Introduction to Modeling and Control of Internal Combustion by Professor Dr. Lino Guzzella, Dr. Christopher H. Onder

By Professor Dr. Lino Guzzella, Dr. Christopher H. Onder (auth.)

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By Professor Dr. Lino Guzzella, Dr. Christopher H. Onder (auth.)

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Moreover, no pressure recuperation takes place. The consequences of this are that the pressure in the narrowest point of the valve is (approximately) equal to the downstream pressure and that the temperature of the flow before and after the orifice is (approximately) the same (hence the name, see the schematic flow model shown in Fig. 8). Using the thermodynamic relationships for isentropic expansion [120] the following equation for the flow can be obtained m(t) = Cd' A(t) . Pin(t) VR . ) is defined by 10 11 Friction can be partially accounted for by discharge coefficients that must be experimentally validated.

Simplified Moore-Greitzer compressor/receiver/throttle system. the system shown in Fig. 9). The physical interpretation of these equations is that the compressor has some delays and time lags (inherent dynamics) which limit the rate at which the mass flow iLe(t) can be changed. These delays are modeled using a firstorder lag with a time constant T e . A second time constant, T m , characterizes the usual dynamics of the manifold. 62) reaches a stable equilibrium, the pressure ratio satisfies the condition lIe = lle(iLe), which corresponds to the behavior of the quasi-static compressor model introduced above.

100-- ~--~- ~~~- l 80~ Xvj[%] 60! ::1 _20 1 o IX Measured l=- Spline Approx. --- 50 100 {}j [DC] 150 200 Fig. 22. Example of a fuel evaporation curve. , [84]). 71) The characteristic length in the thermodynamic analogy of an evaporation problem is given by d x where x indicates which specific geometry is relevant (x = D for droplet and x = F for wall film evaporation). The evaporated mass is mEV = Pfvs· DAB· Af . 72) dx The density PfV8 refers to the fuel vapor at the surface of the droplet. It can be approximated as half of the density of the liquid fuel.

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