{"id":64,"date":"2017-03-09T00:38:05","date_gmt":"2017-03-09T05:38:05","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/tpps\/?post_type=chapter&#038;p=64"},"modified":"2017-11-07T12:46:19","modified_gmt":"2017-11-07T17:46:19","slug":"turbine-efficiency","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/tpps\/chapter\/turbine-efficiency\/","title":{"raw":"Turbine Efficiency","rendered":"Turbine Efficiency"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nOperate the Plant at the following generating capacities to compute the isentropic change in enthalpy and thermal efficiency for the HP turbine.\r\n<ul>\r\n \t<li>35% Load (I13),<\/li>\r\n \t<li>80% Load (I14),<\/li>\r\n \t<li>230 MW (I10).<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Theory<\/h1>\r\nRecall from the First and Second Law of Thermodynamics that the adiabatic process where entropy remains constant provides the maximum energy for work. As shown on the H-S coordinates, the difference in enthalpy, (H<sub>1<\/sub>-H<sub>2<\/sub>), is maximum when the lowest enthalpy (H<sub>2<\/sub>) is reached at the exit conditions. The ideal expansion is, therefore, a vertical line.\r\n\r\n[caption id=\"attachment_154\" align=\"aligncenter\" width=\"2525\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram.jpg\" alt=\"Turbine efficiency.\" class=\"size-full wp-image-154\" height=\"2005\" width=\"2525\" \/><\/a> Turbine efficiency.[\/caption]\r\n\r\nOn the diagram above, T<sub>1<\/sub>, P<sub>1<\/sub> and P<sub>2<\/sub> are known process variables, for example, H<sub>1<\/sub> is determined by using T<sub>1<\/sub> and P<sub>1<\/sub>. H<sub>2<\/sub> then can be found drawing a vertical line from P<sub>1<\/sub> to P<sub>2<\/sub> by following adiabatic isentropic expansion (expansion at constant entropy).\r\n\r\nNon-ideal processes or real processes, however, do not present straight lines as shown on the Mollier diagram due to such factors as friction. If the expansion is not isentropic (i.e. entropy is not constant but it increases), the lowest enthalpy (H<sub>2<\/sub>) cannot be reached at the exit conditions, in other words, H<sub>2\u2019<\/sub> &gt; H<sub>2<\/sub>. This means that \u0394H for the ideal expansion is greater than\u00a0\u0394H for the non-ideal expansion between the same pressure boundaries. The internal turbine efficiency is therefore given by:\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{Turbine} = \\frac{Actual\\ change\\ in\\ enthalpy}{Isentropic\\ change\\ in\\ enthalpy}[\/latex]<\/span><\/code><\/p>\r\n<p style=\"text-align: center\">[latex]\\eta_{Turbine} = \\frac{(H_{1}-H_{2\\prime})}{(H_{1}-H_{2})}[\/latex]<\/p>\r\nThe difference in enthalpy H<sub>2\u2019<\/sub>-H<sub>2<\/sub> is called the reheat factor and is the basis for multi-stage turbines. As can be seen on the Mollier diagram, the pressure curves are divergent. This means that the higher the pressure drop in a single stage turbine the greater the reheat factor and in turn the lower the turbine efficiency. However, if the steam is expanded through multiple stages and between each stage the steam is reheated, higher turbine efficiencies can be achieved. We will see this effect later in the <a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/chapter\/power-plant-efficiency\/\" target=\"_blank\" rel=\"noopener\">Power Plant Efficiency<\/a> lab.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Lab Instructions<\/h3>\r\n<span itemscope=\"\" itemtype=\"http:\/\/schema.org\/WebPage\"><\/span>You will run 3 different initial conditions in this lab:\r\n<ul>\r\n \t<li>35% Load (I13),<\/li>\r\n \t<li>80% Load (I14),<\/li>\r\n \t<li>230 MW (I10).<\/li>\r\n<\/ul>\r\nFor each condition collect the relevant data to compute the isentropic change in enthalpy for the HP turbine. Compare your results, which of the three conditions yield the most favourable results and why?