Profiles of mean temperature and concentration in turbulent flow of a liquid in a pipe and in a boundary layer at a plate

A single equation is obtained which describes the profiles of mean temperature and concentration over the entire thickness of the internal region of a turbulent boundary layer at a wall. Theoretical and experimental data are compared for liquids with 0.026≤Pr≤1000.     

Micromixing models for calculating the average rate of a chemical reaction in a turbulent flow

A model of mixing with a chemical reaction in a uniform, isotropic turbulent flow has been developed on the basis of the statistical-moments method for calculating the hydrodynamic characteristics of a flow and the probability density function of its mixture coefficient for the purpose of determining the correlations responsible for the chemical reaction in the flow. The results of calculations of the average rate of a chemical reaction in a flow by the multizone model and models of micromixing (the mean-square approximation and Langevin models) used for construction of equations for the probability density function were compared.     

Surface-friction coefficient in turbulent flow at a boundary layer

Using Thompson two-parameter velocity profiles equations defining the dependence of the surface-friction coefficient on the integral characteristics of the boundary layer are obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.46, No. 1, pp. 51–56, January, 1984.     

Effect of heat transfer on compressible boundary layer flow over a circular cylinder

Summary The effect of heat transfer on the steady laminar compressible boundary layer flow past a horizontal circular cylinder has been studied. The resulting coupled nonlinear partial differential equations have been solved numerically using a very efficient finite-difference scheme. Specific results are given for the boundary layer separation parameter and the skin friction and heat transfer coefficients.     

Adiabatic turbulent flow of a gas in a cylindrical tube

A solution is given for one-dimensional adiabatic turbulent flow of a compressible gas in a cylindrical tube, taking into account variation of the Re number along the tube and the influence of compressibility on the friction coefficient. The solution is compared with formulas derived in [1] and [2].     

Velocity profile in a turbulent boundary layer of a supersonic gas stream

A semiempirical equation is proposed for relating the coefficients of molecular and turbulent viscosity in the laminar sublayer and in the transition region. Simple formulas are derived for determining the velocity throughout the boundary layer and the frictional stress at the surface of a plate at various values of the Mach number. The results of calculations are compared with experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 1, pp. 112–120, July, 1972.     

Effect of polymer additives on a three-dimensional turbulent boundary layer

By means of an integral method the characteristics of the three-dimensional boundary layer are calculated with allowance for the effect of polymer additives using the Meyer correlation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 3, pp. 369–374, March, 1987.     

Effect of boundary conditions on the heat transfer law for a turbulent boundary layer

The heat transfer at an impermeable plate has been experimentally investigated under various boundary conditions. The conservativeness of the heat transfer law St₀=f(Re _T ^** ) is demonstrated for a monotonic increase of temperature and heat flux along the surface.     

Effect of a homogeneous chemical reaction on heat transfer

Heat and mass transfer processes are investigated in the presence of homogeneous physico-chemical conversions of a substance.Institutes of Mathematics and Mechanics, Academy of Sciences of Turkmenistan, Ashkhabad. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 6, pp. 734–739, June, 1993.     

Length-scale distributions of the concentration pulsations of a passive impurity in a homogeneous turbulent flow

A relation for calculating the probability density function f _t ^λ (ϕ) of the length scales of a passive concentration field in homogeneous turbulence has been obtained by consideration of the joint statistics of the concentration field and its gradient. The closed equation derived for f _t ^λ (ϕ) has been solved numerically using the data of direct numerical modeling of homogeneous turbulence for the mean characteristics involved in the equation as the coefficients. The results obtained for different values of the Schmidt number have been compared. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 6, pp. 131–142, November–December, 2005.     

Studying the effect of the temperature factor on the transition from a laminar to a turbulent regime of flow in a boundary layer

Based on the generalization of experimental data, we propose a formula for the calculation of the effect of the temperature factor and the transition from a laminar flow regime to one that is turbulent in the boundary layer of a plate; this formula has been confirmed by experiments performed in the following range of parameter variation: 0.5 2.6; 0.2 M 3.6; 0.1 9%.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 2, pp.218–224, February, 1969.     

Integral method of calculating a turbulent boundary layer in a uniform gas stream

A previously developed integral method for calculating a turbulent boundary layer with pressure gradient and blowing [1] has been generalized to the case of flow with heat transfer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 3, pp. 500–506, March, 1978.     

