{"id":20871,"date":"2019-01-21T17:18:08","date_gmt":"2019-01-21T17:18:08","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20871"},"modified":"2023-02-18T08:36:09","modified_gmt":"2023-02-18T08:36:09","slug":"boiling-crisis-critical-heat-flux","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/boiling-crisis-critical-heat-flux\/","title":{"rendered":"Boiling Crisis &#8211; Critical Heat Flux"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">The\u00a0<strong>nucleate boiling heat flux<\/strong> cannot be increased indefinitely. At some value, we call it the \u201c<strong>critical heat flux<\/strong>\u201d, the steam produced can form an insulating layer over the surface, which in turn deteriorates the heat transfer coefficient. Dynamic changes of boiling regime associated with exceeding the critical heat flux are widely known as \u201cboiling crisis\u201d.<\/div><\/div>\n<p>This chapter will study <strong>flow boiling<\/strong> in a vertical heated channel. The boiling and heat flux curve regimes are similar (not the same) as those in <a title=\"Pool Boiling \u2013 Boiling Curve\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/pool-boiling-boiling-curve\/\"><strong>pool boiling<\/strong><\/a>. The process also occurs in modern high-pressure forced circulation boilers.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20779\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes-208x300.png\" alt=\"Boiling Curve - Boiling Modes\" width=\"208\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes-208x300.png 208w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes.png 601w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/><\/a>The pioneering work on pool boiling was done in 1934 by\u00a0<strong>S. Nukiyama<\/strong>, who used electrically heated nichrome and platinum wires immersed in liquids in his experiments. Nukiyama was the first to identify <strong>different regimes of pool boiling<\/strong> using his apparatus. He noticed that boiling takes different forms, depending on the value of the wall superheat temperature\u00a0<strong>\u0394T<\/strong><strong><sub>sat<\/sub><\/strong> (also known as the excess temperature)<strong>, <\/strong>defined as the difference between the wall temperature,\u00a0<strong>T<sub>wall<\/sub><\/strong>, and the saturation temperature,<strong>\u00a0T<sub>sat<\/sub><\/strong>.<\/p>\n<p>Four different boiling regimes \u00a0of pool boiling (based on the excess temperature) are observed:<\/p>\n<ul>\n<li><strong>Natural Convection Boiling<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0<strong>\u0394T<\/strong><strong><sub>sat<\/sub><\/strong>\u00a0&lt; 5\u00b0C<\/li>\n<li><strong>Nucleate Boiling<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a05\u00b0C &lt;\u00a0<strong>\u0394T<\/strong><strong><sub>sat<\/sub><\/strong>\u00a0&lt; 30\u00b0C<\/li>\n<li><strong>Transition Boiling<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a030\u00b0C &lt;\u00a0<strong>\u0394T<\/strong><strong><sub>sat<\/sub><\/strong>\u00a0&lt; 200\u00b0C<\/li>\n<li><strong>Film Boiling<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 200\u00b0C &lt;\u00a0<strong>\u0394T<\/strong><strong><sub>sat<\/sub><\/strong><\/li>\n<\/ul>\n<p>These regimes are illustrated on the\u00a0<strong>boiling curve<\/strong>\u00a0in the figure, which is a plot of\u00a0<a title=\"Heat Flux Density \u2013 Thermal Flux\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/heat-flux-density-thermal-flux\/\">heat flux\u00a0<\/a>versus the excess temperature. Although the boiling curve given in this figure is for water, the general shape of the boiling curve remains the same for different coolants. Note that the specific shape of the curve also depends on the system parameters, such as the <a title=\"What is Pressure \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">pressure<\/a> and coolant flow rate. Still, it is practically independent of the geometry of the heating surface. The curve will be different for flow boiling as in the fuel channel, but major results will be similar.<\/p>\n<p><strong>In\u00a0<\/strong><a href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\"><strong>BWRs<\/strong><\/a>, coolant boiling occurs at\u00a0<strong>normal operation,<\/strong> and it is a very desired phenomenon. Typical<strong>\u00a0flow qualities<\/strong>\u00a0in\u00a0<a href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\"><strong>BWR cores<\/strong><\/a>\u00a0are on the order of 10 to 20 %.