2.1. Aerodynamic forces on aerodynamic and bluff bodies

Which are the similarities between bluff and aerodynamic bodies?

they both:

• need a BL

• move at high Re

• have characteristic geometry

• need to be correctly oriented

what does the drag coefficent describe? (car context)

the efficiency of a car

Cd value for efficient cars? (plateau)

0.26

Which are the differences between bluff and aerodynamic bodies?

• aerodynamic bodies

  • BL is thin and attached

  • b«L

  • pressure drag is only 10% of total drag → mostly due to friction

• bluff bodies

  • BL is separated

  • b~L

  • pressure drag is 90% of total drag

if in 2D a bluff body is infinitely long, …

no turbulences, as turbulence is a 3D phenomenon

fixed vs. free separation point

• fixed separation point

  • geometry: triangle

  • imposed with a corner

• free separation point

  • geometry: circle

  • empirically determined by analyzing the pressure gradient

explain the iterative model for bluff body

• consider irrotational flow everywhere except on the surface

• problem: wake not negligible in bluff body, and it’s a rotational area

• so need to find a way to model the wake. Have two issues:

  • uknown separation point

  • potential flow not valid in wake

• assume known separation point → can introduce the Helmholtz model (help us understand what happens in the wake)

  • purely empirical model

  • say that the pressure in the wake (pressure of the base, which is the surface on which the wake insists) is the same as the pressure calculated at the separation point → P_wake=P_s

• now can apply the iterative method in our body made by two contributions: real body + wake

• so, procedure:

  • can apply the panel method to the entire body (body+wake) and estimate the sources for each panel → estimate the velocity and c_P

  • can take the c_P value at P_s and estimate drag using the Helmoltz method

• uses

  • usually the industries use CFD methods, summing the c_P for all elements

  • also used a scale for practical measurements which evaluates the forces acting on different directions

explain the Helmholtz model

• purely empirical model

• say that the pressure in the wake (pressure of the base, which is the surface on which the wake insists) is the same as the pressure calculated at the separation point → P_wake=P_s

procedure for iterative model for bluff body

• can apply the panel method to the entire body (body+wake) and estimate the sources for each panel → estimate the velocity and c_P

• can take the c_P value at P_s and estimate drag using the Helmoltz method

exercise in aerodynamic forces in bluff body

exercises

If the separation happens earlier (ε is bigger) the wake will be larger. The maximum value of c_P is for ε=90 deg. The larger the wake, the more drag we create: the dimension of the wake is a true indicator of the generated drag

the two drag types

• pressure

• friction

two methods for friction drag

• Polhausen method

• simplification of body → transform disk into flat plate → flat plate analogy

explain Polhausen method

• if have pressure distribution on x, by applying Polhausen we can find c_f(x)

• then, we can find total friction → f_total formula → c_f formula

• if we want to simplify this we use flat plate analogy

explain flat plate analogy

• can transform our body into a flat plane and evaluate the friction coefficient of it by using Blasius (assuming a laminar B.L.)

• having a low tau is not always useful because the BL is more fragile: tends to separate more easily → bigger wake → bigger pressure drag

half cylinder exercise (section 2.1)

exercise

with a turbulent BL we have a higher friction (both because tau is higher and because BL is more

what is tau?

shear stress, which is related to skin friction

two flat plates exercise (section 2.1)

exercise