Typical description of wall-bounded flows

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Denis Adams
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4 ? Typical description of wall-bounded flows The boundary layer is divided into different regions based on the the dynamics of mean flow and turbulence & '(*) +, 25? : ; Sublayer y 15 + < 5 Buffer 5 y!"#%$ + < 0 Overlap 0 y + < 0.15δ + 5 u τ = τ w /ρ Core 0.15 y/δ < 1 Potential y/δ > / :<;>=

5 Typical description of wall-bounded flows The two layer approach At least two length and velocity scales needed Inner : Viscous effects are dominant U U si = F inner (y/l si, Re, ) Outer : Inertial effects are dominant. Effects of viscosity are negligible U U U so = F outer (y/l so, Re, ) Matching : U + = U si u τ [ ] lim F inner + U [ ] so lim F outer = F (Re) y/l si u τ y/lso 0 Also, scaling velocity for the Reynolds stresses, u i u j, (R si, R so ) are needed. Equilibrium : Self-similarity of mean flow & Self-preservation of turbulence U si L si U so L so Classical u τ ν/u τ u τ δ, George & Castillo (1997) u τ ν/u τ U δ 99 Zagarola & Smits (1998) u τ ν/u τ U δ /δ δ Other mean flow descriptions by T. B. Nickels (2004), Oberlack (2001), Barenblatt, Chorin, & Prostokishin (2000) Completely self-consistent description of ZPG TBLs based on the classical (logarithmic) theory recently established by Monkewitz et al., 2007 and Chauhan, Monkewitz, & Nagib, 2007

7 Motivation... Universality of overlap parameters? 3080 Classical Phys. Fluids, Vol.The 15, No., October logarithmic 2003 overlap region : U 1 = ln(y + ) + BZanoun, Durst, and Nagib uτ κ There is no consensus for the value of von Ka rma n constant, κ (& B) in wall-bounded flows in the literature. The past experimental interpretations were primarily based on low Reynolds number data. FIG. 1. Values of the constants of the logarithmic law of the wall obtained from various investigations: 共a兲 von Ka rma n constant, and 共b兲 additive constant B. Less than a decade ago we from experiments, the other can be deduced using the above authors aimed at obtaining reliable information regarding the were very lost!! mean momentum equation. In the region close to the wall, mean velocity distribution in two-dimensional fully developed turbulent plane-channel flow. A wide range of the Reynolds number was covered and in this range an overall picture resulted regarding the Re dependence of the timeaveraged velocity profile. For the(2003), high Re Physics range of of thefluids flow, Figure from Zanoun, Durst, & Nagib the analysis of the authors experimental results indicates the existence of a logarithmic mean velocity distribution, with a von Ka rma n constant,, close to 1/e( 0.37). The experi- both of these terms vary strongly. If one is interested in the U (y ) distribution, one should measure (du /dy ) directly and deduce from it the U -variation with y. To measure or to model u 1 u 2 in the region where it is the much larger term in Eq. 共1兲 is not the right way to get U (y ) deduced correctly. A small error in the u 1 u 2 will yield a (y ) distribution.

8 Higher Reynolds Number Boundary Layer Data on a Flat Plate in the NDF with Pressure Gradient Flat Plate Adverse Pressure Gradient (APG) Zero Pressure Gradient (ZPG) Favorable Pressure Gradient (FPG) Strongly Favorable Pressure Gradient (SFPG) Complex Pressure Gradient (CPG)

9 Development of Free-Stream Velocity for different Pressure Gradients U(x) / U(x=0.43) Zero Pressure Gradient (ZPG) Adverse Pressure Gradient (APG) Favorable Pressure Gradient (FPG) Strong Favorable Pressure Gradient (SFPG) Complex Pressure Gradient (CPG) Hot-Wire & Oil-Film Data Stations U inf 1 = x U inf = 0.035x U inf = x U inf = x x [m]

Lessons learned from recent experience: We believe that the value of experimental data in all wall bounded turbulent flows (except the fully developed pipe) is greatly diminished without accurate and

10 Lessons learned from recent experience: We believe that the value of experimental data in all wall bounded turbulent flows (except the fully developed pipe) is greatly diminished without accurate and independent measurement of the wall shear stress. Oil-film interferometry is the best technique to achieve these measurements as long as the oil viscosity is measured accurately for range of temperatures of experiments; accuracy ~ 1.5%.

