{"id":86543,"date":"2024-01-09T13:20:28","date_gmt":"2024-01-09T13:20:28","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=86543"},"modified":"2024-09-11T15:39:55","modified_gmt":"2024-09-11T15:39:55","slug":"choked-flow-due-to-cavitation","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/choked-flow-due-to-cavitation\/","title":{"rendered":"Validation Case: Choked Flow Due to Cavitation"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This validation case belongs to computational fluid dynamics and aims to validate the following parameters:<\/p>\n\n\n\n\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/cavitation\/\"  rel=\" noopener\">cavitation model<\/a>, available for the <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/subsonic-cartesian\/\"  rel=\" noopener\">Multi-purpose solver<\/a> in a pipe section with an orifice plate.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Simulation results were compared to experimental results available in the article &#8220;<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1290072916308092\" target=\"_blank\" rel=\"noreferrer noopener\">Characterization of high-pressure cavitating flow through a thick orifice plate in a pipe of constant cross-section<\/a>&#8220;\\(^1\\), by Ebrahimi <em>et al.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=6589966790991681146&#038;mi=spec%3A4c615cd7-4179-43ee-83b7-8697e659f50d%2Cservice%3ASIMULATION%2Cstrategy%3A73\" class=\"hw-btn    \" rel=\"noopener \" target=\"_blank\"    >\n        View Project    <\/a>\n<\/div>\n\n\n\n\n<h2 id=\"geometry\" class=\"wp-block-heading\" >Geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This validation case uses a simple straight pipe section with an orifice plate, where the arrows indicate the flow direction:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/pipe-cavitation-geometry-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"902\" height=\"503\" nonce='e9d42976172adc2489ef1092f0798334' src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/pipe-cavitation-geometry-1.png\" alt=\"cavitation pipe geometry\" class=\"wp-image-86547\" style=\"width:627px;height:auto\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/pipe-cavitation-geometry-1.png 902w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/pipe-cavitation-geometry-1-300x167.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/pipe-cavitation-geometry-1-768x428.png 768w\" sizes=\"auto, (max-width: 902px) 100vw, 902px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: Pipe geometry based on the experimental setup<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The dimensions of the pipe are listed below:<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td><strong>Dimension<\/strong><\/td><td><strong>Value \\([mm]\\)<\/strong><\/td><\/tr><tr><td>Inlet diameter<\/td><td>28.5<\/td><\/tr><tr><td>Inlet section length<\/td><td>12.7<\/td><\/tr><tr><td>Orifice plate diameter<\/td><td>6.35<\/td><\/tr><tr><td>Orifice plate length<\/td><td>12.7<\/td><\/tr><tr><td>Outlet diameter<\/td><td>28.5<\/td><\/tr><tr><td>Outlet section length<\/td><td>44.45<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Geometry dimensions<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The reference study tackles multiple scenarios, with various combinations of pressures at the inlet and outlet. This validation case focuses on the harshest scenario explored by the reference study, with an inlet pressure of 5000 \\(psi\\).<\/p>\n\n\n\n<h2 id=\"analysis-type-and-mesh\" class=\"wp-block-heading\" >Analysis Type and Mesh<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: Steady-state, <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/subsonic-cartesian\/\"  rel=\" noopener\">Multi-purpose<\/a> with <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/k-epsilon\/\">k-epsilon<\/a> and <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/cavitation\/\"  rel=\" noopener\">Cavitation<\/a> model<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mesh and Element Types<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-black-color\">The<\/span> mesh was created with SimScale&#8217;s <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/subsonic-cartesian\/#mesh-settings\">Multi-purpose<\/a> mesh type, which is a body-fitted structured mesh. A manual sizing definition relative to the CAD was used.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Mesh Type<\/strong><\/td><td><strong>Minimum Cell Size<\/strong><\/td><td><strong>Maximum Cell Size<\/strong><\/td><td><strong>Cell Size on Surfaces<\/strong><\/td><td><strong>Number of cells<\/strong><\/td><td><strong>Element Type<\/strong><\/td><\/tr><tr><td>Manual<\/td><td>1e-5 (relative)<\/td><td>0.005 (relative)<\/td><td>0.0025 (relative)<\/td><td>1137916<\/td><td>3D Hexahedral<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Mesh data for the choked flow due to cavitation validation case<\/figcaption><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1151\" height=\"481\" nonce='e9d42976172adc2489ef1092f0798334' src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh.png\" alt=\"cavitating choked flow pipe mesh\" class=\"wp-image-86548\" style=\"width:618px;height:auto\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh.png 1151w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh-300x125.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh-1024x428.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/mesh-768x321.png 768w\" sizes=\"auto, (max-width: 1151px) 100vw, 1151px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 2: Multi-purpose meshing performed on the valve with refinement around the edge of the valve<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 id=\"simulation-setup\" class=\"wp-block-heading\" >Simulation Setup<\/h2>\n\n\n\n<h3 id=\"material\" class=\"wp-block-heading\" >Material<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Fluid<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Water\n<ul class=\"wp-block-list\">\n<li>Kinematic viscosity \\((\\nu)\\): 5.5668e-7 \\(m^2\/s\\) <\/li>\n\n\n\n<li>Density \\((\\rho)\\): 988 \\(kg\/m^3\\)<\/li>\n\n\n\n<li>Vapor molecular weight: 18 \\(kg\/kmol\\)<\/li>\n\n\n\n<li>Liquid bulk modulus: 2.15e9 \\(Pa\\)<\/li>\n\n\n\n<li>Liquid bulk modulus coefficient: 0<\/li>\n\n\n\n<li>Liquid reference pressure: 1.01325e5 \\(Pa\\)<\/li>\n\n\n\n<li>Saturation pressure: 1.234162e4 \\(Pa\\)<\/li>\n\n\n\n<li>Liquid temperature: 48.9 \\(\u00b0C\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 