I.Igor I. Lipatov

• Corresponding member Russian Academy of Sciences, Professor
• Head of Department at Central Aerohydrodynamic Institute

A weakly nonlinear version of the wave model of a developed turbulent boundary layer is considered. The dispersion characteristics of the main (unstable mode) are qualitatively determined, and the conditions of three-wave resonance of the main mode (Tollmin-Schlichting waves) with the main mode and with waves of a continuous spectrum are analyzed....

The paper aimed at studying the peculiarities of boundary layer on a rotating body. Rotation of axisymmetric bodies is often used for their stabilization at a high velocity motion in the atmosphere. Presented are calculation of boundary layer flow on a rotating cone at zero angle of attack. Longitudinal and full enthalpy profiles in the laminar bou...

The processes of strong local viscous-inviscid interaction in a flow around a flexible surface are studied. Linear and nonlinear processes of flow interaction in a laminar boundary layer with an external supersonic flow are investigated. It was found that there are unstable linear modes for all positive wave numbers under certain conditions for the...

This paper considers, in the framework of the model of the developed turbulent flow of an incompressible fluid over a plate in a boundary layer. The problem investigated the formulation of amplitudes in a single-mode approximation through a weakly nonlinear version of the wave model. The dispersion characteristics of the least damping wave mode are...

Nonlinear interaction and energy loss by harmonics of perturbations propagating upstream are investigated. It is shown how nonlinear interaction of harmonics can form new harmonics.

Asymptotic methods are applied to study a plane turbulent jet of a viscous incompressible fluid flowing out through a narrow slot into a space filled with a fluid. The complete Navier—Stokes equations are considered. The characteristic Reynolds number is assumed to be large, while the jet thickness is small. In analyzing the problem the method of m...

Turbulent mixing layer between the moving 2D viscous incompressible fluid and fluid in rest is studied.The characteristic Reynolds number of the flow is assumed to be large and the layer thickness being small. To analyze the problem, the method of multiple scales was applied, which allowed to find and investigate the steady secondary flow inside th...

Disturbance propagation in laminar boundary layers is investigated at large freestream velocities. An integral relation determining the disturbance propagation velocity in the weak hypersonic interaction regime is obtained for the first time.

The processes of interaction between a laminar boundary layer flow and an external transonic flow under conditions of strong local interaction have been studied. Two kinds of solutions describing the compression flow (near the separation point) and the rarefaction flow have been found.

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...

In this paper, the problems containing two or more small parameters are investigated. In the analysis of such problems, a diagrammatic method is used to visualize the structure of perturbed flow regions, and to estimate the similarity parameters and mathematical models depending on the limiting transitions. The interaction between the laminar flows...

The paper presents an Eulerian derivation of the non-inertial Navier–Stokes equations as an alternative to the Lagrangian fluid parcel approach. To the best knowledge of the authors, this is the first instance where an Eulerian approach is used for such a derivation. This work expands on the work of Kageyama and Hyodo (2006) who derived the incompr...

This paper derives the non-inertial terms, also referred to as fictitious forces, for aero-ballistic cases using an Eulerian approach. These cases display unsteady rates ofchange in acceleration in all six degrees offreedom. Six fictitious forces are identified in the momentum equation. Their origin and nature ofthese forces are elaborated upon. As...

A mathematical unsteady pseudoshock model describing the continuous transition from supersonic to subsonic flow is constructed for a barotropic gas flow in a long flat channel or a nozzle. The model is based on a two-layer scheme of flow with mass transfer including a potential supersonic core and a turbulent boundary layer.

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P 0. The same mechanism of the coherent structure formation is noticed in both nonstationar...

The results of an experimental and numerical investigation of a three-dimensional laminar separated flow in a compression corner are presented. The freestream Mach number M∞ =6. The model under study is a plate with a sharp leading edge on which a step with a 30° inclination angle is mounted. The model width is equal to the plate length from the le...

Direct numerical simulation within the framework of the Navier-Stokes equations is applied to study the mechanism of the generation of transverse structures (streamwise vortices) in the problem of supersonic M = 6 flow over a flat plate, when a shock wave is incident on it. The vortices formed at the lateral edges of the plate are shown to be the s...