\r\n\r\n<\/div>\r\n<h2 style=\"text-align: left\">Hints &amp; Tips<\/h2>\r\nIn addition to various pressure and temperature values; log the following tags in your trends:\r\n<ul>\r\n \t<li>Z03020<\/li>\r\n \t<li>E03018<\/li>\r\n<\/ul>\r\nTo calculate the enthalpy values, you may use an app or online tool such as the Superheated Steam Table: <a href=\"https:\/\/goo.gl\/GdVM4U\">https:\/\/goo.gl\/GdVM4U<\/a>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Deliverables<\/h3>\r\nYour lab report is to include the following:\r\n<ul>\r\n \t<li><strong>Trend plots:<\/strong> Supply all plots taken for each of the 3 conditions,<\/li>\r\n \t<li><strong>Computation:<\/strong> Use MATLAB or MS Excel and calculate the turbine efficiency for the 3 conditions specified,<\/li>\r\n \t<li><strong>Conclusion:<\/strong> Write a summary (max. 500 words, in a text box if using Excel) comparing your results and suggestions for further study.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n\r\nFurther Reading:\r\n<ul>\r\n \t<li><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/WebPage\">Thermodynamics and Heat Power by I. Granet: Vapor power cycles.<\/span><\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>Operate the Plant at the following generating capacities to compute the isentropic change in enthalpy and thermal efficiency for the HP turbine.<\/p>\n<ul>\n<li>35% Load (I13),<\/li>\n<li>80% Load (I14),<\/li>\n<li>230 MW (I10).<\/li>\n<\/ul>\n<\/div>\n<h1>Theory<\/h1>\n<p>Recall from the First and Second Law of Thermodynamics that the adiabatic process where entropy remains constant provides the maximum energy for work. As shown on the H-S coordinates, the difference in enthalpy, (H<sub>1<\/sub>-H<sub>2<\/sub>), is maximum when the lowest enthalpy (H<sub>2<\/sub>) is reached at the exit conditions. The ideal expansion is, therefore, a vertical line.<\/p>\n<figure id=\"attachment_154\" aria-describedby=\"caption-attachment-154\" style=\"width: 2525px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram.jpg\" alt=\"Turbine efficiency.\" class=\"size-full wp-image-154\" height=\"2005\" width=\"2525\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram.jpg 2525w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-300x238.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-768x610.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-1024x813.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-65x52.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-225x179.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/HSDiagram-350x278.jpg 350w\" sizes=\"auto, (max-width: 2525px) 100vw, 2525px\" \/><\/a><figcaption id=\"caption-attachment-154\" class=\"wp-caption-text\">Turbine efficiency.<\/figcaption><\/figure>\n<p>On the diagram above, T<sub>1<\/sub>, P<sub>1<\/sub> and P<sub>2<\/sub> are known process variables, for example, H<sub>1<\/sub> is determined by using T<sub>1<\/sub> and P<sub>1<\/sub>. H<sub>2<\/sub> then can be found drawing a vertical line from P<sub>1<\/sub> to P<sub>2<\/sub> by following adiabatic isentropic expansion (expansion at constant entropy).<\/p>\n<p>Non-ideal processes or real processes, however, do not present straight lines as shown on the Mollier diagram due to such factors as friction. If the expansion is not isentropic (i.e. entropy is not constant but it increases), the lowest enthalpy (H<sub>2<\/sub>) cannot be reached at the exit conditions, in other words, H<sub>2\u2019<\/sub> &gt; H<sub>2<\/sub>. This means that \u0394H for the ideal expansion is greater than\u00a0\u0394H for the non-ideal expansion between the same pressure boundaries. The internal turbine efficiency is therefore given by:<\/p>\n<p style=\"text-align: center\"><code><span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/ql-cache\/quicklatex.com-c20fe687af24aa75e46600c429a793ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#84;&#117;&#114;&#98;&#105;&#110;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#99;&#116;&#117;&#97;&#108;&#92;&#32;&#99;&#104;&#97;&#110;&#103;&#101;&#92;&#32;&#105;&#110;&#92;&#32;&#101;&#110;&#116;&#104;&#97;&#108;&#112;&#121;&#125;&#123;&#73;&#115;&#101;&#110;&#116;&#114;&#111;&#112;&#105;&#99;&#92;&#32;&#99;&#104;&#97;&#110;&#103;&#101;&#92;&#32;&#105;&#110;&#92;&#32;&#101;&#110;&#116;&#104;&#97;&#108;&#112;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"276\" style=\"vertical-align: -9px;\" \/><\/span><\/code><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/ql-cache\/quicklatex.com-a683b9fa824f340250deb4744a5aba72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#84;&#117;&#114;&#98;&#105;&#110;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#40;&#72;&#95;&#123;&#49;&#125;&#45;&#72;&#95;&#123;&#50;&#92;&#112;&#114;&#105;&#109;&#101;&#125;&#41;&#125;&#123;&#40;&#72;&#95;&#123;&#49;&#125;&#45;&#72;&#95;&#123;&#50;&#125;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"147\" style=\"vertical-align: -9px;\" \/><\/p>\n<p>The difference in enthalpy H<sub>2\u2019<\/sub>-H<sub>2<\/sub> is called the reheat factor and is the basis for multi-stage turbines. As can be seen on the Mollier diagram, the pressure curves are divergent. This means that the higher the pressure drop in a single stage turbine the greater the reheat factor and in turn the lower the turbine efficiency. However, if the steam is expanded through multiple stages and between each stage the steam is reheated, higher turbine efficiencies can be achieved. We will see this effect later in the <a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/chapter\/power-plant-efficiency\/\" target=\"_blank\" rel=\"noopener\">Power Plant Efficiency<\/a> lab.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Lab Instructions<\/h3>\n<p><span itemscope=\"itemscope\" itemtype=\"http:\/\/schema.org\/WebPage\"><\/span>You will run 3 different initial conditions in this lab:<\/p>\n<ul>\n<li>35% Load (I13),<\/li>\n<li>80% Load (I14),<\/li>\n<li>230 MW (I10).<\/li>\n<\/ul>\n<p>For each condition collect the relevant data to compute the isentropic change in enthalpy for the HP turbine. Compare your results, which of the three conditions yield the most favourable results and why?<\/p>\n<\/div>\n<h2 style=\"text-align: left\">Hints &amp; Tips<\/h2>\n<p>In addition to various pressure and temperature values; log the following tags in your trends:<\/p>\n<ul>\n<li>Z03020<\/li>\n<li>E03018<\/li>\n<\/ul>\n<p>To calculate the enthalpy values, you may use an app or online tool such as the Superheated Steam Table: <a href=\"https:\/\/goo.gl\/GdVM4U\">https:\/\/goo.gl\/GdVM4U<\/a><\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Deliverables<\/h3>\n<p>Your lab report is to include the following:<\/p>\n<ul>\n<li><strong>Trend plots:<\/strong> Supply all plots taken for each of the 3 conditions,<\/li>\n<li><strong>Computation:<\/strong> Use MATLAB or MS Excel and calculate the turbine efficiency for the 3 conditions specified,<\/li>\n<li><strong>Conclusion:<\/strong> Write a summary (max. 500 words, in a text box if using Excel) comparing your results and suggestions for further study.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox shaded\">\n<p>Further Reading:<\/p>\n<ul>\n<li><span itemscope=\"itemscope\" itemtype=\"http:\/\/schema.org\/WebPage\">Thermodynamics and Heat Power by I. Granet: Vapor power cycles.<\/span><\/li>\n<\/ul>\n<\/div>\n","protected":false},"author":84,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-64","chapter","type-chapter","status-publish","hentry"],"part":30,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/64","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/users\/84"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/64\/revisions"}],"predecessor-version":[{"id":259,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/64\/revisions\/259"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/parts\/30"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/64\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/media?parent=64"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapter-type?post=64"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/contributor?post=64"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/license?post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}