{"id":606,"date":"2013-09-29T18:36:43","date_gmt":"2013-09-29T23:36:43","guid":{"rendered":"http:\/\/tonykordyban.com\/?page_id=606"},"modified":"2014-04-13T20:27:19","modified_gmt":"2014-04-14T01:27:19","slug":"everything-you-know-is-wrong-may-2004","status":"publish","type":"page","link":"http:\/\/tonykordyban.com\/?page_id=606","title":{"rendered":"Everything You Know Is Wrong May 2004"},"content":{"rendered":"

Answers to those Doggone Thermal Design Questions<\/strong><\/p>\n

By Tony Kordyban<\/strong><\/p>\n

Copyright by Tony Kordyban 2004<\/em><\/p>\n

Dear TK,<\/em><\/p>\n

How many grid cells do you use?\u00a0 Jerry says his typical thermal analysis uses between 50,000 and 100,000 grids, but Kim insists that if you don’t have at least a million cells in your CFD simulation, you might as well have just done a hand calculation.\u00a0 Since disk space, RAM, and even processor speed are so cheap and abundant these days, shouldn’t I be using as much grid as I can afford on every single problem and get the maximum possible accuracy?\u00a0 Is there still a good reason to use a coarse grid for anything?\u00a0 Is there such a thing a too much grid? <\/em>
\n \u00a0<\/em><\/p>\n

Bitsy from Manhattan<\/em>\n<\/p>\n

Dear Bitsy,<\/p>\n

I use a lot of grid cells.<\/p>\n

Realize that I started Computational Fluid Dynamics (CFD) for cooling electronics on a 33 MHz 486 PC with a whopping 8 MB of RAM.\u00a0 On that computer a problem with 100,000 grid cells could take three or four days to converge on a solution.\u00a0 So I still think 50,000 is a lot of grid cells.<\/p>\n

Since I’m talking ancient history, let’s go back a little bit and explain what grid cells are in CFD and why it might be a good idea to use a lot of them.<\/p>\n

In a cooling problem you generally want to figure out the flow of a cooling fluid, like air, and how much heat it carries away from solid heat sources, like electronic components, and what the temperature of those heat sources would be.\u00a0 If the geometry is incredibly simple, we could write equations for mass, energy, and momentum balance for the control volume, toss in some boundary conditions, solve them with a calculator, and be done with it.\u00a0 No grid cells.<\/p>\n

By incredibly simple geometry, I mean something like a flat plate with uniform heat flux, parallel to the uniform flow in a wind tunnel.\u00a0 Or a round pipe with a uniform wall temperature.<\/p>\n

Almost anything else is too complicated to write equations for that can be solved analytically.\u00a0 So we discretize the problem.\u00a0 We break the control volume surrounding our electronic assembly into a gazillion tiny pieces.\u00a0 The geometry and flow in each small piece is simple enough so that a set of energy, mass, momentum, etc. equations can be written for it.\u00a0 That gives us six or seven gazillion equations, and six or seven gazillion unknowns.\u00a0 Solving that is just number crunching and lots of tedious bookkeeping, for both of which computers are well suited.<\/p>\n

These chunks, or pieces, are called grid cells.\u00a0 The grid comes from the fact that the numbers crunch a lot easier if the geometry of all the chunks are organized on some kind of regular grid pattern.<\/p>\n

So why should more grid cells be better than fewer?\u00a0 With grid cells we are trying to approximate a smooth, continuous reality with a bunch of discrete, uniform blocks.\u00a0 Like making a model airplane out of Legos.\u00a0 The smaller the blocks are compared to the whole thing, the less we notice their blockiness.\u00a0 For example, how smooth and continuous does this photograph appear?<\/p>\n

\"rockies4\"<\/a><\/p>\n

\n

I bet you would like to have a few more pixels, or grid cells, to increase the resolution of the fine detail, so you could tell what this is a photograph of.\u00a0 Maybe, since this is an Internet article, a photo of a supermodel.<\/p>\n

Let’s double the resolution.<\/p>\n

\u00a0\"rockies3\"<\/a><\/p>\n

You can start to make out some shapes.\u00a0 But even if you squint real hard you can’t tell if it’s a claw hammer or a butterfly emerging from a cocoon.\u00a0 You need more pixels.<\/p>\n

\u00a0\"rockies2\"<\/a><\/p>\n

Doubling the grid cells again helps a lot.\u00a0 You can now tell this is a photo of some kind of bonehead, although you might not be able to use this to ID somebody in a court of law.\u00a0 Let’s double it again.<\/p>\n

\u00a0\"rockies\"<\/a><\/p>\n

You could keep increasing the grid cell number from here (in theory, at least, but this is as good as my cheap digital camera goes), but you probably have all the information you need at this level of resolution.<\/p>\n

The same thing applies to grid cells in CFD.\u00a0 You can keep increasing the grid density forever, but at some point the increase in resolution does not give you any more useful information.<\/p>\n

The general idea is that you want to use the number of grid cells in your problem that guarantee that the solution is Grid Independent.\u00a0 If you use a very coarse grid, you will still get a converged solution.\u00a0 But the temperature values for your electronic components may be suspect.\u00a0 So you increase the number of grid cells.\u00a0 If the temperature results change a lot when you increase the grid, then you can be sure your solution is not Grid Independent.\u00a0 Your results depend on the number of grid cells, so it is grid dependent.\u00a0 Keep increasing the number of grid cells until your results stop changing, as in this hypothetical chart.<\/p>\n

\u00a0\"grid_cells\"<\/a><\/p>\n

If your results change appreciably when you add more grid, then you haven’t used enough grid.\u00a0 Keep adding grid until your results are close to their asymptotic value (they don’t change much anymore.)\u00a0 When that happens, adding more grid adds no more information.\u00a0 It just takes up more computing time and resources.<\/p>\n