id=\"boundary-conditions\" class=\"wp-block-heading\" >Boundary Conditions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using Figure 1 as a base, the table below provides the boundary conditions used in the setup:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Boundary Condition<\/strong><\/td><td><strong>Value<\/strong><\/td><\/tr><tr><td>Pressure inlet \\([psi]\\)<\/td><td>5000 (total pressure)<\/td><\/tr><tr><td>Pressure outlet \\([psi]\\)<\/td><td>345; 506; 1101; 2052; 2502; 2813 (fixed gauge pressure)<\/td><\/tr><tr><td>No-slip wall<\/td><td>Pipe walls and orifice plate<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 3: Boundary conditions for pipe and valve<\/figcaption><\/figure>\n\n\n\n<h2 id=\"result-comparison\" class=\"wp-block-heading\" >Result Comparison<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">As the delta pressure between the inlet and outlet increases, a low-pressure region in the orifice causes bubbles to arise. These bubbles will occupy a portion of the orifice&#8217;s cross-section, limiting the amount of water that can go through, which causes a choked flow phenomenon.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the main parameter of interest is the volumetric flow rate through the system, using the inlet as a reference. The table below summarizes the results:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Outlet Pressure \\([psi]\\)<\/strong><\/td><td><strong>Volumetric Flow Rate &#8211; Reference \\([GPM]\\)<\/strong><\/td><td><strong>Volumetric Flow Rate &#8211; Simulation \\([GPM]\\)<\/strong><\/td><td><strong>Error <\/strong><\/td><\/tr><tr><td>345<\/td><td>77.0<\/td><td>81.8<\/td><td>5.9%<\/td><\/tr><tr><td>506<\/td><td>77.1<\/td><td>81.8<\/td><td>5.7%<\/td><\/tr><tr><td>1101<\/td><td>77.1<\/td><td>81.8<\/td><td>5.7%<\/td><\/tr><tr><td>2052<\/td><td>77.0<\/td><td>81.0<\/td><td>4.9%<\/td><\/tr><tr><td>2502<\/td><td>75.2<\/td><td>72.4<\/td><td>-3.9%<\/td><\/tr><tr><td>2813<\/td><td>70.7<\/td><td>67.9<\/td><td>-4.1%<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 4: Result comparison between the reference study and the simulation results<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Overall, the Multi-purpose solver was able to predict the flow behavior over a wide range of pressures, including choked flow behavior for outlet pressures of around 2050 \\(psi\\) or less.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the post-processor, cavitation is observed by monitoring density and gas volume fractions. The images below show the behavior for the case with the outlet pressure equal to 345 \\(psi\\).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-orifice-plate.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1002\" height=\"694\" nonce='e9d42976172adc2489ef1092f0798334' src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-orifice-plate.png\" alt=\"cavitating flow density choked\" class=\"wp-image-86561\" style=\"width:665px;height:auto\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-orifice-plate.png 1002w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-orifice-plate-300x208.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-orifice-plate-768x532.png 768w\" sizes=\"auto, (max-width: 1002px) 100vw, 1002px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: Low-pressure regions (blue) indicate the formation of bubbles, causing the density to greatly decrease<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The bubbles close to the wall limit the cross-section area that water can flow through, choking the flow. The gas volume fraction shows this behavior more clearly:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-gas-volume-fraction.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1015\" height=\"750\" nonce='e9d42976172adc2489ef1092f0798334' src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-gas-volume-fraction.png\" alt=\"cavitating flow gas volume fraction water\" class=\"wp-image-86562\" style=\"width:672px;height:auto\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-gas-volume-fraction.png 1015w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-gas-volume-fraction-300x222.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2023\/12\/cavitation-gas-volume-fraction-768x567.png 768w\" sizes=\"auto, (max-width: 1015px) 100vw, 1015px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 4: Bubbles (red) in the orifice plate region<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class='hw-block hw-references hw-references'>\n    <p class='hw-references__title'>References<\/p>\n    <ul class='hw-references__list'>\n\n        <li><cite><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1290072916308092\" target=\"_blank\">Behrouz Ebrahimi, Guoliang He, Yingjie Tang, Matthew Franchek, Dong Liu, Jay Pickett, Frank Springett, Dan Franklin,\r\nCharacterization of high-pressure cavitating flow through a thick orifice plate in a pipe of constant cross section,\r\nInternational Journal of Thermal Sciences,\r\nVolume 114,\r\n2017,\r\nPages 229-240.<\/a><\/cite><\/li>\n    <\/ul>\n<\/div>\n\n\n\n<div class=\"hw-block hw-note hw-note--info hw-note\">\n    <div class=\"hw-note__title\">\n        <p class=\"hw-note__titleText\"><i class=\"fa fa-exclamation-circle\" aria-hidden=\"true\"><\/i>Note<\/p>\n    <\/div>\n    <div class=\"hw-note__body\">\n        <p>If you still encounter problems validating your simulation, then please post the issue on our <a href=\"https:\/\/www.simscale.com\/forum\/\">forum<\/a> or <a href=\"mailto:support@simscale.com\">contact us<\/a>.<\/p>\n    <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This validation case belongs to computational fluid dynamics and aims to validate the following parameters: Simulation...","protected":false},"author":114,"featured_media":86565,"parent":17191,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-documentation.php","meta":{"_acf_changed":false,"_crdt_document":"","inline_featured_image":false,"footnotes":""},"class_list":["post-86543","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/86543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/users\/114"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=86543"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/86543\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/17191"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media\/86565"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=86543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}