Sim Ori $—$ Simple orifice model for turbulent flow with volumes at the ports

The Sim Ori component describes the turbulent flow through an orifice if no cavitation occurs using a simple textbook model. The pressure drop is modeled as in Sim Ori No States. Volumes may be added at the ports. 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) [$\mathrm{Pa}$].

Note: This model can cause severe numerical problems for the integration routine if the pressure drop dp becomes very small.

Related Components

 Name Description Resistance with laminar flow and volumes at the ports. Recommended component. 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. Metering Orifice (that is, component Orifice No States with variable diameter). Two orifices in series, one with variable the other with fixed flow area. Differences between basic models are shown by a figure.

 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 $\mathrm{SOr}$ SOr

[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 $d$ $0.001$ $m$ Orifice diameter diameter ${C}_{d}$ $0.707$ Discharge coefficient C_d