modelVolumeRealGas_L4

A 1D tube-shaped control volume considering one-phase heat transfer in a straight pipe with static momentum balance and simple energy balance

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Extends from ClaRa.Basics.Icons.Volume_L4, ClaRa.Basics.Icons.ComplexityLevel (Displays the complexity level inside model icon ).

Information

1. Purpose of model

A 1D tube-shaped control volume considering one-phase and two-phase heat transfer and Pressure Loss in a straight pipe with static momentum balance and simple energy balance. It is a modified version of the model ClaRa.Basics.ControlVolumes.FluidVolumes.VolumeVLE_L4 from ClaRa version 1.3.0.

2. Level of detail, physical effects considered, and physical insight

The pipe can be discretized in the length direction (L4). It uses real gas mixtures (VLEFluids).

It can be chosen if changes in the composition shall be considered or not. In the first case, it considers the time delay of the change of the mass fraction from inlet to outlet.

Compared to the ClaRa version, the simCenter, media model and connectors were exchanged for TransiEnt instances. The two-phase region is deactivated and a xi_nom as well as an m_flow_start is added. Also, different mass balance equations are added. You can choose a quasi-stationary and three different dynamic implementations, see below. Additionally, the parameter variableCompositionEntries can be used in case that not all components are freely variable, e.g. when hydrogen is fed into natural gas.

3. Limits of validity

(no remarks)

4. Interfaces

RealGasPorts

5. Nomenclature

(no remarks)

6. Governing Equations

Velocity at inlet and outlet:

w_inlet=m_flow/(A_cross_FM*rho_inlet)

w_outlet=m_flow/(A_cross_FM*rho_outlet)

flow velocity in energy cells:

w[i]=(m_flow[i]+m_flow[i+1])/(2*rho*A_cross) , for i in 1:N_cv (number of control volumes)

Density in flow model:

rho_FM[i]=(rho[i]+rho[i-1])/2 ,for i in 2:N_cv

and the density in the first and last momentum cell:

rho_FM[1]=(rho_in+rho[1])/2

rho_FM[N_cv+1]=(rho_out+rho[N_cv])/2

Pressure drop due to friction and gravity:

Delta_p_grav[i] =(rho[i]*Delta_x[i] +rho[i-1]*Delta_x[i - 1])/(Delta_x[i - 1] + Delta_x[i])*g_n*(z[i] - z[i - 1]) , for i in 3: N_cv-1

If there is friction at the inlet:

Delta_p_grav[1] =rho[1]*g_n*(z[1] - z_in)

Delta_p_grav[2] =(rho[1]*Delta_x[1] + rho[2]*Delta_x[2])/(Delta_x[2] +Delta_x[1])*g_n*(.z[2] - z[1])

If there is no friction at the inlet:

Delta_p_grav[1] = 0

Delta_p_grav[2] =(rho[1]*Delta_x[1] + rho[2]*Delta_x[2]/2)/(Delta_x[2]/2 +Delta_x[1])*g_n*(z[2] - z_in)

If there is friction at the outlet:

Delta_p_grav[N_cv+1] =rho[N_cv]*g_n*(z_out - z[N_cv])

Delta_p_grav[N_cv] =(rho[N_cv-1]*Delta_x[N_cv - 1] +rho[N_cv]*Delta_x[N_cv])/(Delta_x[N_cv - 1] +.Delta_x[N_cv])*g_n*(.z[N_cv] - z[N_cv - 1])

If there is no friction at the outlet:

Delta_p_grav[N_cv+1] = 0

Delta_p_grav[N_cv] =(rho[N_cv-1]*Delta_x[N_cv - 1]/2 + rho[N_cv]*Delta_x[N_cv])/(Delta_x[N_cv - 1]/2 + Delta_x[N_cv])*g_n*(z_out - z[N_cv - 1])

Fluid mass:

m = V* rho_mix

Equations for calculating the cell states:

The model differentiates between four different kind of mass balances and a constant or variable composition.

