{"id":18507,"date":"2018-12-19T19:19:41","date_gmt":"2018-12-19T19:19:41","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18507"},"modified":"2026-02-16T15:42:27","modified_gmt":"2026-02-16T15:42:27","slug":"turbulent-pipe-flow","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/turbulent-pipe-flow\/","title":{"rendered":"Validation Case: Turbulent Pipe Flow"},"content":{"rendered":"\n\n\n\n<p class=\"wp-block-paragraph\">This turbulent pipe flow validation case belongs to fluid dynamics. The aim of this test case is to validate the following parameters:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pressure drop between the inlet and outlet of the pipe<\/li>\n\n\n\n<li>Velocity distribution across the flow direction<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results of SimScale were compared to a reference solution based on the Power law velocity profile presented by Henryk Kudela in one of his lectures\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=3102769619087593277\" 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 geometry can be seen 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\/10\/Geometry.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Geometry-1024x453.png\" alt=\"pipe geometry turbulence and pressure drop validation\" class=\"wp-image-33633\" width=\"768\" height=\"340\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Geometry-1024x453.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Geometry-300x133.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Geometry-768x340.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Geometry.png 1179w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: The geometry of the pipe to study turbulent flow and pressure drop<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">This is a cylindrical pipe with a diameter of 0.01 \\(m\\), and a length of 1 \\(m\\).<\/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\/incompressible-fluid-flow-analysis\/\"> Incompressible<\/a> steady-state analysis. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Turblence Model<\/strong>: Two turbulence models were tested, the<a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/k-epsilon\/\"> k-epsilon<\/a> and the <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/k-omega-sst\/\">k-omega SST<\/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\">Two approaches were tested in this validation case: Wall functions and full resolution on the walls. For the wall functions, the desired \\(y^+\\) range is [30 , 300], and the generated mesh looks like this:<\/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\/2021\/01\/New-Mesh-turbulent-pipe-flow.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/New-Mesh-turbulent-pipe-flow.jpg\" alt=\"wall treatment with wall functions for boundary layer of mesh\" class=\"wp-image-36322\" width=\"483\" height=\"412\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/New-Mesh-turbulent-pipe-flow.jpg 644w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/New-Mesh-turbulent-pipe-flow-300x256.jpg 300w\" sizes=\"auto, (max-width: 483px) 100vw, 483px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 2: The mesh created for the wall function approach<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Full resolution on the walls requires a \\(y^+\\) lower than \\(1\\), so the final mesh has the following form:<\/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\/10\/Full-resolution-mesh.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Full-resolution-mesh.png\" alt=\"wall treatment with full resolution for boundary layer of mesh\" class=\"wp-image-33636\" width=\"543\" height=\"478\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Full-resolution-mesh.png 724w, https:\/\/frontend-assets.simscale.com\/media\/2020\/10\/Full-resolution-mesh-300x264.png 300w\" sizes=\"auto, (max-width: 543px) 100vw, 543px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: The mesh created for the full resolution approach with inflation layers added<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">More details about the meshes used in the three cases can be seen bellow:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Cases<\/th><th>Near-wall approach<\/th><th>Number of cells<\/th><th>Mesh type<\/th><th>Turbulence model<\/th><\/tr><\/thead><tbody><tr><td>A<\/td><td>Wall functions<\/td><td>176574<\/td><td>Standard<\/td><td>k-omega SST<\/td><\/tr><tr><td>B<\/td><td>Wall functions<\/td><td>176574<\/td><td>Standard<\/td><td>k-epsilon<\/td><\/tr><tr><td>C<\/td><td>Full resolution<\/td><td>1393776<\/td><td>Standard<\/td><td>k-omega SST<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Information on the meshes used for each case<\/figcaption><\/figure>\n\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><strong>Water<\/strong>\n<ul class=\"wp-block-list\">\n<li>\\((\\nu)\\) <em>Kinematic viscosity<\/em>  = 10\\(^{-6}\\) \\(m^2 \\over \\ s\\)<\/li>\n\n\n\n<li>\\((\\rho)\\) <em>Density<\/em>  = 1000 \\(kg \\over\\ m^3\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Boundary Conditions<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Velocity inlet of 1  \\(m \\over \\ s\\)<\/li>\n\n\n\n<li>Pressure outlet of 0 \\(Pa\\)<\/li>\n\n\n\n<li>No-slip walls with wall functions for cases A and B, and full resolution for case C<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Initial Conditions:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Turbulent kinetic energy \\((k)\\) of 3.84e-3 \\(m^2 \\over \\ s^2\\)<\/li>\n\n\n\n<li>Case A &amp; C: Specific dissipation rate (\\(\u03c9\\)) of 88.53 \\(1 \\over \\ s\\)<\/li>\n\n\n\n<li>Case B: Dissipation rate \\((\u03b5)\\) of 3.059e-2 \\(m^2 \\over \\ s^3\\)<\/li>\n<\/ul>\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 velocity profile for turbulent pipe flow is approximated by the Power-law velocity profile equation \\(^1\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\bar{u}_y(r) = \\bar{u}_{y_{max}}\\left(\\frac{R-r}{R}\\right)^{1\/n}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\({u}_{y_{max}}\\): the maximum y-velocity of the cross-section (along the pipe axis)<\/li>\n\n\n\n<li>\\(R\\): the radius of the cylinder<\/li>\n\n\n\n<li>\\(r\\): the distance from the center of the cross-section<\/li>\n\n\n\n<li>\\(n\\): a constant that depends on the Reynolds number, estimated as 7 for this case<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For turbulent flow, the ratio of \\(u_{y_{max}}\\) to the mean flow velocity is a function of \\(Re\\). In this case, this ratio is calculated to be 1.224. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The pressure drop for turbulent flow in pipes is obtained by using the Darcy-Weisbach \\(^2\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\Delta P = f\\ \\frac{\\rho\\ u^2 \\ l}{2 \\ d}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(f\\): is the Darcy friction factor calculated by the solution of the Colebrook equation<\/li>\n\n\n\n<li>\\(\u03c1\\): is the density of the fluid<\/li>\n\n\n\n<li>\\(u\\): is the average velocity of the cross section<\/li>\n\n\n\n<li>\\(l\\): is the length of the pipe<\/li>\n\n\n\n<li>\\(d\\): is the diameter of the cylinder<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">According to the Moody diagram (Figure 4) and for this case, the value of \\(f\\) is 0.0309.