{"id":18406,"date":"2018-08-22T18:21:07","date_gmt":"2018-08-22T18:21:07","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=18406"},"modified":"2023-02-02T08:01:31","modified_gmt":"2023-02-02T08:01:31","slug":"temperature-control-core-inlet-temperature","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/temperature-control-core-inlet-temperature\/","title":{"rendered":"Temperature Control &#8211; Core Inlet Temperature"},"content":{"rendered":"<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div>\n<figure id=\"attachment_17812\" aria-describedby=\"caption-attachment-17812\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/05\/Temperature-gradients-typical-PWR-steam-generator.png\"><img loading=\"lazy\" class=\"size-medium wp-image-17812\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/05\/Temperature-gradients-typical-PWR-steam-generator-300x212.png\" alt=\"Steam generator - counterflow heat exchanger\" width=\"300\" height=\"212\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/05\/Temperature-gradients-typical-PWR-steam-generator-300x212.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/05\/Temperature-gradients-typical-PWR-steam-generator.png 807w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-17812\" class=\"wp-caption-text\">Temperature gradients in typical PWR steam generator.<\/figcaption><\/figure>\n<p>As was written, the interfacing variable is in pressurized water reactors the core inlet temperature, which is fully determined by steam pressure inside steam generators. Note that the core inlet temperature and the steam pressure are interconnected since heat (or power) transferred across a steam generator is:<\/p>\n<p style=\"text-align: center;\"><strong>q = h . \u0394T<\/strong><\/p>\n<p>where:<\/p>\n<ul>\n<li><em>q<\/em> is the amount of heat transferred (heat flux), W\/m<sup>2,<\/sup> i.e., thermal power per unit area<\/li>\n<li><em>h<\/em> is heat transfer coefficient, W\/(m<sup>2<\/sup>.K)<\/li>\n<li>\u0394<em>T<\/em> is the difference in temperature across the steam generator (in this case, the difference between the average temperature of the reactor coolant &#8211; Tavg and the saturation temperature determined by system pressure.<\/li>\n<\/ul>\n<p>For all practical purposes, the heat transfer coefficient (h) is constant since the heat transfer coefficient is a function of the materials used in constructing the steam generator. The U-tubes are completely covered with water.<\/p>\n<figure id=\"attachment_18390\" aria-describedby=\"caption-attachment-18390\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Reactor-Control-Turbine-Control.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18390\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Reactor-Control-Turbine-Control-300x199.png\" alt=\"Reactor Control - Turbine Control\" width=\"300\" height=\"199\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Reactor-Control-Turbine-Control-300x199.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/08\/Reactor-Control-Turbine-Control.png 607w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-18390\" class=\"wp-caption-text\">Sliding Tavg and Sliding psteam Regime. The automatic system follows Tavg, set, but Tavg, the set is a function of turbine load, and it is programmed for the best performance of the entire system.<\/figcaption><\/figure>\n<p>When a reactor is in automatic control, it follows the core inlet temperature \u2013 <strong>T<sub>in<\/sub><\/strong>(or the core average temperature \u2013\u00a0<strong>T<sub>avg<\/sub><\/strong>). Note that T<sub>avg<\/sub>\u00a0= (T<sub>out<\/sub>\u00a0+ T<sub>in<\/sub>) \/ 2. When there is a difference between actual T<sub>in, actual<\/sub>\u00a0and the temperature T<sub>in, set<\/sub>, which is set in the system, the reactor control system initiates control rods movement. For example, when T<sub>in, actual<\/sub>\u00a0&gt; T<sub>in, set<\/sub>, the reactor control system automatically inserts control rods to decrease T<sub>in, actual<\/sub>. The\u00a0<strong>reactor thermal power remains constant<\/strong> because the rod&#8217;s movement only offsets the reactivity from the difference (T<sub>in, actual<\/sub>\u00a0\u2013 T<sub>in, set<\/sub>) x\u00a0<a title=\"Moderator Temperature Coefficient \u2013 MTC\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/moderator-temperature-coefficient-mtc\/\">MTC<\/a>\u00a0= moderator defect.<\/p>\n<p>On the other hand, if the energy demand in the external system increases, more energy is removed from the reactor system, causing the temperature of the reactor coolant (T<sub>in<\/sub>) to decrease. As the reactor coolant temperature decreases, positive reactivity is added, and a corresponding increase in reactor power level results. This reactor power increase occurs without any change in control rods position and without any change in boron concentration. The same inherent stability can be observed as the energy demand on the system is decreased.<\/p>\n<p>The core inlet temperature is directly given by system parameters in <a href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">steam generators<\/a>. When steam generators are operated at approximately 6.0MPa, it means the saturation temperature is equal to 275.6 \u00b0C. Since there must always be \u0394T (~15\u00b0C) between the primary circuit and the secondary circuit, the reactor coolant (in the cold leg) have about 290.6\u00b0C (at HFP) at the inlet of the core. As the system pressure increases, the core inlet temperature must also increase, and this increase causes a slight increase in fuel temperature.<\/p>\n<p>See also: <a title=\"Power Plant Control \u2013 Electric Power Control\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/power-plant-control-electric-power-control\/\">Power Plant Control<\/a><\/p>\n<p>The most significant effect of a variation in temperature upon reactor operation is the addition of positive or negative reactivity. As previously discussed, reactors are generally designed with negative temperature coefficients of reactivity (moderator and fuel temperature coefficients) as a self-limiting safety feature. A rise in reactor temperature results in the addition of negative reactivity. If the temperature rise is caused by an increase in reactor power, the negative reactivity addition slows and eventually turns the increase in reactor power. This is a highly desirable effect because it provides negative feedback in the event of an undesired power excursion.<\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Self-regulating properties of nuclear reactor<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Operating with a <strong>negative MTC<\/strong>\u00a0is\u00a0favorable operational characteristics also during\u00a0<strong>power\u00a0changes<\/strong>. There is an exact <strong>energy balance<\/strong> between the primary and secondary circuits at normal operation. Therefore when the operator decreases the load on the turbine (e.g., due to a grid requirement), the steam demand decreases (see the initial electrical output decrease in the picture). At this moment, the reactor will produce more heat than the steam turbine can consume. This<strong>\u00a0disbalance<\/strong> causes the steam pressure the saturation temperature in the steam generators increases (see II. pressure at the picture). As a result of increasing saturation temperature in the steam generators, the <strong>moderator temperature<\/strong>\u00a0will simply increase (see inlet temperature).\u00a0Increasing the temperature of the moderator adds\u00a0<strong>negative\u00a0reactivity<\/strong>, which reduces reactor power (without any operator intervention). As can be seen, to a certain extent, the reactor is <strong>self-regulating,<\/strong> and the reactor power may be controlled via the steam turbine and via grid requirements. This feature is limited because the range of allowable inlet temperatures is limited. It is power plant-specific, but in general, power changes of the order of units of % are common.\n<p>See also: <a title=\"Reactor Stability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-dynamics\/reactor-stability\/\">Reactor Stability<\/a><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14077\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min.png\" alt=\"self-regulating reactor-min\" width=\"900\" height=\"720\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min.png 900w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min-300x240.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/03\/self-regulating-reactor-min-147x118.png 147w\" sizes=\"(max-width: 900px) 100vw, 900px\" \/><\/a><\/p><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Reactor Operation<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":18387,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18406"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=18406"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18406\/revisions"}],"predecessor-version":[{"id":37022,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18406\/revisions\/37022"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18387"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=18406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}