4 Flow Field Representations A- 5: Unit A-1: Engineering ...

1 Unit A-1: Engineering fundamentals Review Page 1 of 15 AE301 Aerodynamics IUNIT A:Fundamental ConceptsROAD MAP .. A-1: Engineering fundamentals Review A-2: Standard Atmosphere A-3: Governing Equations of Aerodynamics A-4: Airspeed Measurements A-5: Aerodynamic Forces and MomentsAE301 Aerodynamics IUnit A-1: List of Subjects What is Aerodynamics? Engineering Units Review Flow Field Representations Flow Field Properties Equation of StateUnit A-1: Engineering fundamentals Review Page 2 of 15 WHAT IS AERODYNAMICS? Aerodynamics is a branch (means: a specific application) of Fluid Mechanics: (i) Underlying assumption is the fluid as a continuum and, (ii) The working fluid is standard air. CLASSIFICATION OF AERODYNAMICS 1. Density: incompressible (constant density) or compressible 2. Viscosity: inviscid (zero viscousity) or viscous => If viscous: laminar, transitional, or turbulent 3. Velocity (Mach number): subsonic (M < ), transonic ( < M < 1), supersonic (1 < M < 5), or hypersonic (5 < M) => If subsonic: incompressible (M < ) or compressible ( < M) I.

2 Analytical Solution: => Potential Flow Analysis (2-D & 3-D) => Panel Methods (2-D & 3-D) => Thin Airfoil (2-D) / Lifting Line & Surface Methods (3-D) II. Experiment: Wind Tunnel (scale-model tests) / Prototype (full-scale tests) III. Numerical Simulation: Computational Fluid Dynamics (CFD) Unit A-1 Page 1of 8 What is Aerodynamics?1. Density2. Viscosity3. VelocityA. Space (1-D, 2-D, or 3-D)I. Analytical SolutionII. ExperimentIII. Numerical SimulationB. Time (Steady, Periodic, or Unsteady)Unit A-1: Engineering fundamentals Review Page 3 of 15 CONSISTENT AND INCONSISTENT UNITS Consistent (or coherent) units allow physical relationships to be written without the need of conversion factors in the basic formulas. Inconsistent units cannot be used against consistent units (important): inconsistent units must be converted into consistent units, before executing numerical calculation. SI UNIT SYSTEM Kilogram or kg (mass), Meter or m (length), Second or s (time) => Force: Newton (N): 1 N = (1 kg)(1 m/s2) Inconsistent force unit: Kilogram-Force: kgf ( Kilogram-Mass: kgm = kg is consistent unit) Unit conversion: N = 1 kgf (Do you casually use Newtons as a unit of force, or weight.)

3 ?) US CUSTOMARY (ENGLISH) UNIT SYSTEM: Slug (mass), foot or ft (length), Second or s (time) => Force: Pound (lb): 1 lb = (1 slug)(1 ft/s2) Inconsistent mass unit: Pound-Mass: lbm (note: Pound-Force: lbf = lb is consistent unit) Unit conversion: 1 slug = lbm (Do you casually use slugs as a unit of mass ..?) Unit A-1 Page 2of 8 Engineering Units Review (1)1 slug = N = 1 kgf Consistent Unit:Slug / N Inconsistent Unit:lbm / kgfUnit A-1: Engineering fundamentals Review Page 4 of 15 Both measures weight = 15 pounds force / 85 kilogram force Mass is not a measurable property (you can never directly determine the amount of mass, by any measurement method) .. one can only estimate the mass, by measuring the force (weight) generated by the presence of mass, under a known gravitational acceleration (Wmg ). WHAT IS THE BOTTOM LINE? Under the gravitational acceleration on earth ( m/s2 or ft/s2): A substance of 15 pounds mass weighs 15 pounds force.

