{"id":20557,"date":"2018-12-14T17:31:43","date_gmt":"2018-12-14T17:31:43","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20557"},"modified":"2023-02-15T17:43:43","modified_gmt":"2023-02-15T17:43:43","slug":"hydraulic-lift-force","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/hydraulic-lift-force\/","title":{"rendered":"Hydraulic Lift Force"},"content":{"rendered":"<p>Analysis of the <strong>hydraulic lift force<\/strong> is one of the most important analyses in designing a fuel assembly and analyzing the hydraulic compatibility of mixed cores. The vertical forces are induced by upward high-velocity flow through the<a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\"> reactor core<\/a>, and the\u00a0flow path for the reactor coolant through the<a title=\"Reactor Pressure Vessel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/reactor-pressure-vessel\/\"> reactor vessel <\/a>would be:<\/p>\n<ul>\n<li>The coolant enters the <strong>reactor vessel<\/strong> at the inlet nozzle and hits against the <a title=\"Core Barrel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/core-barrel\/\">core barrel<\/a>.<\/li>\n<li>The core barrel forces the water to flow downward in the space between the reactor vessel wall and the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/core-barrel\/\">core barrel<\/a>. This\u00a0space is usually known as the <strong>downcomer<\/strong>.<\/li>\n<li>The flow is reversed up through the core from the bottom of the pressure vessel to pass through the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">fuel assemblies<\/a>, where the coolant temperature increases as it passes through the fuel rods.<\/li>\n<li>Finally, the hotter reactor coolant enters the upper internals region, where it is routed out the outlet nozzle into the hot legs of the primary circuit and goes on to the<strong><a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"> steam generators<\/a>.<\/strong><\/li>\n<\/ul>\n<figure id=\"attachment_14206\" aria-describedby=\"caption-attachment-14206\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14206\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min-300x300.png\" alt=\"Continuity Equation - Flow Rates through Reactor\" width=\"300\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min-300x300.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min-150x150.png 150w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min-66x66.png 66w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/04\/Continuity-Equation-Flow-Rate-min.png 1000w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14206\" class=\"wp-caption-text\">Example of flow rates in a reactor. It is an illustrative example, and the data do not represent any reactor design.<\/figcaption><\/figure>\n<p>Fuel assemblies are held by the <strong>upper guide structure assembly<\/strong>, which defines the top of the core. This assembly is made of stainless steel and has many purposes. The upper guide structure assembly exerts an <strong>axial force<\/strong> on fuel assemblies (through springs in the top nozzle), thus defining the exact position of the fuel assembly in the core. The <strong>upper guide structure assembly<\/strong> flange is held in place and preloaded by the RPV closure head flange. The upper guide structure assembly also guides and protects <a title=\"Control Rods\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/control-rods\/\">control rod<\/a> assemblies and in-core instrumentation.<\/p>\n<p>&nbsp;<\/p>\n<p>Required downforce of the <strong>upper guide structure assembly <\/strong>on fuel assemblies must be carefully calculated. Insufficient downforce can result in the <strong>lift of the fuel assembly<\/strong>. On\u00a0the other hand, an excessive downforce can result in <strong>bowing of fuel assembly<\/strong>, which is also unacceptable.<\/p>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>What is Drag in Physics<\/h2>\n<p>In <a title=\"Fluid Dynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/\">fluid dynamics<\/a>, <strong>drag<\/strong> is a force acting opposite to the relative motion of any moving object. The force a flowing fluid exerts on a body in the flow direction. Unlike other resistive forces, such as dry friction, nearly independent of velocity, <strong>drag forces<\/strong> depend on velocity. <a title=\"Drag Force \u2013 Drag Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/what-is-drag-air-and-fluid-resistance\/drag-force-drag-equation\/\"><strong>Drag force<\/strong><\/a> is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. <strong>Drag<\/strong> is generally caused by two phenomena:<\/p>\n<ul>\n<li>\n<figure id=\"attachment_20487\" aria-describedby=\"caption-attachment-20487\" style=\"width: 218px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/Drag-skin-friction-and-form-drag.png\"><img