AE301 Aerodynamics I UNIT D: Applied Aerodynamics ROAD MAP... D-1: Aerodynamics o 3-D Wings D-2: Boundary Layer and Viscous Eects D-3: XFLR (Aerodynamics Analysis Tool) AE301 Aerodynamics I : List o Subjects What is Boundary Layer? Laminar v.s. Turbulent Flow Flat Plate Laminar Boundary Layer Boundary Layer Transition to Turbulent Flow Ideal v.s. Real Flow Flow Separation Attached v.s. Separated Flow Flow Separation and Stall Viscous Eects on Drag
Page 1 o 12 What is Boundary Layer? BOUNDARY LAYER Boundary layer is a thin layer ormed on the surace o a solid body in a low ield. Due to the viscosity, the velocity within the boundary layer changes with respect to the vertical distance rom the surace (usually non-linearly). The boundary layer grows as the low moves over the body (the boundary layer thickness is deined as: ) Within the boundary layer, the velocity varies rom zero (surace) to the ree stream (edge o the layer): this is called, the boundary layer velocity proile At the surace (wall) o the body, wall shear stress can be given as: w dv dy This wall shear stress is one o the major contributor to the vehicle drag, called the skin riction drag y0
Page 2 o 12 Laminar v.s. Turbulent Flow LAMINAR V.S. TURBULENT FLOWS Laminar low: where the streamlines are smooth and regular, and a luid element moves smoothly along a streamline Turbulent low: where the streamlines break up and a luid element moves in a random, irregular, and chaotic ashion (means streamlines cannot be deined as it is unsteady in nature) Transition rom laminar to turbulent occurs as Reynolds number o the low increases (usually the boundary layer transition point is deined, based on the transition Reynolds number: Retr
Page 3 o 12 Flat Plate Laminar Boundary Layer LAMINAR BOUNDARY LAYER The solution known as Blasius solution o lat plate laminar boundary layer (lat plate means: zero pressure gradient) c x 0.664 (laminar lat plate boundary layer) w w 2 0.5 V q Rex (Lower case c represents the skin riction drag coeicient per unit length at a location o x) x The skin riction coeicient (due to the wall shear stress) will cause the total skin riction drag or the lat plate o length L: L L L dx 0.664q dx 1.328q L w 0.664 0 0 Rex V 0 x V D dx q Total skin riction drag coeicient o the lat plate o length L can be deined as: C D D 1.328q L 1.328 1.328 q S q L(1) q L V V L Re (Upper case C represents the total skin riction drag coeicient o the given lat plate o length L) L
Page 4 o 12 Class Example Problem D-2-1 Related Subjects... Laminar Boundary Layer Consider a low o air over a lat plate (5 cm long in the low direction, and 1 m wide). The reestream conditions correspond to standard sea-level, and the low velocity is 120 m/s. Assuming the laminar low, determine the ollowings: (a) The boundary layer thickness at the trailing edge o the plate (b) The drag orce (due to skin riction) developed on the plate (a) At the trailing edge (x = 5 cm) o the plate, the Reynolds number is: 3 1.225 kg/m 120 m/s0.05 m Vx 5 Rex 4.1110 5 1.78910 kg/ ms Hence, the boundary layer thickness is: 5.2x 5.20.05 m 4 4.06 10 m (0.0406 cm) 5 Rex 4.1110 (b) The total skin riction drag coeicient is: 1.328 1.328 C 2.0710 5 Re 4.1110 3 L 2 3 Note that: 2 2 q 0.5V 0.5 1.225 kg/m 120 m/s 8,820 N/m 2 S 0.05 m1 0.05 m Thereore, the skin riction drag orce can be obtained by: 2 2 3 D qsc 8,820 N/m 0.05 m 2.0710 0.913 N Note that this is the skin riction drag orce on a single surace. Since the lat plate have two suraces (top & bottom suraces), the total skin riction drag orce is: D total 20.913 N 1.826 N
Page 5 o 12 Boundary Layer Transition to Turbulent Flow TURBULENT BOUNDARY LAYER Turbulent boundary layer is thicker than the laminar boundary layer, under the same condition o low Turbulent boundary layer is oten very diicult to analyze: heavily dependent on experimental results TRANSITION FROM LAMINAR TO TURBULENT BOUNDARY LAYER The adverse pressure gradient, rough surace (skin), and many other actors determine boundary layer transition The physical mechanism o boundary layer transition, even or a simple lat plate, is still not completely understood. The boundary layer transition mechanism is still the area o intensive research in aerodynamics today
Page 6 o 12 Class Example Problem D-2-2 Related Subjects... Turbulent Boundary Layer Consider a low o air over a lat plate (5 cm long in the low direction, and 1 m wide). The reestream conditions correspond to standard sea-level, and the low velocity is 120 m/s. I the low is turbulent, determine the ollowings: (a) The boundary layer thickness at the trailing edge o the plate (b) The drag orce (due to skin riction) developed on the plate (a) At the trailing edge (x = 5 cm) o the plate, the Reynolds number is: Vx 5 Rex 4.11 10 Hence, the boundary layer thickness is: 0.37x 0.37 0.05 m 3 1.39 10 m (0.139 cm) Re 0.2 5 4.11 10 0.2 x Note that the turbulent boundary layer is 3.42 times thicker than laminar low (b) The total skin riction drag coeicient is: 0.074 0.074 C 0.00558 Re 0.2 5 4.11 10 0.2 L 2 3 Note that: 2 2 q 0.5V 0.5 1.225 kg/m 120 m/s 8,820 N/m 2 S 0.05 m1 0.05 m The skin riction drag orce can be obtained by: 2 2 D qsc 8,820 N/m 0.05 m 0.00558 2.46 N Note that this is the skin riction drag orce on a single surace. Since the lat plate have two suraces (top & bottom suraces), the total skin riction drag orce is: D total 22.46 N 4.92 N Note that the skin riction drag orce o the turbulent boundary layer is 2.7 times larger than laminar low