<\/p>\n<p>Although the earliest core designs assumed that surface boiling could not be allowed in\u00a0<a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\"><strong>PWRs<\/strong><\/a>, this assumption was soon rejected. Two-phase heat transfer is now one of the normal operation heat transfer mechanisms in PWRs.<\/p>\n<p>In both designs, the\u00a0<strong>nucleate boiling heat flux<\/strong> cannot be increased indefinitely. We call it the \u201c<strong>critical heat flux<\/strong>\u201d (<strong>CHF<\/strong>) at some value. The steam produced can form an insulating layer over the surface, deteriorating the heat transfer coefficient. Dynamic changes of boiling regime associated with exceeding the critical heat flux are widely known as \u201cboiling crisis\u201d.<\/p>\n<p>The\u00a0<strong>boiling crisis<\/strong>\u00a0can be classified as:<\/p>\n<ul>\n<li><strong>dry-out<\/strong>\u00a0(will be described below DNB) in the high-quality region<\/li>\n<li><strong>departure from nucleate boiling (DNB)<\/strong>\u00a0in the subcooled or low-quality region (approximate quality range: from \u20135% to +5%).<\/li>\n<\/ul>\n<p>But the\u00a0<strong>critical heat flux<\/strong>\u00a0is used for both regimes.<\/p>\n<p>Note that the opposite phenomenon to DNB is known as <strong>return to nucleate boiling (RNB)<\/strong> and occurs at point D, known as the <a title=\"Leidenfrost Effect \u2013 Leidenfrost Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/leidenfrost-effect-leidenfrost-point\/\">Leidenfrost point<\/a>.<\/p>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Critical Heat Flux<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-14862\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min-225x300.png\" alt=\"Dryout vs. DNB\" width=\"225\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min-225x300.png 225w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min.png 683w\" sizes=\"(max-width: 225px) 100vw, 225px\" \/><\/a>As was written, in <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/what-is-nuclear-reactor\/\">nuclear reactors<\/a>, limitations of the <strong>local heat flux<\/strong> are of the highest importance for reactor safety. There are thermal-hydraulic phenomena for <a href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">pressurized water reactors<\/a> and <a href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\">boiling water reactors<\/a>, which cause a sudden decrease in <strong>heat transfer efficiency<\/strong>\u00a0(more precisely in the <strong>heat transfer coefficient<\/strong>). These phenomena occur at a certain value of heat flux, known as the \u201c<strong>critical heat flux<\/strong>\u201d. The phenomena that cause heat transfer deterioration are different for PWRs and BWRs.<\/p>\n<p>In both types of reactors, the problem is more or less associated with departure from nucleate boiling. The nucleate boiling heat flux cannot be increased indefinitely, and we call it the \u201c<strong>critical heat flux<\/strong>\u201d (<strong>CHF<\/strong>) at some value. The steam produced can form an insulating layer over the surface, deteriorating the heat transfer coefficient. Immediately after the critical heat flux has been reached, boiling becomes unstable, and film boiling occurs. The transition from nucleate boiling to film boiling is known as the \u201c<strong>boiling crisis<\/strong>\u201d. As was written, the phenomena that cause heat transfer deterioration are different for PWRs and BWRs.<\/p>\n<h2>Departure From Nucleate Boiling &#8211; DNB<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20775\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio-289x300.png\" alt=\"DNBR - Departure from Nucleate Boiling Ratio\" width=\"289\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio-289x300.png 289w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio.png 682w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/a>In the case of <a href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a>, the critical safety issue is named <strong>DNB<\/strong> (<strong>departure from nucleate boiling<\/strong>), which causes the formation of a <strong>local vapor layer<\/strong>, causing a dramatic reduction in heat transfer capability. This phenomenon occurs in the subcooled or low-quality region. The behavior of the boiling crisis depends on many flow conditions (pressure, temperature, flow rate). Still, the boiling crisis occurs at relatively high heat fluxes and appears to be associated with the cloud of bubbles adjacent to the surface. These bubbles or films of vapor reduce the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat <strong>accumulates <\/strong>in the fuel rod, causing the <strong>dramatic rise<\/strong> of cladding and fuel <strong>temperature<\/strong>. Simply, a very high-temperature difference is required to transfer the critical heat flux being produced from the surface of the fuel rod to the reactor coolant (through the vapor layer).