Quasi-stationary:

0=der(rho[i]) , for i in 1:N_cv

0=m_flow[i]-m_flow[i+1] , for i in 1:N_cv

Dynamic:

Here, you can pick three different mathematically identical equations which are treated differently numerically. In the following, only the mathematical notation of the general equations is shown.

der(rho[i])*V[i]=m_flow[i]-m_flow[i+1] , for i in 1:N_cv

For all components considered fully variable:

der(xi[i, j]) = 1/m[i]*((Xi_flow[i, j] - m_flow[i]*xi[i, j]) - (Xi_flow[i + 1, j] - m_flow[i + 1]*xi[i, j])) , for i in 1:N_cv and for j in 1:nc-1 (number of components -1)

For the components which are dependent on other components:

xi[i, j] = (1 - (sum(xi[i, k] for k in variableCompositionEntries[1:end - 1]) + xi_end[i]))/(1 - (sum(xi_nom[k] for k in variableCompositionEntries[1:end - 1]) + 1 - sum(xi_nom)))*xi_nom[j] , for j in dependentCompositionEntries[1:end - 1] and for i in 1:geo.N_cv

For constant composition:

xi[i, j] = xi[j,nom] , for i in 1:N_cv and for j in 1:nc-1

Static momentum balance in the momentum cells:

0 = p[i - 1] - p[i] - Delta_p_fric[i] - Delta_p_grav[i] , for i in 2:N_cv

and for the first and last momentum cell

0 =p_in - p[1] - Delta_p_fric[1] - Delta_p_grav[1]

0 = p[N_cv] - p_out - Delta_p_fric[N_cv + 1] - Delta_p_grav[N_cv + 1]

7. Remarks for Usage

Use of certain heat transfer models can lead to warnings like "Differentiating (if pipe_xy.iCom.m_flow_in[1] > 0.0 then junction_beforePipe.gasBulk.xi[1] else junction_beforePipe.gasBulk.xi[1]) under the assumption that it is continuous at switching.". This can be ignored as long as the composition is set to the same value in every component (even in sinks etc.).

8. Validation

(no remarks)

9. References

copied and changed from ClaRa.Basics.ControlVolumes.FluidVolumes.VolumeVLE_L4, v1.3.0

10. Version History

Model created by Tom Lindemann (tom.lindemann@tuhh.de), Jun 2015

Modified by Carsten Bode (c.bode@tuhh.de), Okt 2015

Modified by Lisa Andresen (andresen@tuhh.de), May 2016

Revised by Carsten Bode (c.bode@tuhh.de), Apr 2018 (updated to ClaRa 1.3.0)

Modified by Carsten Bode (c.bode@tuhh.de), Feb 2019 (added temperature start value)

Modified by Carsten Bode (c.bode@tuhh.de), Sep 2019 (merged constXi and varXi models)

Modified by Carsten Bode (c.bode@tuhh.de), May 2020 (added quasi-stationary equations and simplified equations for only dependent mass fractions)

Modified by Robert Flesch (flesch@xrg-simulation.de), Sep 2020 (included new ICom, exchanged ph fluid models to pT, turned of density derivative calculation)

