{"id":18441,"date":"2018-12-19T10:36:28","date_gmt":"2018-12-19T10:36:28","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18441"},"modified":"2026-02-16T15:42:52","modified_gmt":"2026-02-16T15:42:52","slug":"rotating-zones-taylor-couette-flow","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/rotating-zones-taylor-couette-flow\/","title":{"rendered":"Validation Case: Taylor-Couette Flow"},"content":{"rendered":"\n\n\n\n<p class=\"wp-block-paragraph\">The Taylor-Couette flow validation case belongs to fluid dynamics. This test case aims to validate the following parameters:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rotating wall<\/li>\n\n\n\n<li>Velocity profile<\/li>\n\n\n\n<li>Pressure profile<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">SimScale&#8217;s simulation results were compared to analytical results obtained from methods elucidated in the Scholarpedia article on Taylor-Couette flow\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=6592988122174411328\" 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 so-called Taylor-Couette flow occurs in the gap between two infinitely long concentric cylinders, when at least one of them is rotating. Therefore, the geometry for this project consists of a slice of an annulus between two cylinders, as seen in Figure 1:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-25_17-36-46.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"612\" height=\"321\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-25_17-36-46.jpg\" alt=\"taylor-couette flow geometry\" class=\"wp-image-31809\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-25_17-36-46.jpg 612w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-25_17-36-46-300x157.jpg 300w\" sizes=\"auto, (max-width: 612px) 100vw, 612px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: Annulus between two concentric cylinders, used to study the Taylor-Couette flow.<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The dimensions of the geometry are given in Table 1:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Geometry parameters<\/strong><\/td><td><strong>Dimension \\([m]\\)<\/strong><\/td><\/tr><tr><td>Outer radius (a)<\/td><td>1<\/td><\/tr><tr><td>Inner radius (b)<\/td><td>0.35<\/td><\/tr><tr><td>Thickness of the slice (c)<\/td><td>0.1<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Dimensions of the concentric cylinders.<\/figcaption><\/figure>\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>: <a href=\"https:\/\/www.openfoam.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">OPENFOAM\u00ae<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: Steady-state <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/incompressible-fluid-flow-analysis\/\">incompressible flow<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Turbulence Model<\/strong>: <a href=\"https:\/\/www.simscale.com\/docs\/simwiki\/cfd-computational-fluid-dynamics\/what-is-laminar-flow\/\">Laminar<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mesh and Element Types<\/strong>: The mesh used in this case was created in SimScale with the <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/meshing\/standard\/\">standard algorithm<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Find in Table 2 an overview of the resulting mesh:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Case<\/strong><\/td><td><strong>Mesh Type<\/strong><\/td><td><strong>Cells<\/strong><\/td><td><strong>Element Type<\/strong><\/td><\/tr><tr><td>Taylor-Couette flow<\/td><td>Standard<\/td><td>488457<\/td><td>3D tetrahedral\/hexahedral<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Standard mesh characteristics. The mesh consists of tetrahedral and hexahedral elements.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Find below the standard mesh used for this case:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-31_12-50-58.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"843\" height=\"457\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-31_12-50-58.jpg\" alt=\"standard mesh validation case taylor couette\" class=\"wp-image-32105\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-31_12-50-58.jpg 843w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-31_12-50-58-300x163.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-31_12-50-58-768x416.jpg 768w\" sizes=\"auto, (max-width: 843px) 100vw, 843px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 2: Standard mesh, with region refinements applied to the area around the inner cylinder wall.<\/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>Material<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Viscosity model<\/em>: <em>Newtonian<\/em>;<\/li>\n\n\n\n<li>\\((\\nu)\\) <em>Kinematic viscosity<\/em>: 1e-5 \\(m\u00b2\/s\\);<\/li>\n\n\n\n<li>\\((\\rho)\\) <em>Density<\/em>: 1 \\(kg\/m^3\\).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Boundary Conditions<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Before defining the boundary conditions, the current nomenclature will be used for the rest of this documentation:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_20-42-20.