<p>All coming together now, outside of using related power series expansion to solve some diffeq’s, I wasn’t sure that I’d ever see an actual application for Taylor series.</p>
<p>Taylor series seem a bit esoteric the first time you learn them. They are, however, ubiquitous throughout the more advanced engineering topics.</p>
<p>Once you get over the fact that it’s a pain to write out a Taylor expansion, you can see that it’s a very nice approximation tool.</p>
<p>Wow. Fluid mechanics is so broad I feel like it should be a major by itself.</p>
<p>I am having trouble relating allthe different flows (compressible, incompressible, viscous, inviscid, steady, unsteady, laminar, turbulent, etc…). How do all of them relate to each other?</p>
<p>Does CFD apply to all flows?</p>
<p>Fluid dynamics is very broad. Gives lots of opportunities for finding a niche.</p>
<p>A compressible fluid means the density can change from point to point (air ), but an incompressible fluid doesn’t (one roughly close example of this is water). Usually, flows of things like air at lower speeds can be approximated as incompressible since it shows barely any compressibility effects.</p>
<p>Viscous fluids have friction, inviscid ones have no friction. Friction creates boundary layers and thus separation. When viscous flows are in a regime of a negative pressure gradient, flows tend to be laminar. However, when an adverse pressure gradient is applied enough, a great amount of separation occurs since the flow slows down and moves off the object and can lead to random mixing in the flow, causing the flow at some point and onward to become turbulent.</p>
<p>A steady flow is where properties of the flow from point to point don’t change with time. Unsteady means they can change.</p>
<p>Based on these definitions(assuming I didn’t mess any up too bad), you can have many different flows. CFD can apply to all flows if you know how to do it. It isn’t to say it is perfect in terms of accuracy, but it can do very well at showing the trends and can be pretty accurate if we use supercomputers. So far, some of the toughest areas I have looked at pertain to turbulence modeling. A lot of turbulence models I have seen are statistics based, so obviously this can be hit or miss unless done right. Lots of cool research areas though for these topics.</p>
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<p>(Nearly) every fluid flow in the real world can be described by the compressible Navier-Stokes equations, i.e. they are essentially a compressible, viscous flow. Each other type of flow is an approximation to this most general case. For example, with water, the compressibility is so minute that it can and is effectively treated as zero, meaning we call it an incompressible flow and drop all of the compressibility terms. Certain types of flows can be considered inviscid, in which case they are an approximation to the true flow and the viscous terms are ignored. That happens frequently in the flow outside the boundary layer.</p>
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<p>CFD, like other numerical sciences, can be applied to every problem that is governed by an equation. Provided you have enough of a combination of computing power and time, you may even get an answer! Note: you don’t always have enough computing power and time.</p>
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<p>I’d say that this is greatly oversimplifying things, but really it just isn’t right. There are certain boundary layer instabilities (e.g. Tollmien-Schlichting waves) which are stabilized by a favorable pressure gradient (decreasing pressure in the streamwise direction). On the other hand, there are other instabilities like the crossflow instability (which is dominant on most swept-wing configurations) that are destabilized by a favorable pressure gradient.</p>
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<p>Turbulence modeling is by far my least favorite topic in aerodynamics. This isn’t because it is hard, but because it isn’t based on physics. Instead, it has to do with drawing up statistical trends based on empirical data so that we don’t actually have to solve the full equations and understand what is really happening. Given my personal interests, this just annoys me to no end. That says, it is quite useful, especially to designers, so there will continue to be a great deal of effort in the area and money to be made there, at least until computers get powerful enough to perform a direct numerical simulation (DNS) over, say, and entire wing (or even just the entire chord for that matter).</p>
<p>Thanks for clearing up errors I made and filling in details boneh3ad, I was just saying what I thought I remembered. I definitely haven’t gained an extensive knowledge in turbulence related topics, just learned the simpler stuff really, so thanks. </p>
<p>Also, very interesting with respect to your perspective on the turbulence modeling. I could see why that would bother you, hearing that bugs me as well. I guess we will see how far we come in the next 10 years, maybe then we can do direct simulations that have turbulence.</p>
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<p>I wouldn’t bet on it, at least not with simulations that start from the leading edge and run along the entire chord and include the transition phenomenon. All that information is contained in the Navier-Stokes equations, but the numerical grid required to capture it is so fine that it would probably take the advent of quantum computing to solve it in an economically feasible time, and even that might be pushing it.</p>
<p>CFD sounds interesting. Is CFD in itself pretty wide?
Like if I wanted to do research in CFD for graduate school, would it be too vague if I said “I want to do research in CFD.”</p>
<p>That is really vague, but it would be surprising you knewuch more than that so it wouldn’t be a show stopper. I suppose it would be slightly better if you knew if you’d rather do subsonic or supersonic flows.</p>
<p>Yeah that is vague. There are tons of aspects in it, from certain types of flows to different applications,like using CFD for design optimization, and even finding better numerical methods to use for CFD. There is probably a lot more out there than that too, but that is just some ideas. </p>
<p>As boneh3ad said though, you could probably get away with saying you just want to do CFD research though because not many get too exposed to it before grad school, but it always helps having a clue.</p>
<p>There’s a such thing as being too specific. You risk the chnce of losing other options, especially if you don’t do some serious reading on your potential program’s research areas.</p>
<p>Very true DoubleD. Never want to be too specific.</p>
<p>What is the difference between using commercial code and knowing the fundamentals of computing in regards to CFD research?</p>
<p>Commercial codes are made to get an answer, but not an accurate one. Commercial codes are good for identifying trends. By knowing CFD, you know how to make a higher order of accuracy code and run it to obtain very accurate results in comparison to commercial codes. You can also apply CFD to areas of your choosing by making the code yourself!</p>
<p>I’d describe the commercial codes as jacks of all trades, masters of none. You an get a good answer for simple problems but not nearly all problems and you need to know the fundamentals in order to know where those shortcomings are and how to make up for them.</p>
<p>Oh so are commercial codes mainly for applications? Like the user only knows how to use the code, but didn’t actually make the code themselves.</p>
<p>They are used for project that aren’t too elaborate and don’t need exact answers. And yes, they don’t write these codes themselves. They use what professionals made for them. For example, one of my friends uses it for designing airfoils used on the Formula car he and his club members build so then they can have a good downforce and little drag.</p>
<p>The software doesn’t give very accurate values but it shows him trends, basically meaning he sees the down force to drag ratio between a set of different designs and although they aren’t perfectly accurate, it still gives him a qualitative idea of which design might perform best.</p>
<p>I have to disagree somewhat. Codes like Fluent can give very accurate answers so long as the user knows what he/she is doing. If you understand the limitations of the software and know how to set up and run a well posed problem, then the results are quite accurate for the regimes that the code can mathematically handle. The problem is when people using the codes don’t actually know how they work or why they behave the way they do. That is when you start seeing inaccurate results reported as gospel.</p>
<p>I am new to computational research area.
What other computational research areas are there in engineering, besides CFD?</p>