INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

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1 INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad AERONAUTICAL ENGINEERING TUTORIAL QUESTION BANK Course Name : LOW SPEED AERODYNAMICS Course Code : AAE004 Regulation : IARE - R16 Year : Class : B. Tech IV Semester Branch : Aeronautical Engineering Team of Instructors : Dr. A. Barai, Professor, Department of Aeronautical Engineering Mr. N. V. Raghavendra, Associate Professor, Department of Aeronautical Engineering COURSE OBJECTIVES (COs): The course should enable the students to: I II III IV V VI VII basic philosophy and ideas of flow at different conditions and mediums. the physics behind the governing equations to solve the flow field problems and flow models. Identify theory behind the forces and moments for which conditions the theories are appropriate. Discuss the application of aerodynamics in various engineering disciplines and their effects. the concept of boundary layer flows to increase the performance of the body. Discuss the propeller aerodynamics and the effects of propeller on different wing configurations the various types of wings and their performance at various conditions of aircraft COURSE LEARNING OUTCOMES (CLOs) Students, who complete the course, will be able to demonstrate the ability to do the following: CAAE CAAE CAAE CAAE CAAE CAAE Apply and understand the essential facts, concepts and principles of aerodynamics. Adapt the basic of mathematics, science and engineering for problem solving. Describe principles of physics and aerodynamics to study the Wing-body interference junction. Explain the concept of boundary layer flows to increase the performance of the body. Demonstrate of aerodynamics to develop effective aircraft design and operations. Apply the concept of lifting line theory to study potential flows over different aerofoils.

2 CAAE CAAE CAAE CAAE CAAE CAAE CAAE CAAE CAAE CAAE Identify the elliptic load distribution for obtaining high lift performance on finite wings. Evaluate the source and vortex panel method for non-lifting and lifting aerofoils. Illustrate the propeller aerodynamics and the effects of propeller on the wing. the lift augmentation techniques for high-lift devices and slats. aerodynamic effect of taper and twist applied to wings. Apply temperature effects on boundary layer, transition and turbulent flow regimes. the aerodynamic effect of vortex formation around wings. the effect of sweep in the context of delta wings. the relation between circulation and lift. the various sources of drag including induced drag and skin friction drag. UNIT I INTRODUCTORY TOPICS FOR AERODYNAMICS PART - A (SHORT ANSWER QUESTIONS) S No QUESTIONS Blooms Course Learning taxonomy level Outcomes (CLOs) 1 Derive Laplace equation for potential flow. CAAE004:02 2 D'Alembert's paradox is between theoretical drag and real life drag. Explain this paradox. 3 Magnus effect creates the aerodynamic forces over spinning bodies. Justify the statement. 4 Describe velocity potential for doublet flow. CAAE004:03 5 What are the infinity boundary conditions? CAAE004:01 6 Describe velocity potential for uniform flow. CAAE004:03 7 Explain velocity potential for source and sink flows. CAAE004:03 8 Explain velocity potential for vortex flow. CAAE004:03 9 Describe the difference between non-lifting and lifting flow over a cylinder. CAAE004:03 10 Define and explain Kutta-Joukowski theorem. 