I'm currently studying chemical engineering and for my Bachelor thesis, I'm supposed to model a heated pipe that can be used in a superheater by connecting two pipes via a heatport together. Even though I made a big effort on understanding how I code correctly in Modelica, my code is still not working and I'm getting pretty desperate.
So the model basically has to be applicable for both fluid water and overheated steam, so just one-phase flow in instationary conditions. Heat transfer is supposed to happen convectively. Also, I neglect pressure losses due to friction in this model.
Here´s my idea of how the model is supposed to work: I'm pretty much trying to build a model like the one in the MSL, "Dynamic Pipe", just way more easier so that students who work on the same topic are able to understand my code quickly. So I splitted the pipe into a number of nodes n, the first volume being a inlet state, so basically that state does not really belong to the pipe. After that, the balance equations apply. I´m not quite sure about the momentum equations, so any help on them is highly appreciated. Convective heat transfer is defined by the Model "Convection" from the MSL, Thermal.HeatTransfer.Components. When testing the model with a flow source, a boundary with fixed pressure and a fixed temperature at the wall, I also get the error "Failed to reduce the DAE index" and I have absolutely no idea what that means.
Also, here is my code:
model Pipe_base3
//Import
import Modelica.SIunits.*;
import Modelica.Constants.pi;
replaceable package Medium =
Modelica.Media.Interfaces.PartialTwoPhaseMedium annotation (choicesAllMatching = true);
parameter Integer n=2;
parameter Integer np=1;
// Geometry==================================================================//
parameter Diameter d_pipe = 0.05 "Inner diameter of pipe"
annotation (Dialog(tab="Geometry"));
parameter Length L = 1 "Length of unit"
annotation (Dialog(tab="Geometry"));
parameter Area A_hex = pi * d_pipe * L
"Shell surface of pipe for heat exchange" annotation (Dialog(tab="Geometry"));
parameter Area A_q = (pi/4)*d_pipe^2
annotation (Dialog(tab="Geometry"));
//Initialisation=============================================================//
parameter Medium.Temperature T_start = 403.15 annotation (Dialog(tab="Initialization"));
parameter Medium.SpecificEnthalpy h_start = Medium.specificEnthalpy_pT(p_start, T_start) annotation (Dialog(tab="Initialization"));
parameter AbsolutePressure p_start = Medium.saturationPressure(T_start) annotation (Dialog(tab="Initialization"));
parameter Medium.MassFlowRate m_flow_start = 0.5 annotation (Dialog(tab="Initialization"));
//Temperature, pressure, energy==============================================//
Medium.Temperature T[n+1]( each start=T_start, fixed=false);
Medium.SpecificEnthalpy h[n+1]( each start=h_start, fixed=false);
Medium.AbsolutePressure p[n+1](each start=p_start, fixed=false);
HeatFlowRate Q_flow[n](fixed = false);
Energy U[n](min=0);
Energy KE[n]; //Kinetic Energy
Medium.ThermodynamicState state[n+1];
// Nondimensional Variables + HeatTransfer===================================//
Medium.PrandtlNumber Pr[n](fixed=false);
ReynoldsNumber Re[n](fixed=false);
Real Xi[n];
NusseltNumber Nu[n];
CoefficientOfHeatTransfer alpha[n];
// Thermodynamic properties==================================================//
Medium.SpecificInternalEnergy u[n](fixed=false);
Medium.DynamicViscosity eta[n];
Density rho[n+1];
Medium.SpecificHeatCapacity cp[n];
Medium.ThermalConductivity lambda_fluid[n];
//Segmental properties
Mass ms[n]; //Mass per Segment
MassFlowRate m_flow[n+1]( each start=m_flow_start/np, fixed=false);
Velocity w[n+1](fixed=false);
// Momentum
Force F_p[n];
Momentum I[n];
Force Ib_flow[n];
parameter Boolean init = false;
Modelica.Fluid.Interfaces.FluidPort_a fluidin( redeclare package Medium = Medium, m_flow(start = m_flow_start, min = 0), p(start = p_start))
