**Aerodynamic Theory**

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Aerodynamic Factors

- Streamlines
- Velocity Distribution
- Laminar Flow
- Turbulent Flow
- Viscosity
- Reynolds Number
- Boundary Layer
- Skin Friction Bernoulli’s Principle
- Pitot Tube
- Pressure Coefficient

Streamlines

- Curves associated with a pictorial representation of air flow
- Smoke is commonly used in wind tunnels to represent the streamlines
- Streamlines are used to study air flow

Velocity Distribution

- The nature of the fluid flow
- A measure of changes in air flow’s velocity close to the vehicle

Laminar Flow

- Fluid motion that is "well organized"
- Fluid with parallel velocity vectors
- Generally, laminar flow has the ideal aerodynamic properties

Turbulent Flow

- Fluid motion that is not "well organized"
- Fluid with parallel and other velocity vectors
- Generally, turbulent flow has undesirable properties

Viscosity

- The fluid’s resistance to motion
- Internal fluid forces at the molecular level

- Where, F= fluid viscosity force, m = coefficient of viscosity, V¥ = fluid velocity, h= separation distance, and A= contact area

- Pictorial of fluid viscosity

Example

- What is the force required to pull the upper plate at 5 m/s, if the plate area is 2 m
^{2}, and the fluid between the surfaces is water with the separation distance of 0.04 m (water’s coef. of viscosity is 1.0x10^{-3}Ns/m^{2})

Example

- Using the previous diagram and dimensions,
- How fast will the upper plate move, if the fluid is SAE 30 motor oil with the coef. of
viscosity of 4.0x10
^{-3}Ns/m^{2}and an applied force of 2 N

Reynolds Number

- Quantifies the product of speed times size
- A dimensionless number

- Where, r is fluid density, m is the viscosity, V is the velocity, and L is the length of the object
- Represents the ratio between inertial and viscous forces
- Compensates for scale differences
- Example
- A car has a length of 4 m, travelling at 30 m/s
- Air density is 1.22 Kg/m
^{3} - Air viscosity is 1.8x10
^{-5} - Re = 1.22 x 30 x 4 / (1.8x10
^{-5}) = 8.1x10^{6}

- Re can indicate the nature of the fluid flow
- Higher values indicate turbulent flow
- Lower values indicate laminar flow
- Different flows can be considered the same if they have similar Re values
- Allows scale models to be accurately tested in wind tunnels using different fluids and or velocities

Boundary Layer

- The thin layer of rapid tangential velocity change close to an object’s surface
- Generally increases in thickness (d ) with the length of the object

- Relative velocity
- Zero at the object’s surface
- V¥ at the outer edge of the boundary layer

- Example
- At 60 mph, the boundary layer is about an inch close to the rear of a vehicle
- A thicker boundary layer creates more viscous friction

- A too sudden a change in thickness (transition) can cause flow separation,
- Additional drag (skin friction)
- Loss of down force

Skin Friction

- C
_{f}, skin friction coefficient - Non-dimensional
- Indicates the level of friction between the vehicle’s skin and the air
- t = Friction resistance

Example

- What is the friction resistance (t ) of a plate moving at 30
m/s, with coef. of friction of 0.002 through air with a density of 1.22 Kg/m
^{3}?

t = C

_{f }(0.5r V^{2}) = 0.002 x 0.5 x 1.22 x 30^{2}t = 1.098 N/m

^{2}

Dynamic Pressure

- Where V¥ is the velocity, and r is the fluid density
- Boundary layer is thicker for turbulent flows
- Skin friction (C
_{f}) decreases with Re - At certain speeds, both laminar and turbulent flows are possible
- Flow separation can be delayed in turbulent flow, resulting in a preference for turbulent boundary conditions

Bernoulli’s Principle

- Pressure drop: P1 > P2 > P3
- Height of the fluid decreases with drop in pressure

- Fluid Velocity is greater at the neck, V1 > V¥
- Pressure drop, P1 > P3 > P2
- Fluid pressure drops as fluid velocity increases
- Fluid pressure is inversely proportional to fluid velocity

Bernoulli’s Equation

- where, V = velocity, p = local static pressure, and r = density, for any point on a streamline

- Usually used to compare and calculate pressure and velocity at two different points

Example

- What is the pressure difference on the surface of a vehicle’s grill (V
_{grill}=0), if the vehicle travels at 30 m/s. Air density is 1.22 Kg/m^{3}

Pitot Tube

- Bernoulli’s equation allows measuring any fluid velocity by measuring its pressure

Pressure Coefficient

- Non-dimensional
- Used to measure aerodynamic loads (lift, drag, and side forces)

- TEC452 Home
- Aero Index
- Introduction
- Aerodynamic Theory
- Wind Tunnel
- Computational Fluid Dynamics
- Vehicle Aerodynamics