11 Describe stream function for doublet flow. CAAE004:03 12 Describe stream function for uniform flow. CAAE004:03 13 Describe stream function for source flow. CAAE004:03 14 Describe stream function for vortex flow. CAAE004:03 15 Describe stream function for sink flow. CAAE004:03 PART - B (LONG ANSWER QUESTIONS) 1 Prove that the velocity potential and the stream function for a uniform CAAE004:03 flow satisfy Laplace's equation. 2 Explain the uniform flow and source flows with complete derivations. CAAE004:03 3 Derive the stream function and potential function for the CAAE004:03 combination of uniform, doublet and vortex flows. 4 Derive the stream function and potential function for doublet flow. CAAE004:03 5 Wall boundary conditions and infinity boundary conditions exist for a flow CAAE004:03 over any object. Describe these conditions. 6 Define and derive irrotational and incompressible flow conditions. CAAE004:03

3 7 Derive the stream function and potential function for the combination of uniform and doublet flow. CAAE004:03 8 Obtain the expression for the coefficient of pressure distribution for nonlifting flow over a circular cylinder. CAAE004:03 9 Obtain the expression velocity potential and stream function for a uniform flow in terms of Cartesian and polar co-ordinates. CAAE004:03 10 Describe how the uniform flow and source flow develop flow over a semiinfinite body. CAAE004:03 PART - C (PROBLEM SOLVING AND CRITICAL THINKING QUESTIONS) 1 Explain in detail how combination of a uniform flow and doublet flow produces non-lifting flow over a cylinder. CAAE004:03 2 Derive the stream function and velocity potential for source and sink pair. CAAE004:03 3 Derive the stream function and velocity potential for uniform flow and doublet flow. CAAE004:03 4 Explain in detail how combination of uniform flow, doublet flow and vortex flow produces lifting flow over a cylinder. CAAE004:03 5 Explain the Kutta-Joukowski theorem and Kelvin circulation theorem. CAAE004:15 6 Explain in detail all the elementary flows and their combinations. CAAE004:03 7 Discuss in detail the aerodynamics of spinning tennis ball. 8 Analyze the flow given by the stream function (units: m 2 /s): Ψ = 6x + 12y 9 Consider a circular cylinder in a hypersonic flow, with its axis perpendicular to the flow. Let ϕ be the angle measured between radii drawn to the leading edge (the stagnation point) and to any arbitrary point on the cylinder. The pressure coefficient distribution along the cylindrical surface is given by C p = 2 cos(2ϕ) for 0 ϕ π/2 and 3π/2 ϕ 2π, and C p = 0 for π/2 ϕ 3π/2. Calculate the drag coefficient for the cylinder, based on projected frontal area of the cylinder. 10 Consider the lifting flow over a circular cylinder. The lift coefficient is 5. Determine: (a) the peak (negative) pressure coefficient (b) the location of the stagnation points (c) points on the cylinder where the pressure equals freestream static pressure 1 UNIT II THIN AEROFOIL THEORY PART - A (SHORT ANSWER QUESTIONS) CAAE004:03 CAAE004:03 CAAE004:03 Explain the naming convention for airfoils. 2 Describe center of pressure of an airfoil. 3 Explain starting vortex. CAAE004:13 4 Describe the aerodynamic center of an airfoil. 5 Explain Kutta condition for the steady state flow at the trailing edge. 6 What are high-lift airfoils? CAAE004:10 7 What are high-lift devices? Give examples. CAAE004:10 8 Define airfoil stall. 9 Define zero-lift angle of attack of an airfoil. 10 Define design lift coefficient of an airfoil. 11 Define camber of an airfoil. 12 Define thickness of an airfoil.

