Lecture # 16: Review for Final Exam

Transcription

1 AerE 344 Lecture Notes Lecture # 6: Review for Final Exam Hui Hu Department of Aerospace Engineering, Iowa State University Ames, Iowa 5, U.S.A

2 AerE343L: Dimensional Analysis and Similitude Commonly used nondimensional parameters: Euler number, Eu VL Reynolds number, Re Froude Number, Fr Strohal Number, Str p V V M ach Number, M c Weber Number, We V lg pressureforce inertial force inertial force viscous force inertial force gravity force inertial force compressiblity force l centrifugal force V inertial force V l inertial force surface tension force Similitude: Geometric similarity: the model have the same shape as the prototype. Kinematic similarity: condition where the velocity ratio is a constant between all corresponding points in the flow field. Dynamic similarity: Forces which act on corresponding masses in the model flow and prototype flow are in the same ratio through out the entire flow

3 Measurement Uncertainties Error is the difference between the experimentally-determined value and its true value; therefore, as error decreases, accuracy is said to increase. A error A measured A true Total error, U, can be considered to be composed of two components: a random (precision) component, a systematic (bias) component, We usually don t know these exactly, so we estimate them with P and B, respectively. E A m A true E relative A A error true U B P Repeatability Reproducibility Precision Error Both Bias and Precision Errors Bias error True value X= precision error measured value X= X

4 Measurement Uncertainties p p p V Bernoulli V p p static total static total ) ( ),( R R R P B U Uncertainty in velocity V: J i i i R J i i i R P X R P B X R B ; M j i i j B B For a large number of samples (N>) i i S P N k k i i N k i k i i X N X X X N S ;

5 Pressure Measurement Techniques Deadweight gauges: Elastic-element gauges: Electrical Pressure transducers: Wall Pressure measurements Remote connection Cavity mounting Flush mounting Pressure Measurements inside Flow Field:

6 Velocity measurement techniques Pitot Static Probe Advantage: Simple cheap Disadvantage: averaged velocity only Single point measurements Low measurement accuracy p V p stat ( p V p stat,( Bernoulli ) )

7 Velocity measurement techniques Hotwire Probe Advantage: High accuracy High dynamic response V Flow Field The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor Disadvantage: Single point measurements Fragile, easy to broke Much more expansive compared with pitot-static probe. Current flow through wire dt mc dt w i R w q ( V, T Constant-current anemometry Constant-temperature anemometry w )

8 AerE3L: The nature of light Light as electromagnetic waves. Light as photons. Color of light Index of reflection n c / v c 3x 8 m/ s

9 Index of refraction: Shadowgraph and Schlieren technique n c / v Depend on variation of index of refraction in a transparent medium and the resulting effect on a light beam passing through the test section Shadowgraph systems: are used to indicate the variation of the second derivatives (normal to the light beam) of the index of refraction. shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew Davidhazy ) Schlieren Systems: are used to indicate the variation of the first derivative of the index of refraction Schlieren images of the muzzle blast and supersonic bullet from firing a.3-6 caliber high-powered rifle (by Gary S. Settles )

10 Visualization of a Schockwaves using Schlieren technique After turning on the Supersonic jet Before turning on the Supersonic jet

11 Schlieren vs. Shadowgraph Shadowgraph Displays a mere shadow Shows light ray displacement Contrast level responds to No knife edge used n y Schlieren Displays a focused image Shows ray refraction angle, Contrast level responds to n y Knife edge used for cutoff

12 Y (mm) Particle Image Velocimetry (PIV) Advantage: Whole flow field measurements Non-intrusive measurements Disadvantage: Low temporal resolution Very expansive compared with hotwire anemometers and pitotstatic probes. To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows. To measure the displacements (L) of the tracer particles between known time interval (t). The local velocity of fluid flow is calculated by U= L/t. t=t L L U t t= t +t 8 spanwise vorticity (/s) m/s 6 4 GA(W)- airfoil - -4 shadow region -6 A. t=t B. t=t + s Classic -D PIV measurement X (mm) C. Derived Velocity field

13 PIV System Setup Particle tracers: Illumination system: Camera: Synchronizer: Host computer: to track the fluid movement. to illuminate the flow field in the interest region. to capture the images of the particle tracers. the control the timing of the laser illumination and camera acquisition. to store the particle images and conduct image processing. seed flow with tracer particles Illumination system (Laser and optics) camera Synchronizer Host computer

14 Advanced PIV techniques Stereoscopic PIV technique Dual-plane stereoscopic PIV technique 3-D PTV technique Holograph PIV techniques Defocus PIV technique Z X Laser Sheet Lobed nozzle S-polarized laser beam Mirror # Laser sheet with S-polarization direction Mirror # cylinder lens Polarizer cube P-polarized laser beam Laser sheet with P-polarization direction Measurement region 8mm by 8mm Half wave (/) plate Polarizing beam splitter cubes Double-pulsed Nd:YAG Laser set A Double-pulsed Nd:YAG Laser set B Mirror #4 high-resolution CCD camera 4 65mm Host computer Synchronizer Mirror # mm high-resolution CCD camera 3 Camera Camera Stereo PIV technique high-resolution CCD camera high-resolution CCD camera

