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.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

The stationary and time-dependent aerodynamic coefficients of a slender blunt cone with a flap located near the base section of the model are experimentally investigated. The freestream parameters (M_∞ = 6, Re _L = 0.88 × 10⁷, and γ = 1.4) ensured a turbulent regime of flow over the conical surface and the flap. At high angles of attack (α ～ 10°) laminar-turbulent transition is observable in the separation zone on the leeward side of the body. Emphasis is placed on the determination of the trimming angles of attack for different positions of the center of rotation and the static and dynamic stability coefficients (the model oscillation damping coefficient).     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers

The heat transfer to sharp and slightly blunted flat plates in the zone of oblique shock incidence has been experimentally investigated. The experiments were performed at the Mach numbers M = 6, 8, and 10 and Reynolds numbers ranging from 0.2 × 10⁶ to 1.3 × 10⁶ corresponding to transitional (laminar-turbulent) flow in the shock-induced separation zone. Emphasis is placed on small values of the bluntness radius r. It is established that there exists a threshold value r _th of the radius that bounds the range of its influence on the heat transfer, namely, an increase in r to r _th leads to a sharp reduction in the maximum heat transfer coefficient in the interference zone, whereas a further increase (beyond r _th) has only a slight effect on the maximum heat transfer coefficient. The dependence of r _th on the main hypersonic flow parameters is analyzed. an explanation of the observable phenomena is given.     

Effect of the cone nose bluntness and the ultrasonically absorptive coating on transition in a hypersonic boundary layer

The effect of an ultrasonically-absorptive coating on laminar-turbulent transition on cones with different nose bluntnesses is experimentally investigated. The experiments were performed with a cone with the semi-vertex angle of 7° set at zero incidence in the Mach 8 flow for three Reynolds numbers. A material with a chaotic micropore structure was used as the ultrasonically-absorptive coating. One side of the model, along its generator, was coated with the porous material, while the second represented a rigid surface. The laminar-turbulent transition location was determined from the results of heat flux distribution measurements. The heat flux fluctuations were also measured on the model surface. It was found that the laminar region length increased with an increase in the bluntness radius. The ultrasonically-absorptive coating with a chaotic microstructure effectively stabilizes the boundary layer for all bluntness radii considered, increasing the laminar region length by 30 to 85%.     

Influence of Plate Nose Heating on Boundary Layer Development

The influence of local heating of the metal nose of a thermally insulated plate on the development of the plate boundary layer is experimentally investigated. The possibility of optimizing the flow past the leading edge and suppressing the turbulizing effect of its roughness by means of heating is demonstrated. Heating makes it possible to delay laminar-turbulent transition of the boundary layer considerably at comparatively low Reynolds numbers.     

On the Possibility of Delaying Laminar-Turbulent Transition at High Reynolds Numbers by the Optimal Choice of Body Forces

The possibility of delaying laminar-turbulent transition on a flat plate in a longitudinal viscous incompressible flow by the optimal choice of the body force distribution in the boundary layer is discussed. It is shown that even for very high Reynolds numbers, Re 10¹⁰, a body force distribution can be found such that the corresponding boundary layer flow is absolutely stable, while the total drag of the body is less than that in the absence of body force action on the flow.     

Energy Estimate of the Critical Reynolds Numbers in a Compressible Couette Flow. Effect of Bulk Viscosity

A variational problem of determining the critical Reynolds number of the laminar-turbulent transition is numerically solved within the framework of the nonlinear energy theory of stability of compressible flows. Stability of various modes in the Couette flow of a compressible gas is estimated by the method of collocations. It is demonstrated that the minimum critical Reynolds numbers in the range of the ratio of the bulk viscosity ηb to the shear viscosity η, which is realistic for diatomic gases, are reached for modes of streamwise disturbances. The critical Reynolds numbers increase as the bulk viscosity is increased in the interval η_b = 0-2η, with the maximum increase in the limit being approximately 30%.     

Effect of a steady periodic velocity inhomogeneity on boundary layer stability

Direct numerical simulation is used to investigate laminar-turbulent transition in a boundary layer with a span-periodic inhomogeneity of the velocity profile which is created artificially. It is shown that the presence of the inhomogeneity leads to a slowing down of the growth of unstable perturbations and a delaying of the laminar-turbulent transition.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–52, July–August, 1995.     

Step-induced turbulence in a high-velocity boundary layer

The fact that the stability of the boundary layer on smooth plane bodies (in particular, on a flat plate) at Mach numbers M>5 is very high and laminar-turbulent transition takes place at points fairly distant from the leading edge of the model has given rise to the question: how difficult is it to induce transition (in particular, by means of a step) in a laminar boundary layer at M>5. The present article is devoted to the solution of this problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1989.The authors are grateful to Yu. A. Safronov for assistance with the flow visualization.     

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.     

