Variable Pump $—$ Pump with losses and variable displacement

The Variable Pump component describes a pump with variable displacement and losses.

Implementation

See component Id Var Pump. The delivered flow rate at the outlet port of this model may be different because of flow into volumes and internal and external leakage.

Mechanical efficiency

This model includes a component for constant mechanical loss, set by the parameter mechanicalEfficiencyCoefficient.

 Equations $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{{\mathrm{\rho }}_{\mathrm{oil}}\left({p}_{A\left(\mathrm{abs}\right)},T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)}$ $w={\partial }_{t}\left({\mathrm{\phi }}_{a}\right)$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$

Variables

 Name Value Units Description Modelica ID $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop dp ${p}_{A\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pA_limited ${p}_{B\left(\mathrm{limited}\right)}$ $\mathrm{Pa}$ Limited gauge pressure pB_limited ${p}_{A\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pA_abs ${p}_{B\left(\mathrm{abs}\right)}$ $\mathrm{Pa}$ Absolute pressure pB_abs $q$ $\frac{{m}^{3}}{s}$ Flow rate at connector A q $w$ $\frac{\mathrm{rad}}{s}$ Angular velocity of pump shaft w $T$ $K$ 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 ${P}_{\mathrm{mech}\left(\mathrm{summary}\right)}$ [1] $W$ Mechanical Rotational Power summary_MP ${P}_{\mathrm{hyd}\left(\mathrm{summary}\right)}$ $-\mathrm{Δp}q$ $W$ Hydraulic Power summary_HP ${p}_{\mathrm{sat}}$ [2] $\mathrm{Pa}$ Gas saturation pressure p_sat ${V}_{A}$ VolumeA ${V}_{B}$ VolumeB $\mathrm{Ta}$ Ta ${\mathrm{Ta}}_{1}$ Ta1 $\mathrm{LamnS}$ LamnS $\mathrm{energyLoss}$ energyLoss $\mathrm{fixedTemperature}$ fixedTemperature $\mathrm{fixed}$ fixed $\mathrm{IvP}$ IvP $\mathrm{Rotor}$ Rotor

[1] ${\stackrel{.}{\varphi }}_{a}{\mathrm{\tau }}_{a}+{\stackrel{.}{\varphi }}_{b}{\mathrm{&tau}}_{b}$

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

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Port A, where oil flows into the component ($0, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_A ${\mathrm{port}}_{B}$ Port B, where oil leaves the component ($q<0$, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_B ${\mathrm{flange}}_{a}$ flange_a ${\mathrm{flange}}_{b}$ flange_b $\mathrm{oil}$ oil $\mathrm{commandSignal}$ Input signal commands relative displacement volume commandSignal

Parameters

General Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system external leakage $\mathrm{true}$ If true, a small amount of oil leaks to the tank components externalLeakage 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 ${G}_{\mathrm{ext}}$ ${10}^{-13}$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Conductance of external leakage Gext ${G}_{\mathrm{int}}$ $5.·{10}^{-12}$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Conductance of the internal motor leakage Gint ${\mathrm{D}}_{\mathrm{pump}}$ ${10}^{-4}$ ${m}^{3}$ Displacement per revolution Dpump $J$ $0.01$ $\mathrm{kg}{m}^{2}$ Moment of inertia J $\mathrm{td}$ $0$ Friction coefficient td ${\mathrm{\epsilon }}_{\mathrm{mech}\left(\mathrm{coeff}\right)}$ $1$ Constant for mechanical efficiency mechanicalEfficiencyCoefficient

Oil Parameters

 Name Default Units Description Modelica ID ${V}_{A}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port A volumeA ${V}_{B}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port B volumeB