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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!
I was in the same situation when I started using Modelica: I wanted the features of Modelica.Fluid.Pipes.DynamicPipe but with less complexity (I wanted the code to be more readable and less hierarchical). So, like you, I started building my own pipe model from scratch. However, because I wanted to be able to replace the pressure drop and heat transfer correlations and have great flexibility I ended up with a model of nearly the same complexity as Modelica.Fluid.Pipes.DynamicPipe.
My recommendation to you is to
build your own simple dynamic pipe model without any complex
features. This will only be usable for educational purposes (e.g.
letting other students understand your coding principles)
learn how to use Modelica.Fluid.Pipes.DynamicPipe for problems where you need vary model complexity (number of segment, replaceable pressure drop and heat transfer methods etc.). Modelica.Fluid.Examples.HeatExchanger is an example of how you can use Modelica.Fluid.Pipes.DynamicPipe to model a heat exchanger like the one you request.
Here I've shared an example of a very simple dynamic pipe that can be used as a heat exchanger. The pipe is made from n pipe segments and takes advantage of the fact that you can instantiate an array of components and connect the elements in a for loop.
As for the momentum balance, the correct/complete way is to account for the change in momentum by summing all the forces acting on each control volume (Newton's Second law). However, in most lumped models a steady-state momentum balance is adequate which reduces the equation to a linear or quadratic relation between mass flow rate and pressure drop. Modelica.Fluid.Pipes.DynamicPipe has a number of different presssure/flow correlations to choose from.
Best regards,
Rene Just Nielsen
I have built a small example/test that uses your model. It should be a very simple application of your model. Unfortunately I get the same error message:
Cannot find differentiation function:
Modelica.Media.Water.IF97_Utilities.waterBaseProp_ph(boundary1.p, pipe_base3_1.h[2], 0, 1)
with respect to time
Index reduction basically means that the model contains equations that have no unknown. This is solved by differentiation of these equations with respect to time (which can happen multiple times). For more information you can check
https://www.inf.ethz.ch/personal/cellier/Lect/NSDS/Ppt/nsds_ppt_engl.html
especially lecture 16 and probably the ones before it :)
Therefore the Modelica tool will have to know how to do this differentiation. For equations this is usually done automatically, but for functions it has to be specified by the developer. It seems this is not done for Modelica.Media.Water.IF97_Utilities.waterBaseProp_ph()
which is why you get the error message.
There are basically two possibilities to solve this problem:
You change your model to get rid of or revise the constraint equation (the one which has no unknown). It should be the one shown in the error message: der(pipe_base3_1.rho[2]) = ...
You add the function for differentiation to the medium (I'm not much into the Fluid/Media so I have no idea how complicated that is, so I would try to go with 1. first). How this can be done is shown in https://modelica.org/documents/ModelicaSpec33Revision1.pdf section 12.7
Here is the code of the example:
model PipeTest
Pipe_base3 pipe_base3_1(redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
Modelica.Fluid.Sources.FixedBoundary boundary(
nPorts=1,
p=100000,
redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{-60,-40},{-40,-20}})));
Modelica.Fluid.Sources.FixedBoundary boundary1(
nPorts=1,
p=100000,
redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{60,-40},{40,-20}})));
Modelica.Thermal.HeatTransfer.Sources.FixedHeatFlow fixedHeatFlow[2](Q_flow={0,0})
annotation (Placement(transformation(extent={{-40,20},{-20,40}})));
equation
connect(boundary.ports[1], pipe_base3_1.fluidin) annotation (Line(points={{-40,-30},{-8,-30},{-8,-9}}, color={0,127,255}));
connect(boundary1.ports[1], pipe_base3_1.fluidout) annotation (Line(points={{40,-30},{8,-30},{8,-9}}, color={0,127,255}));
connect(fixedHeatFlow.port, pipe_base3_1.heatport) annotation (Line(points={{-20,30},{0,30},{0,7}}, color={191,0,0}));
annotation (
Icon(coordinateSystem(preserveAspectRatio=false)),
Diagram(coordinateSystem(preserveAspectRatio=false)),
uses(Modelica(version="3.2.2")));
end PipeTest;
Hope this helps...
Hello
My model has a pump with dp = 1 bar and a pipe which reduce the dp of 1 bar. The pump must work in both directions.
Additionally, there is a three-way valve which provides the side with the lower pressure with 3 bar.
