{"id":11766,"date":"2017-03-01T07:30:23","date_gmt":"2017-03-01T06:30:23","guid":{"rendered":"https:\/\/mag.ebmpapst.com\/en\/?p=11766"},"modified":"2025-11-13T09:32:36","modified_gmt":"2025-11-13T08:32:36","slug":"the-formula-for-vorticity","status":"publish","type":"post","link":"https:\/\/mag.ebmpapst.com\/en\/products\/fans\/the-formula-for-vorticity_11766\/","title":{"rendered":"The formula for vorticity"},"content":{"rendered":"
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Oliver Haaf, Group Leader in Proto\u00adtype and Func\u00adtion Devel\u00adop\u00adment for Aero\u00addy\u00adnamics at ebm-papst in Mulfingen<\/figcaption><\/figure>\n<\/div>\n\n\n

A velocity field\u2019s rota\u00adtion is given by the cross product of the direc\u00adtional deriv\u00ada\u00adtive vector (\u2207<\/small><\/span>) and the velocity vector (v<\/span>). It spec\u00adi\u00adfies how fast or how strongly a vortex in a flow field is rotating around its center. The vorticity can be influ\u00adenced by making changes in the blade geom\u00adetry near the gap between the fan and its housing. Noise increases with increasing vorticity.<\/p>\n\n\n\n

For axial fans, the pres\u00adsure differ\u00adence between the intake and outlet sides results in a flow over the fan blades in the vicinity of the housing wall. The flow inter\u00adacts there with the edges, the blade surface and the surrounding housing wall. Vortices form which can raise the noise level by up to 10 dB.<\/p>\n\n\n\n

The gap between the blade tip and the fan housing has a major impact on the noise level, with the noise decreasing as the size of the gap is reduced.<\/p>\n\n\n\n

Winglets can influ\u00adence the vortices with different geome\u00adtries. One possi\u00adbility is to reduce the velocity vector v<\/span> of the vortices. So-called T-winglets increase the flow resis\u00adtance in the gap area, thus reducing the vorticity (\u03c9<\/span> = \u2207<\/small><\/span> \u00d7 v<\/span>) and conse\u00adquently the noise gener\u00adated when the vortices strike solid surfaces.<\/p>\n\n\n\n

The other possi\u00adbility is to reduce the vorticity\u03c9<\/span>by changing the blade contours: The blade is rounded off in the gap area and the edges over which the gap flow streams are removed\u2009\u2014\u2009similar to the winglets on airplane wings. These blades only have an edge on the outlet side of the gap flow, so vortex forma\u00adtion is signif\u00adi\u00adcantly reduced \u2014 this influ\u00adences the gradient vector (del oper\u00adator \u2207<\/small><\/span> = \u2202\/\u2202x, \u2202\/\u2202y, \u2202\/\u2202z) = direc\u00adtional deriv\u00ada\u00adtive vector).<\/p>\n\n\n\n

<\/div>\n\n\n\n
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Sound\u00adcheck for heat\u00adpumps: Psychoa\u00adcoustics for minimum noise gener\u00ada\u00adtion<\/h3>\n\n\n
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<\/a><\/figure>\n<\/div>\n\n\n

Air\/water heat\u00adpumps<\/strong> with heat outputs from 3 to 30 kW enjoy a high level of accep\u00adtance in heating tech\u00adnology. However, they do not work completely silently. It is by no means just the measur\u00adable sound pres\u00adsure level that is crucial, but human noise percep\u00adtion<\/strong>, which is where psychoa\u00adcoustics and its exam\u00adi\u00adna\u00adtion methods come into play.<\/p>\n\n\n\n

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Read the article <\/i><\/a><\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n
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The flow inter\u00adacts in the vicinity of the tip gap with the neigh\u00adboring edges, the blade surface and the surrounding housing wall. The strength of the resulting tip gap vortex depends on the design.<\/figcaption><\/figure>\n<\/div>\n\n\n

The winglet geom\u00adetry that is best suited to a partic\u00adular axial fan is deter\u00admined by the required sepa\u00adra\u00adtion between the rotating (blade) and stationary (fan housing) compo\u00adnents. The inter\u00adac\u00adtion of the two compo\u00adnents is crucial and the geome\u00adtries have to fit in order to achieve optimal results. A good example is provided by the AxiBlade axial fans made of strong, glass-fiber rein\u00adforced plastic that enables the winglet shape to be adapted to the inter\u00adac\u00adtion with the newly devel\u00adoped housing geom\u00adetry, reducing the noise gener\u00adated at the gap.<\/p>\n","protected":false},"excerpt":{"rendered":"

A velocity field\u2019s rota\u00adtion is given by the cross product of the direc\u00adtional deriv\u00ada\u00adtive vector (\u2207) and the velocity vector (v). It spec\u00adi\u00adfies how fast or how strongly a vortex in a flow field is rotating around its center. The vorticity can be influ\u00adenced by making changes in the blade geom\u00adetry near the gap between [\u2026]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"wp_typography_post_enhancements_disabled":false,"footnotes":""},"categories":[16],"tags":[132],"class_list":["post-11766","post","type-post","status-publish","format-standard","hentry","category-fans","tag-acoustics"],"acf":[],"_links":{"self":[{"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/posts\/11766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/comments?post=11766"}],"version-history":[{"count":7,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/posts\/11766\/revisions"}],"predecessor-version":[{"id":22297,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/posts\/11766\/revisions\/22297"}],"wp:attachment":[{"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/media?parent=11766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/categories?post=11766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mag.ebmpapst.com\/en\/wp-json\/wp\/v2\/tags?post=11766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}