Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

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.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

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.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

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.     

A method of joint determination of the effective coefficients of horizontal mixing of large particles and of external heat exchange in an organized fluidized bed

A method is proposed for the joint determination of the coefficients of horizontal particle diffusion and external heat exchange in a stagnant fluidized bed.Notation c_f, c_s, c_n specific heat capacities of gas, particles, and nozzle material, respectively, at constant pressure - D effective coefficient of particle diffusion horizontally (coefficient of horizontal thermal diffusivity of the bed) - d equivalent particle diameter - d_t tube diameter - H₀, H heights of bed at gas filtration velocities u₀ and u, respectively - H_a height of active section - l width of bed - L tube length - l _o width of heating chamber - N number of partition intervals - p=H/H₀ expansion of bed - s_n surface area of nozzle per unit volume of bed - S_h, S_v horizontal and vertical spacings between tubes - t_c, t₀, t_s, t_n, t_w initial temperature of heating chamber, entrance temperature of gas, particle temperature, nozzle temperature, and temperature of apparatus walls, respectively - u₀, u velocity of start of fluidization and gas filtration velocity - y horizontal coordinate - ^*, coefficient of external heat exchange between bed and walls of apparatus and nozzle - ₁, ₁, ₂, ... coefficients in (4) - thickness of tube wall - _b bubble concentration in bed - ₀ porosity of emulsion phase of bed - _n porosity of nozzle - =(t_s – t₀)/(t_c – t₀) dimensionless relative temperature of particles - _n coefficient of thermal conductivity of nozzle material - f, _s, _n densities of gas, particles, and nozzle material, respectively - _be=_s(1 – ₀) (1 – _b) average density of bed - time - _max time of onset of temperature maximum at a selected point of the bed - R =l _o/l Fourier number - Pe = ₁ l ²/D Péclet number - Bi = /_n Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 457–464, September, 1981.     

High-accuracy bench mark solutions to natural convection in a square cavity

A fourth-order high-accuracy finite difference method is presented for the bouyancy-driven flow in a square cavity with differentially heated vertical walls. The two bench mark solutions against which other solutions can be compared were obtained. The present solution is seemed to be accurate up to fifth decimal. The proposed scheme is stable and convergent for high Rayleigh number, and will be applicable to general problems involving flow and heat transfer, especially in three dimensions.List of symbols a thermal diffusivity - g gravitational acceleration - h mesh length in the x-direction - k time step - L side length of cavity - Pr Prandtl number - Ra Rayleigh number = gTL ³/a - t time - T _c, T _h surface temperatures (see Fig. 1a) - T temperature - T temperature difference = T _h - T _c - u, v velocity in the x and y directions, respectively - x, y coordinates - x, y mesh lengths in the x- and y-directions, respectively Greek symbols volumetric expansion coefficient - kinematic viscosity - stream function - vorticity     

Electronic specific heat of La2−xSrxCu1−yMyO4(M=Ga,Zn): Impurity effects on a D-wave superconductor

The electronic specific heat C_el was studied in Ga- and Zn-doped La_2–xSr_xCuO₄ (0.16x0.22) at T10K. Partial substitution of Ga or Zn for Cu suppresses T_c and revives the T-linear electronic specific heat, T, markedly. The (y)/n vs T_c/T_c0 relation for Zn-doped samples with x0.2 is in good agreement with the theoretical one for resonant impurity scattering in a d-wave superconductor, while those for Ga-doped samples and for Zn-doped samples with x 0.2 deviate slightly from the theoretical curve. The deviation will be discussed in relation to changes in the magnetic properties of 3d electrons.     

A numerical method for flexible airfoils in incompressible inviscid flow

Summary The paper deals with the aerodynamic analysis of flexible airfoils, based on a quasi-lattice vortex method (QVLM). The analysis is formulated in matrix form and leads, as in other similar studies, to a linear algebraic system when the angle of attack is nonzero, and to an eigenvalue problem when the incidence angle is zero. The aerodynamic characteristic curvesC _L -,C _m - are presented. Finally, the airfoil shapes for several values of the tension coefficient and angles of attack are drawn. The results obtained with the present method are in good agreement with those reported in previous studies and evidentiate the flexibility of the QVLM as applied to flexible airfoils.Notation A aerodynamic matrix, defined in QVL method, (8) - B matrix, see Eq. (18) - c chord of airfoil - C matrix defined asAB - C _L lift coefficient, 2L/V ² c) - C _p moment coefficient, 2M/(V ² c ²) - C _p pressure coefficient,C _p =2p/(V ² ) - C _T tension coefficient, 2T/(V ² c) - D matrix, see Eq. (11) - I unit matrix - l curvilinear length of the flexible airfoil - N number of collocation points on the airfoil shape - q dynamic pressure, V ² /2 - T tension force in the sail - V freestream velocity - w downwash - x nondimensional coordinate,x/c - X _i control points, Eq. (9) - X _max dimensionless position of the maximum camber - Y _k source points, Eq. (9) - z coordinate normal tox axis - Z nondimensional coordinate,z/c - Z _s camber equation in dimensionless form,z _s /c - incidence with respect to the upstream flow velocity - column vector of the local curvatures {₁, ₂,..., _N } ^T - nondimensional membrane excess ratio - eigenvalue of the problem (23) - _k zeroes of the Chebyshev polynomia of the first kind, 1kN - column vector of the local slopes, {₀, ₁, ₂,..., _N } ^T - column vector, {₁, ₂,..., _N } ^T - ₀ slope at airfoil leading edge     

