{"id":18399,"date":"2018-12-19T09:01:05","date_gmt":"2018-12-19T09:01:05","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18399"},"modified":"2023-11-09T01:13:29","modified_gmt":"2023-11-09T01:13:29","slug":"multi-phase-flow-rising-bubble","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/multi-phase-flow-rising-bubble\/","title":{"rendered":"Validation Case: Rising Bubble"},"content":{"rendered":"\n\n\n\n\n<p class=\"wp-block-paragraph\">This validation case belongs to fluid dynamics and the aim of this test case is to validate the multiphase solver implemented in SimScale with the rising bubble case. Specifically, the following parameters are of interest:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bubble vertical velocity<\/li>\n\n\n\n<li>Bubble center of mass<\/li>\n\n\n\n<li>Bubble profile<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results from SimScale were compared to the results presented in&nbsp;the study &#8220;<a href=\"https:\/\/www.featflow.de\/en\/benchmarks\/cfdbenchmarking\/bubble.html\" target=\"_blank\" rel=\"noreferrer noopener\">Bubble Benchmark<\/a>&#8220;\\(^1\\) done by TU Dortmund.<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=7756819433602426543\" 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\">The domain of interest is a 2-dimensional rectangular space with dimensions as below: <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/09\/Model-1.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"480\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/09\/Model-1.jpg\" alt=\"top view of mesh used for rising bubble validation case\" class=\"wp-image-33496\" style=\"width:289px;height:480px\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/09\/Model-1.jpg 289w, https:\/\/frontend-assets.simscale.com\/media\/2020\/09\/Model-1-181x300.jpg 181w\" sizes=\"auto, (max-width: 289px) 100vw, 289px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: 2-dimensional rectangular fluid domain <\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The width AB, CD is 1 \\(m\\) while the height AD, BC is 2 \\(m\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For simulation purposes, a mesh was created with the <a href=\"https:\/\/openfoamwiki.net\/index.php\/BlockMesh\">blockMesh<\/a> tool in OpenFOAM\u00ae whose details can be found later in the following section.<\/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>Tool Type<\/strong>: OpenFOAM\u00ae<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/multiphase-fluid-flow-analysis\/\">Multiphase<\/a><\/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\">As explained before, the mesh was created with the <a href=\"https:\/\/openfoamwiki.net\/index.php\/BlockMesh\">blockMesh<\/a> tool. This is a uniform mesh with only one cell-layer in the z-axis, this is done to maintain the two-dimensional flow.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Mesh Type<\/strong><\/td><td><strong>Number of cell<\/strong>s<\/td><td><strong>Type<\/strong><\/td><\/tr><tr><td>snappyHexMesh<\/td><td>28800<\/td><td>2D hexahedral<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Mesh settings<\/figcaption><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Mesh-5-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"619\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Mesh-5-1024x619.jpg\" alt=\"uniform hexahedral mesh created with blockmesh for rising bubble validation case\" class=\"wp-image-33658\" style=\"width:1024px;height:619px\"\/><\/a><figcaption class=\"wp-element-caption\">Figure 2: Uniform hexahedral mesh of fluid domain with 1 layer in the z-axis created with blockMesh<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 id=\"simulation-setup\" class=\"wp-block-heading\" >Simulation Setup<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Fluid<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Case 1:<ul><li>Gravity \\((g)\\) : 0.98 \\(m\/s^2\\)<\/li><li>Surface tension \\((\\sigma)\\): 24.5 \\(N\/m\\)<\/li><\/ul>\n<ul class=\"wp-block-list\">\n<li>Material 1:\n<ul class=\"wp-block-list\">\n<li>Kinematic viscosity \\((\\nu)\\): 0.01 \\(m^2\/s\\)<\/li>\n\n\n\n<li>Density \\((\\rho)\\): 1000 \\(kg\/m^3\\)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Material 2:\n<ul class=\"wp-block-list\">\n<li>Kinematic viscosity \\((\\nu)\\): 0.01 \\(m^2\/s\\)<\/li>\n\n\n\n<li>Density \\((\\rho)\\): 100 \\(kg\/m^3\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Case 2<ul><li>Gravity \\((g)\\) : 0.98 \\(m\/s^2\\)<\/li><li>Surface tension \\((\\sigma)\\): 1.96 \\(N\/m\\)<\/li><\/ul>\n<ul class=\"wp-block-list\">\n<li>Material 1:\n<ul class=\"wp-block-list\">\n<li>Kinematic viscosity \\((\\nu)\\): 0.01 \\(m^2\/s\\)<\/li>\n\n\n\n<li>Density \\((\\rho)\\): 1000 \\(kg\/m^3\\)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Material 2:\n<ul class=\"wp-block-list\">\n<li>Kinematic viscosity \\((\\nu)\\): 0.1 \\(m^2\/s\\)<\/li>\n\n\n\n<li>Density \\((\\rho)\\): 1 \\(kg\/m^3\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>The location of the bubble at t = 0 \\(s\\) is at y = 0.5 \\(m\\).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Initial and Boundary Conditions<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial conditions<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Only the global phase fraction was initialized and was set to the value of 1, which is the fluid surrounding the bubble.