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/Moody_diagram-2.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/Moody_diagram-2-1024x642.jpg\" alt=\"moody diagram for pipe flow analytical solution\" class=\"wp-image-27561\" width=\"768\" height=\"482\"\/><\/a><figcaption class=\"wp-element-caption\">Figure 4. Moody diagram for estimating the Darcy friction factor<\/figcaption><\/figure>\n\n\n\n<h2 id=\"result-comparison\" class=\"wp-block-heading\" >Result Comparison<\/h2>\n\n\n\n<h3 id=\"wall-functions\" class=\"wp-block-heading\" >Wall functions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For the &#8220;wall function approach&#8221; the average \\(y^+\\) value on the walls of the pipe is 31.95 for k-omega SST and 32.39 for k-epsilon. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pressure drop along the pipe length can be observed 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\/2021\/01\/Pressure-Drop-Results.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Results.jpg\" alt=\"comparison of pressure drop across the pipe for turbulent flow with wall functions k-epsilon and k-omega SST model\" class=\"wp-image-36356\" width=\"603\" height=\"407\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Results.jpg 804w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Results-300x203.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Results-768x519.jpg 768w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 5: The pressure drop across the pipe with the wall functions approach<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The following graph shows the developed velocity profile, located 60 \\(cm\\) from the inlet:<\/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\/2021\/01\/Velocity-profile-Wall-Functions.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions.jpg\" alt=\"comparison of velocity profiles across the x direction for turbulent pipe flow with wall functions k-epsilon and k-omega SST model\" class=\"wp-image-36357\" width=\"616\" height=\"434\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions.jpg 821w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-300x211.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-768x541.jpg 768w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 6: The velocity profile across the x axis, on a plane located 0.6 \\(m\\) from the inlet with the wall functions approach<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 id=\"full-resolution\" class=\"wp-block-heading\" >Full resolution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For &#8220;full resolution&#8221;, the average value for \\(y^+\\) is 0.017. The corresponding graphs are created:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The pressure drop along the pipe length:<\/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\/2021\/01\/Pressure-Drop-Full-resolution-Results.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Full-resolution-Results.jpg\" alt=\"comparison of pressure drop across the pipe for turbulent flow with full resolution and k-omega SST model\" class=\"wp-image-36360\" width=\"608\" height=\"421\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Full-resolution-Results.jpg 810w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Full-resolution-Results-300x208.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-Drop-Full-resolution-Results-768x532.jpg 768w\" sizes=\"auto, (max-width: 608px) 100vw, 608px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 7: The pressure drop across the pipe with the full resolution approach<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The developed radial velocity profile, located 60 \\(cm\\) from the inlet:<\/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\/2021\/01\/Velocity-profile-Wall-Functions-Full-Resolution-1.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-Full-Resolution-1.jpg\" alt=\"comparison of velocity profiles across the x direction for turbulent pipe flow with full resolution and k-omega SST model\" class=\"wp-image-36361\" width=\"618\" height=\"432\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-Full-Resolution-1.jpg 824w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-Full-Resolution-1-300x210.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Velocity-profile-Wall-Functions-Full-Resolution-1-768x537.jpg 768w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 8: The velocity profile across the x-axis, on a plane located 0.6 (m) from the inlet with the full resolution approach<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Besides good agreement with the Power law model, results show that all approaches and turbulence models are successful in predicting the pressure drop along pipe length for the given meshes.<\/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\/2021\/01\/Pressure.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-1024x592.jpg\" alt=\"pressure distribution on pipe turbulent flow\" class=\"wp-image-36456\" width=\"768\" height=\"444\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-1024x592.jpg 1024w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-300x173.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure-768x444.jpg 768w, https:\/\/frontend-assets.simscale.com\/media\/2021\/01\/Pressure.jpg 1176w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 9: Pressure distribution across the pipe for Case A<\/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.google.com\/url?sa=t&#038;rct=j&#038;q=&#038;esrc=s&#038;source=web&#038;cd=&#038;cad=rja&#038;uact=8&#038;ved=2ahUKEwib6YeXwKLsAhUCt4sKHSyoCOoQFjADegQIDRAC&#038;url=http%3A%2F%2Fwww.itcmp.pwr.wroc.pl%2F~znmp%2Fdydaktyka%2Ffundam_FM%2FLecture_no3_Turbulent_flow_Modelling.pdf&#038;usg=AOvVaw1iYv9ABYCHmDPOfck3Gzse\" target=\"_blank\" rel=\"noopener noreferrer nofollow\">Henryk Kudela &#8211; Turbulent Flow<\/a><\/cite><\/li><li><cite><a href=\"https:\/\/en.wikipedia.org\/wiki\/Darcy%E2%80%93Weisbach_equation\" target=\"_blank\" rel=\"noopener noreferrer nofollow\">Darcy\u2013Weisbach equation<\/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 you 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 turbulent pipe flow validation case belongs to fluid dynamics. The aim of this test case is to validate the...","protected":false},"author":94,"featured_media":36456,"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-18507","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18507","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=18507"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18507\/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\/36456"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}