<\/p>\n<p>In the case of PWRs, the critical flow is <strong>inverted annular flow<\/strong>, while in BWRs, the critical flow is usually annular flow. The difference in flow regime between post-dry-out flow and post-DNB flow is depicted in the figure. In <strong>PWRs<\/strong> at <strong>normal operation,<\/strong> the flow is considered to be single-phase. But a great deal of study has been performed on the nature of <strong>two-phase flow<\/strong> in case of <strong>transients and accidents<\/strong> (such as the<strong> loss-of-coolant accident \u2013 LOCA or trip of RCPs<\/strong>), which are of importance in reactor safety and in must be proved and declared in the <strong>Safety Analysis Report<\/strong> (SAR).<\/p>\n<p>One of the key safety requirements of pressurized water reactors is that a departure from nucleate boiling (DNB) will not occur during steady-state operation, normal operational transients, and anticipated operational occurrences (AOOs). Fuel cladding integrity will be maintained if the minimum DNBR remains above the 95\/95 DNBR limit for PWRs ( a 95% probability at a 95% confidence level). DNB criterion is one of the acceptance criteria in safety analyses as well as it constitutes one of the safety limits in technical specifications.<\/p>\n<p>An important duty of the plant operator is to control plant parameters such that a <strong>safe margin to DNB<\/strong> (or distance from DNB on the heat transfer curve) is maintained. Any sudden, large change in the following plant parameters\/directions will decrease the margin to DNB:<\/p>\n<ul>\n<li><strong>Decrease in reactor coolant pressure<\/strong><\/li>\n<li><strong>Decrease in reactor coolant flow rate<\/strong><\/li>\n<li><strong>Increase in reactor power<\/strong><\/li>\n<li><strong>Increase in reactor coolant inlet temperature<\/strong><\/li>\n<\/ul>\n<p>Therefore, the function of the operators and the plant design is to prevent a sudden, large change in these plant parameters.<\/p>\n<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>Heat Flux Limitations in Nuclear Reactors<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Nuclear reactors produce <strong>enormous amount of heat<\/strong> (energy) in a <strong>small volume<\/strong>. The density of the energy generation is<strong> very large,<\/strong> which puts demands on its heat transfer system (reactor coolant system). For a reactor to operate in a steady-state, all of the heat released in the system must be removed <strong>as fast as it is produced<\/strong>. This is accomplished by passing a liquid or ga搜索引擎优化us coolant through the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\"><strong>core<\/strong><\/a> and through other regions where heat is generated. The heat transfer must be equal to or greater than the heat generation rate or overheating, and possible damage to the fuel may occur.<\/p>\n<p>The temperature in an operating reactor varies from point to point within the system. Consequently, there is always <strong>one fuel rod<\/strong> and <strong>one local volume<\/strong> <strong>hotter<\/strong> than all others. Peak power limits must be introduced to limit these hot places. The peak power limits are associated with such phenomena as the departure from nucleate boiling and the conditions that could cause fuel pellet melt.<\/p>\n<p>Therefore power distribution within the core must be properly limited. These limitations are usually divided into two basic categories:<\/p>\n<ul>\n<li><strong>Limitation of global power distribution<\/strong>\n<ul>\n<li><a title=\"Axial Flux Difference \u2013 Axial Offset Control\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/axial-flux-difference-axial-offset-control\/\"><strong>Axial flux difference<\/strong><\/a><\/li>\n<li><a title=\"Power Tilt \u2013 Flux Tilt \u2013 Quadrant \u2013 Sextant Symmetry\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/power-tilt-flux-tilt-quadrant-sextant-symmetry\/\"><strong>Power tilt<\/strong><\/a><\/li>\n<\/ul>\n<\/li>\n<li><strong>Limitation of local power