Parameters

Type	Name	Default	Description
Integer[:]	dependentCompositionEntries	if variableCompositionEntries[1] == 0 then 1:medium.nc else findSetDifference(1:medium.nc, variableCompositionEntries)	Entries of medium vector which are supposed to be dependent on the variable entries
ClaRa.Basics.Units.DensityMassSpecific[geo.N_cv]	rho_nom	TILMedia.Internals.VLEFluidConfigurations.FullyMixtureCompatible.VLEFluidFunctions.density_phxi(medium, p_nom, h_nom, xi_nom)	Nominal density
Fundamental Definitions
TILMedia.VLEFluidTypes.BaseVLEFluid	medium	simCenter.gasModel1	Medium in the component
Boolean	constantComposition	simCenter.useConstCompInGasComp	true if composition of gas in the pipe is constant (xi_nom will be used)
Integer[:]	variableCompositionEntries	{0}	Entries of medium vector which are supposed to be completely variable
Integer	massBalance	1	Mass balance and species balance fomulation
SI.Pressure	p_min_assert	0	Minimum pressure in component and ports below which the simulation terminates
SI.Pressure	p_max_assert	1000e5	Maximum pressure in component and ports above which the simulation terminates
Boolean	frictionAtInlet	false	True if pressure loss between first cell and inlet shall be considered
Boolean	frictionAtOutlet	false	True if pressure loss between last cell and outlet shall be considered
Nominal Values
ClaRa.Basics.Units.Pressure[geo.N_cv]	p_nom	ones(geo.N_cv)*(simCenter.p_amb_const + simCenter.p_eff_2)	Nominal pressure
ClaRa.Basics.Units.EnthalpyMassSpecific[geo.N_cv]	h_nom	ones(geo.N_cv)*(-1850)	Nominal specific enthalpy for single tube
ClaRa.Basics.Units.MassFlowRate	m_flow_nom	1	Nominal mass flow w.r.t. all parallel tubes
ClaRa.Basics.Units.PressureDifference	Delta_p_nom	1e4	Nominal pressure loss w.r.t. all parallel tubes
ClaRa.Basics.Units.MassFraction[medium.nc - 1]	xi_nom	medium.xi_default	Nominal composition
Initialisation
Integer	initOption	0	Type of initialisation
ClaRa.Basics.Units.EnthalpyMassSpecific[geo.N_cv]	h_start	TILMedia.Internals.VLEFluidConfigurations.FullyMixtureCompatible.VLEFluidFunctions.specificEnthalpy_pTxi(medium, p_start, T_start, xi_start)	Initial specific enthalpy for single tube
ClaRa.Basics.Units.Pressure[geo.N_cv]	p_start	p_nom	Initial pressure
ClaRa.Basics.Units.MassFraction[medium.nc - 1]	xi_start	xi_nom	Initial composition for single tube
ClaRa.Basics.Units.MassFlowRate[geo.N_cv + 1]	m_flow_start	m_flow_nom*ones(geo.N_cv + 1)	Initial mass flow rate
Modelica.Units.SI.Temperature[geo.N_cv]	T_start	ones(geo.N_cv)*simCenter.T_ground	Initial temperature for single tube (used in calculation of h_start)
Initialisation › Model Settings
Boolean	useHomotopy	simCenter.useHomotopy	true, if homotopy method is used during initialisation
Summary and Visualisation
Boolean	showExpertSummary	simCenter.showExpertSummary	True, if an extended summary shall be shown, else false
Boolean	showData	false	True, if a data port containing p,T,h,s,m_flow shall be shown, else false

Connectors

Type	Name	Description
TransiEnt.Basics.Interfaces.Gas.RealGasPortIn	gasPortIn	Inlet port
TransiEnt.Basics.Interfaces.Gas.RealGasPortOut	gasPortOut	Outlet port
ClaRa.Basics.Interfaces.HeatPort_a[geo.N_cv]	heat

Components

Type	Name	Default	Description
String	complexity (from ComplexityLevel)	"??"
TransiEnt.SimCenter	simCenter
Summary	summary
ClaRa.Basics.Units.EnthalpyMassSpecific[geo.N_cv]	h		Cell enthalpy
ClaRa.Basics.Units.Temperature[geo.N_cv]	T		Cell temperature
PressureLoss	pressureLoss		Pressure loss model
HeatTransfer	heatTransfer		heat transfer model
Geometry	geo
MechanicalEquilibrium	mechanicalEquilibrium		Mechanical equilibrium model

Name	Description
Outline
Wall_L4
Inlet
Outlet
Fluid
Summary
PressureLoss
HeatTransfer
Geometry
MechanicalEquilibrium

modelVolumeRealGas_L4

Information

Velocity at inlet and outlet:

Density in flow model:

Pressure drop due to friction and gravity:

Fluid mass:

Equations for calculating the cell states:

Quasi-stationary:

Dynamic:

Static momentum balance in the momentum cells:

Parameters

Connectors

Components

Contents