Restrictor, Long Orifice

Restrictors are discontinuous geometry changes in gas pipes. The pressure loss is characterized by [60]

$$\frac{p_{t_1}}{p_{t_2}} = \left( 1 + \frac{\kappa -1}{2} M_1^2 \right) ^{\zeta \frac{\kappa}{\kappa-1}}$$ (17)

if $\zeta$ is defined with reference to the first section (e.g. for an enlargement, a bend or an exit) and

$$\frac{p_{t_1}}{p_{t_2}} = \left( 1 + \frac{\kappa -1}{2} M_2^2 \right) ^{\zeta \frac{\kappa}{\kappa-1}}$$ (18)

if $\zeta$ refers to the second section (e.g. for a contraction or an entrance). $p_{t_1}$ and $M_1$ are the total pressure and Mach number in section one, $p_{t_2}$ and $M_2$ are the total pressure and Mach number in section two, $\zeta$ is the loss coefficient and $\kappa$ the ratio of the heat capacity at constant pressure to the heat capacity at constant volume. These formulae apply to all restrictors if they are used for compressible fluids.

Restrictors can be applied to incompressible fluids as well, though, by specifying the parameter LIQUID on the *FLUID SECTION card. In that case the pressure losses amount to

$$\Delta_1^2 F = \zeta \frac{\dot{m}^2}{2 g \rho^2 A_1^2 }$$ (19)

and

$$\Delta_1^2 F = \zeta \frac{\dot{m}^2}{2 g \rho^2 A_2^2 },$$ (20)

respectively.

A long orifice is a substantial reduction of the cross section of the pipe over a significant distance (Figure 84).

Figure 84: Geometry of a long orifice restrictor

There are two types: TYPE=RESTRICTOR LONG ORIFICE IDELCHIK with loss coefficients according to [31] and TYPE=RESTRICTOR LONG ORIFICE LICHTAROWICZ with coefficients taken from [39]. In both cases the long orifice is described by the following constants (to be specified in that order on the line beneath the *FLUID SECTION, TYPE=RESTRICTOR LONG ORIFICE IDELCHIK or TYPE=RESTRICTOR LONG ORIFICE LICHTAROWICZ card):

• reduced cross section $A_1$.
• full cross section $A_2$.
• hydraulic diameter $D_h$ defined by $D_h=4 A/P$ where $P$ is the perimeter of the cross section.
• Length $L$ of the orifice.
• oil mass flow in the restrictor (only if the OIL parameter is used to define the kind of oil in the *FLUID SECTION card)

A restrictor of type long orifice MUST be preceded by a restrictor of type user with $\zeta=0$. This accounts for the reduction of cross section from $A_2$ to $A_1$.

By specifying the parameter LIQUID on the *FLUID SECTION card the loss is calculated for liquids. In the absence of this parameter, compressible losses are calculated.

Example files: restrictor, restrictor-oil.