{"id":45937,"date":"2021-06-18T16:58:28","date_gmt":"2021-06-18T16:58:28","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=45937"},"modified":"2022-08-03T16:51:32","modified_gmt":"2022-08-03T16:51:32","slug":"thermal-bridge-case-3","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/thermal-bridge-case-3\/","title":{"rendered":"Validation Case: Thermal Bridge Case 3 &#8211; 3D Corner in Building Construction"},"content":{"rendered":"\n\n\n\n<p class=\"wp-block-paragraph\">This validation case belongs to heat transfer, with the case of a three-dimensional corner where two walls and one floor element meet. The aim of this project is to demonstrate the validity of SimScale\u2019s Heat Transfer solver by replicating the standard test case and comparing the following parameters:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Temperature distribution<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results from SimScale were compared to the reference results presented in the standard EN-ISO 10211, &#8220;Thermal Bridges in Building Construction&#8221;, validation case 3 (Annex C)\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=943281502728513000\" 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 structural corner geometry is shown in figure 1:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-10.png\"><img loading=\"lazy\" decoding=\"async\" width=\"882\" height=\"803\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-10.png\" alt=\"three dimensional structure heat transfer simscale thermal bridge case 3\" class=\"wp-image-45941\" title=\"Model geometry showing the structure\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-10.png 882w, https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-10-300x273.png 300w, https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-10-768x699.png 768w\" sizes=\"auto, (max-width: 882px) 100vw, 882px\" \/><\/a><figcaption>Figure 1: Model geometry showing the two walls and the floor elements that meet in the corner<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">The model is composed of the following parts:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Floor<\/li><li>Horizontal structure (which acts as the thermal bridge)<\/li><li>Internal wall &#8211; upper<\/li><li>Internal wall &#8211; lower<\/li><li>External wall<\/li><li>Insulation<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">For the application of boundary conditions and measurement of result quantities, the surfaces of the structure are classified according to the spaces they belong to:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-14.png\"><img loading=\"lazy\" decoding=\"async\" width=\"746\" height=\"724\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-14.png\" alt=\"surfaces heat transfer simscale thermal bridge\" class=\"wp-image-45987\" title=\"Definition of surfaces in the model\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-14.png 746w, https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-14-300x291.png 300w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/a><figcaption>Figure 2: Definition of surfaces in the model for boundary condition and result referencing<\/figcaption><\/figure>\n\n\n\n<ul class=\"wp-block-list\"><li>Lower internal (\\(\\alpha\\))<\/li><li>Upper internal (\\(\\beta\\))<\/li><li>External (\\(\\gamma\\))<\/li><li>Structure cuts (\\(\\delta\\))<\/li><\/ul>\n\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>: Code_Aster<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/heat-transfer\/\">Heat Transfer<\/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\">The mesh was computed using SimScale&#8217;s standard meshing algorithm, with the fineness parameter maxed up to 10. Statistics of the resulting mesh are presented in Table 1, and illustration shown in Figure 2:<\/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\"><strong>Mesh #<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Mesh Type<\/strong><\/th><th><strong>Element Type<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Number of Nodes<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Number of Elements<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">Standard<\/td><td>1st order tetrahedrals<\/td><td class=\"has-text-align-center\" data-align=\"center\">741457<\/td><td class=\"has-text-align-center\" data-align=\"center\">483998<\/td><\/tr><\/tbody><\/table><figcaption>Table 1: Finite elements mesh details<\/figcaption><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-8.png\"><img decoding=\"async\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/image-8.png\" alt=\"mesh heat transfer simscale thermal bridge\" class=\"wp-image-45939\" title=\"Finite elements tetrahedral mesh\"\/><\/a><figcaption>Figure 3: Finite elements tetrahedral mesh used for the thermal simulation using SimScale&#8217;s standard meshing algorithm<\/figcaption><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"simulation-setup\" >Simulation Setup<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Materials<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Interior Wall<ul><li>\\((\\rho)\\) <em>Density<\/em>: 1700 \\(kg\/m^3\\)<\/li><li><em>Conductivity<\/em>: Isotropic<\/li><li>\\( (\\kappa)\\) ) <em>Thermal conductivity<\/em>: 0.7 \\( W\/(m.K) \\)<\/li><li><em>Specific Heat<\/em>: 800 \\( J\/(kg.K) \\)<\/li><\/ul><\/li><li>Isolation <ul><li>\\((\\rho)\\) <em>Density<\/em>: 200 \\(kg\/m^3\\)<\/li><li><em>Conductivity<\/em>: Isotropic<\/li><li>\\( (\\kappa)\\) ) <em>Thermal conductivity<\/em>: 0.04 \\( W\/(m.K) \\)<\/li><li><em>Specific Heat<\/em>: 1000 \\( J\/(kg.K) \\)<\/li><\/ul><\/li><li>Exterior Wall<ul><li>\\((\\rho)\\) <em>Density<\/em>: 2000 \\(kg\/m^3\\)<\/li><li><em>Conductivity<\/em>: Isotropic<\/li><li>\\( (\\kappa)\\) ) <em>Thermal conductivity<\/em>: 1 \\( W\/(m.K) \\)<\/li><li><em>Specific Heat<\/em>: 1000 \\( J\/(kg.K) \\)<\/li><\/ul><\/li><li>Horizontal