11 ZPG TBLs - Results PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs

12 Skin-friction behavior in ZPG TBLs Coles-Fernholz 1 C f = 2[1/κ ln(re δ ) + C] 2 κ = 0.384, C = 3.3 Coles-Fernholz 2 C f = 2[1/κ ln(re θ ) + C 1 ] 2 κ = 0.384, C = 4.1 Kármán-Schoenherr C f = 0.558C f /[ (C f ) 1/2 ] C f = [ log(2re θ )/0.242 ] Prandtl-Schlichting C f = 0.455(log Re x ) 2.58 A/Re x Prandtl-Kármán C 1/2 f = 4 log(re x Cf ) F. Schultz-Grunow C f = 0.427(log Re x 0.407) Nikuradse C f = Re x Schlichting s fit C f = (2 log Re x 0.65) White C f = 0.455[ln(0.06Re x )] /7 th Law C f = 0.027Re 1/7 x /5 th Law C f = 0.058Re 1/5 x A/Re x GC97 C 1/2 f = 2(55/C i ) [ δ +] γ exp [ A/(ln δ + ) α] ? ' #1@"& '! $?%A:?%BCB%D E@F' G.C 5 0 B%H ' G.C 5 "!"#"$%& ')( *+& "#, & -, & -/. *+& #32 4"562 7& 8 " 032 4"562 7& #, '7& "" 9:<; ')(="/,( 9><; ')(="/,( Various skin-friction relations are fitted to the oil-film measurements from NDF and KTH. Modified by changing only one empirical coefficient to obtain a least-square fit with the high Reynolds number data of KTH and NDF

13 3.6 Skin-friction behavior in ZPG TBLs All the modified relations fit the data within experimental accuracy for all laboratory Reynolds numbers if they are underpinned by the same measurements "! #%$'&(#')+*', -./ #', 0%1'#%$')2.3/465 -./ #', 0%1'#%$')2.3/ & *%# :<; = $%(>; = )"0@?AB2. #')2"#%$%$ C$ = )D"* / 0%:<; = $%(>; = )?AE2 / & AB2+*'& )"FG* C$ = )D"* / 0%?AE2 / & AB2+*'& )"F H-I"J?AE2LK / * 4 0 H $'K).+M The appropriateness of a relation (theory) only from skin-friction measurements cannot be established. At finite Reynolds numbers one has to couple the skin-friction relation with mean velocity description (and turbulence if possible) and put it at test with the experimental data. The differences between the various predictions increase steadily : While they are less than 0.5% at Re θ = 20, 000, they increase to over 40% beyond an Re θ of 16.

14 The Coles-Fernholz type relation and velocity defect in the outer part ,000 40,000 60,000 80, Outer : Inner : U u τ = F inner (y + ) U + = 1 κ ln(re δ ) + C lim F inner = U + = 1 y + κ ln(y+ ) + B W + = U U u τ = F outer (y/ ) lim η 0 F outer = U + U + = 1 κ ln(y/ ) + C Matching : U + = lim F inner + lim F outer = U + y + η 0 (Re δ ) For ZPG TBLs, δ constant. Therefore, either of = U + δ (Rotta-Clauser Delta) or δ (local boundary layer thickness) can be used in the outer part. κ = 0.384, B = 4.17, C = 3.3

15 Inner profile (Monkewitz, Chauhan, & Nagib, 2007), Physics of fluids du + inner = P dy P 25, Ξ = y + du + dy P 23 = b b 1 y + + b 2 y b 1 y + + b 2 y +2 + κb 0 b 2 y + 3 b 0 = κ 1 (κ = 0.384) b 1 b 2 = = h 1 y + + h 2 y + 2 P 25 = (1 b 0 ) 1 + h 1 y + + h 2 y +2 + h 3 y +3 + h 4 y +4 + h 5 y + 5 = h 1 h 2 = h 3 = h 4 = h 5 = Ξ 23 +Ξ 25 ( ); Ξ 23 ( + + ); Ξ 25 ( ); KTH ( ); NDF ( ) ; Carlier & Stanislas (2005) ( ); T. Nickels et al., 2007( ). Comparison of new fit Ξ 23 + Ξ 25 ( ) with previous proposals in the literature. Other functional forms shown for κ = and B = 4.17 are :, Musker (1979);, Modified Musker from Chauhan, Monkewitz, & Nagib, 2007;, Spalding (1961);, Van Driest from White (2006); +, Gersten & Herwig from Schlichting & Gersten (2000)

