集中体积模型中的加热流体

Question

我很难找到准确地写出具有流体流动和热流输出的简单集总体积（例如管道）的能量平衡的最佳方法。我基本上只想在能量平衡中添加一个 Q_loss 项来降低流过的任何流体的温度，但要保持整体模型超级简单（没有摩擦、压力、对流损失等）。

我试图编写一个简单的模型，但我发现方程式比我需要的少了一个。有没有办法在不固定压力的情况下做到这一点？

我的代码（介质不标准，可能需要重新声明）：

model IdealLossPipe
   extends SolarTherm.Interfaces.Models.Pipe;
  Medium.BaseProperties medium;
  replaceable package Medium = SolarTherm.Media.MoltenSalt.MoltenSalt_base
    constrainedby Modelica.Media.Interfaces.PartialMedium
  Modelica.Fluid.Interfaces.FluidPort_a fluid_a(redeclare package Medium =
        Medium);
  Modelica.Fluid.Interfaces.FluidPort_b fluid_b(redeclare package Medium =
        Medium) annotation (Placement(transformation(extent={{110,-10},{90,10}}, rotation=0),
        iconTransformation(extent={{110,-10},{90,10}})));
    parameter Real Q_loss_spec(unit="W/m") = 284 "Heat loss per m of piping";
    SI.HeatFlowRate Q_loss;
    parameter SI.Length length = 13.1 annotation(Dialog(group="Length"));
    parameter SI.Length diameter = 0.052;

    SI.Energy U;
    SI.Mass m;
    SI.Volume V;

equation 
  V = length*(diameter/2)^2*Modelica.Constants.pi;
  m=V*medium.d;
  U=m*medium.u;
  fluid_a.p=medium.p;
  fluid_b.p=medium.p;
  (instream(fluid_a.h_outflow)+fluid_b.h_outflow)/2=medium.h;
  fluid_a.h_outflow=0;
  Q_loss=-length*Q_loss_spec;

  //Mass Balance
  fluid_a.m_flow+fluid_b.m_flow=der(m);

  //Energy Balance
  der(U)= fluid_a.m_flow*inStream(fluid_a.h_outflow) + fluid_b.m_flow*fluid_b.h_outflow + Q_loss;

end IdealLossPipe;

在此先感谢您对我的帮助！！

编辑：删除了我模型中不必要的热端口

Answer 1

我编辑了你的模型（见下文）。一些添加包括 medium 的初始化，如果将这种方法用于基本属性，则这是必需的。仔细查看现有的 open-source 流体库（例如 Modelica 标准库、TRANSFORM 或 ThermoPower）以了解它们如何做事或使用它们的组件会很有帮助。

model IdealLossPipe
  import SI = Modelica.SIunits;

  replaceable package Medium = Modelica.Media.Water.StandardWater
    constrainedby Modelica.Media.Interfaces.PartialMedium annotation (
      choicesAllMatching=true);

  Medium.BaseProperties medium(
    each preferredMediumStates=true,
    p(start=p_start),
    T(start=T_start),
    h(start=Medium.specificEnthalpy(Medium.setState_pT(p_start, T_start))),
    d(start=Medium.density(Medium.setState_pT(p_start, T_start))),
    u(start=Medium.specificInternalEnergy(Medium.setState_pT(p_start, T_start))),
    Xi(start=X_start[1:Medium.nXi]),
    X(start=X_start));

  Modelica.Fluid.Interfaces.FluidPort_a fluid_a(redeclare package Medium =
        Medium) annotation (Placement(transformation(extent={{-90,-10},{-110,10}},
          rotation=0), iconTransformation(extent={{-90,-10},{-110,10}})));
  Modelica.Fluid.Interfaces.FluidPort_b fluid_b(redeclare package Medium =
        Medium) annotation (Placement(transformation(extent={{110,-10},{90,10}},
          rotation=0), iconTransformation(extent={{110,-10},{90,10}})));

  parameter Real Q_loss_spec(unit="W/m") = 284 "Heat loss per m of piping";
  parameter SI.Length length=13.1 annotation (Dialog(group="Length"));
  parameter SI.Length diameter=0.052;

