Analysis and Development of Compact Models for Mass Flows through Butterfly Throttle Valves

Throttles and wastegates are devices used in modern engines for accurate control of the gas flows. It is beneficial, for the control implementation, to have compact and accurate models that describe the flow behavior. The compressible isentropic restriction is a frequently used model, it is simple and reasonable accurate but it has some issues. One special issue is that it predicts that the choking occurs at too high pressure ratios, for example the isentropic model predicts choking at a pressure ratio of 0.52, while experimental data can have choking at 0.4 or even lower. In this work, experimental data is acquired from throttles tested both in a flow bench and mounted as main throttle on a turbocharged gasoline engine. To analyze the flow behavior several flow characterizations are performed at different throttle openings. For the engine installation a special test procedure is adopted and the results show that the engine and the flow bench give the same characteristic behavior of the throttle. In particular, both installations show choking pressure ratios that are significantly lower than what the compressible isentropic restriction predicts. To remedy this and capture the behavior, different modifications of the isentropic model are investigated. Some promising model modifications are analyzed; one that uses the conservation of momentum, energy, and mass to derive a compact expression for the mass flow, and another that uses an ellipse model. All modifications analyzed give lower pressure ratios at choking.