16 Outer profile (Monkewitz, Chauhan, & Nagib, 2007), Physics of fluids Monkewitz, Chauhan, & Nagib, 2007, Physics of fluids 1 U + U + outer = η = y/ [ 1 ] 1 κ E 1(η)+w 0 1 tanh( 2[ w ] 1 η +w 2η 2 +w 8 η 8 ) w 0 = w 1 = w 2 = 28.5 w 8 = E 1 (η) = η exp t dt = γ ln(η) + η + O(η 2 ) for η 1 t [ exp η 1 1 ] η η + O(η 2 ) for η, γ = Euler-Mascheroni constant NDF ( ); KTH ( );, exponential wake function of Chauhan, Nagib, & Monkewitz, 2007;, quartic polynomial of Lewkowicz (1982); , sine wake function of Coles (1956);, wake function of T. B. Nickels (2004)

17 Mean velocity description Alternative formulation with δ Original Musker (1979) inner form : Modified Musker (1979) inner form : U + inner = 1 ( ) y + κ ln a a α (4α + 5a) β + du + inner dy + = 1 s + y+2 κ 1 s + y+2 κ + y+ 3 [ ( R 2 (4α + a) ln a a(4α a) R ( ( y + α ) arctan β ( α + arctan β where, α = ( 1/κ a)/2, β = 2aα α 2, R = α 2 + β 2, s = ar 2. (y+ α) 2 + β 2 ) + y + a ) )] + exp [ ln 2 (y + /30) ] 2.85, Coles (1956) outer form : U outer + = 1 κ ln(y+ ) + B + 2Π W(ξ), ξ y/δ 1 κ [ 1 exp 1 ] New wake function : Wexp(ξ) = 4 (5a 2 + 6a 3 + 7a 4 )ξ 4 + a 2 ξ 5 + a 3 ξ 6 + a 4 ξ 7 ( 1 exp [ (a 2 + 2a 3 + 3a 4 )/4 ] 1 1 ) 2Π ln(ξ), where, a 2 = , a 3 = and a 4 = Composite form : U + inner (y+ ) + 2Π κ W exp(y/δ), ξ y/δ 1

18 Remarkable agreement between data covering a wide range of Reynolds numbers and the fitted composite profile. The agreement is also equally good for data from different experimental facilities with different velocity measurement and acquisition techniques with varying number of data points available for fitting or their wallnormal spacing. Logarithmic composite profile Gives accurate description ! "$# %'&() *+,-.$#$ &/ 01$2 ) "$# 3 ) 4 #$ ) 3 " 5 "1 5 "67) Similar to the conventional Clauser plot the composite profile now can be fitted to U versus y to determine, u τ, δ, & Π.!#"$%#&$'( Gives excellent indirect prediction of U

19 Experiments studied in canonical wall-bounded flows ZPG TBLs 1950, Schubauer & Klebanoff 1952, Klebanoff & Diehl 1958, D. W. Smith & Walker 1968, Coles & Hirst - Bell - Wieghardt - Riabouchinsky 1980, Karlsson 1981, Purtell, Klebanoff, & Buckley 1986, Ahn 1988, Spalart (DNS) 1988, Wark 1988, Erm 1991, Nagano, Tagawa, & Tsuji 1992, Naguib 1994, R. W. Smith 1995, H.-H. Fernholz, Krause, Nockemann, & Schober 1996, Osaka, Kameda, & Mochizuki 1997, Hites 1998, Bruns 1999, Tsuji 1999, Österlund 2000, DeGraff & Eaton 2001, Skote (DNS) 2002, Knobloch & Fernholz 2004, Nagib, Christophorou, & Monkewitz 2005, Carlier & Stanislas 2007, T. Nickels, Marusic, Hafez, Hutchins, & Chong PG TBLs 1989, Watmuff 1993, Spalart & Watmuff (DNS) 1994, Skare & Krogstad 1995, Marusic & Perry 1998, Jones 1998, H. H. Fernholz & Warnack 2001, Skote (DNS) 2004, Nagib, Christophorou, & Monkewitz 2008, Spalart, Johnstone, & Coleman (DNS of Ekman layer) Pipe flows 1998, AGARD-AR Perry, Henbest, & Chong - Durst, Jovanović, & Sender - den Toonder & Nieuwstadt 2003, McKeon, Princeton Superpipe 2005, Monty Channel flows 1987, Kim, Moin, & Moser (DNS) 1998, AGARD-AR Wei & Willmarth - Niederschulte, Adrian, & Hanratty - Comte-Bellot 2001, Christensen 2001, Fischer, Jovanović, & Durst 2003, Zanoun 2004, Jiménez, del Álamo, & Flores (DNS) 2005, Monty

