Aero Review

Lagrangian vs. Eulerian

Dimension of Aero Problems

Bernoulli’s Equations

Bernoulli’s Assumptions

• Irrotational

• Incompressible

• No Heat Transfer

• No E lost or added

• Steady-state flow

Pitot Tube

Absolute Pressure

Static Pressure

Gauge Pressure

Dynamic Pressure

The Fluid Particle

Conservation of Mass

Simplifications of the Conservation of Mass

Reynolds Ratio

Nondimensional number weighing the relative magnitude of the inertia forces / viscosity forces

Internal Flow and Reynolds Ranges

Regions of Internal Flow

External Flow

Lift

DragaW

Wall Shear Stress

Gradient

Divergence

Curl

Dimensional Analysis

Buckiingham Pi Theorem

Pi Groups

Original variables, repeating variables

Problem Steps for Buckingham Pi Theorem

Approaches to examining fluid flow

Pathline

Streakline

Streamline

Angular Velocity

Vorticity

curl of the vector field

Irrotational vs. Rotational Flow

Circulation

Stream Functions

Velocity Potential

Inviscid Flows

• Incompressible

• Irrotational

• Inviscid

Elementary Flows

1. Uniform

2. Source/Sink

3. Vortex

4. Doublet

Stagnation Point

Force Experience

Pressure Coefficient

D’Alembert’s Paradox

Mathematically, drag force on a cylinder is zero

Lifting Flow

Airfoil

Symmetric vs. Cambered Airfoils

Mean Camber Line

half thickness - more precisely?

Center of Pressure

Locations for resultant force

Big players in wing performance

Camber

Thickness

NACA4 Wing Naming

Angle of Attack

Zero Lift Angle of Attack

Stall

Kutta-Joukowski

Vortex Filament

Vortex Sheet

Modeling AIrfoils Using Vortex Sheets

Thin Airfoil Theory

Zooming out, airfoil can be represented as a vortex sheet on a camber line

Airfoil Stagnation Point

Kutta Condition

Airfoil wants stagnation point to be on the trailing edge

• Airfoil left in flow long enough, will always calibrate to have circulation where the second stagnation point is at the trailing edge

Vortex Shedding

Kelvin’s Circulation Theorem

Drag on an Object

• Skin-friction

• Pressure

Flow Seperation

Flow around Slender vs. Blunt Body

Material Derivative

Rate of change of a property following a fluid element (usually an intensive property - unchanging with amount/mass/size)

Reynolds Transport Theorem

Navier Stokes

Forces acting on a fluid

Body Forces

Surface Forces

Body Forces

Surface Forces

Simplifications of Navier Stokes

Turbulence

Reynolds Decomposition of Velocity

Grid Turbulence

Length Scales

Energy Cascade in Turbulence

Kolmogorow Scales

Length Scale

Time Scale

Reynold’s-Averaged Navier Stokes

Reynold Stresses

Turbulent Boundary Layers

Critical Length

Boundary Layer Thickness

Skin Friction Drag as a Function of Local Reynolds

Mach Number

Specific Heat Ration

Standard Atmosphere

Layers of the Atmosphere

Subsonic Nozzle

Supersonic Nozzle

Supersonic Expansion

Shock Waves

Normal Shock

Oblique Shock

Wave Angle

Airplane Parts

Principal Axes

Flaps on the plane

Ailerons