4 A substance of 85 kilogram mass weighs 85 kilogram force. Problems: Pound mass (lbm) is inconsistent mass unit, and cannot be used against pound force (lb). Kilogram force (kgf) is inconsistent unit, and cannot be used against kilogram mass (kg). SO, WHAT DO YOU NEED TO DO IN Engineering ANALYSIS? Unit A-1 Page 3of 8 Class Example Problem A-1-1 Related Subjects .. Engineering Units Review Suppose, if you go to FRY S and measure a bunch of fruits .. The scale says, 15 pounds. Does this mean: 15 pounds mass, or 15 pounds force?A standard health meter in Japan indicates everything in kilograms. Suppose, if you step onto a Japanese health meter and it indicates, 85 kilograms. Does this mean: 85 kilogram force, or 85 kilogram mass?_____Unit A-1: Engineering fundamentals Review Page 5 of 15 Homework A-1-1 R1-3 A person X weighs 200 pounds on the earth s surface. (a) If this person X is located on the moon (1/6 gravity of earth), determine the mass of this person X in pounds.

5 (b) If this person X is located on the moon (1/6 gravity of earth), determine the weight of this person X in pounds. A person Y weighs 90 kilograms on the earth s surface. (c) If this person Y is located on the moon (1/6 gravity of earth), determine the mass of this person Y in kilograms. (d) If this person Y is located on the moon (1/6 gravity of earth), determine the weight of this person Y in kilograms. (e) Do you think it is a great idea to act like a typical non- Engineering type person (such as a customer representative of a supermarket), saying pounds are pounds and/or kilograms are kilograms, what s the problem? YES or NO. Explain WHY. Hints .. Apply Wmg (weight = mass times gravitational acceleration). 1 lbm of object weighs 1 lb on earth (at g = ft/s2). 1 kg of object weighs 1 kgf on earth (at g = m/s2). Mass never change, while weight (the force developed, due to mass ) depends on gravitational acceleration.

6 Name:_____ Student ID:_____ _____Unit A-1: Engineering fundamentals Review Page 6 of 15 STANDARD UNITS FOR AERODYNAMIC PROPERTIES Pressure (SI Unit): N/m2 (Pascal, or Pa ), 1,000 Pa = 1 kPa Pressure (US Customary Unit): lb/in2 (psi), lb/ft2 (psf) Pressure unit conversion: 1 psi = 144 psf Density: kg/m3 (SI Unit) / slugs/ft3 (US Customary Unit) Temperature (SI Unit): Celsius ( C), Kelvin (K) / K = C + 273 Temperature (US Customary Unit): Fahrenheit ( F), Rankine ( R) / R = F + 460 Gas Constant (Standard Air): 287 J/(kg K), 1,716 (ft lb)/(slug R) COMMON MISHAPS OF UNITS Angle of Attack: may be given in degrees or radians. Temperature: the problem may be given in relative scales ( C / F), but usually need to use absolute scales (K / R) in calculations. Pressure: you need to know either absolute or gage pressure. Do you use inches in your calculation? Unit A-1 Page 4of 8 Engineering Units Review (2)0 F = 460 R0 C = 273 K1 atm(Standard Sea-Level) = 2,116 lb/ft21 atm(Standard Sea-Level) = 105N/m21 ft= m1 lb = N1 mile= 5,280 ft1 h = 3,600 s60 mph= 88 ft/sUnit A-1: Engineering fundamentals Review Page 7 of 15 STREAKLINE AND PATHLINE A streakline is the line defined in a flow Field by continuously injecting infinitesimally small particles at a fixed location.

