8. Jet and Film

Mingyu KangTeam Korea

LevitationProblem #5

1

PhenomenonInvestigate the effect Oscillation

Produce the maximum angle of tiltForce AnalysisBernoulliCoanday, r axis (x, y or r, h)Bernoulli Coanda Magnus scale ( )3Flow ChartMomentum flow conservation

Gaussian curve distributionDrag force

GravityBernoulli effect

Coanda effect(Boundary layer thickness)

Force equilibriumAirstreamVelocity ProfileOptimization(Maximum angle of tilt)Pitot tube experiment

Airstream velocity

Mass of ball

Free Airstream Velocity ProfileMomentum flow conservation of free jetVelocity at the CenterAssume that the velocity is even at the narrow area of the center.7

Experiment: Velocity at the CenterPitot tubeanemoemeterResultResultVelocity Profile: Gaussian CurveAssume Gaussian curve profile:Momentum conservation!? K fitting!( )R,y11

Experiment: Velocity ProfileResult

Height = 10cm, U = 24m/s

c 13ErrorAirstream velocity at the opening is weaker at the edge!Velocity at the Opening slide11 15

Experiment

Experimental Setting

?17JAVA Image Processing

Controlling the Mass of the Ball

Clay

Drag Force

33 24Theory: y-Equilibrium PositionCause of ErrorGaussian curve assumptionCompression effectCompression effect c !

26Compression of the AirstreamExperiment Setting: Compression of the Airstream

Force sensorExperiment Result: Compression of the AirstreamCompression!1cm 2cm x log scale? Or 0~0.2 29

Bernoulli Effect : curl of velocity = 0TURBULENCE ? ..31Bernoulli EffectCoanda EffectViscous forceNo-slip ConditionP is constant in x direction 34Coanda EffectCoanda EffectBernoulli effect is the major one!

7m/s40Motion of the Ball

TheoryExperiment

OptimizationTheory: OptimizationAirstream velocity optimizationReproducible ?44Mass of the ball Optimization

Experiment: OptimizationMax(FP/FD) ?! 46Experiment: OptimizationConclusionVelocity ProfileGaussian Curve& Momentum flow ConservationOptimization, turbulence 48

Thank You!

Spin of the ball

Turbulence and Bernoulli EffectThe streamline form of Bernoulli's equation tells us that energy density is conserved along a streamline. That is, the total energy per unit volume is the same for each point on the streamline. If the curl of the velocity field is zero, then we know that the energy per unit volume is the same for all streamlines.

Energy conservation : conservative force. Work irrelevant on integration pathVelocity curl Is not zero -> Non-conservative force exists

51But in my modelBernoulli equation appliedin a SINGLE streamlineAlthough cause of error,still VALID in turbulent situations!Ignoring gravity term in Bernoulli equation8.5m/s at 8cm heightReynolds numberF=-kv : Re < 154Conservative Drag ForceUnder assumptions thatVelocity of the ball can be ignored compared to velocity of the airstream2. Drag force is a decreasing function of height

We can apply drag force fieldjust like gravitational field

Starting point of the balldoes not matter!Equilibrium position / stable conditionwould not significantly matterHow measure maximum angle of tilt?Ten times of trialWhen stably levitated for more than ten seconds, PASS!

Drag force change due to motion of the ballNEGLIGIBLE!Gaussian Curve AssumptionAssume Gaussian curve profile:Experimental proof: Coanda < Bernoulli

Liquid NitrogenOuter layer:No interaction withthe ball surfaceJAVA codepublic void obtainFilteredImage(){for (int w=1; w20 && red[w][h]-green[w][h]>20){copyImg.setRGB(w,h,RED.getRGB());}

else {copyImg.setRGB(w,h,WHITE.getRGB())} } }JAVA codepublic double[] center(){int xsum, ysum, count = 0;;;double[] c = new double[2];for (int w=1; w