Aero Class #2

8/6/2019 Aero Class #2

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ASCI 309 – Class #2

• The topics for tonight are Basic Aerodynamicsand Airspeed Measurement. We’ll start withan introduction to the dynamics of moving air,

discuss the effects of moving air on a body,and finish with how to measure the speed of moving air. First you need to be aware thatonly the relative motion of the air over the

body is important. Either the air can moveover the body or the body can move throughthe air. The effect on the body is the same.



Gas Dynamics

• The two primary equations under consideration

tonight are the Continuity Equation (based on the

conservation of mass) and Bernoulli’s Equation

(based on the conservation of energy).

• Continuity Equation: dm/dt=ρAU=con., that is,

dm/dt(kg/s)=ρ(kg/m3)•A(m2)•U(m/s)=con. or

dm/dt(slugs/s)=ρ(slugs/ft3

)•A(ft2

)•U(ft/s)=con.,where: dm/dt=mass flow rate, A=cross-sectional

flow area (like the area between two streamlines)





Gas Dynamics

• We are following the flow of air between two

streamlines or through a stream tube. By

definition, there is no flow across streamlines.

• Bernoulli’s Equation: p+ρgh+ρU2/2=con. This is

the conservation of energy/unit volume in the

flowing stream. If the flow is horizontal or gas

flow, changes in the term ρgh may beneglected, leading to the simpler form:

p + ρU2/2 = con.



Pressure Conversions

• Here are some relations among the commonly

used units for pressure:

atmospheric pressure at sea level

1 atm = 1.013x105 n/m2 = 101.3 kPa =

1013 mbar = 2116 lbs/ft2 = 14.7 lbs/in2 =

29.92 in Hg = 760 mm Hg = 406 in water





Gas Dynamics

• Consider the converging nozzle shown below.

The flow must accelerate from 1 to 2 since the

flow area decreases and the mass flow rate is

constant. (ρAU)2=(ρAU)1. Further, the static

pressure decreases, (p+ρU2/2)2=(p+ρU2/2)1.

1

2





Aerodynamic Forces

• The aerodynamic forces on a body in a moving

fluid can be resolved into components in the

stream direction and at right angles to the

stream direction. On an airplane wing they are

called respectively, the drag, D, and the lift, L.

The drag is due to both a form drag, ex. a flat

plate turned into the wind, and a friction dragas the body shears through the viscous air.



Aerodynamic Forces

• The lift is created by the airspeed being faster

over the top of the wing and slower over the

bottom of the wing. This is the result of either

the shape of the wing and/or inclining the

wing upward at an angle with respect to the

wind (called the angle of attack, α). Recall

Bernoulli’s eqn., as the velocity increases thestatic pressure decreases. The pressure

difference times the wing area equals the lift.





Airspeed Measurement

• I have used three methods to measure

airspeed:

– Pitot-static tubes to measure 1D steady airflow &

a Cobra probe to measure 2D steady airflow

– Hot-wire anemometers to measure 1D, 2D, & 3D

turbulent airflow

– Laser anemometers to measure 1D, 2D, & 3Dturbulent airflow





Pitot-Static Probe

• Airspeed measurement by a Pitot-static probe

is based on ps + ρU2/2 = pt. U=√2(pt-ps)/ρ

Recall ρ = ps/RT, so to accurately measure the

velocity, U, we must also accurately measurethe static pressure and temperature. The

static pressure can be measured by the

judicious location of a static pressure tap. Thestatic temperature measurement is a bit more

difficult as we shall soon see.





Cobra Probe



Hot Wire Anemometer Probe



3D Hot Wire Probe

• Dantek (formerly DISA) built me the world’s

first 3-wire, hot-wire anemometer probe and

multi-channel, analog signal, data reduction

network. I used this system to gather data in a3D, turbulent boundary layer and published

the results in a PhD thesis and at an ASME

Fluids Engineering Conference.



Laser Anemometry



Laser Anemometry (LDA)

• I made LDA measurements:

– in a cold-flow, sudden-expansion, combustor

model and downstream of an operating

combustor (1D).

– in the pre-chamber of an automotive diesel

engine (1D).

– of the flow from fuel nozzle models (2D & 3D). – in a turbine vane cascade (3D).







Airflow Classifications

• The viscosity of air can be neglected except in

the region near a solid surface called the

boundary layer. Here layers of air at different

velocities shear across each other like thepages of a book. This results in equations of

motion of the air which contain more

variables than there are equations. Eitherassumptions must be made relating two

variables or experiments must be made.