loading=\"lazy\" class=\"size-full wp-image-20487\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/Drag-skin-friction-and-form-drag.png\" alt=\"Drag - skin friction and form drag\" width=\"228\" height=\"343\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/Drag-skin-friction-and-form-drag.png 228w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/Drag-skin-friction-and-form-drag-199x300.png 199w\" sizes=\"(max-width: 228px) 100vw, 228px\" \/><\/a><figcaption id=\"caption-attachment-20487\" class=\"wp-caption-text\">Source: wikipedia.org License: CC BY-SA 3.0<\/figcaption><\/figure>\n<p><a title=\"Skin Friction \u2013 Friction Drag\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/what-is-drag-air-and-fluid-resistance\/skin-friction-friction-drag\/\"><strong>Skin Friction<\/strong><\/a>. In general, when a fluid flows over a <strong>stationary surface<\/strong>, e.g., the flat plate, the bed of a river, or the pipe wall, the fluid touching the surface is brought <strong>to rest<\/strong> by the <strong>shear stress<\/strong> at the wall. The <a title=\"Boundary Layer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/boundary-layer\/\"><strong>boundary layer<\/strong><\/a> is the region in which flow adjusts from zero velocity at the wall to a maximum in the mainstream of the flow. Therefore, a moving fluid exerts tangential shear forces on the surface because of the <strong>no-slip condition<\/strong> caused by viscous effects. This type of <strong>drag force<\/strong> depends especially on the geometry, the roughness of the solid surface, and the type of fluid flow.<\/li>\n<li><a title=\"Form Drag \u2013 Pressure Drag\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/what-is-drag-air-and-fluid-resistance\/form-drag-pressure-drag\/\"><strong>Form Drag<\/strong><\/a>. <strong>Form drag,<\/strong> also known as <strong>pressure drag,<\/strong> arises because of the shape and size of the object. This type of drag force is an interesting consequence the <strong><a title=\"Bernoulli\u2019s Theorem\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/bernoullis-theorem\/\">Bernoulli\u2019s effect<\/a>. <\/strong>According to Bernoulli\u2019s principle, faster-moving air exerts less pressure, and this causes that there can be a pressure difference between surfaces of the object. The general size and shape of the body are the most important factors in <strong>form drag<\/strong>. Generally, bodies with a larger presented geometric cross-section will have higher drag than thinner bodies.<\/li>\n<\/ul>\n<p>Both of these forces, in general, have components in the direction of flow, and thus the resulting <strong>drag force<\/strong> is due to the combined effects of <strong>pressure<\/strong> and <strong>skin friction<\/strong> forces in the flow direction.<\/p>\n<p>When the friction and pressure drag coefficients are available, the total drag coefficient is determined by simply adding them:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-form-drag-coefficients.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20488\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-form-drag-coefficients.png\" alt=\"skin friction - form drag - coefficients\" width=\"308\" height=\"54\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-form-drag-coefficients.png 308w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-form-drag-coefficients-300x54.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/a><\/p>\n<p>Most drag is due to <strong>friction drag<\/strong> at low <strong><a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds numbers<\/a><\/strong>, especially for highly streamlined bodies such as airfoils. On the other hand, the <a title=\"Head Loss \u2013 Pressure Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/head-loss\/\">pressure drop<\/a> is significant at a\u00a0<strong>high Reynolds number<\/strong>, which increases form drag.<\/p>\n<p>The components of the pressure and skin friction forces in the <strong>normal direction<\/strong> to flow tend to move the body in that direction, and their sum is called<strong><a title=\"Lift Force\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/lift-force\/\"> lift<\/a><\/strong>.<\/p>\n<p>The<strong> lift<\/strong> is an upward-acting force on an aircraft wing or <strong>airfoil <\/strong>in aeronautics.<strong> Bernoulli\u2019s principle<\/strong> requires airfoil to be of an <strong>asymmetrical shape<\/strong>.<\/p>\n<h2>Drag Force &#8211; Drag Equation<\/h2>\n<p>The <strong>drag force,<\/strong> <strong>F<sub>D<\/sub><\/strong>, depends on the <a title=\"What is Density \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">density<\/a> of the fluid, the upstream velocity, and the size, shape, and orientation of the body, among other things. One way to express this is by using the <strong>drag equation<\/strong>. The <strong>drag equation<\/strong> is a formula used to calculate the <strong>drag force<\/strong> experienced by an object due to movement through a fluid.