Near-wall turbulence in the axisymmetric flow of weak acqueous polymer solutions

The axisymmetric turbulent boundary layer is computed by using a finite-difference method and its fluctuation characteristics are determined on the basis of a generalized mixing-path hypothesis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 4, pp. 545–550, April, 1990.     

A multidomain boundary element method for two equation turbulence models

The paper deals with the multidomain Boundary Element Method (BEM) for modelling 2D complex turbulent flow using low Reynolds two equation turbulence models. While the BEM is widely accepted for laminar flow this is the first case, where this method is applied for a complex flow problems using k–ε turbulence model. The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as subdomain technique. The resulting system matrix is overdetermined, sparse, block banded and solved using fast iterative linear least squares solver. The simulation of turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model.     

Particular solutions for axisymmetric Helmholtz-type operators

In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R³. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides by Fourier-polynomials or bivariate polynomials. This inevitably leads to analytical solving a sequence of ordinary differential equations (ODEs.) The analytic formulas and their precision are checked using mathematica. In fact, by using an infinite precision technique, the particular solutions can be obtained with infinite precision themselves. This work will form the basis for numerical algorithms for solving axisymmetric heat equation.     

Calculation of the characteristics of countercurrent axisymmetric jets

On the basis of analysis and generalization of experimental data, a method is proposed for calculating the parameters of the interaction of two coaxial jets flowing in opposite directions from circular nozzles of different diameters.Notation d, D diameter of the nozzles for the small- and large-diameter jets - density - x, y coordinates - u, U averaged longitudinal component of velocity of the small- and large-diameter jets - L_ax distance between nozzles - q relative impulse - G mass rate of the medium - 2r width of the jet - _i, L_i lengths of the flow zones of the small- and large-diameter jets, where i=1, 2 - range of the jet - 2B distance between corresponding points of lines of maximum velocity of the large-diameter jet Indices 0 initial state - m maximum value - ax value on the axis - d large-diameter jet - y_0.5 distance from the axis to the point at which the velocity is equal to half the velocity on the axis Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 725–729, May, 1989.     

Similarity prediction of wall jets past axisymmetric bodies for power-law fluids

Summary The similarity solution is presented for laminar wall jets on bodies of revolution for power-law fluids. The functional dependence of the length and velocity similarity scales on a shape parameter and a flow behaviour index is determined. Discussion dealing with flow invariance, modified Mangler's transformation and with previously published results is carried out.     

Self-similar solutions of the Stefan problem

Investigation is made of one of the self-similar regimes in the problem of a crystal growing from a pure melt with an isothermal surface. This regime is shown to exist only in the case of two-dimensional, cylindrical, or spherical geometry of the crystal and also when a two-dimensional crystal grows on a surface isometric to the surface of revolution. Modeling of the spherical crystal growth by two-dimensional crystallization on the surface of revolution is discussed.Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia. Translated from Inchenerno-Fizicheskii Zhurnal, Vol. 63, No. 4, pp. 468–472, October, 1992.     

Near-wall function for turbulence closure models

 The Wall Function for large eddy simulation (LES) proposed by Cabot is extended to the turbulence closure models. Predicted results are discussed and compared with well-documented experimental results. The model with Cabot's Wall Function significantly reduces the computing resources (CPU and storage) required and in most cases improves predicted results. Received 10 September 2001 / Accepted 3 May 2002     

Self-similar solutions of the external condensation problem

A new class of self-similar solutions of the external condensation problem is constructed, which takes account of the change in the process parameters a long the length of the condensation section.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 2, pp. 338–343, August, 1978.     

Analytic solutions for axisymmetric magnetostatic systems involving iron

The analytic solutions are given for three simple axisymmetric systems involving toroidal conductors and iron. The solutions can be used for testing and gauging the accuracy of three-dimensional numerical schemes. In each case it is demonstrated how the fields can be calculated from a spherical harmonic expansion. This provides a unified and efficient method for calculating the fields.     

Application of integral-relation method in using complex models of turbulence

The generalization of the integral-relation method to the case when turbulence models with two differential equations for the turbulent flow properties is considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 3, pp. 517–521, March, 1979.     

