かなり前だが、この記事にて、熱サイクルを通じて熱から仕事を得るには、”気体”相の流体を使う必要が有る（液相流体のみでは動力を発生させられない）ことを示そうとしたが行詰った。今回、やり方を変えてサイクルシミュレーションを再度試み、当時言おうとしていた事と逆の結果に辿り着いた。
記事を通して言いたいこと（結論）
例によって、冒頭で述べておく。
- 液相の流体だけを用いても熱サイクルを通じて仕事を取出す（動力を発生させる）事は出来る。最もシンプルな理想熱サイクルの計算で確認した。
- 液相流体でも可とは言っても、熱授受に応じて圧力・密度（体積）に変化が起きるという特性が必要条件。完全非圧縮性流体のパッケージを使うと計算自体回らない。
モデル化対象（とその周辺について）
ルノアールサイクル
熱力学を一通り履修していても聞いたことがない人がいるかもしれない。あまり実用的でないが故、実世界で殆ど利用される事が無い少しマニアックな熱サイクルだ。実はルノアール氏が世界初の内燃機関に用いた熱サイクルであり、熱力学発展史の中では非常に重要な存在だったりする。この機に心のノートにメモ位はしておこう。
実用的ではないと述べたが、その反面、熱サイクルとして最もシンプルという特徴もある。そのため、純粋に熱サイクルについて学ぶ題材として良いし、時折シンプルさが強く求められるところで実用に供されたりもする。この記事で登場した「パルスジェットエンジン」がその例で、第2次対戦時にドイツ軍のV1飛行爆弾の発動機に使われた。
下図の通り、加熱、膨張、排熱の３プロセスからなる熱サイクルだ。オットーサイクルやディーゼルサイクル等の一般的な理論サイクルと異なり、加熱前に圧縮プロセスが無い点が最大の特徴だ。この圧縮プロセスを省いていることにより、熱効率が低い。（それ故にオットーやらディーゼルやら別の熱サイクルに取って代わられた。）
古今東西エンジン図鑑―その生い立ち・背景・技術的考察
エンジン工学 ―内燃機関の基礎と応用
pulsejet wikipediaページ
Lenoir cycle wikipediaページ
シミュレーションモデル
- 実行モデルのフルパス： FluidSystemComponents.CommonAnyFluid.Examples.Thermodynamics.LenoirCycleIdeal00_ex03
- githubのライブラリページリンク
Diagram
ルノアールサイクル1巡の計算を行うコンポーネントを新造する。今回限りのモデルを造っても良いが、inputをインターフェイスで与えられるようじして汎用性を持ったblockにする。
下図の通り、サイクル計算に必要なインプットである、流体の最初の状態量、投入熱量、流体の質量/体積をconnectorを介して与えるようになっている。また、流体の最終状態量と生成仕事を取り出せるようにoutput real connectorを備えておいた（expandable connectorを置いてあるので不要かもしれないが）。
今回のモデリングは殆ど総てがコードの直書きなので、参考としてコンポーネントのソースを次項に記しておく。コンポーネントのコードも、実行用モデルのコードも総てgithubで公開しているのだが、アイコンの外観に関する箇所などが長大で見難いので、計算に必要な変数宣言と方程式記述箇所をハイライトして示す。
ソースコード
前述した通り、物理計算に必要な変数宣言と方程式部分をハイライトする。それ以外はインターフェイスだったり、アイコン外観だったりと使い勝手に関わる箇所なので無視して頂きたい。
FluidSystemComponents.CommonAnyFluid.Thermodynamics.LenoirCycleIdeal00
本サイクルは状態が3つのみなので方程式は少ない。
——————————————————————————-
within FluidSystemComponents.CommonAnyFluid.Thermodynamics;
block LenoirCycleIdeal00
/********************************************************
imports
********************************************************/
import Modelica.Constants;
import FluidSystemComponents.Types.Switches;
import FluidSystemComponents.Utilities;
/********************************************************
Declaration
********************************************************/
/* ---------------------------------------------
Package
--------------------------------------------- */
replaceable package Medium = Modelica.Media.Interfaces.PartialMedium annotation(
choicesAllMatching = true);
/* ---------------------------------------------
Switches
--------------------------------------------- */
parameter Switches.switch_input_ThermodynamicState switch_u_thermoState = Switches.switch_input_ThermodynamicState.use_T_for_ThermodynamicState "" annotation(
Dialog(group = "switch"),
choicesAllMatching = true,
Evaluate = true,
HideResult = true);
parameter Switches.switch_input_fluidQuantity switch_u_fluidQuantity = Switches.switch_input_fluidQuantity.use_mass "" annotation(
Dialog(group = "switch"),
choicesAllMatching = true,
Evaluate = true,
HideResult = true);
/* ---------------------------------------------
parameters
--------------------------------------------- */
//********** Others **********
parameter Integer nPts_hs_par[3] = {10, 10, 10} "" annotation(
Dialog(group = "Others"),
choicesAllMatching = true,
Evaluate = true,
HideResult = false);
parameter Integer nPts_Ts_par[3] = {10, 10, 10} "" annotation(
Dialog(group = "Others"),
choicesAllMatching = true,
Evaluate = true,
HideResult = false);
parameter Integer nPts_pv_par[3] = {10, 10, 10} "" annotation(
Dialog(group = "Others"),
choicesAllMatching = true,
Evaluate = true,
