Variable Pump With Loss $—$ Pump with table based displacement and mechanical and volumetric losses

The Variable Pump With Loss component describes a pump with variable displacement and losses. Note that this component has external leakage.

Implementation

See the component 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 component allows for table-based mechanical efficiency, set by the table table_eps_m, with w in the first column and mechanicalEfficiency in the second column. Table-based mechanical efficiency can be switched off by clearing the variableMechanicalEfficiency parameter and setting a constant loss with the eps_m_constant parameter.

Volumetric efficiency

This component allows for table-based volumetric efficiency, set by the table table_volumetricEfficency, with n [$\mathrm{rpm}$] in the first column, dp in first row, and volumetricEfficiency in table. Table-based volumetric efficiency can be switched off by clearing the variableVolumetricEfficiency parameter and setting a constant loss with the volumetricEfficiency_constant parameter.

Variable displacement

This component allows for table-based displacement, set by the table table_Dpump, with sweptVolume in the first column and Dpump in the second column. It can be switched off by clearing the variableVolume parameter and setting a constant Dpump with the D_pump_constant parameter. When variableVolume is selected, a conditional connector, sweptVolume, appears which is used as input to the table.

 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 $\mathrm{energyLoss}$ energyLoss $\mathrm{fixedTemperature}$ fixedTemperature $\mathrm{fixed}$ fixed $\mathrm{VarPump}$ VarPump $\mathrm{Rotor}$ Rotor $n$ n ${\mathrm{Δp}}_{1}$ dp1 ${\mathrm{VE}}_{\mathrm{table}}$ volumetricEfficiency_table ${\mathrm{Dpump}}_{\mathrm{table}}$ Dpump_table ${w}_{1}$ w1 ${\mathrm{\epsilon }}_{\mathrm{mech}}$ eps_m_table $\mathrm{const}$ const ${\mathrm{const}}_{1}$ const1 ${\mathrm{const}}_{2}$ const2

[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 swept volume Connector of Real input signal sweptVolume

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 ${G}_{P\left(\mathrm{int}\right)}$ ${10}^{-13}$ $\frac{{m}^{3}}{s\mathrm{Pa}}$ Conductance of internal leakage GPint $J$ $0.01$ $\mathrm{kg}{m}^{2}$ Moment of inertia J $\mathrm{td}$ $0$ Friction coefficient# td table volumetric efficiency [0,0,1; 0,9/10,9/10; 1,9/10,9/10] Table for volumetric efficiency table_volumetricEfficiency ${\mathrm{table}}_{\mathrm{Dpump}}$ [0,1/10000; 1,1/10000] Table for Dpump table_Dpump table eps[m] [0,9/10; 1,9/10] Table for mechanical efficiency, eps_m table_eps_m variable volume $\mathrm{true}$ Include variable displacement, Dpump variableVolume variable volumetric efficiency $\mathrm{true}$ Include variable volumetric efficiency variableVolumetricEfficiency variable mechanical efficiency $\mathrm{true}$ Include variable mechanical efficiency variableMechanicalEfficiency ${\mathrm{D}}_{\mathrm{pump}\left(\mathrm{constant}\right)}$ ${10}^{-4}$ D_pump, if constant value D_pump_constant ${\mathrm{VE}}_{\mathrm{constant}}$ $\frac{9}{10}$ VolumetricEfficiency, if constant value volumetricEfficiency_constant ${\mathrm{\epsilon }}_{\mathrm{mech}\left(\mathrm{const}\right)}$ $\frac{9}{10}$ Mechanical efficiency, if constant value eps_m_constant

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