The elastic field near a point of a transition from frictional contact to frictionless contact

The asymptotic nature of the elastic field is studied at the point of transition from frictional contact to frictionless contact between two different elastic bodies. The nature depends on the direction of slip, and the singular stress field appears when the body with smaller /(–1) (: the shear modulus, =3–4, : Poisson's ratio) slips towards the region of frictional contact, while no singularities appear when the direction of slip is opposite. The order of the singularity is smaller than 1/2 regardless of the level of friction.     

Asynchronous parametric suppression of resonance vibrations of hyghly nonlinear systems

Conclusions The investigations have shown that the auxiliary asynchronous parametric excitation ca be used to effectively suppress resonance vibrations in systems with highly nonlinear elast characteristics. Either local or wideband suppression of the resonance regime can be achieved, depending on the relation between the frequencies of the primary external and auxiliary parametric excitations (/=const or /const); also, the width and positions of the instability intervals can be controlled. This affords the possibility of using auxiliary parametric excitation not only to enhance the efficiency of nonlinear antivibration systems (by wideband suppression of resonance vibrations), but also for the design of fundamentally new resonance devices to monitor the frequency and amplitude of vibrations by exploiting the effect of local instability of the resonance regime.Polytechnic Institute, Riga. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 102–107, May, 1991.     

Zur Verknüpfung von Stoffübergang und physikalischen bzw. chemischen Wandvorgängen in technischen Reaktoren

In technical reactors like catalytic honeycombreactors with a reaction at the wall and with an unknown field of concentrationc _A (r,z) the diffusive flux _A,D.w is replaced by the transferflux _A,. The transferflux _A, i.e. the Sherwood-number only depends on processes, which effect the diffusive flux, i.e. the gradient of concentration c _A /r¦ _w . For vaporisation with a constant concentrationc _A,w at the wall or for a heterogeneous reaction with a variable concentrationc _A,w the fluidstream would be such a process. In any case Sherwood-numberSh depends only on Bodenstein-numberBo and is — even for a heterogeneous reaction — no function of Damköhler-number. Only in case of a homogeneous reaction in the fluid phase there is a influence on the gradient of concentration and it followsSh (Bo, Da _I).According toSh _neu (Bo, Da _II) the gradient of concentration c _A /r in _A,D is replaced in _A, by the mean concentration and not, as usual, by the difference of concentration . Both concentrations depends on the Damköhler-numberDa _II. The difference of concentrations shows either no or only little dependence ofDa _II (this illustrates the quality of representation of _A,D,w by _A, ). If is defined by , than _neu depends onDa _II Sh _neu =Sh _neu (Bo, Da _II). According to this definition of _neu no new facts will arise. The common theoretical or experimental values of orSh are applicable to every process with heterogeneous reactions. In analogous cases the following explanations are also valid for heat-transfer at the wall, if a heterogeneous reaction takes place.Zusammenfassung In technischen Reaktoren, wie z. B. einem katalytischen Wabenrohrreaktor, in denen sich das Konzentrationsfeldc _A (r, z) nicht genau ermitteln läßt, ersetzt die Übergangsstromdichte _A, vereinfachend die Diffusionsstromdichte _A,D,w an die Wand. Die Übergangsstromdichte _A, bzw. dieSh-Zahl ist nur von den Vorgängen abhängig, die die Diffusionsstromdichte an die Wand, _A,D,w , d. h. den Konzentrationsgradienten c _A /r¦ _w beeinflussen. Bei Verdampfung mit konstanter Wandkonzentrationc _A,w oder bei einer heterogenen Reaktion an der Wand mit veränderlichemc _A,w ist ein solcher Vorgang z. B. die Strömung, d. h. in beiden Fällen istSh =Sh (Bo) und hängt auch bei einer heterogenen Reaktion nicht von der Damköhler-II-Zahl ab. Nur wenn in der strömenden Phase (zusätzlich) eine homogene Reaktion vorliegt [12], hat diese einen Einfluß auf den Gradienten und es giltSh =Sh (Bo, Da _I).Die AbhängigkeitSh _neu (Bo, Da _II) entsteht definitorisch dadurch, daß der in _A,D auftretende Gradient c _A /r in _A, z. B. durch eine mittlere Konzentration ( _neu), statt wie üblich durch eine Konzentrationsdifferenz , erfaßt wird. Beide Konzentrationen sind von der DamköhlerzahlDa _II abhängig, ihre Differenz aber nicht bzw. wenig (worin sich die Güte der Abbildbarkeit von _A,D,w durch _A, verdeutlicht). Läßt man also in der Definitionsgleichung für die Stoffübergangszahl die veränderliche Wandkonzentrationc _A,w weg, dann entsteht eine entsprechende starke Abhängigkeit der Größe _neu (bzw.Sh _neu) von derDa-II-Zahl:Sh _neu=Sh _neu (Bo, Da _II). Neue Sachverhalte werden mit solchen Definitionen von _neu nicht begründet. Die üblichen theoretisch oder experimentell ermittelten - oderSh-Werte können beim Auftreten von Stoffwandlungsvorgängen an der Wand für reaktionstechnische Berechnungen verwendet werden. Die folgenden Ausführungen gelten bei gegebener Analogie auch für den Wärmeübergang mit physikalischen oder chemischen Wandvorgängen, wie Verdampfung oder chemischer Wandreaktion.     

