Dynamics of vapor bubbles in nitrogen tetroxide under conditions of pipe depressurization

A study was made of the effect of nonequilibrium phase transformations on the dynamics of vapor bubbles with the sudden occurrence of a pressure drop.Notation C_pv, C specific heat capacities (at constant pressure) of the vapor and liquid - _v, densities - T_v, T temperatures - V_v, V velocities - P_v, P pressures - W_v, W mass velocities on the bubble surface - _v, thermal conductivities of the vapor and liquid - adiabatic exponent of the vapor - surface tension - kinematic viscosity - j rate of phase transformations - m mass - heat of phase transformation Indices v vapor phase - liquid phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 764–769, May, 1988.     

Acoustic Excitation of Noncircular Turbulent Jets

Results of experimental investigation of turbulent mixing in jets flowing out of nozzles with different cross sections in the case of low and highfrequency acoustic excitation of the jets are presented. The influence of the shape of the cross section of a nozzle on the acousticexcitation sensitivity of a jet flowing out of it is analyzed.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

Analysis of the parameters of discrete particle motion in axisymmetric turbulent impinging jets

The parameters of discrete particle motion in axisymmetric turbulent impinging air jets are determined.Notation x, y coordinates (Fig. 1) - v_x jet velocity - V_o maximum jet velocity - r_o nozzle radius - l _i length of the initial jet section - L spacing between the nozzle and the collision plane - ¯x dimensionless coordinate referred to the nozzle radius - ¯x_i dimensionless length of the initial section referred to the nozzle radius - d particle diameter - ₁ jet density - particle density - c_x particle drag coefficient - v particle velocity - v₁ axial jet velocity - kinematic coefficient of the flow viscosity - ¯x_o dimensionless coordinate referred to the distance L - d_c cement particle diameter - d_s sand particle diameter - ¯v_i dimensionless velocity of particle insertion into the jet, referred to V_o Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 813–817, November, 1979.     

Extension of the quasilinear method of determining thermophysical characteristics to the case of anisotropic materials

The article reports on the initial part of the stage of regular thermal regime of a plate heated by a constant heat flux, and a method is suggested for determining thermal conductivity and thermal diffusivity.Notation T temperature of the plate - T₀ binitial temperature of the plate and ambient temperature - g volume density of the heat sources - q heat flux density - _x thickness of the plate - _x thermal conductivity along the x axis - a _x thermal diffusivity along the x axis - heat transfer coefficient - Fo Fourier number - B Biot number - density of the material of the plate - c heat capacity - t time Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 611–616, October, 1988.     

Numerical studies of three turbulent slot jets with and without moving surface

Summary This study presents the numerical predictions of the fluid flow and heat transfer characteristics for three turbulent impingement slot jets. The turbulent governing equations are solved by a control-volume-based finite-difference method with power-law scheme, the well knownK- model, and its associate wall function to describe the turbulent behavior. The velocity and pressure terms of momentum equations are solved by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) method. In this study nonuniform staggered grids are used. The parameters interesting include entrance Reynolds number (Re), dimensionless nozzle to surface space (H/W), dimensionless pitch (H/W), and dimensionless velocity ratio (U _s /V _j ). The computed results show that the dimensionless pitch has a strong influence on the heat transfer characteristics. In the case with surface motion, it is found that the skin friction coefficient of the impinging surface is strongly affected by the surface motion, but the heat transfer characteristic is not significant in the range of 0.05U _s /V _j 0.25.Nomenclature C ₁,C ₂,C turbulent constant - C _f skin friction coefficient - E constant - G generation rate of turbulent kinetic energy - H distance between the nozzle and the impingement surface - i turbulence intensity - K turbulent kinetic energy - Nu local Nusselt number - P pitch - q heat flux - Re Reynolds number - S source term - T temperature - U friction velocity - U _s velocity of surface motion - V _j jet velocity - U, V x, y component velocity - W nozzle width - y ⁺ dimensionless distance from the wall - dependent variables - diffusion coefficient of equation - thermal diffusivity of fluid - density - von Kármán constant - turbulent Prandtl number - dynamic viscosity - kinematic viscosity - _w wall shear stress - turbulent energy dissipation rate - length scale constant     

