On the stability margin of equilibrium states of a capillary liquid in a slit

The stability margin is determined for symmetric equilibrium shapes of the free surface of a liquid suspended in a slit and subject to gravity and surface tension. The calculations are made in the range of variation of the parameters, the wetting angle and the Bond number, adjoining the boundary of the stability region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–93, July–August, 1979.     

Cauchy problem for the equation of evolution of small perturbations of the surface of ablating wedge (cone) shapes

The Cauchy problem for small perturbations of the surface of steady-state ablating shapes was formulated and studied in [1]. The conclusion of that study concerning the fundamental difference between the properties of the problem in the plane (=0) and axisymmetric (v=1) cases is shown to remain valid for wedge and cone shapes — for a cone the solution is unique, but for a wedge the choice of solution requires the introduction of an additional condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–182, January–February, 1988.     

Comparison of integrated characteristics and shapes of profiled contours of laval nozzles with “smooth” and “abrupt” contractions

The influence of the selection of the generator of subsonic sections of plane and axisymmetric Laval nozzles on the integrated characteristics and on the shapes of their profiled supersonic parts is investigated in the approximation of an ideal (inviscid and nonheat-conducting) gas. Nozzles with a smooth entrance and with an abrupt contraction are compared for the same flow rates and size restrictions on the whole nozzle, not only to its supersonic part. In such a formulation, in accordance with [1], nozzles with abrupt contractions in the flow of ideal gas in them should be expected to have the best characteristics. This is confirmed by the results of the calculations performed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 129–137, July–August, 1986.The authors are grateful to V. A. Vostretsova for her help in the work.     

On the shape of bodies ablating in a supersonic gas stream

When objects move at a high velocity in a dense medium, their front surfaces undergo intense heating. There can then be a strong interaction between the oncoming flow and the surface of the body in which the body is not merely subject to the thermal and force effect of the stream but also significantly changes the flow field itself due to the intense blowing of ablation products from its surface and the change in the geometry of the front surface. Experimental and numerical investigations into the various regimes of strong interaction have established how stable shapes are adopted by bodies ablating in a supersonic gas stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–21, January–February, 1981.     

Hopf bifurcation in a three-dimensional system

In this paper,Liapunor-Schmidl reduction and singularity theory are employed to discuss Hopf and degenerate Hopf bifureations in global parametric region in a three-dimensional system x=-βx+y, y=-x-βy(1-kz), z=β[α(1-z)-ky²], The conditions on existence and stability are given.     

On the shapes of swirling annular jets of a liquid

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. A critical analysis of the investigations into jets from centrifugal nozzles is contained in [1]. These investigations elucidated the experimentally observed tulip and bubble jet shapes, and also predict the existence of annular jets of periodic shape. However, simplifications of the flow details are made to obtain the results. For example, in the equations describing the equilibrium of the forces acting on the film, no allowance is made for forces that arise on account of the curving of its shape in the meridional sections nor for the variability of the tangential velocity component in the field of the centrifugal forces. In the present paper, the method of [2] is used to derive equations that describe the flow of swirling annular jets of liquid with uniform profile of the longitudinal velocities in an undisturbed ideal medium with allowance for surface tension and gravity forces and also the pressure difference outside and within the jet. The results of calculations are given that illustrate the dependence of the jet shapes on the relative contributions of the capillary and inertial forces and also the pressure difference, the intensity of the initial swirling, the angle at which the liquid leaves the nozzle, and the gravity force.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 144–148, September–October, 1979.I am grateful to V. Ya. Shkadov for interest in the work.     

Nonaxisymmetric equilibrium shapes of a drop on a plane

A nonuniform temperature distribution, the presence of surface-active substances and impurities, and also other factors lead to a change in the wetting angle along a plane. A study is made of the influence of a small perturbation of the equilibrium contact angle on the shape of the free surface of the liquid. Two cases are considered: a surface of small slope in a gravity field and a nearly spherical shape under conditions of weightlessness. The equilibrium shapes of a liquid drop on an inclined plane under conditions of hysteresis of the wetting are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 164–167, July–August, 1983.I thank I. E. Tarapov and I, I, Ievlev for constant interest in the work and valuable comments.     

One-dimensional problem of a shock in a gas

The self-similar problem of the motion of a cold gas subjected to an instantaneous impulse is considered. A solution is constructed in the neighborhood of the known exact solution for a gas with a specific heat ratio =1.4 [1–4]. An analytic expression is obtained in this neighborhood for the dependence of the index of self-similarity n on the parameter h, which is related to the adiabatic index by h=(+1)/(–1). The results of a numerical calculation of n versus h are compared with the analytic expression.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 74–78, November–December, 1973.     

Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes

Measurements in the viscous sublayer of a flat-plate turbulent boundary layer in air, using single hot-wire sensors with lengths from 1–60 viscous length scales show that, at a given distance from the surface, the turbulence intensity, flatness factor, and skewness factor of the longitudinal velocity fluctuation are nearly independent of wire length when the latter is less than 20–25 times the viscous length scale (i.e. 20–25 wall units), and decrease significantly and abruptly for larger wire lengths. This conclusion is consistent with other workers' probability density functions of streak spacing: the lateral spacing of streaks in the viscous sublayer is 80–100 wall units on average with minimum spacing of 20–25 wall units, which implies that signals would be strongly attenuated by wires whose length exceeds 20–25 wall units. To achieve wire lengths of less than 20–25 wall units, subminiature hot wire probes like those described by Ligrani and Bradshaw (1987), having lengths as small as 150 m, are necessary for sublayer measurements in typical laboratory wind tunnels. As well as the measurements mentioned above, dissipation spectra are presented, to show the effect of spanwise averaging on the high-frequency motions, which is necessarily more severe than the effect on overall intensities.     

Investigation of isothermal flow of a mixture of gas and particles in a channel of variable section

Isothermal flow of a gas with particles is investigated analytically, which makes it possible to analyze all possible flow regimes in channels of different shapes. It is shown that in a channel of constant section there are two possibilities: either an equilibrium regime is established with constant flow parameters, or the gas reaches the velocity of sound, and then further flow in the channel is impossible (blocking of the channel). In a contracting nozzle, blocking also occurs if the channel is sufficiently long. In an expanding nozzle when there are particles in the gas with a velocity lower than the gas velocity, it is possible to have flow regimes with transition through the velocity of sound: a subsonic flow goes over into a supersonic flow and, conversely, it is also possible to have a flow in which there is blocking of the channel, which is quite different from the flow of a pure gas in an expanding nozzle and is due to the influence of interphase friction on the flow. The variation of the pressure along the flow can be nonmonotonic with points of local maximum or minimum which do not coincide with the singular point at which the gas velocity reaches the velocity of sound. In the case of nonequilibrium gas flows with particles in a Laval nozzle, the velocity of the gas may become equal to the isothermal velocity of sound not only in the exit section of the nozzle or in its expanding part, as noted in [4–6], but also at the minimal section, since it is possible to have flows for which the velocities of the phases are equalized at this section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 61–68, October–December, 1981.     

Development of temperature-compensated resistance strain gages for use to 800°C

This paper describes the development and evaluation of temperature-compensated resistance strain gages for use to 800°C. These gages included single-element gages and double-element half-bridge gages. The filament of single-element gages was fabricated from specially developed Fe–Cr–Al–V–Ti–Y alloy wire. When bonded to high-temperature Ni-based alloy GH39 after stabilization at 800°C for one hour, the apparent strain from room temperature to 800°C was less than 2000 m/m. Double-element gages were fabricated from Pt–W–Re–Ni–Cr–Y alloy wire (active grid) and Pt–Ir alloy wire (compensating grid). When bonded to different high-temperature alloy specimens and stabilized, and when ballast resistance in series with the compensating grid adjusted suitably, the gages' apparent strains from room temperature to 800°C were less than 2400 m/m.Effects of preoxidization of Fe–Cr–Al wire on the characteristics of the single-element gages are described.     

Calculation of axisymmetric cavities downstream of a disk in subsonic compressible fluid flow

Cavitation subsonic water flow past a disk is calculated in accordance with the Riabouchinsky scheme by a finite-difference method at Mach numbers M0.95 and cavitation number –0.02. The calculated results are compared with the data of slender body theory and the results obtained from some approximate formulas.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1996.     

Radiative heat transfer in an emitting,absorbing, and scattering compressed layer

The aim of the paper is to investigate the screening of radiation from the high-temperature part of the compressed layer by the two-phase ablation products of a graphite axisymmetric body moving under the following conditions through a hypersonic air flow: V = 12–18 km/sec, p_s = 10⁵ Pa, R = 1–3 m, and /₀ = (2.54–5.73)·10^–4. Steady and unsteady sublimation regimes of graphite ablation with strong blowing are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1984.     

