{"id":4883,"date":"2016-06-02T17:50:43","date_gmt":"2016-06-02T06:50:43","guid":{"rendered":"https:\/\/www.computationalfluiddynamics.com.au\/?p=2343"},"modified":"2016-06-02T17:50:43","modified_gmt":"2016-06-02T06:50:43","slug":"tips-on-modelling-non-newtonian-fluid-viscosity","status":"publish","type":"post","link":"https:\/\/www.leapaust.com.au\/blog\/cfd\/tips-on-modelling-non-newtonian-fluid-viscosity\/","title":{"rendered":"Tips on modelling non-Newtonian fluid viscosity"},"content":{"rendered":"<div id=\"bsf_rt_marker\"><\/div><p>Following on from our recent post on\u00a0how to handle scanned\u00a0biomedical data (&#8220;<strong><a href=\"https:\/\/www.computationalfluiddynamics.com.au\/how-to-shrink-wrap-a-biomedical-stl-file-in-fluent-meshing\/\">How to Shrink Wrap a biomedical STL File<\/a><\/strong>&#8220;), let&#8217;s consider another complexity that we typically encounter in CFD of\u00a0biomedical applications: non-Newtonian viscosity of fluids such as blood.<\/p>\n<p>In CFD, we commonly\u00a0run simulations\u00a0using fluids that are modelled as Newtonian, which are defined as having a linear relationship between viscous shear stress and shear strain.\u00a0 A result of this linear relationship is that the viscosity of Newtonian fluids is invariant. \u00a0However, many fluids we encounter in industry do not strain linearly with respect to viscous shear and are thus considered non-Newtonian.<\/p>\n<p>In some\u00a0cases, a non-Newtonian fluid may be assumed to behave in a Newtonian manner, just as it is often acceptable to model air or other gas as incompressible within\u00a0certain conditions.\u00a0 However, just as there are many scenarios in which a gas must\u00a0be modelled with an ideal- or real-gas relationship (instead of incompressible) to produce useful CFD results, there are also\u00a0<span style=\"text-decoration: underline;\">many situations\u00a0which necessitate the accurate capture of shear-dependent variations in viscosity<\/span>.<\/p>\n<p>Let\u2019s look at how to\u00a0setup the material properties of blood as a non-Newtonian fluid. According to literature, a common shear-thinning model used to replicate\u00a0blood is the Carreau-Yasuda model, which takes the form of:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-2346\" src=\"https:\/\/www.leapaust.com.au\/blog\/wp-content\/uploads\/2016\/06\/blood-viscosity.png\" alt=\"blood-viscosity\" width=\"360\" height=\"124\" \/><\/p>\n<p>where \u00b5<sub>0<\/sub> is the zero-shear viscosity, \u00b5<sub>\u221e<\/sub> is the infinite-shear viscosity, and <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\dot{}\" alt=\"\\dot{}\" align=\"absmiddle\" \/><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\inline&amp;space;\\dot{}\\gamma\" alt=\"\\inline \\dot{}\\gamma\" align=\"absmiddle\" \/>\u00a0is the shear strain rate.\u00a0 All other variables, as well as \u00b5<sub>0<\/sub> and \u00b5<sub>\u221e<\/sub>, are experimental fit parameters.<\/p>\n<p>&nbsp;<\/p>\n<p>This model results in viscous\u00a0behaviour such as that shown below:<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-2347\" src=\"https:\/\/www.leapaust.com.au\/blog\/wp-content\/uploads\/2016\/06\/blood-viscosity-graph.png\" alt=\"blood-viscosity-graph\" width=\"674\" height=\"519\" \/><\/p>\n<p style=\"text-align: center;\">Figure 1. Viscosity behaviour of a fluid using\u00a0the Carreau-Yasuda model.<\/p>\n<p>Looking at the graph, clearly there are regimes in which a Newtonian approximation could be sufficient.\u00a0 It should be just as clear however, that some regimes require capturing the non-Newtonian behaviour in order to achieve any sort of sensible CFD result and capture all important flow behaviour.<\/p>\n<p>In CFX, the Carreau-Yasuda model is built in, meaning you can simply apply the coefficients directly.\u00a0 In Fluent, we can apply the same model via UDF using the DEFINE_PROPERTY macro.\u00a0 The <a href=\"https:\/\/info.leapaust.com.au\/acton\/attachment\/9346\/f-035d\/1\/-\/-\/-\/-\/carreau-yasuda-viscosity.c\">UDF written for this is available here<\/a>.<\/p>\n<p>Having applied this material model to a\u00a0<strong><a href=\"https:\/\/www.computationalfluiddynamics.com.au\/how-to-shrink-wrap-a-biomedical-stl-file-in-fluent-meshing\/\">CFD simulation of\u00a0our imported\u00a0aorta STL geometry<\/a><\/strong>, we can now easily\u00a0observe and understand the relationship between shear stress and viscosity by comparing the results\u00a0below:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-2356\" src=\"https:\/\/www.leapaust.com.au\/blog\/wp-content\/uploads\/2016\/06\/aorta-results.png\" alt=\"aorta-results\" width=\"2535\" height=\"1288\" \/><\/p>\n<p>In summary, we have learnt that applying a non-Newtonian model to the fluid you are simulating is straightforward in ANSYS CFD (either CFX or FLUENT) and this can be an important step to improving the relevance and usefulness\u00a0of your CFD simulation results in some fields. \u00a0So the next time your CFD model includes blood, gels, <a href=\"http:\/\/www.ansys.com\/Solutions\/Solutions-by-Industry\/Consumer-Goods\/Food-and-Beverage\">foodstuffs, oils<\/a>, or any other non-Newtonian fluid, don\u2019t forget that an appropriate material model is just a few mouse-clicks away!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Many fluids we encounter in industry do not strain linearly with respect to viscous shear and are thus considered non-Newtonian. This post explores how to model non-Newtonian viscosity of fluids in ANSYS CFD, using blood as an example.<\/p>\n","protected":false},"author":3,"featured_media":4287,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","footnotes":""},"categories":[323],"tags":[174,391,396,244,453,460,513],"class_list":["post-4883","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cfd","tag-ansys-cfd","tag-biomedical-cfd","tag-cfd-simulation-accuracy","tag-material-properties","tag-modelling-of-blood","tag-non-newtonian-fluid","tag-viscosity"],"_links":{"self":[{"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/posts\/4883","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/comments?post=4883"}],"version-history":[{"count":0,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/posts\/4883\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/media\/4287"}],"wp:attachment":[{"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/media?parent=4883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/categories?post=4883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.leapaust.com.au\/blog\/wp-json\/wp\/v2\/tags?post=4883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}