Blasius_laminar_BL

Blasius_laminar_BL - Blasius flat plate boundary layer...

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Here the function Rkadapt is used, which is similar to rkfixed except it internally uses adaptable spacing instead of fixed spacing (more accuracy where needed). It reports at fixed spacing however. η start 0 := η end 10 := num_steps 2000 := Z Y1guess ( ) Rkadapt YBC Y1guess () η start end , num_steps , D , := Now find the correct boundary condition, using the root function, and then re-set Y1guess to this best value: best root Z Y1guess num_steps 1 + 3 , 1 Y1guess , := best 0.332057 = Zfinal Rkadapt YBC best η start end , num_steps , D , := Middle portion of Zfinal (to find δ ): Bottom portion of Zfinal (to check boundary conditions): η Y 1 =f '' Y 2 =f ' Y 3 =f η Y 1 =f '' Y 2 =f ' Y 3 =f Zfinal 1234 1999 2000 2001 9.99 99526·10 -9 1 8.269213 9.995 19427·10 -9 1 8.274213 10 42908·10 -9 1 8.279213 = Now generate a plot of the similarity variables: n 1 num_steps .. := 0 0.5 1 1.5 2 0 1 2 3 4 5 6 Blasius BL Similarity Solution f'', f', and f eta Zfinal n1 , Zfinal , Zfinal , Zfinal n2 , Zfinal n3 , , Zfinal n4 , , Blasius flat plate boundary layer similarity solution by the Runge-Kutta method J. M. Cimbala The equation to solve is f''' + cff'' = 0, where prime denotes d/d η. Here, let c = 1/2. c 0.5 := ORIGIN 1 := We will define a vector Y which contains three unknowns, Y
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