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modelica - 在 Modelica/Dymola 中对加热管道进行建模

问题描述

我目前正在学习化学工程，对于我的学士论文，我应该通过将两个管道通过热端口连接在一起来模拟一个可用于过热器的加热管道。尽管我为理解我如何在 Modelica 中正确编码做出了很大努力，但我的代码仍然无法正常工作，我变得非常绝望。

因此，该模型基本上必须适用于流体水和过热蒸汽，因此仅适用于静止条件下的单相流。传热应该以对流方式发生。此外，我忽略了该模型中由于摩擦引起的压力损失。

这是我对模型应该如何工作的想法：我非常想构建一个类似于 MSL 中的模型，“动态管道”，只是更容易让从事同一主题工作的学生能够快速理解我的代码。所以我把管道分成了n个节点，第一个体积是入口状态，所以基本上那个状态并不真正属于管道。之后，平衡方程适用。我不太确定动量方程，因此非常感谢对它们的任何帮助。对流热传递由 MSL 中的“对流”模型 Thermal.HeatTransfer.Components 定义。在使用流源、壁面具有固定压力和固定温度的边界测试模型时，我也收到错误“无法降低 DAE 指数”

另外，这是我的代码：

        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;

非常感谢您！

标签： modelicadymolafluid-dynamics

解决方案

当我开始使用 Modelica 时，我也遇到了同样的情况：我想要它的功能Modelica.Fluid.Pipes.DynamicPipe但不那么复杂（我希望代码更具可读性和层次更少）。所以，和你一样，我开始从头开始构建自己的管道模型。但是，因为我希望能够替换压降和传热相关性并具有很大的灵活性，所以我最终得到了一个与Modelica.Fluid.Pipes.DynamicPipe.

我给你的建议是

  1. 构建您自己的简单动态管道模型，无需任何复杂功能。这仅可用于教育目的（例如让其他学生了解您的编码原则）
  2. 了解如何使用Modelica.Fluid.Pipes.DynamicPipe不同模型复杂性（分段数量、可更换压降和传热方法等）的问题。Modelica.Fluid.Examples.HeatExchanger是一个示例，说明如何使用Modelica.Fluid.Pipes.DynamicPipe您所要求的方式对热交换器进行建模。

在这里，我分享了一个可以用作热交换器的非常简单的动态管道的示例。管道由n管段制成，并利用了您可以实例化组件数组并在for循环中连接元素的事实。

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积上的所有力相加来解释动量的变化（牛顿第二定律）。然而，在大多数集总模型中，稳态动量平衡就足够了，它将方程简化为质量流量和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。

此致，

雷内·尼尔森

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