Flow in a turbocharger turbine is highly unsteady in nature as it responds to the exhaust
manifold of an internal combustion (IC) engine. Despite this it is conventional
to use quasi-steady turbine models in one-dimensional turbocharged engine simulations,
even though they cannot reproduce the known hysteresis of turbine mass flow and performance
characteristics recorded under pulsating flow conditions. Using filling-and-emptying
models improves the situation by permitting mass accumulation in the turbine
volute. Depending on the unsteadiness level, this approach may still be insufficient to
capture true turbine operation since neither method can resolve unsteady effects due to
pressure wave action in the flow. It is unclear when transition occurs between filling-and-
emptying and wave action modes.
To this end, a proprietary computational gas dynamics code in C++ is presented to
simulate the unsteady, compressible flow inherent to IC engine exhaust manifolds. The
Euler equations for one-dimensional inviscid flow are discretized to provide second-order,
conservative, shock-capturing finite difference schemes able to resolve wave propagation
in ducts with area variation, wall friction and heat transfer. A wave action turbine
volute model is constructed using bespoke boundary conditions. Validation against experimental
data shows satisfactory agreement for pulse frequencies up to 40 Hz, and
improved instantaneous swallowing capacity prediction at all tested frequencies compared
to quasi-steady calculations.
Fourier series characterization of on-engine pulse waveforms reveals multiple harmonic
components, causing significant regions of divergence between filling-and-emptying and
wave action predicted hystereses. Comparison of concurrent wave action and filling-and-emptying
simulations applying simpler sinusoidal waveforms allows development of the
unsteadiness measures FSt and FSt(p). An approximate guideline to ensure a filling-and-emptying
mode stipulates FSt [Symbol appears here. To view, please open pdf attachment]0.15 and FSt(p) [Symbol appears here. To view, please open pdf attachment]0.02. Evaluation of FSt and FSt(p)
for an example on-engine case indicates certain wave action already by 1600 rev/min,
borne out by subsequent inspection of the swallowing capacity traces.