4 13 Define angle of attack of an airfoil. 14 Explain the importance of Kelvin s circulation theorem. 15 Describe the two boundary conditions used in Vortex Panel Method to obtain flow over an airfoil. PART - B (LONG ANSWER QUESTIONS) 1 Starting with the expression for the vortex strength along the chord of the airfoil, as given by thin airfoil theory, obtain the linear relation between the lift coefficient and the angle of attack. 2 Describe the stalling of an airfoil and the related aerodynamic phenomena. 3 Prove that the local jump in tangential velocity across a vortex sheet is equal to the local sheet strength. 4 Describe high-lift airfoils. 5 Describe high-lift devices and why they are needed. CAAE004:10 6 Explain with sketch the thin aerofoil theory. 7 Explain in detail, thin airfoil problem in non-lifting cases and their solutions. 8 Explain in detail, thin airfoil problem in lifting cases and their solutions. 9 Explain Kutta condition and its significance for the case of steady flow over an airfoil. 10 Explain profile drag of an airfoil. PART C (PROBLEM SOLVING AND CRITICAL THINKING) 1 Consider the experimental data for lift coefficient and moment coefficient about the quarter-chord point for an NACA 2412 airfoil (Source: Abbott and von Doenhoff, Theory of Wing Sections, McGraw-Hill Book Company, New York, 1949; also, Dover Publications Inc., New York, 1959). Calculate the lift and moment about the quarter chord (per unit span) for this airfoil when the angle of attack is 4 and the freestream is at standard sea level conditions with a velocity of 50 ft/s. The chord of the airfoil is 2 ft. 2 Consider an NACA 2412 airfoil with a 2-m chord in an airstream with a velocity of 50 m/s at standard sea level conditions. If the lift per unit span is 1353 N, calculate the angle of attack? 3 Starting with the definition of circulation, derive Kelvin's circulation theorem 4 Consider a thin, symmetric airfoil at 1.5 angle of attack. From the results of thin airfoil theory, calculate the lift coefficient and the moment coefficient about the leading edge. 5 Consider an NACA 2412 airfoil with a chord of 0.64 m in an airstream at standard sea level conditions. The freestream velocity is 70 m/s. The lift per unit span is 1254 N/m. Calculate (a) The angle of attack (b) The drag per unit span. (c) The moment per unit span about the aerodynamic center. (Use the experimental data for NACA 2412 airfoil on lift coefficient, drag coefficient and moment coefficient about aerodynamic center, source: Abbott and von Doenhoff, Theory of Wing Sections, McGraw-Hill Book Company, New York, 1949; also, Dover Publications Inc., New York, 1959) 6 For the NACA 2412 airfoil, calculate and compare the lift-to-drag ratios at angles of attack of 0, 4, 8, and 12 degrees. The Reynolds number is Plot (C l /C d ) versus AOA. What do you infer from the graph? 7 Consider an NACA 2412 airfoil with a chord of 0.64 m in an airstream at standard sea level conditions. The freestream velocity is 70 m/s. The lift per unit span is 1254 N/m. Calculate the strength of the steady-state starting vortex.

5 8 Analyze the steady-state flow velocities at the trailing edge (T.E.) of an airfoil: (a) Having a finite angle at the T.E. (b) Having a cusped T.E. Evaluate the vorticity at the T.E. in the above cases. 9 For a particular airfoil section, the pitching moment coefficient about an axis a third of the chord behind the leading edge varies with the lift coefficient in the following manner: C l C m Calculate the location of aerodynamic center, and the value of the pitching moment coefficient at zero left, C m0. 10 Consider a thin, symmetric airfoil at 1.5 angle of attack. From the results of thin airfoil theory, calculate the lift coefficient C l, and the moment coefficient about the leading edge, C m,le UNIT-III FINITE WING THEORY PART - A (SHORT ANSWER QUESTIONS) 1 Define induced drag. CAAE004:16 2 Explain Biot-Savart Law. 3 Explain the formation of trailing vortices. CAAE004:13 4 Define and explain Kelvin circulation theorem. CAAE004:15 5 Explain Rankine s vortex. 