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.     

Laminar boundary layer on blunt bodies with account for vorticity of the external flow

This paper presents the technique for and results from numerical calculations of the hypersonic laminar boundary layer on blunted cones with account for the vorticity of the external flow caused by the curved bow shock wave. It is assumed that the air in the boundary layer is in the equilibrium dissociated state, but the Prandtl number is assumed constant, =0.72. The calculations were made in the range of velocities 3–8 km/sec, cone half-angles _k=0°–20°. With account for the vortical interaction of the boundary layer with the external flow, the distribution of the thermal flux and friction will depend on the freestream Reynolds number (other conditions being the same). In the calculations the Reynolds number R, calculated from the freestream parameters and the radius of the spherical blunting, varies from 2.5·10³ to 5.10⁴. For the smaller Reynolds numbers the boundary layer thickness on the blunting becomes comparable with the shock standoff, and for R<2.5·10³ it is apparent that we must reconsider the calculation scheme. With R>5·10⁴ for cones which are not very long the vortical interaction becomes relatively unimportant. The results of the calculations are processed in accordance with the similarity criteria for hypersonic viscous gas flow past slender blunted cones [1, 2].     

On laminar flow through a uniformly porous pipe

Numerous investigations ([1] and [4–9]) have been made of laminar flow in a uniformly porous circular pipe with constant suction or injection applied at the wall. The object of this paper is to give a complete analysis of the numerical and theoretical solutions of this problem. It is shown that two solutions exist for all values of injection as well as the dual solutions for suction which had been noted by previous investigators. Analytical solutions are derived for large suction and injection; for large suction a viscous layer occurs at the wall while for large injection one solution has a viscous layer at the centre of the channel and the other has no viscous layer anywhere. Approximate analytic solutions are also given for small values of suction and injection.

Nomenclature

General r distance measured radially - z distance measured along axis of pipe - u velocity component in direction of z increasing - v velocity component in direction of r increasing - p pressure - density - coefficient of kinematic viscosity - a radius of pipe - V velocity of suction at the wall - r ²/a ² - R wall or suction Reynolds number, Va/ - f() similarity function defined in (6) - u ₀() eigensolution - U(0) a velocity at z=0 - K an arbitrary constant - B _K Bernoulli numbers Particular Section 5 perturbation parameter, –2/R - ² a constant, –K - x / - g(x) f()/ Section 6 perturbation parameter, –R/2 - ² a constant, –K - g() f() - g _c ()=g() near centre of pipe - * point where g()=0 Section 7 2/R - ² K - t (1–)/ - w(t, ) [1–f(t)]/ - ₀, ₁ constants - g() f()– ₀ - ₀/ - ₀ a constant - * point where f()=0     

Combined effect of longitudinal riblets and LEBU-devices on turbulent friction on a plate

The possibility of reducing turbulent friction with the help of large-eddy-breakup devices (LEBUs) and riblets is studied experimentally. The tests were conducted in a low-turbulence wind tunnel on a flat plate for 2·10⁶ Re 7·10⁶. The local friction coefficient was measured using internal strain-gauge balances, and the total drag was estimated by the momentum-transfer method. It is shown that a combination of LEBUs and riblets makes it possible to reduce the total turbulent friction drag of a flat plate 1800 mm long by 16%. The effects of the length of a ribbed surface on the efficiency of friction reduction and of LEBUs and riblets on the structure of a turbulent boundary layer are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–46, May–June, 1995.     

Critical heat fluxes in boiling of liquid nitrogen underheated to saturation point in forced-flow conditions

This paper gives the results of experimental determinations of the critical heat fluxes in the boiling of Liquid nitrogen in forced-flow conditions in the mass velocity range 2 · 10³-40 · 10³ kg/m² · sec, pressure range 29 · 10⁴–245 · 10⁴ N/m², and at underheatings corresponding to the onset of normal boiling crises.Notation q₀ critical heat flux - r heat of vaporization - i enthalpy of flow corresponding to saturation point - i enthalpy of flow corresponding to liquid temperature - surface tension - density of liquid - density of saturated vapor - C _f friction factor - W_g mass velocity - Fr_* Froude number - g acceleration due to gravity     

