Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Introduction to Aerospace Engineering Aerodynamics 7&8 Prof. H. Bijl ir. N. Timmer 7 & 8. Laminar and turbulent flows Anderson 4.15 - end of chapter 4. Osborne Reynolds Ludwig Prandtl 1842-1912 1874-1953 Subjects lecture 7 & 8 • Viscous flows • Laminar boundary layers • Turbulent boundary layers • Transition • Separation 3 Viscous flow Up till now we have only dealt with frictionless flow. What is the effect of friction ? …. D Inviscid flow (No friction) Viscous flow (friction) NO DRAG FINITE DRAG 4 Viscous flow In real life the flow at the surface adheres to the surface because of friction between the gas and the solid material: Right at the surface the velocity is zero 5 Boundary layer Friction force Boundary layer (exaggerated) V In the vicinity of the surface there is a thin region of retarded flow: the boundary layer The pressure through the boundary layer in a direction perpendicular to the surface is constant 6 Viscous flow Inside the boundary layer Bernoulli’s law is not valid!!!!!! 7 Viscous flows Shear stress can be Boundary layer written as : velocity profile τ = μ dU w boundary layer dy y=0 thickness, δ shear stress, τw (schuifspanning) skin friction drag μ = absolute viscosity coefficient or viscosity Air at standard sea level : μ=1.789*10-5 kg/ms) 8 Viscous flows, some definitions δ V∞ x ==ρ∞∞ V x V ∞ x Reynolds number : Re x μ∞∞ν dimensionless, and varies linearly with x Laminar flow : streamlines are smooth and regular and a fluid element moves smoothly along a streamline Turbulent flow : streamlines break up and a fluid element moves in a random irregular way 9 Laminar boundary layer, boundary layer thickness Consider flat plate flow. What is boundary layer thickness δ and skin friction drag Df at location x? V∞ δ x δ = 5.2 x From laminar boundary layer theory : Rex Thus δ is proportional to : √x (parabolically) 10 Laminar boundary layer, skin friction drag τw x dx L 1 (unit width) width) Total force = total pressure force + total friction force Total friction force on element dx is: τw(x)⋅dx⋅1 = τw(x) dx L τ Total skin friction drag is: D f = w dx o 11 Laminar boundary layer, skin friction drag For the skin friction coefficient we find from laminar boundary layer theory : τ w τ w 0.664 c f = = = x 1 2 q∞ Rex ρ ∞V ∞ 2 C τ x Thus fx and w decrease as increases The skin friction at the beginning of the plate is larger than near the trailing edge. To calculate the total aerodynamic force we must integrate! 12 Laminar boundary layer, skin friction drag L L L dx 0.664 q∞ dx D f = c f . q∞ dx = 0.664q∞ = x V ∞ /ν x o o Rex o dx = x -1/2 = 2 x x 0.664 q∞ 1.328q∞ L Df = 2 L = V∞ / ν∞ V∞ L/ ν∞ Df Define total skin friction drag coefficient as Cf = q∞S 1.328 L 1.328.L 1.328 = = C = Cf ⋅ f ReL S ReL L 1 ReL 13 Results for a turbulent boundary layer δ turbulent δ laminar Due to the action of turbulence : no exact solution for turbulent boundary layers ! From experiments : 0.37x δ = Note : C varies as L-1/5 for turbulent flow 0.2 f Rex while it changes as L-1/2 for laminar flow. 0.074 C = Thus the friction in a turbulent boundary layer f 0.2 ReL is larger than in a laminar flow 14 Transition Osborne Reynolds (1842-1912) Pipe flow experiment 15 Transition Re > 2300 : transition from laminar to turbulent flow Osborne Reynolds (1842-1912) Development of turbulent flow in pipes observed and sketched by Reynolds (from his original paper) 16 Transition Cf transition turbulent laminar Re 17 Transition Flat plate flow 18 Transition Flow visualization experiment 19 Transition Tollmien- Three-dimensional Fully Schlichting vortex turbulent waves breakdown flow Stable U∞ laminar flow Growth of Generation of Span wise vorticity turbulent spots 20 Ludwig Prandtl (1875-1953) •Boundary Layer theory (1904) •Wing theory (1918 - 1919) •Contributions to the theory of supersonic flow & turbulence •Development of wind tunnels and other aerodynamic equipment •Theory of plasticity and of meteorology. 