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li> Boundary conditions<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">To simulate the rising bubble phenomenon, custom boundary conditions were used. The specific settings of the boundary conditions can be seen in the table below:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Parameter<\/strong><\/td><td><strong>Top and Bottom<\/strong><\/td><td><strong>Left and Right<\/strong><\/td><td><strong>Front and Back<\/strong><\/td><\/tr><tr><td>Velocity <\/td><td>Fixed Value &#8211; 0 \\(m\/s\\)<\/td><td>Slip<\/td><td>Empty 2D<\/td><\/tr><tr><td>Pressure <\/td><td>Fixed flux pressure &#8211; 0 \\(Pa\\)<\/td><td>Fixed flux pressure &#8211; 0 \\(Pa\\)<\/td><td>Empty 2D<\/td><\/tr><tr><td>Phase fraction<\/td><td>Zero gradient<\/td><td>Zero gradient<\/td><td>Empty 2D<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Custom boundary conditions for each parallel face<\/figcaption><\/figure>\n\n\n\n<h2 id=\"reference-solution\" class=\"wp-block-heading\" >Reference Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The reference solution for the center of mass and the rising velocity is given by the following equations:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$X_c = (x_c,y_c) = \\frac{\\int_{\\Omega_2}x\\,dx}{\\int_{\\Omega_2}1\\,dx} \\tag{1}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$U_c = \\frac{\\int_{\\Omega_2}u\\,dx}{\\int_{\\Omega_2}1\\,dx} \\tag{2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(X_c\\): x- and y-coordinates of the center of the bubble <\/li>\n\n\n\n<li>\\(\\Omega_2\\): the region the bubble resides\\(^1\\)<\/li>\n\n\n\n<li>\\(U_c\\): rising velocity of the bubble<\/li>\n\n\n\n<li>\\(u\\): velocity of the center of the bubble <\/li>\n<\/ul>\n\n\n\n<h2 id=\"result-comparison\" class=\"wp-block-heading\" >Result Comparison<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The comparison for the center of mass and the rising velocity of the bubble obtained from SimScale against the reference results obtained from the &#8220;<a href=\"https:\/\/www.featflow.de\/en\/benchmarks\/cfdbenchmarking\/bubble.html\">Bubble Benchmark<\/a>&#8220;\\(^1\\) is shown in figures below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"305\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-1024x305.jpg\" alt=\"comparison of the bubble's center of mass for each case between simscale and reference study\" class=\"wp-image-33661\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-1024x305.jpg 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-300x89.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-768x228.jpg 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/CenterOfMassComparison-3-1536x457.jpg 1536w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: Temporal center of mass comparison for each case between results from SimScale and reference study<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-1024x298.jpg\" alt=\"comparison of the bubble's rising velocity for each case between simscale and reference study\" class=\"wp-image-33662\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-1024x298.jpg 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-300x87.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-768x223.jpg 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/RisingVelocityComparison-3-1536x446.jpg 1536w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 4: Temporal rising velocity comparison for each case between results from SimScale and reference study<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The movement of the bubble for each case can be seen in the animation below:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-video aligncenter\"><video height=\"992\" style=\"aspect-ratio: 942 \/ 992;\" width=\"942\" autoplay loop muted preload=\"none\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/11\/rising-bubble-1-1.mp4\" playsinline><\/video><figcaption class=\"wp-element-caption\">Animation 1: Case 1 rising bubble deformation<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-video aligncenter\"><video height=\"992\" style=\"aspect-ratio: 942 \/ 992;\" width=\"942\" autoplay loop muted preload=\"none\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/11\/rising-bubble-2.mp4\" playsinline><\/video><figcaption class=\"wp-element-caption\">Animation 2: Case 2 rising bubble deformation<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\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.featflow.de\/en\/benchmarks\/cfdbenchmarking\/bubble.html\" target=\"_blank\">TU Dortmund, Bubble Benchmark<\/a><\/cite><\/li>\n    <\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This validation case belongs to fluid dynamics and the aim of this test case is to validate the multiphase solver implemented...","protected":false},"author":94,"featured_media":0,"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-18399","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18399","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\/94"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=18399"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18399\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/17191"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}