Questions and Answers in Aerodynamics

Questions and Answers in Aerodynamics Based on Fundamentals of Aerodynamics by John Anderson Jr., McGrawHill Inc.

- D Viswanath

Contents

Contents

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1 Q and A in Aerodynamics

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1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.2

Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.3

Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References

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Chapter 1 Q and A in Aerodynamics 1.1

Introduction

(1) What is aerodynamics? Study of the movement of a body in the presence of air is called aerodynamics and this study is vitally important for the design of aircraft, missiles and rockets. (2) How do you distinguish between solids, liquids and gases? Put them in a large closed container, solid will not change i.e., its shape and boundaries will remain the same; whereas the liquid will change its shape to conform to that of the container and will take on the same boundaries as the container up to the maximum depth of the liquid and the gas will completely fill the container, taking on the same boundaries as the container. When a force is applied tangentially to the surface of a solid, the solid will experience a finite deformation, and the tangential force per unit area-the shear stresswill usually be proportional to the amount of deformation. In contrast, when a tangential shear stress is applied to the surface of a fluid (liquid or gas), the fluid will experience a continuously increasing deformation, and the shear stress will be proportional to the rate change of momentum. The most fundamental distinction is at atom and molecular level i.e., spacing between molecules. In solids, molecules are closely packed while in liquids and gases spacing is large. Hence intermolecular forces are much weaker and motion of molecules occurs freely particular throughout gases. 1

(3) What is hydrodynamics? Study of flow of liquids is called hydrodynamics. (4) What is gas dynamics? Study of flow of gases is called gas dynamics. (5) How do you distinguish between external and internal aerodynamics? The applications in prediction of forces and moments on, and heat transfer to (aerodynamics heating), bodies moving through a fluid is called external aerodynamics since they deal with external flows over a body. In contrast, the applications in determination of flows moving internally through ducts, calculation and measurement of flow properties inside rocket and air-breathing engines, engine thrust or flow conditions in test section of wind tunnel is called internal aerodynamics. (6) What are the basic aerodynamic quantities? The four basic aerodynamic quantities are pressure, density, temperature and flow velocity. A fifth quantity is streamlines. (7) Define pressure. Pressure p is the normal force per unit area exerted on a surface due to time rate of change of momentum of the gas molecules impacting or crossing that surface (point property-scalar). (8) Define density. Density, ρ, is defined as the mass per unit volume (point property-scalar). (9) Define temperature. The temperature T of a gas is directly proportional to the average kinetic energy of the molecules of the fluid.(point property-scalar) In fact, if KE is the molecular kinetic energy, then temperature is given by 3 KE = kT 2

(1.1)

where k is Boltzmann constant. (10) Define flow velocity. The principal focus of aerodynamics is fluids in motion. Hence, flow velocity is important. The velocity of a flowing gas at any fixed point B in space can be defined as the velocity of an infinitesimally small fluid element as it sweeps through 2

B. The flow velocity V has both magnitude and direction and hence is a vector quantity (p, ρ and T are scalar quantities). (11) Define a streamline. A moving fluid element traces out a fixed path in space. As long as the flow is steady (no fluctuations with time), this path is called a streamline of the flow. Drawing the streamlines of the flow field is an important way of visualizing the motion of the gas. (12) Describe shear stress in brief. If two streamlines are rubbing at each other, friction plays a role and exerts a force on one of the streamlines acting tangentially in the direction of the force. The shear stress is the limiting form of the magnitude of the frictional force per unit area. In aerodynamic applications, the value of shear stress at a point on a streamline is proportional to the spatial rate of change of velocity of normal to the streamline at that point. (13) What are aerodynamic forces and moments? No matter how complex the body shape may be, the aerodynamic forces and moments on the body are due entirely to only to two basic sources: (a) Pressure distribution, p, over the body surface (force per unit area normal to the surface) (b) Shear stress distribution, τ , over the body surface (force per unit area tangential to the surface) The net effect of p and τ distributions integrated over the complete body surface is a resultant aerodynamic force R and moment M on the body. (14) Define lift and drag in terms of aerodynamic force R. The aerodynamic force R can be split into components L = lift = component perpendicular to the relative wind Vinf (also called free stream velocity) D = drag = component of R parallel to Vinf (15) Define normal force and axial force in terms of chord. The chord c is the linear distance from the leading edge to the trailing edge of the body. Aerodynamic force R is split into components perpendicular and parallel to the chord and by definition 3

