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MAE 5130: VISCOUS FLOWS

MAE 5130: VISCOUS FLOWS. Falkner-Skan Wedge Flows November 9, 2010 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. OVERVIEW. m=0 Blasius flow over a flat plate with a sharp leading edge 0 < m < 1

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MAE 5130: VISCOUS FLOWS

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  1. MAE 5130: VISCOUS FLOWS Falkner-Skan Wedge Flows November 9, 2010 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

  2. OVERVIEW • m=0 • Blasius flow over a flat plate with a sharp leading edge • 0 < m < 1 • Flow over a wedge with half-angle, q=m/(m+1) with 0 < q < p/2 • m=1 • Flow toward a stagnation point (Hiemenz flow) • 1 < m < 2 • Flow into a corner, with q > p/2 • Flows of this type are difficult to produce experimentally) • m > 2 • No corresponding simple ideal flow (but mathematically solvable)

  3. FALKNER-SKAN: m=0, BLASIUS FLAT PLATE • 0 < h < 10 • d2f/dh2(0)=0.33206 f f’ f’’

  4. FALKNER-SKAN: m=1, PLANE STAGNATION POINT FLOW (Hiemenz flow) • 0 < h < 10 • d2f/dh2(0)=1.23259 f f’ f’’

  5. FALKNER-SKAN: m=0.2, COMPRESSION FLOW • 0 < h < 10 • d2f/dh2(0)=0.6213 • This corresponds to a compression wedge of 30° f f’ f’’

  6. FALKNER-SKAN: m=-0.082569, COMPRESSION FLOW • 0 < h < 10 • d2f/dh2(0)=0.087126 • This corresponds to an expansion of 16.2° f f’ f’’

  7. FALKNER-SKAN: m=-0.09043, SEPARATION POINT • 0 < h < 10 • d2f/dh2(0)=0 • This corresponds to an expansion angle of only 17.9° f f’ f’’

  8. FALKNER-SKAN PROFILES • Parameter m indicates the external velocity variation through ue=u0xm • Key Questions from Section 4-3.3 • Compare results with Figure 4-11 in White • Compare differences with White’s b parameter and m shown in figure to left • What is relation between similarity variable in White and similarity variable on ordinate axis shown in figure to left? Retarded Flows Accelerated Flows

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