{"id":66,"date":"2017-03-09T00:51:59","date_gmt":"2017-03-09T05:51:59","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/tpps\/?post_type=chapter&#038;p=66"},"modified":"2017-11-08T12:23:36","modified_gmt":"2017-11-08T17:23:36","slug":"power-plant-efficiency","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/tpps\/chapter\/power-plant-efficiency\/","title":{"raw":"Power Plant Efficiency","rendered":"Power Plant Efficiency"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nOperate the Plant at full generating capacity and compute the Power Plant Efficiency when the plant is operating:\r\n<ul>\r\n \t<li>Under normal conditions,<\/li>\r\n \t<li>With the cooling water temperature very high (lake water temperature: 35\u00b0C),<\/li>\r\n \t<li>Without regeneration.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Theory<\/h1>\r\nExcluding hydroelectric power plants, most power generating plants employ a type of boiler and steam turbine. A schematic diagram of a simple steam power plant is shown below:\r\n\r\n[caption id=\"attachment_50\" align=\"aligncenter\" width=\"606\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle.jpg\" alt=\"Schematic diagram of a steam power plant\" width=\"606\" height=\"407\" class=\"size-full wp-image-50\" \/><\/a> Schematic diagram of a steam power plant[\/caption]\r\n\r\nHigh-pressure steam leaves the boiler and enters the turbine. The steam expands in the turbine and does work which enables the turbine to drive the electric generator. The exhaust steam leaves the turbine and enters the condenser where heat is transferred from the steam to cooling water. The pressure of the condensate leaving the condenser is increased in the pump thereby enabling the condensate to flow into the boiler. This thermodynamic cycle is known as the Rankine Cycle.\r\n<h2>The Rankine Cycle Efficiency<\/h2>\r\nAs noted above, some heat is always lost from the steam to cooling water. In addition, feed pumps consume energy thus reducing the net work output. Rankine Cycle Efficiency then can be expressed as:\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{Rankine} = \\frac{Net\\ work\\ output}{Heat\\ supplied\\ in\\ the\\ boiler}[\/latex]<\/span><\/code><\/p>\r\nor\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{Rankine} = \\frac{W_{Turbine}-W_{Pump}}{Q_{boiler}}[\/latex] <\/span><\/code><\/p>\r\n<p style=\"text-align: left\">referring to the diagram above and using the enthalpy values in the Rankine cycle, we can write:<\/p>\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{Rankine} = \\frac{(h_{1}-h_{2})-(h_{4}-h_{3})}{(h_{1}-h_{4})}[\/latex]<\/span><\/code><\/p>\r\n\r\n<h2>Improvements to the Rankine Cycle Efficiency<\/h2>\r\n<h3 style=\"text-align: left\">Effect of Pressure and Temperature on the Rankine Cycle<\/h3>\r\nIf the exhaust pressure drops from P<sub>4<\/sub> to P<sub>4<\/sub>' with the corresponding decrease in temperature at which heat is rejected in the condenser the net work is increased by area 1-4-4'-1'-2'-2-1 (see diagram below)\r\n\r\n[caption id=\"attachment_58\" align=\"aligncenter\" width=\"998\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress.jpg\" alt=\"Effect of exhaust pressure\" width=\"998\" height=\"674\" class=\"size-full wp-image-58\" \/><\/a> Effect of exhaust pressure[\/caption]\r\n\r\nIn a similar way, if the steam is superheated in the boiler, it is evident that the work is increased by area 3-3'-4'-4-3 (see diagram below):\r\n\r\n[caption id=\"attachment_60\" align=\"aligncenter\" width=\"1049\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat.jpg\" alt=\"Effect of superheating\" width=\"1049\" height=\"745\" class=\"size-full wp-image-60\" \/><\/a> Effect of superheating[\/caption]\r\n\r\nSuperheating the steam is done by increasing the time the steam is exposed to the flue gases. The result of superheating is that for a given power output, the plant using superheated steam will be of smaller size than that using dry saturated steam.