1. 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. 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,  =m/(m+1) with 0 <  <  /2 m=1 –Flow toward a stagnation point (Hiemenz flow) 1 < m < 2 –Flow into a corner, with  >  /2 –Flows of this type are difficult to produce experimentally) m > 2 –No corresponding simple ideal flow (but mathematically solvable)

3. 3 FALKNER-SKAN: m=0, BLASIUS FLAT PLATE 0 <  < 10 d 2 f/d  2 (0)=0.33206 f f’ f’’

4. 4 FALKNER-SKAN: m=1, PLANE STAGNATION POINT FLOW (Hiemenz flow) 0 <  < 10 d 2 f/d  2 (0)=1.23259 f f’ f’’

5. 5 FALKNER-SKAN: m=0.2, COMPRESSION FLOW 0 <  < 10 d 2 f/d  2 (0)=0.6213 This corresponds to a compression wedge of 30° f f’ f’’

6. 6 FALKNER-SKAN: m=-0.082569, COMPRESSION FLOW 0 <  < 10 d 2 f/d  2 (0)=0.087126 This corresponds to an expansion of 16.2° f f’ f’’

7. 7 FALKNER-SKAN: m=-0.09043, SEPARATION POINT 0 <  < 10 d 2 f/d  2 (0)=0 This corresponds to an expansion angle of only 17.9° f f’ f’’

8. 8 FALKNER-SKAN PROFILES Parameter m indicates the external velocity variation through u e =u 0 x m Key Questions from Section 4-3.3 –Compare results with Figure 4-11 in White –Compare differences with White’s  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? Accelerated Flows Retarded Flows