HideResult = false);
parameter Integer nPts_us_par[3] = {10, 10, 10} "" annotation(
Dialog(group = "Others"),
choicesAllMatching = true,
Evaluate = true,
HideResult = false);
parameter Integer nPts_pVol_par[3] = {10, 10, 10} "" annotation(
Dialog(group = "Others"),
choicesAllMatching = true,
Evaluate = true,
HideResult = false);
//********** Initialization Parameters **********
//--- fluidState_1 ---
parameter Modelica.SIunits.Pressure p_state1_init(displayUnit = "Pa") = 101.3 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_1"));
parameter Modelica.SIunits.Temperature T_state1_init(displayUnit = "K") = 288.15 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_1"));
parameter Modelica.SIunits.SpecificEnthalpy h_state1_init(displayUnit = "J/kg") = T_state1_init * 1.004 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_1"));
parameter Modelica.SIunits.SpecificEntropy s_state_1_init = 7000.0 "" annotation(
Dialog(tab = "Initialization", group = "others"));
//--- fluidState_2 ---
parameter Modelica.SIunits.Pressure p_state2_init(displayUnit = "Pa") = 101.3 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_2"));
parameter Modelica.SIunits.Temperature T_state2_init(displayUnit = "K") = 288.15 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_2"));
parameter Modelica.SIunits.SpecificEnthalpy h_state2_init(displayUnit = "J/kg") = T_state1_init * 1.004 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_2"));
parameter Modelica.SIunits.SpecificEntropy s_state_2_init = 7000.0 "" annotation(
Dialog(tab = "Initialization", group = "others"));
//--- fluidState_3 ---
parameter Modelica.SIunits.Pressure p_state3_init(displayUnit = "Pa") = 101.3 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_3"));
parameter Modelica.SIunits.Temperature T_state3_init(displayUnit = "K") = 288.15 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_3"));
parameter Modelica.SIunits.SpecificEnthalpy h_state3_init(displayUnit = "J/kg") = T_state1_init * 1.004 * 1000 "" annotation(
Dialog(tab = "Initialization", group = "fluidState_3"));
parameter Modelica.SIunits.SpecificEntropy s_state_3_init = 8000.0 "" annotation(
Dialog(tab = "Initialization", group = "others"));
/* ---------------------------------------------
Internal variables
--------------------------------------------- */
Modelica.SIunits.SpecificEntropy s_state[3] "specific entropy, state 1" annotation(
Dialog(tab = "Variables", group = "start attribute", enable = false, showStartAttribute = true));
Modelica.SIunits.Mass massFluidCycle "mass of fluid in single cycle";
Modelica.SIunits.Volume Vol[3] "volume, state 1 - 3";
Modelica.SIunits.SpecificVolume v[3] "specific volume, state 1 - 3";
Modelica.SIunits.Heat Q_1_2 "heat injected into fluid, in process of const. vol. heat addition";
Modelica.SIunits.Heat Q_3_1 "heat rejected from fluid, in process of const. pressure heat addition";
Modelica.SIunits.Work WoutCycle "work output, single cycle";
Modelica.SIunits.Work W_2_3 "work, expansion, state 2 -> 3";
Real PR_2_1 "Pressure Ratio, P2/P1";
Real ER_3_2 "Expansion Ratio, Vol3/Vol2";
Real effThermal "Thermal efficiency";
//---
Modelica.SIunits.SpecificEnthalpy arr_h[4];
Modelica.SIunits.SpecificEnergy arr_u[4];
Modelica.SIunits.SpecificEntropy arr_s[4];
Modelica.SIunits.Pressure arr_p[4];
Modelica.SIunits.Volume arr_V[4];
Modelica.SIunits.SpecificVolume arr_v[4];
Modelica.SIunits.Temperature arr_T[4];
/* ---------------------------------------------
Internal objects
