Turbulence and hot-wire measurements Mek 4600

Transcription

1 Trblence and hot-wre measrements Mek 4600 Mrat Ttkn Insttte for Energy Technology (IFE) Process and Fld Flow Technology Keller, Norway École Centrale de Llle Laboratore de Mécanqe de Llle (LML) Vlleneve d'ascq, France Hot-wre rake of 143 sngle-wre probes 1

2 Trblence! What s t? Realzatons of soltons to the governng eqatons and bondary condtons. Most engneerng flows are trblent. 2

3 3 Instantaneos Naver-Stokes Eqatons (NSE): x x x p x t ~ ~ 1 ~ ~ ~ 2 Contnty eqaton: 0 ~ k k x Is trblence stll a problem? What abot Naver-Stokes Eqatons? C.-L. Naver G.G. Stokes

4 There are some real dsadvantages assocated wth these eqatons. These Naver-Stokes eqatons are non-lnear de to convectve term: ~ ~ x Most soltons of nterest are random (or stochastc ) and chaotc n character. All scales of moton are mportant to the dynamcs; none are neglgble. 4

5 Do we really bother wth ths? The answer s YES! Trblence s almost everywhere: Aero/hydrodynamcs (Arplanes, shps, sbmarnes, road vehcles, trans) (Ppelne, channels, dstrbton systems) Envronmental flows Indstral processes (chemcal and mltphase) Combston Energy technology (gas trbnes, wnd trbnes, ) 5

6 The range of scales n real trblent flows s enormos typcally 10 5 to Trblent bondary layer Van Dyke, 1982 Re nerta vscos The hgher Re, the greater the separaton of scales. 6

7 It s very dffclt to measre every scale and wll be many decades before comptng them drectly. Cascade of trblence knetc energy from scale to scale Energy Physcal space Strctre fnctons: Spectral space Energy spectra: 7

8 The prmary goal of any trblence research s to be able to predct or at least model trblence. Flow Physcs (DNS & Experments) Trblence Modelng Flow control Valdaton Applcaton (Performance Enhancement and Energy Effcency) 8

9 What can we do then? One obvos way s to dvde flow nto mean and flctatons (the so called Reynolds decomposton). e.g., mean: flctaton: ), ( ), ~ ( ), ( ), ~ ( ), ( t x U t x t x t x t x U Ensemble average < > s space and tme-dependent. 9

10 One has to be carefl when comptng statstcal qanttes n trblence: 10 Streamwse velocty behnd a grd n a wnd tnnel

11 11

12 12

13 It s not easy to get the statstcs rght n trblence measrements; n partclar hgh order moments. 13

14 Atocorrelaton of two random and one perodc process 14

15 Integral tme scale s obtaned by ntegratng the area nder the atocorrelaton coeffecent. 15

16 Plggng the Reynolds decomposton nto the NSE yelds the Reynolds Averaged N-S eqatons (RANS). Mean momentm eqaton: t U x U x P x (v) s the so-called Reynolds stress. It s a flow property. Workng aganst mean flow gradent and extracts energy to trblence at large scales. 16

17 Now we have a closre problem de to : No new eqatons, 9 (6 ndependent) new nknowns Orgnal gradent dea: (Bossnesq (1877)) t U x 130 years snce the trblent vscosty, k-epslon models are st another way to gess. It has been proven that smple deas/approaches do not work n ths problem 17

18 Reynolds stress models are another way k k k k k x p p x Dt D ) ( 1 k k k k k x x x p x p x U x U 1 Usng Naver-Stokes eqatons to `bld a set of eqatons for the Reynolds stress tensor. The nmber of nknowns s now 52, bt only 13 eqns! Presence of pressre presents a hge problem! (non-localty) 18

19 Anybody who does research n trblence shold keep followng ponts n mnd: The flow at a sngle pont s related to the flow at every other pont, and at all prevos tmes (Tradc Interactons). Even the terms n or averaged eqatons are NON-LOCAL n both space and tme. Ths presents real problems for trblence models, snce all closres are LOCAL. 19