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG _c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG _c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG _c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m^–2; - G loss shear modulus,N·m^–2; - G _c calculated storage shear modulus,N·m^–2; - G _c calculated loss shear modulus,N·m^–2; - G _e equilibrium shear modulus,N·m^–2; - G _ec calculated equilibrium shear modulus,N·m^–2; - G(t) relaxation shear modulus,N·m^–2; - G _c (t) calculated relaxation shear modulus,N·m^–2; - G ^*(t) pseudo relaxation shear modulus,N·m^–2; - H relaxation spectrum,N·m^–2; - t time,s; - relaxation time,s; - angular frequency, rad·s^–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].     

The falling needle viscometer a new technique for viscosity measurements

A new type of viscometer, the Falling Needle Viscometer (FNV) has been developed. It has several advantages over the better known Falling Ball Viscometer (FBV) including better control over the trajectory and terminal velocity and a wall correction which is an integral part of the analytical solution.A Stokes' type solution for the FNV is presented which is compared with experimental measurements made on Glycerol. Experiments were also conducted with a Falling Ball Viscometer and Weissenberg Rheogoniometer using the same fluid and a comparison made among the three systems.Glycerol viscosities measured with the FNV agreed with those measured by the FBV and Weissenberg Rheogoniometer within approximately one percent. It is concluded that the Falling Needle Viscometer is a useful device that in some situations is superior to the Falling Ball Viscometer.

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Das Nadelfall-Viskosimeter, eine neue Technik zur Zähigkeitsmessung

Zusammenfassung Es wurde ein neues Gerät zur Zähigkeitsmessung, as Nadelfall-Viskosimeter (FNV) entwickelt. Gegenüber dem bekannteren Kugelfall-Viskosimeter (FBV) besitzt es einige Vorteile wie eine bessere Kontrolle über die Bahnkurve und die Endgeschwindigkeit sowie eine Wandkorrektur, die Bestandteil der analytischen Lösung ist.Für das FNV wird eine Lösung vom Stokes'schen Typ vorgestellt und mit experimentellen Meßergebnissen an Glycerin verglichen. Meßwerte am selben Fluid mit Hilfe eines FBV und eines Weissenberg-Rheogoniometers erlaubten einen Vergleich zwischen den drei Systemen.Die mit dem FNV gemessenen Zähigkeiten stimmten mit den anderen Werten innerhalb etwa 1% überein. Daraus wird geschlossen, daß das FNV ein nützliches Gerät ist, das dem FBV auf einigen Gebieten überlegen ist.

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Nomenclature

Roman letters a Radius of needle or sphere (cm) - b Radius of container (cm) - b ⁺ Ratio of container to needle diameterb/a - C _w Wall correction factor of sphere - d Diameter of needle or sphere (cm) - ECF End correction factor of a finite needle with hemisphere tips - g Gravitational constant - G ⁺ Dimensionless number - L Total needle length minus one diameter (cm) - L Total length of needle (cm) - L ⁺ Total needle length minus one diameter over diameter-L/d - L⁺ Total length to diameter of needle - p Pressure (N/m²) - p ⁺ Dimensionless number - L ⁺/b ⁺ Total needle length to diameter of system - r Radial coordinate (cm) - r ⁺ Dimensionless radial distance(r/a) - Re Reynolds number or - u Velocity in the system length direction (cm/s) - u ⁺ Dimensionless velocity (u/U ) - U _t Measured terminal velocity of needle or sphere (cm/s) - U Terminal velocity of sphere in an unbounded fluid or terminal velocity of a long enough needle (cm/s) - U ⁺ Dimensionless number - T Temperature (°C) - z Coordinate in container length direction (cm) Greek letters Shear rate (l/s) - p Pressure difference - Dynamic viscosity (Ns/m²) - Kinematic viscosity (m²/s) - _f Density of fluid (kg/m³) - _s Density of needle or sphere (kg/m³) - ⁺ Dimensionless density Dedicated to Professor E. R. G. Eckert on the occasion of his 80th birthday     

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.     