\r\n<h3>The Reheat Cycle<\/h3>\r\nAbove we noted that the efficiency of the Rankine cycle is increased by superheating the steam. If metals could be found that would allow us to reach higher temperatures, the Rankine cycle could be more efficient. To improve the efficiency, the reheat cycle has been developed which is shown schematically below:\r\n\r\n[caption id=\"attachment_51\" align=\"aligncenter\" width=\"633\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat.jpg\" alt=\"Rankine Cycle with Reheat\" width=\"633\" height=\"437\" class=\"size-full wp-image-51\" \/><\/a> Rankine Cycle with Reheat[\/caption]\r\n\r\nIn this cycle, the steam is expanded to some intermediate pressure in the turbine and is then reheated in the boiler, after which it expands in the low-pressure turbine to the exhaust pressure. Rankine Cycle with reheat thermal efficiency can be expressed as:\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{thermal} = \\frac{W_{12}+W_{67}-W_{43}}{Q_{41}+Q_{26}}[\/latex] <\/span><\/code><\/p>\r\n\r\n<h3>The Regenerative Cycle<\/h3>\r\nAnother variation from the Rankine cycle is the regenerative cycle, which involves the use of feedwater heaters. During the process between states 2 and 2' the feedwater is heated and the average temperature is much lower during this process than during the vaporization process 2'-3. In other words, the average temperature at which heat is supplied in the Rankine cycle is lower than in the Carnot cycle 1'-2'-3-4-1', and consequently the efficiency of the Rankine cycle is less than that of the corresponding Carnot cycle. The relationship between Carnot cycle and Rankine cycle is shown below.\r\n\r\n[caption id=\"attachment_59\" align=\"aligncenter\" width=\"1016\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen.jpg\" alt=\"Relationship between Carnot cycle and Rankine cycle\" width=\"1016\" height=\"683\" class=\"size-full wp-image-59\" \/><\/a> Relationship between Carnot cycle and Rankine cycle[\/caption]\r\n\r\nIn the regenerative cycle, feedwater enters the boiler at some point between 2 and 2'. As a result, the average temperature at which heat is supplied is increased. A schematic of practical cycle is shown below:\r\n\r\n[caption id=\"attachment_52\" align=\"aligncenter\" width=\"1244\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen.jpg\" alt=\"Regenerative cycle\" width=\"1244\" height=\"894\" class=\"size-full wp-image-52\" \/><\/a> Regenerative cycle[\/caption]\r\n<h2>The Plant Thermal Efficiency<\/h2>\r\nIn order to calculate the overall plant thermal efficiency, we need to adjust the formulas above to incorporate heat added in the reheater sections of the boiler:\r\n<p style=\"text-align: center\"><code><span>[latex]\\eta_{thermal} = \\frac{W_{Turbines}-W_{Pumps}}{Q_{boiler}+Q_{Reheat1}+Q_{Reheat2}}[\/latex] <\/span><\/code><\/p>\r\n\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Lab Instructions<\/h3>\r\nRun the initial condition I10 230 MW_oil_auto:\r\n<ul>\r\n \t<li>Draw a T-S diagram of the Rankine cycle (not to scale) including reheat and regeneration,<\/li>\r\n \t<li>Using Trend Group Directory, collect the relevant process values,<\/li>\r\n \t<li>Calculate the overall thermal efficiency of the plant:\r\n<ul>\r\n \t<li>Under normal conditions,<\/li>\r\n \t<li>When the cooling water temperature is very high (Set the Variable List Page 0100, tag#: T00305 to 35\u00b0C),<\/li>\r\n \t<li>When all the steam extraction valves are closed (i.e. no regeneration and T00305 set to 10\u00b0C).<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 style=\"text-align: left\">Hints &amp; Tips<\/h2>\r\nIn this lab, you are essentially calculating the Rankine Cycle thermal efficiency. However, you need to take the reheat cycle into consideration and log the following tags in your trends:\r\n<ul>\r\n \t<li>Q02395 Reheater 1 transferred heat<\/li>\r\n \t<li>Q02375 Reheater 2 transferred heat<\/li>\r\n<\/ul>\r\nFor Boiler Feedwater Inlet Temperature, you may use the Startup Heat Exchanger Feedwater Outlet Temperature tag#: T02447.\r\n\r\nFor the second calculation, locate the Variable List Page 0100 as shown below:\r\n\r\n[caption id=\"attachment_44\" align=\"aligncenter\" width=\"711\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp.jpg\" alt=\"Lake water temperature setting\" width=\"711\" height=\"351\" class=\"size-full wp-image-44\" \/><\/a> Lake water temperature setting[\/caption]\r\n\r\nFor the third calculation, make sure you closed all steam extraction valves and set T00305 to 10\u00b0C:\r\n\r\n[caption id=\"attachment_45\" align=\"aligncenter\" width=\"1600\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction.jpg\" alt=\"No steam extraction\" width=\"1600\" height=\"861\" class=\"size-full wp-image-45\" \/><\/a> No steam extraction[\/caption]\r\n\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\" target=\"_blank\" rel=\"noopener\">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>T-S diagram:<\/strong> As per instructions above,<\/li>\r\n \t<li><strong>Trend plots:<\/strong> Supply all plots taken for this lab,<\/li>\r\n \t<li><strong>Computation:<\/strong> Use MATLAB or MS Excel and calculate the overall thermal efficiency of the plant as per Lab Instructions.