Ind Hole $—$ Inductance of a small hole

The IndHole component describes the inductance of an oil column in a small, sharp-edged hole and includes the observed increase compared with the theoretical value. The model is valid for sharp-edged holes with:

$0.5⟦\mathrm{mm}⟧$ $<$ $d$ $<$ $1.0⟦\mathrm{mm}⟧$

and

$1<\frac{d}{\ell }$ $<$ $20$

There is a check to determine whether the following condition is met:

$d<\ell$

The geometric volume of the lumped volume at each port is computed from the parameters length and area. Use the modifier(s)

VolumeA(port_A(p(start=1e5,fixed=true)))

and/or

VolumeB(port_A(p(start=1e5,fixed=true)))

to set the initial condition(s) for the pressure of the lumped volume(s) $\left[\mathrm{Pa}\right]$.

Use the modifier

IndHolnV(q(start=1e-6,fixed=true))

to set the initial condition for the flow rate of the inductance [${m}^{3}$ / $s$].

 Equations $\mathrm{\nu }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $\mathrm{\rho }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$

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 ${V}_{A}$ VolumeA ${V}_{B}$ VolumeB $\mathrm{IndHolnV}$ IndHolnV

[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

Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system use volume A $\mathrm{true}$ If true, a volume is present at port_A useVolumeA use volume B $\mathrm{true}$ If true, a volume is present at port_B useVolumeB ${V}_{A}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port A volumeA ${V}_{B}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port B volumeB $\ell$ $0.015$ $m$ Hole length length $d$ $8.5·{10}^{-4}$ $m$ Hole diameter diameter