7 The idea of streakline is the pure experimental method (Eulerian). A pathline is the line defined by tracing a path of an individual particle. A pathline can be visualized by injecting small particles in the flow Field . The idea of pathline is a particle trace (Lagrangian). FLOW VELOCITY AND STREAMLINE For a steady flow, a moving fluid element traces out a fixed path in space, called a streamline. Streamlines are mathematical concept. Hence, streamlines can be formed by equations of streamlines in a given flow Field . A streamline is a line, at which the velocity vector is tangent along its path. NEWTONIAN FLUID SHEAR STRESS Due to the viscosity, the shear stress will be developed between the adjacent streamlines. For Newtonian fluids: dVdy ( : absolute or dynamic viscosity). Unit A-1 Page 5of 8 Flow Field RepresentationsUnit A-1: Engineering fundamentals Review Page 8 of 15 FLOW Field PROPERTIES AND STANDARD UNITS Common properties in aerodynamics that can define flow Field at a point: (1) Pressure: p = p (x,y,z,t): units => lb/ft2 (psf), lb/in2 (psi), N/m2, Pa Pressure in absolue value: psia, psfa Pressure in gage value: psig, psfg (2) Density / Specific Volume: = (x,y,z,t): units => slugs/ft3, kg/m3 Specific Volume: 1v (volume per unit mass: inverse of density) (3) Temperature: T = T (x,y,z,t): units => F, C, R, K Absolute Scale Temperature (conversion): R = F + 460 / K = C + 273 VELOCITY (A VECTOR PROPERTY) (4) Velocity: ( , , , )x y z t VV: vector property (= magnitude + direction) Vector Notation: publication / handwritten VVV Unit Vectors.

8 I j k (Cartesian) / rz e ee (cylindrical) Unit A-1 Page 6of 8 Flow Field Properties in "absolute" pressurepsiapsi in "gage" pressurepsigpsi 1 (Specific Volume)v Unit A-1: Engineering fundamentals Review Page 9 of 15 EQUATION OF STATE A perfect (ideal) gas is the one in which the intermolecular forces are negligible. Specific (R) and universal () gas constants for a standard air: Note 1): Pressure must be in absolute pressure (not gage pressure). Note 2): Temperature must be in absolute scale (K / R, not C / F). IDEAL GAS MODELS IN AERODYNAMICS Rule of Thumb (means usually, but not always true) Calorically Perfect => Thermally Perfect => Non Ideal Gas Ideal Gas of Air Ideal Gas of Air of Air Subsonic Supersonic Hypersonic The difference between thermally and calorically perfect gases will be discussed later!

9 Unit A-1 Page 7of 8 Equation of State= 8,314 J/(kg mole K) = 104(ft lb)/(slug mole R)M= kg/(kg mole) or slug/(slug mole) Calorically Perfect Ideal Gas of Air Thermally Perfect Ideal Gas of Air Non-Ideal Gas of AirUnit A-1: Engineering fundamentals Review Page 10 of 15 Unit A-1 Page 8of 8 Class Example Problem A-1-2 Related Subjects .. Equation of State The air is flowing on a wing of Boeing 787 Dreamliner at cruise. The pressure and density of air measured were psi (absolute) and slugs/ft3, respectively. What is the temperature (in F) of the air at that point?_____Unit A-1: Engineering fundamentals Review Page 11 of 15 Homework A-1-2a R1-2 At a point of the surface of a supersonic fighter jet aircraft, the air temperature and pressure are: 20 C and 30 psia, respectively. Calculate the air density at this point, both in SI (kg/m3) and Customary (slugs/ft3) units. Hints .. Use conversion: 1 ft = m.

10 Use conversion: 1 lb = N. Use conversion: 1 K = R. Name:_____ Student ID:_____ _____Unit A-1: Engineering fundamentals Review Page 12 of 15 Homework A-1-2b 1-1 An automobile tire (with an internal volume of 150 ft3) is inflated to the gage pressure of 35 psi (assume a typical day at Prescott, Arizona: means equivalent to the standard 5,000 ft atmospheric condition: patm = psi). If the air temperature inside the tire is 100 F, determine the followings (note that gravity is approximately equal to the standard sea-level value): (a) What is the air density, in pounds per cubic inches, in this tire? (b) What is the weight of air, in pounds, in this tire? (c) What is the mass of air, in pounds, in this tire? Hints .. Apply pRT (ideal gas equation of state). The gas constant for standard air is: 1,716 ft lb/slug R or 287 J/kg K. Pressure and temperature must both be absolute for ideal gas equation of state. Apply Wmg (weight = mass times gravitational acceleration).