Metering Ori No States Given Area $—$ Metering orifice with a specified area and laminar/turbulent flow without cavitation

The pressure drop is modeled as in the component Metering Ori No States. The orifice dimension is given by the value at the input connector as a diameter in $\left[m\right]$.

 Equations $\left\{\begin{array}{cc}\left\{\mathrm{dpeff}=\mathrm{dpacting},\mathrm{dpeffu}=0,\mathrm{pmax}=0,\mathrm{pmin}=0,\mathrm{pminab}=0,\mathrm{alpha_dmax}=0,\mathrm{delta_pk}=0\right\}& \mathrm{checkvalve}\\ \left\{\begin{array}{cc}\left\{\mathrm{dpeff}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{dpeffu}& 0<\mathrm{Δp}\\ -\mathrm{dpeffu}& \mathrm{otherwise}\end{array}\right\\right),\mathrm{dpeffu}=\mathrm{noEvent}\left(\left|\mathrm{pmax}-\mathrm{pmin}\right|\right),\mathrm{pmax}=\mathrm{max}\left({p}_{A\left(\mathrm{limited}\right)},{p}_{B\left(\mathrm{limited}\right)}\right),\mathrm{pmin}=\left\{\begin{array}{cc}\mathrm{pmax}-\mathrm{delta_pk}& \mathrm{pminab}<\mathrm{pmax}-\mathrm{delta_pk}\\ \mathrm{pminab}& \mathrm{otherwise}\end{array}\right\,\mathrm{pminab}=\mathrm{min}\left({p}_{A\left(\mathrm{limited}\right)},{p}_{B\left(\mathrm{limited}\right)}\right),\mathrm{alpha_dmax}=\frac{827}{1000}-\frac{17\ell }{2000\mathrm{D}},\mathrm{delta_pk}={\mathrm{α\left[k\right]}}^{2}{\left(\frac{\sqrt{\mathrm{max}\left(0,\mathrm{pmax}\right)}}{\mathrm{alpha_dmax}}+\frac{10\mathrm{\nu }\left(1+\frac{9\ell }{4\mathrm{D}}\right)\sqrt{2}}{\mathrm{α\left[k\right]}\sqrt{\frac{1}{\mathrm{\rho }}}\mathrm{D}}\right)}^{2}\right\}& \mathrm{cavitation}\\ \left\{\mathrm{dpeff}=\mathrm{Δp},\mathrm{dpeffu}=0,\mathrm{pmax}=0,\mathrm{pmin}=0,\mathrm{pminab}=0,\mathrm{alpha_dmax}=0,\mathrm{delta_pk}=0\right\}& \mathrm{otherwise}\end{array}\right\& \mathrm{otherwise}\end{array}\right\$ $\left\{\begin{array}{cc}\left\{\left\{\begin{array}{cc}\left\{\mathrm{\lambda }=0,\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff}\left(\mathrm{Δp}=\mathrm{dpeff}-{p}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\nu }=\mathrm{\nu },\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right)\right\}& \mathrm{Transition}=1\\ \left[\mathrm{qunsigned},\mathrm{\lambda }\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}=\mathrm{dpeff}-{p}_{\mathrm{open}},{C}_{d}={C}_{d},{\mathrm{\lambda }}_{c}={\mathrm{\lambda }}_{c},\mathrm{\nu }=\mathrm{\nu },\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right)& \mathrm{otherwise}\end{array}\right\,\left\{\begin{array}{cc}{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}-{p}_{\mathrm{open}}\\ 0& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{checkvalve}\\ {q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}-{p}_{\mathrm{open}}\\ -\mathrm{qunsigned}& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\,\mathrm{q_reg}={q}_{\mathrm{noleak}},{p}_{\mathrm{open}}={p}_{\mathrm{trans}},{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=1\\ \left\{\mathrm{\lambda }=0,\mathrm{q_reg}={q}_{\mathrm{noleak}},\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.laminar}\left(\mathrm{Δp}=\mathrm{dpeff},G=G\right),{p}_{\mathrm{open}}=0,{q}_{\mathrm{noleak}}=\mathrm{qunsigned},{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=2\\ \left\{\mathrm{\lambda }=0,\mathrm{q_reg}={q}_{\mathrm{noleak}},\mathrm{qunsigned}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}=\mathrm{dpeff},{C}_{d}={C}_{d},\mathrm{flownumber}=\mathrm{false},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{orif}=\mathrm{orif}\right),{p}_{\mathrm{open}}=0,{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{qunsigned}& 0\le \mathrm{dpeff}\\ -\mathrm{qunsigned}& \mathrm{otherwise}\end{array}\right\\right),{q}_{\mathrm{open}}=0\right\}& \mathrm{flowcond}=3\\ \left\{\left\{\begin{array}{cc}{q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{smooth}\left(0,\left\{\begin{array}{cc}\mathrm{qunsigned}& {p}_{\mathrm{open}}<\mathrm{dpeff}\\ \mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& 0\le \mathrm{dpeff}-{p}_{\mathrm{closed}}\\ 0& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{checkvalve}\\ {q}_{\mathrm{noleak}}=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{smooth}\left(0,\left\{\begin{array}{cc}\mathrm{qunsigned}& {p}_{\mathrm{open}}<\mathrm{dpeff}\\ \mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& 0\le \mathrm{dpeff}-{p}_{\mathrm{closed}}\\ \mathrm{smooth}\left(0,\left\{\begin{array}{cc}-\mathrm{qunsigned}& \mathrm{dpeff}<-{p}_{\mathrm{open}}\\ -\mathrm{q_reg}& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\\right)& \mathrm{otherwise}\end{array}\right\,\left\{\begin{array}{cc}\left\{\left\{\begin{array}{cc}{q}_{\mathrm{open}}=\frac{\left(\frac{1}{G}+\sqrt{\frac{1}{{G}^{2}}+\frac{2{p}_{\mathrm{closed}}\mathrm{\rho }}{{C}_{d}^{2}{A}^{2}}}\right){C}_{d}^{2}{A}^{2}}{\mathrm{\rho }}& \mathrm{Transition}=2\\ {q}_{\mathrm{open}}=\frac{\left(\frac{1}{G}-\frac{\mathrm{\rho }{k}_{1}\mathrm{\nu }}{2\mathrm{D}A}+\sqrt{{\left(-\frac{1}{G}+\frac{\mathrm{\rho }{k}_{1}\mathrm{\nu }}{2\mathrm{D}A}\right)}^{2}+\frac{2{p}_{\mathrm{closed}}\mathrm{\rho }{k}_{2}}{{A}^{2}}}\right){A}^{2}}{\mathrm{\rho }{k}_{2}}& \mathrm{otherwise}\end{array}\right\,\mathrm{\lambda }=0,{p}_{\mathrm{open}}={p}_{\mathrm{closed}}+\frac{{q}_{\mathrm{open}}}{G}\right\}& \mathrm{regparam}=1\\ \left\{\left\{\begin{array}{cc}{p}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.inv_lossCoeff}\left(q={q}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\rho }=\mathrm{\rho },\mathrm{\nu }=\mathrm{\nu },\mathrm{D}=\mathrm{D}\right)& \mathrm{Transition}=1\\ {p}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.inv_dischargeCoeff}\left(q={q}_{\mathrm{open}},{C}_{d}={C}_{d},\mathrm{\rho }=\mathrm{\rho },\mathrm{D}=\mathrm{D}\right)& \mathrm{otherwise}\end{array}\right\,\mathrm{\lambda }=0,{q}_{\mathrm{open}}=\frac{{\mathrm{Re}}_{\mathrm{trans}}\mathrm{\nu }A}{\mathrm{D}}\right\}& \mathrm{regparam}=2\\ \left\{\left\{\begin{array}{cc}\left\{\mathrm{\lambda }=0,{q}_{\mathrm{open}}=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff}\left(\mathrm{Δp}={p}_{\mathrm{open}},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},{k}_{1}={k}_{1},{k}_{2}={k}_{2},\mathrm{\nu }=\mathrm{\nu },\mathrm{orif}=\mathrm{orif}\right)\right\}& \mathrm{Transition}=1\\ \left[{q}_{\mathrm{open}},\mathrm{\lambda }\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff}\left(\mathrm{Δp}={p}_{\mathrm{open}},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},{C}_{d}={C}_{d},\mathrm{flownumber}=\mathrm{false},\mathrm{orif}=\mathrm{orif}\right)& \mathrm{otherwise}\end{array}\right\,{p}_{\mathrm{open}}={p}_{\mathrm{trans}}\right\}& \mathrm{otherwise}\end{array}\right\,\left[\mathrm{qunsigned},\mathrm{q_reg}\right]=\mathrm{Hydraulics.Restrictions.Basic.PressureDrop.conditionalFlow}\left(\mathrm{Δp}=\mathrm{dpeff},\mathrm{\rho }=\mathrm{\rho },A=A,\mathrm{D}=\mathrm{D},\mathrm{Transition}=\mathrm{Transition},\mathrm{regtype}=\mathrm{regtype},\mathrm{\nu }=\mathrm{\nu },{p}_{\mathrm{closed}}={p}_{\mathrm{closed}},{p}_{\mathrm{open}}={p}_{\mathrm{open}},{q}_{\mathrm{open}}={q}_{\mathrm{open}},{k}_{1}={k}_{1},{k}_{2}={k}_{2},{C}_{d}={C}_{d}\right)\right\}& \mathrm{otherwise}\end{array}\right\$ $\mathrm{\nu }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $\mathrm{\rho }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}$ $q={q}_{\mathrm{noleak}}+{q}_{\mathrm{leak}}$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${m}_{\mathrm{flow}\left(A\right)}+{m}_{\mathrm{flow}\left(B\right)}=0$

