Leading Edge Textbook Notes v2a2S#` cjk2iq2d4x5yqh1zsw
Chapter 1: General Aerodynamic Concepts
-High Reynold numbers = speeds, fluids and body sizes faster than 30 mph
-Auto industry uses A as frontal area. Aerospace uses top view for A
CdA is drag area
Drag Force equation is 1/2pCdA(VHeadwind+Vcar)^2
Cd changes with speed, as V increases, Cd drops
Drag becomes main force when going 30+ mph
Total aero drag = pressure drag + viscous friction + induced drag + interference drag
Pressure drag:
Pressure drag is dominant in passenger cars
Pressure drag is when flow separates from the trailing edge
When flow separates, low pressure area is left behind car which sucks the cars back
Pressure drag depends on frontal area
Viscous friction:
Skin friction: viscous shearing of fluid tangential to body
If flow is attached, skin friction will be dominant, same friction as running knife through honey
Boundary layer drag:
-Boundary layer starts at nose at stagnation pressure
-velocity at stagnation point is zero and max pressure
-as flow goes uphill, the flow accelerates and pressure decreases
-when flow goes back down car, pressure approaches to stagnation pressure
-boundary layer becomes thicker along airfoil, since it becomes thicker it can never reach the original stagnation pressure
-the pressure difference causes the car to be sucked back
-failure of pressure recovery can be graphed with cp plot
-if no boundary layers, the tail would return to stagnation value of 2
-proportional to wetted area
Induced drag:
-proportional to lift/downforce
-induced drag is lift/downforce
-KE of vortices causes work done by vehicle
-Lift can be used to reduce drag if airfoil is positioned vertically relative to ground - sailing
Interference drag:
-everything else, grit of cg, stickers, holes
-boundary layer and interference drag is main source of drag for solar csrs
CdA:
-wetted area is total surface area
-cd is a measure of how well the designer manage state of boundary layer
-use wetted area for solar cars
Solar viscosity ratio = solar array area / cdA
Chapter 2: Basic fluid mechanics
There is zero velocity at the surface - no slip
Re = pVl/mu = Vl/v
v is kinematic viscosity
Vehicles use Rex and ReL
Rex characteristic length is distance x from leading edge
ReL is total length
ReD is for ducts and sedimented of duct
Reynolds number predicts turbulence
Boundary layers:
Boundary layers have a different speed than free steam velocity
No slip is the reason dust exists
In turbulent boundary layers , the velocity gradient of the layers is steeper (higher shear rate) which causes higher skin drag
Turbulent air mixed with free stream air
Between laminar and turbulent region is transition region
-reason why boundary layer thickens is the transition from laminar to turbulent region
Boundary layer thickness of laminar region is
5x/sqrt(Rex) where x is distance from leading edge
Turbulent thickness is 0.375x/(Rex)^2
Displacement thickness
Coefficients are 1.72 and 0.046
-variables for boundary layers can be determined experimentally
Refer to page 34 for boundary layers growth
A negative pressure gradient helps stabilize the boundary layer
Want to achieve a grain roughness of 0.1mm
-shining a light tangentially on a dark surface can detect high and low spots
-how mit sands is they wet sand up to 600 grit and then wax the car. What’s recommended after is using #320 carborundum paper and wax again
Make sure no edges of stickers in nose or tail
Try and get all the stickers edges by back of car
Circular leading edge causes crossbow, and disrupts laminar layer and could cause transition sooner
Make livery white so car is cool - boundary layer
Avoid adverse pressure gradients when designing your body
Boundary layer has a chance of rolling up which abrupt junction in canopy
When doing tuft testing, tuft flutter means there is turbulence
You want turbulent flow around array so array cools better
Riblets reduce skin drag and practical on bellypan
Riblets thicken laminar sublayer and help it make a layer again
Riblet tape exists but expensive
Possible to make a riblet array - grooved array lamination
Chapter 3: Aerodynamic Forces on Bodies
-Methods of reducing skin friction drag include extending laminar flow region, reducing air speeds, reducing wetter area
-Solving for drag of flat plate:
Solve for Re of the fluid, velocity, and plate length
Impose a transition-location ratio and look up Cf,wet
To find drag area, find Cf,wet by area
-As the wetted area is increased by 10%, the CdA increases by a similar amount
-A 10% change of xt/L results in a drag area change of 8%
-for a body with no flow separation, skin friction accounts for 90% of total drag
-largest drag reduction caused by extending laminar flow - 10% laminar flow extension causes 7.4% reduction of drag
-10% reduction in body length reduces drag by 7.1%
-10% reduction in thickness reduced drag by 3%
-making a side profile that is aerodynamic is inportant for drag
-increasing xt/L means extending laminar flow region. More effective than smaller frontal area
-nose contours are inportant, in next next gen, make separate nose
-a square lateral edge can raise drag in crosswind
-nose wrap of 20 degrees is recommended to help moderate drag in crosswind
-for vehicle bodies with aspect ratios (width/length)) of about 0.3-0.5, pressure distribution is highly 3d
-cp plots are inportant to visualize how pressure is distributed across the chord of the car
-need cp of top of car and bottom of car to visualize both flows
-eliminate lift
-most airplanes have cambered airfoils because camber produces lift at 0 AOA
-a symmetric airfoil near the ground produces downforce
-when this airfoil is cambered such that its belly is flattened, the induced drag can be eliminated
-absence of trailing vortices shed from rear corners of car is confirmation that no lift is generated
-presence of vortices can be detected by placing tufts on trailing edge corners
-sometimes induced drag is cancelled out by vortices from canopy and trailing edge vortices - called quadrupole vortices and hard to predict
-location of vortices can be detected by noticing tuft spins vigorously
-for solar cars, e (span efficiency factor) is 0.8 to 2 and aspect rate of wing is 0.5
-Solar cars are low AR wings cruising near the ground with wheels
-may be wise for body to create downforce at 0 yaw to prepare for lift from crosswind
-if you can have the tail of the car point down, it will help with stability
-with a tail pointing upwards, you could feel car being sucked down
-bellypan should be parallel to ground to generate desired cp distribution
-important to curve front portion of bellypan to increase laminar flow
-trailing edge should be same height off ground as stagnation point
-at very low clearances, the higher the camber, the lower the drag. Opposite is true as ground clearance increases
-make members read 3.3.3
-for very lowcbellypan heights, the drag is high.