21 Other functional forms for ZPG TBLs

22 Typical description of wall-bounded flows The two layer approach At least two length and velocity scales needed Inner : Viscous effects are dominant U = Finner (y/lsi, Re, ) Usi Outer : Inertial effects are dominant. Effects of viscosity are negligible U U = Fouter (y/lso, Re, ) Uso Matching : + U Usi = uτ lim y/lsi Finner Uso + uτ lim Fouter = F (Re) y/lso 0 Also, scaling velocity for the Reynolds stresses, u0i u0j, (Rsi, Rso ) are needed. Equilibrium : Self-similarity of mean flow & Self-preservation of turbulence Usi Lsi Uso Lso Classical uτ ν/uτ uτ δ, George & Castillo (1997) uτ ν/uτ U δ99 ν/uτ Zagarola & Smits (1998) uτ U δ /δ δ Other mean flow descriptions by T. B. Nickels (2004), Oberlack (2001), Barenblatt, Chorin, & Prostokishin (2000) Completely self-consistent description of ZPG TBLs based on the classical (logarithmic) theory recently established by Monkewitz et al., 2007 and Chauhan, Monkewitz, & Nagib, 2007 PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs 7 of 37

23 Mean flow similarity George & Castillo (1997) U + = 1 κ ln y+ + B, Ξ y + du + dy + Ξ = 1 κ for log law. U + = C i (y + + a + ) γ, Γ (y+ + a + ) U + du + dy + Γ = γ for GC97 power law. Diagnostic functions establish the validity of logarithmic form in the overlap region , Re θ 5, 500;, Re θ 8, 200;, Re θ 14, 000; +, Re θ 21, 000;, Re θ 39, 500

24 When you are up to your ass in alligators, it is important to remember that your original intent was merely to drain the swamp

25 Mean flow similarity George & Castillo (1997) U+ = 1 ln y + + B, κ U + = Ci (y + + a+ )γ, Γ du + dy + Ξ= (y + + a+ ) du + U+ dy + Γ=γ Ξ y+ 1 κ for log law. for GC97 power law. Diagnostic functions establish the validity of logarithmic form in the overlap region Reθ = 14, Reθ = 39, , Reθ 5, 500;, Reθ 8, 200;, Reθ 14, 000; +, Reθ 21, 000; M, Reθ 39, 500

26 Mean flow similarity George & Castillo (1997) With original coefficients With modified coefficients

27 Clauser ratio, /δ Ratio of over δ is an important parameter indicating the validity of Clauser theory. /δ reaches its asymptotic value near 3.5 and remains a constant consistent with classical theory Invalidates arguments of power law theory of George & Castillo (1997) D δ = Re [ ] δ δ = exp 2Π + κ(b C )

28 Pressure Gradient Turbulent Boundary Layers

29 Skin-friction in PG TBLs NDF Data For the Strongly Favorable Pressure Gradient case, U + shows trends with x and U ; i.e., non-equilibrium development. C f CPG SFPG FPG APG 40 APG 50 APG 60 CPG 40 CPG 50 CPG 60 FPG 40 FPG 50 FPG 60 SFPG 40 SFPG 50 SFPG 60 ZPG : NDF ZPG : KTH ZPG oil film data fit APG ,000 20,000 30,000 40,000 50,000 60,000 70,000 Re