N = Normal force = component of R perpendicular to c A = Axial force = component of R parallel to c. (16) Define free stream velocity Vinf

(17) Define angle of attack. The angle of attack α is defined as the angle between c and Vinf . It is also the angle between lift component, L, and normal component, N, and between drag component, D, and axial component, A. The geometrical relation between these two sets of components is given by L = Ncosα − Asinα

(1.2)

D = Nsinα + Acosα

(1.3)

(18) Define Center of Pressure. Center of pressure (xcp ) is defined as the location where the resultant of a distributed load effectively acts on the body. If moments were taken about the center of pressure, the integrated effect of the distributed loads would be zero. An alternate definition of the center of pressure is that point on the body about which the aerodynamic moment is zero. (19) What are the criteria for two flows to be similar? The criteria for two flows to be similar are: (a) The bodies and any other solid boundaries are geometrically similar for both flows. (b) The similarity parameters are the same for both flows. Re and Minf are two parameters, which are by far the dominant similarity parameters. If two or more flows are similar, then the force coefficients CL , CD , etc., are the same. (20) Define Reynolds number. (21) Define Mach number. (21) What are the various Mach number regimes? The various Mach Number Regimes are:4

(i) Subsonic Flow M < 0.8 (ii) Transonic Flow 0.8 < M < 1 (iii) Transonic Flow 1 < M < 1.2 (iv) Supersonic Flow M > 1.2 (v) Hypersonic Flow M > 5 (22) Differentiate between continuum flow and free molecule flow.

(a) The mean distance that a molecule travels between collision with neighboring molecules is defined as Mean free path. (b) If mean free path is orders of magnitude smaller than the size of body, then flow appears to the body as continuous substance. Molecules impact the body surface so frequently that the body cannot distinguish the individual molecular collisions and that surface feels the fluid as a continuous medium. Such flow is called Continuum flow. (c) If (a) is on the same order as the body scale, body surface can feel distinctly each molecular impact. Such flow is called Free molecular flow. (d) Space shuttles encounter free molecular flow at the extreme outer edge of the atmosphere where the air density is too low that (a) becomes on the order of the shuttle size. (23) Differentiate between compressible and incompressible flows. Flow in which the density ρ is constant is called incompressible. Flow where the density is variable is called compressible. Generally low velocity (M < 0.3) flows are incompressible and high velocity flows are compressible. (24) Differentiate between inviscid and viscous flows. All real flows, which exhibit the effect of transport phenomena are called viscous flow. Velocity and temperature of the fluid near to the solid body is changing. This is called no slip condition. Flow adjacent to the body surface is considered to be viscous. This region is called boundary layer. Beyond the boundary layer flow is inviscid.

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Flow that is assumed to involve no friction, thermal conduction or diffusion (no transport phenomena) is called inviscid flow. Reynolds number is very high. Inviscid flows do not exist in nature. Many practical aerodynamic flows can be assumed as inviscid. Velocity and temperature of the fluid near to the solid body is not affected by the presence of the wall. This is called slip condition. (25) Differentiate between laminar and turbulent flows. If the path lines of various fluid elements are smooth and regular, the flow is called as laminar flow. If the motion of fluid element is very irregular and tortuous, the flow is called turbulent flow. The average flow velocity near a solid surface is larger for a turbulent flow in comparison with laminar flow. A turbulent flow does not separate from the surface as rapidly as laminar flow because energy of the fluid element close to the surface is larger. (26) What is boundary layer?