  // Initialization
  parameter SI.Pressure p_start=1e5;
  parameter SI.Temperature T_start=293.15;
  parameter SI.MassFraction X_start[Medium.nX]=Medium.X_default "Mass fraction";

  SI.HeatFlowRate Q_loss;
  SI.Energy U;
  SI.Mass m;
  SI.Volume V;

equation 

  V = length*(diameter/2)^2*Modelica.Constants.pi;
  m = V*medium.d;
  U = m*medium.u;

  Q_loss = -length*Q_loss_spec;

  //Mass Balance
  fluid_a.m_flow + fluid_b.m_flow = der(m);

  //Energy Balance
  der(U) = fluid_a.m_flow*inStream(fluid_a.h_outflow) + fluid_b.m_flow*inStream(
     fluid_b.h_outflow) + Q_loss;

  // Port definitions
  fluid_a.h_outflow = medium.h;
  fluid_b.h_outflow = medium.h;
  fluid_a.p = medium.p;
  fluid_b.p = medium.p;
  fluid_a.Xi_outflow = medium.Xi;
  fluid_b.Xi_outflow = medium.Xi;
  fluid_a.C_outflow = inStream(fluid_b.C_outflow);
  fluid_b.C_outflow = inStream(fluid_a.C_outflow);
end IdealLossPipe;

要记住的一件事是模型的 "flow vs volume" 或 "non-state (flow) vs state (non-flow/volume)" 表示。暴露状态的端口设置连接器状态变量的值（即流体压力），而 non-state 端口设置连接器的流量变量（即流体质量流量）。因此，对于流体，您要确保不连接每个设置压力（状态变量）的端口。与质量流量相似，但求解器往往更宽容。

作为参考，您的模型设置了状态变量（fluid_a.p = medium.p、fluid_b.p = medium.p）。一个简单的模型示例希望将每个端口与设置质量流量的模型连接，例如 fluid_a 上的质量流量源和后跟 fluid_b.[=17 上的压力边界的阻力元件=]

model Example
  Unnamed pipe(redeclare package Medium = Modelica.Media.Water.StandardWater,
      Q_loss_spec=10000)
    annotation (Placement(transformation(extent={{-68,4},{-48,24}})));
  Modelica.Fluid.Sources.Boundary_pT boundary(
    nPorts=1,
    redeclare package Medium = Modelica.Media.Water.StandardWater,
    p=100000,
    T=293.15) annotation (Placement(transformation(extent={{34,2},{14,22}})));
  Modelica.Fluid.Sources.MassFlowSource_T boundary1(
    nPorts=1,
    redeclare package Medium = Modelica.Media.Water.StandardWater,
    m_flow=1,
    T=293.15)
    annotation (Placement(transformation(extent={{-124,2},{-104,22}})));
  Modelica.Fluid.Valves.ValveLinear valveLinear(
    redeclare package Medium = Modelica.Media.Water.StandardWater,
    dp_nominal=100000,
    m_flow_nominal=1)
    annotation (Placement(transformation(extent={{-30,4},{-10,24}})));
  Modelica.Blocks.Sources.Constant const(k=1)
    annotation (Placement(transformation(extent={{-52,30},{-32,50}})));
equation 
  connect(boundary1.ports[1], pipe.fluid_a) annotation (Line(points={{-104,12},{
          -86,12},{-86,14},{-68,14}}, color={0,127,255}));
  connect(pipe.fluid_b, valveLinear.port_a)
    annotation (Line(points={{-48,14},{-30,14}}, color={0,127,255}));
  connect(valveLinear.port_b, boundary.ports[1]) annotation (Line(points={{-10,14},
          {2,14},{2,12},{14,12}}, color={0,127,255}));
  connect(const.y, valveLinear.opening)
    annotation (Line(points={{-31,40},{-20,40},{-20,22}}, color={0,0,127}));

end Example;

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