<\/li>\r\n \t<li><span><strong>Conclusion:<\/strong> Write a summary (max. 500 words, in a text box if using Excel) comparing your results and suggestions for further study.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n\r\nFurther\u00a0Reading:\r\n<ul>\r\n \t<li>Applied Thermodynamics for Engineering Technologists by T. D. Eastop and A. McConkey: Steam Plant.<\/li>\r\n \t<li>Fundamentals of Classical Thermodynamics SI Version by G. J. Van Wylen and R. E. Sonntag: Vapor power cycles.<\/li>\r\n \t<li>Thermodynamics and Heat Power by I. Granet: Vapor power cycles.<\/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 full generating capacity and compute the Power Plant Efficiency when the plant is operating:<\/p>\n<ul>\n<li>Under normal conditions,<\/li>\n<li>With the cooling water temperature very high (lake water temperature: 35\u00b0C),<\/li>\n<li>Without regeneration.<\/li>\n<\/ul>\n<\/div>\n<h1>Theory<\/h1>\n<p>Excluding hydroelectric power plants, most power generating plants employ a type of boiler and steam turbine. A schematic diagram of a simple steam power plant is shown below:<\/p>\n<figure id=\"attachment_50\" aria-describedby=\"caption-attachment-50\" style=\"width: 606px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle.jpg\" alt=\"Schematic diagram of a steam power plant\" width=\"606\" height=\"407\" class=\"size-full wp-image-50\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle.jpg 606w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle-300x201.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle-65x44.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle-225x151.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycle-350x235.jpg 350w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/a><figcaption id=\"caption-attachment-50\" class=\"wp-caption-text\">Schematic diagram of a steam power plant<\/figcaption><\/figure>\n<p>High-pressure steam leaves the boiler and enters the turbine. The steam expands in the turbine and does work which enables the turbine to drive the electric generator. The exhaust steam leaves the turbine and enters the condenser where heat is transferred from the steam to cooling water. The pressure of the condensate leaving the condenser is increased in the pump thereby enabling the condensate to flow into the boiler. This thermodynamic cycle is known as the Rankine Cycle.<\/p>\n<h2>The Rankine Cycle Efficiency<\/h2>\n<p>As noted above, some heat is always lost from the steam to cooling water. In addition, feed pumps consume energy thus reducing the net work output. Rankine Cycle Efficiency then can be expressed as:<\/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-e08d56f85b44f5e1e806b49e63800391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#82;&#97;&#110;&#107;&#105;&#110;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#78;&#101;&#116;&#92;&#32;&#119;&#111;&#114;&#107;&#92;&#32;&#111;&#117;&#116;&#112;&#117;&#116;&#125;&#123;&#72;&#101;&#97;&#116;&#92;&#32;&#115;&#117;&#112;&#112;&#108;&#105;&#101;&#100;&#92;&#32;&#105;&#110;&#92;&#32;&#116;&#104;&#101;&#92;&#32;&#98;&#111;&#105;&#108;&#101;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"260\" style=\"vertical-align: -9px;\" \/><\/span><\/code><\/p>\n<p>or<\/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-b3fca5604f0f695d8cfe198bbbbe04b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#82;&#97;&#110;&#107;&#105;&#110;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#87;&#95;&#123;&#84;&#117;&#114;&#98;&#105;&#110;&#101;&#125;&#45;&#87;&#95;&#123;&#80;&#117;&#109;&#112;&#125;&#125;&#123;&#81;&#95;&#123;&#98;&#111;&#105;&#108;&#101;&#114;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"205\" style=\"vertical-align: -9px;\" \/> <\/span><\/code><\/p>\n<p style=\"text-align: left\">referring to the diagram above and using the enthalpy values in the Rankine cycle, we can