Simple Pump $—$ Pump with constant displacement and losses

The Simple Pump component describes a pump with constant displacement and losses. It also includes external and internal leakage.

Implementation

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

Mechanical efficiency

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

Assumptions

Constant mechanical loss and displacement.

 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 $\mathrm{ICP}$ ICP $\mathrm{Rotor}$ 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

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 ${G}_{P\left(\mathrm{int}\right)}$ ${10}^{-13}$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Conductance of internal leakage GPint $J$ $0.01$ $\mathrm{kg}{m}^{2}$ 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