--------------------------------------------- */
Medium.BaseProperties fluidState[3](
p(start = {p_state1_init, p_state2_init, p_state3_init}, min = {0.0 + 1.0e-10,0.0 + 1.0e-10,0.0 + 1.0e-10}),
T(start = {T_state1_init, T_state2_init, T_state3_init}, min = {0.0 + 1.0e-10, 0.0 + 1.0e-10, 0.0 + 1.0e-10}),
h(start = {h_state1_init, h_state2_init, h_state3_init}, min = {0.0 + 1.0e-10, 0.0 + 1.0e-10, 0.0 + 1.0e-10}),
state(p(start= {p_state1_init, p_state2_init, p_state3_init})),
state(T(start= {T_state1_init, T_state2_init, T_state3_init}))
) "fluid states";
Utilities.arr_hs_const_p_00 curve_hs[3](redeclare package Medium = Medium, nPts_par = nPts_hs_par) annotation(
Placement(visible = true, transformation(origin = {-30, 70}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Utilities.arr_Ts_const_p_00 curve_Ts[3](redeclare package Medium = Medium, nPts_par = nPts_Ts_par) annotation(
Placement(visible = true, transformation(origin = {-30, 40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Utilities.arr_us_const_p_00 curve_us[3](redeclare package Medium = Medium, nPts_par = nPts_us_par) annotation(
Placement(visible = true, transformation(origin = {-30, 10}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Utilities.arr_pv_const_s_00 curve_pv[3](redeclare package Medium = Medium, nPts_par = nPts_pv_par) annotation(
Placement(visible = true, transformation(origin = {-30, -20}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Utilities.arr_pVol_const_s_00 curve_pVol[3](redeclare package Medium = Medium, nPts_par = nPts_pVol_par) annotation(
Placement(visible = true, transformation(origin = {-30, -50}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
/* ---------------------------------------------
Interface
--------------------------------------------- */
PropulsionSystem.Types.SubelementBus subelementBus1 annotation(
Placement(visible = true, transformation(origin = {60, 100}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {70, 100}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_p_fluidState_1(unit = "Pa", displayUnit = "Pa") annotation(
Placement(visible = true, transformation(origin = {-120, 20}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, 20}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_T_fluidState_1(unit = "K", displayUnit = "K") if switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_T_for_ThermodynamicState annotation(
Placement(visible = true, transformation(origin = {-120, -10}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -10}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_h_fluidState_1(unit = "J/kg", displayUnit = "J/kg") if switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_h_for_ThermodynamicState annotation(
Placement(visible = true, transformation(origin = {-120, -40}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_u_fluidState_1(unit = "J/kg", displayUnit = "J/kg") if switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_u_for_ThermodynamicState annotation(
Placement(visible = true, transformation(origin = {-120, -70}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -70}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_Xi_fluidState_1[Medium.nXi] annotation(
Placement(visible = true, transformation(origin = {-120, -100}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, -100}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealInput u_Qin(unit = "J", displayUnit = "J") annotation(
