Channel $—$ Basic model for channel geometry

The Channel component calculates the pressure loss for flow through different geometries. The component takes into consideration surface roughness.

 Equations $\mathrm{\nu }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\nu }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $\mathrm{\rho }=\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $q=\frac{{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}$ $\mathrm{Δp}={p}_{A\left(\mathrm{limited}\right)}-{p}_{B\left(\mathrm{limited}\right)}$ ${m}_{\mathrm{flow}\left(A\right)}=\mathrm{Modelica.Fluid.Dissipation.PressureLoss.Channel.dp_internalFlowOverall_MFLOW}\left(\mathrm{IN_con}=\mathrm{IN_con},\mathrm{IN_var}=\mathrm{IN_var},\mathrm{Δp}=\mathrm{Δp}\right)$ ${p}_{A\left(\mathrm{abs}\right)}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{A\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{A},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${p}_{B\left(\mathrm{abs}\right)}={p}_{B}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${p}_{B\left(\mathrm{limited}\right)}=\mathrm{max}\left({p}_{B},{p}_{\mathrm{vapour}\left(\mathrm{oil}\right)}-{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}\right)$ ${m}_{\mathrm{flow}\left(A\right)}+{m}_{\mathrm{flow}\left(B\right)}=0$

Variables

 Name Value Units Description Modelica ID $\mathrm{Δp}$ $\mathrm{Pa}$ Pressure drop dp $q$ $\frac{{m}^{3}}{s}$ 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 $\mathrm{\eta }$ [2] $\mathrm{Pa}s$ Upstream dynamic viscosity eta

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

[2] $\mathrm{Modelica.Media.Air.MoistAir.Utilities.spliceFunction}\left(x=\mathrm{Δp},\mathrm{pos}=\mathrm{oil.dynamicViscosity}\left(p={p}_{A\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={\mathrm{oil.v}}_{\mathrm{gas}},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{neg}=\mathrm{oil.dynamicViscosity}\left(p={p}_{B\left(\mathrm{abs}\right)},T=T,{v}_{\mathrm{air}}={\mathrm{oil.v}}_{\mathrm{gas}},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right),\mathrm{Δx}=100\right)$

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

General Parameters

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

Hydraulic Resistance Parameters

 Name Default Units Description Modelica ID $\mathrm{geometry}$ [1] Choice of geometry for internal flow geometry $K$ $0$ $m$ Roughness (average height of surface asperities) K $L$ $1$ $m$ Length L ${d}_{\mathrm{ann}}$ ${d}_{\mathrm{cir}}$ $m$ Small diameter d_ann ${\mathrm{D}}_{\mathrm{ann}}$ $2{d}_{\mathrm{ann}}$ $m$ Large diameter D_ann ${d}_{\mathrm{cir}}$ $0.01$ $m$ Internal diameter d_cir ${a}_{\mathrm{ell}}$ $\frac{3}{4}{d}_{\mathrm{cir}}$ $m$ Half length of long base line a_ell ${b}_{\mathrm{ell}}$ $\frac{1}{2}{a}_{\mathrm{ell}}$ $m$ Half length of short base line b_ell ${a}_{\mathrm{rec}}$ ${d}_{\mathrm{cir}}$ $m$ Horizontal length a_rec ${b}_{\mathrm{rec}}$ ${a}_{\mathrm{rec}}$ $m$ Vertical length b_rec ${a}_{\mathrm{tri}}$ ${d}_{\mathrm{cir}}\left(1+\sqrt{2}\right)$ $m$ Length of base line a_tri ${h}_{\mathrm{tri}}$ $\frac{1}{2}{a}_{\mathrm{tri}}$ $m$ Height to top angle perpendicular to base line h_tri $\mathrm{\beta }$ [2] $\mathrm{rad}$ Top angle beta

[1] $\mathrm{Modelica.Fluid.Dissipation.Utilities.Types.GeometryOfInternalFlow.Circular}$

[2] $\frac{1}{2}\mathrm{\pi }$