Viscous Flow Analysis Research Articles

Backward-Facing Step Flow Analysis Using the Fourth-Order Finite-Difference Method.

In the incompressible viscous fluid flow analyses, the backward-facing step flow problem has been investigated as a benchmark problem with the inflow and outflow boundary conditions for testing the effectiveness of a new numerical scheme. In this research, the corrected fourth-order finite difference method is employed for this fluid flow analysis. This method was originally proposed by authors through the error analysis approach and has been successfully applied for viscous fluid flow and natural convection problems in a square cavity. In this study, the backward-facing step now was simulated for the Reynolds numbers of 800 and 1000, and the steady solutions were obtained. The effects of the sizes of computational meshes to the reattachment lengths are investigated, and the mesh-independent solutions are obtained. We confirm the agreement of our results with other research works and the effectiveness of our corrected fourth-order finite difference method for viscous fluid flow analyses with inflow and outflow boundary conditions.

Numerical analysis of dusty hypersonic viscous gas flow over a flat plate

Numerical analysis of dusty hypersonic viscous gas flow over a flat plate

309 二次元粘性流れ解析における格子ボルツマン法と従来型数値解法との比較に関する検討(O.S.3-2 熱流体解析における新潮流2)(オーガナイズドセッション3 : 熱流体解析における新潮流)

309 二次元粘性流れ解析における格子ボルツマン法と従来型数値解法との比較に関する検討(O.S.3-2 熱流体解析における新潮流2)(オーガナイズドセッション3 : 熱流体解析における新潮流)

Analysis of Linear Viscous Flow with a Free Surface in a Circular Cylinder Subjected to Small-Amplitude Circular Oscillations

A fluid flow with a free surface inside a circular cylinder subjected to horizontal, circular oscillation was analyzed theoretically and numerically under the assumption of small-amplitude oscillation and high Reynolds number. It was shown that the nature of the oscillatory flow is of a standing-wave type when projected onto the axial plane and of a progressive-wave type when projected onto the azimuthal plane. The Stokes drift motion in the azimuthal direction and the steady streaming velocity at the edge of the bottom- and side-wall boundary layers are then used in the numerical computation for the steady axisymmetric recirculatory flow outside the boundary layers. We have found that the solutions can be well predicted by asymptotic analysis for the full Navier–Stokes equations in the low streaming-Reynolds-number limit. A simple experiment on flow visualization revealed a good agreement in the surface flow pattern on the bottom wall. It also provided steady recirculatory flows that were not much different from the numerical results on the whole.

Finite element analysis of incompressible viscous flow with moving free surface by selective volume of fluid method

A numerical technique for simulating incompressible viscous flow with free surface is presented. The flow field was calculated by the penalty finite element formulation. In this work, a modified volume of fluid (VOF) method based on four node elements in 2D geometry was proposed for its compatibility with the irregular meshes generally used with the finite element method (FEM). Numerical analyses were done for two benchmark examples, namely the broken dam problem and the solitary wave propagation problem. The numerical results showed close agreement with the existing data. In order to demonstrate the effectiveness of the proposed numerical scheme, mold filling process was studied.

Viscous-Flow Two-Dimensional Analysis Including Secondary Flow Effects

During the last few decades extremely powerful Quasi-three-dimensional (3D) codes and fully 3D Navier-Stokes solvers have been developed and successfully utilized in the design process and optimization of multistage axial-flow compressors. However, most of these methods proved to be difficult in handling and extremely time consuming. Due to these disadvantages, the primary stage design and stage matching as well as the off-design analysis is nowadays still based on fast 2D methods incorporating loss-, deviation- and end wall modeling. Only the detailed 3D optimization is normally performed by means of advanced 3D methods. In this paper a fast and efficient 2D calculation method is presented, which already in the initial design phase of multistage axial flow compressors, considers the influence of hub leakage flows, tip clearance effects, and other end wall flow phenomena. The method is generally based on the fundamental approach by Howard and Gallimore (1992). In order to allow a more accurate prediction of skewed and nondeveloped boundary layers in turbomachines, an improved theoretical approach was implemented. Particularly the splitting of the boundary layers into an axial and tangential component proved to be necessary in order to account for the change between rotating and stationary end walls. Additionally, a new approach is used for the prediction of the viscous end wall zones including hub leakage effects and strongly skewed boundary layers. As a result, empirical correlations for secondary flow effects are no longer required. The results of the improved method are compared with conventional 2D results including 3D loss- and deviation-models, with experimental data of a three-stage research compressor of the Institute for Jet Propulsion and Turbomachinery of the Technical University of Aachen and with 3D Navier-Stokes solutions of the V84.3A compressor and of a multistage Siemens research compressor. The results obtained using the new method show a remarkable improvement in comparison with conventional 2D methods. Due to the high quality and the extremely short computation time, the new method allows an overall viscous design of multistage compressors for heavy duty gas turbines and aeroengine applications.