Placement(visible = true, transformation(origin = {-120, 80}, extent = {{-20, -20}, {20, 20}}, rotation = 0), iconTransformation(origin = {-110, 80}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
//-----
Modelica.Blocks.Interfaces.RealInput par_Vol1(unit = "m3", displayUnit = "m3") if switch_u_fluidQuantity == Switches.switch_input_fluidQuantity.use_Volume "valid if switch_u_fluidQuantity==use_volume" annotation(
Placement(visible = true, transformation(origin = {-60, 120}, extent = {{-20, -20}, {20, 20}}, rotation = -90), iconTransformation(origin = {-60, 110}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
Modelica.Blocks.Interfaces.RealInput par_massFluid(unit = "kg", displayUnit = "kg") if switch_u_fluidQuantity == Switches.switch_input_fluidQuantity.use_mass "valid if switch_u_fluidQuantity==use_mass" annotation(
Placement(visible = true, transformation(origin = {-20, 120}, extent = {{-20, -20}, {20, 20}}, rotation = -90), iconTransformation(origin = {-20, 110}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
//-----
Modelica.Blocks.Interfaces.RealOutput y_WoutCycle(unit = "J", displayUnit = "J") annotation(
Placement(visible = true, transformation(origin = {110, 80}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, 80}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealOutput y_p_fluidState_3(unit = "Pa", displayUnit = "Pa") annotation(
Placement(visible = true, transformation(origin = {110, 20}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, 20}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealOutput y_T_fluidState_3(unit = "K", displayUnit = "K") annotation(
Placement(visible = true, transformation(origin = {110, -10}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, -10}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealOutput y_Xi_fluidState_3[Medium.nXi] annotation(
Placement(visible = true, transformation(origin = {110, -100}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, -100}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealOutput y_h_fluidState_3(unit = "J/kg", displayUnit = "J/kg") annotation(
Placement(visible = true, transformation(origin = {110, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, -40}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Blocks.Interfaces.RealOutput y_u_fluidState_3(unit = "J/kg", displayUnit = "J/kg") annotation(
Placement(visible = true, transformation(origin = {110, -70}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {110, -70}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
//********************************************************************************
equation
/* ---------------------------------------------
Connections, interface - internal variables
--------------------------------------------- */
connect(curve_pVol[3].u_m, massFluidCycle);
connect(curve_pVol[3].u_Xi, fluidState[3].Xi);
connect(curve_pVol[3].u_s, s_state[3]);
connect(curve_pVol[3].u_pLower, fluidState[1].p);
connect(curve_pVol[3].u_pUpper, fluidState[3].p);
connect(curve_pVol[2].u_m, massFluidCycle);
connect(curve_pVol[2].u_Xi, fluidState[2].Xi);
connect(curve_pVol[2].u_s, s_state[2]);
connect(curve_pVol[2].u_pLower, fluidState[1].p);
connect(curve_pVol[2].u_pUpper, fluidState[2].p);
connect(curve_pVol[1].u_m, massFluidCycle);
connect(curve_pVol[1].u_Xi, fluidState[1].Xi);
connect(curve_pVol[1].u_s, s_state[1]);
connect(curve_pVol[1].u_pLower, fluidState[1].p);
connect(curve_pVol[1].u_pUpper, fluidState[2].p);
//---
connect(curve_hs[3].u_Xi, fluidState[3].Xi);
connect(curve_hs[3].u_p, fluidState[3].p);