20 How mch of these can be measred n the lab? --- Unfortnately, not mch! Partcle Image Velocmetry: 2, or 3 component of velocty at very hgh spatal resolton, Most of the systems provde low temporal resolton, Measrement feld s often small, Near-wall and low trblence measrements are very dffclt. Laser Doppler Anemometry - Very good at hgh trblence measrements, - Handles very near-wall regon, - Sngle pont measrements, - Can provde reasonable samplng freqences. 20

21 We wll focs on the most common measrement methodology sed n trblence reasearch (even today). Hot wre anemometry: 1, 2, or 3 component of velocty at very hgh temporal resolton, Based on heat balance along the sensor element, Sngle pont measrements, Dstrbance to the flow, Poor response n hgh trblence and recrclaton, Cheap compared to the others, Easy to manfactre n-hose. 21

22 Operatng prncple (as vsalzed by Dantec) 22

23 Last lectre: Trblence Statstcs Atocorrelaton Integral tme scale Effectve nmber of samples Record length Varablty of estmator Hot wre anemometry Today: Hot wre anemometry Calbraton Some examples Spectral measrements Practcal desgn of experment. 23

24 Fnte probe sze lmts the resolvable smallest scale. Non-resolvable sgnal Resolvable sgnal Exp. Fld Mech Ct-off freqency n practce :

25 Crrent I Sensor dmensons: length ~1 mm dameter ~5 mcrometer Velocty U Sensor (thn wre) Wre spports (St.St. needles) 25

26 All dates back to 1914: L.V. Kng (Phl. Trans. Roy. Soc., A214, ). On the convecton og heat from small cylnders n a stream of fld: Determnaton of the convecton constants of small platnm wres wth applcaton to hot-wre anemometry. where the dmensonless heat transfer rate (Nsselt nmber): The Reynolds nmber: Overheat rato: 26 I 2 R w2 = E 2 = (T w -T a )(A + B U n ) Kng s law

27 Hot-wre temperatre profles: 27 Freymth, 1979

28 Schematcs of the anemometer crct: Wheatstone brdge 28

29 How t looks n realty: 29

30 Calbraton before and/or after the experment s needed n order to convert voltages to veloctes. E 2 = A + B n Kng s Law U = C 0 + C 1 E + C 2 E 2 + C 3 E 3 + C 4 E 4 Polynomal calbraton 30

31 The relaton s fond by crve fttng to the calbraton data sng least sqare method. 31

32 Two component measrements need cross-wres; and anglar calbraton 32

33 Calbraton of cross-wres may be more troblesome and dffclt than expected. θ 2 U 2 U 3 θ 1 U 1 33

34 We pt all yor anglar calbratons onto one sngle crve for each of the sensors! 34

35 More dffclt and tme consmng to perform ths way! 35

36 Axsymmetrc far wake s very dffclt to measre becase of small velocty defct. U =15 m/s D = 20 mm Re D = x/d = 50 36

37 Brdge oscllatons and qantzaton error (even for 16 bt A/D converter) are bg problems n ths case. 37 Johansson et al, JFM, 2006

38 21.6 m long wnd tnnel of Laboratore de Mécanqe de Llle (LML) s nqe to condct bondary layer research. 38

39 A hot-wre rake of 143 sngle wre probes to get both spatal and temporal nformaton abot the flow. Probe postonng s crcal z-poston : 0, ± 4.0 mm, ± 12.0 mm, ± 28.0 mm, ± 60.0 mm, ±100.0 mm, ± mm y-poston : 0.3 mm, 0.9 mm, 2.1 mm, 4.5 mm, 9.3 mm, 18.9 mm, mm, 76.5 mm, mm, mm, mm

40 Some practcal nfo: Fast (spectral) or slow measrement Example: ppe flow Large scale ~ R Characterstc velocty ~ U centerlne Tme scale of large scales ~ R/U cl Small scale: Kolmogorov mcroscale 40 Ct-off freqency n practce :

41 41