Examination of pressure oscillations arising in the computation of cascade flow using a boundary‐fitted co‐ordinate system

Abstract

SUMMARYThe incompressible flow through a two-dimensional cascade is computed using the SIMPLE algorithm in a boundary-fitted co-ordinate system, With the standard staggered grid arrangement the numerical solution was found to allow localized pressure oscillations to persist adjacent to the periodic boundaries. These oscillations were found to be a consequence of the extended momentum control volumes which are required in this region of the cascade. Such control volumes may be removed by the use of appropriately non-staggered velocity storage locations, which are also desirable in the boundary-fitted system since the Cartesian velocity components are no longer related to the grid line orientations. However, this storage permits the propagation of global pressure oscillations, which were previously suppressed by the staggered grid arrangement. This paper attempts to define a solution procedure which uses non-staggered velocity locations and is able to eliminate the consequent global pressure oscillations. To achieve this aim, two forms of pressure correction scheme were considered. The first implemented the scheme proposed by Vanka et al. but was found to be inadequate in the open part of the cascade, whereas the second employed a modification of the scheme proposed by Rhie and Chow and was found to be successful in all regions of the flow. The results computed using this scheme were compared with the available experiment results.

Computation of Flow Past Complex Geometries Using MAC Algorithm on Body-Fitted Coordinates

“…Consequently, an iterative pressure-velocity correction is carried out similar to that followed in MAC method. The work of Lapworth (1988) which points out the prime difficulty in dealing with highly skewed bodyfitting grids, arising in the form of pressure oscillations is worth mentioning. The problem is very much similar to the checkerboard oscillation problem in computations involving non-staggered grids.…”

“…Mostly staggered grids were employed for computations using body-fitted coordinates having staggered Cartesian as well as physical velocities. Lapworth (1988) identified the trouble associated with conventionally staggered grids in the form of pressure oscillations arising in flow computations involving highly skewed meshes. He reported that for highly skewed meshes such as those used for computing flow past turbine blades, the cells on the computational plane no longer follow the directional sense of the discretized differential terms on staggered physical grids.…”

Computation of the Jet-Wake Flow Structure in a Low Speed Centrifugal Impeller

“…The elliptic nature of the solution is obtained by repeating complete marching sweeps of the flow field until a converged solution is obtained. The present three dimensional elliptic calculation procedure is a direct extension of the two dimensional procedure developed by Lapworth (1988) The geometry of the Ghost impeller and the five measurement stations used by Johnson (1979) are illustrated in Fig. 2a.…”

“…Hence, the present Ghost computations are a natural precursor to a study of Eckardt's impeller in which the effects of compressibility and tip leakage are significant. The present three dimensional flow model has been developed from the two dimensional elliptic model used by Lapworth (1988) to compute cascade flows. The numerical model solves finite volume approximations to the primitive variable flow equations using the SIMPLE algorithm (Patankar and Spalding, 1972) in an arbitrary generalised coordinate system.…”

Computing Flows on General Three-Dimensional Nonsmooth Staggered Grids

“…As a consequence, nonstaggered (or colocated) discretization is much more widespread for the Navier-Stokes equations than staggered discretization and prevails in commercial codes. An incomplete list of publications taking this route is [23,25] (one-sided discretization of div u and grad p); [1,2,9,19,20,29,35,40,45,46,51,52,59,61,62,96] (using the pressure-weighted interpolation method of Rhie and Chow [61]); and [4,10,12,21,34,43,44,50,49,60,63,65,64,72,77,80] (employing artificial compressibility). But for incompressible flows, a price has to be paid for the ease of handling general coordinates that nonstaggered discretization brings.…”