Lecture #06 Hotwire anemometry: Fundamentals and instrumentation

Transcription

1 AerE 344 Lecture otes Lecture #06 Hotwre anemometry: Fundamentals and nstrumentaton Dr. Hu Hu Department of Aerospace Engneerng Iowa State Unversty Ames, Iowa 500, U.S.A

2 Thermal anemometers: Techncal Fundamentals - Measure the local flow velocty through ts relatonshp to the convectve coolng of electrcally heated metallc sensors. Hot wre anemometers: for clean ar or other gas flows Hot flm anemometers: for lqud or some gas flows

3 How a Hot wre Sensor Works The electrc current ( flowng through the wre generates heat ( R w Flow Feld V In equlbrum, ths must be balanced by heat lost (prmarly convectve to the surroundngs. Electrc current,, through wre

4 Techncal Fundamentals Heat transfer characterstcs: Convecton (nature convecton, forced convecton or mxed convecton dependng on Rchardson numbers Conducton to the supportng prong Radaton: <0.%, s neglgble. u q lk ( Tw T u (Re, Pr, Gr, M, Kn, a T, l / d, Hot wre Flud flow V,T T Ud Re ; 3 g( Tw T d Gr ; Kn c p / cv d Tw T at T M Re Pr V M c prongs

5 Techncal Fundamentals Followng Kng s Law (95, Accordng to Colls and Wllams (959: u ( Re u 0.48Re 0.5 ( 0.45 ( a T n m u ( A B Re ( at 0.7, a T 0.7, for for 44 Re Re 44 For a gven sensor and fxed overheat rato, The above equaton can transfer as the relatonshp between the voltage output, E, of the hot-wre operaton crcut and the flow velocty T w E T A Wre temperature cannot be measured drectly, but can be estmated from ts relatonshp to the wre resstance, R w, drectly measured by the operatng brdge. For metallc wres: BV n R w R r [ a ( T T] r w ar : thermal resstvt y coeffcen T : reference temepature r t

6 Techncal Fundamentals Flow Feld V The hot wre s electrcally heated. If velocty changes for a unsteady flow, convectve heat transfer changes, wre temperature wll change and eventually reach a new equlbrum. Current flow through wre The rate of whch heat s removed from the sensor s drectly related to the velocty of the flud flowng over the sensor

7 Techncal Fundamentals For a sensor placed n a unsteady flow, the unsteady energy equaton wll become: dt mc dt m : c : q : w R w q ( V, T the massof the sensor specfch heat of the sensor convectve heat flux q q ( V, The above equaton has three unknowns:, (or R w and V To render ths equaton solvable, one must keep wth the electrc current,, or the sensor temperature ( constant, whch can be acheved wth the use of sutable electrc crcuts. The correspondng methods are known as: (. Constant-current anemometry (. Constant-temperature anemometry w

8 Constant-current anemometry Rs R w R s E Voltage follower C E c E E o o /( R / R s s E Rw const The voltage output wll be R w E o R w sensor R c Compensaton crcut R c. The unsteady energy equaton s hghly-nonlnear. When lnearzed n the vcnty of an operaton pont, namely at a partcular flow speed, V op, and sensor temperature, op, t leads to the followng frst-order dfferental equaton: dtw T T K ( V V : w w ( w wo p T op dt a tme constant, whch s proportonal to the overheat rato, and a statc senstvty, Snce voltage, E, s proportonal to, Rw, whch, n turn, s lnearly related to Tw, the lnearzed E-V relatonshp wll be: de w ( E Eop K( V Vop dt s usually ~ ms for thn hot-wre and ~ 0 ms for slm cylndrcal hot-flm. w : For flow wth varable velocty or temperature, overheat rato wll vary as well. Flow low speed flow, t may result n burnout, for hgh-speed flow, senstvty s low K T

