{"id":2235,"date":"2016-03-13T15:51:12","date_gmt":"2016-03-13T15:51:12","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=2235"},"modified":"2016-03-13T15:51:12","modified_gmt":"2016-03-13T15:51:12","slug":"entropyminimizing-the-compressor-work","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/entropyminimizing-the-compressor-work\/","title":{"rendered":"ENTROPY:MINIMIZING THE COMPRESSOR WORK"},"content":{"rendered":"<div class=\"shphd6a0dcb8ad89f2\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '61e5902552e2353963d8d2f1bd1f4a8f',\n\t\t'format' : 'iframe',\n\t\t'height' : 250,\n\t\t'width' : 300,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/61e5902552e2353963d8d2f1bd1f4a8f\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.shphd6a0dcb8ad89f2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.shphd6a0dcb8ad89f2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.shphd6a0dcb8ad89f2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.shphd6a0dcb8ad89f2 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.shphd6a0dcb8ad89f2 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\">\u25a0 <b>MINIMIZIN<\/b><b>G THE COMPRESSOR WORK<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">We have just shown that the work input to a compressor is minimized when the compression process is executed in an internally reversible manner. When the changes in kinetic and potential energies are negligible, the compressor work is given by (Eq. 7\u201353)<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0228.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0228\" border=\"0\" alt=\"ENTROPY-0228\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0228_thumb.jpg\" width=\"221\" height=\"38\"><\/a><\/font> <\/p>\n<h6 align=\"justify\"><font size=\"5\">Obviously one way of minimizing the compressor work is to approach an internally reversible process as much as possible by minimizing the irreversibilities such as friction, turbulence, and nonquasi-equilibrium compression. The extent to which this can be accomplished is limited by economic considerations. A second (and more practical) way of reducing the compressor work is to keep the specific volume of the gas as small as possible during the compression process. This is done by maintaining the temperature of the gas as low as possible during compression since the specific volume of a gas is proportional to temperature. Therefore, reducing the work input to a compressor requires that the gas be cooled as it is compressed.<\/font><\/h6>\n<p align=\"justify\"><font size=\"5\">To have a better understanding of the effect of cooling during the compression process, we compare the work input requirements for three kinds of processes: <i>an isentropic process <\/i>(involves no cooling), <i>a polytropic process <\/i>(involves some cooling), and <i>an isothermal process <\/i>(involves maximum cool- ing). Assuming all three processes are executed between the same pressure levels (<i>P<\/i>1 and <i>P<\/i>2) in an internally reversible manner and the gas behaves as an ideal gas (<i>P<\/i>u = <i>RT<\/i>) with constant specific heats, we see that the compression work is determined by performing the integration in Eq. 7\u201356 for each case, with the following results:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0229.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0229\" border=\"0\" alt=\"ENTROPY-0229\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0229_thumb.jpg\" width=\"180\" height=\"187\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0230.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0230\" border=\"0\" alt=\"ENTROPY-0230\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0230_thumb.jpg\" width=\"387\" height=\"173\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The three processes are plotted on a <i>P<\/i><i>&#8211;<\/i>u diagram in Fig. 7\u201345 for the same <\/font><font size=\"5\">inlet state and exit pressure. On a <i>P-<\/i>u diagram, the area to the left of the <\/font><font size=\"5\">process curve is the integral of u <i>dP. <\/i>Thus it is a measure of the steady-flow compression work. It is interesting to observe from this diagram that of <i>P<\/i>2 the three internally reversible cases considered, the adiabatic compression<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">(<i>P<\/i>u <i>k <\/i>= constant) requires the maximum work and the isothermal compression (<i>T <\/i>= constant or <i>P<\/i>u = constant) requires the minimum. The work input requirement for the polytropic case (<i>P<\/i>u <i>n <\/i>= constant) is between these two and <\/font><font size=\"5\">decreases as the polytropic exponent <i>n <\/i>is decreased, by increasing the heat <\/font><font size=\"5\">rejection during the compression process. If sufficient heat is removed, the <\/font><font size=\"5\">value of <i>n <\/i>approaches unity and the process becomes isothermal. One common way of cooling the gas during compression is to use cooling jackets around the casing of the compressors.