15 Laminar Flows and Turbulent Flows ' ' ; ' w w w v v v u u u... ),,, ( T t t dt t z y x u T u ' ' ; ' w v u ') ( ') ( ; ') ( ') ( w v dt u T u T t t o

16 Boundary Layer Flow at y, u. 99U Displacement thickness: y Momentum thickness:

17 Review of Quasi-D Nozzle Flow da A ( M ) du u Throat M= u increasing M< M> Throat M= u decreasing M> M<

18 P increasing P increasing st, nd and 3 rd critic conditions st critic condition st critic condition 3st critic condition

19 Lab #: Flow visualization by using smoke wind tunnel Path line Streak lines Streamline Streamlines (experiment)

20 Lab#: Wind Tunnel Calibration A E Settling chamber Contraction section V Test section 4 p A p E p C * q T C * V q =.5*V Linear curve fitting Experimental data P = P A -P E (Pa)

21 Lab #3: Pressure Sensor Calibration and Uncertainty Analysis Task #: Pressure Sensor Calibration experiment A pressure sensor Setra pressure transducer with a range of +/- 5 inho It has two pressure ports: one for total pressure and one for static (or reference) pressure. A computer data acquisition system to measure the output voltage from the manometer. A manometer of known accuracy Mensor Digital Pressure Gage, Model, Range of +/- inho A plenum and a hand pump to pressurize it. Tubing to connect pressure sensors and plenum Lab output: Calibration curve Repeatability of your results Uncertainty of your measurements tubing Setra pressure transducer (to be calibrated) Mensor Digital Pressure Gage A computer A plenum hand pump

22 cp --> Cp Lab#4 Measurements of Pressure Distributions around a Circular Cylinder Y P Incoming flow R Cp distribution around a cylinder P P V C p V V ( V sin ) 4sin V X EFD CFD AFD theta (rad ) --> Angle, Deg.

23 Y (inches) Lab#5: Airfoil Pressure Distribution Measurements NACA airfoil with 3 pressure tabs X (inches).4 Lift Coefficient, C l L V C l c C L = Experimental data Drag Coefficient, C d D V C d c Experimental data Angle of Attack (degrees) Angle of Attack (degrees)

24 y x 8 mm Pressure rake with 4 total pressure probes (the distance between the probes d=mm) Lab 6: Airfoil Wake Measurements and Hotwire Anemometer Calibration y x )] ) ( ( ) ( [ )] ) ( ( ) ( [ dy U y U U y U C C C U da U y U U y U U C U D C D D

25 y Lab 7: Hot wire measurements in the wake of an airfoil Pressure rake with 4 total pressure probes (the distance between the probes d=mm) x 8 mm Lab#3 Test conditions: Velocity: V=5 m/s Angle of attack: AOA=, and deg. Date sampling rate: f=hz Number of samples:, (s in time) No. of points: ~5 points Gap between points: ~. inches Lab#4 Hotwire probe

26 Lab#8: Measurements of Boundary Layer over a Flat Plate To conduct velocity profile measurements at downstream locations. Displacement thickness: To determine boundary layer thickness and drag coefficient based on the velocity measurement results. Momentum thickness: Drag coefficient: C d L Pitot rake Y X

27 Lab#9: Visualization of Shockwaves using Schlieren technique Underexpanded flow Flow close to 3 rd critical Overexpanded flow nd critical shock is at nozzle exit Tank with compressed air Test section st critical shock is almost at the nozzle throat.

28 Lab#: Set Up a Schlieren and/or Shadowgraph System to Visualize a Thermal Plume Point Source Candle plume

29 Lab#: Pressure Measurements in a de Laval Nozzle Tank with compressed air Test section Tap No. Distance downstream of throat (inches) Area (Sq. inches)

30 Y /C * Lift Coefficient, C l Y /C * Lab#: PIV measurements of the Unsteady Vortex Structures in the Wake of an Airfoil L V C l c C L = Experimental data Airfoil stall m/s GA(W)- airfoil shadow region Before stall -6 vort: Angle of Attack (degrees) X/C * Drag Coefficient, C d D V C d c Experimental data - 5 m/s GA(W)- airfoil shadow region After stall.5 Airfoil stall -4 vort: X/C * 8 Angle of Attack (degrees)

31 Y pixel Y pixel Lab#3: Stereoscopic PIV technique and Applications X Laser Sheet Z Camera Camera Stereo PIV technique 8 8 Re C 5,; 5. deg. X/C = X pixel Displacement vectors in left camera 5 5 X pixel Displacement vectors in right camera