Numerical modeling of thermal regimes during the assembly of a multicomponent system

Results are presented from a numerical modeling of the solution of a problem involving optimization of the thermal regime in the assembly of integrated circuits. The modeling was performed on array processors of hybrid computers.Notation T_g gas temperature - heat-transfer coefficient - c_V specific heat capacity - thermal conductivity - time - q heat flux - L internal heat of phase transformations or other internal transformations - c_Ve effective volumetric heat capacity - density - q_V power of internal heat sources Indices g gas - c convection, contact - sp spectral - r radiative - L phase transformation - V volumetric - 0 initial - e environment - liquidus - s solidus - s surface - total Abbreviations R-R resistance circuit - Liebmann method - T Gel'perin method Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 793–798, May, 1989.     

Study of thermal and gasdynamic characteristics of a subsonic plasma air jet

Results are presented from a numerical analysis and experimental study of the enthalpy and velocity distributions along and across a subsonic plasma air jet.Notation x, r axial and radial coordinates - u, v axial and radial components of velocity - density - viscosity - emissivity - r_0.5 radius at which local value of velocity or enthalpy is half its axial value - , radii of dynamic and thermal boundary layers - q heat flux, kW/m² - h, h_w stagnation enthalpy and enthalpy at wall temperature, kJ/kg - p, p stagnation pressure and static pressure, Pa - R radius of curvature of spherical front part of body Indices 0 teconditions at nozzle edge - m conditions on jet axis - conditions on outer boundary of jet Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 34–39, January, 1982.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Generalized fracture mechanics

According to Andrews' generalized fracture mechanics theory [1], the fracture energy of a solid is given by = ₀ where ₀ is a surface energy and a loss function whose form is explicit. The loss function has been evaluated experimentally for four highly extensible materials, styrenebutadiene rubber, ethylene-propylene rubber, plasticized PVC and polyethylene and at various rates of crack propagation. The quantity ₀ has also been calculated from existing theory and a prediction thus obtained for fracture energy. The results indicate good agreement between experiment and theory and thus appear to corroborate the generalized formulation of fracture mechanics in its application to non-linear inelastic materials.     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

A flat jet in a granular bed of finite height

The distribution of gas flows in the vicinity of the jet is discussed and the conditions of disruption of the static equilibrium of the bed, the formation and growth of a cavity, and the jet breakthrough of the bed are investigated qualitatively.Notation a, b functions calculated in [11] - C, C constants in (7) - F derivative of the complex potential - f function in (6) - G function defined in (19) - H dimensionless height of bed - h height of cavity - k coefficient introduced in (15) - p, po pressure inside bed and in cavity - p dimensionless pressure drop - Q, q dimensional and dimensionless jet flow rates - q₁, q₂ critical values - T dimensionless height of cavity - T₀, T₁ T₁, T₂ characteristic values of T - u,v filtration velocities - u, u_* initial filtration velocity in the bed and minimum fluidization velocity - u_o velocity scale introduced in (14) - u * velocity scale introduced in (14) - u* velocity of fictitious flow defined in (15) - U complex velocity - Z=X+iY, z=x+iy dimensionless coordinates - z=x+iy dimensional coordinates - coefficient of hydraulic resistance - parameter from (5) - specific weight of particles' material - porosity - =+i coordinates in the plane obtained from z=x+iy as a result a of conformai transformation - _m value of giving a minimum of the function G - f complex and real flow potentials - angle of internal friction - stream function - angle of inclination of boundaries of the region of plastic flow to the vertical Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 804–812, November, 1979.     

Universal simulation of degenerating homogeneous turbulence

The problem of universal simulation of the dynamics of a turbulent velocity field (universal in the sense of arbitrary values of the Reynolds turbulence number) is treated on the basis of the moment model in the second approximation.Notation ¯q² _i ² double the kinetic turbulence energy - _u ² =5v¯q²/_u Taylor turbulence scale squared - _u=v1/x_k)²> kinetic-energy dissipation function - N_Re,=¯q²_u / Reynolds turbulence number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 46–52, January, 1982.     

