the Tollmien–Schlichting wave instability in this flow are treated in an accompanying paper (part 2 of the present report).

The electrostatic interaction of a system of two single dust particles in a plasma-sheath environment with flowing ions has been investigated quantitatively. It is shown that attractive net ``binding'' forces between the negatively charged particles exist, leading to the formation of a dust molecule. By laser manipulation of the dust particles, it is demonstrated that the attraction is asymmetric in such a way that it acts only on one of the particles. Moreover, the net forces between the particles can be reversibly changed between attraction and repulsion.

Experimental and theoretical studies of the effect of an ultrasonically absorptive coating (UAC) on hypersonic boundary-layer stability are described. A thin coating of fibrous absorbent material (felt metal) was selected as a prototype of a practical UAC. Experiments were performed in the Mach 6 wind tunnel on a $7^{\circ}$ half-angle sharp cone whose longitudinal half-surface was solid and other half-surface was covered by a porous coating. Hot-wire measurements of ‘natural’ disturbances and artificially excited wave packets were conducted on both solid and porous surfaces. Stability analysis of the UAC effect on two- and three-dimensional disturbances showed that the porous coating strongly stabilizes the second mode and marginally destabilizes the first mode. These results are in qualitative agreement with the experimental data for natural disturbances. The theoretical predictions are in good quantitative agreement with the stability measurements for artificially excited wave packets associated with the second mode. Stability calculations for the cooled wall case showed the feasibility of achieving a dramatic increase of the laminar run using a thin porous coating of random microstructure.

▪ Abstract Recent considerable progress in the field of rarefied hypersonic computational fluid dynamics (CFD) gives reason to address its evolution to an independent CFD branch that covers many fundamental and closely related applied problems of high-altitude aerothermodynamics of space vehicles. The primary purpose of this review is to describe the main numerical methods and real gas models for investigation of problems of rarefied hypersonic flows, and to review results that we believe demonstrate most clearly the achievements and capabilities of the field of rarefied hypersonic CFD in the last years.

Well-resolved large-eddy simulations (LES) are performed in order to investigate flow phenomena and turbulence structure of the boundary layer along a supersonic compression ramp. The numerical simulations directly reproduce an available experimental result. The compression ramp has a deflection angle of $\beta\,{=}\,25^\circ$ . The mean free-stream Mach number is $M_\infty\,{=}\,2.95$ . The Reynolds number based on the incoming boundary-layer thickness is $Re_{\delta_0}\,{=}\,63\,560$ in accordance with the reference experiment. These simulations overcome deficiencies of earlier direct numerical simulations (DNS) and LES in terms of ramp-deflection angle, Reynolds number and spanwise size of the computational domain which is required for capturing the essential flow phenomena. The filtered conservation equations for mass, momentum and energy are solved with a high-order finite-difference scheme. The effect of subgrid scales is modelled by the approximate deconvolution model. About $18.5\,{\times}\,10^6$ grid points are used for discretizing the computational domain. To obtain mean flow and turbulence structure the flow is sampled 1272 times over 703 characteristic time scales of the incoming boundary layer. Statistical data are computed from these samples. An analysis of the data shows good agreement with the experiment in terms of mean quantities such as shock position, separation and reattachment location, skin-friction and surface-pressure distributions, and turbulence structure. The computational data confirm theoretical and experimental results on fluctuation amplification across the interaction region. In the wake of the main shock a shedding of shocklets is observed. The temporal behaviour of the coupled shock–separation system agrees well with experimental data. Unlike previous DNS the present simulation data provide indications of a large-scale shock motion. Also, evidence for the existence of three-dimensional large-scale streamwise structures, commonly referred to as Görtler-like vortices, is found.

Microwave tomographic imaging is one of the new technologies which has the potential for important applications in medicine. Microwave tomographically reconstructed images may potentially provide information about the physiological state of tissue as well as the anatomical structure of an organ. A two-dimensional (2-D) prototype of a quasi real-time microwave tomographic system was constructed. It was utilized to reconstruct images of physiologically active biological tissues such as an explanted canine perfused heart. The tomographic system consisted of 64 special antennae, divided into 32 emitters and 32 receivers which were electronically scanned. The cylindrical microwave chamber had an internal diameter of 360 mm and was filled with various solutions, including deionized water. The system operated on a frequency of 2.45 GHz. The polarization of the incident electromagnetic field was linear in the vertical direction. Total acquisition time was less than 500 ms. Both accurate and approximation methods of image reconstruction were used. Images of 2-D phantoms, canine hearts, and beating canine hearts have been achieved. In the worst-case situation when the 2-D diffraction model was used for an attempt to "slice" three-dimensional (3-D) object reconstruction, we still achieved spatial resolution of 1 to 2 cm and contrast resolution of 5%.