Stability of Thermal Vibrational Flow in an Inclined Liquid Layer Against Finite‐Frequency Vibrations

Stability of the flow that arises under the action of a gravity force and streamwise finitefrequency vibrations in a nonuniformly heated inclined liquid layer is studied. By the Floquet method, linearized convection equations in the Boussinesq approximation are analyzed. Stability of the flow against planar, spiral, and threedimensional perturbations is examined. It is shown that, at finite frequencies, there are parametricinstability regions induced by planar perturbations. Depending on their amplitude and frequency, vibrations may either stabilize the unstable ground state or destabilize the liquid flow. The stability boundary for spiral perturbations is independent of vibration amplitude and frequency.     

Flow of a polymer with a high value of the relaxation time and low viscosity

A nonlinear model of an elastoviscous polymer is used to describe a number of experimental factors associated, in particular, with the solidification of the moving medium. It is assumed that this flow suppression is connected with the existence in the polymer system of a large relaxation time with low weight, whose influence on the flow is associated with certain forms of nonlinear deformation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–10, November–December, 1988.     

Shear Instability at the “Explosion Product–Metal” Interface for Sliding Detonation of an Explosive Charge

Periodic perturbations at the explosion product–metal interface were studied experimentally. Experiments were performed for both spherical and plane geometry. Critical conditions of wave formation (detonation velocity of an explosive charge D 6.9 mm/sec) are determined, and an explanation of this effect is given. It is found experimentally that a dynamic pulse causes intense plastic strains at the explosion products–metal interface, leading to thermal softening of the steel boundary layer. In this layer, Kelvin–Helmholtz instability occurs. Calculationanalytical estimates of the critical boundary unstable wavelength agree satisfactorily with experimental results.     

Hypersonic flow past blunt-edged delta wings

A method is proposed for calculating hypersonic ideal-gas flow past blunt-edged delta wings with aspect ratios = 100–200. Systematic wing flow calculations are carried out on the intervals 6 M 20, 0 20, 60 80; the results are analyzed in terms of hypersonic similarity parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–179, September–October, 1990.     

Stationary travelling waves on a film flowing down an inclined plane

At small flow rates, the study of long-wavelength perturbations reduces to the solution of an approximate nonlinear equation that describes the change in the film thickness [1–3]. Steady waves can be obtained analytically only for values of the wave numbers close to the wave number _n that is neutral in accordance with the linear theory [1, 2]. Periodic solutions were constructed numerically for the finite interval of wave numbers 0.5_{n n} in [4]. In the present paper, these solutions are found in almost the complete range of wave numbers 0 _n that are unstable in the linear theory. In particular, soliton solutions of this equation are obtained. The results were partly published in [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–146, July–August, 1980.     

Nonlinear stabilization of unstable acoustical vibrations in a bounded heat-evolving medium

The working process in many power units, taking place with the evolution of energy, under determined conditions is acoustically unstable in a linear approximation. The problem of determination of the amplitudes of the unstable waves, set up as a result of the pumping of energy from the unstable mode to the damping mode with their linear interaction is of practical interest. In this paper equations are derived for the fully established amplitudes of plane acoustical vibrations in a three-wave approximation, taking account of boundary impedances, breaking down the internal resonance of the acoustical overtones excited. The discussion regards a high-temperature heat-evolving gas, whose general stability conditions were formulated in [1] and discussed also in [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 34–41, November–December, 1978.     