9 Constant-current anemometry Rs R w R s E Voltage follower C E c E E o o /( R / R s s E Rw const The voltage output wll be R w E o R w sensor R c Compensaton crcut R c. The unsteady energy equaton s hghly-nonlnear. When lnearzed n the vcnty of an operaton pont, namely at a partcular flow speed, V op, and sensor temperature, op, t leads to the followng frst-order dfferental equaton: dtw T T K ( V V : w w ( w wo p T op dt a tme constant, whch s proportonal to the overheat rato, and a statc senstvty, Snce voltage, E, s proportonal to, Rw, whch, n turn, s lnearly related to Tw, the lnearzed E-V relatonshp wll be: de w ( E Eop K( V Vop dt s usually ~ ms for thn hot-wre and ~ 0 ms for slm cylndrcal hot-flm. w : For flow wth varable velocty or temperature, overheat rato wll vary as well. Flow low speed flow, t may result n burnout, for hgh-speed flow, senstvty s low K T

10 Constant-temperature anemometry (CTA - Electrc current through the sensor s adjustable contnuously through an electrc feedback system, and n response to the changes n convectve coolng, to make the temperature of the hot wre keep n constant. The unsteady energy equaton becomes steady equaton. Dynamc response of the anemometer s the same as ts statc response wth a wde frequency range. mc dt dt w R w q ( V, T w R w q ( V 0

11 Constant-temperature anemometry (CTA- R R R Esw Eoffset Rsw Ew EB - E + Rd Rw sensor Dfferental amplfer Constant temperature crcut Sensor, Rw, comprses one leg of the Wheatstone brdge. An adjustable decade resstor array, Rd, compress opposte leg of the brdge. The brdge rato R/R s fxed, and R/R 0~0 to make sure to supply most of the avalable power to the sensor. The two mdponts of the brdge are connected the nput of a hgh-gan, low nose dfferental amplfer, whose out put s fed back to the top of the brdge. If R/Rd= R/Rw, then EB-Ew=0, the amplfer output wll be zero. If Rd s ncreased to a value R d, the resultng brdge mbalance wll generate an nput mbalance to the amplfer. The amplfer wll create some current through both legs of the brdge. The addtonal current through the hot wre wll create addtonal joule heatng, whch tend to ncrease ts temperature and thus ts resstance, untl the resstance ncreasng suffcently to balance the brdge once more.

12 Varous effects and error source Velocty orentaton effects: Effectve coolng velocty V eff = V cos. In realty, flow velocty tangental to the sensor would result n coolng. V eff = V (cos + k sn / Typcal values of K are 0.05 and 0.0. Hot wre Flud flow V,T T prongs

13 Varous effects and error source Prong nterference effects: Interference of the prongs and the probe body may produce addtonal complcatons of the heat transfer characterstcs. For example a stream n bnormal drecton wll produce hgher coolng than a stream wth the same velocty magntude but n the normal drecton. In realty,v eff = (V + K V T + h V B / V, V T and V B are the normal tangtal and bnormal velocty components. Typcally, h =.~. To mnmze the effect, t usually use long and thn prongs. Tapered prongs are also recommended. Hot wre prongs Flud flow V,T T

14 Varous effects and error source Heat conducton effects: Prevous analyss s based on -D assumpton wth l/d =. In realty, the effect of end conduct may effect the accuracy of the measurement results Cold length, l c = 0.5*d ((K w /K(+a R /u / Hot wre Flud flow V,T T K w s thermal conductvty of the sensor K s thermal conductvty of the flud a R s overheat rato Effect of the sensor length l/l c A recent study has demonstrate that end conducton effects are expected to decrease sgnfcantly as the Reynolds number ncreasng prongs

15 Varous effects and error source Compressblty effects: The velocty and temperature felds around the sensor become qute complcated when M>0.6. V T0 For M. S S S V T 0 S V S Hot wre Flud flow V,T T Modfed Kng s law for compressble flow: E A n 0.55 B( V n prongs

