Numerical Flow Calculations

Abstract

Real flows are described by partial differential equations which cannot be solved analytically in the general case. By dividing a complex flow domain into a multitude of small cells, these equations can be solved in an approximate manner by numerical methods. Because of their wide range of application, numerical flow calculations ("computational fluid dynamics" or "CFD" for short) have become a special discipline of fluid dynamics.The information given in this chapter is intended to help the understanding and interpretation of numerical flow calculations of centrifugal pumps. The focus is on viscous methods since these provide the best chance of describing realistically the boundary layers and secondary flows in decelerated flow on curved paths as encountered in radial and semi-axial pumps. This statement is not meant to preclude that simpler methods may be applied meaningfully to make a first design.The following discussion of CFD methods and possibilities focuses also on limits and uncertainties of CFD modeling as well as on quality criteria and issues in CFD applications, Sects. 8.3.2, 8.3.3, 8.8 and 8.10. OverviewBecause of the complex flow phenomena in centrifugal pumps, the design of impellers, diffusers, volutes and inlet casings is frequently based on empirical data for determining the flow deflection in the impeller and estimating performance and losses. The design of flow channels and blades then relies on experience and coefficients which originate from test data, Chaps. 3 and 7. The availability of relatively inexpensive computers with high computing powers has fostered the development of numerical methods which are able to solve the 3-dimensional Navier-Stokesequations in complex components with reasonable effort. Therefore, numerical methods are used also in the pump industry with the object of optimizing the hydraulic components, to increase the reliability of performance prediction and thus to reduce testing costs. Computational fluid dynamics are still in a phase of development.