Boundary layer stability on a rotating disk with corotation of the surrounding fluid

The stability of the steady self-similar flow in the boundary layer on a rotating disk of infinite radius with corotation of the surrounding fluid is analyzed by the normal mode method. The spectral problem for infinitesimal three-dimensional disturbances is solved by a collocation method with expansion of the amplitude functions in Chebyshev polynomials. It is established that for all values of the parameter 0, equal to the ratio of the angular velocities of the fluid and the disk, the lower critical Reynolds number is determined byA-type, waves, whose development is governed by the parallel instability mechanism typical of an Ekman layer. TheB-type instability, associated with the presence of an inflection point on the velocity profile, disappears when 4. The neutral surfaces are calculated for Karman flow (=0) and Bödewadt flow (). It is found that in Karman flowA-type waves may grow at values of the Reynolds number several times smaller than the critical Reynolds number for spiral vortices. The results of the analysis are compared with the available experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 69–77, September–October, 1992.     

Plane Problem of Vibrations of an Elastic Floating Plate under Periodic External Loading

The Wiener–Hopf technique is used to construct an analytical solution of the problem of vibrations of a semiinfinite elastic floating plate under periodic external loading. The solution is obtained in explicit form ignoring draft. The dependences of the amplitudes of surface waves and iceplate deflection on the loading distribution and frequency, ice thickness, and liquid depth are studied numerically. It is established that for some types of acting load, no waves propagate in the plate and liquid and the plate vibrations are standing waves localized near the loading region. An example of such vibrations is given and a condition for the occurrence of localized vibrations is found.     

Instability of a plane axisymmetric flow with a shear discontinuity in the velocity profile

It is proposed to investigate the stability of a plane axisymmetric flow with an angular velocity profile (r) such that the angular velocity is constant when r < r_O – L and r > r_O + L but varies monotonically from ₁ to ₂ near the point r_O, the thickness of the transition zone being small L r_O, whereas the change in velocity is not small ¦₂ – ₁¦ ₂, ₁. Obviously, as L O short-wave disturbances with respect to the azimuthal coordinate (k=m/r_O 1/r_O) will be unstable with a growth rate-close to the Kelvin—Helmholtz growth rate. In the case L=O (i.e., for a profile with a shear-discontinuity) we find the instability growth rate _O and show that where the thickness of the discontinuity L is finite (but small) the growth rate does not differ from _O up to terms proportional to kL 1 and 1/m 1. Using this example it is possible to investigate the effect of rotation on the flow stability. It is important to note that stabilization (or destabilization) of the flow in question by rotation occurs only for three-dimensional or axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–114, January–February, 1985.     

Interpolation formulas for maxwell viscosity of certain metals as a function of shear-strain intensity and temperature

The purpose of this study is the construction of interpolation formulas for the dependence of Maxwell viscosity, a quantity which is the reciprocal of shear-strain relaxation time , on shear-strain intensity and temperature for several metals: iron, aluminum, copper, and lead. This function was interpolated in various temperature and deformation velocity ranges in accordance with available experimental data for iron (0 10⁷ sec^–1, 200 ° T 1500 °); aluminum (0 10⁷ sec^–1, 300 ° T 900 °); copper (0 10⁵ sec^–1, 300 ° T 1300 °); lead (0 10⁶ sec^–1, 90 ° T 400 °); temperatures in °K.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 114–118, July–August, 1974.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Hydrodynamic instability of the contact zone between accelerated gases

An experimental apparatus for investigating Rayleigh-Taylor instability in the transition layer between two gases at accelerations g 10⁵g₀ (g₀ is the acceleration of gravity) is described. The constantly acting acceleration is communicated to the contact zone by the compression wave formed ahead of a flame front. The linear stage of development is investigated together with the effect of the thickness of the contact zone. It is shown that on the interval 0.3 < <- ( is the wavelength of the disturbance at the edge of the contact zone) the rate of growth of the perturbation amplitude 0.5₀, where ₀ is the amplitude growth rate for media separated by an interface with a discontinuous change of density.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 15–21, November–December, 1991.     

