Energy efficiency in pumps

Experimental study on regaining the tangential velocity energy of axial flow pump

The objective of this paper is to present a fast and reliable CFD model that is able to simulate stationary and transient operations of multistage compressors and turbines. This analysis tool is based on an adapted version of the Euler equations solved by a time-marching, finite-volume method. The Euler equations have been extended by including source terms expressing the blade-flow interactions. These source terms are determined using the velocity triangles and a row-by-row representation of the blading at mid-span. The losses and deviations undergone by the fluid across each blade row are supplied by correlations. The resulting flow solver is a performance prediction tool based only on the machine geometry, offering the possibility of exploring the entire characteristic map of a multistage compressor or turbine. Its efficiency in terms of CPU time makes it possible to couple it to an optimization algorithm or to a gas turbine performance tool. Different test-cases are presented for which the calculated characteristic maps are compared to experimental ones.

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A quasi-one-dimensional CFD model for multistage turbomachines

This paper describes a throughlow analysis tool based on a modern finite-volume approach. The numerical model is obtained by averaging the 3-D Navier-Stokes equations in the blade passage, keeping only the axisymmetric part of the equations. The averaging reduces the spatial dimension of the problem but introduces additional terms, the blade forces, which have to be modeled. In the present viscous throughflow model, the 2-D annulus endwall flow is captured by the resolution of the Navier-Stokes equations coupled to a simple mixing-length turbulence model. This allows to simulate high energy interactions and high losses near the endwalls. However, 3-D features such as tip or corner flows cannot be predicted in axisymmetric computations. In the present contribution, these 3-D effects are modeled using empirical correlations from the literature. They are introduced into the equations, together with the profile losses, by the so-called distributed loss model. Two test-cases, a high subsonic single stage compressor and a low speed three stage compressor, show the potential of the method.

A Throughflow Analysis Tool Based on the Navier-Stokes Equations

This contribution is dedicated to the modeling of the end-wall flows in a throughflow model for turbomachinery applications. The throughflow model is based on the Euler or Navier-Stokes equations solved by a Finite-Volume technique. Two approaches are presented for the end-wall modeling. The first one is based on an inviscid formulation with dedicated 3-D distributions of loss coefficient and deviation in the end-wall regions. The second approach is directly based on a viscous formulation with no-slip boundary condition along the annular end-walls and blade force modification in the region close to the end-walls. The throughflow results are compared to a series of 3-D Navier-Stokes calculations averaged in the circumferential direction. These 3-D calculations were performed on the three rotors of a low pressure axial compressor, for a series of tip clearance values.

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Modeling of 3-D Losses and Deviations in a Throughflow Analysis Tool

A model of the spanwise variation of the three-dimensional flow effects on deviation is proposed for middle-stage rotors and stators. This variation is taken as the difference above or below that predicted by blade element theory at any spanwise location. It was found that the stator variation is strongly affected by the end-wall boundary-layer thickness as well as camber, solidity, and blade channel aspect ratio. Rotor variation was found to depend on end-wall boundary layer thickness and tip clearance normalized by blade span. If these parameters are known or can be calculated, the models provide a reasonable approximation to the spanwise variation of deviation for middle compressor stages operating at low to high subsonic inlet Mach numbers.

Modeling the 3-D Flow Effects on Deviation Angle for Axial Compressor Middle Stages

Three-dimensional spanwise pressure loss and flow angle deviation variations have been deduced from NASA, university, and industrial sources from middle-stage research compressors operating near design point. These variations are taken as the difference above or below that predicted by blade element theory at any spanwise location. It was observed that the magnitude of the three-dimensional loss and deviation in the endwall regions is affected by hub and casing boundary layer thickness, camber, solidity, and blade channel aspect ratio for stators and rotor hubs. Rotor tip variations were found to depend on casing boundary layer thickness and tip clearance. Simple design point loss models derived from these data can aid in the design of axial compressor middle stages.

W. B. Roberts

Papers

Modeling the 3-D Flow Effects on Deviation Angle for Axial Compressor Middle Stages

Design Point Variation of Three-Dimensional Loss and Deviation for Axial Compressor Middle Stages