21 • Prandtl and his water tunnel (TU Hannover 1904) 22 • FLOW OVER A PLATE WITH A SEMI-CIRCULAR LEADING EDGE Zhiyin Yang and Peter Voke Fluids Research Center, University of Surrey, U.K. The image represents the results of a hybrid DNS/LES (by Zhiyin Yang and Peter Voke) computation of separation, transition and reattachment of the flow over a plate with a semicircular leading edge 23 Transition Skin friction y ∂ (mm) τ = μ u ∂y laminar turbulent u/V transition V Flat plate flow 24 Transition transition V turbulent laminar xcr The critical Reynolds number at which transition occurs is difficult to find. It should be found from experimental data applicable for the given problem 25 Laminar-Turbulent Transition on airfoils Transition “point” Laminar Turbulent B.L. B/L V Laminar boundary layer: thin, low skin friction drag Turbulent boundary layer: thick, high skin friction drag 26 transition turbulent laminar V Airfoil model vertically spanning the wind tunnel 27 Laminar flow favourable τ < τ We have seen that : wla minar wturbulent Vast majority of flows is TURBULENT ! => We may adapt the geometry of the airfoil such that it favors laminar flow. We then have Laminar flow airfoils. Favorable pressure gradient laminar flow airfoil Favorable pressure gradient 28 Flow Separation Why is it important? When does it occur ? CFD example 29 Alternating separating vortices on a cilinder (Karman street) 30 Unsteady behavior of construction due to separation 31 Flow separation separation point Separation due to a positive pressure gradient 32 Separation From: Van Dyke: “An Album of fluid motion” aluminum powder in water 33 Flow Separation Effect of pressure pressure distribution without separation distribution strong adverse -Cp separated flow pressure gradient moderate adverse pressure gradient attached flow -1.0 34 DU 91-W2-250 35 -4 C p α = 0 degr. -3 -2 -1 0 1 x/c (%) 0 20406080100 36 -4 C p α = 2.6 degr. -3 -2 -1 0 1 x/c (%) 0 20406080100 37 -4 C p α = 5.6 degr. -3 -2 -1 0 1 x/c (%) 0 20406080100 38 -4 Cp α = 7.2 degr. (l/d)max -3 -2 -1 0 1 x/c (%) 0 20406080100 39 -4 Cp α = 9.2 degr. (Cl,max) -3 -2 -1 0 1 x/c (%) 0 20406080100 40 -4 Cp α = 9.2 degr. (Cl,max) -3 transition -2 -1 Separation at x/c=92% 0 1 x/c (%) 0 20406080100 41 -4 Cp -3 α = 9.2 degr. (Cl,max) -2 α = 7.2 degr. (l/d)max -1 0 1 x/c (%) 0 20406080100 42 -4 Cp -3 -2 Separation at x/c=35% 18.2 degr. -1 0 1 x/c (%) 0 20406080100 43 Flow Separation Why is it important ? Loss in lift (airfoil) Increase in pressure drag Generation of unsteady loads Example : Interaction of separated vortex flow with vertical stabilizer (F18) 44 Flow Separation • Effect of turbulence u/U Turbulent boundary layer has more flow kinetic energy near the surface. Thus flow separation may be postponed. laminar turbulent Boundary layer 45 Viscous drag Drag due to viscous effects = friction drag + pressure drag = profile drag C = C + C Dp Dpressure Dfriction 46 Influence of the Reynolds number a Re=300000 Cd high b Re=650000 Cd lower c ≈ Re=1200000 Cd Cd(b) 47 Effect on CD of shape and Re-no. 48 Pressure drag Drag distribution Pressure drag on Cylinder Friction drag V θ 49 Two objects with the same drag force 5 (ReD=10 ) diameter D V 10D 50 51 Artificial transition Flow over a sphere free transition artificial transition Re = 15000 Re = 30000 52 Artificial transition 53 Use in sports: example 1 :speed skating Effect of zigzag strips 54 lower leg 1.4 Cd 1.2 smoothsmooth cilinder cylinder 1 0.8 0.6 coolmax 0.4 0.2 0 0 100,000 200,000 300,000 400,000 Reynoldsgetal Measured drag characteristics of different fabrics on a cylinder 55 lower leg 1.4 Cd 1.2 smooth cilinder 1 0.8 0.6 coolmax 0.4 0.2 0 0 100,000 200,000 300,000 400,000 Reynoldsgetal 56 lower leg 1.4 Cd 1.2 smooth cilinder 1 0.8 0.6 coolmex 0.4 0.2 0 0 100,000 200,000 300,000 400,000 Reynoldsgetal 57 lower leg 1.4 Cd 1.2 smooth cilinder 1 0.8 0.6 coolmax+strips coolmax 0.4 0.2 0 0 100,000 200,000 300,000 400,000 Reynolds no. 58 59 Position of the strips 60 Gianni Romme World records speed skating men 5000 m: 8.36.6 Jaap Eden Hamar 1894 6.34.96 J. Olav Koss Hamar 1994 6.30.62 Gianni Romme H’veen 1997* 6.22.20 Gianni Romme Nagano 1998 6.21.49 Gianni Romme Galgary 1998 Current: 6.03.32 Sven Kramer Galgary 2007 Result: 8.4 seconds off WR * First on clap skates 61 Experimenting with aerodynamics Cathy Freeman, 400 m. gold medalist, Sydney Olympics 2000 62 Example 2 Case study : Usain Bolt 100m men world record holder 63 Measured effect of strips on the total aerodynamic drag: • strips on lower legs -3 to -11 % • strips on the cap -2 to -6 % 64 Location Berlin air density 1.20 kg/m^3 parameters Bolt length 1.96 m mass 86 kg Cd*S-total 0.82 Cd*S-legs 0.246 distance 100 m min sec 09.58 V-average 10.44 m/s 3 P = Cd.S.½.ρ.V First calculate the required power for the time of 9.58 s P = 560 Watts propulsion (V=10.44 m/s) 65 Pprop = 560 Watts Location air density 1.20 kg/m^3 parametersBolt length 1.96 m mass 86 kg Cd*S-total 0.806 Cd*S-legs 0.231 -6% V3 = P /C .S.½.ρ.