Variables

 Name Value Units Description Modelica ID $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop dp $q$ $\frac{{m}^{3}}{s}$ Flow rate flowing into port_A q ${p}_{A\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pA_limited ${p}_{B\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pB_limited $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Upstream density rho $\mathrm{\nu }$ $\frac{{m}^{2}}{s}$ Upstream kinematic viscosity nu ${p}_{A\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pA pA_abs ${p}_{B\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pB pB_abs $T$ $K$ Local temperature T ${p}_{A\left(\mathrm{summary}\right)}$ ${p}_{A}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${p}_{B\left(\mathrm{summary}\right)}$ ${p}_{B}$ $\mathrm{Pa}$ Pressure at port B summary_pB ${\mathrm{Δp}}_{\mathrm{summary}}$ $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop summary_dp ${q}_{\mathrm{summary}}$ $q$ $\frac{{m}^{3}}{s}$ Flow rate flowing into port_A summary_q ${P}_{\mathrm{hyd}\left(\mathrm{summary}\right)}$ $-\mathrm{Δp}q$ $W$ Hydraulic Power summary_HP ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat ${q}_{\mathrm{leak}}$ ${G}_{\mathrm{leak}}\mathrm{Δp}$ $\frac{{m}^{3}}{s}$ Leakage flow q_leak ${q}_{\mathrm{noleak}}$ $\frac{{m}^{3}}{s}$ Flow rate through component q_noleak $\mathrm{dpeff}$ $\mathrm{Pa}$ Effective pressure drop dpeff $A$ ${A}_{\mathrm{commanded}}$ ${m}^{2}$ Orifice area A $\mathrm{D}$ $0$ $m$ Orifice diameter D ${q}_{\mathrm{open}}$ $\frac{{m}^{3}}{s}$ Flow when fully open orifice q_open ${p}_{\mathrm{open}}$ $\mathrm{Pa}$ Pressure when fully open orifice p_open $\mathrm{dpacting}$ $0$ $\mathrm{Pa}$ Acting, i.e. delayed pressure differential dpacting $G$ $0$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Hydraulic conductance $G=\frac{\mathrm{∂q}}{\mathrm{∂p}}$ G $\mathrm{\lambda }$ Flow coefficient lambda

[1] $\mathrm{oil.gasSaturationPressure}\left(T=T,{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$

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 ${A}_{\mathrm{commanded}}$ Commanded Area commandedArea

Parameters

General Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system $\mathrm{Transition}$ $1$ 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

Constant Parameters

 Name Default Units Description Modelica ID $\mathrm{orif}$ $2$ Orifice dimension orif $\mathrm{flowcond}$ $1$ 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

Constants

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