16 Varous effects and error source Temperature varaton effects: Calbraton at Temperature T. Correlaton s needed f real measurements wll be conducted at Temperature T. When the flow temperature vares from poston to poston or contan turbulent fluctuatons, correctons s much more complcated. It requres smultaneous flow temperature measurements. Sv s ncreasng wth overheat rato a T. At extremely low a T, a thermal anemometer s totally nsenstve to velocty varatons, and becomes a resstance thermometer. The sensor s called cold wre. Hot wre Flud flow V,T T prongs

17 Varous effects and error source Composton effects: Composton of flow may affect the convectve heat transfer from a thermal anemometer n as much as t affect the heat conductvty of surroundng flud. It requres smultaneous measurements of flud speces concentraton. Hot wre Flud flow V,T T prongs

18 Varous effects and error source Reverse flow and hgh-turbulence effects: thermal anemometer could not resolve velocty orentaton. Forward flow can not be dentfed from reversng flow In hghly turbulent flow (turbulent ntensty >5%, reverse flow wll occurr statstcally some tme, therefore, usng thermal anemometer for the flow velocty measurement may result qute large measurement uncertanty. Pulsed Hot wre concept Hot wre Flud flow V,T T prongs

19 Mult-sensor probes Cross-wre (X-wre desgn: V V eff A eff B V V ( V ( V ( V ( V eff A eff A V V V V eff B eff B V V V V V V eff-b V V eff-a V

20 Mult-sensor probes Three sensor desgn Four sensor desgn:

21 Dameter of hot wres L = 0.8 ~.5 mm D = ~ 5 m for conventonal applcatons D = ~ 0 m for hgh-speed applcatons D = ~ m for low speed applcatons Prongs: usually tapered to be d mm

22 Lecture #05 Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements Dr. Hu Hu Department of Aerospace Engneerng Iowa State Unversty Ames, Iowa 500, U.S.A

23 Y /C *00 Aerodynamc Performance of An Arfol Lft Coeffcent, C l L V C l c C L = Expermental data Arfol stall Y /C * m/s GA(W- arfol shadow regon Before stall -60 vort: Angle of Attack (degrees X/C * Drag Coeffcent, C d D V C d c Expermental data m/s GA(W- arfol shadow regon After stall 0.05 Arfol stall -40 vort: X/C * Angle of Attack (degrees

24 Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements

25 Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements

26 Y (nches Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements C p P V P C p Before stall upper surface lower surface x / c C p After stall upper surface lower surface X (nches ACA00 arfol wth 49 pressure tabs x / c

27 Y (nches Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements What you wll have avalable to you for ths porton of the lab: A Ptot probe already mounted to the floor of the wnd tunnel for acqurng dynamc pressure throughout your tests. A Setra manometer to be used wth the Ptot tube to measure the ncomng flow velocty. A thermometer and barometer for observng ambent lab condtons (for calculatng atmospherc densty. A computer wth a data acquston system capable of measurng the voltage from your manometer. The pressure sensor you calbrated last week A ACA 00 arfol that can be mounted at any angle of attack up to 5.0 degrees. Two 6-channel Scanvalve DSA electronc pressure scanners X (nches 30 5

28 Calculatng arfol lft coeffcent and drag coeffcent by numercally ntegratng the surface pressure dstrbuton around the arfol: Determnaton of the Aerodynamc Performance of a Low Speed Arfol based on Pressure Dstrbuton Measurements / / p p p p p p y, y, y y x x x y y x x x x p / ' y p A / ' (7 ' ' (6 ' ' / / y p A A x p 'cos 'sn ' 'sn 'cos ' A D A L

29 Requred Plots for the Lab Report You must generate plots of C P for the upper and lower surfaces of the arfol for the angles of attack that you tested. Make comments on the characterstcs of the C P dstrbutons. Calculate C L and C D by numercal ntegraton C P for the angles of attack assgned to your group. You must report the velocty of the test secton and the Reynolds number (based on arfol chord length for your tests. You must provde sample calculatons for all the steps leadng up to your fnal answer. You should nclude the frst page of the spreadsheet used to make your calculatons