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"795\" height=\"435\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_20-42-20.jpg\" alt=\"identification of patches for boundary conditions taylor-couette flow\" class=\"wp-image-31860\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_20-42-20.jpg 795w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_20-42-20-300x164.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_20-42-20-768x420.jpg 768w\" sizes=\"auto, (max-width: 795px) 100vw, 795px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: Nomenclature for the assignment of boundary conditions.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the table below, the configuration for both velocity and pressure are given at each of the boundaries:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Nomenclature<\/strong><\/td><td><strong>Boundary Type<\/strong><\/td><td><strong>Velocity<\/strong><\/td><td><strong>Pressure<\/strong><\/td><\/tr><tr><td>Inner wall<\/td><td>Custom<\/td><td>Rotating wall: 0.001 \\(rad\/s\\) around the positive y-axis<\/td><td>Zero gradient<\/td><\/tr><tr><td>Outer wall<\/td><td>Custom<\/td><td>Fixed value: 0 (no-slip condition)<\/td><td>Zero gradient<\/td><\/tr><tr><td>Sides<\/td><td>Custom<\/td><td>Symmetry<\/td><td>Symmetry<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 3: Summary of the boundary conditions used for all cases<\/figcaption><\/figure>\n\n\n\n<h2 id=\"reference-solution\" class=\"wp-block-heading\" ><strong>Reference Solution<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The analytical solution\\(^1\\) for Taylor-Couette flow is computed from the simplified Navier-Stokes in cylindrical coordinates. Before calculating the velocity and pressure profiles, we need to calculate two constants, \\(A\\) and \\(B\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$A = \\frac {\\omega_{out}R_{out}^2-\\omega_{in}R_{in}^2}{R_{out}^2-R_{in}^2} \\tag {1}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$B = (\\omega_{in} &#8211; \\omega_{out})R_{out}^2\\frac {R_{in}^2}{R_{out}^2-R_{in}^2} \\tag{2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(\\omega_{in}\\) and \\(\\omega_{out}\\) \\([rad\/s]\\) are the rotational velocities of the inner and outer walls, respectively;<\/li>\n\n\n\n<li>\\(R_{in}\\) and \\(R_{out}\\) \\([m]\\) are the inner and outer walls&#8217; radius.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The resulting velocity profile \\(U\\) is a function of radius \\(r\\). The equation is given below:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$U(r) = Ar + \\frac {B}{r} \\tag {3}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly, for pressure \\(P\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P(r) = A^2\\frac {r^2}{2}+2ABln(r)-\\frac {B^2}{2r^2} \\tag {4}$$<\/p>\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 velocity and pressure variation in the radial direction obtained with SimScale are compared to the analytical solution.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_22-16-48.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"942\" height=\"409\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_22-16-48.jpg\" alt=\"pressure and velocity profiles taylor-couette flow\" class=\"wp-image-31865\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_22-16-48.jpg 942w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_22-16-48-300x130.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-27_22-16-48-768x333.jpg 768w\" sizes=\"auto, (max-width: 942px) 100vw, 942px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 4: Result comparison between SimScale&#8217;s results and the analytical solution, for velocity and pressure.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In Figure 5, we can see the velocity profile due to the rotation of the inner wall.<\/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\/09\/velocity-contours-taylor-couette-flow.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/09\/velocity-contours-taylor-couette-flow.png\" alt=\"velocity contours taylor-couette flow\" class=\"wp-image-80274\" style=\"width:569px;height:512px\" width=\"569\" height=\"512\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2023\/09\/velocity-contours-taylor-couette-flow.png 741w, https:\/\/frontend-assets.simscale.com\/media\/2023\/09\/velocity-contours-taylor-couette-flow-300x270.png 300w\" sizes=\"auto, (max-width: 569px) 100vw, 569px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 5: Velocity magnitude contours obtained in the present validation case with the standard mesher.<\/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.scholarpedia.org\/article\/Taylor-Couette_flow\" target=\"_blank\">\u201cScholarpedia. Taylor-Couette flow&#8221;<\/a><\/cite><\/li>\n    <\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The Taylor-Couette flow validation case belongs to fluid dynamics. This test case aims to validate the following...","protected":false},"author":94,"featured_media":80274,"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-18441","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18441","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=18441"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18441\/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\/80274"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}