|M.Sc Student||Berlowitz Ella|
|Subject||On the Effect of the Mach Number and Altitude on the|
Performance of Small Centrifugal Compressor
|Department||Department of Aerospace Engineering||Supervisors||Professor Emeritus Yeshayahou Levy|
|Dr. Savely Khosid|
|Full Thesis text - in Hebrew|
The performance of turbomachinery systems (i.e. turbine and compressor systems) is influenced by many parameters, including the Reynolds number. The Reynolds number is a dimensionless parameter expressing the ratio between inertial forces and viscous forces. The Reynolds number also quantifies the relative importance of these two types of forces for given flow conditions.
Turbomachinery systems operating at high altitude suffer from reduced efficiency of components, especially compressors. Efficiency of turbomachinery (η) is a measure of the loss of energy of the fluid flowing through the passages of the rotating part, due to viscous effects. This is governed by the flow Reynolds number (Re), and increases with reducing Re as described in the well known Moody's diagram.
For a compressor operating at high altitude and, hence, at low ambient pressure, the Reynolds number decreases due to low air density. As a result, boundary-layer thickness in the compressor passages increases, thereby decreasing the effective flow areas throughout the compressor and causing degradation in its performance. This phenomenon is known as the "Reynolds effect" in turbomachinery.
A review of the literature reveals a commonly used relation between compressor efficiency (η) and Reynolds number (Re):
where ηreƒ and Reref are the values at the reference (design) point, and the exponent n ranges between 0.1÷0.2. This relation indicates that for small compressors having low design point efficiencies the influence of "Reynolds effect" becomes significant.
The present research describes the effect of Reynolds number on the performance of a small centrifugal compressor. The investigated compressor is incorporated in a small gas turbine and its main characteristics are: pressure ratio 4.22, impeller exit diameter is less than 90 [mm], and efficiency of 70% at the design point. The research is based on a series of experiments performed in an Altitude Test Facility (ATF) at different altitudes (up to 30kft) and Mach numbers (up to 0.8).
The ATF is a complex facility with multiple control systems (for control of pressures, temperatures, air flows etc.) with their own dynamics. Therefore maintaining stable parameters in the test chamber adjusted to the ambient conditions at high altitude becomes a challenge. Accompanied by the compressor dynamics, this leads to scattering of measurement results around the steady-state values. Hence, the first stage of the study was to process the experimental measurements and to identify the representative points. This was done using an algorithm based on the dynamics of the measured system that allows excluding unsteady measurements. A statistically representative group of steady-state points with small deviation has been obtained, as an output.
The second stage was to calculate the compressor pressure ratio, temperature rise, mass flow, adiabatic efficiency, and Reynolds number from the steady-state representative points of the experiments. The compressor Reynolds number was computed by the inlet total density, impeller exit tip speed, impeller exit tip diameter and the inlet dynamic viscosity.
The third stage was to examine the effect of simulated flight conditions, i.e. altitude and Mach number, on the operating line of the compressor. The performance of a compressor can be presented by curves of pressure ratio and efficiency plotted against mass flow for various values of rotational speed. These characteristics are dependent on the pressure and temperature at the compressor inlet. Therefore it is common practice to use corrected values of mass flow, rotational speed, pressures and temperatures in order to present the compressor operating lines obtained for different flight conditions on the same figure.
The operating lines were drawn on the performance map of the compressor (pressure ratio vs. corrected mass flow) and on the efficiency map of the compressor (adiabatic efficiency vs. corrected mass flow). A comparison between operating lines under different ambient conditions shows an effect of Reynolds number on pressure ratio, corrected temperature rise and adiabatic efficiency of the compressor. Furthermore, it was shown that in order to compensate the total pressure loss due to lower Reynolds number, the work invested to rotate the compressor increased and is expressed as higher corrected total temperature rise.
A graph of Reynolds number versus the loss in efficiency was depicted on a logarithmic scale. Most of the results were concentrated between two curves of the power coefficient n=0.1÷0.2 which are common values in the literature, showing good agreement with the exponential correlation stated above. The results indicate that the performance of the tested compressor decreased (by 2-4%) corresponding to the decrease in Reynolds number (by 26-46%), as predicted.
Experiments reported in the literature tested the compressor as a standalone unit typically attached to a driver in a compressor test rig. The present research investigated the compressor while being part of a gas turbine, fully simulating flight conditions. Therefore the outcome of this study may be implemented and may contribute to a better understanding of gas turbine performance analysis.
One of the most important performance parameters indicating gas turbine efficiency is specific fuel consumption (SFC). Great efforts are invested in the design stage of gas turbines in order to achieve the desired SFC. A decrease in compressor performance at high altitudes has significant influence on the performance of gas turbine systems. It has been demonstrated that a decrease of 1% in compressor efficiency will cause an approximate increase of 1.3% in SFC for the tested gas turbine. Clearly, such an effect cannot be ignored in mission analysis.
The results of this study may be summarized as follows:
Small centrifugal compressor performance was investigated based on experiments performed in an Altitude Test Facility allowing fully simulated flight conditions. An algorithm based on the dynamics of the measured system was used to exclude unsteady measurements. The compressor operating lines were drawn on top of the compressor maps using the representative steady state measurements. It has been demonstrated that the performance of the compressor decreases (2-4%) with the decrease in Reynolds number (26-46%). This is significant result since a 1% decrease in compressor efficiency will cause ~1.3% increase in the SFC of the gas turbine. These results are in good agreement with the commonly used exponential correlation between Reynolds number and loss in efficiency. The outcome of this study may be implemented in the prediction analyses of gas turbine performance.