connect(curve_hs[3].u_sUpper, s_state[2]);
connect(curve_hs[3].u_sLower, s_state[1]);
connect(curve_hs[2].u_Xi, fluidState[2].Xi);
connect(curve_hs[2].u_p, fluidState[2].p);
connect(curve_hs[2].u_sUpper, s_state[2]);
connect(curve_hs[2].u_sLower, s_state[1]);
connect(curve_hs[1].u_Xi, fluidState[1].Xi);
connect(curve_hs[1].u_p, fluidState[1].p);
connect(curve_hs[1].u_sUpper, s_state[3]);
connect(curve_hs[1].u_sLower, s_state[1]);
//---
connect(curve_pv[1].u_pUpper, fluidState[2].p);
connect(curve_pv[1].u_pLower, fluidState[1].p);
connect(curve_pv[1].u_s, s_state[1]);
connect(curve_pv[1].u_Xi, fluidState[1].Xi);
connect(curve_pv[2].u_pUpper, fluidState[2].p);
connect(curve_pv[2].u_pLower, fluidState[1].p);
connect(curve_pv[2].u_s, s_state[2]);
connect(curve_pv[2].u_Xi, fluidState[2].Xi);
connect(curve_pv[3].u_pUpper, fluidState[3].p);
connect(curve_pv[3].u_pLower, fluidState[1].p);
connect(curve_pv[3].u_s, s_state[3]);
connect(curve_pv[3].u_Xi, fluidState[3].Xi);
//---
connect(curve_Ts[3].u_Xi, fluidState[3].Xi);
connect(curve_Ts[3].u_p, fluidState[3].p);
connect(curve_Ts[3].u_sUpper, s_state[3]);
connect(curve_Ts[3].u_sLower, s_state[2]);
connect(curve_Ts[2].u_Xi, fluidState[2].Xi);
connect(curve_Ts[2].u_p, fluidState[2].p);
connect(curve_Ts[2].u_sUpper, s_state[3]);
connect(curve_Ts[2].u_sLower, s_state[2]);
connect(curve_Ts[1].u_Xi, fluidState[1].Xi);
connect(curve_Ts[1].u_p, fluidState[1].p);
connect(curve_Ts[1].u_sUpper, s_state[3]);
connect(curve_Ts[1].u_sLower, s_state[1]);
//---
connect(curve_us[3].u_Xi, fluidState[3].Xi);
connect(curve_us[3].u_p, fluidState[3].p);
connect(curve_us[3].u_sUpper, s_state[3]);
connect(curve_us[3].u_sLower, s_state[2]);
connect(curve_us[2].u_Xi, fluidState[2].Xi);
connect(curve_us[2].u_p, fluidState[2].p);
connect(curve_us[2].u_sUpper, s_state[3]);
connect(curve_us[2].u_sLower, s_state[2]);
connect(curve_us[1].u_Xi, fluidState[1].Xi);
connect(curve_us[1].u_p, fluidState[1].p);
connect(curve_us[1].u_sUpper, s_state[3]);
connect(curve_us[1].u_sLower, s_state[1]);
//--- u ---
fluidState[1].p = u_p_fluidState_1;
fluidState[1].Xi = u_Xi_fluidState_1[1:Medium.nXi];
if switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_T_for_ThermodynamicState then
fluidState[1].T = u_T_fluidState_1;
elseif switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_h_for_ThermodynamicState then
fluidState[1].h = u_h_fluidState_1;
elseif switch_u_thermoState == Switches.switch_input_ThermodynamicState.use_u_for_ThermodynamicState then
fluidState[1].u = u_u_fluidState_1;
end if;
Q_1_2 = u_Qin;
//--- par ---
if switch_u_fluidQuantity == Switches.switch_input_fluidQuantity.use_Volume then
Vol[1] = par_Vol1;
elseif switch_u_fluidQuantity == Switches.switch_input_fluidQuantity.use_mass then
massFluidCycle = par_massFluid;
end if;
//--- y ---
y_p_fluidState_3 = fluidState[3].p;
y_T_fluidState_3 = fluidState[3].T;
y_h_fluidState_3 = fluidState[3].h;
y_u_fluidState_3 = fluidState[3].u;
y_Xi_fluidState_3[1:Medium.nXi] = fluidState[3].Xi;
y_WoutCycle = WoutCycle;
/* ---------------------------------------------
Eqns describing physics
--------------------------------------------- */
massFluidCycle = Vol[1] * fluidState[1].d;
v[1] = 1.0 / fluidState[1].d;
s_state[1] = Medium.specificEntropy(fluidState[1].state);
//--- state1 - state2 ---
// const. vol. heat addition, closed system
Vol[2] = Vol[1];
fluidState[2].d = massFluidCycle / Vol[2];
v[2] = 1.0 / fluidState[2].d;
fluidState[2].Xi = fluidState[1].Xi;
