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.

[1]  B. R. Baliga,et al.  A CONTROL VOLUME FINITE-ELEMENT METHOD FOR TWO-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER , 1983 .

[2]  R. J. Schnipke,et al.  A monotone streamline upwind finite element method for convection-dominated flows , 1985 .

[3]  Gerry E. Schneider,et al.  NUMERICAL SOLUTION OF PROBLEMS IN INCOMPRESSIBLE FLUID FLOW: TREATMENT OF THE VELOCITY-PRESSURE COUPLING , 1979 .

[4]  M. Cross,et al.  A critical evaluation of seven discretization schemes for convection–diffusion equations , 1985 .

[5]  The significance of chequerboarding in a Galerkin finite element solution of the Navier‐Stokes equations , 1981 .

[6]  Paul E. Allaire.  Basics of the Finite Element Method: Solid Mechanics, Heat Transfer, and Fluid Mechanics , 1985 .

[7]  J. G. Rice,et al.  Flow visualization in a laboratory vaned diffuser , 1987 .

[8]  Michael A. Leschziner,et al.  Discretization of nonlinear convection processes: A broad-range comparison of four schemes , 1985 .

[9]  R. D. Jackson,et al.  Heat Transfer 1 , 1965 .

[10]  Robert L. Lee,et al.  The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2 , 1981 .

[11]  D. Kershaw.  The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations , 1978 .

[12]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[13]  M. Yovanovich,et al.  Finite-element solution procedures for solving the incompressible, Navier-Stokes equations using equal order variable interpolation , 1978 .

[14]  A. G. Hutton,et al.  THE NUMERICAL TREATMENT OF ADVECTION: A PERFORMANCE COMPARISON OF CURRENT METHODS , 1982 .