Simscape Reference

Constant Volume Chamber (2P)
• ṁA is the mass flow rate into the chamber through port A.
Accompanying a mass flow rate into the chamber is a change in fluid density, associated
with a change in fluid pressure, internal energy, or both. The rate of change of the fluid
mass in the chamber follows from the alternate mass conservation equation
where:
ÈÊ
∂r
ˆ
Á
Ë ∂ ¯
˜ + Ê
Á
∂ r ˆ ˘
Í ṗ Ë ∂ ˜ u̇ ˙ V = ṁ +
ÎÍ
p I
u u I A M .
¯ p ˚˙
•
Ê ∂r
ˆ
Á
Ë ∂p ˜
¯ u is the partial derivative of density with respect to pressure at constant specific
internal energy.
•
Ê ∂r
ˆ
Á ˜
Ë ∂u¯
p
is the partial derivative of density with respect to specific internal energy at
constant pressure.
• V is the chamber volume.
• ∊ M is a correction term.
The density partial derivatives are computed by the finite difference method using the
specific volume lookup tables specified in the Two-Phase Fluid Properties (2P) block. The
block linearly interpolates the computed values to obtain the partial derivatives in the
entire pressure-specific internal energy continuum.
To prevent numerical discontinuities at the phase-transition boundaries, the block
blends the density partial derivatives of the various domains using a cubic polynomial
function. At a vapor quality of 0–0.1, this function blends the partial derivatives of the
subcooled liquid and two-phase mixture domains. At a vapor quality of 0.9–1, it blends
the derivatives of the two-phase mixture and superheated vapor domains.
The smoothing applied to the density partial derivatives introduce numerical errors into
the alternate mass conservation equation. To correct for these errors, the block adds the
correction term
M
=
M - V v I
,
t
1-45