-at some height; the drag curve becomes relatively flat. Use that as bellypan height
-for a solar car with a width of about 2 m and length of 5 m, the bellypan height should be 6 to 14 inches
-yarn tufts should be attached to rear corners of the car to look for shed vorticity
-the nose should wrap around the front corners smoothly past about 20 degrees of rotation from the nose
-you can nose up the vehicle to give bellypan flow a better pressure gradient
-do not create lift since it is too complex and solar car tires are too thin
-I’d vortex shedding off the rear corners of the body cannot be avoided, team can use winglets to roll the vortex more efficiently
-we want cp to be behind cg
-with a cp behind cg, the vehicle steers into the wind creating a clockwise rotation
-make members read chapter 3.4
-if cp is ahead of cg, vehicle steers away from wind which makes you lose control
-positing co behind cg is easy with a central canopy
-weight should be biased on the front wheels
-gm subtracted added six small rudders to move cp rearward to help crosswind stability
-advantages to place cp as low as possible to minimize roll moment
-wheel covers can be designed as sails instead of placing fin
-advantage with top mounted sails is they can be removed depending on whether
-picking one y tells tendency of vehicle to pitch nose up or nose down
-a vehicle that pitches nose down is prefersble
-find pitching moment of front and rear axles?
-in some wind tunnels, vehicle can be mounted in a turntable for operator to use a yaw sweep
-fused bodies reduce wetted areas
-to reduce crosswind lift, design belly to be flat so pressure distribution becomes more robust to crosswind
reduce rear end lift in crosswinds, use a profile with poor lift characteristics such as a spine
-sail can be wheel fairing or vertical airfoil on top of car
-airfoil travels straight into a crosswind
-theta dw is the downwash angle which reduces the angle of attack of the wind
-if you have a permanent sale and a large fin, it is not advantageous as it increases wetted area
-sail of pumpkin seed was a 64-015 shape and were steered
-for teaching sail, start with airfoil and how airplanes fly, with lift
-then show how a component of lift creates thrust from the angle of attack
-canopy, wheel covers, and fin can create thrust
-have to look at the angle specifically for a fin to make sure that the thrust gained is more than the side force created
-most thrust force than drag force created
-isn’t there some drag force created from the fin. So what you are looking for is thrust > side force + drag force at a certain angle for it to be beneficial?
Chapter 4: Vehicle-Level Aerodynamic Details
-fusing canopy reduces junction drag
-drag penalty reduction if you fillet radius of wheel fairing to main body
-is fusing wheel cover with main body possible?