Distribution of the phase front in the freezing of finely-dispersed soils

The process of the freezing of soils is examined with allowance for the migration of moisture in the freezing and thaw zones.Notation , x time and space coordinates - t, W, L dimensionless values of temperature, moisture content, and ice content - c,a, D volumetric heat capacity, diffusivity, and diffusion of moisture - density of the skeleton - W_e equilibrium value of moisture content - enthalpy of phase transformations - _* characteristic time - , gw, , dimensionless values of temperature, moisture content, ice content, and diffusion coefficient of the moisture - Fo Fourier criterion - Ste Stefan number - n empirical constant Indices 0, 1, and 2 pertain to the initial and boundary states Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 805–810, May, 1989.     

Numerical simulation of an explosive plasma generator in the gasdynamic approximation

A two-dimensional gasdynamic model of a plasma generator is proposed. A numerical solution of the problem is obtained, and peculiarities of the gasdynamic flow are considered. Results are compared with experiment.Notation T temperature - p pressure - N number of gas particles per unit volume - w gas mass velocity vector with components w_z=u and w_r=v - z axial coordinate - r radial coordinate - t time - E total specific energy of gas - specific internal energy - density - V plate velocity - E_in initial plate energy - M plate mass - S plate area - p pressure difference between left and right sides of plate - t, z, r time and space steps - k<1 Courant number - c velocity of sound in the gas Indices 0 initial value - * characteristic dimensional quantities - i, j grid cell indices along z and r - n number of time step - () symbol denoting intermediate values of gasdynamic variables in a time layer Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 859–867, November, 1979.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Effect of the weight of the admixture on the turbulence structure of a two-phase jet

The effect of gravity on the turbulence structure of an inclined two-phase jet is evaluated according to the Prandtl theory of mixing length.Notation C_x drag coefficient for a particle - D_p particle diameter - g_i components of the acceleration g due to gravity acting on a particle in the direction of jet flow (g_i=g sin ) and in the direction normal to it (g_i=g cos ) - V_poi ^±, V_goi ^± fluctuation components of the velocities of the particles and gas, respectively, at the end of a mole formation - V_fi free-fall velocity of a particle - l _u mixing length - m_p particle mass - t _p length of time of particle-mole interaction - V_pi ^±, V_gi ^± positive and negative fluctuation velocities of particles and of the gas respectively, with the components u_p ^±, u_g ^±, v_p ^±, v_g ^±, k=V_goi/V_fi - V_i ^± relative velocity of the gas - jet inclination angle relative to the earth's surface - empirical constant - _u, jet boundaries in terms of velocity and concentration - _u=y/ _u dimensionless velocity ordinate - =y/ dimensionless concentration ordinate - admixture concentration - u_m, _m velocity and the concentration of the admixture at the jet axis - _g dynamic viscosity of the gas - _s, _g densities of the particle material and of the gas - _g, _p shearing stresses in the gas and in the gas of particles - _m, ₀ shearing stresses in the mixture and in pure gas, respectively Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 422–426, March, 1981.     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

Turbulent mixing of fluids with different densities flowing through a pipe

A one-dimensional model of a disperse mixture in a turbulent stream is constructed, with the mutual effect of mixture concentration and turbulence intensity taken into account.Notation ₀ mean-over-the-section density - p pressure - _t turbulent viscosity - U average longitudinal velocity - g acceleration of gravity - angle of pipe inclination from the horizontal - x, r cylindrical coordinates - t time - V average radial velocity - C average concentration - D_t turbulent diffusivity - c₀ mean-over-the-section concentration - K effective turbulent diffusivity - U₀ mean flow velocity - X distance, in the moving system of coordinates - a pipe radius - ₀ frictional stress at the inside surface of the pipe - u_* transient turbulent velocity - b turbulence intensity - l linear scale factor - chemical potential of mixture - density of mixture - d₁, d₂ densities of homogeneous fluids - y₊ thickness of laminar layer - y distance from the inside pipe surface - ₊ derivative of velocity at the layer boundary on the turbulent side - hydraulic drag - Gr Grashof number - Re Reynolds number - ₁, ₂, coefficients in the equation for K_* - K_* dimensionless effective diffusivity - =U₀t/2a dimensionless time - =X/2a dimensionless distance Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 992–998, June, 1972.