基于Modelica/Dymola的加热管建模

Question

我目前正在学习化学工程，为了完成我的学士学位论文，我应该对一个可以用于过热器的加热管道进行建模，通过一个加热口将两个管道连接在一起。即使我花了很大的努力来理解我是如何在Modelica中正确编码的，我的代码仍然不能工作，我变得非常绝望。

因此，该模型基本上必须同时适用于液态水和过热蒸汽，因此在瞬时条件下只适用于单相流。热传递被认为是对流发生的。此外，在这个模型中，我忽略了由于摩擦造成的压力损失。

这是我关于这个模型的工作原理的想法:我正在尝试构建一个类似于MSL中的模型，“动态管道”，只是更简单，这样从事相同主题工作的学生就能够快速理解我的代码。所以我把管道分成多个节点n，第一个体积是一个入口状态，所以基本上这个状态并不真正属于管道。在此之后，应用平衡方程。我对动量方程不是很确定，所以对它们的任何帮助都是非常感谢的。对流换热是由MSL，Thermal.HeatTransfer.Components的“对流”模型定义的。当使用流量源、具有固定压力和固定温度的边界来测试模型时，我也得到了错误“未能降低DAE指数”，我完全不知道这是什么意思。

另外，下面是我的代码：

        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;

提前谢谢你！

Answer 1

当我开始使用Modelica时，我也处于同样的境地:我想要Modelica.Fluid.Pipes.DynamicPipe的特性，但复杂度更低(我希望代码更易读，层次更少)。所以，像你一样，我从头开始构建我自己的管道模型。然而，因为我希望能够替换压降和热传递关系，并具有更大的灵活性，所以我最终得到了一个几乎与Modelica.Fluid.Pipes.DynamicPipe相同的复杂性的模型。

我给你的建议是

1. 无需任何复杂功能即可构建您自己的简单动态管道模型。这将仅用于教育目的(例如，让其他学生了解您的编码principles)
2. learn如何在需要不同模型复杂性(段数、可替换压降和热传递方法等)的情况下使用Modelica.Fluid.Pipes.DynamicPipe解决问题)。Modelica.Fluid.Examples.HeatExchanger是一个例子，展示了如何使用Modelica.Fluid.Pipes.DynamicPipe对热交换器进行建模，就像您请求的那样。

Here我分享了一个非常简单的动态管道的例子，它可以用作热交换器。管道由n管道段组成，它利用了这样一个事实，即您可以实例化组件数组并在for循环中连接元素。

至于动量平衡，正确/完整的方法是通过将作用在每个控制体上的所有力相加来说明动量的变化(牛顿第二定律)。然而，在大多数集中模型中，稳态动量平衡是足够的，它将方程简化为质量流量与压降之间的线性或二次关系。Modelica.Fluid.Pipes.DynamicPipe有许多不同的压力/流量相关性可供选择。

诚挚的问候,

Rene Just Nielsen