The perturbed flow in a laminar boundary layer is investigated when there are heating elements on the body surface. The flow is assumed to be laminar and subsonic everywhere. It is shown that such flows can be described within the scope of free interaction theory. A solution of a plane steady-state problem is constructed in the linear approximation...

Presented are buffet onset in 2-D and 3-D numerical investigation. Programme ANSYS was used to provide computations. 2-D Navier- Stokes equations solutions with the turbulence model have been obtained for the profile NACA 0012, solutions for three-D Navier-Stokes equations have been obtained for the wing ONERA M6. For 2-D flows boundaries of regime...

Two different (symmetric and asymmetric) methods of decomposition of a broad class of linear and nonlinear hydrodynamic-type systems based on their splitting into several simpler equations are described. Linearized equations of motion of a viscous compressible barotropic gas (liquid) are investigated. Exact solutions of nonlinear equations for a vi...

Investigated are the local flows in the laminar boundary layers in the vicinity of heating elements. On the basis of asymptotical analysis, mathematical models are formulated and similarity parameters are found. Determined are the flow parameters providing flow control (separation, transition). Presented are the results of numerical and analytical...

We analyze the disturbed flow in the supersonic laminar boundary layer when local heated elements are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal sources. We construct the numerical solution for flat supersonic problem in the viscous asymptotic layer in whic...

The dependence of the eigenvalues characterizing the disturbance propagation in hypersonic boundary layers on the temperature factor and the surface motion velocity is investigated. The eigenvalues are shown to decrease with an increase in the wall enthalpy. The results of the study are important for formulating well-posed problems for the time-dep...

Disturbance propagation processes in supersonic laminar and turbulent boundary layers and in channels have been studied. Analysis of the corresponding subcharacteristics leads to an integral relation determining the velocity of disturbance propagation. The study of flows in a turbulent boundary layer described by a simple model leads to a conclusio...

Local flow in the boundary layer in the vicinity of a porous surface region has been studied. Mathematical models are formulated and similarity parameters are determined using the asymptotic analysis. Numerical and analytical results that describe the viscid-inviscid interaction of laminar flows near porous surfaces are presented. This method of pa...

Presented are the numerical and the experimental results describing laminar/turbulent boundary layer transition on thin blunted cones at freestream Mach numbers of M = 6.1 and 8. Shown is the common influence of cone nose bluntness, semi-angle of cones, and Mach and Reynolds numbers on the boundary layer transition. The present results, concerning...

The problem of disturbed flow in the laminar boundary layer when heating elements are located on the surface is investigated. The flow is described by the theory of viscous-inviscid interaction with full Navier – Stokes equations. We apply the triple-deck model of the flow and describe asymptotic multiscale structure for the supersonic case. Using...

The problem of disturbed flow in the laminar boundary layer is investigated when a heating element is located on the surface of the body. The flow is supposed to be laminar one. It is shown that the problem may be solved in terms of free interaction theory. The solution of linear flat problem is constructed. The results of asymptotic analysis are a...

We have studied the domain of applicability of a model of continuum mechanics based on the Navier-Stokes equations for the hypersonic flow of a viscid gas past a plate with sharp leading edge. An asymptotic analysis of the hypersonic flow of a rarefied gas is based on the kinetic equation for gases with internal degrees of freedom. The singularity...

his is the first book in English devoted to the latest developments in fluid mechanics and aerodynamics. Written by the leading authors in the field, based at the renowned Central Aerohydrodynamic Institute in Moscow, it deals with viscous gas flow problems that arise from supersonic flows. These complex problems are central to the work of research...

Using the Maxwell method, transfer equations describing molecular gas flows in viscous shock and hypersonic boundary layers are obtained. It is shown that, in contrast to the Navier-Stokes approximation, the kinetic model proposed makes it possible correctly to describe hypersonic flow around bodies under conditions of strong nonequilibrium of the...

