{"id":18104,"date":"2018-12-15T18:57:29","date_gmt":"2018-12-15T18:57:29","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18104"},"modified":"2025-08-29T17:34:15","modified_gmt":"2025-08-29T17:34:15","slug":"aerodynamics-flow-around-the-ahmed-body","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/aerodynamics-flow-around-the-ahmed-body\/","title":{"rendered":"Aerodynamics: Flow around the Ahmed Body"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This validation case belongs to fluid mechanics, representing the aerodynamics of the Ahmed body study. The aim of this test case is to validate the following parameters: <\/p>\n\n\n\n\n\n\n<ul class=\"wp-block-list\">\n<li>Drag coefficient computation<\/li>\n\n\n\n<li>Velocity profiles<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results of SimScale were compared to the experimental data presented in [Ahmed]\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=2966030768813915000&#038;mi=spec%3A66cef90e-a950-4cc8-a588-63c4c6adee1e%2Cservice%3ASIMULATION%2Cstrategy%3A647\" class=\"hw-btn    \" rel=\"noopener \" target=\"_blank\"    >\n        View Project    <\/a>\n<\/div>\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"geometry\">Geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The geometry is created based on the simplified aerodynamic body used by Ahmed et al\\(^1\\). See Figure 1 for dimensions and Figure 2 for the geometry. The slant angle (\\(\\phi\\)) is set to 25\u00b0. The body is placed in a wind tunnel 6 \\(m\\) x 5 \\(m\\) x 13.5 \\(m\\) in order to limit the aerodynamic blockage effect.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-diag.png\"><img loading=\"lazy\" decoding=\"async\" width=\"787\" height=\"352\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-diag.png\" alt=\"ahmed body geometry dimensions\" class=\"wp-image-27336\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-diag.png 787w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-diag-300x134.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-diag-768x344.png 768w\" sizes=\"auto, (max-width: 787px) 100vw, 787px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: Dimensions of the Ahmed Body<\/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\/04\/AhmedBody-geometry-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"673\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-geometry-1-1024x673.png\" alt=\"ahmed body geometry\" class=\"wp-image-27338\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-geometry-1-1024x673.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-geometry-1-300x197.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-geometry-1-768x505.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-geometry-1.png 1418w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 2: Three-dimensional view of the geometry used in the study<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"analysis-type-and-mesh\">Analysis Type and Mesh<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tool Type<\/strong>: <a href=\"https:\/\/openfoam.org\/\">OpenFOAM\u00ae<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: Turbulent <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/incompressible-fluid-flow-analysis\/\">Incompressible <\/a>fluid flow <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mesh and Element Types<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Mesh <\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Mesh Type<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Number of Cells<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh 1<\/td><td class=\"has-text-align-center\" data-align=\"center\">Standard<\/td><td class=\"has-text-align-center\" data-align=\"center\">3,746,887<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh 2<\/td><td class=\"has-text-align-center\" data-align=\"center\">Standard<\/td><td class=\"has-text-align-center\" data-align=\"center\">6,915,859<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh 3<\/td><td class=\"has-text-align-center\" data-align=\"center\">Standard<\/td><td class=\"has-text-align-center\" data-align=\"center\">10119321<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Mesh details<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong><a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/meshing\/standard\/\">Standard Mesher<\/a> <\/strong>algorithm with tetrahedral and hexahedral cells was used to generate the mesh, with refinements near the walls and in the wake region (see Figure 3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"355\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-1024x355.png\" alt=\"ahmed body simulation mesh\" class=\"wp-image-107521\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-1024x355.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-300x104.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-768x266.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-1536x532.png 1536w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/mesh-ahmed-body-2048x709.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: Mesh #3 of the three meshes investigated in the Ahmed body validation case<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A typical property of the generated mesh is the \\(y^+\\) (&#8220;<em>y-plus<\/em>&#8220;) value, which is defined as the non-dimensionalized distance to the wall, <a href=\"https:\/\/www.simscale.com\/forum\/t\/what-is-y-yplus\/82394\">learn more<\/a>. A \\(y^+\\) value of 1 would correspond to the upper limit of the laminar sub-layer.<\/p>\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>Wall treatment<\/p>\n    <\/div>\n    <div class=\"hw-note__body\">\n        <p><ul><li><em>Full Resolution in the near-wall region<\/em>: The first cell lies at most at the boundary of the laminar sub-layer and no further. Here, \\(y^+\\) value is 1 or below.<\/li><li><em>Use of wall-functions to resolve the near-wall region<\/em>: There is no need to place cells very close to the laminar sub-layer, and typically \\(30 \\le y^+ \\le 300\\).<\/li><\/ul><\/p>\n    <\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">An average \\(y^+\\) value of 1 was used for the inflation layer around the body, and 150 for the floor. The <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/global-settings\/k-omega-sst\/\">\\(k-\\omega\\) SST<\/a> turbulence model was chosen, with full resolution for near-wall treatment of the flow around the body and with wall function for the floor.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"simulation-setup\">Simulation Setup<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"material\">Material<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Fluid<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Air with a kinematic viscosity of 1.5 x 10<sup>-5<\/sup> \\(kg\/ms\\) is assigned as the domain fluid.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"boundary-conditions\"><strong>Boundary Conditions<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The boundary conditions for the simulation are shown in Figure 4 below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"666\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20-1024x666.png\" alt=\"ahmed body boundary conditions\" class=\"wp-image-107494\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20-1024x666.