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20495\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-formula.png\" alt=\"drag force - drag equation - formula\" width=\"261\" height=\"257\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-formula.png 261w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-formula-52x50.png 52w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-formula-66x66.png 66w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><\/a><\/p>\n<p>The reference area, A, is defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For hollow objects, the reference area may be significantly larger than the cross-sectional area, but for non-hollow objects, it is the same as a cross-sectional area.<\/p>\n<h2>Example: Drag Force &#8211; Drag Coefficient &#8211; Fuel Bundle<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20407\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel-254x300.png\" alt=\"Hydraulic Diameter - Fuel Channel\" width=\"254\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel-254x300.png 254w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel.png 316w\" sizes=\"(max-width: 254px) 100vw, 254px\" \/><\/a>Calculate the <strong>friction drag<\/strong> of a <strong>single fuel rod<\/strong> inside a reactor core at normal operation (design flow rate). Assume that this fuel rod is part of a fuel bundle with the rectangular fuel lattice, and this fuel bundle does not contain spacing grids. Its height is <strong>h = 4m,<\/strong> and the core flow velocity is constant and equal to <strong>V<\/strong><strong><sub>core<\/sub><\/strong><strong> = 5 m\/s.<\/strong><\/p>\n<p>Assume that:<\/p>\n<ul>\n<li>the outer diameter of the cladding is: <strong>d = 2 x r<\/strong><strong><sub>Zr,1<\/sub><\/strong><strong> = 9,3 mm<\/strong><\/li>\n<li>the pitch of fuel pins is: <strong>p = 13 mm<\/strong><\/li>\n<li>the <a title=\"Relative Roughness of Pipe\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/relative-roughness-of-pipe\/\">relative roughness<\/a> is <strong>\u03b5\/D = 5&#215;10<\/strong><strong><sup>-4<\/sup><\/strong><\/li>\n<li>the fluid <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">density<\/a> is: <strong>\u03c1 = 714 kg\/m<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<li>the core flow velocity is constant and equal to <strong>V<\/strong><strong><sub>core<\/sub><\/strong><strong> = 5 m\/s<\/strong><\/li>\n<li>the average <a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">temperature<\/a> of reactor coolant is: <strong>T<\/strong><strong><sub>bulk<\/sub><\/strong><strong> = 296\u00b0C<\/strong><\/li>\n<\/ul>\n<h2>Calculation of the Reynolds number<\/h2>\n<p>To calculate the<a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\"> Reynolds number<\/a>, we have to know:<\/p>\n<ul>\n<li>the outer diameter of the cladding is: <strong>d = 2 x r<\/strong><strong><sub>Zr,1<\/sub><\/strong><strong> = 9,3 mm<\/strong> (to calculate the hydraulic diameter)<\/li>\n<li>the pitch of fuel pins is: <strong>p = 13 mm<\/strong> \u00a0(to calculate the hydraulic diameter)<\/li>\n<li>the dynamic viscosity of saturated water at 300\u00b0C is: <strong>\u03bc = 0.0000859 N.s\/m<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>the fluid density is: <strong>\u03c1 = 714 kg\/m<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<\/ul>\n<p><strong>The hydraulic diameter, D<\/strong><strong><sub>h<\/sub><\/strong>, is a commonly used term when handling flow in <strong>non-circular tubes and channels<\/strong>. The <strong>hydraulic diameter of the fuel channel<\/strong>, <em>D<\/em><em><sub>h<\/sub><\/em>, is equal to <strong>13,85 mm<\/strong>.<\/p>\n<p>See also: <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">Hydraulic Diameter<\/a><\/p>\n<p>The <strong>Reynolds number <\/strong>inside the fuel channel is then equal to:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20412\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png\" alt=\"reynolds number - example\" width=\"593\" height=\"78\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png 593w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example-300x39.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/a><\/p>\n<p>This fully satisfies the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\"><strong>turbulent conditions<\/strong><\/a>.