Unsteadiness of transonic convex-corner flows

An experimental investigation was conducted to study the transonic convex-corner flow in a turbulent boundary layer. The unsteadiness of the interaction was characterized by a local peak pressure fluctuation and the deviation of higher order moments from an effective Gaussian. The peak pressure fluctuations are correlated and compared with results from other studies.     

Conservative calculations of non-isentropic transonic flows

The classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations. The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge. Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.     

Cavity effects on transonic convex-corner flows

An experimental study was conducted to investigate the transonic convex-corner flows, with and without the presence of an upstream cavity. Measurements were made for the effect of cavity type, including transitional and closed-type cavities, on the mild and extensively separated turbulent boundary layer. The effect of spacing distance between the trailing edge of the cavity and the corner was also studied. It is found that the downstream convex-corner flow is affected by the presence of an upstream cavity, particularly near the corner. The closed-type cavity with smaller spacing distance results in upstream movement of the shock wave and higher level of surface pressure fluctuations.     

Wave disturbances in transonic separated flows

The results of an investigation of the nature and role of wave disturbances in transonic separated flows are presented. The effect of these disturbances on flow formation and stability, as well as on the characteristics of the pressure fluctuations and the time-average flow parameters, is considered.     

Equations of transonic flows of relaxing mixtures

Transonic flows of chemically active gas mixtures whose composition is defined by an arbitrary number of reactions are considered. Conditions ensuring a closeness of the frozen and equilibrium velocities of sound are imposed on the equations of state. An approximate system of equations for vectors of particle velocity and completeness of reactions is obtained as a result of an asymptotic analysis of the system of Euler equations and the equations of chemical reactions associated with them. This system reduces to two equations containing only components of the particle velocity; the order of one of them equals the number of reactions increased by one, while the second equation expresses the nonvorticity condition of the stream. Various limit cases dependent on the magnitude of eigenvalues of the relaxation matrix are pointed out.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 139–148, July–August, 1977.     

The theory of transonic vortical gas flows

For cases of plane and axisymmetric transonic vortical gas flows, the approximate equations for the stream function are constructed directly on the physical plane in the vicinity of the sonic-line point at which the entropy is extremal. Certain particular solutions are found which are generalizations of the familiar integrals of transonic gasdynamics without vortices.The author wishes to thank Yu. D. Shmyglevskii for helpful discussions of this study.     

Asymptotic analysis of equilibrium states for rotating turbulent flows

The equilibrium states of homogeneous turbulence simultaneously subjected to a mean velocity gradient and a rotation are examined by using asymptotic analysis. The present work is concerned with the asymptotic behavior of quantities such as the turbulent kinetic energy and its dissipation rate associated with the fixed point (/kS)=0, whereS is the shear rate. The classical form of the model transport equation for (Hanjalic and Launder, 1972) is used. The present analysis shows that, asymptotically, the turbulent kinetic energy (a) undergoes a power-law decay with time for (P/)<1, (b) is independent of time for (P/)=1, (c) undergoes a power-law growth with time for 1<(P/)<(C ₂–1), and (d) is represented by an exponential law versus time for (P/)=(C ₂–1)/(C ₁–1) and (/kS)>0 whereP is the production rate. For the commonly used second-order models the equilibrium solutions forP/,II, andIII (whereII andIII are respectively the second and third invariants of the anisotropy tensor) depend on the rotation number when (P/kS)=(/kS)=0. The variation of (P/kS) andII versusR given by the second-order model of Yakhot and Orzag are compared with results of Rapid Distortion Theory corrected for decay (Townsend, 1970).     

Entropy and vorticity corrections for transonic flows

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non-uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.     

Three-dimensional effect on transonic rectangular cavity flows

Experiments are performed to study the characteristics of rectangular cavity flows. Mean and fluctuating surface pressures in a Mach 1.28 turbulent flow past rectangular cavities are obtained. The cavity length-to-depth ratio (L/D) is varied from 2.43 to 43.00, while the length-to-width ratio (L/W) is 0.5, 1.0 and 2.0. The three-dimensional effect is significant on the trailing edge vortex, which affects the peak pressure ahead of the rear face, pressure gradient and levels of pressure fluctuation near the trailing edge, particularly for closed and transitional cavity flows. L/W and Mach number are important for the definition of critical L/D for the cavity flowfield models. Received: 12 March 1999/Accepted: 30 August 2000     

Numerical solution of subsonic and transonic cascade flows

In this work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken. Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.     

Two-dimensional transonic vortex flows of an ideal gas

Equations are obtained for two-dimensional transonic adiabatic (nonisoenergetic and nonisoentropic) vortex flows of an ideal gas, using the natural coordinates (=const is the family of streamlines, and =const is the family of lines orthogonal to them). It is not required that the transonic gas flow be close to a uniform sonic flow (the derivation is given without estimates). Solutions are found for equations describing vortex flows inside a Laval nozzle and near the sonic boundary of a free stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–109, September–October, 1973.     

Asymptotic theory of separation flows

A review is given of the results of theoretical investigations of the separation of laminar and turbulent boundary layers in an incompressible fluid obtained on the basis of matched asymptotic expansions valid at large Reynolds numbers (Re). The global picture of the separation flow behind a body of finite size as Re is investigated.Paper presented at Fifth All-Union Symposium on Theoretical and Applied Mechanics, Alma-Ata, 1981.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 20–30, March–April, 1982.     

Equation of nonsteady transonic flows of an ideal gas

At the present time, there are several different equations for describing a transonic, nonsteady, irrotational flow of an ideal perfect gas ([1], Table 1), depending on the ratios between the small characteristic parameters of the flow. In order to extend the range of application of these equations, a composite equation is formed from them (for example, the equations for small and large Strouhal numbers in the theory of oscillation of a wing are combined). In this paper, a more general equation is obtained for the plane flow of this class by means of natural orthogonal coordinates (family of equipotential lines and streamlines) without the use of estimates, for which the equation by comparison with the composite equation contains a new nonlinear term. Accurate solutions of the equation are found, describing nonsteady transonic flows in plane nozzles; one of them describes the process of the establishment of a design cycle in Laval nozzles with immovable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 105–109, January–February, 1977.     

Asymptotic MHD flows in channels

A numerical and experimental study is made of the possibility of the onset of inertialess flow regimes in a conducting fluid in channels of complex geometry under the influence of a strong external field. The region of existence is determined for the inertialess regime from the Hartmann numbers and the MHD interaction parameter and asymptotic estimates are obtained for the drag coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 159–163, March–April, 1985.     

Stabilization law for transonic flows around bodies of revolution

A mathematical foundation is presented for the law of gas-parameter stabilization during near-sonic flow of a stream around bodies, which is known in experimental aerodynamics. The quantitative formulation of this law relies on a simple asymptotic analysis of the solutions of the Karman equations. The numerical computation performed for the velocity field around a body of revolution whose meridian section is a Chaplygin profile confirmed the deductions of asymptotic theory to high accuracy.     

Numerical simulation of viscous transonic flows over an airfoil

High Reynolds number viscous transonic flow is described based on an interaction of the potential outer flow with the boundary layer and wake. Following the procedure of Lighthill (1958), the solutions in these domains are matched to each other through boundary conditions. The solution to the complete problem is obtained iteratively through successive computations of the flows in the outer and inner domains. Both old and new algorithms are used for the iteration process and subsequent problem solution. Results are given for all the airfoils from the Experimental Data Base for Computer Program Assessment (AGARD-AR-138, 1979). A comparison of these results with experimental data shows the degree of agreement between these unbounded airfoil flow simulations and real transonic flow over the central part of a straight wing.