But there is a problem with my model: Always if I want to use a pump from the standard library, it does not work… Does anybody have any ideas how to solve this problem, if possible with standard library blocks? (I would like to have standard library blocks because of the parameters like pump characteristics, …)
Here is the image: Model
Thank you!
model Modell_online
Pump_mflow pump_mflow3(redeclare package Medium =
Modelica.Media.Water.ConstantPropertyLiquidWater, show_T=true)
annotation (Placement(transformation(
extent={{-10,-10},{10,10}},
rotation=270,
origin={-50,10})));
Modelica.Fluid.Pipes.StaticPipe pipe(
redeclare package Medium =
Modelica.Media.Water.ConstantPropertyLiquidWater,
length=0.5,
diameter=0.1,
redeclare model FlowModel =
Modelica.Fluid.Pipes.BaseClasses.FlowModels.NominalLaminarFlow (
dp_nominal=100000, m_flow_nominal=3),
p_a_start=400000,
p_b_start=300000) annotation (Placement(transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={-10,10})));
Modelica.Blocks.Sources.Pulse pulse(
amplitude=2,
offset=-1,
period(displayUnit="min") = 600)
annotation (Placement(transformation(extent={{-100,60},{-80,80}})));
inner Modelica.Fluid.System system
annotation (Placement(transformation(extent={{-140,80},{-120,100}})));
Modelica.Fluid.Sources.Boundary_pT p_source(
redeclare package Medium =
Modelica.Media.Water.ConstantPropertyLiquidWater,
nPorts=1,
p=300000) annotation (Placement(transformation(
extent={{10,-10},{-10,10}},
rotation=0,
origin={70,10})));
Modelica.Blocks.Continuous.FirstOrder firstOrder(T(displayUnit="s") = 10)
annotation (Placement(transformation(extent={{-60,60},{-40,80}})));
VarEx VarEx_1(redeclare package Medium =
Modelica.Media.Water.ConstantPropertyLiquidWater) annotation (Placement(
transformation(
extent={{10,-10},{-10,10}},
rotation=270,
origin={30,10})));
equation
connect(pump_mflow3.port_b, pipe.port_a) annotation (Line(points={{-50,0},{-50,
-20},{-10,-20},{-10,0}}, color={0,127,255}));
connect(pipe.port_b,pump_mflow3. port_a) annotation (Line(points={{-10,20},{-10,
40},{-50,40},{-50,20}}, color={0,127,255}));
connect(pulse.y, firstOrder.u)
annotation (Line(points={{-79,70},{-62,70}}, color={0,0,127}));
connect(p_source.ports[1], VarEx_1.port_ExpansionVessel)
annotation (Line(points={{60,10},{40,10}}, color={0,127,255}));
connect(VarEx_1.port_warm, pump_mflow3.port_a) annotation (Line(points={{30,20},
{30,40},{-50,40},{-50,20}}, color={0,127,255}));
connect(VarEx_1.port_cold, pipe.port_a) annotation (Line(points={{30,0},{30,-20},
{-10,-20},{-10,0}}, color={0,127,255}));
connect(firstOrder.y, pump_mflow3.m_flow_set) annotation (Line(points={{-39,70},
{-30,70},{-30,10},{-38,10}}, color={0,0,127}));
annotation (Icon(coordinateSystem(preserveAspectRatio=false, extent={{-140,
-100},{140,100}})), Diagram(coordinateSystem(preserveAspectRatio=
false, extent[enter image description here][1]={{-140,-100},{140,100}})),
experiment(StopTime=1200));
end Modell_online;
A similar question was asked in Backflow Orifice (Zeta).
You'll need a heat sink to remove the heat generated by the pump in a closed circuit.
The MSL pumps have limited capability of flow reversal.
I made a small package with some examples here https://drive.google.com/file/d/1LEn2_ifoFTrdX33JEe2awQmvePBERVVz/view?usp=sharing
In example 3, note that it is not a true closed circuit since the pressure sink also acts as a heat sink.
The paper On the formulation of steady-state initialization problems in object-oriented models of thermo-hydraulic systems might be of interest to you.
Best regards,
Rene Just Nielsen
I was playing with OpenModelica using the PowerSystem library and found something curious.
To have a full grasp of what the equation constraints from the block's classes are, I always open each block individually and instantiate it, to have the full list of variables and equations of the flattened model.
However, I noticed that when I do it, the instantiated model has additional equations that are not defined in the code concerning the block's class or any parent's class, nor exists when I use the block in another model.
For instance, when instantiating the class for a simple Resistor (AC1ph_DC), it adds the equations equating the currents to zero (the last four equations):
R[1] * i[1] = v[1];
R[2] * i[2] = v[2];
v[1] = term_p.v[1] - term_n.v[1];
v[2] = term_p.v[2] - term_n.v[2];
i[1] = term_p.i[1];
i[2] = term_p.i[2];
(...)
term_p.i[1] = 0.0;
term_p.i[2] = 0.0;
term_n.i[1] = 0.0;
term_n.i[2] = 0.0;
Is this done automatically by OpenModelica to have a solvable system when instantiating just the resistor? Is there any documentation on that available?
Also, is there any "more correct" way to visualize the flattened class code of any block?
In Modelica, flow variables that are not connected are set to zero.