Viscous flow analysis using a parallel unstructured multigrid solver

Viscous flow analysis using a parallel unstructured multigrid solver

Modified Galerkin Analysis for the Unsteady Three-Dimensional Viscous Fluid Flow (Approach by the Error Analysis Technique).

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the convection-diffusion problems and the two-dimensional viscous fluid flows. In the modified Galerkin method, since the inertia term is considered explicitly, only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, this modified Galerkin method is applied to the three-dimensional incompressible viscous fluid flow analysis coupled with the Semi-Implicit Method for Pressure-Linked Equations formulation. The cubic cavity flow problem sare investigated for the Reynolds number of 400, 1000, 2000 and 3200. Finally, we confirmed the effectiveness of our proposed method.

Flow Cytometric Analysis by Using Micro-Machined Flow Chamber.

Effect of the flow characteristics in a newly developed micro-machined sheath flow chamber on the accuracy of cytometric analysis was investigated. The chamber was formed by laminating three 100-μm-thick photo-etched metal plates. Sample fluid containing cells, which enters the chamber via an axial specimen nozzle, is enveloped by a buffering sheath-fluid and transported to a capillary channel. Microscopic observation and three-dimensional viscous flow analysis predict that the dispersion of cells in the capillary channel is favorably reduced when the Reynolds number is between 500 and 750, which is value associated with low deviation of the analytical results. The five classifications of human white blood cells were determined. and this verified that change of the deviation depends on the Reynolds number. The results confirm Reynolds number of 500-750 is appropriate for good classification.

Solution of a transcendental eigenvalue problem via interval analysis

A knowledge of the complex roots λ of the transcendental eigenvalue equation sin λα=± λsin α is essential in the analysis of the slow viscous fluid flow in the neighbourhood of a sharp corner which subtends an angle α ϵ (0, 2π] to the fluid. Existing methods for finding all roots λ essentially require an a priori knowledge of the solution structure; given that { λ 1, λ 2, …, λ m } are known, gl m+1 is determined via iterations, and/or a solution procedure initiated by λ m . We present herein a general interval analysis method which exhaustively finds all roots λ via only the original eigenvalue equation: no other information is required. The interval-analysis method automatically guarantees root existence and uniqueness while simultaneously providing error bounds.

Three-dimensional linear stability analysis of incompressible viscous flows using the finite element method

The linear stability of incompressible flows is investigated on the basis of the finite element method. The two-dimensional base flows computed numerically over a range of Reynolds numbers are perturbed with three-dimensional disturbances. The three-dimensionality in the flow associated with the secondary instability is identified precisely. First, by using linear stability theory and normal mode analysis, the partial differential equations governing the evolution of perturbation are derived from the linearized Navier–Stokes equation with slight compressibility. In terms of the mixed finite element discretization, in which six-node quadratic Lagrange triangular elements with quadratic interpolation for velocities (P2) and three-node linear Lagrange triangular elements for pressure (P1) are employed, a non-singular generalized eigenproblem is formulated from these equations, whose solution gives the dispersion relation between complex growth rate and wave number. Then, the stabilities of two cases, i.e. the lid-driven cavity flow and flow past a circular cylinder, are examined. These studies determine accurately stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode by means of the Krylov subspace method and discuss the mechanism of instability. For the cavity flow, the estimated critical results are Rec=920.277±0.010 for the Reynolds number and kc=7.40±0.02 for the wave number. These results are in good agreement with the observation of Aidun et al. and are more accurate than those by the finite difference method. This instability in the cavity is associated with absolute instability [Huerre and Monkewitz, Annu. Rev. Fluid Mech., 22, 473–537 (1990)]. The Taylor–Goertler-like vortices in the cavity are verified by means of the reconstruction of three-dimensional flows. As for the flow past a circular cylinder, the primary instability result shows that the flow has only two-dimensional characteristics at the onset of the von Karman vortex street, when Re<49. The estimated critical values of primary instability are Rec=46.389±0.010 and Stc=0.126 for the Strouhal number. These values are very close to the observation data [Williamson, J. Fluid Mech., 206, 579–627 (1989)] and other stability results [Morzynski and Thiele, Z. Agnew. Math. Mech., 71, T424–T428 (1991); Jackson, J. Fluid Mech., 182, 23–45 (1987)]. This onset of vortex shedding is associated with the symmetry-breaking bifurcation at the Hopf point. Copyright © 1999 John Wiley & Sons, Ltd.

Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator–Strut–Splitter Aerodynamic Flow Interactions

Large circumferentially varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single blade row three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV–frame system to obtain a circumferentially nonuniform stator stagger angle distribution to reduce the upstream static pressure disturbance further. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV–strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV–frame analysis included the uniformly staggered OGV configuration and the variably staggered OGV configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably staggered OGV configuration and showed less upstream flow nonuniformity with the uniformly staggered OGV configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow nonuniformity with the uniformly staggered OGV configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly and variably staggered OGV configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

A new velocity decomposition for viscous flows: lighthill's equivalent-source method revisited

A convenient decomposition for vector fields is presented that falls within the vast class of potential-vorticity decompositions of the type υ = V ¯ ϕ + w , which includes the classical Helmholtz and Clebsch decompositions. The distinguishing feature of the present decomposition is that the rotational velocity contribution w (obtained by a line-integration along a path normal to the boundary) vanishes in much of the irrotational region. As a consequence, in the irrotational region one obtains υ = V ¯ ϕ . The mathematical formulation of the problem and the application to the analysis of incompressible viscous flows around solid bodies are discussed. For flows in which the vortical region is concentrated in a thin layer surrounding the surface of the body and the wake mid-surface, the relationship between the present formulation and the classical Lighthill's equivalent-source approach is addressed. In addition, an exact extension of the Lighthill formulation is presented. The equivalence of the two approaches is established. Numerical results for the reconstruction of the two-dimensional velocity field (from a prescribed vorticity field) are presented to illustrate the differences between various approaches.

Finite element techniques for wind engineering

Abstract This paper deals with the development of a variable-node element and its application to the adaptive h -version mesh refinement-recovery for incompressible viscous flow analysis. The element which has variable mid-side nodes and forms the transition zone between the refined and unrefined zones is efficiently used for constructing a refined mesh without generating distorted elements. A modified Gaussian quadrature is needed to evaluate the element matrix due to the discontinuity of derivatives of the shape functions used for the element. The penalty function method which can reduce the number of independent variables is adopted for the purpose of computational efficiency and selective reduced integration is carried out for the convection and pressure terms to preserve the stability of the solution. For economical analysis of transient problems, not only the mesh refinement but also the mesh recovery is needed. The numerical examples show that the optimal mesh for the finite element analysis of a flow around the structures can be obtained automatically by the proposed scheme.

Computation of Three-Dimensional Compressible Flow From a Rectangular Nozzle With Delta Tabs

A three-dimensional viscous flow analysis is performed using a time-marching Reynolds-averaged Navier-Stokes code for a 3:1 rectangular nozzle with two delta tabs located at the nozzle exit plane to enhance mixing. Two flow configurations, a subsonic jet case and a supersonic jet case using the same tab configuration, which were previously studied experimentally, are computed and compared with the experimental data. The experimental data include streamwise velocity and vorticity distributions for the subsonic case, and Mach number distributions for the supersonic case, at various axial locations downstream of the nozzle exit. The computational results show very good agreement with the experimental data. In addition, the effect of compressibility on vorticity dynamics is examined by comparing the vorticity contours of the subsonic jet case with those of the supersonic jet case which were not measured in the experiment.