The paper consists of two parts devoted correspondingly to the experimental opportunities and results along with the computational methods and results obtained mainly in the Central Aerohydrodynamic Institute (TsAGI).

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer a...

Supersonic flow of a viscous gas about a flat plate at large but subcritical Reynolds numbers is considered. It is assumed that the gas is a binary mixture of atoms and diatomic molecules and that the temperature of the surface is not higher than the level at which molecules begin to dissociate at the local pressure values. The flow in the vicinity...

The general problem of propagation of three-dimensional disturbances in viscous supersonic flows is considered in the framework of characteristic analysis. Unlike previous results for linear disturbances we deduce a condition determining nonlinear characteristic surfaces which is exact and therefore allows both qualitative and quantitative studies...

A temporal stability analysis of compressible Taylor-Couette flow is analyzed. The studied flow is contained between two concentric cylinders of infinite length, which are rotating with different angular velocities and are kept at different surface temperatures. It is shown that for large Reynolds numbers regimes of flow instability exist for which...

Some hydrodynamical problems in which viscous-inviscid interaction is important are analysed. These problems are: disturbances propagation in channels, three-dimensional nonlinearly disturbed flows and the blow-off phenomenon.

The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near th...

The processes of wave disturbance propagation in a supersonic boundary layer with self-induced pressure [1–4] are analyzed. The application of a new mathematical apparatus, namely, the theory of characteristics for systems of differential equations with operator coefficients [5–8], makes it possible to obtain generalized characteristics of the disc...

Possible regimes of viscous-inviscid interaction at transonic external flow velocities are investigated. It is shown that different flow regimes can exist depending on the relation between such parameters as the disturbance amplitude and the Mach and Reynolds numbers. Corresponding mathematical models are formulated and the solutions of some proble...

This work is devoted to the investigation of self- similar solutions for steady wall jets. The problem is considered in the context of two- and three- dimensional Prandtl boundary layer equations, and three- dimensional parabolized Navier-Stokes equations for Newtonian and non-Newtonian fluids. In contrast to dimensional analysis, which does not al...

Using the method of moments in the space of wavenumbers, a class of models of a developed turbulent flow of an incompressible fluid in a flatplate boundary layer is proposed. The models are based on an analysis of the Navier–Stokes equations that describe the behavior of dynamic coherent structures associated with vorticity generation and also the...

Resumen Resumen Thiswork is devoted to the investigation of self-similar solutions forsteady wall jets. The problem is considered in the contextof two- and three-dimensional Prandtl boundary layer equations, and three-dimensional parabolized Navier --Stokes equations for Newtonian and non-Newtonian f...

The ``pseudoshock" flow description is unresolved problem from the applied and fundamental points of view. This phenomenon takes place in the channel when some obstacle retards the supersonic flow or if the pressure exceeds some critical value near the exit part of the section (Bogdonoff 1955, Crocco et al 1954). Surface heat flux and skin friction...

Flow past an isolated, small, three–dimensional roughness located on a plate is investigated theoretically and numerically. Depending on roughness scales, there are different local disturbed flow regimes. The so–called ‘compensation regime’ is characterize by conservation of boundary–layer thickness for which the flow near the roughness does not in...

DISTURBANCES PROPAGATION IN SUPERSONIC BOUNDARY LAYERS The perturbations propagation and development is the constitutive part of stability problem. Mathematical description of perturbations propagation is controlled by characteristics. In this report the main attention is restricted to the boundary layer flow analysis. To describe the perturbations...

The asymptotic structure of perturbed laminar flows, which are described by problems with unsteady, discontinuous boundary conditions, is investigated. As a result of an asymptotic analysis, the structure of the flow domains is found and appropriate boundary conditions are formulated. Numerical solutions are obtained for one of the processes, which...

Many practical problems in aeronautics are connected with unsteady transonic viscous flows. These problems are buffet, stall, unsteady high angle of attack flows etc. The decisive role in all these problems play the processes of viscous-inviscid interaction. These processes are important when separation takes place, they are significant also for di...