Structure <ul><li>\\((\\rho)\\) <em>Density<\/em>: 5000 \\(kg\/m^3\\)<\/li><li><em>Conductivity<\/em>: Isotropic<\/li><li>\\( (\\kappa)\\) ) <em>Thermal conductivity<\/em>: 2.5 \\( W\/(m.K) \\)<\/li><li><em>Specific Heat<\/em>: 600 \\( J\/(kg.K) \\)<\/li><\/ul><\/li><li>Floor<ul><li>\\((\\rho)\\)<em> Density<\/em>: 1000 \\(kg\/m^3\\)<\/li><li><em>Conductivity<\/em>: Isotropic<\/li><li>\\( (\\kappa)\\) ) <em>Thermal conductivity<\/em>: 1 \\( W\/(m.K) \\)<\/li><li><em>Specific Heat<\/em>: 800 \\( J\/(kg.K) \\)<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Boundary Conditions<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The model considers convective heat transfer from the surfaces of the structure to the corresponding spaces. The interior spaces are at 20\\(\u00b0C\\) and 15\\(\u00b0C\\), and the exterior is at 0\\(\u00b0C\\). Also, the standard specifies the heat transfer properties in terms of the thermal resistance \\(R\\), which must be converted to the heat transfer coefficient used in SimScale, according to:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">$$ h = \\frac{1}{R} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The following boundary conditions were used in the simulation (see Figure 2 for illustration):<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Lower internal faces \\(\\alpha\\):<ul><li>Convective heat flux<\/li><li>(\\(T_0\\)) Reference temperature 20\\(\u00b0C\\)<\/li><li>Heat transfer coefficient 5 \\(W\/(K.m^2)\\)<\/li><\/ul><\/li><li>Upper internal faces \\(\\beta\\):<ul><li>Convective heat flux<\/li><li>(\\(T_0\\)) Reference temperature 15\\(\u00b0C\\)<\/li><li>Heat transfer coefficient 5 \\(W\/(K.m^2)\\)<\/li><\/ul><\/li><li>External faces \\(\\gamma\\):<ul><li>Convective heat flux <\/li><li>(\\(T_0\\)) Reference temperature 0\\(\u00b0C\\)<\/li><li>Heat transfer coefficient 20 \\(W\/(K.m^2)\\)<\/li><\/ul><\/li><li>Structure cuts \\(\\delta\\):<ul><li>Adiabatic (applied by default)<\/li><\/ul><\/li><\/ul>\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 reference solution\\(^1\\) for the structure is given in terms of the minimum temperatures and heat fluxes at the control surfaces.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"result-comparison\" >Result Comparison<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The computed temperature values from the simulation are presented in Table 2, and compared to the expected values from the standard:<\/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\">Result<\/th><th class=\"has-text-align-center\" data-align=\"center\">Reference Value<\/th><th class=\"has-text-align-center\" data-align=\"center\">SimScale Value<\/th><th class=\"has-text-align-center\" data-align=\"center\">Deviation<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Minimum temperature on \\(\\alpha\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">11.32\\(\u00b0C\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">11.29\\(\u00b0C\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.03\\(\u00b0C\\)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Minimum temperature on \\(\\beta\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">11.11\\(\u00b0C\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">11.12\\(\u00b0C\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.01\\(\u00b0C\\)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Heat Flow on \\(\\alpha\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">46.09\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">45.75\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.74%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Heat Flow on \\(\\beta\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">13.89\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">13.76\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.72%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Heat Flow on \\(\\gamma\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">59.98\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">59.60\\(W\\)<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.63%<\/td><\/tr><\/tbody><\/table><figcaption>Table 2: Results comparison for the quantities of interest<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The acceptance criterion states that the difference between the computed temperatures by the method being validated and the listed temperatures shall not exceed 0.1\\(\u00b0C\\). For the Heat Flows, the deviation should not exceed 1%. Thus, it is found that the SimScale solver is accepted under the standard&#8217;s validation case 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/Temperature.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2021\/06\/Temperature-1024x768.png\" alt=\"temperature plot heat transfer simscale\" class=\"wp-image-45988\" title=\" Temperature contours in the structure\"\/><\/a><figcaption>Figure 5: Temperature contours in the corner structure, showing gradient from hot to cold regions<\/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.iso.org\/standard\/65710.html\"target=\"_blank\">\u201cISO 10211 &#8211; Thermal bridges in building construction \u2014 Heat flows and surface temperatures \u2014 Detailed calculations&#8221;<\/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 heat transfer, with the case of a three-dimensional corner where two walls and one floor...","protected":false},"author":115,"featured_media":45988,"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-45937","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/45937","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\/115"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=45937"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/45937\/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\/45988"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=45937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}