Flow visualization in a laboratory vaned diffuser

An experimental model of a vaned diffuser with rectangular flow cross-sections was constructed of clear plastic for flow visualization studies. A swirl generator was used to induce fluid rotation without subjecting the diffuser to any unsteady and irregular impeller flow phenomena. The blades were of a thin circular arc shape. The clear plastic construction allowed large-scale flow visualization with tufts attached to the diffuser wall and dye injected into the separation regions. Four conditions were tested: a vaneless, a four-vaned, a six-vaned, and eight-vaned diffuser. Each test was conducted at an average Reynolds number of 20 000, based on passage thickness. In the absence of diffuser blades the flow angle was not radially constant, as a result of the viscous effects, varying as much as 11° from the ideal 16°. With four blades installed, separation began at 23% of the blade length from the leading tip. At the peak development of the separation regions 34% of the flow area was blocked. Separation began at 27% from the leading edge when six blades were used. Finally, with eight blades in place, separation began at 50% of the blade length from the leading tip; at the peak development of the separation regions 64% of the flow area was blocked.     

Laser velocimetry measurements in a laboratory vaned diffuser

Laser velocimetry measurements were made within a laboratory radial vaned diffuser with three different blade configurations. Measurements were made through passages with four, six and eight blades installed at off design conditions. Also, in the eight blade diffuser measurements were made between the blade passage exit and diffuser exit so that the complete secondary flow could be defined. The flow was found to separate from the blades and form large separation zones. The separation zones consisted primarily of two vortices rotating in opposite directions. At the passage exit the separation region encompassed 23% of the circumferential area for the four blade diffuser, 45% for the six blade and 40% in the eight blade diffuser. Separation occurred at 23%, 27% and 50% from the leading edge of the blades for the 4, 6 and 8 bladed diffusers, indicating that more blades better controlled the separation. Turbulence intensities ranged from approximately 5% to 15% in the primary flow and reached a few hundred percent in the secondary flow within the separation regions.     

Measurements in the vaneless diffuser of a radial flow compressor

Results from an experimental study of flow behaviour at the inlet of a vaneless diffuser of a centrifugal compressor are presented. Measurements from a crossed hot-wire probe are given for operating points having inlet flow coefficients ranging from 0.006 to 0.019 at different Reynolds numbers. Instantaneous, time-averaged, and phase-averaged absolute velocity and flow angle at the diffuser inlet are deduced from the hot-wire signals after correction for mean density variations. These results show how flow behaviour varies in stable, rotating stall and surge regimes of compressor operation     

Nonisothermal flow of a viscous incompressible fluid in a two-dimensional diffuser

The velocity and temperature distributions in a viscous incompressible fluid flow in a two-dimensional diffuser are analyzed. Fully developed flow is considered, i.e., the influence of the entrant section is disregarded. It is assumed that the diffuser walls are maintained at a temperature depending on the polar radius. The dynamic viscosity is considered to be an exponential function of the temperature. The problem is reduced to the solution of a system of ordinary differential equations, which is solved by the method of successive approximations. The convergence of the iterative scheme is proved.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–48, July–August, 1973.The author is indebted to L.A. Galin and N. N. Gvozdkov for assistance with the study.     

Finite element solution of flow between eccentric cylinders with viscous dissipation

A computational study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.     

Finite element analysis of flow in a gas-filled rotating annulus

Linearized multidimensional flow in a gas centrifuge can be described away from the ends by Onsager's pancake equation. However a rotating annulus results in a slightly different set of boundary conditions from the usual symmetry at the axis of rotation. The problem on an annulus becomes ill-posed and requires some special attention. Herein we treat axially linear inner and outer rotor temperature distributions and velocity slip. An existence condition for a class of non-trivial, one-dimensional solutions is given. New exact solutions in the infinite bowl approximation have been derived containing terms that are important at finite gap width and non-vanishing velocity slip. The usual one-dimensional, axially symmetric solution is obtained as a limit. Our previously reported finite element algorithm has been extended to treat this new class of problems. Effects of gap width, temperature and slip conditions are illustrated. Lastly, we report on the compressible, finite length, circular Couette flow for the first time.     