The present paper reports an experimental study of the development of plane monochromatic waves in the boundary layer on a flat plate at Mach number M = 2.0. The wave characteristics of the plane waves are obtained. Three-dimensional disturbances with an angle of the wave vector to the flow χ = 50–70° are found to be the most unstable. It is shown that the disturbances, consisting of vortical and compressible modes, are engendered in a supersonic boundary layer by a local source of artificial disturbances. It is found that an increase in the bluntness of the leading edge of a plate stabilizes three-dimensional disturbances of a vortical mode.

The plasma crystal is shown to exhibit a nonequilibrium two-step phase transition due to particle heating by ion streaming motion in the sheath. In a nonlinear model, the energy increase due to an ion induced instability is found to be separated from the melting transition. The plasma crystal melts at a much higher particle energy than expected from classical models. This behavior is explained by preferred destabilization of short-wavelength modes in the plasma crystal.

Experimental investigations of the boundary layer receptivity, on the sharp leading edge of a at plate, to acoustic waves induced by two-dimensional and three- dimensional perturbers, have been performed for a free-stream Mach number M ∞ = 5.92. The fields of controlled free-stream disturbances were studied. It was shown that two-dimensional and three-dimensional perturbers radiate acoustic waves and that these perturbers present a set of harmonic motionless sources and moving sources with constant amplitude. The disturbances excited in the boundary layer were measured. It was found that acoustic waves impinging on the leading edge generate Tollmien–Schlichting waves in the boundary layer. The receptivity coefficients were obtained for several radiation conditions and intensities. It was shown that there is a dependence of receptivity coefficients on the wave inclination angles.

The natural occurrence of Tollmien-Schlichting (TS) waves has so far only been observed in boundary layers subjected to moderate levels of free stream turbulence ( Tu < 1%), owing to the difficulty in detecting small-amplitude waves in highly perturbed boundary layers. By introducing controlled oscillations with a vibrating ribbon, it is possible to study small-amplitude waves using phase-selective filtering techniques. In the present work, the effect of TS-waves on the transition is studied at Tu = 1.5%. It is demonstrated that TS-waves can exist and develop in a similar way as in an undisturbed boundary layer. It is also found that TS-waves with quite small amplitudes are involved in nonlinear interactions which lead to a regeneration of TS-waves in the whole unstable frequency band. This results in a significant increase in the number of turbulent spots, which promote the onset of turbulence.

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The dynamical stability of finite two-dimensional clusters of charged micrometer sized particles is studied experimentally in a dusty plasma, where the particles experience a screened interaction. For clusters containing 19 and 20 particles the intershell rotation barrier height is measured quantitatively by applying a well defined torque on the clusters' outer shell by the radiation pressure of two opposing laser beams. Moreover, a complex behavior is found for the 19-particle cluster where structural transitions occur together with the intershell rotation showing that the presence of shielding can basically change the least stable modes in finite clusters. The measured crystal properties have been compared with Monte Carlo simulations. Quantitative agreement is found when nonideal effects are taken into account.

The non-stationary behaviour of near-limit premixed flame propagating in a microchannel with temperature gradient was theoretically investigated. A one-dimensional (1D) nonlinear evolutionary equation of the flame front was obtained. The nonlinear model outlined the flame stabilization, nonlinear flame oscillations and flames with repetitive extinction and ignition processes that were observed in experiments.

The problem of transition between regular and Mach reflection of planar shock waves over straight wedges in steady flows was numerically studied by the DSMC method. It is shown that the transition from regular to Mach reflection takes place, in accordance with the detachment criterion, while the opposite transition occurs at smaller angles. The hysteresis effect was observed at increasing and decreasing shock wave angles.

The mechanism of turbulence amplification in shock-wave/boundary layer interactions is reviewed, and a new turbulence amplification mechanism is proposed based on the analysis of data from direct numerical simulation of an oblique shock-wave/flat-plate boundary layer interaction at Mach 2.25. In the upstream part of the interaction zone, the amplification of turbulence is not essentially shear driven, but induced by the interaction of the deceleration of mean flow with streamwise velocity fluctuations, which causes a rapid increase of turbulence intensity in the near-wall region. In the downstream part of the interaction zone, the high turbulence intensity is mainly due to the free shear layer generated in the interaction zone. During the initial stage of turbulence amplification, the characteristics of wall turbulence, including compact velocity streaks, streamwise vortices and an anisotropic Reynolds stress, are well preserved. The mechanism proposed explains the high level of turbulence in the near-wall region observed in some experiments and numerical simulations.

