Flow over an obstruction with the generation of nonlinear waves on the free surface: Limiting regimes

A numerical-analytic method of calculating a subcritical flow over an obstruction is proposed. This method is based on the identification of the asymptotics of the behavior of a wave train in unknown functions. The method makes it possible to calculate both steep and long waves. The effectiveness of the method is demonstrated for the problem of flow over a vortex. The concept of the limiting flow regime as a regime with the maximum value of the perturbation parameter for which steady flow still persists is introduced. Various types of the limiting regimes obtained in the calculations are analyzed.Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 108–117, March–April, 1995.     

Unsteady reflection of a shock wave from a body with a cylindrical recess

In a number of cases of supersonic flow past bodies with recesses pulsations in the flow arise [1–3]. Experiments [4, 5] indicate that stabilization of the steady supersonic flow past the body with a recess on which a shock wave is incident takes place after a series of oscillations of the bow wave. Numerical calculation of the interaction of a supersonic jet with a cylindrical cavity [6] reveals that damped pressure pulsations arise inside the cavity if the jet is homogeneous, and undamped pulsations it is inhomogeneous. The authors explain the damping of the pulsations by the influence of artificial viscosity. This paper investigates experimentally and theoretically (by numerical methods) the oscillations of the bow shock wave and the parameters of the flow behind it in the case of unsteady reflection of a shock wave from a body with a cylindrical recess turned towards the flow. The problem is posed as follows. A plane shock wave with constant parameters impinges on a cylinder with a cavity. The unsteady flow originating from this interaction is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1984.     

Warm up of an automotive catalyst substrate by pulsating flow: a single channel modelling approach

Rapid warm up of an automotive catalyst substrate is important for early light off. This work considers the results from a model of warm up in a single channel. The mass flow is pulsating with high amplitude, about 75% of mean flow, but without flow reversal. The flow regime is laminar within the channel. Pulsations occur with frequency in the range 16–100 Hz, and are important in close-coupled systems where the catalyst is located near to the engine and where the rate of rise of gas inlet temperature with time is rapid, about 15 K/s. The use of a single channel model with conjugate heat transfer enables the heat transfer coefficient to be evaluated and compared with results from steady flow simulations. The value of the augmentation factor based on heat flux is found to be less than unity. The value of the augmentation factor based on heat transfer coefficient depends on the method for calculating the mean heat transfer coefficient, but is generally less than unity. The changes caused by pulsations will be small in practical systems. Changes in wall temperature found in the simulations are the result of the cumulative effect of changes in the mass flow rate.     

Influence of particles on turbulent flow in channels

In this work, the equations of balance of the second single-point moments of pulsations of the carrier phase are used to analyze the influence of particles on the intensity of pulsation motion. Besides dissipation due to pulsation phase slip, these equations take account the effect of dissipation of small-scale vortices on the particles and also of the additional transfer of pulsations by particles due to the particles being drawn into the pulsating motion and the migration of particles across the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–48, January–February, 1985.     

On the conditions of formation of population inversion of atomic levels in a thermally heated recombining plasma

A theoretical investigation is made into the recombination of a thermally heated plasma of a monatomic gas which undergoes gas-dynamic cooling in a supersonic nozzle. A method of approximate analytic calculation makes it possible to determine the necessary conditions for the existence of an effective recombination regime of the flow out of the nozzle that makes possible population inversion of the excited electronic levels of the atom. The conditions of occurrence of inversion are studied as functions of the parameters characterizing the state of the plasma in the reservoir in front of the entrance to the nozzle, the shape of size of the nozzle, and the working substance. Use of the method of blocks of levels made it possible to calculate the degree of expansion needed for the formation of inversion between transitions with different wavelengths, and also to estimate the gain and the specific radiation energy in these transitions. Numerical estimates of the values of the parameters for the case of an argon plasma are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–97, November–December, 1979.We thank S. A. Losev for discussing the results and for helpful comments.     