级环境下叶片扩压器流场的实验与数值研究

为了研究离心压缩机级环境下的非定常干扰的基本流动现象,并验证多级叶轮机械的CFD软件的分析能力, 对一大尺度离心压缩机的叶片扩压器流场进行了实验测量和数值计算. 实验采用了固定热线、相位锁定------系综平均技术,用常温热线风速仪对叶轮后的叶片扩压器通道内不同周向、径向和轴向位置处的非定常速度进行了测量,同时提出了非定常强度的概念,以定量考核非定常的影响.实验结果表明, 叶片扩压器内的非定常流动非常复杂,其时间周期并非叶轮叶片通过时间,随着与离心叶轮之间的距离增大,非定常扰动逐渐减弱,但一直延续到叶片扩压器的出口.另外,对该实验压缩机级开展了两个不同的数值计算,并与实验数据进行了比较：定常数值计算软件采用了作者发展的确定应力模型,非定常数值计算是用商业软件NUMECA实现的,计算采用了滑移界面技术. 两个计算结果与实验在扩压器的进口截面处吻合得很好.     

Finite element analysis of the axially symmetric motion of an incompressible viscous fluid in a spherical annulus

This paper presents results obtained by employing a modified Galerkin finite element method to analyse the steady state flow of a fluid contained between two concentric, rotating spheres. The spheres are assumed to be rigid and the cavity region between the spheres is filled with an incompressible, viscous, Newtonian fluid. The inner sphere is constrained to rotate about a vertical axis with a prescribed angular velocity, while the outer sphere is fixed. Results for the circumferential function Ω, streamfunction ψ, vorticity function ζ and inner boundary torque T₁ are presented for Reynolds numbers Re ? 2000 and radius ratios 0.1 ? α ? 0.9. The method proved effective for obtaining results for a wide range of radius ratios (0.1 ? α ? 0.9) and Reynolds numbers (0 ? Re ? 2000). Previous investigators who employed the finite difference method experienced difficulties in obtaining results for cases with radius ratios α ? 0.2, except for small Reynolds numbers (Re ? 100). Results for Ω, Ψ, ζ and T₁ obtained in this study for radius ratios 0.8 ≤ α ≤ 0.9 verified the development of Taylor vortices reported by other investigators. The research indicates that the method may be useful for analysing other non-linear fluid flow problems.     

Slow flows of a viscous liquid in a conical diffuser

We show the applicability of Stokes' approximation at large distances from the vertex of a cone. We discuss the statement of the problem and formulate new asymptotic representations of the solution, which replace the paradoxical solution of Harrison for cone vertex angles α≥120°. A solution of the problem concerning the axially symmetric Stokes' flow of a viscous liquid in a conical diffuser was first obtained by Harrison [1] (see also [2, 3]). The velocity field of this flow has the form $$\upsilon _R = \frac{{3Q}}{{2\pi R^2 }}\frac{{\cos ^2 - \cos ^2 \alpha }}{{\left( {1 - \cos \alpha } \right)^2 \left( {1 + 2\cos \alpha } \right)}}, \upsilon _\theta = 0$$ where R and Θ are spherical coordinates, Θ=0 and Θ=α correspond, respectively, to the axis and to the wall of the diffuser, and Q is the volumetric outflow rate of the liquid. We note that the values of the velocity in this purely radial flow become infinite when the angle α approaches 120°.     

Lagrangian finite element analysis applied to viscous free surface fluid flow

A new Lagrangian finite element formulation is presented for time-dependent incompressible free surface fluid flow problems described by the Navier-Stokes equations. The partial differential equations describing the continuum motion of the fluid are discretized using a Galerkin procedure in conjunction with the finite element approximation. Triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides a viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs are demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.     

Finite element analysis of density flow using the velocity correction method

A finite element method is proposed for the analysis of density flow which is induced by a difference of density. The method employs the idea that density variation can be pursued by using markers distributed in the flow field. For the numerical integration scheme, the velocity correction method is successfully used, introducing a potential for the correction of velocity. This method is useful because one can use linear interpolation functions for velocity, pressure and potential based on the triangular finite element. The final equations can be formulated using the quasi-explicit finite element method. A flume in a tank with sloping bottom has been analysed by the present method. The computed results show extremely good agreement with the experimental observations.     

Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite element analysis of air flow around permeable sand fences

A numerical study of the turbulent air flow in a trench trap and the turbulent flow around a permeable sand fence is reported in this paper. The two-dimensional modified k–ε turbulence model proposed by Kato and Launder is used to predict the turbulent characteristics of the air flow. The discretization method for the governing equations is the three-step Taylor/Galerkin finite element method proposed by the authors. For the flow in a trench trap the numerical results are compared with experimental data obtained under realistic conditions using a large wind tunnel. For the air flow around a permeable sand fence a pressure loss model is used to represent the effect of the porosity of the fence on the flow field. © 1997 John Wiley & Sons, Ltd.     

Discrete element study of viscous flow in magnetorheological fluids

Using discrete element simulations, we gain insight into the structure of a magnetorheological fluid (MRF) under shear. In simulations with flat walls, the particles arrange in chains, sheet-like structures, or columns along the magnetic field lines, depending on the strength of the applied external magnetic field. Corresponding to the structure formation, three different types of failure mechanisms can be identified. For the characterization of the different regimes, specific particle coordination numbers are introduced. The three structural regimes can be distinguished and described by means of these coordination numbers. To analyze the contact between the MRF particles and the walls of the shear cell, additional simulations with rough walls have been conducted. The resulting structure formation could be successfully classified by the introduced coordination numbers. Based on the analysis of the shear stress transmission both in the case of flat and rough walls, possibilities for shear stress enhancement for technological applications are discussed.     

Characterization of viscous fingering in a radial Hele-Shaw cell by image analysis

Methods based on image analysis and mathematical morphology are proposed to study fingering patterns obtained in a radial Hele-Shaw cell. They have been used to study miscible displacement patterns obtained under various conditions of initial viscosity, viscosity ratio and injection rate. Their application domain can be extended to other type of fingering patterns as well as diffusion-limited aggregates. Received: 28 October 1997/Accepted: 16 April 1998     

Finite element analysis of non-Newtonian fluid flow in 2-d branching channel

This paper presents finite element analysis of non-Newtonian fluid flow in 2-d branching channel. The Galerkin method and mixed finite element method are used. Here the fluid is considered as incompressible, non-Newtonian fluid with Oldyord differential-type constitutive equation. The non-linear algebraic equation system which is formulated with finite element method is solved by means of continuous differential method. The results show that finite element method is suitable for the analysis of non-Newtonian fluid flow with complex geometry.     

Flow of a viscous liquid in a conical diffuser in the presence of heat transfer

In this work a solution has been derived for the motion of an incompressible liquid with a temperature dependent viscosity in a conical diffuser. The inertia and diffusion terms are neglected in the equations of motion and heat conduction. It is assumed that the temperature of the diffuser wall is inversely proportional to the spherical radius. It is shown that the stream function and temperature are uniformly convergent series, the terms of which satisfy an infinite system of normal differential equations. An investigation has been made of the behavior of the flow pattern and the effects of a temperature gradient on the radial velocity component. The method has been used to resolve the flow of a liquid between two coaxial cones.     

Density-contrast instabilities in finite element modelling of slow viscous flow

Finite element methods are often used to model Earth processes involving slow viscous or viscoelastic flow. Inertial terms of the Navier-Stokes equations are neglected in very slow flows, so timestep size is not limited by the Courant instability. However, where there is advection of density contrasts in a gravitational field, over-advection can lead to numerically induced flow oscillations. We derive analytic results for the maximum stable timestep size in two cases: a free surface over a fluid of uniform density, and a free surface kept level by sedimentation/erosion, but with a density gradient in the underlying medium. Using parameters appropriate to the Earth's crust we show that the density-contrast instability occurs for timesteps larger than 3000 years for the constant-density case. For a fluid with a density gradient of 10 kg/m³ per km the solution is stable for timesteps up to about 200,000 years if full erosion/sedimentation is implemented.