ESDU 03012:2010

INTRODUCTION

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

The use of appropriate mean values is important, 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.

This Data Item complements a group of Items concerned with the
definition of mean values and mean-value sets for the
one-dimensional representation of steady, spatially non-uniform
flows and their use in the analysis of system performance.
References 5 and 7 are concerned primarily with definition of the
reference-mean mean-value-set for compressible
flow^*. If there are no constraints on the choice of mean
values, use of the reference-mean set is recommended . Its
principal advantages over historical approaches to flow averaging
are that it is thermodynamically-consistent, it 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 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 Data Item provides information on the use of, and background
to, a computer program for calculation of mean-value properties at
a section in a duct flow. The methods are applicable to steady,
spatially non-uniform (profiled) compressible flows, assumed to be
essentially axial, i.e. free from significant crossflows
such as radial flow and swirl. The flow property profiles may be
derived from experimental measurements, in which case measurement
uncertainties on the raw measurements are assumed to be accounted
for separately so that the calculation starts with a "corrected"
set of measurements. Alternatively, the flow property profiles may
be derived from computational fluid dynamics analysis methods or
specified as analytical power-law profiles.

Section 2 relates the notation used in output files from the
program to notation used in the text of the Data Items. Some
specific terminology used to describe gas property calculations is
also explained.

Section 3 describes access to the program, which is available as
an executable file.

The input data required by the program are described in Section
4. The program requires input of profile information for static
pressure, total pressure or axial velocity and total temperature or
profile definition by input of power-law parameters. The principal
application is to radial profiles in circular or annular ducts and
profiles across one direction only of rectangular ducts. However, a
more general input option is included that allows for profiles
varying in two dimensions and for other duct shapes.

Output from the program is described in Section 5. The program
calculates local property values across the profile and uses these
to derive sectionally-integrated values and mean values. Although
use of the reference-mean-set is recommended, the program
calculates a wide range of mean-value properties from other
definitions for comparison with the reference-mean set and for
continuity with previously-used methods. The calculated mean values
fall into one of several groups as described below.

• Mean property values that form part of thermodynamically
self-consistent mean-value-sets, notably the reference-mean values
(Appendix A.3).

• Mean-set factors allowing the derivation of
sectionally-integrated extensive properties of the profiled flow
from the mean property values (Appendix A.3). A minimum number of
these factors forms an essential part of any complete
mean-value-set.

• Mean values that are part of groups for which, historically,
only a few basic mean properties have been used, such as
mass-derived mean values. These groups have, where possible, been
extended to cover a full set of mean flow properties. Often the
original derivations were restricted to isenergic (uniform total
temperature) flows of calorically-perfect gases. Again the methods
have been extended to cover the more general case with
total-temperature profiles and for thermally-perfect gases where
this is feasible (Appendix A.4).

• Miscellaneous mean values that are derived from particular
mean-specific extensive properties, such as enthalpy-derived mean
values (Appendix A.5).

• Profile factors relating two different mean-value definitions
of a particular property. These are useful in indicating the
magnitudes of differences between definitions. In this program
these profile factors nearly all use the reference-mean-set values
as the comparison (Appendices A.3, A.4, A.5).

Two worked examples are described in Section 6, for which input
and output files are listed in Appendix D.

Appendix A gives brief descriptions of the mean-value properties
calculated. Appendix B lists the unit sets allowed in the program
and gives conversion factors and other default parameters included
within the program. Appendix C gives a glossary of some terms used
in the Item and related terms that may be encountered in the
literature.

* Reference 9 considers the application of the same methodology
to incompressible flows.