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20-300x195.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20-768x500.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2025\/08\/image-20.png 1133w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 4: Boundary conditions applied to the faces of the Ahmed body fluid domain<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Boundary Condition <\/strong><\/td><td><strong>Face<\/strong><\/td><td><strong>Value<\/strong><\/td><\/tr><tr><td>Velocity inlet \\([m\/s]\\)<br>Turb. kinetic energy \\([m^2\/s^2]\\)<br>Specific dissipation rate \\([1\/s]\\)<\/td><td>Inlet<\/td><td>60 <br>0.135<br>180.1<\/td><\/tr><tr><td>Pressure outlet \\([Pa]\\)<\/td><td>Outlet<\/td><td>0 (Fixed gauge pressure)<\/td><\/tr><tr><td>Slip wall<\/td><td>Side and top faces<\/td><td>&#8211;<\/td><\/tr><tr><td>No slip wall &#8211; Wall function<\/td><td>Bottom face (Ground)<\/td><td>&#8211;<\/td><\/tr><tr><td>No slip wall &#8211; Full resolution<\/td><td>Car body<\/td><td>&#8211;<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Boundary Conditions for the Ahmed Body simulation<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The free stream velocity of the simulation is 60 \\(m\/s\\), so that the Reynolds number based on the length of the body \\(L\\) is 4.29e6. Those are the same values presented in the original experiment of Ahmed and Ramm\\(^1\\).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"reference-solution\">Reference Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The experimental solution is presented in Figure 4 in the reference paper\\(^1\\) giving the value for the drag force coefficient for the slant angle \\(\\phi\\) = 25\u00b0:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">$$ C_{d} = 0.2875 $$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"result-comparison\">Result Comparison<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"drag-coefficient\"><strong>Drag Coefficient<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The drag force is defined as<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">$$  F_{d}={\\frac {1}{2}}\\rho \\,U^{2}\\,C_{d}\\,A_x $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where \\(A_x\\) (0.115 \\(m^2\\)) is the projected area of the Ahmed body in the streamwise direction and \\(F_{d}\\) the drag force. The drag force and drag coefficient were determined by the integration of surface pressure and shear stress over the entire Ahmed body (<strong>except for the 4 stilts acting as support<\/strong>). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mesh #2 was selected due to its accuracy and favorable results in relation to the simulation time. The resulting drag coefficient of the Ahmed body, closest to the reference solution as yielded by Mesh #2, was computed to be <strong>0.2915<\/strong>, which is within a <strong>1.217 %<\/strong> error margin of the measured value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Table 2 shows the result of the mesh independence study:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Mesh <br><\/th><th class=\"has-text-align-center\" data-align=\"center\">DRAG<br>FORCE \\([N]\\)<\/th><th class=\"has-text-align-center\" data-align=\"center\">DRAG <br>COEFFICIENT<\/th><th class=\"has-text-align-center\" data-align=\"center\">REFERENCE<\/th><th class=\"has-text-align-center\" data-align=\"center\">ERROR [%]<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh #1<\/td><td class=\"has-text-align-center\" data-align=\"center\">73.776<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2985<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2875<\/td><td class=\"has-text-align-center\" data-align=\"center\">3.65<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh #2<\/td><td class=\"has-text-align-center\" data-align=\"center\">72.043<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2915<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2875<\/td><td class=\"has-text-align-center\" data-align=\"center\">1.217<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mesh #3<\/td><td class=\"has-text-align-center\" data-align=\"center\">70.186<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2835<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2875<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1.39<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Results comparison and computed errors<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The difference in the error percentage magnitude between Mesh #2 and Mesh #3 is 0.173, indicating that the drag coefficient values are acceptable.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"wake-flow-patterns\"><strong>Wake Flow Patterns<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The velocity streamline contour of the mean flow obtained with the simulation is reported in Figure 5, together with experimental results of reference.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"702\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10-1024x702.png\" alt=\"ahmed body wake velocity vectors\" class=\"wp-image-35683\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10-1024x702.png 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10-300x206.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10-768x526.png 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/12\/image-10.png 1154w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 5: Velocity vectors and contours plotted with SimScale&#8217;s online post-processor<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-experiemental-results.png\"><img loading=\"lazy\" decoding=\"async\" width=\"677\" height=\"409\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-experiemental-results.png\" alt=\"ahmed body wake experimental results\" class=\"wp-image-27343\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-experiemental-results.png 677w, https:\/\/frontend-assets.simscale.com\/media\/2020\/04\/AhmedBody-experiemental-results-300x181.png 300w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 6: Experimental results for comparison showing a schematic of the streamlines over the Ahmed body<\/figcaption><\/figure>\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.sae.org\/publications\/technical-papers\/content\/840300\/\" target=\"_blank\" rel=\"nofollow noopener\">S.R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984<\/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 validation case belongs to fluid mechanics, representing the aerodynamics of the Ahmed body study. The aim of this test...","protected":false},"author":94,"featured_media":9757,"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-18104","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18104","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=18104"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18104\/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\/9757"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}