6 What is the effect of an elliptic wing planform? 7 What is drag polar? 8 How does induced drag coefficient vary with aspect ratio of the wing? 9 What is downwash? 10 Define the two vortex theorems given by Helmholtz. 11 Explain bound vortex. 12 Describe the vortex filament statement of Helmholtz s vortex theorem. 13 What is downwash? 14 What is source panel method? 15 What is vortex panel method? 16 What is vortex breakdown? CAAE004:14 17 What is geometric twist of the wing? CAAE004:11 18 What is taper of the wing? CAAE004:11 19 Define aspect ratio of the wing? 20 Explain primary and secondary vortices on a delta wing? CAAE004:14 PART B (LONG ANSWER QUESTIONS) 1 Obtain the expression for induced drag and minimum induced drag for elliptic planform. 2 Consider a vortex filament of strength Г in the shape of a closed circular loop of radius R. Obtain an expression for the velocity induced at the center of the loop in terms of Г and R. 3 Consider the same vortex filament as mentioned in the problem above. Consider also a straight line through the center of the loop, perpendicular CAAE004:16 CAAE004:16 CAAE004:16

6 to the plane of the loop. Let A be the distance along this line, measured from the plane of the loop. Obtain an expression for the velocity at distance A on the line, as induced by the vortex filament. 4 The measured lift slope for the NACA airfoil is degree -1, and α L0 =-1.3. Consider a finite wing using this airfoil, with AR = 8 and taper ratio = 0.8. Assume that δ= τ. Calculate the lift and induced drag coefficients for this wing at a geometric angle of attack = 7 o. 5 Explain starting, bound and trailing vortices of wings. CAAE004:16 6 Explain in detail Prandtl s lifting line theory. 7 Describe primary and secondary vortex formation on Delta wings. CAAE004:14 8 Explain the source and vortex panel methods. 9 Explain in detail vortex filament statement of Helmholtz's vortex theorems. 10 Explain elliptic loading and wings of elliptic platform PART C (PROBLEM SOLVING AND CRITICAL THINKING) Explain in detail vortex filament statement of Helmholtz's vortex theorems Biot-Savart Law. Explain in brief Lanchester s experiment and Prandtl s lifting line theory. Explain elliptic loading & wings of elliptic platforms. Derive the expression for minimum induced drag for Elliptic platform. Explain in detail the use of quarter chord and three- quarter chord points in vortex panel method for wings. a) Lifting surface theory predicts better lift distribution on a wing with a low aspect ratio and of any type of given planform. Demonstrate the verification of the statement. b) Compare the formulation in (a) above with that in the classical lifting line theory with details. 6 Describe how the source panel method differs from the vortex panel method? Also describe the formulation of a source panel method for a non-lifting flow over a circular cylinder. A constant strength vortex panel of strength 50 units is located on the axis from X 7 1 =3.5 to X 2 =6.65. Determine the influence of this vortex panel at a point P (4.5, 4.5) to evaluate V (u, w). Develop the expressions used for determining velocity potential. 8 The Piper Cherokee (a light, single-engine general ayiation aircraft) has a wing area of 170 ft 2 and a wing span of 32 ft. Its maximum gross weight is 2450 lb. The wing uses an NACA airfoil, which has a lift slope of degree -1 and α L=0 = -3. Assume τ = If the airplane is cruising at 120 mi/h at standard sea level at its maximum gross weight and is in straight-and-level flight, calculate the geometric angle of attack of the wing. 9 Consider the airplane and flight conditions given above. The span efficiency factor e for the complete airplane is generally much less than that for the finite wing alone. Assume e = Calculate the induced drag for the airplane in the above problem. 10 Explain starting, bound and trailing vortices of wings and explain their formation. UNIT-IV FLOW PAST NON-LIFTING BODIES AND INTERFERENCE EFFECTS PART A (SHORT ANSWER QUESTIONS) 1 What is a non-lifting body? Give examples.