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.     

Untersuchungen des Blasensiedens einiger verflüssigter Gase und ihrer binÄren Mischungen

Zusammenfassung Die Arbeit behandelt das Blasensieden an einer ebenen, horizontalen, 64·10^–4m² gro\en KupferoberflÄche von Stickstoff, Methan, Aethan und Gemischen aus Stickstoff/Methan und Methan/Aethan bei verschiedenen Drücken. Die Messwerte und empirischen Ausgleichskurven sind angegeben. Die Daten für die binÄren Gemische bestÄtigen die Gleichung von Happel und Stephan.

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Heat transfer in nucleate boiling of liquified gases and their binary mixtures

The paper deals with pool boiling of nitrogen, methane, ethane and mixtures of nitrogen/methane and methane/ethane at different pressures. The boiling surface was a horizontal, plan copper disk of 64·10^–4m²· The measured data points and their fit by an empirical correlation are given. For mixtures the correlation of Happel and Stephan provides a good agreement with the results.

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Formelzeichen a₁, a₂, a₃ Konstanten - b₁,b₂ Konstanten - K Konstante - n,n₁,n₂ Konstanten - p Druck Pa, M Pa - p_red reduzierter Druck (p/p_kritisch) - q^* WÄrmestromdichte W/m² - R_p Rauhtiefe m - x Molanteil der leichter flüchtigen Komponente in der Flüssigkeit - y Molanteil der leichter flüchtigen Komponente im Dampf - WÄrmeübergangskoeffi-W m^–2 K^–1zient - _i idealer WÄrmeüber-W m^–2K^–1 - _i gangskoeffizient - realer WÄrmeübergangs-W m^–2K^–1 - _r koeffizient - T Temperaturdifferenz K     

Turbulence intensity and turbulent transport characteristics behind gratings in pipes

The magnitudes of the variance ² of the concentration distribution C(y) of a material being mixed in a stream behind turbulizing gratings in a pipe are measured. The impurity (helium) was inserted in the air stream via a thin pipe mounted directly behind one of the grating orifices. The intensity of the turbulent stream velocity pulsations behind the grating was measured by the method of helium diffusion. Estimates of the magnitudes of the turbulent diffusion coefficient D and the diffusion scale of turbulencel were given on the basis of these measurements. Characteristics of the turbulent stream behind gratings in wind tunnels have been investigated in [1–3], for example. The process of turbulent diffusion behind gratings has been studied to a lesser degree. The flow directly behind the grating is of greatest interest for practice, but in the majority of papers the measurements have been made at a distance x from the grating which exceeds (10–20)M, where M is the distance, or step, between the centers of the grating orifices. Moreover, as a rule, the gratings investigated possessed low hydraulic drag and the intensity of stream turbulence ahead of them was considerably lower than ahead of the technical mixing apparatus.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–42, January–February, 1973.     

Gradientenabhängigkeit der Viskosität verdünnter Lösungen von Fadenmolekülen

Zusammenfassung Es wird über die Gradientenabhängigkeit der Viskosität von Polymeren mit hohem Molekulargewicht in Lösungsmitteln üblicher Viskosität berichtet. Die Ermittlung von [] für verschwindenden Gradienten []_G0 und besonders für sehr hohe Gradienten []_G wird diskutiert.Der gemessene Gradientenbereich erstreckt sich vonG=10¹ bis 3 · 10⁴ sec^–1. Bei unserem Präparat mit dem höchsten Molekulargewicht, einem Polymethylmeth-acrylat vonM=16 · 10⁶, ergibt dies ₀-Werte bis 190, wenn ₀ die theoretisch als maßgeblicher Parameter benutzte Größe ₀=M · [] ₀ · ₀/RT ist. Wir beobachteten im gesamten recht großen ₀-Bereich für unsere Lösungsmittel ( ₀<6 · 10^–3 Poise) eine kontinuierliche Abnahme von []. Diese ist um so ausgeprägter, je höher []_G=0 wird.Vorgetragen auf der Jahrestagung der Deutschen Rheologen vom 11.–13. Mai 1964 in Berlin-Dahlem. - Teil einer Dissertation (D 77) der Universität Mainz.Herrn Prof.G. V. Schulz danken wir für anregende Diskussionen.Der eine von uns (B. N.) dankt der Alexan-der-von-Humboldt-Stiftung für ein Stipendium. Der Deutschen Forschungsgemeinschaft danken wir für eine Sachbeihilfe.     

