Nondimensional numbers and Similarity [Aerodynamics #4]

[@Zaphk]

Im an Elec Eng about to a Masters in aero. I just had a pre-course done in aerodynamics and struggled alot after data dumped with equations. After reviewing your aerodynamics #1 to 4, I found your teaching to be refreshing and understood why the coefficients are so significant when it comes to experiments. Also helped me understand what the Wright brothers were doing. Thanks!

[@prof.vanburen]

Glad you enjoyed it! Good luck with your Masters program and I hope you find some interesting intersections of electrical engineering and aerodynamics.

[@msergejev]

You are an excellent explainer! Thank you for this video series.

[@prof.vanburen]

Thank you!! I'm glad you like them

[@chanabasayyamathad4123]

Thank you ...... Your videos are so simple and precise to understand and effectively educatable.....

[@prof.vanburen]

Thanks!! Glad you enjoyed them

[@kairavmehta6607]

I'm currently a first year btech student studying Information technology but I can properly understand all the concepts! Thank you!

[@prof.vanburen]

Awesome! I'm glad you like it

[@tom_winguill]

9:08 wright brothers family name is synonymous with aerodynamics? what do you mean sir?

[@prof.vanburen]

The Wright Brothers were the first to controlled powered flight (this is a somewhat debated claim). Regardless of validity of being first, their name has become attached to the field of aerodynamics in the same way that Tesla and Edison are attached to electricity.

[@huyleang8018]

Hi Professor, 1. For a propeller, if we intend to keep Re similarity, we then choose L=D and V=Omega*R as tip speed ratio. However, if we implement blade element momentum, every blade element spanwise will have different Re numbers. Considering downscale 5m Diameter turbine to a 0.8m Diameter turbine and the blade element at 1/5R, meaning 0.5 and 0.16m respectively, do we need to ensure the Re equal among those? 2. Why do we choice V=Omega*R? Looking forward to hearing from you. Thanks. Huy.

[@prof.vanburen]

Thanks for your patience! Just getting to comments after a short stint away. This is a good question. In these cases, there are multiple velocity scales (tip speed vs forward speed) and it is very hard to preserve all the non-dimensional numbers when scaling down. If you scale down in size, usually you need to increase velocity to compensate. This means, needing much higher rotation angular velocities of the turbine (to preserve tip speed ratio), which introduces all different sorts of problems. Definitely a challenge! Tip velocity is just a lateral velocity component, there is still usually a forward velocity. Typically, you choose based on which one is dominant.

[@mohammedouallal2]

Hello, Nice job you are doing withh these lecture. Just a small carification, for the sake of logic. The body length for a human may differ, if covering 5 km by walking, the body length would be the step distance, which is typically 0.5 m to 0.6 m. Now when you run it does not change dramatically. So the dimensionless distance for 5000 m would be in that case, between 8333 to 10000.

[@prof.vanburen]

Thanks! Yep, I think you make a great point that the meaningful reference dimension (in this case length) is problem-dependent and often there are multiple to choose from. In this case, you could make the argument that the step distance is directly correlated to body length, so it would effectively be the same. Either way, there is a lot of wiggle room in choosing reference lengths.

[@mohammedouallal2]

@@prof.vanburen sure! this is just my rigorous nature :)). A human being can crawl too :p

[@kadircanss]

thanks for your extraordinary labor, it was perfectly helpful to understand the main concept. But fortunately, ı couldn't get the point when it comes the similarities. İs there any more precise definition about why Cp are equal for different scaled shapes. Or is there any resource that may help me in that subject. Thx again

[@prof.vanburen]

My pleasure! I looked through the video again because I wanted to be sure, I am not sure where Cp (which is sometimes pressure coefficient) pops up, but I suspect you mean Cl instead, as in the lift coefficient? If so, I should say first that Cl does not *perfectly* stay the same at different scales. Other concepts like turbulence and Reynolds number come into play here. However, for the most part, it is sufficiently equal across a wide range of different scales. This is because take into account all the variables that impact lift when we scale the problem. A bigger airfoil would produce bigger force at the same air speed, but lift coefficient takes that into account by scaling with the area. Does this help at all? Otherwise, I think the text by Anderson might be helpful here. Otherwise, my video in fluid mechanics on non-dimensional numbers more completely goes over these concepts in a way that is not restricted to aerodynamics.

[@jimliu7086]

Thank you!

[@prof.vanburen]

You're welcome!

[@stellar8606]

In the fluid mechanics course for non dimensionalising we took inertia force as pu^2L^2, why are we taking it here as 1/2 pu^2L^2?

[@prof.vanburen]

Confusingly, it's just a matter of convention. Often, constants are dropped when doing estimation analysis and the constant was dropped in Fluid Mechanics. However, in Aerodynamics the dynamic pressure (1/2 rho * u^2) is everywhere because it shows up predominantly in the Bernoulli equation, which is super important, so all the aerodynamic force/moment constants tend to be normalized by the 1/2 rho*u^2*L^2. There are different ways to derive the inertia force scaling and Aerodynamics and Fluid Mechanics approach it from a different perspective. Note that, even in Aerodynamics, Reynolds Number is defined with the 1/2 dropped.