write:<\/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-0df776718e286c9ecd3d0b4c9b192428_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#82;&#97;&#110;&#107;&#105;&#110;&#101;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#40;&#104;&#95;&#123;&#49;&#125;&#45;&#104;&#95;&#123;&#50;&#125;&#41;&#45;&#40;&#104;&#95;&#123;&#52;&#125;&#45;&#104;&#95;&#123;&#51;&#125;&#41;&#125;&#123;&#40;&#104;&#95;&#123;&#49;&#125;&#45;&#104;&#95;&#123;&#52;&#125;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"201\" style=\"vertical-align: -9px;\" \/><\/span><\/code><\/p>\n<h2>Improvements to the Rankine Cycle Efficiency<\/h2>\n<h3 style=\"text-align: left\">Effect of Pressure and Temperature on the Rankine Cycle<\/h3>\n<p>If the exhaust pressure drops from P<sub>4<\/sub> to P<sub>4<\/sub>&#8216; with the corresponding decrease in temperature at which heat is rejected in the condenser the net work is increased by area 1-4-4&#8242;-1&#8242;-2&#8217;-2-1 (see diagram below)<\/p>\n<figure id=\"attachment_58\" aria-describedby=\"caption-attachment-58\" style=\"width: 998px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress.jpg\" alt=\"Effect of exhaust pressure\" width=\"998\" height=\"674\" class=\"size-full wp-image-58\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress.jpg 998w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress-300x203.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress-768x519.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress-65x44.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress-225x152.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_ExhPress-350x236.jpg 350w\" sizes=\"auto, (max-width: 998px) 100vw, 998px\" \/><\/a><figcaption id=\"caption-attachment-58\" class=\"wp-caption-text\">Effect of exhaust pressure<\/figcaption><\/figure>\n<p>In a similar way, if the steam is superheated in the boiler, it is evident that the work is increased by area 3-3&#8242;-4&#8242;-4-3 (see diagram below):<\/p>\n<figure id=\"attachment_60\" aria-describedby=\"caption-attachment-60\" style=\"width: 1049px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat.jpg\" alt=\"Effect of superheating\" width=\"1049\" height=\"745\" class=\"size-full wp-image-60\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat.jpg 1049w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-300x213.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-768x545.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-1024x727.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-65x46.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-225x160.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Superheat-350x249.jpg 350w\" sizes=\"auto, (max-width: 1049px) 100vw, 1049px\" \/><\/a><figcaption id=\"caption-attachment-60\" class=\"wp-caption-text\">Effect of superheating<\/figcaption><\/figure>\n<p>Superheating the steam is done by increasing the time the steam is exposed to the flue gases. The result of superheating is that for a given power output, the plant using superheated steam will be of smaller size than that using dry saturated steam.<\/p>\n<h3>The Reheat Cycle<\/h3>\n<p>Above we noted that the efficiency of the Rankine cycle is increased by superheating the steam. If metals could be found that would allow us to reach higher temperatures, the Rankine cycle could be more efficient. To improve the efficiency, the reheat cycle has been developed which is shown schematically below:<\/p>\n<figure id=\"attachment_51\" aria-describedby=\"caption-attachment-51\" style=\"width: 633px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat.jpg\" alt=\"Rankine Cycle with Reheat\" width=\"633\" height=\"437\" class=\"size-full wp-image-51\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat.jpg 633w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat-300x207.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat-65x45.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat-225x155.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/RankineCycleWithReheat-350x242.jpg 350w\" sizes=\"auto, (max-width: 633px) 100vw, 633px\" \/><\/a><figcaption id=\"caption-attachment-51\" class=\"wp-caption-text\">Rankine Cycle with Reheat<\/figcaption><\/figure>\n<p>In this cycle, the steam is expanded to some intermediate pressure in the turbine and is then reheated in the boiler, after which it expands in the low-pressure turbine to the exhaust pressure. Rankine Cycle with reheat thermal efficiency can be expressed