distribution<\/strong>\n<ul>\n<li><a title=\"Heat Flux Hot Channel Factor \u2013 FQ(z)\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/heat-flux-hot-channel-factor-fqz\/\"><strong>Local Heat Flux<\/strong><\/a><\/li>\n<li><a title=\"Nuclear Enthalpy Rise Hot Channel Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/nuclear-enthalpy-rise-hot-channel-factor\/\"><strong>Enthalpy Rise in Hot Channel<\/strong><\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n<h2>Critical Heat Flux for DNB &#8211; Correlations<\/h2>\n<p>As was written, the <strong>boiling crisis<\/strong> can be classified as<strong> dry-out<\/strong> (will be described below DNB) in the high-quality region and <strong>departure from nucleate boiling (DNB)<\/strong> in the subcooled or low-quality region (approximate quality range: from \u20135% to +5%). But the <strong>critical heat flux<\/strong> is used for both regimes.<\/p>\n<h3>DNB &#8211; W-3 Correlation<\/h3>\n<p>One of the most well-known design correlations for predicting <strong>departure from nucleate boiling<\/strong> is the <strong>W-3 correlation<\/strong> developed at the <strong>Westinghouse Atomic Power Division by Tong<\/strong>. It is applicable for subcooled and low to moderate quality flows. The <strong>W-3 correlation<\/strong> is a function of coolant <a title=\"What is Enthalpy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\">enthalpy<\/a> (saturated and inlet), <a title=\"What is Pressure \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">pressure<\/a>, <a title=\"Vapor Quality \u2013 Dryness Fraction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/vapor-quality-dryness-fraction\/\">quality<\/a>, and coolant mass flux:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20791\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png\" alt=\"CHF - Critical Heat Flux - Correlation\" width=\"489\" height=\"46\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png 489w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation-300x28.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/a><\/p>\n<p>The correlation W-3 is for critical heat flux in uniformly heated channels. To account for non-uniform heat fluxes, Tong introduced the correction factor, F.<\/p>\n<p>Special Reference: Tong, L. S., Weisman, Joel. Thermal Analysis of Pressurized Water Reactors. Amer Nuclear Society, 3rd edition, 5\/1996. ISBN-13: 978-0894480386.<\/p>\n<h3>Cold Wall Factor &#8211; CWF<\/h3>\n<p>Tong, L. S., and Weisman, Joel also introduce a new factor known as the \u201c<strong>cold wall factor<\/strong>\u201d, which corrects CHF in a channel containing an unheated wall (e.g., channel adjacent to control rod guide tube). In these channels, the liquid film builds up along the cold wall, and this fluid is not effective in cooling the heated surface. The fluid cooling the heated surface is at higher enthalpy than calculated without the assumption of a cold wall. Note that there is an assumption that cold wall deteriorates heat transfer compared to channel with all sides heated at the <strong>same bulk exit enthalpy<\/strong>.<\/p>\n<h3>CHF Look-up Tables<\/h3>\n<p><strong>CHF look-up tables<\/strong> are used widely to predict the critical heat flux (CHF). The CHF look-up table is a normalized data bank for a vertical 8 mm water-cooled tube. The 2006 CHF look-up table is based on a database containing more than 30,000 data points, and they cover the ranges of 0.1\u201321 Mpa pressure, 0\u20138000 kg.m<sup>\u20132<\/sup>.s<sup>-1<\/sup> (zero flow refers to pool-boiling conditions) mass flux and \u20130.5 to 1 vapor quality (negative qualities refer to subcooled conditions).<\/p>\n<p>Special Reference: GROENEVELD, D.C. et al., The 2006 look-up table, Nuclear Engineering and Design 237 (2007), 1909\u20131922.<\/p>\n<h2>Departure from Nucleate Boiling Ratio &#8211; DNBR<\/h2>\n<p>As was written, in the case of <a href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a>, the critical safety issue is named <strong>DNB<\/strong> (<strong>departure from nucleate boiling<\/strong>), which causes the formation of a <strong>local vapor layer<\/strong>, causing a dramatic reduction in heat transfer capability. Note that the DNB-risk must be considered even for BWRs, which have a significantly bottom-peaked axial power profile.