A spherical wave in a viscoelastic half-space

The propagation of spherical waves in an isotropie elastic medium has been studied sufficiently completely (see, e.g., [1–4]). it is proved [5, 6] that in imperfect solid media, the formation and propagation of waves similar to waves in elastic media are possible. With the use of asymptotic transform inversion methods in [7] a problem of an internal point source in a viscoelastic medium was investigated. The problem of an explosion in rocks in a half-space was considered in [8]. A numerical Laplace transform inversion, proposed by Bellman, is presented in [9] for the study of the action of an explosive pulse on the surface of a spherical cavity in a viscoelastic medium of Voigt type. In the present study we investigate the propagation of a spherical wave formed from the action of a pulsed load on the internal surface of a spherical cavity in a viscoelastic half-space. The potentials of the waves propagating in the medium are constructed in the form of series in special functions. In order to realize viscoelasticity we use a correspondence method [10]. The transform inversion is carried out by means of a representation of the potentials in integral form and subsequent use of asymptotic methods for their calculation. Thus, it becomes possible to investigate the behavior of a medium near the wave fronts. The radial stress is calculated on the surface of the cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 139–146, March–April, 1976.     

Nonstationary gas flow with shock waves in a supersonic compressor

Shock waves are formed in the channels between blades in a compressor working in the transsonic state, and the positions of these vary periodically and produce strong vibrations in the blades. The effect is extremely complex and is dependent on a large number of parameters. Here we present a simplified model for the effect, which can be examined theoretically. It is assumed that the nonstationary pulsations in the flow and the amplitudes in the oscillations of the shock waves are small, and therefore one can employ a steady-state flow whose characteristics may be taken as given, including the mean position of the shock waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 41–47, September–October, 1973.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Velocity field in a cylindrical hydrocyclone

The flow in a cylindrical hydrocyclone is investigated at moderate Reynolds numbers. Such a flow regime is realized in a hydrocyclone when, for example, certain solid particles are separated. The flow is calculated in the frame-work of the theory of an inviscid incompressible fluid, since the influence of turbulent pulsations on the flow structure in the investigated flow regime (Reynolds numbers of the order of a few thousand) is slight. Comparison of the results with experimental data indicates good qualitative agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 12–20, November–December, 1980.I thank Yu. P. Gupalo and Yu. S. Ryazantsev for discussing the work and for valuable comments.     

Some results obtained on studying the flow of liquid films by stroboscopic visualization

The characteristic features of stroboscopic visualization and the possibilities of using this method for studying the flow of thin films are considered. The velocity field and the field of turbulent pulsations are studied experimentally for the film flow of liquids with Reynolds numbers of R = 40–1770.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 140–143, March–April, 1972.     

Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body

The flow with a free-stream Mach number M _∞ = 6 around a cylindrical body with a sharp spike is studied. The existence of a supersonic reverse flow for one of the phases of the pulsating flow regime is experimentally validated. A range of spike lengths is determined, which ensures a region of a supersonic reverse flow near the side surface of the spike. The time of existence of the supersonic reverse flow region is shown to be 0.15 of the period of pulsations if the spike length equals the model diameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 30–39, July–August, 2007.     

Hydroshock theory in a two-phase gas-liquid mixture in a slug flow regime

A study is made of the intensity of a hydroshock in a two-phase gas-liquid mixture in a slug flow regime in the case when a pipeline is shut off by a liquid slug. The intensity is studied as a function of the length of the shut-off section of the liquid slug, the content of gas bubbles in the liquid slugs, and the pipeline shut-off law, and with allowance for the shock-wave character of the process [1, 2]. The calculated data using the shock-wave theory agree well with the experimental data of [3] and, unlike the results of the linear theory of [3], make it possible to determine the intensity of the hydroshock not only in the case of weak waves, but also in the case of waves of moderate intensity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 188–190, September–October, 1985.     

Experimental investigation of nonstationary flow in cavities in a supersonic flow

An experimental investigation was made into the flow and pressure pulsations in cylindrical cavities open toward a supersonic flow and set up at zero angle of attack (i.e., the cavity axis and the direction of the flow coincide).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 180–183, September–October, 1979.     