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Multistag<\/b><b>e Compression with Intercooling<\/b><\/font> <\/p><div class=\"gzrmc6a0dcb8ad8c18\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '0c1eb4c533eaedb7b996f49a5a4983a9',\n\t\t'format' : 'iframe',\n\t\t'height' : 300,\n\t\t'width' : 160,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/0c1eb4c533eaedb7b996f49a5a4983a9\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.gzrmc6a0dcb8ad8c18 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.gzrmc6a0dcb8ad8c18 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.gzrmc6a0dcb8ad8c18 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.gzrmc6a0dcb8ad8c18 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.gzrmc6a0dcb8ad8c18 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"phuaj6a0dcb8ad8b0f\" ><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0778475562755157\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 300x600 hydraulics-and-pneumatics -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:600px\"\n     data-ad-client=\"ca-pub-0778475562755157\"\n     data-ad-slot=\"3735577695\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.phuaj6a0dcb8ad8b0f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.phuaj6a0dcb8ad8b0f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.phuaj6a0dcb8ad8b0f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.phuaj6a0dcb8ad8b0f {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.phuaj6a0dcb8ad8b0f {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\">It is clear from these arguments that cooling a gas as it is compressed is desir<\/font><font size=\"5\">able since this reduces the required work input to the compressor. However, often it is not possible to have adequate cooling through the casing of the compressor, and it becomes necessary to use other techniques to achieve effective cooling. One such technique is <b>multistage compression with inter- cooling, <\/b>where the gas is compressed in stages and cooled between each stage by passing it through a heat exchanger called an <i>intercooler. <\/i>Ideally, the cooling process takes place at constant pressure, and the gas is cooled to the initial temperature <i>T<\/i>1 at each intercooler. Multistage compression with intercooling is especially attractive when a gas is to be compressed to very high pressures. The effect of intercooling on compressor work is graphically illustrated on <i>P-<\/i>u and <i>T-s <\/i>diagrams in Fig. 7\u201346 for a two-stage compressor. The gas is compressed in the first stage from <i>P<\/i>1 to an intermediate pressure <i>P<\/i><i>x<\/i>, cooled at constant pressure to the initial temperature <i>T<\/i>1, and compressed in the second stage to the final pressure <i>P<\/i>2. The compression processes, in general, can be modeled as polytropic (<i>P<\/i>u <i>n <\/i>= constant) where the value of <i>n <\/i>varies be- tween <i>k <\/i>and 1. The colored area on the <i>P-<\/i>u diagram represents the work saved as a result of two-stage compression with intercooling. The process paths for single-stage isothermal and polytropic processes are also shown for <\/font><font size=\"5\">comparison.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0231.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0231\" border=\"0\" alt=\"ENTROPY-0231\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0231_thumb.jpg\" width=\"194\" height=\"208\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0232.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0232\" border=\"0\" alt=\"ENTROPY-0232\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0232_thumb.jpg\" width=\"534\" height=\"191\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The size of the colored area (the saved work input) varies with the value of the intermediate pressure <i>P<\/i><i>x<\/i>, and it is of practical interest to determine the conditions under which this area is maximized. The total work input for a two- stage compressor is the sum of the work inputs for each stage of compression, as determined from Eq. 7\u201357<i>b<\/i>:<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0233.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0233\" border=\"0\" alt=\"ENTROPY-0233\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0233_thumb.jpg\" width=\"368\" height=\"132\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">That is, <i>to minimize compression work during two-stage compression, the pressure ratio across each stage of the compressor must be the same. <\/i>When this condition is satisfied, the compression work at each stage becomes identical, that is, <i>w<\/i>comp I, in = <i>w<\/i>comp II, in.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0234.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0234\" border=\"0\" alt=\"ENTROPY-0234\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0234_thumb.jpg\" width=\"373\" height=\"185\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0235.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0235\" border=\"0\" alt=\"ENTROPY-0235\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0235_thumb.jpg\" width=\"417\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0236.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"ENTROPY-0236\" border=\"0\" alt=\"ENTROPY-0236\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/ENTROPY-0236_thumb.jpg\" width=\"361\" height=\"177\"><\/a><\/font> <\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 MINIMIZING THE COMPRESSOR WORK We have just shown that the work input to a compressor is minimized when the compression process is executed in an internally reversible manner. When the changes in kinetic and potential energies are negligible, the compressor work is given by (Eq. 7\u201353) Obviously one way of minimizing the compressor work [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/entropyminimizing-the-compressor-work\/\" class=\"more-link\" >Continue reading&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2235"}],"collection":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/comments?post=2235"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2235\/revisions"}],"predecessor-version":[{"id":2236,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/2235\/revisions\/2236"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=2235"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=2235"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=2235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}