One-dimensional representation of steady@ spatially non-uniform flow. An equivalent mean-value set for compressible flow. Part 1. Implementation for an ideal@ calorically-perfect gas
"INTRODUCTION Despite the fact that some degree of spatial non-uniformity is present in the flow in all real systems@ design and performance analysis methods for ducted-flow systems often involve an explicit or implicit assumption that the flow is uniform. Consequently@ it is often necessary to formulate a set of representative mean properties to describe the flow and to use those in the analysis methods. This Data Item describes a mean-value set based on an equivalent-state@ reference-mean-flow model derived from measured*@ local properties at a cross section of the flow in a duct. The flow considered is a steady@ spatially non-uniform (profiled)@ compressible flow of an ideal@ calorically-perfect gas. It is assumed to be axial and free from significant swirl. Measurement uncertainties on the raw measurements are assumed to be accounted for separately so that the definition starts with a ""corrected"" set of measurements. The model allows for the simultaneous variation of total and static temperatures and pressures and other flow properties across the section in the flow and is applicable to both subsonic and supersonic flow. The Item is one of a group concerned with the definition of a mean-value set for the one-dimensional representation of conditions@ at a cross section of a duct@ of a steady@ profiled flow and their use in the analysis of system performance. Other Items in the group include Reference 2@ for ideal@ thermally-perfect gas flow (using a ""true-cp"" basis)@ Reference 3@ presenting numerical examples of the application@ and Reference 4@ presenting a mean-value set for incompressible flow. The layout of the Item is as follows. ? Section 2 gives the notation used in the Item. ? Section 3 considers the equations for the entropy of the flow and introduces the logarithmic-mean values of properties. ? Section 4 defines the reference-mean flow that forms the basis of the mean-value set. ? Section 5 considers the extensive properties of the reference-mean flow and the profile factors that relate them to corresponding properties of the measured@ profiled flow. ? Section 6 considers the representation of the mass flow. ? Section 7 considers the represnetation of the momentum and absolute stream force of the non-uniform flow. ? Section 8 summarises the derivation of the mean-value set. ? Section 9 presents selected analytical examples illustrating applications of the reference-mean-flow model to ducted flows and continuous-flow@ adiabatic compression and expansion processes. ? Appendix A summarises the equations for the mean-value set. ? Appendix B provides a glossary of terms as they are used in this Data Item. The mean-value set provides a means of characterising a profiled flow at a particular cross section in the flow. In order to assess the performance of a system it will be necessary to make measurements at more than one cross section and derive corresponding mean-value sets at each measurement section. The application of the reference-mean-flow model at the measurement sections in continuous flow systems leads to a correct representation of the entropy at each section and hence to a proper accounting of the reversible and actual work or heat transfer in the processes between the measurement sections. Thus a correct distribution of work and irreversibilities among the components of multi-process systems can be made@ avoiding the attribution of artificial flow-mixing losses to system components upstream or downstream of a measurement section. The reference-flow model@ based on the conservation of entropy and mass flux between the profiled and reference-mean flows@ provides a useful unification of the treatment of continuous@ adiabatic flows as illustrated by the schema in Sketch 1.1. Calorically-perfect gas flows emerge as special cases when cp is kept constant. Isenergic flows emerge as special cases when the total temperature is constant everywhere. Uniform flows are special cases when all properties are uniform across the section (flat profiles). The flow model applies to incompressible flows@ both profiled and uniform@ when the density is made constant. The present mean-value set provides a basis for the assessment and comparison of historical and alternative mean values and mean-value sets. * The term ""measured"" may be extended to include local property values from computational methods (CFD)."