ESDU Engineer

Mean Values In Ducted Flows

Design and performance analysis methods for ducted flow systems often involve an assumption that the flow properties, such as pressure and temperature, are uniform across a section. In practice, some degree of non-uniformity is present in all real systems and consequently, it is often necessary to formulate a set of representative mean properties to describe the flow and to use in the analysis methods.

The use of appropriate mean values is necessary, for example, in the calculation of component performance when the inlet and outlet profiles are significantly different and in cases where the variation of properties across a profile is large. Mean values are often used to provide a simplified flow description at component interfaces and an appropriate choice is particularly important in ensuring consistency between calculations for separate components of a system, such as a gas turbine engine, that may be analysed independently by different groups.

It is not possible to define a directly equivalent uniform “mean flow” that represents the profiled flow exactly and any complete mean-value-set must include both mean property values and profile factors to allow recovery of the sectional flow properties. Historically, a variety of approaches have been used, usually based around a desire to represent a particular aspect of the flow such as its total pressure or total temperature and the consequences for other properties have often been overlooked.

Mr D.D. Williams, working with ESDU under the guidance of the Internal Flow Panel and the Compressible Flow Working Party, has developed a new mean value methodology. The method is based on conservation of mass flow rate and entropy flux, with the mean total pressure being derived from a rational extension of the uniform flow concept of a reservoir state. Its principal advantages over historical approaches to flow averaging are that it is thermodynamically-consistent, all mean properties being directly related by the one-dimensional gas dynamics equations without factors.

The method, termed the reference-mean method, retains the correct sectional entropy and therefore allows a true measure of efficiency for processes in which profiles change. It is application-independent, providing a universal definition across component interfaces and it also avoids attributing hypothetical losses to the flow upstream or downstream of the measurement station. It requires no more input information than that required for any mass-flow based method.

The method has been applied in Data Items 95011 (for a constant cp gas) and 97029 (for a variable cp gas) to steady, spatially non-uniform, compressible flows, assumed to be essentially axial. Shortly to be issued is Data Item 03012 to accompany a computer program for calculation of a wide variety of mean-value properties. Further Items under development relate to examples of application of the reference-mean mean-value-set to process performance calculations and application of the methodology to incompressible flows.

An example of the way in which the choice of averaging method can affect performance calculations is shown in the chart, showing the efficiencies of two turbines in series. The calculations are based on data supplied to ESDU by a manufacturer. It can be seen that not only the values of efficiency but also their relative magnitudes depend on the choice of mean values.

Brian Freeman is the Senior Engineer in the Fluid Mechanics Group and he can be contacted at bfre@esdu.com.