Structure of unidimensional temperature stresses

Using the structural approach, the temperature stresses are examined in a semiinfinite rod, insulated on the lateral faces and rigidly fixed at the end. A comparative analysis is made for three heat-transfer models.Notation k(t) heat flux relaxation function - (t) internal energy relaxation function - T rod temperature - ambient temperature - t time - x coordinate along the rod - _xx(x, t) stress - u(x, t) displacement - (x, t) deformation - c₀=(E/)^1/2 speed of sound in the rod under isothermal conditions - E elasticity modulus - density of the material - _t coefficient of thermal expansion - thermal-conductivity coefficient - a thermal-diffusivity coefficient - b thermal-activity coefficient - c_q=(a/_r)^1/2 velocity of heat propagation - _r heat flux relaxation time - (t) unique Heaviside function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 912–921, November, 1977.     

Relationship between thermal conductivity,speed of sound,and isobaric heat capacity of liquids

Using two liquids-water and toluene — as an example, the author determines the dependence of the coefficient of thermal conductivity on the speed of sound and isobaric molar heat capacity for high state parameters.Notation coefficient of thermal conductivity - u speed of sound - _S same for a saturated liquid - c isobaric molar heat capacity - density - p_s same, for a saturated liquid - p pressure - p_s same, for a saturated liquid - R gas constant - T absolute temperature - x coefficient of thermal activity - x _s same, for a saturated liquid - L, constants in Eqs. (1) and (2) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 311–314, August, 1980.     

Tangent modulus tensor in plasticity under finite strain

Summary The tangent modulus tensor, denoted as , plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for have been derived in Refs. [1]–[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux are addressed. Associated and non-associated models are accommodated, as is plastic incompressibility. A constitutive inequality with uniqueness implications is formulated which extends the condition for stability in the small to finite strain. Modifications of are presented which accommodate kinematic hardening. As an illustration, is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.Notation B strain displacement matrix - C=F ^T F Green strain tensor - compliance matrix - D=(L+L ^T )/2 deformation rate tensor - D fourth order tangent modulus tensor - tangent modulus tensor (second order) - d VEC(D) - e VEC() - E Eulerian pseudostrain - F, F _e ,F _p Helmholtz free energy - F=x/X deformation gradient tensor - f consistent force vector - residual function - G strain displacement matrix - h history vector - h time interval - H function arising in tangent modulus tensor - I, I ₉ identity tensor - i VEC(I) - k ₀,k ₁ parameters of yield function - K _g geometric stiffness matrix - K _T tangent stiffness matrix - k _k kinematic hardening coefficient - J Jacobian matrix - L=v/x velocity gradient tensor - m unit normal vector to yield surface - M strain-displacement matrix - N shape function matrix - n unit normal vector to deformed surface - n ₀ unit normal vector to undeformed surface - n unit normal vector to potential surface - r, R, R ₀ radial coordinate - s VEC() - S deformed surface - S ₀ undeformed surface - t time - t, t ₀ traction - t VEC() - VEC( ) - t VEC() - t _r reference stress interior to the yield surface - t t–t _r - T kinematic hardening modulus matrix - u=x–X displacement vector - U permutation matrix - v=x/t particle velocity - V deformed volume - V ₀ undeformed volume - X position vector of a given particle in the undeformed configuration - x(X,t) position vector in the deformed configuration - z, Z axial coordinate - vector of nodal displacements - =(F ^T F–I)/2 Lagrangian strain tensor - history parameter scalar - , azimuthal coordinate - elastic bulk modulus - flow rule coefficient - twisting rate coefficient - elastic shear modulus - iterate - Second Piola-Kirchhoff stress - Cauchy stress - Truesdell stress flux - deviatoric Cauchy stress - Y, Y yield function - residual function - plastic potential - X, Xe, Xp second order tangent modulus tensors in current configuration - X, Xe, Xp second order tangent modulus tensors in undeformed configuration - (.) variational operator - VEC(.) vectorization operator - TEN(.) Kronecker operator - tr(.) trace - Kronecker product     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Specific heat measurements of intercalation compounds M x TiS2 (M=3d transition metals) using ac calorimetry technique

Specific heats of 3d transition metal intercalates of 1T-CdI₂-type TiS₂, M _x TiS₂ (M=V, Cr, Mn, Fe, Co, and Ni; 0x1), have been measured in the temperature range 1.6–300 K using an ac calorimetry technique. The electronic specific heat coefficient (2–100 mJ/mole K²) and the Debye temperature _D (240–430 K) are found to depend on the guest 3d metals and their concentrations. All the intercalates show anomalous specific heat at low temperatures following an – lnT dependence ( and are constants), as found in dilute alloys.     