Wärmeübertragung in einem axial rotierenden,durchströmten Rohr im Bereich des thermischen Einlaufs

Zusammenfassung Der Einfluß der Rotation auf das Temperaturprofil und die Wärmeübergangszahl einer laminaren Rohrströmung im Bereich des thermischen Einlaufs wird theoretisch untersucht. Es wird angenommen, daß das Geschwindigkeitsprofil voll ausgebildet ist. Die Rotation hat einen destabilisierenden Einfluß auf die Laminarströmung, die umschlägt und turbulent wird. Aufgrund der Anfachung der Turbulenz durch die Rotation verbessert sich die Wärmeübertragung mit steigender Rotations-Reynoldszahl und die thermische Einlauflänge nimmt beträchtlich ab.

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Heat transfer in an axially rotating pipe in the thermal entrance region. Part 2: Effect of rotation on laminar pipe flow

The effects of tube rotation on the temperature distribution and the heat transfer to a fluid flowing inside a tube are examined by analysis in the thermal entrance region. The flow is assumed to be hydrodynamically fully developed. The rotation has a destabilizing effect on the laminar pipe flow, causing a transition to turbulent flow. Therefore, a remarkable increase in heat transfer with increasing rotational Reynolds number can be observed. The thermal entrance length decreases remarkably with growing rotational Reynolds number.

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Formelzeichen a Temperaturleitzahl - C _n , ,C ₁,C ₃ Konstanten - c _p spezifische Wärme bei konstantem Druck - D Rohrdurchmesser - E Funktion nach Gl. (16) - H _n Eigenfunktionen - l hydrodynamischer Mischungsweg - l _q thermischer Mischungsweg - N=Re /Re Reynoldszahlenverhältnis - Nu Nusseltzahl - Nu Nusseltzahl für die thermisch voll ausgebildete Strömung - Pr Prandtlzahl - Pr _t turbulente Prandtlzahl - Wärmestromdichte - Re _* Schubspannungsreynoldszahl - R _s Eigenfunktionen - Durchfluß-Reynoldszahl - Re =v D/v Rotations-Reynoldszahl - R Rohrradius - r Koordinate in radialer Richtung - Dimensionslose Koordinate in radialer Richtung - T Temperatur - T _b bulk temperature - mittlere Axialgeschwindigkeit - v Geschwindigkeit - dimensionsloser Wandabstand - Integrationsvariable - Integrationsvariable - , dimensionslose Temperaturen - Wärmeleitzahl - _p Eigenwerte - kinematische Viskosität - Dichte - tangentiale Koordinate - , Hilfsfunktionen Indizes m in der Rohrmitte - r radial - w an der Rohrwand - z axial - 0 am Rohreintritt - 0 ohne Rotation - tangential     

Shear softening and thixotropic properties of wheat flour doughs in dynamic testing at high shear strain

Shear softening and thixotropic properties of wheat flour doughs are demonstrated in dynamic testing with a constant stress rheometer. This behaviour appears beyond the strictly linear domain (strain amplitude ₀ 0.2%),G,G and |^*| decreasing with ₀, the strain response to a sine stress wave yet retaining a sinusoidal shape. It is also shown thatG recovers progressively in function of rest time. In this domain, as well as in the strictly linear domain, the Cox-Merz rule did not apply but() and | ^*())| may be superimposed by using a shift factor, its value decreasing in the former domain when ₀ increases. Beyond a strain amplitude of about 10–20%, the strain response is progressively distorted and the shear softening effects become irreversible following rest.     

Calculation of heat transfer accompanying hypersonic three-dimensional flow of air over slender blunt-nosed cones

The effective length method [1, 2] has been used to make systematic calculations of the heat transfer for laminar and turbulent boundary layers on slender blunt-nosed cones at small angles of attack ( + 5° in a separationless hypersonic air stream dissociating in equilibrium (half-angles of the cones 0 20°, angles of attack 0 15°, Mach numbers 5 M 25). The parameters of the gas at the outer edge of the boundary layer were taken equal to the inviscid parameters on the surface of the cones. Analysis of the results leads to simple approximate dependences for the heat transfer coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 173–177, September–October, 1981.     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.     

Experimental study of stability of strongly underexpanded laminar free and impact jets

The growth rates of density fluctuations in the mixing layer of strongly underexpanded lowdensity jets are measured by the electronbeam technique within the range of Reynolds numbers Re_L = 50 – 230. Regimes of selfinduced oscillations are determined for these flow conditions in the case of a jet incident normally onto a finitesize target. Results on the frequency of pressure oscillations on the target are obtained and compared with the spectra of the growth rates of density fluctuations in the mixing layer of free jets. It is shown that selfinduced oscillations cannot be sustained because of the development of instability in the mixing layer of the jet.