Streamwise Computation of Three-Dimensional Flows Using Two Stream Functions

1993 ◽  
Vol 115 (2) ◽  
pp. 233-238 ◽  
Author(s):  
M. S. Greywall
Keyword(s):  
Boundary Conditions ◽  
Stream Function ◽  
Potential Flow ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Spatial Coordinate ◽  
Independent Variables ◽  
Dependent Variables ◽  
Stream Functions ◽  
Flow Through

An approach to compute three-dimensional flows using two stream functions is presented. The independent variables used are χ, a spatial coordinate, and ξ and η, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since the value of a stream function is constant along the solid boundaries, this choice of variables makes it easy to satisfy the boundary conditions. To illustrate the approach, computations of incompressible potential flow through a circular-to-rectangular transition duct are also presented.

A Three-Dimensional Numerical Method for Turbomachinery Blading

1992 ◽  
Author(s):  
C. W. Gu ◽  
J. Z. Xu ◽  
J. Y. Du
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Stream Function ◽  
Three Dimensional ◽  
Computational Results ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Stream Functions ◽  
Derivatives Of ◽  
Convergent Solution

By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.

Three Dimensional Thermoacoustic Oscillation in a Premix Combustor

2001 ◽  
Author(s):  
S. Akamatsu ◽  
A. P. Dowling
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Linear Equations ◽  
Three Dimensional ◽  
Total System ◽  
Mean Flow ◽  
Modal Coupling ◽  
Rate Of Heat Release ◽  
Flow Through ◽  
Combustion Processes

A theory is developed to describe high frequency three-dimensional thermoacoustic waves in a simplified geometry representing a typical premix combustor. The theory considers linear modes of frequency ω and circumferential mode number m i.e. proportional to eiωt+imθ. The radial and axial dependence is determined for a cylindrical combustor. Simple geometries are investigated systematically to analyze the effect of different inlet boundary conditions to the combustion chamber on the frequency of oscillation and on the susceptibility to instability, both near and away from the cut-off frequencies. The model includes a one-dimensional mean flow, radial mode coupling and idealized combustion processes, which are added in stages to build up an understanding of the complicated acoustics of the premix combustor geometry. It is demonstrated that the flow through the premix ducts provides a frequency-dependent boundary condition at combustor inlet and causes modal coupling. Generalized linear equations of conservation of mass, momentum and energy, together with boundary conditions, are solved to identify the eigenfrequencies, ω, of the total system. Then Real ω determines the frequency of the oscillation, while Imaginary ω indicates the growth rate of the disturbance. It is found that strong resonant peaks in the pressure waves exist close to the cut-off condition for acoustic waves and that the relationship between the unsteady rate of heat release and the flow significantly influences the instability of oscillation.

Modeling Thermal Microspreading Resistance in Via Arrays

2016 ◽  
Vol 138 (1) ◽  
Author(s):  
Michael Fish ◽  
Patrick McCluskey ◽  
Avram Bar-Cohen
Keyword(s):  
Boundary Conditions ◽  
Effective Properties ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Simulation Software ◽  
Electronic Packages ◽  
Isothermal Boundary ◽  
Unit Cells ◽  
Flow Through ◽  
Management Techniques

As thermal management techniques for three-dimensional (3D) chip stacks and other high-power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To reduce the computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudohomogeneous medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties are found to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “microspreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal microspreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of microspreading resistance and mitigate its contribution to the overall thermal behavior of such substrate–via systems. Finite element modeling (FEM) of TXV unit cells is performed using commercial simulation software (ansys).

Two and Three-Dimensional Flow using Finite Elements

1969 ◽  
Vol 73 (707) ◽  
pp. 961-964 ◽  
Author(s):  
J. H. Argyris ◽  
G. Mareczek ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Boundary Conditions ◽  
Stream Function ◽  
Three Dimensional ◽  
Finite Domain ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Triangular Elements ◽  
Compressibility Effects

The method of finite elements is in certain cases advantageous when dealing with flow problems in a finite domain. This is particularly so when attempting to include subcritical compressibility effects. In the present note we first consider the two-dimensional flow using TRIC and TRIM-like triangular elements in conjunction with the concept of the stream function, which is assigned to the nodal points of the elements. The application of the stream function allows a direct and exact satisfaction of the boundary conditions. Strictly the elements in question could also be used in conjunction with the potential function but the observance of the boundary conditions is then cumbersome.

scholarly journals A high-precision algorithm for axisymmetric flow

1995 ◽  
Vol 1 (1) ◽  
pp. 11-25
Author(s):  
A. Gokhman ◽  
D. Gokhman
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Stream Function ◽  
Potential Flow ◽  
Axisymmetric Flow ◽  
Curvilinear Coordinates ◽  
Shape Functions ◽  
Quadrilateral Elements ◽  
Orthogonal Curvilinear Coordinates ◽  
Double Integrals

We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.