<\/p>\n<p>DNB occurs when the local heat flux reaches a value of critical heat flux. This phenomenon occurs in the subcooled or low-quality region (approximate quality range: from \u20135% to +5%). The behavior of this type of boiling crisis depends on many flow conditions (pressure, temperature, flow rate) since the critical heat flux is generally a function\u00a0 of coolant <a title=\"What is Enthalpy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-enthalpy\/\">enthalpy<\/a>\u00a0(saturated and inlet),\u00a0<a title=\"What is Pressure \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">pressure<\/a>,\u00a0<a title=\"Vapor Quality \u2013 Dryness Fraction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/vapor-quality-dryness-fraction\/\">quality<\/a>,\u00a0and coolant mass flux:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20791\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png\" alt=\"CHF - Critical Heat Flux - Correlation\" width=\"489\" height=\"46\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation.png 489w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/CHF-Critical-Heat-Flux-Correlation-300x28.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/a><\/p>\n<p>This type of boiling crisis occurs at relatively high heat fluxes and appears to be associated with the cloud of bubbles adjacent to the surface. These bubbles or films of vapor reduce the amount of incoming water. Since this phenomenon deteriorates the heat transfer coefficient and the heat flux remains, heat <strong>accumulates <\/strong>in the fuel rod, causing a <strong>dramatic rise<\/strong> of cladding and fuel <strong>temperature<\/strong>. Simply, a very high-temperature difference is required to transfer the critical heat flux being produced from the surface of the fuel rod to the reactor coolant (through the vapor layer). In the case of PWRs, the critical flow is <strong>inverted annular flow<\/strong>, while in BWRs, the critical flow is usually annular flow.<\/p>\n<p>One of the key safety requirements of pressurized water reactors is that a departure from nucleate boiling (DNB) will not occur during steady-state operation, normal operational transients, and anticipated operational occurrences (AOOs). Fuel cladding integrity will be maintained if the minimum <strong>DNBR remains above<\/strong> the 95\/95 <strong>DNBR limit<\/strong> for PWRs ( a 95% probability at a 95% confidence level). DNB criterion is one of the acceptance criteria in safety analyses as well as it constitutes one of the safety limits in technical specifications. The establishment of a minimum DNB ratio provides a major limitation on the design of water-cooled reactors, and this phenomenon limits the maximal thermal power of each PWR.<\/p>\n<p><strong>DNB ratio (DNBR &#8211; Departure from Nucleate Boiling Ratio)<\/strong> measures the margin to critical heat flux. DNBR is defined as:<\/p>\n<p><em> the critical heat flux at a specific location and specific coolant parameters divided by the operating local heat flux at that location<\/em>.<\/p>\n<p><em><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20792\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-definition.png\" alt=\"DNBR - definition\" width=\"242\" height=\"82\" \/><\/a><\/em><\/p>\n<p>The reactor core must be designed to keep the DNBR larger than the minimum allowable value (known as the correlation limit) during steady-state operation, normal operational transients, and anticipated operational occurrences (AOOs). For predicting departure from nucleate boiling, CHF can be, for example, determined using the W-3 correlation developed at the Westinghouse Atomic Power Division. If these correlations were perfect (without uncertainties), the criterion would be simple:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-criterion.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20793\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-criterion.png\" alt=\"DNBR - criterion\" width=\"278\" height=\"74\" \/><\/a><\/p>\n<p><em>Local heat flux must be lower than critical heat flux (i.e., DNBR must be higher than one).<\/em><\/p>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20775\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio-289x300.png\" alt=\"DNBR - Departure from Nucleate Boiling Ratio\" width=\"289\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio-289x300.png 289w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/DNBR-Departure-from-Nucleate-Boiling-Ratio.png 682w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/a>But in reality<\/strong>, no correlation is perfect, and uncertainties must be involved in this calculation. As indicated in the figure, these uncertainty bands or error bounds establish a minimum acceptable value for the DNB Ratio, which may be significantly greater than one. Uncertainties may reach about 20%, and therefore the DNBR must be larger than, for example, <strong>DNBR<sub>lim<\/sub> = 1,2<\/strong>.