Notice that I didn’t say that Grid Independence gives you an accurate answer.\u00a0 My chart has a line marked “true” value.\u00a0 It can be very different from the asymptote, if there is some other source of error.\u00a0 Perhaps you entered 5 milliwatts instead of 5 watts for component power.\u00a0 All the grid in the world won’t make your results accurate.\u00a0 Grid Independence only eliminates the grid size as a source of error.<\/p>\n

So now you think you know it all.\u00a0 Start with a coarse grid, and then keep adding more grid until the results stop changing.\u00a0 Grid Independence is the goal.<\/p>\n

Not so simple, Bitsy.<\/p>\n

There is such a thing as too much grid, maybe even before you achieve Grid Independence.\u00a0 It has to do with that dreaded topic — Turbulence Modeling and the Boundary Layer.<\/p>\n

Some treatments of the boundary layer in CFD code expect you to add lots of grid next to solid walls, to resolve the velocity and temperature profiles inside the boundary layer.\u00a0 In that case, the more grid, especially right next to the wall, the better.\u00a0 The more detail you resolve in the boundary layer, the better your calculation of heat transfer will be.<\/p>\n

But some treatments of the boundary layer, especially those that deal with turbulent flow, are smarter than that.\u00a0 They are built on the assumption that it takes too much grid to resolve the boundary layers everywhere.\u00a0 They try to capture the behavior of the boundary layer with just one layer of grid cells touching the wall, using a non-CFD technique called The Law of the Wall Theory.\u00a0 I won’t (and can’t) explain the Law of the Wall.\u00a0 Let me just tell you this about it:\u00a0 it assumes that the whole boundary layer thickness is contained inside the first layer of grid cells touching the wall.\u00a0 If the grid cells are smaller than the boundary layer thickness, then the Law of the Wall calculation doesn’t work properly.\u00a0 The wall friction and convective heat transfer and the wall temperature results won’t be accurate.<\/p>\n

So study up on your turbulence treatments and make sure you understand the kind of grid each one needs.\u00a0 Some CFD codes offer half a dozen different methods of dealing with turbulence, and the grid requirements for each can be different.\u00a0 Making the grid too fine near the walls can lead to errors.<\/p>\n

One final point:\u00a0 It’s not so important what the total number of grid cells is — its is more important to place them well.<\/p>\n

Use lots of grid to resolve areas where the flow changes speed or direction rapidly, like where it comes out of a fan, or where it zooms around a sharp corner.\u00a0 Another place to load up on the grid cells is around a dense concentration of power, because the temperature is going to vary a lot over a small area.\u00a0 Use relatively coarse grid in areas where the geometry is uniform and smooth, and the flow does not change speed or direction.\u00a0 Here is another analogy:<\/p>\n

\u00a0\"rockies5\"<\/a><\/p>\n

Check out the dotted-line box in this photo.\u00a0 If we could add more resolution, would you rather add more inside the box, where all you will get is more uniform gray pixels, or would you rather add detail around something interesting, like the serrated edge on T-Rex’s tooth?<\/p>\n

Selectively add grid where it will give more USEFUL information.\u00a0 That way, maybe you can get just as accurate, just as useful, just as grid independent results with 100,000 cells as Kim can get with his indiscriminate use of 1,000,000 grid cells.<\/p>\n

\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/p>\n

Isn\u2019t Everything He Knows Wrong, Too?<\/strong><\/p>\n

The straight dope on Tony Kordyban<\/em><\/strong><\/p>\n

Tony Kordyban has been an engineer in the field of electronics cooling for different telecom and power supply companies (who can keep track when they change names so frequently?) for the last twenty years.\u00a0 Maybe that doesn\u2019t make him an expert in heat transfer theory, but it has certainly gained him a lot of experience in the ways NOT to\u00a0cool electronics.\u00a0 He does have some book-learnin\u2019, with a BS in Mechanical Engineering from the University of Detroit (motto:Detroit\u2014 no place for wimps) and a Masters in Mechanical Engineering from Stanford (motto: shouldn\u2019t Nobels count more than Rose Bowls?)<\/p>\n

\"\"In those twenty years Tony has come to the conclusion that a lot of the common practices of electronics cooling are full of baloney.\u00a0 He has run into so much nonsense in the field that he has found it easier to just assume \u201ceverything you know is wrong\u201d (from the comedy album by Firesign Theatre), and to question everything against the basic principles of heat transfer theory.<\/p>\n

Tony has been collecting case studies of the wrong way to cool electronics, using them to educate the cooling masses, applying humor as the sugar to help the medicine go down.\u00a0 These have been published recently by the ASME Press in a book called, \u201cHot Air Rises and Heat Sinks:\u00a0 Everything You Know About Cooling Electronics Is Wrong.\u201d\u00a0 It is available direct from ASME Press at 1-800-843-2763 or at their web site at\u00a0http:\/\/www.asme.org\/pubs\/asmepress<\/a>,\u00a0\u00a0<\/em><\/strong>Order Number 800741.<\/p>\n","protected":false},"excerpt":{"rendered":"

Answers to those Doggone Thermal Design Questions By Tony Kordyban Copyright by Tony Kordyban 2004 Dear TK, How many grid cells do you use?\u00a0 Jerry says his typical thermal analysis uses between 50,000 and 100,000 grids, but Kim insists that if you don’t have at least a million cells in your CFD simulation, you might […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-606","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/606","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=606"}],"version-history":[{"count":2,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/606\/revisions"}],"predecessor-version":[{"id":614,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/606\/revisions\/614"}],"wp:attachment":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}