Hydraulic Performance of a Mixed-Flow Pump: Unsteady Inviscid Computations and Loss Models

2001 ◽  
Vol 123 (2) ◽  
pp. 256-264 ◽  
Author(s):  
B. P. M. van Esch ◽  
N. P. Kruyt
Keyword(s):  
Potential Flow ◽  
Flow Model ◽  
Three Dimensional ◽  
Hydraulic Performance ◽  
Mixed Flow ◽  
Global Performance ◽  
Flow Through ◽  
Loss Models ◽  
Potential Flow Model ◽  
Flow Pump

The hydraulic performance of an industrial mixed-flow pump is analyzed using a three-dimensional potential flow model to compute the unsteady flow through the entire pump configuration. Subsequently, several additional models that use the potential flow results are employed to assess the losses. Computed head agrees well with experiments in the range 70 percent–130 percent BEP flow rate. Although the boundary layer displacement in the volute is substantial, its effect on global characteristics is negligible. Computations show that a truly unsteady analysis of the complete impeller and volute is necessary to compute even global performance characteristics; an analysis of an isolated impeller channel and volute with an averaging procedure at the interface is inadequate.

scholarly journals A Simplified Method for 3-D Potential Flow in Turbomachinery Using Vortex Sheet Boundary Conditions

1987 ◽  
Author(s):  
H. Jiang ◽  
R. Cai ◽  
Y. Zhu
Keyword(s):  
Boundary Conditions ◽  
Potential Flow ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
Three Dimensional Flow ◽  
Blade Row ◽  
Simplified Method ◽  
Outlet Flow ◽  
Two Sides

Within the framework of inviscid flow theory, the character of three-dimensional flow in turbomachinery blade row is discussed. One of the important differences between 3-D and 2-D flow in turbomachinery is the discontinuity of velocity at the two sides of trailing edge and across downstream boundary. The inconsistency of the traditional periodicity conditions for downstream boundary and of the axisymmetric assumption for outlet flow with the three-dimensionality of turbomachinery flow is discussed also. For 3-D potential flow, the vortex sheet boundary conditions (VSBC) for downstream boundary and a fully 3-D condition for outlet flow are presented. A simplified method is developed by implementation of VSBC on a fixed vortex boundary in order to predict the fully 3-D flow in blade passage as well as downstream of blade row. In the present investigation two calculations are carried out. In one calculation the traditional boundary conditions are imposed while in another one the VSBC are used to demonstrate the capability of the newly develped boundary conditions. The agreement between some calculated results and the theoretical analysis is very well.

scholarly journals Pulsatile flow in ventricular catheters for hydrocephalus

2017 ◽  
Vol 375 (2096) ◽  
pp. 20160294 ◽  
Author(s):  
Á. Giménez ◽  
M. Galarza ◽  
U. Thomale ◽  
M. U. Schuhmann ◽  
J. Valero ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Computational Study ◽  
Three Dimensional ◽  
Mathematical Methods ◽  
Basic Principles ◽  
Heart Beating ◽  
Ventricular Catheters ◽  
Flow Through ◽  
Three Dimensional Models ◽  
Previous Computational Study

The obstruction of ventricular catheters (VCs) is a major problem in the standard treatment of hydrocephalus, the flow pattern of the cerebrospinal fluid (CSF) being one important factor thereof. As a first approach to this problem, some of the authors studied previously the CSF flow through VCs under time-independent boundary conditions by means of computational fluid dynamics in three-dimensional models. This allowed us to derive a few basic principles which led to designs with improved flow patterns regarding the obstruction problem. However, the flow of the CSF has actually a pulsatile nature because of the heart beating and blood flow. To address this fact, here we extend our previous computational study to models with oscillatory boundary conditions. The new results will be compared with the results for constant flows and discussed. It turns out that the corrections due to the pulsatility of the CSF are quantitatively small, which reinforces our previous findings and conclusions. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

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