Demonstration of balance-based space averaging and modelling in view of blading—diffuser interaction

Abstract

Abstract

Advanced experimental and numerical methods in the field of fluid dynamics and turbomachinery are increasingly successful in describing real flowfields, i.e. fields that are generally three-dimensional and unsteady. For many purposes, e.g. flow characterization, it is necessary to reduce these flowfields step by step to three-, two- or one-dimensional large-scale unsteady flowfields. This procedure permits a lower-level simulation of the flowfields. However, many averaging approaches are arbitrary or succeed in balancing the flowfields in only a few physical aspects. The first author has already shown the steps of a balance-based procedure that avoids this limitation. Small-scale time averaging of (probabilistically) turbulent inhomogeneities by means of irreversible and reversible small-scale time averaging processes on a threefold infinitesimal control volume element has already been demonstrated. The present paper demonstrates the balance-based procedure of space averaging. It is carried out by averaging generally three-dimensional small-scale time-averaged (deterministic) inhomogeneities using irreversible and reversible space averaging processes on onefold infinitesimal and finite control surfaces. The procedure is, similarly to small-scale time averaging, based on conservative and independent non-conservative small-scale time-averaged integral balance equations. The general concept is to represent all the relevant fluxes through the control surface by appropriate average quantities or numbers. The full use of the vector equations for the linear and angular momentum is important. One of the consequences in space averaging is the introduction of a wrench (parallel linear and angular momentum vectors), which is generally used only in mechanics for the reduction of force systems in space. The flowfield inhomogeneity is described on all dimensional levels via the diffusion intensity of the irreversible averaging process, and, only for space averaging, via the distance vector and the parameter of the wrench. A numerical example on different dimensional levels is presented in detail. The procedure also illustrates the basis of a new and more complete two-and one-dimensional large-scale unsteady theory generally in fluid dynamics and especially in turbomachinery.