Metering Ori No States $—$ Metering orifice with variable area and laminar/turbulent flow without cavitation

The Metering Ori No States component describes the laminar/turbulent flow through an orifice if no cavitation occurs.

Pressure drop/flow rate

The pressure drop across the orifice may be described in two different ways:

 1 By means of the loss coefficient $K$:

$\mathrm{Δp}=\frac{1}{2}\frac{K\mathrm{\rho }{q}^{2}}{{A}^{2}}$

where $K$ is given by:

$K=\frac{{k}_{1}}{\Re }+{k}_{2}$

 2 By means of the discharge coefficient ${c}_{d}$:

$Q={c}_{d}A\sqrt{\frac{2\mathrm{Δp}}{\mathrm{\rho }}}$

where ${c}_{d}$ is given by

${c}_{d}={C}_{d}\mathrm{tanh}\left(\frac{2\mathrm{\lambda }}{{\mathrm{\lambda }}_{c}}\right)$

$\mathrm{\lambda }=\frac{\mathrm{D}\sqrt{\frac{2\mathrm{Δp}}{\mathrm{\rho }}}}{\mathrm{\nu }}$

Note that when

${k}_{2}=\frac{1}{{C}_{d}^{2}}$

and

${k}_{1}=\frac{1}{2}\frac{{\mathrm{\lambda }}_{c}}{{C}_{d}}$

both descriptions are equivalent at high and low Reynolds numbers (Re).

Orifice dimension

The dimension of the orifice is given by the input signal (u) at the connector. The dimension of the input signal may be

 1 An area
 2 A diameter
 3 A relative area, the maximal area being defined by a nominal point (${p}_{\mathrm{nom}}$, ${q}_{\mathrm{nom}}$, ${\mathrm{\rho }}_{\mathrm{nom}}$) at turbulent conditions
 4 A relative diameter, the maximal diameter being defined by a nominal point (${p}_{\mathrm{nom}}$, ${q}_{\mathrm{nom}}$, ${\mathrm{\rho }}_{\mathrm{nom}}$) at turbulent conditions

${\mathrm{Δp}}_{\mathrm{nom}}=\frac{1}{2}\frac{{k}_{2}{\mathrm{\rho }}_{\mathrm{nom}}{q}_{\mathrm{nom}}^{2}}{{A}_{\mathrm{eq}}^{2}}$

Variables used in the above equations

 $\mathrm{Δp}$ pressure drop across orifice $\left[\mathrm{Pa}\right]$ $K$ loss coefficient $\mathrm{\rho }$ mass density, from FluidProp $\left[\frac{\mathrm{kg}}{{m}^{3}}\right]$ $q$ flow rate $\left[\frac{{m}^{3}}{s}\right]$ $A$ area of the orifice $\left[{m}^{2}\right]$; $A=\frac{1}{4}\mathrm{\pi }{\mathrm{diameter}}^{2}$; $\mathrm{diameter}$ is input at the signal connector $\left[m\right]$ $\mathrm{k1}$ parameter of the orifice, describes laminar flow $\mathrm{k2}$ parameter of the orifice, describes turbulent flow k2 = $\frac{1}{{C}_{d}^{2}}$ $\Re$ Reynolds number

The mass and flow forces are not included.

Related Components

 Name Description Resistance with laminar flow. Resistance with laminar flow and externally commanded conductance. The component, based on the loss coefficient K, describes both flow regimes: laminar for very small Reynolds numbers and turbulent for higher Reynolds numbers (default model). The component describes both flow regimes, using an interpolation polynomial. Orifice component checking for cavitation. Simple textbook component, using a constant discharge coefficient. It is valid for turbulent flow only; severe numerical problems for laminar flow. Two orifices in series, one with variable the other with fixed flow area. Differences between basic models are shown by a figure.

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Layout of port where oil flows into an element ($0<{m}_{\mathrm{flow}}$, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_A ${\mathrm{port}}_{B}$ Hydraulic port where oil leaves the component (${m}_{\mathrm{flow}}<0$, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_B $\mathrm{oil}$ oil $u$ Command u

Parameters

General Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system $\mathrm{orif}$ [1] Orifice dimension orif $\mathrm{Transition}$ $1$ Transition model Transition ${k}_{1}$ $10$ Laminar part k1 ${k}_{2}$ $2$ ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2 ${C}_{d}$ $\frac{1}{\sqrt{{k}_{2}}}$ Max discharge coefficient C_d ${\mathrm{\lambda }}_{c}$ $\frac{2{k}_{1}}{\sqrt{{k}_{2}}}$ Critical flow number lambdac ${p}_{\mathrm{nom}}$ ${10}^{6}$ $\mathrm{Pa}$ Nominal pressure drop pnom ${q}_{\mathrm{nom}}$ $1.89·{10}^{-5}$ $\frac{{m}^{3}}{s}$ Nominal volume flow rate qnom ${\mathrm{\rho }}_{\mathrm{nom}}$ $865$ $\frac{\mathrm{kg}}{{m}^{3}}$ Nominal density rhonom

[1] $\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.orifinput.D}$

Constant Parameters

 Name Default Units Description Modelica ID $\mathrm{flowcond}$ $1$ Flow condition flowcond reg type $0$ Regularization type regtype reg param $0$ Regularization parameter regparam $\mathrm{cavitation}$ $\mathrm{false}$ Cavitation cavitation $\mathrm{checkvalve}$ $\mathrm{false}$ checkvalve $\ell$ $0$ $m$ Orifice length; $1<\frac{\ell }{d}$ length ${\Re }_{\mathrm{trans}}$ $0$ Transition Reynolds number Re_trans ${p}_{\mathrm{trans}}$ $0$ $\mathrm{Pa}$ Transition pressure p_trans ${p}_{\mathrm{closed}}$ $0$ $\mathrm{Pa}$ Cracking pressure p_closed ${G}_{\mathrm{leak}}$ $0$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Leakage conductance G_Leak ${C}_{d}$ $\mathrm{Cd_eq}$ Cd

Constants

 Name Value Units Description Modelica ID $\mathrm{α\left[k\right]}$ $0.649$ alpha_k