(27) What is Prandtl-Glauert compressibility correction

(28) Differentiate between rotational and irrotational flows.

(29) State Bernoulli’s equation.What are its applications? Bernoulli’s equations have several applications like of flow of ducts (velocity measurement in Venturi and low-speed tunnels) and measurement of airspeed using Pitot tube. (30) Explain Navier Stokes equations and Euler’s equations.

(31) Define velocity potential and stream function

(32) Explain Laplace equation. Governing Equation for Irrotational, Incompressible Flow : Laplace Equation. 6

Any irrotational, incompressible flow has a velocity potential and stream function for 2-D flow that both satisfy Laplace equation. Conversely, any solution of Laplace’s equation represents the velocity potential or stream function (2-D) for an irrotational incompressible flow. (33) Outline the general approach to solve an irrotational, incompressible flow. The general approach to the solution of irrotational, incompressible flows can be summarized as follows: Solve Laplace’s equation for φ or ψ along with proper boundary conditions. Obtain the velocity from V = ∆φ or u =

∂ψ ∂y

and v =

∂ψ . ∂x

Obtain the pressure from Bernoulli’s equation. (34) What are the basic flow equations used for solving practical aerodynamic problems? Continuity Equation, Momentum Equation, Energy Equation (35) Explain Substantial Derivative

(36) Explain Streamline.

(37) Explain Vorticity. Hint: Twice angular velocity. (38) Explain Circulation. Circulation is a fundamental tool for the calculation of aerodynamic lift. The circulation is simply the negative of the line integral of velocity around a closed curve in the flow. It is kinematic property depending only on the velocity field and the choice of the curve C. (39) Explain Stream function.

(40) Explain Velocity Potential.

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(41) What are the various models of the fluid used for solving aerodynamic problems. Finite Control Volume (a) Fixed in space (b) Moving with the fluid Infinitesimal Fluid Element (c) Fixed in space (d) Moving with the fluid (42) What is the physical principle of Continuity Equation? Mass can neither be created nor destroyed. Net mass flow out of control volume through surface S (B)= time rate of decrease of mass inside control volume V. (43) What is the physical principle of Momentum Equation? Physical principle : Force = time rate of change of momentum. F =body forces +Pressure forces +viscous forces G= Net flow of momentum out of CV across surface S H=Time rate of change of momentum due to unsteady fluctuations of flow properties inside V . G+H =F (44) What is the physical principle of Energy Equation? Physical principle : Energy can be neither created nor destroyed. it can only change in form. B1= rate of heat added to fluid inside CV from surroundings. B2=rate of work done on fluid inside CV. B3=rate of change of energy of fluid as it flows through CV. B1 + B2 = B3

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(45) Distinguish between conservation and non-conservation form. Conservation form: Governing flow equations that are directly obtained from the flow model which is fixed in space. Non-conservation form : Governing flow equations that are directly obtained from a flow model which is moving with the flow. (46) Explain gradient of a scalar field. Hint: Maximum rate of change per unit length. (47) Explain divergence of a vector field. Hint: The time rate of change of volume per unit volume. (48) Explain strain.

(49) Give the equation of state for a perfect gas. P = ρRT P V = RT where P =pressure;V =volume;ρ=density;R=proportionality constant. (50) Give the thermodynamic relation for a calorifically perfect gas. Internal energy, e = cv T

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1.2

Thermodynamics

(1) Define entropy. (2) Define enthalpy. (3) State the laws of thermodynamics. (4) Define adiabatic process. (5) Define a reversible process. (6) Define an isentropic process. (7) What is an isocline? (8) Distinguish between internal combustion and external combustion engines. (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) 10

(22) (23) (24) (25)

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1.3

Propulsion

(1) Distinguish between solid, liquid and hybrid propellants. (2) Distinguish between turbojet, ramjet and scram jets. (3) Distinguish between piston engines, turbo-propeller engines and turbojet engines. (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) 12

(22) (23) (24) (25)

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References

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