<\/p>\n<p>As can be seen from the figure, the CHF significantly decreases with increasing coolant enthalpy. Therefore the minimal value of DNBR is not necessarily in the center of the core. The Minimum DNB Ratio (MDNBR) occurs at the location where the critical heat flux and the operating heat flux are the closest, and it is usually in the upper part of the core. Moreover, at the channel inlet where the coolant subcooling is the highest, we would expect the heat flux necessary to cause DNB at this location to be extremely high. On the other hand, at the channel exit where the coolant enthalpy is highest, the heat flux necessary to cause DNB should be lowest.<\/p>\n<p>Special Reference: Tong, L. S., Weisman, Joel. Thermal Analysis of Pressurized Water Reactors. Amer Nuclear Society, 3rd edition, 5\/1996. ISBN-13: 978-0894480386.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/critical-heat-flux-vs-local-heat-flux.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20776\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/critical-heat-flux-vs-local-heat-flux.png\" alt=\"critical heat flux vs local heat flux\" width=\"582\" height=\"622\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/critical-heat-flux-vs-local-heat-flux.png 582w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/critical-heat-flux-vs-local-heat-flux-281x300.png 281w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/a><\/p>\n<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>The Nuclear Enthalpy Rise Hot Channel Factor \u2013 F\u0394H<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">See also: <a title=\"Hot Channel Factors \u2013 Peaking Factors\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/hot-channel-factors-peaking-factors\/\">Hot Channel Factors<\/a><\/p>\n<p>The <a title=\"Nuclear Enthalpy Rise Hot Channel Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-operation\/normal-operation-reactor-control\/nuclear-enthalpy-rise-hot-channel-factor\/\">Nuclear Enthalpy Rise Hot Channel Factor \u2013 F<sup>N<\/sup><sub>\u0394H<\/sub><\/a>\u00a0is defined as:<\/p>\n<ol>\n<li>The ratio of the integral of linear power along the fuel rod on which minimum departure from nucleate boiling ratio occurs (during AOOs) to the average fuel rod power in the core.<\/li>\n<li>The ratio of the integral of linear power along the fuel rod with the highest integrated power [kW\/rod] to the average rod power [kW\/rod].<\/li>\n<\/ol>\n<p>Operation within the <strong>Nuclear Enthalpy Rise Hot Channel Factor \u2013 F<sup>N<\/sup><sub>\u0394H<\/sub><\/strong> limits prevents departure from nucleate boiling (DNB) during accidents limiting from DNB point of view. For example, a loss of forced reactor coolant flow accident, a loss of normal feedwater flow, or an inadvertent opening of a pressurizer relief valve. The <strong>Nuclear Enthalpy Rise Hot Channel Factor F<sup>N<\/sup><sub>\u0394H<\/sub><\/strong> is an assumption in these and other analyses, as well as it is an assumption for Safety Limits (SLs) calculations. Its merit is that F<sup>N<\/sup><sub>\u0394H<\/sub> provides information about power distribution as well as about the coolant temperature (enthalpy), and both are crucial for DNB occurrence. Operation beyond the Nuclear Enthalpy Rise Hot Channel Factor \u2013 F<sup>N<\/sup><sub>\u0394H<\/sub>\u00a0could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).<\/p>\n<\/div><\/div><\/div>\n<h2>Post-DNB Heat Transfer<\/h2>\n<p>The nucleate boiling heat flux cannot be increased indefinitely. We call it the \u201c<strong>critical heat flux<\/strong>\u201d (<strong>CHF<\/strong>) at some value. The steam produced can form an insulating layer over the surface, which deteriorates the heat transfer coefficient. This is because a large fraction of the surface is covered by a vapor film, which acts as thermal insulation due to the low thermal conductivity of the vapor relative to that of the liquid. Immediately after the critical heat flux has been reached, boiling becomes unstable, and transition boiling occurs. The transition from nucleate boiling to film boiling is known as the \u201c<strong>boiling crisis<\/strong>\u201d. Since the heat transfer coefficient decreases beyond the CHF point, the transition to film boiling is usually inevitable.