Q_1_2 = massFluidCycle * (fluidState[2].u - fluidState[1].u);
s_state[2] = Medium.specificEntropy(fluidState[2].state);
PR_2_1 = fluidState[2].p / fluidState[1].p;
//--- state2 - state3 ---
// isentropic expansion, pressrue of after-expansion fixed, open system
fluidState[3].d = massFluidCycle / Vol[3];
v[3] = 1.0 / fluidState[3].d;
s_state[3] = Medium.specificEntropy(fluidState[3].state);
fluidState[3].Xi = fluidState[2].Xi;
s_state[3] = s_state[2];
W_2_3 = massFluidCycle * (fluidState[3].h - fluidState[2].h);
Vol[3] / Vol[2] = ER_3_2;
//--- state3 - state1 ---
// const. pressrue heat rejection, open system
fluidState[1].p = fluidState[3].p;
Q_3_1 = massFluidCycle * (fluidState[1].h - fluidState[3].h);
//---
WoutCycle = (-1.0) * W_2_3;
//---
if 0.0 <= u_Qin then
effThermal = WoutCycle / Q_1_2;
else
effThermal = 0.0;
end if;
//----------
for i in 1:3 loop
arr_p[i]= fluidState[i].p;
arr_h[i]= fluidState[i].h;
arr_u[i]= fluidState[i].u;
arr_T[i]= fluidState[i].T;
arr_s[i]= s_state[i];
arr_V[i]= Vol[i];
arr_v[i]= v[i];
end for;
arr_p[4]= fluidState[1].p;
arr_h[4]= fluidState[1].h;
arr_u[4]= fluidState[1].u;
arr_T[4]= fluidState[1].T;
arr_s[4]= s_state[1];
arr_V[4]= Vol[1];
arr_v[4]= v[1];
annotation(
defaultComponentName = "LenoirCycle",
Icon(graphics = {Rectangle(fillColor = {255, 255, 255}, fillPattern = FillPattern.Solid, extent = {{-100, 100}, {100, -100}}), Text(origin = {0, -80}, extent = {{-100, 10}, {100, -10}}, textString = "%name"), Bitmap(origin = {2, 10}, extent = {{-94, 78}, {86, -70}}, imageSource = 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coordinateSystem(initialScale = 0.1)));
end LenoirCycleIdeal00;
——————————————————————————-
モデル情報
シミュレーション実行
- LenoirCycle.u_Qin
- LenoirCycle.WoutCycle
- LenoirCycle.fluidState[2].T
- LenoirCycle.fluidState[2].p
- LenoirCycle.effThermal
- p-V diagram, h-s diagram
Input
途中で投入熱量を増し、生成仕事（出力）が増加することを確認する。
Variables
熱サイクルは成立し、仕事を生成出来ている。しかし、生成仕事は小さく、投入した熱量の1/10程度。意図通り、投入熱量の増大に呼応して、生成仕事が増大しているのも確認出来る。
加熱後状態（状態２）の流体温度。100 [degC] を超えているが、加熱に伴って圧力が激増しているため相変化は起きずに投入熱量に呼応して上昇している。
液体も気体同様に、加熱すると膨張する。そして、加熱を等容で行っている為、体積が増えられない代わりに圧力が上昇する（＊ただしこれは圧縮性の再現を含む物性モデルを使わないと計算出来ない筈）。そして、それを膨張させることで体積・比エンタルピに変化が生じて仕事に変換され、熱サイクルが成り立つ。
記事の結論が、液体の水だけで熱サイクルが成立する、なのだが、飽くまで「理論上は」の話。サイクル計算上成立させられても、これを現実の機器で実装させられるかは別の話となる。容器、バルブ、配管、熱交換器等がこのレベルの圧力や圧力変動に耐えられるかが問題となる。後述の熱効率が低いことも理由だが、実装の困難さも液相の水だけを用いた熱機関が実世界に存在しない理由ではないかと思う。
上述した通り、投入した熱量に対して生成出来ている熱量は非常に少なく、熱効率が非常に低い。原因は大きく2点有る。１つはルノアールサイクルが、圧縮プロセスを持たない故の特性として熱効率が低いということ。2点目が、作動流体に液体を用いているため、膨張プロセスの圧力変化が小さいということ。
y軸レンジが0から1だと見え難いが、拡大すると、投入熱量の増加に応じて熱効率が上昇しているのが確認出来る。この点は気体を用いた一般的な熱サイクルで燃焼温度を上げるほど熱効率が高くなるのと同様だ。
p-Vとh-sの軌跡を観ると、確かに上述した図と似たものとなっていることを確認できる（p-Vの形が大きく違って見えるのは、物性から決まる断熱膨張プロセスの線（等エントロピ線）の形の差異）。
最後に作動流体を空気にした場合と水にした場合を並べて観ておこう。上述した、作動流体が水であるが故に熱効率が低い点が理解出来る。
作動流体を空気にした場合との比較（上：空気、下：水）：
一瞥すると、水を用いている場合の方が仕事が多く取り出せるように見える（p-V線図に囲まれた領域がサイクルから取り出される仕事）かもしれないが、横軸方向の変化範囲に注目して頂きたい。空気の場合は膨張により体積が2倍以上に増加するのに対して、水の場合は数%程度しか増加しない。このため、投入した熱の殆どは等圧排熱プロセスで系の外に捨てられてしまい、有効な仕事として取り出される量は極めて少ない。（＊軸レンジを揃えたグラフを並べたい所だが、範囲が違い過ぎて水のサイクルの図が潰れたものになってしまう。）
h-s線図も確認。この図では、線で囲われた領域ではなく、膨張プロセスでの縦軸方向の降下量が、作動流体1 [kg] あたりの生成仕事なので、熱効率の善し悪しを比べ易い。（今回はy軸レンジを揃えており、投入熱量も揃えている。）
下図の通り、水は空気に比べて膨張プロセスの比エンタルピ落差が小さい。作動流体の物性、というより液体か気体かで生じる違いであり、ほぼ総ての熱機関で気体が使われているのはこの為だ。
後書き・まとめ
冒頭で述べた結論の繰り返しとなるが。
- 液相の流体だけを用いても熱サイクルを通じて仕事を取出す（動力を発生させる）事は出来る。最もシンプルな理想熱サイクルの計算で確認した。
- 液相流体でも可とは言っても、熱授受に応じて圧力・密度（体積）に変化が起きるという特性が必要条件。完全非圧縮性流体のパッケージを使うと計算自体回らない。
以上
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