as:<\/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-ce4d0d796791048fe2c0438395c6fd27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#116;&#104;&#101;&#114;&#109;&#97;&#108;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#87;&#95;&#123;&#49;&#50;&#125;&#43;&#87;&#95;&#123;&#54;&#55;&#125;&#45;&#87;&#95;&#123;&#52;&#51;&#125;&#125;&#123;&#81;&#95;&#123;&#52;&#49;&#125;&#43;&#81;&#95;&#123;&#50;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"184\" style=\"vertical-align: -9px;\" \/> <\/span><\/code><\/p>\n<h3>The Regenerative Cycle<\/h3>\n<p>Another variation from the Rankine cycle is the regenerative cycle, which involves the use of feedwater heaters. During the process between states 2 and 2&#8242; the feedwater is heated and the average temperature is much lower during this process than during the vaporization process 2&#8242;-3. In other words, the average temperature at which heat is supplied in the Rankine cycle is lower than in the Carnot cycle 1&#8242;-2&#8242;-3-4-1&#8242;, and consequently the efficiency of the Rankine cycle is less than that of the corresponding Carnot cycle. The relationship between Carnot cycle and Rankine cycle is shown below.<\/p>\n<figure id=\"attachment_59\" aria-describedby=\"caption-attachment-59\" style=\"width: 1016px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen.jpg\" alt=\"Relationship between Carnot cycle and Rankine cycle\" width=\"1016\" height=\"683\" class=\"size-full wp-image-59\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen.jpg 1016w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen-300x202.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen-768x516.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen-65x44.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen-225x151.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/TS_Regen-350x235.jpg 350w\" sizes=\"auto, (max-width: 1016px) 100vw, 1016px\" \/><\/a><figcaption id=\"caption-attachment-59\" class=\"wp-caption-text\">Relationship between Carnot cycle and Rankine cycle<\/figcaption><\/figure>\n<p>In the regenerative cycle, feedwater enters the boiler at some point between 2 and 2&#8242;. As a result, the average temperature at which heat is supplied is increased. A schematic of practical cycle is shown below:<\/p>\n<figure id=\"attachment_52\" aria-describedby=\"caption-attachment-52\" style=\"width: 1244px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen.jpg\" alt=\"Regenerative cycle\" width=\"1244\" height=\"894\" class=\"size-full wp-image-52\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen.jpg 1244w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-300x216.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-768x552.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-1024x736.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-65x47.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-225x162.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/Regen-350x252.jpg 350w\" sizes=\"auto, (max-width: 1244px) 100vw, 1244px\" \/><\/a><figcaption id=\"caption-attachment-52\" class=\"wp-caption-text\">Regenerative cycle<\/figcaption><\/figure>\n<h2>The Plant Thermal Efficiency<\/h2>\n<p>In order to calculate the overall plant thermal efficiency, we need to adjust the formulas above to incorporate heat added in the reheater sections of the boiler:<\/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-b35c824c44ba00788affe26af7a16610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#116;&#97;&#95;&#123;&#116;&#104;&#101;&#114;&#109;&#97;&#108;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#87;&#95;&#123;&#84;&#117;&#114;&#98;&#105;&#110;&#101;&#115;&#125;&#45;&#87;&#95;&#123;&#80;&#117;&#109;&#112;&#115;&#125;&#125;&#123;&#81;&#95;&#123;&#98;&#111;&#105;&#108;&#101;&#114;&#125;&#43;&#81;&#95;&#123;&#82;&#101;&#104;&#101;&#97;&#116;&#49;&#125;&#43;&#81;&#95;&#123;&#82;&#101;&#104;&#101;&#97;&#116;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"262\" style=\"vertical-align: -9px;\" \/> <\/span><\/code><\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Lab Instructions<\/h3>\n<p>Run the initial condition I10 230 MW_oil_auto:<\/p>\n<ul>\n<li>Draw a T-S diagram of the Rankine cycle (not to scale) including reheat and regeneration,<\/li>\n<li>Using Trend Group Directory, collect the relevant process values,<\/li>\n<li>Calculate the overall thermal efficiency of the plant:\n<ul>\n<li>Under normal conditions,<\/li>\n<li>When the cooling water temperature is very high (Set the Variable List Page 0100, tag#: T00305 to 35\u00b0C),<\/li>\n<li>When all the steam extraction valves are closed (i.e. no regeneration and T00305 set to 10\u00b0C).