See 9.2 in Modelica Specification:
https://modelica.org/documents/ModelicaSpec33Revision1.pdf
I have a model of a tank that I am creating as follows:
model Tank "Simple model of a tank"
parameter Real volume=1 "tank volume (m^3)";
parameter Integer num_ports=1 "Number of ports";
parameter Real static_pressure=1 "Internal Tank Pressure";
parameter Real initial_level = 0;
Stream[num_ports] ports "Stream Connectors";
Real level "Level in % 0-100";
protected
Real vol "Volume of medium in the tank";
Real pressure(start=static_pressure) "Pressure inside the tank";
initial equation
level = initial_level;
/* Pressure */
equation
pressure = vol * 0.01; // Add correct factor here to get from volume to pressure change (based on height and head)
for i in 1:num_ports loop
ports[i].pressure = static_pressure + pressure;
end for;
/* Volume Flow */
equation
der(vol) = sum(ports.m_flow); // Add density factor to get form mass flow to Volume Flow
level = vol * 100 / volume;
end Tank;
How can I make it so that when the level <=0 the tank will not allow any flows with a negative value (no ports can have fluid leaving, but fluid can still enter)? I feel like I am missing something trivial, but can't seem to find a way without having too many equations (over-determined system).
Thanks
You could try with a when equation:
when level < 0 then
reinit(level, 0)
end when;
I am trying to build a very simple model of a distributed thermofluid volume in Modelica and am struggling to implement it correctly with the stream operator. This volume uses DryAirNasa as the medium, and I would like it to have no mass storage, no pressure drop, and no energy storage (much like the Modelica.Fluid.Pipes.StaticPipe model). However, I would like to explicitly perform an energy balance so that there can be heat transfer interactions. I would also prefer not to define the mass flow rate in this model, but let it be defined in one of the boundaries attached to an end of the pipe (e.g., Modelica.Fluid.Sources.MassFlowSource_h).
I have created a test implementation of such a model, but this model apparently lacks one equation according to Dymola. I would appreciate any insights into how to fix this model so that it is correct. If I add the equation
port_a.h_outflow = Medium.specificEnthalpy(state_a)
to the equation section, the model has the same number of equations and unknowns, but I don't have any good justification for adding such an equation.
model AirFlowTemp
// Objective: create a component that has no pressure drop, no mass storage,
and no energy storage, but that has a heat input.
import SI=Modelica.SIunits;
final replaceable package Medium=Modelica.Media.Air.DryAirNasa;
AirFlow.AirFlowPort port_a(redeclare package Medium
= Medium);
AirFlow.AirFlowPort port_b(redeclare package Medium
= Medium);
Interfaces.HeatPort heatPort;
Medium.EnthalpyFlowRate[2] H_flow "enthalpy flow";
SI.HeatFlowRate Q_flow "heat flow rate";
Medium.Temperature T_mean;
Medium.ThermodynamicState state_a;
Medium.ThermodynamicState state_b;
equation
// no pressure drop across the component.
port_a.p = port_b.p;
// Assume that there is no mass storage in the volume
0 = port_a.m_flow + port_b.m_flow;
// Energy balance
H_flow[1] = semiLinear(port_a.m_flow, inStream(port_a.h_outflow), inStream(port_b.h_outflow));
H_flow[2] = semiLinear(port_b.m_flow, inStream(port_b.h_outflow), inStream(port_a.h_outflow));
0 = Q_flow + H_flow[1] + H_flow[2];
state_a = Medium.setState_ph(port_a.p, inStream(port_a.h_outflow));
state_b = Medium.setState_ph(port_b.p, inStream(port_b.h_outflow));
T_mean = (Medium.temperature(state_a) +
Medium.temperature(state_b))/2;
heatPort.Q_flow = Q_flow;
heatPort.T = T_mean;
end AirFlowTemp;
connector AirFlowPort
replaceable package Medium = Modelica.Media.Interfaces.PartialMedium;
Medium.AbsolutePressure p;
flow Medium.MassFlowRate m_flow;
stream Medium.SpecificEnthalpy h_outflow;
stream Medium.MassFraction Xi_outflow[Medium.nXi];
end AirFlowPort;
connector HeatPort
extends Modelica.Thermal.HeatTransfer.Interfaces.HeatPort;
end HeatPort;
I had the same problem doing the same thins about 4 weeks ago.
Try if this works out as a step to get closer to right use of inStream.
Remove
Medium.EnthalpyFlowRate[2] H_flow "enthalpy flow"
SI.HeatFlowRate Q_flow "heat flow rate";
Interfaces.HeatPort heatPort;
SI.HeatFlowRate Q_flow "heat flow rate";
Medium.Temperature T_mean;
T_mean = (Medium.temperature(state_a) + Medium.temperature(state_b))/2;
heatPort.Q_flow = Q_flow;
heatPort.T = T_mean;
=> just testing the pipe, without the heatPort
Use
port_a.outflow*port_a.m_flow = inStream(port_b.outflow)*port_b.m_flow;
port_b.outflow*port_b.m_flow = inStream(port_a.outflow)*port_a.m_flow;
instead of:
H_flow[1] = semiLinear(port_a.m_flow, inStream(port_a.h_outflow), inStream(port_b.h_outflow));
H_flow[2] = semiLinear(port_b.m_flow, inStream(port_b.h_outflow), inStream(port_a.h_outflow));
0 = Q_flow + H_flow[1] + H_flow[2];
Change your Test for no heatport
=> Does this work?
Regards
Uwe