Nonstationary expulsion of a viscous fluid from a pipe

The problem of expulsion of one viscous fluid by another in a circular pipe with a nonstationary pulsating laminar motion is considered. It is found that the imposition of pulsations of a definite frequency on the process of stationary expulsion can result in an increase in the coefficient of expulsion to 10–12%.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 170–171, March–April, 1977.     

Formation and propagation of cylindrical shock waves in a pulsed induction discharge

An experimental investigation was made into the formation and propagation of cylindrical collapsing shock waves in a pulsed induction gas discharge. The shock fronts were made visible and their propagation velocity measured by means of the schlieren method in conjunction with high-speed cine photography in the photoscanning regime and frame-by-frame detection, which made it possible, using the experimental data, to analyze the formation and propagation of the shock waves. A physical picture of the individual stages in the development of the discharge is given on the basis of the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–133, January–February, 1981.We are thankful to Yu. P. Raizer for helpful discussions of the work.     

Development of three-dimensional disturbances in a boundary layer with pressure gradient

The results of an experimental investigation of the three-dimensional stability of a boundary layer with a pressure gradient are presented. A low-turbulence subsonic wind tunnel was employed. The development of a three-dimensional wave packet of oscillations harmonic in time in the boundary layer on a model wing is studied. The amplitudephase distributions of the pulsations in the wave packet are subjected to a Fourier analysis. Spectral (with respect to the wave numbers) decomposition of the oscillations enables the flow stability with respect to plane waves with different directions of propagation to be examined. The results are compared with the corresponding data obtained in flat plate experiments. The effect of the pressure gradient on the development of the three-dimensional spectral components of the disturbances and the dispersion properties of the flow is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 85–91, May–June, 1988.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Stability of a nonisothermal boundary layer in the presence of periodic perturbations of the exterior flow velocity

The stability of a laminar boundary layer in the presence of high-frequency time-periodic perturbations of the exterior flow velocity, in particular, acoustic vibrations, is investigated in a series of papers which are reviewed in detail in monograph [1]. The mechanisms by which such perturbations influence the stability and transition to the turbulent flow regime can vary. For example, they can lead to the deformation of the averaged field of the basic flow. However, there was good reason not to discuss the effect of this type of perturbation earlier, as it was considered that the change in the basic flow was very small even for perturbations of great amplitude. The aim of the present paper is to demonstrate how perturbations or pulsations in the exterior flow velocity can, by changing the basic flow, have a strong influence on the stability of the laminar boundary layer of a gas under appreciably nonisothermal conditions. Examples of calculations that support this assertion are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–186, September–October, 1984.The authors wish to thank A. A. Maslov for his help with the calculations.     

Mixed boundary-value problems of profiling of supersonic nozzles and channels

In the framework of the inverse method of numerical profiling of the supersonic part of nozzles and channels, two new mixed boundary-value problems of gas dynamics are formulated and solved with boundary conditions specified both along and across the flow. A modification of the grid-characteristic method with respect to layers formed by streamlines is constructed. The solution of the posed mixed problems makes it possible to profile a class of flat and axisymmetric nozzles and channels larger than the known class. Transition channels, which transform one expanding flow into another for which the flow at the exit is close to that from a source, are constructed Channel profiles are obtained with a bend in the generator that suppress shock waves on the wall. The results are presented of profiling of exit channels with contact discontinuity, and also channels that realize discontinuities in the exit sections, these being made isentropic by means of compression characteristics focused at the points of the discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 112–118, July–August, 1983.We thank U. G. Pirumov, M. Ya. Ivanov, and A. N. Kraiko for helpful discussions.     

Stokes waves on a cavity surface in a rotating fluid

The axisymmetric flow of an inviscid incompressible fluid rotating about a cavity with constant pressure is considered. Due to the centrifugal force, on the cavity surface waves may exist, in particular, waves with a break in the wave base where the cavity meridional sections form the angle 2/3, i.e. Stokes waves. A method of finding these waves from the boundary-value problem for the fluid velocity potential is described. For an infinite cavity, the dependence of the wave parameters on the cavitation number, calculated using the pressure in the cavity, is given.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1996.