Experimental investigation of separation of turbulent boundary layer in vicinity of a step

The results of an experimental investigation of the separation of a turbulent boundary layer in the vicinity of a step on a flat plate at M = 2 and 3, and Re = U/v = (26–66)·10⁶ m^–1 are given. The step height was varied from 3 to 16 mm, which corresponded to the range of relative heights 1.1 h/ 7.6, where is the thickness of the boundary layer at the point at which the pressure starts to increase in front of the step. The obtained data for the pressure distribution in front of the step, and on its face and top surface, and the results of probe measurements in the separation and adjacent regions provide a more accurate scheme of the flow. The obtained data are compared with the results of other investigations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 73–80, September–October, 1977.We express our thanks to A. M. Kharitonov for valuable comments made during the discussion of this work, and also to M. A. Gol'dfel'd for kindly providing the experimental data for axisytnmetric steps.     

Flow of soft solids squeezed between planar and spherical surfaces

The force to squeeze a Herschel–Bulkley material without slip between two approaching surfaces of various curvature is calculated. The Herschel–Bulkley yield stress requires an infinite force to make plane–plane and plane–concave surfaces touch. However, for plane–convex surfaces this force is finite, which suggests experiments to access the mesoscopic thickness region (1–100 m) of non-Newtonian materials using squeeze flow between a plate and a convex lens. Compared to the plane–parallel surfaces that are used most often for squeeze flow, the dependence of the separation h and approach speed V on the squeezing-time is more complicated. However, when the surfaces become close, a simplification occurs and the near-contact approach speed is found to vary as V h⁰ if the Herschel–Bulkley index is n<1/3, and V h^(3n-1)/(2n) if n 1/3. Using both plane–plane and plane–convex surfaces, concordant measurements are made of the Herschel–Bulkley index n and yield stress ₀ for two soft solids. Good agreement is also found between ₀ measured by the vane and by each squeeze-flow method. However, one of the materials shows a limiting separation and a V(h) behaviour not predicted by theory for h<10 m, possibly owing to an interparticle structure of similar lengthscale.     

Calculation of the pressure on the side surface of bodies consisting of a spherical segment joined to an inverted cone in a supersonic stream

The results of investigations of inviscid flow over inverted cones with nose consisting of a spherical segment were published for the first time in Soviet literature in [1–4]. In the present paper, a numerical solution to this problem is obtained using the improved algorithms of [5, 6], which have proved themselves well in problems of exterior flow over surfaces with positive angles of inclination to the oncoming flow. It is shown that the Mach number 2 M , equilibrium and nonequilibrium physicochemical transformations in air (H = 60 km, V = 7.4 km/sec, R₀ = 1 m), and the angle of attack 0 40° influence the investigated pressure distributions. A comparison of the results of the calculations with drainage experiments for M = 6, = 0-25° confirms the extended region of applicability of the developed numerical methods. Also proposed is a simple correlation of the dependence on the Mach number in the range 1.5 M of the shape of the shock wave near a sphere in a stream of ideal gas with adiabatic exponent = 1.4.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 178–183, January–February, 1981.     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

Flow of a viscous gas in a shock layer with equilibrium chemical reactions

Steady flow of supersonic air over a sphere is examined, allowing for viscosity, heat conduction, and actual physical and chemical processes. Flow in the shock layer at flight speeds in the range 3 km/sec V10 km/sec (10⁴R10⁶) is investigated, under the assumption of local thermodynamic equilibrium. The flow is described by simplified Navier-Stokes equations, which are solved by a finite difference method. The case of a cooled surface is examined. The distribution of gasdynamic parameters is obtained in different flow regimes. The distribution of heat flux and friction coefficient is investigated as a function of the oncoming-stream parameters and the sphere radius. The shape and position of the shock wave are determined, and the stream lines and sonic lines are constructed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 150–153, July–August, 1970.The authors thank Yu. P. Lun'kin and F. D. Popov for their help in formulating the problem and their constant interest.     