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2 style=\"text-align: left\">Hints &amp; Tips<\/h2>\n<p>In this lab, you are essentially calculating the Rankine Cycle thermal efficiency. However, you need to take the reheat cycle into consideration and log the following tags in your trends:<\/p>\n<ul>\n<li>Q02395 Reheater 1 transferred heat<\/li>\n<li>Q02375 Reheater 2 transferred heat<\/li>\n<\/ul>\n<p>For Boiler Feedwater Inlet Temperature, you may use the Startup Heat Exchanger Feedwater Outlet Temperature tag#: T02447.<\/p>\n<p>For the second calculation, locate the Variable List Page 0100 as shown below:<\/p>\n<figure id=\"attachment_44\" aria-describedby=\"caption-attachment-44\" style=\"width: 711px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp.jpg\" alt=\"Lake water temperature setting\" width=\"711\" height=\"351\" class=\"size-full wp-image-44\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp.jpg 711w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp-300x148.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp-65x32.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp-225x111.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/LakeWaterTemp-350x173.jpg 350w\" sizes=\"auto, (max-width: 711px) 100vw, 711px\" \/><\/a><figcaption id=\"caption-attachment-44\" class=\"wp-caption-text\">Lake water temperature setting<\/figcaption><\/figure>\n<p>For the third calculation, make sure you closed all steam extraction valves and set T00305 to 10\u00b0C:<\/p>\n<figure id=\"attachment_45\" aria-describedby=\"caption-attachment-45\" style=\"width: 1600px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction.jpg\" alt=\"No steam extraction\" width=\"1600\" height=\"861\" class=\"size-full wp-image-45\" srcset=\"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction.jpg 1600w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-300x161.jpg 300w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-768x413.jpg 768w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-1024x551.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-65x35.jpg 65w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-225x121.jpg 225w, https:\/\/pressbooks.bccampus.ca\/tpps\/wp-content\/uploads\/sites\/134\/2017\/03\/NoExtraction-350x188.jpg 350w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/a><figcaption id=\"caption-attachment-45\" class=\"wp-caption-text\">No steam extraction<\/figcaption><\/figure>\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\" target=\"_blank\" rel=\"noopener\">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>T-S diagram:<\/strong> As per instructions above,<\/li>\n<li><strong>Trend plots:<\/strong> Supply all plots taken for this lab,<\/li>\n<li><strong>Computation:<\/strong> Use MATLAB or MS Excel and calculate the overall thermal efficiency of the plant as per Lab Instructions.<\/li>\n<li><span><strong>Conclusion:<\/strong> Write a summary (max. 500 words, in a text box if using Excel) comparing your results and suggestions for further study.<\/span><\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox shaded\">\n<p>Further\u00a0Reading:<\/p>\n<ul>\n<li>Applied Thermodynamics for Engineering Technologists by T. D. Eastop and A. McConkey: Steam Plant.<\/li>\n<li>Fundamentals of Classical Thermodynamics SI Version by G. J. Van Wylen and R. E. Sonntag: Vapor power cycles.<\/li>\n<li>Thermodynamics and Heat Power by I. Granet: Vapor power cycles.<\/li>\n<\/ul>\n<\/div>\n","protected":false},"author":84,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-66","chapter","type-chapter","status-publish","hentry"],"part":30,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/66","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":3,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions"}],"predecessor-version":[{"id":261,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions\/261"}],"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\/66\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/media?parent=66"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/pressbooks\/v2\/chapter-type?post=66"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/contributor?post=66"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/tpps\/wp-json\/wp\/v2\/license?post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}