The propagation of disturbances in three-dimensional boundary layers under the conditions of a global and a local strong inviscid-viscous interaction is analyzed. A system of subcharacteristics is found based on the condition for the pressure-related subcharacteristic, and an algebraic relation that gives the propagation velocity of disturbances is...

The perturbations propagation and development is the constitutive part of stability problem. Perturbations propagation is responsible for non stationary aerodynamic effects including separation and hysteresis phenomena. The processes leading to the perturbations propagation are diffusion and convection.

The development of disturbances in viscous compressible flows caused by centrifugal forces is investigated. On the basis of an asymptotic analysis of the Navier-Stokes equations at high Reynolds and G�rtler numbers, mathematical models describing the development of three-dimensional unstable vortex structures are constructed. Various linear boundar...

Unsteady processes involving the propagation of perturbations in two-dimensional boundary layers are analysed in the strong interaction regime. A system of characteristics and subcharacteristics corresponding to wave processes in gas dynamics as well as convection and diffusion processes is determined. A system of equations describing the processes...

AIAA, Theoretical Fluid Mechanics Meeting, 1st, New Orleans, LA, June 17-20, 1996 The problem considered is a description of the flow in the laminar boundary layer under the action of discontinuous boundary conditions. These flows are investigated using asymptotic analysis. The method of matched asymptotic expansions is used to investigate the comp...

The evolution of Goertler vortices in a fluid boundary layer is investigated analytically using an asymptotic analysis of Navier-Stokes equations. It is shown that such an approach makes it possible to identify the principal mechanisms of flow instability, determine similarity parameters, and simplify boundary value problems. Various aspects of Goe...

Asymptotic analysis of the Navier-Stokes equations for large Reynolds and Gortler numbers makes it possible to determine the basic mechanisms of development of flow instability, find the similarity parameters, and simplify the boundary-value problems, whose solution is of great theoretical and applied significance. Different aspects of the developm...

A problem on symmetry flow on a plate of a finite length for a regime of strong viscous-nonviscous interaction is discussed. The flow around a flat plate with zero attack angle and near its trailing edge is under consideration. Typical Reynolds number is suggested to be large, but of subcritical value so as the flow in a wall boundary layer and aft...

A study is made of a laminar boundary layer near a cold plate in the regime of weak viscous -inviscid interaction in the limit in which the free-stream Mach number tends to infinity and the temperature factor to zero. Local disturbed flow regions formed due to the presence of small elements of roughness on the surface of the plate are investigated....

A nonlinear asymptotic analysis of the Görtler vortex development within the whole range of their wave length variation at high values of the Reynolds and Görtler numbers is performed. Boundary-value problems are formulated for characteristic regimes, similarity parameters are obtained. Numerical and analytical solutions are obtained in a linear ap...

The neighborhood of the discontinuity point of the surface temperature and catalytic properties in chemically nonequilibrium supersonic laminar flow of a binary mixture past a cold plate is investigated for Reynolds numbers approaching infinity. It is found that, in the vicinity of the discontinuity point, chemical reactions may occur on the cataly...

A study is made of laminar flow in the vicinity of a step located at the bottom of a boundary layer. It is shown that, for a certain value of a parameter proportional to the ratio of the step height to the boundary layer thickness, a restructuring of the separation zone occurs in front of the step. Numerical and analytical solutions are obtained fo...

The structure of a flow formed as a result of evenly distributed injection from a plane porous surface is analyzed for the case of the transition of boundary layer flow to a separated flow including a mixing region and a region of nonviscous wall flow. In particular, the problem of supersonic flow of a viscous gas past a wedge, with evenly distribu...

In this paper, we investigate the structure of the flow that arises in the case of uniformly distributed injection from a plane permeable surface, under conditions that ensure a transition from a flow in a boundary layer to a detached flow including a mixing layer and a region of inviscid wall flow.

i. We consider flow of a hypersonic viscous gas over a triangular semi-infinite wing (Fig. i). We introduce a rectangular coordinate system with axesx~ andy7 directed along the normal to one of the edges and along the edge, and the yrZ axis directed along the normal to thewing surface. We consider the regime of strong interaction of the flow in the...