James G. Rice

The influence of axial diffusion on convective heat and mass transfer in a horizontal CVD reactor

Abstract A recently developed steamline-upwind finite-element technique is applied to convective heat and mass transfer in a horizontal CVD reactor with an inclined susceptor. The results of sample calculations are presented to show that natural convection is suppressed at high velocities, at low pressures, and in microgravity. The uniformity of deposition away from the leading edge is improved by increasing the angle of inclination of the susceptor to the direction of flow; however, the deposition rate is highest at the leading edge. An optimal flowrate for a given angle of inclination is predicted by the calculations that is in agreement with experimental observation. The results show that axial diffusion plays a role under typical operating conditions for chemical vapor deposition and influences the reaction distribution.

Comparison of measured and predicted thermal mixing tests using improved finite difference technique

Abstract The numerical diffusion introduced by the use of upwind formulations in the finite difference solution of the flow and energy equations for thermal mixing problems was examined. The relative importance of numerical diffusion in the flow equations, compared to its effect on the energy equation was demonstrated. The flow field equations were solved using both first order accurate upwind, and second order accurate differencing schemes. The energy equation was treated using the conventional upwind and a mass weighted skew upwind scheme. Results presented for a simple test case showed that, for thermal mixing problems, the numerical diffusion was most significant in the energy equation. The numerical diffusion effect in the flow field equations was much less significant. A comparison of predictions using the skew upwind and the conventional upwind with experimental data from a two dimensional thermal mixing test are presented. The use of the skew upwind scheme showed a significant improvement in the accuracy of the steady state predicted temperatures.

Flow visualization in a laboratory vaned diffuser

Abstract 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.

Examination of a new finite element method applied to convection heat transfer

Abstract A new finite element formulation for two-dimensional viscous flow and convection heat transfer is presented. The current method was designed in particular to be competitive with finite difference methods in terms of storage requirements, solution times, and range of applicability. Novel features of the formulation include the use of a streamline upwind approximation for the advection terms and an equal order velocity and pressure approximation. The current paper focuses on the features of the method which allow the formulation to be competitive with available finite difference methods. The method is illustrated by application to two examples including a natural convection example and a forced convection example.

Finite element analysis of the viscous flow in a vaned radial diffuser

Abstract A new finite element method was used to analyze an experimental model of a radial vaned diffuser. The new method includes a streamline upwind formulation for the advection terms in the governing equations. The streamline upwind significantly reduces numerical diffusion while maintaining the stability of the conventional upwind formulation. The new finite element method also incorporates an iterative equal-order, velocity-pressure solution method based on the well-known SIMPLER algorithm. The results of the analysis are compared to flow visualization studies of the experimental model. The flow separation point for the four blade diffuser was predicted to occur at 19, 6% of the blade length from the leading edge. The experimentally determined value was 23% of the blade length. For the eight blade diffuser model, separation was predicted to occur at 43% of the blade length from the leading edge, as compared to the experimentally observed value of 50% of the blade length. With this performance comparison, the proposed finite element method has been demonstrated to be reliable for predicting complex fluid flows.

Simplex finite element analysis of viscous incompressible flow with penalty function formulation

Abstract Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constrain and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.

Improved convergence of themally coupled problems

Abstract A common problem encountered in the solution of strongly coupled combined flow and heat transfer problems is a very slow rate of convergence or lack of convergence altogether. The implementation of a simultaneous solution technique for the solution of the energy, momentum, and continuity equations in conjunction with additional coupling terms from the gravity source term is described. The results show the striking effectiveness of the additional coupling in the solution of a “standard” coupled problem. The effectiveness of this technique increases both with increased Rayleigh number and increased problem (grid) size. The inclusion of source term coupling into a simultaneous solution is, moreover, a very simple matter with no increase of bandwidth and an unmeasurable increase in computer time required per iteration.

Penalty Function Finite Element Analysis of Steady Viscous Incompressible Flow in Rotating Coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuille flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimental measurements.Copyright