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20779\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes-208x300.png\" alt=\"Boiling Curve - Boiling Modes\" width=\"208\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes-208x300.png 208w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Boiling-Curve-Boiling-Modes.png 601w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/><\/a>A further increase in the heat flux is not necessary to maintain film boiling. A film of vapor fully covers the surface, significantly reducing the convection coefficient since the vapor layer has a lower heat transfer ability. As a result, the excess temperature shoots up to a very high value. Beyond the <a title=\"Leidenfrost Effect \u2013 Leidenfrost Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/leidenfrost-effect-leidenfrost-point\/\">Leidenfrost point<\/a>, a continuous vapor film blankets the surface, and there is no contact between the liquid phase and the surface. In this situation, the heat transfer is both by radiation and conduction to the vapor. The heated surface stabilizes its temperature at point E (see figure). If the material is not strong enough for withstanding this temperature, the equipment will fail by damage to the material.<\/p>\n<h2>Critical Power Ratio &#8211; Dryout<\/h2>\n<p><strong><span style=\"font-weight: 400;\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Flow-Boiling-Dryout.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20773\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Flow-Boiling-Dryout-257x300.png\" alt=\"Flow Boiling - Dryout\" width=\"257\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Flow-Boiling-Dryout-257x300.png 257w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/01\/Flow-Boiling-Dryout.png 858w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/a>In BWRs, a similar phenomenon is known as <\/span><b>\u201cdry-out,\u201d<\/b><span style=\"font-weight: 400;\"> and it is directly associated with <\/span><b>changes in flow pattern<\/b><span style=\"font-weight: 400;\"> during evaporation in the high-quality region. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the <\/span>liquid wall\u00a0<b>film may exhaust,<\/b><span style=\"font-weight: 400;\"> and the wall may be <\/span><b>dried out<\/b><span style=\"font-weight: 400;\">. At normal, the fuel surface is effectively cooled by boiling coolant. However, when the heat flux exceeds a <\/span><b>critical value <\/b><span style=\"font-weight: 400;\">(CHF \u2013 critical heat flux), the flow pattern may reach the <\/span><b>dry-out conditions<\/b><span style=\"font-weight: 400;\"> (a thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated due to a <\/span><b>drastically increased fuel surface temperature<\/b><span style=\"font-weight: 400;\">. In the high-quality region, the crisis occurs at a lower heat flux. Since the flow velocity in the vapor core is high, post-CHF heat transfer is much better than low-quality critical flux (i.e., for PWRs, temperature rises are higher and more rapid).<\/span><\/strong><\/p>\n<p>Typical <strong>flow boiling<\/strong> modes in a <strong>vertical channel<\/strong> are depicted in the figure. This figure shows the typical order of the flow regimes encountered from inlet to outlet of a <strong>heated channel<\/strong>. At the inlet, the <strong>liquid enters subcooled<\/strong> (at a lower temperature than saturation). In this region, the flow is single-phase. As the liquid heats up, the wall temperature correspondingly rises. As the <strong>wall temperature exceeds the saturation temperature<\/strong> (e.g., 285\u00b0C at 6.8 MPa), <strong>subcooled nucleate boiling begins<\/strong>. Bubbles nucleate in the superheated thermal <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/boundary-layer\/\">boundary layer<\/a> on the heated wall but tend to <strong>condense in the subcooled bulk<\/strong>.