Correlations study in shock wave/turbulent boundary layer interaction

The shock waves/turbulent boundary layer interaction is a problem of critical importance that is frequently encountered in designing flying vehicles. Presently, the most topical issue is the investigation of nonstationary phenomena (in particular, low-frequency effects) involved in this interaction. We have experimentally studied separated flows in the zone of interaction between an obliquely incident shock wave and a turbulent boundary layer at a Mach number of M = 2. Correlation data in the separation zone and the upstream flow were obtained. It is established that low-frequency oscillations in the reflected shock are related to the pulsation in the inflow boundary layer.     

The temperature recovery factor in a boundary layer on a permeable plate

A numerical investigation of the boundary layer on a permeable wall in a supersonic gas flow is performed using a differential turbulence model. Temperature recovery factors are obtained for a series of Prandtl numbers and gas suction or injection in a wide range of the permeability factor from critical injection to asymptotic suction. With the example of air injection into a supersonic air flow, two methods for determining the temperature of a heat-insulated permeable wall are considered. The first is to solve the problem with a boundary condition of zero heat flux to the wall. The second is similar to an experimental method when the temperature of the gas injected at a section along the plate length becomes equal to the wall temperature. The heat-insulated wall temperatures and temperature recovery factors obtained by these two methods for injection below the critical one are close to each other. In case of critical injection, these two methods yield different results.     

The non-linear evolution of modulated waves in a boundary layer

The series of experiments by Schubauer and Skramstad (1948) provided the first experimental evidence of the role that the instability of Tollmien-Schlichting waves played in the transition of a zero pressure-gradient flat plate boundary layer. The initial experiments studied the oscillations in the boundary layer excited by the freestream fluctuations. This was only possible after the background disturbances in the wind tunnel had been reduced to a very low level. The background wind tunnel environment excited a broad band of amplitude modulated disturbance waves that grew as they propagated downstream, eventually leading to the formation of turbulent spots. Further experiments used artificial two-dimensional harmonic excitation to produce regular wavetrains that could be directly compared with linear theory. Unfortunately, two-dimensional harmonic excitation of this type has also been used in many of the subsequent nonlinear transition investigations; the modulation of the disturbance waves, essential in nonlinear studies, has been largely ignored. Gaster and Grant (1975) used a short duration acoustic pulse to excite the boundary layer and found that the modulated wavepacket that was created admitted bursts of high frequency oscillations. These occurred at amplitudes that were insufficient to generate non-linear behaviour in purely periodic wavetrains. Gaster (1980) suggested that the modulation of the wavepacket played an important role in the non-linear region of transition. This investigation used computer generated deterministic white noise to excite the boundary layer on a flat plate through a single buried loudspeaker. This type of excitation produced amplitude modulated T-S waves at some point downstream from the source. By repeatedly exciting the boundary layer with the same white noise sequence it was possible to map the entire flow-field with a single hot-wire probe and so study the evolution of the modulated wavetrains and the eventual development of turbulent spots. The modulated wavetrains were found to grow initially according to linear theory. But downstream, departures from the linear pattern were observed at isolated time instants. The amplitude of the irregular portions of the signal increased rapidly with downstream distance until bursts of oscillations of frequencies five or six times the basic T-S frequency were observed. These regions developed even higher frequency bursts until a turbulent spot could be considered to have formed. Excitation signals of various amplitudes with different phase relations between the spectral components were used in these experiments. It was found that the phases between the Fourier components played an important role in the highly non-linear behaviour that is the precursor to a turbulent spot. Novel signal processing techniques, such as the wavelet transform and Singular Value Decomposition were used to investigate the fine structure and the propagation characteristics of the high frequency disturbances.     

Interaction of a turbulent boundary layer with an elastic plate

An approximate method is presented for the determination of the efficiency with which an elastic plate reduces turbulent friction, and experimental results are also presented.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 2, pp. 220–225, February, 1989.     

A three-dimensional laminar boundary layer on a permeable plate

We examine the laminar boundary layer on a permeable half-plane for the case in which the streamline of the outside flow is a parabola, and in which the velocity of suction or expulsion is proportional to (x + const)^1/2. We have found the velocity profiles in the boundary layer, as well as the frictional stress distribution on the half-plane.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.16, No. 3, pp. 389–397, March, 1969.     

Numerical simulation of the interaction between reflected shock wave and near-wall boundary layer

The interaction of a shock wave, reflected from the flat end of a cylindrical shock tube, with a cocurrent gas flow at the side wall, is considered in the axisymmetric case. The Navier-Stokes system of equations has been numerically integrated in the thin layer approximation using a predictor-corrector scheme. The appearance of a recirculation gas flow structure behind the reflected shock front and the evolution of this structure in the reflected wave going away from the tube end are analyzed. The corresponding patterns of constant density lines and the velocity vector field are presented.     

The thermal boundary layer of a non-fourier power-law fluid on a plate with a variable surface temperature

The equation for the thermal boundary layer of a non-Fourier powerlaw fluid on a flat plate with an exponential distribution of surface temperature is reduced to an ordinary equation and solved by the method of finite differences. The effect of the exponent on the temperature profile and on the heat-transfer coefficient is determined. It is demonstrated that the asymptotic solutions of the equation for large are nearly exact.     