The rheology of polymeric liquid crystals

The molecular theory of Doi has been used as a framework to characterize the rheological behavior of polymeric liquid crystals at the low deformation rates for which it was derived, and an appropriate extension for high deformation rates is presented. The essential physics behind the Doi formulation has, however, been retained in its entirety. The resulting four-parameter equation enables prediction of the shearing behavior at low and high deformation rates, of the stress in extensional flows, of the isotropic-anisotropic phase transition and of the molecular orientation. Extensional data over nearly three decades of elongation rate (10^–2–10¹) and shearing data over six decades of shear rate (10^–2–10⁴) have been correlated using this analysis. Experimental data are presented for both homogeneous and inhomogeneous shearing stress fields. For the latter, a 20-fold range of capillary tube diameters has been employed and no effects of system geometry or the inhomogeneity of the flow-field are observed. Such an independence of the rheological properties from these effects does not occur for low molecular weight liquid crystals and this is, perhaps, the first time this has been reported for polymeric lyotropic liquid crystals; the physical basis for this major difference is discussed briefly. A Semi-empirical constant in eq. (18), N/m² - c rod concentration, rods/m³ - c ^* critical rod concentration at which the isotropic phase becomes unstable, rods/m³ - C interaction potential in the Doi theory defined in eq. (3) - d rod diameter, m - D semi-empirical constant in eq. (19), s^–1 - D _r lumped rotational diffusivity defined in eq. (4), s^–1 - rotational diffusivity of rods in a concentrated (liquid crystalline) system, s^–1 - D _ro rotational diffusivity of a dilute solution of rods, s^–1 - f distribution function defining rod orientation - F tensorial term in the Doi theory defined in eq. (7) (or eq. (19)), s^–1 - G tensorial term in the Doi theory defined in eq. (8) - K _B Boltzmann constant, 1.38 × 10^–23 J/K-molecule - L rod length, m - S scalar order parameter - S tensor order parameter defined in eq. (5) - t time, s - T absolute temperature, K - u unit vector describing the orientation of an individual rod - rate of change ofu due to macroscopic flow, s^–1 - v fluid velocity vector, m/s - v velocity gradient tensor defined in eq. (9), s^–1 - V mean field (aligning) potential defined in eq. (2) - x coordinate direction, m - Kronecker delta (= 0 if = 1 if = ) - _r ratio of viscosity of suspension to that of the solvent at the same shear stress - _s solvent viscosity, Pa · s - ^* viscosity at the critical concentrationc ^*, Pa · s - v ₁, v₂ numerical factors in eqs. (3) and (4), respectively - deviatoric stress tensor, N/m² - volume fraction of rods - ⁰ constant in eq. (16) - ^* volume fraction of rods at the critical concentrationc ^* - average over the distribution functionf(u, t) (= d ²u f(u, t)) - gradient operator - d ²u integral over the surface of the sphere (|u| = 1)     

Shock heating of plasma in a rapidly increasing magnetic field

The experimental excitation of intense collisionless shock waves (M 5) with subsequent plasma compression by the magnetic field of a shock coil is described. A magnetic plug > 20 kOe is produced in 100 × 10^–9 sec by a current generator, a long line with 250-kV water insulation and a characteristic impedance of l At an initial deuterium-plasma density of 2 × 10¹⁴ cm^–3, shock waves with a front width of 20c/₀₃and a velocity of 5 × 10₇ cm/sec are recorded. The ion energy after the accumulation, determined from the neutron yield, turns out to be 2 ke V. Axial shock waves excited by the plasma flow beneath the shock coil are observed.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, No. 2, pp. 28–38, March–April, 1970.The authors thank G. I. Budker and R. Z. Sagdeev for formulating the problem, R. I. Soloukhin for interest in the study, and S. P. Shalamov for construction of the apparatus.     

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.