Stability of a supersonic near-wall flow over a shallow grooved plate in the freestream of Mach 6 is investigated by means of numerical simulations and wind-tunnel experiments. Numerical solutions of two-dimensional Navier–Stokes equations are used to model propagation of artificial disturbances of several fixed frequencies generated by an actuator placed on the wall. It is shown that the high-frequency forcing excites unstable waves in the flat-plate boundary layer. These waves are relevant to the second-mode instability. The wavy wall damps the disturbances in a high-frequency band while it enhances them at lower frequencies. Stability experiments are conducted in the Institute of Theoretical and Applied Mechanics Tranzit-M shock tunnel under natural freestream conditions. The measured disturbance spectra are similar to those predicted numerically. They contain a peak associated with the second-mode instability. This peak is damped by the wavy wall, while a marginal increase of the disturbance amplitude is observed at lower frequencies. Although the experiments qualitatively confirm the wavy-wall stabilization concept, further stability and transition measurements are needed to clarify its robustness.

Theoretical and experimental studies of hypersonic boundary-layer stabilization using a passive porous coating of regular microstructure are discussed. Propagation of disturbances inside pores is simulated with linear acoustic theory including the gas rarefaction effect. This model provides boundary conditions for stability analysis of boundary-layer disturbances on the porous wall. Experiments were conducted in the Mach 6 wind tunnel on a 7-deg half-angle sharp cone whose longitudinal half-surface is solid and whose other half-surface is covered by a perforated sheet comprising equally spaced cylindrical blind microholes. Hot-wire measurements of natural disturbances and artificially excited wave packets are conducted on both solid and porous surfaces. Natural disturbance spectra indicate that the second mode is a dominant instability. The porous coating stabilizes the second mode and weakly affects the first mode. Measurements of artificially excited wave packets show that the porous coating leads to substantial decrease of the wave-packet growth. The experimental data on phase speeds and amplitudes of the second-mode disturbances are compared with theoretical predictions. Satisfactory agreement is obtained for both solid and porous surfaces. This study confirms the concept of hypersonic boundary-layer stabilization by passive porous coatings, which can be used for laminar flow control.

The stability of a flat plate boundary layer modulated by stationary streamwise vortices was studied experimentally in the T-324 low speed wind tunnel in Novosibirsk. Vortices were generated inside the boundary layer by means of roughness elements arranged in a regular array along the spanwise (z-) direction. Transition is not caused directly by these structures, but by the growth of small amplitude traveling waves riding on top of the steady vortices. This situation is analogous to the transition process in Görtler and cross-flows. The waves were found to amplify up to a stage where higher harmonics are generated, leading to turbulent breakdown and disintegration of the spanwise boundary layer structure. For strong modulations, the observed instability is quite powerful, and can be excited ‘‘naturally’’ by small uncontrollable background disturbances. Controlled oscillations were then introduced by means of a vibrating ribbon, allowing a detailed investigation of the wave characteristics. The instability seems to be associated with the spanwise gradients of the mean flow, ∂U/∂z, and at all z-positions, the maximum wave amplitude was found at a wall-normal position where the mean velocity is equal to the phase velocity of the wave, U(y)=c, i.e., at the local critical layer. Unstable waves were observed at frequencies well above those for which Tollmien–Schlichting (TS) waves amplify in the Blasius boundary layer. Excitation at lower frequencies and milder basic flow modulations showed that TS-type waves may also develop. The relation between TS-type waves and the observed high-frequency instability is discussed in the light of previous authors’ findings.

A critical analysis of some recent experimental and computational research of 2-D and 3-D shock wave/turbulent boundary layer interaction (SWTBLI) is carried out. The specific stages of turbulent boundary layer separation development in a vicinity of compression ramps, forward- and backward- facing steps, one- and double-fin configurations are considered. The flowfield topology and principal physical processes are analyzed and specified for different cases of SWTBLI. The examples of modern numerical modeling on a basis of the Reynolds-averaged Navier-Stokes equations with various turbulence models as well as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are demonstrated and compared. The perspectives and problems of future SWTBLI studies are discussed.