7 2 What is a lifting body? Give examples. 3 Explain in brief the method of singularities. 4 What are the commonly used singularities to model potential flows over airfoils? 5 What are the limitations of panel methods? 6 Explain the meaning of wing-fuselage interference. 7 Draw the upwash and downwash distribution on the fuselage as a result of the wing. 8 Draw the upwash and downwash distribution on the wing as a result of the fuselage. 9 Explain with the help of a diagram what is fuselage thickness ratio? 10 Write short notes on the general effects of the propeller slipstream on the CAAE004:09 wing and tail. 11 Describe the meaning of empennage of an aircraft. CAAE004:03 12 Explain slipstream. CAAE004:03 13 Describe the effect of fuselage on wing. CAAE004:03 14 What is a slender body? CAAE004:03 15 What is Oswald s efficiency factor? CAAE004:03 PART B (LONG ANSWER QUESTIONS) 1 Explain non-lifting and lifting bodies and give examples. 2 Describe the method of singularities. How is it used to study potential flow over an arbitrary body? 3 Explain the basic methodology to study potential axisymmetric flow past a slender body of revolution, using the method of singularities. 4 Explain the basic methodology to study potential transverse flow past a slender body of revolution, using the method of singularities. 5 Describe the upwash and downwash distribution on the fuselage as a result of the wing. 6 Draw the upwash and downwash distribution on the wing as a result of the fuselage. 7 Describe the asymmetric flow over a wing-fuselage system for a highwing airplane. How does this affect the rolling moment compared to a wing? 8 Describe the asymmetric flow over a wing-fuselage system for a midwing airplane. How does this affect the rolling moment compared to a wing? 9 Describe the asymmetric flow over a wing-fuselage system for a lowwing airplane. How does this affect the rolling moment compared to a wing? 10 Describe studies on the general effects of the propeller slipstream on the wing and tail. PART C (PROBLEM SOLVING AND CRITICAL THINKING) CAAE004:09 1 Demonstrate the methodology to study potential axisymmetric flow past a slender body of revolution, using the method of singularities. 2 Demonstrate the methodology to study potential transverse flow past a slender body of revolution, using the method of singularities. 3 Describe the methodology to obtain the total lift of a wing-fuselage system in symmetric incident flow, using the method of singularities. 4 How is the flow past a wing-fuselage system different in symmetric versus asymmetric incident flows? 5 Analyze the drag coefficient for an entire aircraft. Give an expression to estimate this drag coefficient.

8 6 An aircraft weighing 40,000 lbs, has a wing area of 350 ft 2 and a wing span of 50 ft. At sea-level, the aircraft flies at (a) 200ft/sec (b) 600ft/sec. For the entire aircraft, determine the estimated values of the induced drag and the associated drag coefficients for the two cases? Note that lift = weight in level flight. Also, assume Oswald efficiency factor of Calculate the pressure coefficient distribution around a non-lifting circular cylinder using the source panel method. 8 The NACA0012 aerofoil is a symmetric airfoil. So, when it is placed in a potential flow at zero angle of attack, it is a non-lifting body. For this case, with the source panel method, using the aerofoil shape, write a code to generate the distribution of source strength. Plot the distribution of source strength versus distance along the chord. 9 Extend the source panel code for NACA0012 airfoil (at zero AOA) to generate the tangential flow speed distribution over the airfoil surface. Plot the distribution. 10 Extend the source panel code for NACA0012 airfoil (at zero AOA) to generate the pressure coefficient distribution. Plot the distribution. UNIT-V BOUNDARY LAYER THEORY PART - A (SHORT ANSWER QUESTIONS) 1 Draw and explain the temperature profile in the boundary layer. 2 Define displacement thickness. 3 Define boundary layer thickness. 4 Describe temperature boundary layer. 5 Draw and explain the velocity profile in the boundary layer. 6 Define momentum and energy thickness. 7 Explain adverse pressure gradient. 8 Explain favourable pressure gradient. 9 Define the boundary conditions for the boundary layer. 10 Describe transition and its effects on flow over airfoil. 11 What is Prandtl s mixing length? 12 What is a wake? 13 What is Sutherland s law for dynamic viscosity? 14 What is fully-developed flow? 15 Define velocity defect. PART - B (LONG ANSWER QUESTIONS) 1 Derive skin friction drag and pressure drag by integration of tangential stresses and normal stresses respectively 2 Explain the boundary layer growth along a flat surface 3 Explain in detail momentum thickness and displacement thickness. 4 Discuss in detail laminar, transition and turbulent flows 5 Derive the boundary layer equations 6 Derive the Blasius solution for flat plate problem 7 Discuss in detail the flow separation phenomena. 8 Discuss the effect of transition and surface roughness on the flow over airfoil. 9 Show that in steady state, the pressure at any station along the boundary layer is constant in the direction normal to the surface.

