Fuel Injection Systems
A description of the processes in injection systems entaills the interdisciplinary application of methods of fluid mechanics, technical mechanics, thermodynamics, electrical engineering and control engineering. Pressures are very high and pilot injection
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Fuel Injection Systems Walter Egler, Rolf Ju¨rgen Giersch, Friedrich Boecking, Ju¨rgen Hammer, Jaroslav Hlousek, Patrick Mattes, Ulrich Projahn, Winfried Urner, and Bj¨orn Janetzky
5.1
Injection Hydraulics
A description of the processes in injection systems entaills the interdisciplinary application of methods of fluid mechanics, technical mechanics, thermodynamics, electrical engineering and control engineering. Pressures are very high and pilot injection to the main injection requires a minimum delivery of 1.5 mm3 of fuel per injection with a metering accuracy of – 0.5 mm3 in flexibly selectable intervals. This imposes substantial demands on the quality of models and numerical methods. Moreover, the processes in the compressible fluid are profoundly transient. Thus, components are endangered by cavitation erosion and can be excited to oscillations with high mechanical loads. Substantially influencing fuel properties and bearing or plunger/liner clearances in pumps, the considerable heating of the fuel by throttling and frictional losses must be quantifiable as well.
5.1.1
Equation of State for Fuels
Knowledge of the fluid properties is the prerequisite for understanding and modeling hydraulic behavior. Density r and specific volume v = 1/r describe the compressibility of fuel and test oil. The literature contains a number of approaches based on systematic measurements in high pressure labs that approximate the densities or specific volumes of fluids as a function of pressure p and temperature T [5-1]. One, the modified Tait equation vð p; TÞ ¼ v0 ðTÞ 1 þ CðTÞln ppþBðTÞ 0 þBðTÞ v0 ðTÞ ¼ a1 þ a2 T þ a3 T 2 þ a4 T 3 BðTÞ ¼ b1 þ b2 =T þ b3 =T 2 CðTÞ ¼ c1 þ c2 T
(5-1Þ
has consistently proven itself for diesel fuels and test oils where p0 is the ambient pressure.
U. Projahn (*) Robert Bosch GmbH, Diesel Systems, Stuttgart, Germany e-mail: [email protected]
Changes of state proceed so rapidly during an injection that they may be considered adiabatic. Compression and expansion processes with insignificant frictional and momentum losses may additionally be regarded as reversible and thus as isentropic. Since a2 ¼ ðdp=drÞs ¼ 1=r2 ðdp=dvÞs
(5-2Þ
applies to the speed of sound a(p, T) at constant entropy s, it characterizes both the rate of linear pressure wave propagation and local isentropic pressure changes. According to [5-2], isentropic changes of state additionally correlate with the change of temperature ðdT=dpÞs ¼ T=ðcp r2 Þðdr=dTÞp ¼ T=cp ðdv=dTÞp
(5-3Þ
The following correlation relates the specific heat capacity cp to the speed of sound at a known density r(p, T) cp ¼ ðdr=dTÞ2p =½ðdr=dpÞT 1=a2 T=r2 ¼ ðdv=dTÞ2p =½ðdr=dpÞT þ ðv=aÞ2 T
(5-4Þ
Thus, the description of state behavior is theoretically completed when the correlations r(p, T) or v(p, T) and a(p, T) or cp(p, T) are established. However, the partial derivatives make the equation extremely susceptible to error. Thus, an inherently consistent, accurate approximation is difficult to obtain by means of empirical equations of
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