住宅空调数值模拟的模型比较

应用CFD技术分别用LVEL模型和标准k-ε模型对住宅空调的舒适度以及空气龄进行了数值模拟。结果表明LVEL紊流模型对HVAC系统的模拟是快捷和有效的。     

The method of fundamental solutions for axisymmetric potential problems

In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two classes of axisymmetric potential problems. In the first, the boundary conditions as well as the domain of the problem, are axisymmetric, and in the second, the boundary conditions are arbitrary. In both cases, the fundamental solutions of the governing equations and their normal derivatives, which are required in the formulation of the MFS, can be expressed in terms of complete elliptic integrals. The method is tested on several axisymmetric problems from the literature and is also applied to an axisymmetric free boundary problem. Copyright © 1999 John Wiley & Sons, Ltd.     

Self-similar solutions of the magnetohydrodynamic boundary layer system for a dilatable fluid

Summary A rigorous mathematical analysis is given for a magnetohydrodynamic boundary layer problem, which arises in the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting dilatable fluid along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. In the self-similar case, the problem is transformed into a third-order nonlinear ordinary differential equation with certain boundary conditions, which is proved to be equivalent to a singular initial value problem for an integro-differential equation of first order. With the aid of the singular initial value problem, the uniqueness, existence, and nonexistence results for generalized normal solutions are established.     

Soliton-like solutions and periodic form solutions for two variable-coefficient evolution equations using symbolic computation

Summary. Some variable-coefficient generalizations of some nonlinear evolution equations (NLEEs) bear more realistic physical importance. By means of a generalized Riccati equation expansion (GREE) method and a symbolic computation system – Maple – we investigate the variable-coefficient Fisher-type equation and the nearly concentric KdV equation. As a result, rich families of exact analytic solutions for these two equations, including the non-travelling waves and coefficient functions soliton-like solutions, singular soliton-like solutions, and periodic form solutions, are obtained.     

Comparative analysis of turbulence models

A comparative analysis is performed for a complete locally anisotropic turbulence model of the second order and existing turbulence models. The comparison draws on experimental data, data of a direct numerical simulation of the nonstationary Navier-Stokes equations for a developed channel flow and a uniform channel flow with a constant velocity shift, and results for turbulence damping behind a grid. The K-ɛ model and the quasi-isotropic turbulence model are shown to have marked disadvantages, especially in describing turbulent flows with a high degree of anisotropy of pulsatory motion. Use of a locally anisotropic turbulence model improves the accuracy of determining Reynolds stresses. Consideration is given to the advantages and disadvantages of the turbulence models discussed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 328–339, March—April, 2000.     

Finite strain elastic closed form solutions for some axisymmetric problems

Summary In this paper, rate type constitutive equations using the Jaumann and 2nd Piola-Kirchhoff stress rate are used to develop axisymmetric finite strain, elastic, closed form solutions for a variety of loading conditions. We examined several cases comprizing compression-extension loading conditions, simple shear and cavity expansion conditions. Results from small strain analyses are used to indicate strain ranges for which such analyses will provide satisfactory solutions. For all the cases examined, except simple shear, the 2nd Piola-Kirchhoff stress rate does not appear to be a suitable stress rate to describe a material which follows a rate-type constitutive equation for strains greater than about 40%. The Jaumann stress rate solution shows oscillatory shear stress for axisymmetric simple shear similar to that found earlier by many other authors for rectangular (or cuboidal) condition. Negative excess pore water pressure (suction) at the cavity wall during the expansion of a cylindrical cavity was also observed in Jaumann stress rate solution.     

Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

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.     

Probabilistic treatment of fracture using two failure models

A probabilistic methodology for brittle fracture based on two local failure models is presented. Probabilistic fracture parameters are obtained using a weakest link and a chain-of-bundles formulation. Both models define limiting distributions for the fracture stress described by a two-parameter Weibull distribution. Numerical procedures employing measured toughness data and finite element solutions are also described to calibrate the Weibull parameters. An application of the methodology then follows to predict geometry and stable crack growth effects on the distribution of macroscopic fracture toughness (J_c) for a high-strength steel. Measured fracture toughness values for a high-constraint geometry that exhibit no prior ductile tearing are effectively ‘transferred' to a different geometry having much lower constraint and in which tearing precedes cleavage. The inherent difficulty in predicting the scatter of experimental fracture toughness, as well as constraint and ductile tearing effects, within the scope of conventional procedures appears greatly reduced in the framework presented in this work.