Critical Reynolds number of the couette flow of a vibrationally excited diatomic gas energy approach

An energy balance equation for plane-parallel flows of a vibrationally excited diatomic gas described by a two-temperature relaxation model is derived within the framework of the nonlinear energy theory of hydrodynamic stability. A variational problem of calculating critical Reynolds numbers Re_cr determining the lower boundary of the possible beginning of the laminar-turbulent transition is considered for this equation. Asymptotic estimates of Re_cr are obtained, which show the characteristic dependences of the critical Reynolds number on the Mach number, bulk viscosity, and relaxation time. A problem for arbitrary wave numbers is solved by the collocation method. In the realistic range of flow parameters for a diatomic gas, the minimum critical Reynolds numbers are reached on modes of streamwise disturbances and increase approximately by a factor of 2.5 as the flow parameters increase.     

On the Viscous Drag of a Plate with Spherical Recesses

The drag of flat plates with spherical recesses was measured using the direct balance method. The experiments were run in a low-turbulence wind tunnel with a cross-section measuring 1000 × 1000 mm and a length of 400 mm. Three surfaces with recesses 7.0, 3.9, and 1.3 mm in diameter and 0.5, 0.3, and 0.2 mm deep, respectively, were tested. It is shown that on the Reynolds and Mach number ranges Re= (3–9)· 10⁶ and M 0.3 the spherical recesses add to the drag of a flat plate in turbulent flow. The recesses have almost no effect on the location of laminar-turbulent transition, which occurs at Re_t 3· 10⁶.     

Effect of bulk viscosity on Kelvin-Helmholtz instability

An energy functional leading to a resolvable variational problem for determining the critical Reynolds number of laminar-turbulent transition Re _cr is constructed within the framework of the nonlinear energy stability theory of compressible flows. Asymptotic estimates containing the characteristic dependence in the main order are obtained for the stability of various modes of Couette compressible gas flow. The asymptotics considered are long-wave approximations. This suggests that the obtained dependence describes the effect of bulk viscosity on the large-scale vortex structures characteristic of Kelvin-Helmholtz instability. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 73–84, May–June, 2008.     

A new method for computing turbulence in compressible laminar-turbulent transition and boundary layers--PSE＋DNS

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers is proposed. It is especially useful for computation of laminar-turbulent transition and turbulence starting from small-amplitude disturbances. The laminar stage, up to the beginning of the breakdown in laminar-turbulent transition, is computed by parabolized stability equations (PSE). The direct numerical simulation (DNS) method is used to compute the transition process and turbulent flow, for which the inflow condition is provided by using the disturbances obtained by PSE method up to that stage. In the two test cases incfuding a subsonic and a supersonic boundary layer, the transition locations and the turbulent flow obtained with this method agree well with those obtained by using only DNS method for the whole process. The computational cost of the proposed method is much less than using only DNS method.     

PSE as applied to problems of transition in compressible boundary layers

A new idea of using the parabolized stability equation (PSE) method to predict laminar-turbulent transition is proposed. It is tested in the prediction of the location of transition for compressible boundary layers on flat plates, and the results are compared with those obtained by direct numerical simulations (DNS). The agreement is satisfactory, and the reason for this is that the PSE method faithfully reproduces the mechanism leading to the breakdown process in laminar-turbulent transition, i. e., the modification of mean flow profile leads to a remarkable change in its stability characteristics.     

Combining the SSG/LRR-<Emphasis Type="Italic">ω</Emphasis> differential reynolds stress model with the detached eddy and laminar-turbulent transition models

The procedure of incorporating the detached eddy method and a model of laminar-turbulent transition into the SSG/LRR-ω turbulence model is presented. The approach proposed can be regarded as the generalization of the existing models intended to perform calculations with the SST turbulence model to the case of their use with the SSG/LRR-ω model. The advantage of the approach developed over the RANS turbulence models based on the Boussinesq hypothesis is demonstrated with respect to the problems of flow past an airfoil and cold jet outflow.     

Mach Wave Effect on Laminar-Turbulent Transition in Supersonic Flow over a Flat Plate

The effect of a Mach wave (N wave) on laminar-turbulent transition induced by the first instability mode (Tollmien–Schlichting wave) in the flat-plate boundary layer is investigated on the basis of the numerical solution of Navier–Stokes equations at the freestream Mach number of 2.5. In accordance with the experiment, the N wave is generated by a two-dimensional roughness at the computation domain boundary corresponding to the side wall of the test section of a wind tunnel. It is shown that the disturbance induced by the backward front of the N wave in the boundary layer has no effect on the beginning of transition but displaces downstream the nonlinear stage of the first mode development. The disturbance induced by the forward front of the N wave displaces the beginning of transition upstream.     

Optimization of laminar-turbulent transition delay by means of local heating of the surface

The stability and position of laminar-turbulent transition in the boundary layer on a body heated near the leading edge are analyzed. The point of transition is found using the linear theory of the stability of plane-parallel flow and thee ^N -method. It is shown that by heating a tiny area near the leading edge to a temperature exceeding that of the oncoming flow by a factor of two to four, transition may be delayed, even on a thermally insulated surface. For highly radiating surfaces the energy saved by reducing the friction drag may exceed the heating energy by a factor of three. It is shown that by varying the pressure distribution and surface heating it is possible either to increase the airfoil lift for a fixed transition point or delay transition for a fixed lift.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 90–99, July–August, 1995.