Page 740 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Exterior noise: Assessment and control C HAPTER 22.1

drawn back into the cylinder) particularly at low engine where T is the temperature, s is specific entropy, h is
speeds and this is important for stable idle. Combustion specific enthalpy and v is specific volume. This can be
instability manifests itself as a cylinder-to-cylinder re-written as
variation in IMEP. Low valve overlap is beneficial for
low-speed torque. Twenty degree overlap is a typical T ds ¼ dh 1 dp (22.1.22)
compromise for producting gasoline engines. dx dx r dx
Substituting equation (22.1.22) into equation (22.1.19)
22.1.3.10.3 On the flow through the intake valve gives
Knowledge of the gas dynamics at the intake valve is
2
vu v u
useful to the refinement engineer. A non-conservative vt þ vx 2 ¼ Tds dh (22.1.23)
form of the conservation of momentum equation for
a fluid in three dimensions is (Hirsch, 1988)
Now the total (or stagnation) enthalpy H is given as
du u 2

r ¼ VpI þ V,s þ rf e (22.1.17) H ¼ h þ (22.1.24)
dt 2
where and substituting the differential of equation (22.1.24)
into equation (22.1.23)
vp vp vp
grad p ¼ Vp ¼ i þ j þ k
vx vy vz vu ¼ Tds dH (22.1.25)
vt
i; j; k are unit vectors
Now for the assumption of homentropic flow, equation
I is the unit tensor
(22.1.25) reduces to:
s is the viscous shear stress tensor
f e is the external force vector vu
p is pressure vt þ dH ¼ 0 (22.1.26)
r is density
u is the velocity vector Now along a streamline the stagnation enthalpy is con-
The total inertial term on the left-hand side of equa- stant, so
tion (22.1.17) can be re-written as the sum of linear, vu
kinetic and rotational forces: þ H ¼ H 0 ¼ constant (22.1.27)
vt

du vu u 2 A scalar potential function f can be declared so that
r ¼ r þ V u x (22.1.18)
dt vt 2
u ¼ Vf (22.1.28)
where x is known as the vorticity vector. vf
Simplifying the analysis to consider only one di- u ¼ vx in a 1-D model (22.1.29)
mension x, and neglecting viscosity effects, external
forces and vorticity, equation (22.1.17) reduces to the and thereby create what is known as a potential flow
familiar non-linear inviscid Euler equation (see Appendix model given by:
21.1G for a derivation):
vf
þ H ¼ H 0 ¼ constant (22.1.30)
vt
vu v u 2 1 vp
þ ¼ (22.1.19) 1
vt vx 2 r vx For an ideal gas, where a is the speed of sound (m s )
and g is the ratio of specific heats c p /c v
From the second law of thermodynamics (for instance 2
Zemansky and Dittman (1997)): h ¼ a (22.1.31)
g 1
Tds ¼ dh vdp (22.1.20)
and so using equation (22.1.24), equation (22.1.30) can
or be written for flow along a streamline (or a Fanno line) as:

ds dh dp vf a 2 u 2 a 2 0
T ¼ v (22.1.21) þ þ ¼ (22.1.32)
dx dx dx vt g 1 2 g 1

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