Fluid Dynamics > QUESTIONS & ANSWERS > AAE 333 -Fluid Mechanics Fall 2020 Homework #11ALL ANSWERS CORRECT,100% SCORE (All)

AAE 333 -Fluid Mechanics Fall 2020 Homework #11ALL ANSWERS CORRECT,100% SCORE

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AAE 333 Fluid Mechanics Fall 2020 Homework #11 Due: Friday, December 8, 2020 (NO LATE HW ALLOWED) (3 problems worth 40 points) 1. [15] Flow straighteners are arrays of narrow ducts placed in wind tunnels to remove swirl and other in-plane secondary velocities. They can be idealized as empty square boxes constructed by vertical and horizontal plates as shown in the figure. The cross-section of the box is a by a and the box length is L. The air density, viscosity, and flow velocity are , µ, and U, respectively. a) To avoid significant blockage, the maximum displacement thickness of the boundary layer at each of the side walls of the box must not exceed 0.02 (i.e. 2%) of the cell width a. Assuming laminar flat plate flow, derive a formula for the maximum box length L in terms of , µ, a, and U. b) Assuming again laminar flat plate flow and an array of N by N boxes, derive a formula for the total drag on the bundle of boxes. Problem 1 Solution: a) Displacement thickness: ߜଵ ൌ ଵ.଻ଶ௫ ඥோ௘ೣ We need to have ߜଵ ൑ 0.02ܽ at ݔൌ .ܮTherefore, 2. [15 points] Assume the velocity from an inviscid analysis of the flow over a certain airfoil can be approximated by where c is the chord length of the airfoil. (a) Determine which parts of the airfoil (which values of x/c) have favorable or adverse pressure gradients. (b) Use Thwaites' method to compute the momentum boundary layer thickness, 2/c, over the length of the airfoil for the case when the Reynolds number based on chord length is Rec = 10,000. (Hint: (i) nondimensionalize Thwaites' method so it is in terms of nondimensional quantities, and (ii) for the sake of this homework problem treat the arc length s and the coordinate x as the same.) (c) Plot (using a computer) as functions of x/c the momentum thickness, 2/c; the rate of change, d2/dx; shape factor, H; and local skin friction coefficient, cf. (d) Compare the quantities in part (c) to those of a boundary layer on a flat plate at the same chord Reynolds number. How does the local pressure gradient affect the results? Does the boundary layer on the airfoil separate? If so, where? AAE 333 Fluid Mechanics Fall 2017 Problem 2 Solution: (a) From Bernoulli’s equation (steady)

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