Nonlinear Instability in the Region of Laminar-Turbulent Transition in Supersonic Three-Dimensional Flow over a Flat Plate

Direct numerical simulation is applied to obtain laminar-turbulent transition in supersonic flow over a flat plate. It is shown that, due to the nonlinear instability, Tollmien–Schlichting waves generated in the boundary layer lead to the formation of oblique disturbances in the flow. These represent a combination of compression and expansion waves, whose intensities can be two orders higher than that of external harmonic disturbances. The patterns of the three-dimensional flow over the plate are presented and the structures of the turbulent flat-plate boundary layers are described for the freestream Mach numbers M = 2 and 4.     

Computations of Interaction of an Incident Oblique Shock Wave with a Turbulent Boundary Layer on a Flat Plate

Results of numerical simulation of interaction between an oblique shock wave and a turbulent boundary layer formed in a supersonic (Mach number M =5) flow past a flat plate are presented. The computations are performed for three cases of interaction of different intensity, which result in an attached or detached flow. Numerical results are compared with experimental data. The effect of flow turbulence and shockwave unsteadiness on flow parameters is studied.     

Growth of artificially induced disturbances in a supersonic boundary layer

This work proposes a method of inducing artificial disturbances of adjustable amplitude in a supersonic boundary layer. Using the proposed method, an experimental study is made of the development of a three-dimensional wave packet of low intensity at a frequency of 20 kHz in the boundary layer of a flat plate at Mach number M = 2.0. The Fourier components of the wave packet are determined. The data obtained are compared with the results of calculating the linear stability of the supersonic boundary layer in a plane-parallel flow approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–43, September–October, 1984.     

Characteristics of an unstably localized disturbance in a compressed boundary layer

Experiments have demonstrated [1] that the transition of streamline-type flow into turbulent flow in a boundary layer occurs as a result of the formation and development of turbulent spots apparently arising from small natural disturbances. A study of the nonlinear evolution and interaction of localized disturbances requires knowledge of their characteristics to a linear approximation [2]. In the current work, results are presented of calculations of such characteristics for the first two unstable modes in a supersonic boundary layer on a two-dimensional plate (M = 4.5, T_w = 4.44).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–53, January–February, 1976.     

锥体效应对超音速湍流边界层统计特性的影响

通过直接数值模拟,计算了空间模式下,来流马赫数为2.5, 半锥角为$5^{\circ}$, 零攻角的绝热钝锥湍流边界层,研究了湍流的统计特性,并把结果与超音速平板湍流边界层和马赫数为6的高超音速钝锥湍流边界层的结果进行了比较,重点定量地考察了锥体效应对边界层湍流统计特性的影响. 研究发现,锥体效应对平均温度剖面以及压缩性的影响是显著的;而其它统计量,比如速度壁面律、雷诺应力的分布和湍动能各项的贡献等,受锥体效应的影响很小.      

Interaction of hydrodynamic external disturbances with the boundary layer

Disturbances produced by external flow vorticity in a supersonic boundary layer are studied. It is shown that both vortical and nonvortical waves play an important role. The calculations are performed for subsonic and supersonic flows for a Mach number M=2.     

Supersonic Flow Past an Obstacle with a Clearance at the Base

The supersonic air flow structure and the pressure distribution in the vicinity of a vertical cylinder suspended over the surface of a plate with a turbulent boundary layer are studied experimentally. The effects of the free-stream Mach number and the width of the clearance between the cylinder base and the surface on the dimensions of the separated flow region and the pressure distribution in the latter are examined.     

STUDY OF MECHANISM OF BREAKDOWN IN LAMINARTURBULENT TRANSITION OF SUPERSONIC BOUNDARY LAYER ON FLAT PLATE

Spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that, during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance, when they became larger, leads to remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.     

Cone in a supersonic flow near a surface with a turbulent boundary layer

The published information about the interaction of incident shocks and a turbulent boundary layer relate to cases of a thin boundary layer ( 1–3 mm) on a flat surface. The present study relates to supersonic flow with Mach number M = 3 and stagnation pressure p₀=1.2 MPa past cones near a surface with a thick boundary layer formed on a plate abutting the lower edge of a plane nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–180, July–August, 1991.     