30 PG TBLs deviations from ZPG Presence of pressure gradient changes the structure of mean flow. Changes in κ, B and Π along with U +. Corresponding changes in u 2 also observed !"!#$&% ' (" )!"+*,$&% *- (. / 01+ *,#(($&% *,.*-" 2 / 01+ *,. ' $&% # (

31 Overlap parameters in all wall-bounded flows studied The von Kármán coefficient, κ and the intercept B for ALL wall-bounded flows have a common behavior. A simple curve fit to κ B versus B can reduce the number of empirical constants in a turbulence model based on the logarithmic law ! " $#$%&' (*)*+ + ",(*)*+ + ",(*)*+! ",(*)*+ -/.2- + ", #9%

32 Channel forms & Pipefor Flows Other functional ZPG TBLs PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs

33 Traditionally the Kármán constant is estimated from the overlap region (loglayer) alone, which leads to a great deal of uncertainty, especially at lower Re, and the various approaches used often incorporate Results assumptionszpg thattbls have- not been fully validated (e.g., limits of overlap region). The uncertainty can be greatly reduced with the help of empirically-based "composite profiles" for the various wallbounded flows, that are carefully constructed to satisfy several constraints. PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs

34 Channels & Pipes The composite profile Channels & Pipes : uv du + y+ + = 1 u2τ dy + Reτ 2 + duinner dy + 1 y+ y+ + s κ s Reτ = +2 1 y + + y+3 s κ + U + = Uinner + dn U + dy + n Wpipe 2Π W(η), κ η y/h 1 =0 n is odd 6= 0 n is even η=1 i h 1 1 exp (4p2 + 6p3 + 7p4 )η 3 + p2 η 4 + p3 η 6 + p4 η 7 ln(η) 3 = 1 2Π 1 exp (p2 + 3p3 + 4p4 )/3 where, p2 = 4.075, p3 = and p4 = i exp (3c2 + 6c3 + 7c4 )η + c2 η + c3 η + c4 η ln(η) 2 = 1 2Π 1 exp (c2 + 4c3 + 5c4 )/2 h Wchannel where, c2 = 20.22, c3 = 17.1 and c4 = The composite profiles for Channels and Pipes fit accurately to both DNS and experimental data. Fit provides the local κ, B and Π. PhD defense Preliminaries ZPG TBLs PG TBLs Pipes & Channels DNS 57

35 DNS of wall-bounded flows Near wall region Z y+ ν duτ uv du + 2 =1+ U + dy + ZPG TBLs : uτ dy uτ dx 0 + ν P + uv du PG TBLs : 2 + =1+ 3 y uτ dy + uτ x y uv du + =1 Channels & Pipes : uτ dy H 0 du + 3 c1 y + + dy du + ν P y + c2 y + + dy uτ x + y+ du c3 y + + dy Reτ Near the wall DNS of various flows show a cubic behavior for Reynolds shear stress, uv However, differences between DNS of ZPG TBLs by Spalart (1988) and Skote (2001) are observed for 1 du + /dy +.! "$# % & ' ( )+*,-. 0/ $ 132 & ' ( )+*, ' ( )+*, ' ( )+*,-. 0/ $ 13298;:< A 4 #B C $ 6D6 1 E $"$> F " E 1 We have also found differences at higher y + for the gradient of total stress for these two DNS M PhD defense GIHKJKL 00 1 Preliminaries ZPG TBLs PG TBLs Pipes & Channels DNS 61

38 Superpipe data Further evaluation Ψi is almost constant across y for κ = 0.41 but the magnitude of Ψi decreases with increasing Reynolds number. Ψi for κ = is has a very good constant behavior for y + > 600. Ψo is clearly constant across y/r for κ = 0.41, except the data with Reτ. 11, Ψi = U Ψo = (Uc+ U + )+ ln(y/r) Bo κ ln(y + ) B κ 300 < y + < 0.15Reτ PhD defense Preliminaries ZPG TBLs PG TBLs Comment on consistency, and single κ for all Re versus composite profile approach yielding κ(re). Pipes & Channels DNS 65 1

40 ! "$#$%!&'(%! *),+$-!&/.! *),+$0$%!) 1243$5! ! "$-!&'("! -!&/.! $: ;*< 6 9! %!)$&'(:!!&/.! "