-cd is negative when sailing
-could make a half fairing attached to the bottom shell instead of a full wheel clver
-easy service and easy to make
-one way to reduce drag is to align one side of the wheel fairing to the lateral edge of the car
-an appendage should be mounted such that it intersects the main body perpendicularly
-the junction with the smallest radius was the most favorable
-the sharper fillet reduces separation but was deemed unsuitable for a high AOA
-optimum junction radius between canopy and body
-if one side of fairing is aligned with body, better (dynamic wheel fairings)
-as wheel turns, cd increases in wheel cover and it scales linearly
-make junction angle with main body perpendicular
-flat belly pan and if you mount wheel cover there helps drag
-drag penalty reduction to fillet wheel cover
-optimum fillet radius is 4-6% of the airfoil chord
-thickness/chord ratio for fairing should be less than 8%
-vortex around wheel fairing is horseshoe vortex
-fillet does not help reduce vortex and makes it grow more
-linear fillet at 63 degrees is better for drag reduction, not parabolic
-make wheel fairing sharp helps for drag
-same idea with sharp nose
-if you extend chord fillet to length of the chord, flow doesn’t separate
-rim cover should be slightly convex
-after convex rim cover, flat rim cover and then tri-spoke wheel
-speed has no effect on cd
-extra drag of spiked contributed to higher rolling resistance
-wheel cutout can be hourglass shape to minimize size
-you can include a small ramp before the wheel curious (triangle extrusion) so wind flows over the cutout
-Air cares more about the cutouts than the wheel fairings
-wheels had half fairings
-can have a seal that steers with the wheel
-have a plate on the floor of the bottom shell that steers with the wheels
-hourglass shake cutout reducers drag by 17%
-sealing wheel wells is inportsnt for road debris
-wheel fairing should be full, swept, and sealed
-having a full wheel fairing prevents drag by 300%
-having a 3 wheeled car is best for drag that is designed like next gen
-half fairings are much easier to service
-strut type suspensingbthat opens wheel fairing
-wheel fairing houses were made with Kevlar
-if front junction is too sharp, horseshoe vortice form
-contour the solar array upward to minimize the base area so no rear separation
-can add vortex generators in canopy (small find) that increases performance in yaw
-best to have vortex generators in back of canopy
-major design variable is canopy length/height ratio
-l/h=4.5 )-/ no separation from other team
-book says l/h of 6 is most optimum
-cp of car should not exceed +6 at junction of canopy
-junction radius should be about 20% of bubble chord
-look at cp plots for next gen design
-bury stickers with clear coat
-you can have turn signals embedded into canopy instead of Jose so less drag in nose
-trailing edge truncation has an exponential drag increase
-having a knife edge is important
-light assembly can be inset several centimeters from the absolute edge
-JU solar car minimizes gaps and seams by not having a traditional canopy
-groove of array has 3.% increase in drag
-can tape seams between top shell and bottom shell
-vinyl wrapping is the way to go
-can have a whole in high pressure or low pressure zone of canopy
-you can have a duct for battery, motor, and driver
-they were all naca in the bottom of the car
-protruding or nose duct is better than naca duct since naca duct has to be sized for airflow
-small vent hole at high pressure region near base of canopy for driver
-velocity into the system should be minimized but exit velocity is maximized
-inlet should be at high pressure region and outlet should be at low pressure region
-exhaust is parallel to free stream flow
-the area for the duct inlet should be big and the area for the duct outlet should be as small as possible
Chapter 5: Aerodynamic Drag of the Entire Vehicle
-you could construct a ¼ scale model of the car
-you should care about surface finish and reynolds number to check laminar flow in scale model
-CFD is used to check the proper pressure distribution (Cp plot)
-can also use CFD to check the turbulence transition region
-a good co plot should progressively get more negative since it’s good for laminar flow
-cp plot helps show separation such as canopy
-cp for lifting airfoil is -2
-area between top and bottom cp plots shows whether lift occurs
-cp spikes in excess of .7 show a horseshoe vortices
-when doing wind tunnel testing, should make sure liquid is not too rich so fluid flows
-mit used carbon and kerosene
-puddle forms at separation point in flow viz
-surface must be dark for transition region to show
-tuft testing in drive days
-you can adjust the angle of the attack of body for testing by changing suspension
-cannot mount wheel fairings crooked
-wheel fairings move COP rearward
-can have rear tail fins to help push COP
-you can shift to smaller fairings in the front to push COP
-in steady flow, tufts should be stuck to surface
-it is recommended for Both sides of car to be tufted
-most important place to attach tufts is trailing edge and corners and lateral edges
-tufts af trailing edge should be 6 inches long
-with no lift, tufts should be free of oscillation and flow parallel to car
-tufts about bubble body junction should be 2 cm long
-if flow separates in back of bubble, tufts should reverse direction or flutter
-can put tufts on fins to assess crosswind direction and where the air is going with the airfoils
-after tuft testing, you can do flow viz
-you apply solution with paint roller and sponge mop on body of car, and then run the car for a minute
-shape of the transition front may be quite erratic
-wake take data acq can be used to assess transient transition affects
-should have a heat shrink film for kerosene testing
-the film could be Mylar
-smooth streaks indicate laminar flow and if flow oscillates, it is turbulent
-cover array if doing flow viz
-velocity of vehicle relative to airstream can be measured with a Potomac tube
-if significant crosswinds, a Kiel tube can also be used
-drag measurements can be conducted with a wake rake
-a rake is an array of pressure sensors that can be strapped to trailing edge
-only way to directly assess drag impact of wheel fairings
Chapter 6: Real World Examples
-slightly negative camber of main body means no lift with no crosswind and downforce with crosswind
-crosswind lift effects should be minimized by having a spined rear section
-seal front wheel wells
-use canopy region for stickers
-if you increase the nose so AOA is 1.8, helps drag
-other improves are knife-edge trailing edge and tighter sealing
-you can cancel downforce by curving the array forwards toward the tail
-improve ventilation by eliminating naca ducts
-Design goals: avoid flow separation while minimizing wetter area. Body should be as narrow as possible
-to generate zero lift, body should have a camber of about 3-6% at longitudinal cebterline