Inverse design and Optimization of Aircraft Wings
Hello all,
I have a very simple question with regards to using the inverse design method to produce a desired wing airfoil. Most of the time, what drives us to get the "Optimal Shape Desired" is by looking at the "desired Pressure distribution", and by modeling this pressure distribution we can them come up with our wing. That's why it's called the INVERSE DESIGN. My question is: How do I know what the best pressure distribution is in the first place? Obviously it depends on the requirements of the aircraft that I'm trying to build. But does it depend on the weight of the aircraft mainly? or to make my question easier to understand, What pressure distribution would be ideal to what kind of situations? Thank you 
Re: Inverse design and Optimization of Aircraft Wi
inverse problem an be thought as a case of optimization problem, so we need to minimize a object function through the CG or other numerical optimization technique. you can take the resist of the airfoil as the object function, i think. Regards

Re: Inverse design and Optimization of Aircraft Wi
>My question is: How do I know what the best pressure distribution is in the first place? Obviously it depends on the requirements of the aircraft that I'm trying to build. But does it depend on the weight of the aircraft mainly? or to make my question easier to understand, What pressure distribution would be ideal to what kind of situations?
Furthermore, how do you even know that there exists a geometry that gives you the prescribed pressure? This is the main disadvantage of inverse design methods: A solution is not guaranteed. Optimization methods circumvent this situation by weakening the requirement to come "as close as possible" to the prescribed pressure distribution. How do you know what pressure distribution is good? I suppose it has a lot to do with experience. What we usually want is the highest possible ratio of lift vs. drag. Based on (bad) experience, we definitely know what we *don't* want to see in a pressure distribution: Compression shocks and separations. What we want is a healthy, smooth distribution that provides reasonable loading. Besides, I would say that usually you don't start from scratch but already have a design that you simply want to improve. All you need to do, then, is to look at the pressure distribution you have and tweak it to make it look better (for example smoother), or to get higher lift: A perfect application for optimization methods. 
Re: Inverse design and Optimization of Aircraft Wi
To add a little more.
You may know what lift you want and how much drag you are willing to accept. You dont want shocks or other adverse pressure gradients since they can promote separation. And you need lot of experience. Inverse design is not an optimization problem. As Mani mentioned, you have a problem of existence. Every pressure distribution may not be realizable. There are some conditions on the pressure distribution for incompressible flow which will guarantee a solution. But with the advent of new optimization methods based on control theory and developments in numerical algorithms, it is now more common to take an optimization approach rather than an inverse design approach. 
Re: Inverse design and Optimization of Aircraft Wi
idea!!! Maybe if we run one optimization to find the "optimal" cp distributions (witch is very low in cpu cost, no N.S. solver) and then an inverse design on that "optimal" cp distribution...
So if cpu cost of the inverse design is less than the hard optimization cpu cost we have something... Stelios Kyriacou 
Re: Inverse design and Optimization of Aircraft Wi
>idea!!! Maybe if we run one optimization to find the "optimal" cp distributions (witch is very low in cpu cost, no N.S. solver) and then an inverse design on that "optimal" cp distribution...
You must be either joking or there is some conceptual misunderstanding. a) I don't know where you get the idea that optimization doesn't take any time. Optimization methods require flow evaluations (solving the NS equations). Even with the most efficient methods (e.g. using adjoint equations), each iteration takes about as much time as a steadystate solution, and you need to run many of those iterations. Inverse methods, on the contrary, solve an inverse set of equations and are much faster, albeit with the disadvantages mentioned earlier. b) Once you have an optimized solution, you are done. The wing shape is part of the result of the optimization. Running an inverse method on top of that doesn't add anything useful. 
Re: Inverse design and Optimization of Aircraft Wi
well Mani ...
No i'm not Joking optimization takes time IF you have to solve the N.S. equations(expensive evaluation tool). what i'm saying is: evaluation tool : via bezier points (or some other shape control method) create the Cp distribution and integrate them (No N.S. solver,No CPU COST practically)to get Cl, Cd and what ever you wont. Optimize Cp distribution on your criteria. after you have you optimized Cp distribution name it target Cp and run an inverse design algorithm (That takes TIME). So if : inverse design TIME < pure Optimization Time you have something. That may answer to Simon to how you know which Cp distribution to use as target? except experience!!! I was expecting from the community to say that this would give impossible target Cp distribution, which in the and comes to use proper constrains S.K. p.s. it was just a thought don't really see it as something i'll implement. 
Re: Inverse design and Optimization of Aircraft Wi
>evaluation tool : via bezier points (or some other shape control method) create the Cp distribution and integrate them (No N.S. solver,No CPU COST practically)to get Cl, Cd and what ever you wont. Optimize Cp distribution on your criteria.
I see. We seem to miscommunicate on what is meant by "optimization", at least until this point in the discussion. The term optimization was used here to refer to a method that solves for a wing shape which results in a prescribed (given) pressure distribution. The underlying equations are the NS equations, which need to be solved by the optimizer (alternatively: the inverse equations are solved by the inverse method). What you are talking about is a completely different problem: How to relate a given lift or pressure drag to a pressure distribution. That really doesn't take much time as a relatively trivial preprocessing step to the real problem above. 
Re: Inverse design and Optimization of Aircraft Wi
exactly! you can see it as a preprocessing step !!!
S.K. p.s. By the way Optimization refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set . Wiki 
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