Boundary layer solution for the turbulent swirling decay flow through a fixed pipe: SBR at the inlet

In this study the developing turbulent swirling pipe flow is investigated both numerically and analytically. Governing equations are derived accompanying the boundary layer assumptions. Uniform and solid body rotation (SBR) distributions are taken into account for the axial and tangential velocities at the inlet of the pipe, respectively. Beyond the boundary layers, the flow pattern is considered to be the potential flow. Making use of the fourth-order Runge–Kutta scheme, the numerical solution of the differential equations is obtained. Further more, by simplifying the governing equations for large Rossby number, the analytical solution is performed. The results of numerical and analytical swirl intensity have been compared which shows reasonable agreement. As an alternative solution, a CFD analysis has been done, having applied FLUENT software to support the ability of our methodology.     

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.     

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.     

Unsteady compressible boundary layer swirling flow in a nozzle and a diffuser

This paper presents the results of the study of unsteady swirling boundary-layer flow of compressible fluid in a nozzle and a diffuser when the free stream velocity, mass transfer and wall temperature vary arbitrarily with time. The set of coupled nonlinear partial differential equations governing the flow which involves three independent variables has been solved numerically using an implicit finite-difference scheme. Both the heat transfer and skin friction are strongly affected by the free stream velocity, variation of the density-viscosity product across the boundary layer, mass transfer and swirl parameter. However, the variation of the wall temperature with time strongly affects only the heat transfer. Also, separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction.     

Experimental study of diffuser channels with a near-separating turbulent boundary layer

Results of experimental studies are shown concerning the aerodynamic characteristics of diffusers with the transition profile designed for a near-separating turbulent boundary layer. The test results are shown to agree closely with calculations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 3, pp. 518–523, September, 1971.The author thanks A. S. Ginevskii for assistance in carrying out this work.     

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 heat transfer on the entrance segment of a tube with a sharp inlet edge. 2. Correction for the entrance segment under turbulent boundary layer conditions

A correction relation _X=f(Re_d;X/d) is proposed for the entrance segment, where turbulent flow occurs in a surface boundary layer developing upon completing the transient process. An elevated local heat transfer intensity in a separated flow region beyond a sharp inlet edge is considered to be a consequence of the M-shaped velocity field profile that exists over a substantial length of the entrance segment.Kiev Polytechnic Institute, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp. 139–143, August 1993.     

The structure of a turbulent boundary layer

According to the wave mechanism of turbulence, pulsation in the hydrodynamic parameters results from a superposition of perturbations arising at the wall and then spreading in the flow in the form of spherical wave packets. At the flow boundary, where the fluid velocity is characterized by a large gradient, the acoustic rays of these waves exhibit bending and reversal toward the wall, whereby the trajectories with various initial orientations are interweave and the wave packets are broken. The pulsation of parameters in the region of wave packet breakage results in the formation of a turbulent boundary layer. Upon the reflection of waves, the flow velocity oscillations immediately at the wall cease that corresponds to a laminar sublayer of the turbulent boundary layer.     

The numerical calculation of turbulent boundary layer development

A mathematical model of the two-dimensional, incompressible turbulent boundary layer in arbitrary pressure gradient described and solved in earlier work¹ is solved by an implicit finite difference method. Comparisons of skin friction coefficient and momentum thickness values for the two methods for four test cases of different character indicate that the present method is a useful alternative to the method of characteristics which was used in previous work. One feature of the present method is that allowance is made for the logarithmic character of the velocity profile when constructing one of the finite difference expressions.     

Heat transfer in the initial segment of a rotating tube in the case of turbulent gas flow

On the basis of theory of local modeling we have determined the effect exerted by rotation on heat transfer in the initial segment of a tube in the case of turbulent gas flow. We have derived approximate working formulas which are compared with experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 4, pp. 597–602, April, 1969.Deceased.     

Turbulent flow in a boundary layer on the inlet and outlet sides of a rotating channel

Expressions are obtained for approximately determining the shear stresses on the outlet and inlet sides of a rotating channel on the basis of a turbulence energy balance equation, A. N. Kolmogorov's hypothesis, and the Monin-Obukhov similitude theory.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 977–986, December, 1981.     

Properties of transverse distributions of local heat exchange coefficients in the initial section of rectangular channels with mixed flow in the boundary layer

It is shown that with mixed flow in the boundary layer at the dynamic initial section of a rectangular channel the local heat exchange coefficients are considerably lower at the middle part of the wall than near the corners.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.27, No. 3, pp. 402–408, September, 1974.     

The distribution of tangential stresses in an incompressible turbulent boundary layer

We investigate an isothermal turbulent boundary layer with positive pressure gradient. We obtain results on the distribution of tangential stresses in the layer which are approximated by a simple computation equation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 4, pp. 666–673, April, 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.     

Calculation of a turbulent monodisperse flow in an axisymmetric channel

A stationary isothermal model of the aerodynamics of a two-phase flow in an axisymmetric channel has been constructed with allowance for the turbulent and pseudoturbulent mechanisms underlying the transfer of the solid phase momentum. The equations of dispersed phase motion are closed at the level of the equations for the second moments of the pulsation velocities of particles, whereas the equation of momentum transfer of the carrier is closed on the basis of a one-parameter model of turbulence extended to the case of two-phase turbulent flows. The results of calculations are compared with experimental data. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 844–855, September–October, 2008.     

Experimental study of non-steady-state turbulent flow in an axisymmetric diffusor

Results of an experimental study of the structure of an oscillating flow in a conical diffusor are presented and evaluated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 1, pp. 37–41, July, 1986.     

Spectral measurements in a turbulent boundary layer at a permeable plate with injection

The intensity spectra of longitudinal, transverse, and lateral velocity fluctuations were measured with a thermoanemometer in the boundary layer at a permeable plate, at various injection levels V_w/U from 0 to 0.0243.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 6, pp. 1109–1113, June, 1973.     

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.