The temperature of an adiabatic surface at a turbulent boundary layer

A calculation of the temperature decrease of an adiabatic surface at a supersonic turbulent boundary layer is conducted. It is shown that the temperature decrease is a consequence of the appearance of a vortex chain in the flow near the walls. Comparison of calculated data with experimental gives qualitative agreement.Notation V incident flow velocity - V_v vortex velocity - v local velocity - u induced velocity - T thermodynamic temperature - T_w, T recovery temperature and undisturbed flow temperature - L length of depression - h₀ depth of depression - h distance from vortex center to wall - b relative vortex velocity - l _v vortex spacing - r recovery coefficient - R₀ recovery coefficient on smooth surface - c_p gas heat capacity at constant pressure - n vortex passage frequency - Re Reynolds number - M Mach number - velocity potential - time - vortex intensity Translated from Ihzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 903–908, May, 1971.     

Local and integral turbulent boundary layer characteristics on a convex surface in diffusor flow

A semiempirical method is proposed for computing the local and integral characteristics of the turbulent boundary layer on a convex surface under conditions of a positive longitudinal pressure gradient. By using the method proposed, graphical dependences are obtained that characterize the influence of curvature on the form-parameter, the thickness of the momentum loss, the thickness of the viscous sublayer, and the relative flow coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 6, pp. 916–920, June, 1990.     

A model for turbulent dissipation rate in a constant pressure boundary layer

Estimation of the turbulent dissipation rate in a boundary layer is a very involved process. Experimental determination of either the dissipation rate or the Taylor microscale, even in isotropic turbulence, which may occur in a portion of the turbulent boundary layer, is known to be a difficult task. For constant pressure boundary layers, a model for the turbulent dissipation rate is proposed here in terms of the local mean flow quantities. Comparable agreement between the estimated Taylor microscale and Kolmogorov length scale with other data in the logarithmic region suggests usefulness of this model in obtaining these quantities experimentally.     

Compressible turbulent boundary layer on a permeable plate with injection of foreign gas

A numerical solution is obtained for equations of motion, diffusion, and energy using a three-parameter model of turbulence for boundary layer with different thermal boundary conditions on a permeable plate with injection of foreign gas. For an ideal gas with constant values of Prandtl and Schmidt numbers, the numerical solution is compared with limiting dependences for dimensionless temperature and enthalpy of gas on the wall. For helium/xenon mixtures with a low value of Prandtl number, the effect of intensity of injection and of the values of Reynolds and Mach numbers on the integral and local characteristics of flow and heat and mass transfer is investigated.     

Natural convection in a turbulent boundary layer at a wall with variable temperature

The problem of natural convection in a turbulent boundary layer at a wall with variable temperature (or thermal flux) is solved by the integrals method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 4, pp. 687–692, April, 1973.     

The asymptotic boundary layer on a circular cylinder in axisymmetric micropolar fluid flow

An asymptotic boundary layer analysis is presented using the theory of micropolar fluids due to Eringen. The laminar boundary layer induced on the outside of a long, slender cylinder due to the flow of an incompressible micropolar fluid parallel to the axis of the cylinder is investigated. For reasons of both analytical and practical interests the boundary layer characteristics far down stream from the leading edge are analyzed on the basis of their asymptotic nature. Asymptotic series solutions for the velocity and micro-rotation fields are obtained. An expression for the new micropolar boundary layer thickness is derived. Central to the present investigation is the result that while calculating the skin friction one should take into account the total surface stress effects, not only due to the usual shear stresses but also due to the couple stresses. As a result, it is shown that the micropolar theory does predict a reduction in skin friction as is observed in experiments thus confirming Eringen's well known conjecture.     

Oscillating flow in a tube with formation of a boundary layer of solvent

It is shown that the presence of a boundary layer of solvent can lead to a sharp increase in the velocity of an oscillating flow of viscoelastic fluid.Prof. Z. P. Shul'man was the scientific editor.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 2, pp. 238–243, February, 1980.     

Influence of velocity gradient and wall proximity on the readings of a pitot tube in measurement of surface friction and velocity distribution in a turbulent boundary layer

The authors present results of an experimental investigation of the correlations and readings of a Pitot tube in measuring velocity in a turbulent boundary layer. A new calibration relation is proposed for measuring surface friction.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 6, pp. 895–904, June, 1985.