Page 7 o 12 Class Example Problem D-2-3 Related Subjects... Boundary Layer Transition The wing span o Wright Flyer I (biplane) is 40 eet 4 inches, and the planorm area o each wing is 255 t 2. Assume that the wing is rectangular shape. I the airplane is in light with 30 mph (under the standard sea-level light condition), estimate the skin riction drag on the wings. Assume that the transition Reynolds number is 6.510 5. The general solution procedure: (1) Calculate D or the combined area A + B, assuming that the low is completely turbulent (2) Obtain the turbulent D or the are B only, by calculating the turbulent D or area A and subtracting this rom the result o part (1) (3) Calculate the laminar D or the area A (4) Add results rom parts (2) & (3) to obtain total drag on the complete surace area A + B (5) Note that the Wright Flyer I is a biplane and has total 4 suraces (top & bottom and 2 wings), so the total skin riction drag on the complete biplane wing coniguration will be the 4 o the skin riction drag on a single surace, calculated rom part (4)
Page 8 o 12 Ideal v.s. Real Flow RECALL: [IDEAL V.S. REAL FLOW: CIRCULAR CYLINDER] (UNIT B-3) As we learned in Unit B-3, the pressure distribution around circular cylinder (ideal low) is symmetric, thus no lit and no drag will be produced. This is known as d Alembert s paradox. Flow separation, due to the adverse pressure gradient, and resulting complex wake region induces the non-symmetric pressure distribution, thus pressure drag due to separation is the main drag contributor o real lows around circular cylinder IDEAL V.S. REAL FLOW: AERODYNAMICS OF AIRFOILS AND WINGS A very similar analogy (that we employed or the analysis o low over a circular cylinder) can also be applied or the aerodynamics o airoils and wings. The ormation o boundary layer and its behavior (transition rom laminar to turbulent lows, as well as the low separation, due to the pressure gradient) plays very important roles in generations o aerodynamic lit and drag o airoils and wings
Page 9 o 12 Flow Separation RECALL: [PRESSURE GRADIENT] (UNIT B-1) p (pressure) is a unction o spatial coordinates: p p x, y The mathematical representation: pressure gradient, p, is a vector such that: Magnitude = maximum rate o change o p per unit length o the coordinate space at the given point Direction = direction o the maximum rate o change o p at the given point dp Using pressure gradient, directional pressure change can be given: p ˆ ds n (This is how much change o pressure takes place in the direction speciied by the line vector ˆn : more commonly called physical pressure gradient ) FLOW SEPARATION Pressure gradient: dp/ds (along the surace o an airoil) may be avorable (negative) or adverse (positive), and adverse pressure gradient causes low to separate rom the surace
Page 10 o 12 Attached v.s. Separated Flow FLOW SEPARATION ON AN AIRFOIL Flow separation on an airoil causes: A drastic loss o lit (stall) A major increase in drag, caused by pressure drag due to separation FLOW SEPARATION AND STALL At extremely high angles o attack, the low separates rom the top surace o an airoil, leading it to stall. Desired post-stall characteristics (smooth and gradual stall or sudden violent stall) and ease o recovery are important design actors o airoil
Page 11 o 12 Flow Separation and Stall RECALL: [LEADING EDGE STALL] (UNIT C-4) Example: NACA 4412 Characteristics o relatively thin airoils with thickness ratios between 10 and 16 percent o the chord length. Post-stall: rapid loss o the lit (not desirable) RECALL: [EFFECTS OF AIRFOIL THICKNESS ON STALL] (UNIT C-4) Thin airoil: thin airoil is desired or high-speed applications (rom high transonic to supersonic), in order to minimize proile and wave drags. Thick airoil (example: NACA 4421): thick airoil is usually desired, especially or low-speed applications (low subsonic), due to the avorable stall characteristics (Trailing Edge Stall).
Page 12 o 12 Viscous Eects on Drag VISCOUS EFFECTS ON DRAG The presence o viscosity in a low produces two sources o drag: Skin riction drag (due to shear stress on the surace o the body, called the wall shear stress) => this is oten called Parasite Drag Pressure drag (due to low separation) => this is oten called Drag due to Separation Trade-o between these two drag components may be possible by careully engineered design: or example, Natural Laminar Flow (NLF) airoil (NACA 6-series) Gol ball dimples RECALL: [THE DRAG POLAR] (UNIT D-1) The induced drag ( C ) is the drag due to lit (3-D eect) Di. The proile drag (cd) is a drag on a 2-D airoil, rom which includes: (i) drag due to skin riction ( or parasite) drag and (ii) drag due to pressure (or separation) drag: c c c d d, d, p The total drag on an airplane is: C D 2 CL "Proile" Drag "Induced" Drag cd e AR