9 10 Describe aerodynamic heating at stagnation point. PART C (PROBLEM SOLVING AND CRITICAL THINKING) Some engineers wish to obtain a good estimate of the drag and boundarylayer thickness at the trailing edge of a miniature wing. The chord and span of the wing are 6mm and 30mm respectively. A typical flight speed is 5m/s in air (kinematic viscosity = 15 x 10-6 m 2 /s, density = 1.2 kg/m 3 ). They decide to make a superscale model with chord and span of 150 mm and 750 mm respectively. Measurements on the model in a water channel flowing at 0.5m/s (kinematic viscosity = 1x10-6 m 2 /s, density = l000 kg/m 3 ) gave a drag of 0.19N and a boundary-layer thickness of 3 mm. Estimate the corresponding values for the prototype. Consider Mach 4 flow at standard sea level conditions over a flat plate of chord 5 in. Assuming all laminar flow and adiabatic wall conditions, calculate the skin friction drag on the plate per unit span. The wing on a Piper Cherokee general aviation aircraft is rectangular, with a span of 9.75 m and a chord of 1.6 m. The aircraft is flying at cruising speed (141 mi/h) at sea level. Assume that the skin friction drag on the wing can be approximated by the drag on a flat plate of the same dimensions. Calculate the skin friction drag: (a) If the flow were completely laminar (which is not the case in real life) (b) If the flow were completely turbulent (which is more realistic). Compare the two results. The streamwise velocity component for a laminar boundary layer is sometimes assumed to be roughly approximated by the linear relation 4 where δ = 1.25 x Assume that we are trying to approximate the flow of air at standard sea-level conditions past a flat plate where u e = m/s. Calculate the streamwise distribution of the displacement thickness (δ*), the velocity at the edge of the boundary layer (v e ), and the skin-friction coefficient (C f ). 5 Air at standard day sea-level atmospheric pressure and 5 o C flows at 200 km/h across a flat plate. Compare the velocity distribution for a laminar boundary layer and for a turbulent boundary layer at the transition point, assuming that the transition process is completed instantaneously at that location. Assume that the transition Reynolds number for this incompressible flow past a flat plate is 500, A thin equilateral-triangle plate is immersed parallel to a 12 m/s stream of water 20 C, as in Fig. Assuming Re tr = , estimate the drag of this plate. 7 A long, thin flat plate is placed parallel to a 20-ft/s stream of water at 20 C. Calculate the distance x from the leading edge at which the boundary-layer thickness be 1 in? 8 Are low-speed, small-scale air and water boundary layers really thin? Consider flow at U = 1ft/s past a flat plate 1 ft long. Compute the boundary-layer thickness at the trailing edge for (a) air and (b) water at 20 C. 9 A sharp flat plate with L=1m and b=3m is immersed parallel to a stream of velocity 2 m/s. Obtain the drag on one side of the plate, and at the trailing

10 edge find the thicknesses δ, δ*, and θ for (a) air, ρ = 1.23 kg/m 3 and ν = 1.46X10-5 m 2 /s, and (b) water, ρ = 1000 kg/m 3 and ν = 1.02 X 10-6 m 2 /s. 10 The radiator systems on many of the early racing aircraft were flush mounted on the external surface of the airplane. We will assume that the local heat-transfer rate can be estimated using the flat-plate relations. Calculate the local heating rate for x = 3.0 m when the airplane is flying at 468 km/h at an altitude of 3 km? The surface temperature is 330 K. Assume that the transition Reynolds number for this flow past a flat plate is 500,000. Prepared By: Dr. A Barai, Professor HOD, AE