Stability and Transition on a Swept Cylinder in a Supersonic Flow

Results of experimental investigations of the evolution of natural disturbances and laminar–turbulent transition in a supersonic boundary layer on the attachment line of a circular cylinder with a sweep angle of 68° and a freestream Mach number M = 2 are presented. The experimental studies are supplemented by calculations of the mean flow and stability characteristics. Flow regimes in the boundary layer on the attachment line are determined by a hotwire technique as functions of the Reynolds number and height of twodimensional roughness elements. The results are compared with NASA (Ames) experiments.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

Investigation of the heat transfer mechanism in supersonic turbulent boundary layers

A method is described for calculating turbulent Prandtl numbers from Mach number and total temperature profiles in supersonic boundary layers. The calculations are based on boundary layer measurements in the Mach number range from 3.5 to 5. The investigations clearly indicate that in addition to accurate profile measurements reliable values of shear stress and heat flux at the wall must exist, in order to be able to calculate the turbulent Prandtl number in the viscous regime of the boundary layer. For flow conditions with and without heat transfer, the derived turbulent Prandtl numbers indicate that the turbulent transport of heat decreases much faster towards the wall than the turbulent transport of momentum. The results of the analysis show that only the unequivocal qualitative result of increasing turbulent Prandtl numbers in the viscous region of the boundary layer, can be expected. The variation of the turbulent Prandtl number can be described successfully using a simple approximation, based on the mixing length concept, and is applied to the calculation of total temperature distribution using the law of the wall for compressible flow.     

Numerical Investigation of Multi-Jet Channel Flows

The results of a numerical simulation of the three-dimensional outflow of a system of circular supersonic turbulent jets into a cocurrent supersonic (or subsonic) air flow in a partially bounded region are given. Solutions are obtained by the splitting method using a matrix sweep of the parabolized Navier-Stokes equations. Assuming that the flow is nonseparated in the boundary layer, features of the three-dimensional structure of the jet system are investigated as functions of the pressure ratio number and the jet and cocurrent flow Mach numbers.     

Investigation of the effect of heavy gas injection into a supersonic boundary layer on laminar-turbulent transition

The effect of distributed tangential injection of heavy SF₆ gas into the wall zone of a boundary layer on the supersonic flow stability and laminar-turbulent transition is experimentally and theoretically investigated at the freestream Mach number M_∞ = 2. For the first time it is experimentally shown that in the case of this injection laminar-turbulent transition is downstream displaced.     

Joint permeability and roughness effect on the supersonic flat-plate boundary layer stability and transition

The joint effect of the permeability and the roughness of the flat plate surface on the boundary layer stability and laminar-turbulent transition is experimentally and theoretically investigated at the freestream Mach number M_∞ = 2. It is shown that, as a certain roughness value is reached, and with increase in the porous coating thickness (on a certain range), the boundary layer stability against natural disturbances diminishes and laminar-turbulent transition is displaced toward the leading edge of the model.     

Turbulization of the wake behind a single roughness element on a blunted body at a hypersonic Mach number

The influence of a cylinder-shaped single roughness element on the laminar–turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone model at the Mach number M = 5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400–500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.     

Constant temperature hot-wire anemometer practice in supersonic flows

The performance of a constant-temperature inclined hot-wire in a supersonic flow is critically examined. It is shown that empirical heat transfer correlations commonly used for calibrating hot wires in subsonic flow cannot be used when the flow is supersonic. Calibration and measurement procedures appropriate to supersonic flow are suggested, together with the possible limits on their validity. The instrument was used to measure the mass-weighted Reynolds shear stress in a zero pressure gradient Mach 2.9 turbulent boundary layer. A comparison with the available data suggests good agreement, as long as the normal Mach number remains supersonic under all conditions.     

Linear evolution of controlled disturbances in the supersonic boundary layer on a swept wing

The linear development of controlled disturbances in the three-dimensional supersonic boundary layer on a swept model wing with a sharp leading edge is experimentally investigated at the Mach number 2. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances are obtained. The asymmetry of these characteristics, due to the secondary flow in the three-dimensional boundary layer, is confirmed.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.