Turbulent thermal boundary layer on a flat plate with a thermally insulated section

The influence of an initial adiabatic section on the heat transfer coefficient is studied on the assumption that the heat transfer law is expressed in the form St=A/Re _T ^**m Prⁿ. In addition, the temperature distribution on a thermally insulated wall is obtained when heat transfer occurs over the initial section.     

The problem of the boundary layer at a thermally isolated plate

New solutions are given for the energy equation of a compressible boundary layer at a plate in absence of heat transfer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 1, pp. 39–44, January, 1970.     

Interaction of a shock wave with a turbulent boundary layer on a heated surface

The interaction of a shock wave with a turbulent boundary layer has been studied. A stream has been diagnosed using non-invasive visualization (schlieren method). During the investigation the effect of surface heating on the length of boundary layer separation has been studied. It has been discovered that during surface heating the dependence of the length of separation on the temperature ratio is approximated using a linear law.     

Compressible turbulent boundary layer on a permeable plate with injection of foreign gas

A numerical solution is obtained for equations of motion, diffusion, and energy using a three-parameter model of turbulence for boundary layer with different thermal boundary conditions on a permeable plate with injection of foreign gas. For an ideal gas with constant values of Prandtl and Schmidt numbers, the numerical solution is compared with limiting dependences for dimensionless temperature and enthalpy of gas on the wall. For helium/xenon mixtures with a low value of Prandtl number, the effect of intensity of injection and of the values of Reynolds and Mach numbers on the integral and local characteristics of flow and heat and mass transfer is investigated.     

Calculation of the incompressible laminar boundary layer on a plate with slot suction

The dependence of the characteristics of an incompressible laminar boundary layer on the flow rate of fluid removed by suction through transverse slots on the surface of a plate is investigated on the basis of the momentum equation.     

Heat transfer in a transient boundary layer on a porous plate

We present the results of an experimental study and a procedure for calculation of the effect of intense injection of various coolants on stability loss in laminar flow and on heat transfer in a transient boundary layer on a porous plate in a longitudinal flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 2, pp. 197–203, August, 1977.     

Laminar boundary layer with dispersed impurity entrained from a plate surface

A model of a gas-dispersed laminar boundary layer (LBL) on a semiinfinite plate is proposed. Unlike the majority of published works, in which the dispersed impurity permeates through an external LBL boundary, in the present work the source of the dispersed phase is the particles entrained by a flow from a surface in the flow with a small longitudinal velocity. In the LBL, the particles get into a region where the longitudinal velocity of the carrier-medium is large; therefore the Safman lift force is directed upwards and tends to carry them out of the LBL. As a result of increasing the dispersed impurity velocity, their concentration rapidly falls at a distance from the surface. Downward from the flow, the flux of porticles entrained from the surface decreases to zero, the LBL becomes a one-phase flow.Kaliningrad Engineering Institute for Fishing Industry and the Fishery. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 2, pp. 189–193, August, 1992.     

Turbulent boundary layer on a plate in an incompressible liquid with mass injection

Within the limits of a semi-empirical theory based on a two-layer system, as proposed in [5], an examination is made of the influence of mass addition, homogeneous with the main flow, on friction and the parameters of the turbulent boundary layer (thickness of the laminar sublayer, velocity at the edge of the laminar sublayer, etc.).     

Stability of the free-convection boundary layer on a vertical permeable plate

The hydrodynamic stability of flow in a free-convection boundary layer on a permeable plate is numerically investigated. The effect of the plate nonisothermicity and the injection blowing intensity on the critical parameters is determined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 3, pp. 382–387, March, 1985.     

An experimental investigation of the Reynolds number effect on a normal shock wave-turbulent boundary layer interaction on a curved wall

Summary The presented experiment concerned an interaction between a normal shock wave, terminating a local supersonic area in a curved duct, and a turbulent boundary layer developed along the convex wall. This paper deals with the Reynolds number effect upon the interaction structure.The measurements included flow parameters distribution determination, boundary layer development through the interaction area and the shock wave topography visualization. In order to gain more information about separation the wall oil tracing has been applied. The comparison of our results with other published data is presented.With 11 FiguresThe experiments have been carried out at the Institut für Strömungslehre und Strömungsmaschinen, Karlsruhe Universität, Karlsruhe, Federal Republic of Germany.     

Aerodynamic structure of a flat plate laminar boundary layer with diffusion flame

An aerodynamic structure of a laminar boundary layer over a flat plate with uniform fuel injection from the flat plate and with diffusion flame is investigated numerically. Elliptic type conservation equations are used to take into account the pressure variation within the boundary layer. Velocities and the pressure are solved numerically by SIMPLER algorithm. One step irreversible chemical reaction of methane is assumed. An Arrhenius type chemical reaction rate model is assumed and the pre-exponential factor is varied from 1.0 × 10¹² to 1.0 × 10³⁰ m³/(kg s) as a parameter of the reactivity in order to elucidate the effect of the reactivity on the structure of the boundary layer. When the chemical reaction is very fast, the leading edge of the reaction zone reaches the flat plate. As the chemical reaction rate is decreased with a decrease in the pre- exponential factor, the leading edge of the reaction zone parts from the flat plate and it shifts downstream. The fuel is injected in front of the leading edge of the reaction zone, where the air is dominant, and the oxygen penetrates into the fuel dominant zone through the region between the leading edge and the flat plate. As a consequence, a premixed gas is formed around the leading edge of the reaction zone. The premixed gas seems to react in the region apart from the main visible flame.Part of this work was presented at ICCM 86, Tokyo, Japan, May 25–29, 1986