annotation (Placement(transformation(extent={{-90,-100},{-70,-80}}),
iconTransformation(extent={{-90,-100},{-70,-80}})));
Modelica.Fluid.Interfaces.FluidPort_b fluidout( redeclare package Medium = Medium, m_flow(start = -m_flow_start, max = 0), p(start = p_start), h_outflow(start=h_start))
annotation (Placement(transformation(extent={{70,-100},{90,-80}}),
iconTransformation(extent={{70,-100},{90,-80}})));
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a[n] heatport
annotation (Placement(transformation(extent={{-10,60},{10,80}}),
iconTransformation(extent={{-10,60},{10,80}})));
Modelica.Blocks.Interfaces.RealOutput[n] alpha_output annotation (Placement(
transformation(extent={{-100,38},{-140,78}}), iconTransformation(extent={{-100,
38},{-140,78}})));
protected
parameter Volume vn = (A_q * L) / n; //Volume per segment
parameter Real x[n] = linspace((L/n), L, n);
parameter Length length = L/n;
initial equation
for i in 1:(n+1) loop
//h[i] = Medium.specificEnthalpy_pTX(p_start, T_start, {1});
p[i] = p_start;
end for;
equation
//Port equations=============================================================//
fluidout.p = p[n];
//fluidin.p-fluidout.p=p[1]-p[n+1];
fluidout.h_outflow = h[n];
fluidout.m_flow = -m_flow[n+1];
//===========================================================================//
h[1]=inStream(fluidin.h_outflow);
p[1]=fluidin.p;
state[1]=Medium.setState_ph(p[1],h[1]);
T[1]=Medium.temperature(state[1]);
rho[1]=Medium.density(state[1]);
m_flow[1]=fluidin.m_flow/np;
m_flow[1]=A_q*rho[1]*w[1];
for i in 1:(n) loop
// Heatport equations======================================================//
T[i] = heatport[i].T;
Q_flow[i] = heatport[i].Q_flow;
// Momentum Balance =======================================================//
der(I[i]) = Ib_flow[i] - F_p[i];
I[i]=m_flow[i]*length;
Ib_flow[i] = (p[i+1]*w[i+1]*w[i+1] - p[i]*w[i]*w[i])*A_q*np;
F_p[i] = (A_q*p[i+1]-A_q*p[i]);
// Energy Balance=========================================================//
U[i] = ms[i] * u[i];
KE[i] = 0.5*ms[i]*w[i+1]*w[i+1];
der(U[i]+KE[i])=m_flow[i]*(h[i]+0.5*w[i]) - m_flow[i+1]*(h[i+1]+0.5*w[i+1]) + Q_flow[i];
der(rho[i+1])= -((rho[i+1]-rho[i])*w[i+1] + (w[i+1]-w[i])*rho[i+1]); //Konti
ms[i]=vn*rho[i+1];
T[i+1]=Medium.temperature(state[i+1]);
state[i+1] = Medium.setState_ph(p[i+1], h[i+1], 1); //Sets thermodynamic state from which other properties can be determined
u[i] = Medium.specificInternalEnergy(state[i+1]);
cp[i] = Medium.specificHeatCapacityCp(state[i+1]);
rho[i+1] = Medium.density(state[i+1]);
eta[i] = Medium.dynamicViscosity(state[i+1]);
lambda_fluid[i] = Medium.thermalConductivity(state[i+1]);
Re[i] * eta[i] = (rho[i+1] * abs(w[i+1]) * d_pipe);
Pr[i] *lambda_fluid[i] = (eta[i] * cp[i]);
Xi[i] = (1.8 * log10(abs(Re[i])+1) - 1.5)^(-2);
Nu[i] = ((Xi[i]/8)*Re[i]*Pr[i])/(1+12.7*sqrt(Xi[i]/8)*((Pr[i])^(2/3)-1))*(1+(1/3)*(d_pipe/x[i])^(2/3));
Nu[i] = Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.NusseltNumber(alpha[i], d_pipe, lambda_fluid[i]);
alpha_output[i] = alpha[i] * (A_hex/n);
m_flow[i+1] = A_q * w[i+1] * rho[i+1];
// der(p[i]) = - w[i]*der(w[i]) * rho[i];
// 0 = m_flow[i-1] - m_flow[i];
// der(rho[i]) = -((rho[i]-rho[i-1])*w[i] + (v[i]-v[i-1])*rho[i]);
//m_flow[i] = A_q * w[i] * rho[i]; //Calculation of flow velocity
//ms[i] = vn * rho[i]; //Mass per segment
//Calculation of thermodynamic properties for each segment=================//
//Heat Transfer============================================================//
end for;
fluidin.h_outflow = h[1]; //
annotation (Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100},
{100,100}}), graphics={Line(
points={{-80,-80},{-80,94},{-80,100},{0,20},{80,100},{80,-80}},
color={0,0,255},
smooth=Smooth.None), Line(
points={{-60,-60},{-60,-48},{-60,0},{60,0},{60,-60},{48,-40},{72,-40},
{60,-60}},
color={0,0,255},
smooth=Smooth.None)}), __Dymola_selections);
end Pipe_base3;
Thank you so much in advance!
