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<li class="toctree-l1"><a class="reference internal" href="chap1_balanceEquations_Chap.html">1. Balance equations</a></li>
<li class="toctree-l1"><a class="reference internal" href="chap2_thermMachinesBasics_Chap.html">2. Thermal machines: Basics</a></li>
<li class="toctree-l1"><a class="reference internal" href="chap3_CompExpGas_Chap.html">3. Compression / Expansion of Gas and vapors</a></li>
<li class="toctree-l1"><a class="reference internal" href="chap4_ThermalEngines_Chap.html">4. Heat engines</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="chap5_ThermalGenerators_Chap.html">5. Heat pumps and refrigerators</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="chap5_1GasGenerator.html">5.1. Gas heat pump and refrigeration cycle</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">5.2. Vapor compression machines</a></li>
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<div class="section" id="vapor-compression-machines">
<h1><span class="section-number">5.2. </span>Vapor compression machines<a class="headerlink" href="#vapor-compression-machines" title="Permalink to this headline">¶</a></h1>
<p>The major part of heat pumps and refrigerators are working using phase change. During the compression, the fluid is vapor so they are named <strong>Vapor compression machines</strong>.</p>
<div class="figure align-center" id="id1">
<span id="fig-chap5-vaporcompmachine"></span><a class="reference internal image-reference" href="_images/vaporCompMachine.png"><img alt="_images/vaporCompMachine.png" src="_images/vaporCompMachine.png" style="width: 642.3px; height: 311.7px;" /></a>
<p class="caption"><span class="caption-number">Figure 5.3: </span><span class="caption-text">Vapor compression machine (Heat pump or Refrigerator) cycle.</span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
<p>Compared to the <em>reverse Hirn cycle</em>, the differences are:</p>
<blockquote>
<div><ul class="simple">
<li><p>In the compressor (generally a reciprocating compressor with piston), liquid may not be admitted. Point 1 shoul be at least saturated vapor.</p></li>
<li><p>The energy that can be obtained by using an expansion machine in transformation 3-4 is low compared to those necessary to compress vapor during transformation 1-2. Thus, it is replaced by a simple expansion valve (throttle valve) where the expansion becomes at constant enthalpy. This process is called <strong>laminating</strong> (<a class="reference internal" href="chap1_3Applications.html#sec-chap1-laminating"><span class="std std-numref">Section 1.2.4: </span></a>).</p></li>
</ul>
</div></blockquote>
<p>As for any heat pump or refrigerator, (<a class="reference internal" href="chap2_2Cycles.html#equation-copr">Eq.2.11</a>, and <a class="reference internal" href="chap2_2Cycles.html#equation-cophp">Eq.2.10</a>) the <em>coefficients of performance</em> of <em>vapor compression machines</em> are:</p>
<div class="math">
<p><img src="_images/math/661277aa5c05e611d04f3ca306f1a91b7c2b0b9f.svg" alt="COP_{R} = \frac{1}{\frac{|q_{23}|}{|q_{41}|}-1} \qquad \text{and} \qquad COP_{HP} = \frac{1}{1-\frac{|q_{41}|}{|q_{23}|}}"/></p>
</div><p>Because no machine is working in transformations 2-3 and 4-1, application of the balance energy equation reads:</p>
<div class="math">
<p><img src="_images/math/07d5403fa99940a303dc196b130450eef1966fdb.svg" alt="|q_{23}| = \dot{m} (h_3-h_2) \qquad \text{ and } \qquad |q_{41}| = \dot{m} (h_4-h_1)"/></p>
</div><p>such that the thermal efficiency of <em>vapor compression machines</em> becomes:</p>
<div class="math" id="equation-copvaporcompmach">
<p><span class="eqno">(5.2)<a class="headerlink" href="#equation-copvaporcompmach" title="Permalink to this equation">¶</a></span><img src="_images/math/a355e8f6f0cc975b0e74ce61d202321e8d37802b.svg" alt="COP_{R} = \frac{1}{\frac{h_2-h_3}{h_1-h_4}-1} \qquad \text{and} \qquad COP_{HP} = \frac{1}{1-\frac{h_1-h_4}{h_2-h_3}}"/></p>
</div><div class="admonition caution">
<p class="admonition-title">Caution</p>
<p>The fluid can not be considered as an <strong>ideal gas</strong> since a phase change occurs from liquid to vapor and reversely. In practice calculs are performed thanks to <em>thermodynamics tables</em>.</p>
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