Viscosity

• Imagine a dinner plate covered with molasses

– now tip the plate so that the molasses flows

to one edge. The top layer flows downhill

while the bottom layer remains fixed to theplate – in between the molasses is being

sheared. This is what happens to the air in the

boundary layer. The shear stress τ is given byτ=μ dU/dy. μ = viscosity, dU/dy = velocity

gradient.



Viscosity

• μ(s.l. std.) = 1.789x10-5 kg/m-s

= 3.737x10-7 slug/ft-s

• μ = μ(T) = [6x10-8 T(K) + 4x10-7] kg/m-s

= [4.812x10-10 T(°R) + 1.264x10-7] slug/ft-s

• The variation with temperature above is an

approximate fit to graphs from several

textbooks.



Airflow Classifications

• In practice the flow may be initially laminar

but quickly goes through a transition to

turbulent flow as evidenced by slide 11 where

the flow over the top of the wing is seen to beturbulent just after it begins to expand.

Several conditions promote a transition to

turbulent flow, e.g. surface roughness (thedimples on a golf ball) or an adverse pressure

gradient (expanding flow in a diffuser).





Compressible Flow

• To analyze compressible flow we need to

review some concepts from Thermodynamics.

The usual method to introduce Thermo is to

examine the processes that take place in acylinder-piston arrangement (next slide).

Trapped in the cylinder is an amount of gas,

say n moles. Initially the gas is at some p, V, T.Boyle’s Law states that if T is a constant then

the product pV=con. or p2V2=p1V1.





Compressible Flow

• Plotting this relation on a p-V diagram (next

slide) you see that moving up the curve

represents a compression and down the

curve, an expansion. The area under thecurve has a significant interpretation. It is the

work input during a compression and the

work output during an expansion.





Compressible Flow

• We next need to consider the First Law of

Thermodynamics which is the Conservation of

Energy including heat transfer and thermal

energy. ΔU = Q – Wk. ΔU: change inmolecular energy, a function of T only. Q: heat

flow across a boundary. Wk: work done by a

moving boundary. There are four primaryprocesses that can be illustrated on a p-V

diagram (next slide).





Compressible Flow

• p=con.(isobaric), V=con.(isochroic),

T=con.(isothermal), Q=0(adiabatic). These four

processes, the perfect gas law, and the First

Law of Thermo form the basis for internalcombustion engines which we will discuss

later. The processes can be visualized as

follows: p=con., a fixed weight is placed atopthe piston; V=con., the cylinder is a fixed wall

container like a can; T=con., the cylinder is





Compressible Flow

• Compressible flow:

T0/T1 = 1 + [(γ-1)/2]M12

• Isentropic flow:

p0/p1 = {1+[(γ-1)/2]M12}γ/(γ-1)

ρ0/ρ1 = {1+[(γ-1)/2]M12}1/(γ-1)

Ucal2

= [2aSL2

/(γ-1)] ({[(p0-p1)/pSL]+1}(γ-1)/γ

-1)aSL ,pSL standard sea level values

Utrue : use a1 , p1 (local values)



Compressible Flow

• You can use the preceding equations or

perhaps the simplest move would be to use

the chart on the next slide to provide a

compressibility correction to convert theCalibrated Air Speed (CAS) to Equivalent Air

Speed (EAS). The True Air Speed (TAS) is

obtained by: TAS = EAS/√σ (Fig. 1.1, Hurt) oruse (Fig. 1.6, Hurt). The conversions are:

1 ft =0.3048m and 1 knot = 0.5144 m/s.





Problems 3 & 4

• The airspeed indicator of an airplane reads

355 knots. There are no instrument or

position errors. If the airplane is flying at a

pressure altitude of 25,000 ft, find theequivalent airspeed, EAS. (Hurt, Fig 1.6, p.12)

• Find the true airspeed (TAS) of the airplane in

the preceding problem if the outside airtemperature is -40 C. (Hurt, Fig 1.6, p.13)

A k l d t



Acknowledgements

• Slide 3 – Anderson, Introduction to Flight

• Slide 11 – Anderson, Ibid

• Slide 13 – Anderson, Ibid

• Slide 16 – Dr. Z, PhD thesis

• Slide 17 – DANTEK, poster

• Slide 19 – DANTEK , poster

• Slide 29 – Serway, Physics for Sci. & Engineers

• Slide 31 – Serway, Ibid

• Slide 33 – Young & Freedman, Univ. Physics

l d f l

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Aero Class #2