EXPERIMENTAL INVESTIGATION AND THEORETICAL TREATMENT OF THE ROLE OF TURBULENT STRESSES IN AXIAL FLOW COMPRESSORS

Oussama C. JADAYEL

If the flow behind an axial compressor rotor were to be examined at a point in space, correlations between the directional velocity components would be realized.  This, in effect, is equivalent to the presence of six turbulent stress components.  However, it would not be known whether thèse stresses arose from the random turbulent fluctuations behind each blade, or from the pitch-wise variation of the steady relative blade-to-blade flow. which is periodic.

The first part of this thesis reports on an experiment which was undertaken to determine the separate influence of thèse two factors, namely: random turbulence and periodic unsteadiness.  Whereas the former is responsible the conventional Reynolds stresses, the latter is seen to be at the origin of the Apparent stress tensor.  A system of measurements is described here, in which a non-orthogonal hot-wire probe was used to sample data at different radii down-stream of an isolated axial rotor.  By employing a phase-locking  procedure over two blade pitches, it was possible to build a picture of the absolute flow structure.  The adopted sampling technique permitted the spatial variation of the turbulence levels as well as the individual Reynolds stresses to be calculated from the instantaneous velocities.  The apparent stresses, an objective of the project, were evaluated once the periodic unsteadiness of the mean pitch-wise flow had been established.  The above measurements revealed strong turbulent activity to be taking place along the blade wakes and reaching its highest levels nearer to the annulus walls.  Furthermore, it was realized that the apparent stresses were of appreciable magnitude, comparable to, and sometimes exceeding their Reynolds counter-parts.  The limitations of the method are also discussed.

In the light of thèse findings a theoretical model was proposed.  Herein, turbulence is modelled in terms of an effective eddy viscosity which was related to a particular macroscopic mixing length.  Accordingly, the mechanism of dissipation is fixed and so, any flow irreversibilities could be calculated.  The three-dimensional equations of motion, together with those of continuity and energy, were derived in the relative frame of a turbomachine, allowing entropy and heat transport to take place at a turbulent Prandtl number of unity.  In developing the model, an important conclusion was reached, namely, that in the general case of a compressible, viscous flow, rothalpy did not preserve its value along a streamline.  Thereafter, the model was included in an S2 code and was used to calculate the flow through the experimental rotor.  Results suggested that turbulence is responsible for a good proportion of the losses encountered in an axial compressor.

 The S2 program was also used to check the outcomes of another loss model, termed The Entropy Shock Model. The calculation was developed as a means for estimating the entropy rise as well as the mean flow deflection on the basis that losses exist down-stream of the rotor.  Here, the losses are treated as an overall value which is made up of a skin-friction component and a two-dimensional wake mixing component.  During the analysis any boundary layer calculations were avoided by relating a previously determined static pressure coefficient to the amount of diffusion, and hence blockage, over the blade surfaces.  Losses were then generated through a sudden diffusion process somewhere down-stream of the blade row.  Pressure traverses conducted up- and downstream of the rotor provided the necessary pressure coefficient profiles, and acted as the basis on which the computed loss distributions could be assessed.  It was found, however, that thèse distributions did not agree sufficiently closely with experiments.