<\/p>\n<p><span data-preserver-spaces=\"true\">Further increase in liquid temperature causes the liquid bulk to reach its\u00a0<\/span><strong><span data-preserver-spaces=\"true\">saturation temperature<\/span><\/strong><span data-preserver-spaces=\"true\">, and the convective boiling process passes through the\u00a0<\/span><a class=\"editor-rtfLink\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/bubbly-flow-two-phase-flow\/\" target=\"_blank\" rel=\"noopener\"><strong><span data-preserver-spaces=\"true\">bubbly flow\u00a0<\/span><\/strong><\/a><span data-preserver-spaces=\"true\">into the\u00a0<\/span><a class=\"editor-rtfLink\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/plug-flow-slug-flow\/\" target=\"_blank\" rel=\"noopener\"><strong><span data-preserver-spaces=\"true\">slug flow<\/span><\/strong><\/a><span data-preserver-spaces=\"true\">. Increasing\u00a0<a class=\"editor-rtfLink\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/void-fraction-two-phase-flow\/\" target=\"_blank\" rel=\"noopener\">void fraction<\/a>\u00a0causes the structure of the flow to become unstable. The boiling process passes through the\u00a0<strong>slug and\u00a0<\/strong><a class=\"editor-rtfLink\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/churn-flow-froth-flow\/\" target=\"_blank\" rel=\"noopener\"><strong>churns flow<\/strong><\/a>\u00a0into the\u00a0<a class=\"editor-rtfLink\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/annular-flow-two-phase-flow\/\" target=\"_blank\" rel=\"noopener\"><strong>annular flow regime<\/strong><\/a>\u00a0with its characteristic annular film of the liquid. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the <strong>liquid wall\u00a0film may exhaust<\/strong>, and the wall may be\u00a0<strong>dried-out<\/strong>.\u00a0<\/span>The wall temperature significantly rises at the dry-out point to dissipate the applied heat flux. The post-dry-out flow (<a title=\"Mist Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/mist-flow\/\">mist or drop flow<\/a>) in the heated channel is undesirable because such a flow regime is accompanied by significantly higher wall temperatures and high fluctuation of wall temperatures.<\/p>\n<p>In this case, engineers define a parameter known as the <strong>minimum critical power ratio (MCPR)<\/strong> instead of DNBR. The <strong>critical power ratio (CPR)<\/strong> is used for determining the thermal limits of boiling water reactors.<\/p>\n<p><strong>Definition of CPR :<\/strong><\/p>\n<p><em>The CPR is that power in the assembly that is calculated by application of the appropriate correlation(s) to cause some point in the assembly to experience boiling transition, divided by the actual assembly operating power.<\/em><\/p>\n<p>Special Reference: Tong, L. S., Weisman, Joel. Thermal Analysis of Pressurized Water Reactors. Amer Nuclear Society, 3rd edition, 5\/1996. ISBN-13: 978-0894480386.<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<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>Heat Transfer:<\/strong>\n<ol>\n<li>Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley &amp; Sons, Incorporated, 2011. ISBN: 9781118137253.<\/li>\n<li>Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.<\/li>\n<li>U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.<\/li>\n<\/ol>\n<p><strong>Nuclear and Reactor Physics:<\/strong><\/p>\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. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics. Addison-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. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.<\/li>\n<li>Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.<\/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>D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.<\/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>Boiling and Condensation<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\" 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":"<p>This chapter will study flow boiling in a vertical heated channel. The boiling and heat flux curve regimes are similar (not the same) as those in pool boiling. The process also occurs in modern high-pressure forced circulation boilers. The pioneering work on pool boiling was done in 1934 by\u00a0S. Nukiyama, who used electrically heated nichrome &#8230; <a title=\"Boiling Crisis &#8211; Critical Heat Flux\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/boiling-crisis-critical-heat-flux\/\" aria-label=\"More on Boiling Crisis &#8211; Critical Heat Flux\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":20709,"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\/20871"}],"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=20871"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20871\/revisions"}],"predecessor-version":[{"id":37368,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20871\/revisions\/37368"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20709"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=20871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}