<\/p>\n<h2>Calculation of the Skin Friction Coefficient<\/h2>\n<p style=\"text-align: left;\"><strong>The friction factor<\/strong> for turbulent flow depends strongly on the <strong>relative roughness. <\/strong>It is determined by the Colebrook equation or can be determined using the <a title=\"Moody Diagram\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/moody-diagram\/\"><strong>Moody chart<\/strong><\/a>. The <strong>Moody chart <\/strong>for <strong>Re = 575 600 <\/strong>and <strong>\u03b5\/D = 5 x 10<\/strong><strong><sup>-4<\/sup><\/strong> returns following values:<\/p>\n<ul>\n<li>the<a title=\"Darcy Friction Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-friction-factor-2\/\"><strong> Darcy friction factor<\/strong><\/a> is equal to <strong>f<\/strong><strong><sub>D<\/sub><\/strong><strong> = 0.017<\/strong><\/li>\n<li>the<a title=\"Fanning Friction Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/fanning-friction-factor\/\"><strong> Fanning friction factor<\/strong><\/a> is equal to <strong>f<\/strong><strong><sub>F<\/sub><\/strong><strong> = f<\/strong><strong><sub>D<\/sub><\/strong><strong>\/4 = 0.00425<\/strong><\/li>\n<\/ul>\n<p>Therefore the skin friction coefficient is equal to:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-coefficient-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20533\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-coefficient-example.png\" alt=\"skin friction coefficient - example\" width=\"377\" height=\"186\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-coefficient-example.png 377w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/skin-friction-coefficient-example-300x148.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/a><\/p>\n<h2>Calculation of the Drag Force<\/h2>\n<p>To calculate the <strong>drag force<\/strong>, we have to know:<\/p>\n<ul>\n<li>the skin friction coefficient, which is: <strong>C<\/strong><strong><sub>D,friction<\/sub><\/strong><strong> = 0.00425<\/strong><\/li>\n<li>the area of pin surface, which is: <strong>A = \u03c0.d.h = 0.1169 m<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>the fluid <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">density<\/a>, which is: <strong>\u03c1 = 714 kg\/m<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<li>the core flow velocity, which is constant and equal to <strong>V<\/strong><strong><sub>core<\/sub><\/strong><strong> = 5 m\/s<\/strong><\/li>\n<\/ul>\n<p>From the <strong>skin friction coefficient, <\/strong>which is equal to the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/fanning-friction-factor\/\"><strong>Fanning friction factor<\/strong><\/a>, we can calculate the frictional component of the <strong>drag force. <\/strong>The drag force is given by:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20534\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-example.png\" alt=\"drag force - example\" width=\"452\" height=\"72\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-example.png 452w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/drag-force-example-300x48.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/a><\/p>\n<p>Assuming that a fuel assembly can have, for example, 289 fuel pins (17&#215;17 fuel assembly), the<strong> frictional component<\/strong> of the <strong>drag force <\/strong>is then of the order of <strong>kilonewtons<\/strong>. Moreover, this drag force originates purely from the skin friction on the fuel bundle. But typical PWR fuel assembly contains other components which influence the fuel assembly hydraulics:<\/p>\n<ul>\n<li><strong>Fuel rods<\/strong>. Fuel rods contain fuel and burnable poisons.<\/li>\n<li><strong>Top nozzle<\/strong>. Provides the mechanical support for the fuel assembly structure.<\/li>\n<li><strong>Bottom nozzle<\/strong>. Provides the mechanical support for the fuel assembly structure.<\/li>\n<li><strong>Spacing grid<\/strong>. Ensures an exact guiding of the fuel rods.<\/li>\n<li><strong>Guide thimble tube<\/strong>. Vacant tube for control rods or in-core instrumentation.<\/li>\n<\/ul>\n<p>As was written, the second component of the drag force is the form drag. <strong>Form drag,<\/strong> also known as <strong>pressure drag,<\/strong> arises because of the <strong>shape<\/strong> and <strong>size<\/strong> of the object. The <strong>pressure drag<\/strong> is proportional to the difference between the pressures acting on the front and back of the immersed body and the frontal area.<\/p>\n<h2>Pressure Drop &#8211; Fuel Assembly<\/h2>\n<p>In general, total <strong>fuel assembly <\/strong><strong>pressure drop<\/strong> is formed by fuel bundle frictional drop (dependent on <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/relative-roughness-of-pipe\/\">relative roughness<\/a> of fuel rods, <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds number<\/a>, <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">hydraulic diameter<\/a>, etc.) and other pressure drops of structural elements (top and bottom nozzle, spacing grids, or mixing grids).<\/p>\n<p>In general, it is not so simple to calculate pressure drops in fuel assemblies (especially the spacing grids), and it belongs to the key <strong>know-how<\/strong> of certain fuel manufacturers. Mostly, pressure drops are measured in <strong>experimental hydraulic loops<\/strong>\u00a0rather than calculated.