Var Pump $—$ Pump with variable input displacement and volumetric efficiency

This component describes an ideal pump with constant displacement.

Implementation

The flow rate (q) is given by:

q = Dpump $\cdot$ w $\cdot$ volumetricEfficiency / (2 $\cdot$ $\mathrm{\pi }$)

If the inlet pressure is lower than the atmospheric pressure, the delivered flow rate becomes smaller. Flow from port_A to port_B is considered positive.

Variables used in the above equation

 q Flow rate at the outlet port $\left[\frac{{m}^{3}}{s}\right]$ Dpump Displacement per revolution $\left[{m}^{3}\right]$ w Angular velocity $\left[\frac{\mathrm{rad}}{s}\right]$ volumetricEfficiency Volumetric Efficiency (0-1)

Assumptions

Ideal pump with constant displacement (that is, no losses included).

 Equations $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $n=\frac{30w}{\mathrm{\pi }}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{{\mathrm{\rho }}_{\mathrm{oil}}\left({p}_{A\left(\mathrm{abs}\right)},T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)}$ $q={q}_{\mathrm{ideal}}\mathrm{VE}$ $w={\partial }_{t}\left({\mathrm{\phi }}_{a}\right)$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${\mathrm{\phi }}_{a}={\mathrm{\phi }}_{b}$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${q}_{\mathrm{ideal}}=\frac{1}{2}\frac{{\mathrm{D}}_{\mathrm{pump}}w}{\mathrm{\pi }}$ $-\frac{1}{2}\frac{\mathrm{Δp}{\mathrm{D}}_{\mathrm{pump}}}{\mathrm{\pi }}=\mathrm{flange_a.tau}+\mathrm{flange_b.tau}$ ${m}_{\mathrm{flow}\left(A\right)}+{m}_{\mathrm{flow}\left(B\right)}=0$

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 $n$ $\frac{1}{\mathrm{min}}$ Pump rpm n ${q}_{\mathrm{ideal}}$ Ideal flow q_ideal

[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 $\mathrm{VE}$ volumetricEfficiency ${\mathrm{D}}_{\mathrm{pump}}$ Dpump

Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system