41 "! #%$%&"'()&"!+*-,%."'0/ "! #%&%,%1%. 234%5" "! #%."'()#"!."'0/ "! %: ;+< 6 9 "! &"*%'():"! "'0/ "! #

42 ! "$#$%!&'(%! *),+$-!&/.! %$$"$#$" 0132$4! ! "$-!&'("! -!&/.! $9 :*; 5 8! %!)$&'(9!!&/.! "

43 "! #%$%&"'()&"!+*-,%."'0/ "! &%&% %1%& 234%5" "! #%."'()#"!."'0/ "! %1 :+; 6 9 "! &"*%'()1"! "'0/ "! #

44 "!!$#"% & ' #

Channels & Pipes The wake parameter, Π Π for pipe flows is higher than that for channel flows, although they have the same governing equation and boundary condition.

46 Channels & Pipes The wake parameter, Π Π for pipe flows is higher than that for channel flows, although they have the same governing equation and boundary condition. Parallel flows do not show the development of Π at low Reynolds numbers. 1 "! #%$ &()+ ' *-,/., 12/3.14 "! #6587"9": "! #658;" "< 9"7"=>58?13 0 9"7"=>58;"3 0 ADCFE1GIH L 4J.1K 4 3 M/2/ M/ : 3 M/NO, J, 4 4 3QPR S3 0, 2/ 7"3, M/NO K 2/BADCFE1GIH L. 2/! T. 2 L U.14 2WVXA/CFE1GIHJ 4J4 Y,/, VXA/CFE1GIH J 4.Z.14, PR7"3 KZ[ M/2/ 1 J2 9 KJ, M/2\A/CFE1GIH U.14 2WVXA/CFE1GIHJ ] %3 ^Q = K ^, ^J3 ^ _5 = 2/ 12/3 Na`b,/. FN.1,/, TN 2/T dcfe1gihsjkhml = K ^, ^J3 ^ _5 = 2/ 12/3 NaN.1,/, NT2/ dcfe1gihsjkhml = K ^, ^J3 ^ _5 n 4 N.1,/, TN 2/T dcoe1gihpjkhml qsr>t6jkhvu l qsw xytijkhvz1{ PhD defense Preliminaries ZPG TBLs PG TBLs Pipes & Channels DNS 59

47 !"

48 8 6 "!#

50 Introduction... The parallel flow in pipes and channels y = 2H U(2H) = 0 dp /dx y = H y U 0 u y y = 0 u x U(0) = 0 Continuity : u x + v y = 0 x momentum : 1 P ρ x + y [ ν U y u v y momentum : 1 P ρ y + v 2 y = 0 ] = 0

51 l c = Relevant Viscous Length Scale = ν / u τ = R / R + ; Independent of Fluid, Pressure, etc. CICLoPE Bertinoro, October

52 I C E T International Collaboration on Experiments in Turbulence: Coordinated Measurements in High Reynolds Number Turbulent Boundary Layers from Three Wind Tunnels Hassan Nagib IIT Alexander Smits Princeton University Ivan Marusic University of Melbourne P. Henrik Alfredsson KTH and ICET Team 62nd Annual Meeting of the APS Division of Fluid Dynamics Minneapolis, MN, November 22-24, 2009

53 APS Session on Turbulent Boundary Layers: Experimental Studies 1. ICET - International Collaboration on Experiments in Turbulence: Coordinated Measurements in High Reynolds Number Turbulent Boundary Layers from Three Facilities. H. NAGIB, A. SMITS, I. MARUSIC, P. H. ALFREDSSON and ICET Team. 2. Accurate and Independent Measurements of Wall-Shear Stress in Turbulent Flows. J-D. RÜEDI, R. DUNCAN, S. IMAYAMA, K. CHAUHAN and ICET Team. 3. Pitot Probe Corrections for Measurements in Turbulent Boundary Layers. J. MONTY, S. BAILEY, M. HULTMARK, B. McKEON and ICET Team. 4. Challenges in Hot Wire Measurements in Wall-Bounded Turbulent Flows. R. ÖRLU, N. HUTCHINS, T. KURIAN, A. TALAMELLI and ICET Team. 5. Mean Flow Measurements with Pitot Probes in High Reynolds Number Boundary Layers. S. BAILEY, M. HULTMARK, R. DUNCAN, B. McKEON and ICET Team. 6. Mean Flow Measurements with Hot Wires in High Reynolds Number Boundary Layers. R. DUNCAN, N. HUTCHINS, A. SEGALINI, J. MONTY and ICET Team. 7. Turbulence Measurements with Hot Wires in High Reynolds Number Boundary Layers. J. FRANSSON, N. HUTCHINS, R. ÖRLU, M. CHONG and ICET Team.

