{"id":28746,"date":"2013-05-21T18:39:40","date_gmt":"2013-05-21T13:09:40","guid":{"rendered":"http:\/\/www.kopykitab.com\/blog\/?p=28746"},"modified":"2013-05-21T18:39:40","modified_gmt":"2013-05-21T13:09:40","slug":"sensitivity-coefficient-formulas","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/sensitivity-coefficient-formulas\/","title":{"rendered":"Sensitivity Coefficient Formulas"},"content":{"rendered":"<h1 style=\"text-align: center;\">Sensitivity Coefficient Formulas<\/h1>\n<p><b>Sensitivity coefficient with respect to rate coefficients<\/b><\/p>\n<p>In flame calculations:<\/p>\n<p><img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_1.gif\"><\/p>\n<p>where\u00a0<span style=\"font-size: xx-small;\"><b><i>F<\/i><\/b><\/span>\u00a0is a target value.<br \/>\n<span style=\"font-size: xx-small;\"><b><i>S\u00a0<\/i><\/b><\/span>is computed by the Chemkin code.<\/p>\n<p>For non-flame calculations we use two-side finite-difference formula:<\/p>\n<p><img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_2.gif\"><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p><b>Sensitivity coefficient with respect to heats of formation<\/b><\/p>\n<p>In flame calculations:<\/p>\n<p><img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_3.gif\"><\/p>\n<p>where\u00a0<img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_5.gif\" align=\"top\">\u00a0is computed by the Chemkin code.<\/p>\n<p>For non-flame calculations:<\/p>\n<p><img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_4.gif\"><\/p>\n<p>The following temperatures were used in the calculations of sensitivity coefficient with respect to heats of formation:<\/p>\n<ul>\n<li>For shock tube and reactor experiments &#8211; initial temperature<\/li>\n<li>For low pressure flame experiments (N chemistry) &#8211; \u0005temperature at the peak of the CH or CN concentration<\/li>\n<li>For flame speeds &#8211; 1000 K<\/li>\n<\/ul>\n<p>For all calculations\u00a0<img alt=\"\" src=\"http:\/\/www.me.berkeley.edu\/gri-mech\/version30\/targets30\/wzgr\/sens_6.gif\" align=\"top\">\u00a0= 1000 cal.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sensitivity Coefficient Formulas Sensitivity coefficient with respect to rate coefficients In flame calculations: where\u00a0F\u00a0is a target value. S\u00a0is computed by the Chemkin code. For non-flame calculations we use two-side finite-difference formula: &nbsp; Sensitivity coefficient with respect to heats of formation In flame calculations: where\u00a0\u00a0is computed by the Chemkin code. For non-flame calculations: The following temperatures &#8230; <a title=\"Sensitivity Coefficient Formulas\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/sensitivity-coefficient-formulas\/\" aria-label=\"More on Sensitivity Coefficient Formulas\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[4773],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28746"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=28746"}],"version-history":[{"count":0,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28746\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=28746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=28746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=28746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}