# Development and Validation of a Mathematical Model for Surge in Radial Compressors: (Alternative Format Thesis)

• Kate Powers

Student thesis: Doctoral ThesisPhD

### Abstract

Radial compressors are found in many systems including automotive engines, air-conditioning systems, and aircraft axillary power units. The work in this thesis focuses on the application of automotive turbochargers but the methodology is applicable for all uses.

Turbocharger compressors increase the power output of an engine. They are limited at low flow rates by compressor surge. Surge is characterised by low frequency oscillations in mass flow and pressure, and is often damaging to the compressor.

There have been many attempts to model and predict the point of surge onset, usually via map-based models. Many of these rely on calibration to experimental or CFD data. This has two main disadvantages: (i) the model requires calibrating each time a change in the compressor geometry occurs, and (ii) there is no way to gain insight into the physical causes of surge.

The work in this thesis aims to address these problems by developing a new model for surge starting from the fundamental equations of fluid motion, and only including a minimal number of fitted parameters. All models are developed using mathematical averaging techniques and validated by conducting experiments of a compressor operating in stable, surge and reverse flow regimes.

The resulting surge model has been able to capture both mild surge, where oscillations occur without any full flow reversal, and deep surge, where flow is observed travelling in the reverse direction through the compressor. This is the first time any model has been able to capture and explain the existence of both types of surge.

During model development, it was discovered that incidence losses at the impeller inlet and diffuser recirculation were the main factors that determine the location of surge onset. Also, explanations were found for observed phenomena like the quiet period that is sometimes observed during surge.

Finally, stability analysis was performed on the reduced order surge model, and the existence of both supercritical and subcritical Hopf bifurcations were discovered. This analysis reinforced and explained the behaviour of the model simulations.
Date of Award 16 Jun 2021 English University of Bath Paul Milewski (Supervisor), Chris Brace (Supervisor), Chris Budd (Supervisor) & Colin Copeland (Supervisor)

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