54 Scope Zero pressure gradient (ZPG) boundary layers at high Reynolds numbers are the focus. Over the past few years, four groups have made systematic comparison between several measurement techniques and three facilities. The development length of the boundary layers and the freestream velocity in the three facilities range from 5.5 to 22 m, and from to 60 m/s, respectively. Various arrangements for adjustable test section ceilings are employed to generate ZPG boundary layers over the range of momentum thickness Reynolds numbers from 11,000 to 70,000. Oil film interferometry (OFI) is employed to directly measure the wall shear stress, and various sizes of Pitot probes and types of hot-wire sensors are used.

55 Objectives Compare the high Reynolds number, ZPG boundary layers formed in three facilities. Establish a reliable estimate for the accuracy and repeatability of OFI. Evaluate the performance of hot-wire probes with different characteristics and of various anemometer units. Compare the mean velocity profiles measured by hot wires and Pitot probes. Explain differences between overlap region parameters measured by hot wires and Pitot probes; e.g., the value of κ

56 0.8m x 1.2m x 7m Adjustable Ceiling

57 High Re wind tunnel, University of Melbourne Pressure Adjustment Scheme for Test Section 1m x 2m x 27m

58 1.3m x 1.5m x m Adjustable Ceiling

Requirements for Accurate Measurements of Wall Distance in High Reynolds Number Wall-Bounded Turbulence Continuous and accurate monitoring of wall distance.

61 Requirements for Accurate Measurements of Wall Distance in High Reynolds Number Wall-Bounded Turbulence Continuous and accurate monitoring of wall distance. Accurate measurement of velocity near the wall; i.e., minimize probe interference effects. Utilize theoretical, DNS or low Re results to correct wall distance: Linear velocity region; often not accessible. Rely on location for peak in rms velocity. Utilize DNS and low Re experimental data in buffer region; e.g., talk AA00007 by Fransson et al. See also talk BN00004 by Alfredsson et al.

66 U y +

67 20 15 U y +

68 20 15 U y +

69 κ composite mm, S1, uncorrected 0.3 mm, S2, uncorrected 0.3 mm, S3, uncorrected mm, S1, uncorrected 0.51 mm, S2, uncorrected 0.51 mm, S3, uncorrected 0.89 mm, S1, uncorrected 0.89 mm, S2, uncorrected 0.89 mm, S3, uncorrected mm, S1, uncorrected 1.8 mm, S2, uncorrected 1.8 mm, S3, uncorrected 0.3 mm, S1, corrected 0.3 mm, S2, corrected mm, S3, corrected 0.51 mm, S1, corrected 0.51 mm, S2, corrected 0.51 mm, S3, corrected 0.89 mm, S1, corrected mm, S2, corrected 0.89 mm, S3, corrected 1.8 mm, S1, corrected 1.8 mm, S2, corrected 1.8 mm, S3, corrected Re δ *

70 Conclusions See next six talks. Criteria regarding the acceptable tolerance in streamwise pressure gradient for ZPG boundary layers have been better defined. The requirement of direct and accurate measurements of wall-shear has been reinforced, and caution has again been demonstrated for use of correlations based on other experiments, that may not be representative. We have a great deal more to learn from the data we have gathered over last two years and their comparison to other measurements and recent DNS results. The need for turbulence correction for Pitot measurements is an important aspect of continuing efforts within ICET. These turbulence corrections could bring the values of the estimated κ closer to those based on hot-wire measurements in the same boundary layer.

74 CICLoPE Laboratory and facility design features Jean-Daniel Rüedi - ICTP (Working in Forlì)

ZPG TBLs - Results PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs

ZPG TBLs - Results PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs ZPG TBLs - Results PhD defense - Kapil Chauhan Preliminaries ZPG TBLs PG TBLs Logarithmic composite profile Compared with past