A finite element analysis of steady viscous flow in triangular cavities

A finite element formulation of the Navier—Stokes equations, written in terms of the stream function, ψ, and vorticity, ω, for a Newtonian fluid in the absence of body forces, is used to solve the problem of flow in a triangular cavity, driven by the uniform motion of one of its side walls. A key feature of the numerical method is that the difficulties associated with specifying ω at the corners are addressed and overcome by applying analytical boundary conditions on ω near these singularities. The computational results are found to agree well with previously published data and, for small stagnant corner angles, reveal the existence of a sequence of secondary recirculations whose relative sizes and strengths are in accord with Moffatt's classical theory. It is shown that, as the stagnant corner angle is increased beyond approximately 40°, the secondary recirculations diminish in size rapidly.

Rheological Behavior of Superplastic Nanocrystalline and Amorphous Materials

Rheological behavior of two groups of superplastic materials is analyzed on the base of mass-transfer mechanics considerations. The first group is distinguished by ultra-fine grains as the basic mass-transfer units and includes FSS alloys, HSR alloys as well as crystallizing meta melts The second group unifies materials which exhibit superplastic and superplastic-like ow on the basis of moving atoms or their groups as mass-transfer units. Inorganic glass-forming systems (non-metallic as well as metallic), polymers and materials which display phase-transformation superplasticity may be included into this group. An analysis of apparent shear viscosity in superplastic flow of this materials as the function of solid-phase volume fracture as well as of strain rate and deformation temperature shows the evidence of rheological similarity among the materials mentioned above. Rheological properties of all these materials vary inside the range between pure viscous and viscoplastic types Thermodynamical analysis of viscous flow of metallic glasses show that the typical mass-transfer unit in supercooled liquid state is a group of atoms limited by two to three co-ordination spneres High-strain-rate superplasticity and very low shear viscosity exhibited by bulk amorphous alloys are considered as the promising features for development of new metal forming technologies.

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated.

Studies on the Numerical Simulation of Polymeric Liquid Flow and Polymer Processing.

This paper summarizes our studies on the numerical flow analysis of polymeric liquids and its application to the industrial problems in the polymer processing. The contents include three parts. The first part is a review about development of numerical technique of viscoelastic flow analysis to obtain the solution at high deformation rate. We used the streamline-upwind (SU) finite element method with the sub-elements for stress components to simulate the extrudate swell at high Weissenberg number (We). The calculation using the Giesekus model with a single relaxation time was feasible over hundreds of We in the planar and capillary extrude swell, but the calculation was impossible for We > 3 in the annular extrudate swell. We proposed the new technique of under-relaxation method, which introdnced the virtual Newtonian stress in order to increase the numerical stability. The calculation by the new technique combined with the SU method was successful in obtaining the solution over hundreds of We in the annular extrudate swell problem. The second part is a review of numerical studies on polymeric liquid flow in the basic flow fields. We performed the viscoelastic flow analysis using the several kinds of constitutive models in the contraction flow and extrudate swell. The simulation results using the viscoelastic model with a single relaxation time were compared with the experimental data of stress field measured by the flow birefringence technique and the agreement better than 20~30% in accuracy was obtained in the lower shear rate region. The simulation results also gave the several explanations about the mechanism of corner vortex and entrance pressure drop in the contraction flow, swelling phenomena in the extudate swell, etc. On the other hand, the simulation using the constitutive models with multiple relaxation times gave the useful information, especially on the effect of material polymer. The last part is application to the industrial problems in polymer processing. The technique of viscoelastic flow analysis was applied to the film casting and the effect of elongational viscosity on the film shape was found. The technique was also applied to the development of prediction of prison formation in blow molding. The viscous non-Newtonian flow analysis was applied to the three-dimensional flow analysis and the evoluation of mixing performance in the twin screw extruder.

Finite Element Error Analysis Approach for Three-Dimensional Incompressible Viscous Fluid Flow Analysis

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the analyses of convection-diffusion problems and two-dimensional viscous fluid flow problems. In this modified Galerkin method, the inertia term is considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, we proposed a new finite element formulation for three-dimensional incompressible viscous fluid flow analysis. This formulation (‘MS’ algorithm and ‘MSR’ algorithm) is based on the modified Galerkin method coupled with the Semi-Implicit Method for Pressure-Linked Equations. The cubic cavity flow problems were investigated for the Reynolds number of 400, 1,000, 2,000 and 3,200 using non-uniform meshes. Finally, we confirmed the effectiveness of our proposed method through the comparison with other research works.