Leakage $—$ Leakage component

This is a model for a leakage component. For further information, see Templates.Leakage.

 Equations $\left\{\begin{array}{cc}\mathrm{m_flow}=\frac{\mathrm{\rho }\mathrm{\pi }r{c}^{3}\left(1+\frac{3{e}^{2}}{2{c}^{2}}\right)\mathrm{Δp}}{6\mathrm{\mu }\mathrm{L_p}}& \mathrm{otherwise}\end{array}\right\$ $0=f\mathrm{switch}+{f}_{A}+{f}_{B}$ $0=-f\mathrm{switch}+{f}_{A\left(\mathrm{support}\right)}+{f}_{B\left(\mathrm{support}\right)}$ $\mathrm{\nu }=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{nu_a}& 0<\mathrm{Δp}\\ \mathrm{nu_b}& \mathrm{otherwise}\end{array}\right\\right)$ $\mathrm{\rho }=\mathrm{noEvent}\left(\left\{\begin{array}{cc}\mathrm{rho_a}& 0<\mathrm{Δp}\\ \mathrm{rho_b}& \mathrm{otherwise}\end{array}\right\\right)$ $\mathrm{T_a}={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $\mathrm{T_b}={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $f=0$ ${m}_{\mathrm{flow}}={m}_{\mathrm{flow}\left(A\right)}$ ${m}_{\mathrm{flow}}={m}_{\mathrm{flow}\left(A\right)}$ $\mathrm{\mu }=\mathrm{ν}\mathrm{ρ}$ ${\mathrm{\nu }}_{a}={\mathrm{\nu }}_{\mathrm{oil}}\left({p}_{\mathrm{abs}}={p}_{a\left(\mathrm{abs}\right)},T=\mathrm{T_a},{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ ${\mathrm{\nu }}_{b}={\mathrm{\nu }}_{\mathrm{oil}}\left({p}_{\mathrm{abs}}={p}_{b\left(\mathrm{abs}\right)},T=\mathrm{T_b},{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ ${p}_{a}={p}_{A}$ ${p}_{a\left(\mathrm{abs}\right)}={p}_{a}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{b}={p}_{B}$ ${p}_{b\left(\mathrm{abs}\right)}={p}_{b}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ $\mathrm{rho_a}={\mathrm{\rho }}_{\mathrm{oil}}\left({p}_{\mathrm{abs}}={p}_{a\left(\mathrm{abs}\right)},T=\mathrm{T_a},{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $\mathrm{rho_b}={\mathrm{\rho }}_{\mathrm{oil}}\left({p}_{\mathrm{abs}}={p}_{b\left(\mathrm{abs}\right)},T=\mathrm{T_b},{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ ${s}_{a\left(\mathrm{rel}\right)}={s}_{A}-{s}_{A\left(\mathrm{support}\right)}$ $\mathrm{Δp}={p}_{a}-{p}_{b}$ ${s}_{\mathrm{ab}\left(\mathrm{rel}\right)}=L$ ${s}_{\mathrm{ab}\left(\mathrm{rel}\right)}=\mathrm{switch}\left({s}_{B}-{s}_{A}\right)$ ${s}_{B\left(\mathrm{support}\right)}=L\mathrm{switch}+{s}_{A\left(\mathrm{support}\right)}$ ${m}_{\mathrm{flow}\left(A\right)}+{m}_{\mathrm{flow}\left(B\right)}=0$

Variables

 Name Value Units Description Modelica ID ${{s}_{\mathrm{rel}}}_{a}$ $m$ Relative position of flangeA wrt supportA s_rel_a ${{s}_{\mathrm{rel}}}_{\mathrm{ab}}$ $m$ Relative position of flangeB wrt flangeA s_rel_ab $f$ $N$ Force acting in positive direction of flangeA f ${T}_{a}$ $K$ Temperature at port A T_a ${T}_{b}$ $K$ Temperature at port B T_b ${p}_{a}$ $\mathrm{Pa}$ Pressure at port A p_a ${p}_{b}$ $\mathrm{Pa}$ Pressure at port B p_b ${{p}_{a}}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure at port A p_a_abs ${{p}_{b}}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure at port B p_b_abs ${\mathrm{\rho }}_{a}$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density at port A rho_a ${\mathrm{\rho }}_{b}$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density at port A rho_b ${\mathrm{\nu }}_{a}$ $\frac{{m}^{2}}{s}$ Viscosity at port A nu_a ${\mathrm{\nu }}_{b}$ $\frac{{m}^{2}}{s}$ Viscosity at port B nu_b ${m}_{\mathrm{flow}}$ $\frac{\mathrm{kg}}{s}$ Leakage mass flow m_flow $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop dp ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat

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

Connections

 Name Description Modelica ID $\mathrm{supportA}$ supportA $\mathrm{supportB}$ supportB $\mathrm{flangeA}$ flangeA $\mathrm{flangeB}$ flangeB $\mathrm{oil}$ Fluid property model oil $\mathrm{portA}$ portA $\mathrm{portB}$ portB

Parameters

General Parameters

 Name Default Units Description Modelica ID $\mathrm{reverse}$ $\mathrm{false}$ Reverse the sign convention, see documentation for details reverse $\mathrm{switch}$ $\left\{\begin{array}{cc}-1& \mathrm{reverse}=\mathrm{true}\\ 1& \mathrm{otherwise}\end{array}\right\$ -1 if reverse, else 1 switch $r$ $m$ Radius of cylinder bore r $c$ $m$ Radial clearance (0

Constant Parameters

 Name Default Units Description Modelica ID $L$ $0$ $m$ Element length L