<\/p>\n<p>Engineers use the <a title=\"Pressure Loss Coefficient \u2013 PLC\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/head-loss\/pressure-loss-coefficient-plc\/\"><strong>pressure loss coefficient<\/strong><\/a>, <strong>PLC<\/strong>. It is noted K or <strong>\u03be<\/strong> \u00a0(pronounced \u201cxi\u201d). This coefficient characterizes <a title=\"Head Loss \u2013 Pressure Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/head-loss\/\">pressure loss<\/a> of a certain hydraulic system or a part of a hydraulic system, and it can be easily measured in hydraulic loops. The pressure loss coefficient can be defined or measured for both straight pipes and especially for<a title=\"Minor Head Loss \u2013 Local Losses\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/minor-head-loss-local-losses\/\"><strong> local (minor) losses<\/strong><\/a>.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/PLC-Pressure-loss-coefficient-equations.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20526\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/PLC-Pressure-loss-coefficient-equations.png\" alt=\"PLC - Pressure loss coefficient - equations\" width=\"339\" height=\"375\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/PLC-Pressure-loss-coefficient-equations.png 339w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/12\/PLC-Pressure-loss-coefficient-equations-271x300.png 271w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/a><\/p>\n<p>Using data from the example mentioned above, the <strong>pressure loss coefficient<\/strong> (only frictional from the straight pipe) is equal to <strong>\u03be = f<sub>D<\/sub>L\/D<sub>H<\/sub> = 4.9<\/strong>. But the overall pressure loss coefficient (including spacing grids, top, and bottom nozzles, etc.) is usually about three times higher. This PLC (<strong>\u03be = 4.9<\/strong>) causes the pressure drop to be of the order of (using the previous inputs) <strong>\u0394p<sub>friction<\/sub><\/strong> = \u00a04.9 x 714 x 5<sup>2<\/sup>\/ 2 = <strong>43.7 kPa<\/strong> (without spacing grids, top, and bottom nozzles). About three times higher real PLC means about three times higher <strong>\u0394p<sub>fuel\u00a0<\/sub><\/strong>will be.<\/p>\n<p>The overall reactor pressure loss, <strong>\u0394p<sub>reactor<\/sub><\/strong>, must include:<\/p>\n<ul>\n<li>downcomer and reactor bottom<\/li>\n<li>lower support plate<\/li>\n<li>fuel assembly including spacing grids, top and bottom nozzles, and other structural components &#8211; <strong>\u0394p<sub>fuel<\/sub><\/strong><\/li>\n<li>upper guide structure assembly<\/li>\n<\/ul>\n<p>As a result, the overall reactor pressure loss &#8211; <strong>\u0394p<sub>reactor<\/sub><\/strong> is usually of the order of hundreds kPa (let\u2019s say 300 &#8211; 400 kPa) for design parameters.<\/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>Reactor Physics and Thermal Hydraulics:<\/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>Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871<\/li>\n<li>Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2<\/li>\n<li>Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,\u00a0John Wiley &amp; Sons, 2006, ISBN:\u00a0978-0-470-03037-0<\/li>\n<li>Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,\u00a0ISBN 978-1-4020-8670-0.<\/li>\n<li>U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.<\/li>\n<li>White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN:\u00a0978-0077422417<\/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>Nuclear Fuel<a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\" 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>Analysis of the hydraulic lift force is one of the most important analyses in designing a fuel assembly and analyzing the hydraulic compatibility of mixed cores. The vertical forces are induced by upward high-velocity flow through the reactor core, and the\u00a0flow path for the reactor coolant through the reactor vessel would be: The coolant enters &#8230; <a title=\"Hydraulic Lift Force\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/hydraulic-lift-force\/\" aria-label=\"More on Hydraulic Lift Force\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":198,"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\/20557"}],"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=20557"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20557\/revisions"}],"predecessor-version":[{"id":37297,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20557\/revisions\/37297"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/198"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=20557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}