Pressure pulsations on the surface of a sphere in a subsonic stream

Many data are available on the drag C_x and the distribution of the static pressure over the surface of a sphere [1, 2]. However, there are virtually no data on pulsations of the pressure over the surface of a sphere. In the present paper, the results are given of an investigation of the total and spectral levels of the pressure pulsations at different points of the surface of a sphere at M 0.5–1.0 and Re (1.7–2.7)·.10⁶. It was found that the strongest pressure pulsations occur on the side in the region of the angle 90°. In this region at M 0.6–0.8 the relative total level o/q where q is the velocity head in the oncoming stream, reaches values 0.18–0.22. It was established that at M = 0.7–0.9 narrow-band maxima occur in the spectra of the pressure pulsations at frequencies Sh fD/V = 0.2–0.3. Data are also presented on the pulsations of the base pressure behind a spherical segment with short cylindrical and conical trailing edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–168, September–October, 1981.     

Shock Thickness in Monatomic Gases

The entropy balance of a Navier–Stokes–Fourier fluid is used to predict the thickness of a shock wave as a function of the Mach number. The results are in good agreement with experimental observations. Indeed the agreement of our thermodynamic calculations with experiments is better than that of the actual solution of the Navier–Stokes–Fourier equations by Gilbarg and Paolucci [1].     

Development,current state of the art,and applications of local interaction theory. Review

Local interaction theory comprises studies based on the representation of the force and thermal characteristics of the action of a medium on a body at a certain point on its surface as functions of the local velocity, the angle between the velocity direction and the normal to the surface, and the global parameters, which are constant at all points on the surface.In this review, we will trace the history of the theory and analyze the main results concerning the development of particular local interaction models, the calculation of the integral characteristics and the determination of optimal body shapes, the general properties of the model and practical methods based on them, and nontraditional fields of local model application.Along with the general results, we will focus on the most important fields of local model application, such as aerodynamics, gasdynamics, and rarefied gas dynamics.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–18, May–June, 1996.     

Experimental investigation of flow in nozzles of gas-dynamic lasers

To produce an active medium in a gas-dynamic laser, it is necessary to ensure rapid and deep cooling of a mixture of gases (usually CO₂-N₂-H₂O). For this, one uses, as a rule, flat supersonic nozzles with a corner point that are designed for obtaining a flow with Mach number M=4.5–6. The requirements on their dimensions and profile are determined by the kinetics of the relaxation processes in the expanding gas stream and the need to obtain at the exit a sufficiently uniform field of the gas-dynamic parameters. Because of the complexity of making nozzles, one frequently uses simplified shapes, which generate shock waves in the resonator cavity. This increases the divergence of the laser beam and reduces the population inversion of the vibrational levels of the CO₂ molecule [1] because of the growth of the temperature and the density behind shock waves. Therefore, for the correct interpretation of the results of measurements of the gain of a weak signal and correct comparison with calculations, it is necessary to make a combined study of the inversion properties of the flow and the aerodynamics of the flow. In the present work, we have investigated the flow structure in a number of small flat nozzles. Data on measurements of in a gas-dynamic laser using these nozzles are given in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 178–182, September–October, 1980.     

Efficient Extreme Value Prediction for Nonlinear Beam Vibrations Using Measured Random Response Histories

Predicted extreme exceedance probabilities associated withexperimental measurements of highly non-linear clamped-clamped beamvibrations driven by band-limited white-noise, are compared using twodifferent approaches for application to short data sets. The firstapproach uses response history measurements to calibrate a discretedynamic model using a Markov moment method appropriately matched toextreme value prediction via finite element solution of theFokker–Planck (FPK) equation. The dynamic model is obtained via theWoinowsky–Krieger equation with added empirical damping. Stationary FPKsolutions are used to obtain mean crossing rates, and for the purpose ofextreme value prediction, crossings are assumed to be independent. Thesecond approach uses a Weissman type I asymptotic estimator, justifiedby use of the Hasofer–Wang hypothesis test. Both methods are comparedwith exceedance probabilities obtained using data from long experiments in which dependence between extreme values is excluded. Thepaper shows that by exploiting the Weissman estimator in a forwardpredictive mode, very accurate exceedance probabilities can be obtainedfrom relatively small amounts of measured data. The calibrated modelbased predictions are consistently in error as a result of non-linearcoupling effects not included in the model – this coupling isimplicitly accounted for in the Weissman predictions.     

On the perturbation front structure for transport processes with spatial–temporal nonlocality

The onedimensional problem of the propagation of a perturbation front from a point instantaneous source for transport processes with spatial–temporal nonlocality is considered. A class of nonlocality kernels with a singularity of the form t^–1 for small times is used. The front propagation speed v is calculated and an expression for perturbations in the vicinity of the front is derived in the form of an asymptotic series in powers of the parameter = t – xv^–1.     

Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.