Instability of the self-similar front of a phase transition

The stability of self-similar diffusional processes with respect to small disturbances of plane, cylindrical, and spherical phase interfaces is investigated.Notation c weight concentration in solution - D coefficient of diffusion - K curvature - n angular number - R radius of cylinder or sphere - r, r radial coordinate and disturbance of the surface r=R - t time - u velocity of front - x, y, z linear coordinates - X coordinate of front - x disturbance of a plane front - parameter of growth rate - coefficient of surface tension - parameter introduced in (8) or (21) - , dimensionless disturbance of surface of the front and its amplitude - , , , dimensionless coordinates - , angular coordinates - H dimensionless wave number - wavelength of disturbance - concentration in solid - dimensionless time - (), amplitudes of disturbances of concentration - dimensionless concentration - dimensionless growth increment of disturbances Indices 0 and states at a plane front and in the solution far from the front - anasterisk state at a curved front - m fastest growing disturbances - a degree sign pertains to self-similar variables Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 818–827, May, 1981.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

The contributions of microrotation of lubricant molecules in a thin film journal bearing

Summary Characteristics of a journal bearing were computed for thin film lubrication accounting for microrotation of the lubricant molecules using both the half-Sommerfeld and Reynolds boundary conditions. Although the Reynolds boundary conditions produced higher pressure and loads, the effects of microrotation studied by both schemes showed similar trends. Primary characteristics that effect the contributions of microrotation to the load carrying capacity of the journal bearing were identified. These characteristics were varied and their effects on the load capacity of the journal bearing are shown.Nomenclature a circumference of the shell, 2R - a ₁,a ₂,a ₃ constants - c radial difference between the shaft and shell, [R-r] - c ₁,c ₂,c ₃,c ₄ solving partial differential equations constants - e eccentricity - F ^* body force per unit mass - G substitute function for integration - h film thickness - j microinertia constant of the fluid - K ₁,K ₂ defined after Eq. (2.27) - l material length, - L ^* body couple - m - N coupling number, - p pressure - p ₀ ambient pressure - Q fluid flux flow through the cavity cross section - r shaft radius - R shell radius - R _h modified Reynold number, - R _l Reynolds number, - t time - u, v velocity components inx-andy-direction, respectively - u ₀ velocity of the shaft surface - V velocity vector - W load carrying capacity - W load component resulting from pressure parallel to the line of centers - W load component resulting from pressure perpendicular to the line of centers - x, y, z Cartesian coordinates - , , , micropolar viscosity coefficients - ₁, ₂ parameters of boundary conditions for the microrotation vector at the shell and shaft, respectively - the deviate angle of the load direction from the line of centers - e/c - , Newtonian viscosity coefficients - microrotation velocity vector - microrotation velocity component in thez-direction - angular velocity of the shaft - ^* thermodynamic pressure - mass density of the lubricant fluid - polar angle around the journal bearing - ^* angle which satisfies Reynold's B.C.     

Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole

Summary The flow of a viscous ferrofluid over a stretching sheet in the presence of a magnetic dipole is considered. The fluid momentum and thermal energy equations are fomulated as a five-parameter problem, and the influence of the magneto-thermomechanical coupling is explored numerically. It is concluded that the primary effect of the magnetic field is to decelerate the fluid motion as compared to the hydrodynamic case, thereby increasing the skin friction and reducing the heat transfer rate at the sheet.Nomenclature a distance - c constant - c _p specific heat at constant pressure - C _f wall friction coefficient - e 2.71828 ... - f dimensionless stream function - H magnetic field - k thermal conductivity - K constant - M magnetization - Nu _x local Nusselt number - p pressure - P dimensionless pressure - Pr Prandtl number, c _p/k - Re _x local Reynolds number, cx ²/ - T temperature - u velocity component along the sheet - v velocity component normal to the sheet - x coordinate along the sheet - y coordinate normal to the sheet - dimensionless distance - ferrohydrodynamic interaction parameter - constant - dimensionless Curie temperature - dimensionless coordinate - dimensionless temperature - viscous dissipation parameter - dynamic viscosity - ₀ permeability - dimensionless coordinate - density - shear stress - magnetic potential - stream function