R. Monti, G. Zuppardi, A. Esposito - WIT Press · 2014. 5. 14. · Institute of Aerodynamics 'Umberto Nobile', Naples, Italy ABSTRACT An integration of computation and experimental

Measuring the skin friction coefficient by a

computer assisted thermographic technique

R. Monti, G. Zuppardi, A. Esposito

Institute of Aerodynamics 'Umberto Nobile',

Naples, Italy

ABSTRACT

An integration of computation and experimental thermographic technique isproposed as a method for the measurement of the skin friction coefficient in2-D, incompressible, turbulent flows. The method consists in measuring, by anunsteady Computerized Thermographic Technique (CTT), the Stantonnumber distribution on the model surface and scaling down the local Stantonnumber to the skin friction coefficient by a Reynolds analogy factor (St/cf).The not-intrusive feature and the high space resolution of CTT allows thismethod to overcome the shortcomings of conventional techniques. Themethod has been validated on a flat plate at Reynolds numbers per meter(Re/L) of about 7x10$ [m'l] and 2x1 0̂ [nT*], and tested on a NACA 0012airfoil at Reynolds number, based on the model chord (ReJ, of about1.5x10$, in the range of angle of attack 0° - 4°. The results compare favorablywith the measurements taken by the Preston tube and the ones obtained byprocessing, by the Spalding "law of the wall", the local mean boundary layervelocity, taken by a hot wire anemometer.

INTRODUCTION

In the aerodynamic design of an airplane component it is important to knowthe different contributions to the aerodynamic force. The aerodynamic dragbreakdown, in fact, allows the designer to evaluate the relative importance ofeach contribution and therefore to improve the aerodynamic configuration ofthe component under study.

The skin friction drag coefficient is computed by the surface integration ofthe local skin friction coefficients (ĉ); its correct computation requires precisemeasurement of the skin friction at large number of measurement points. Still

Transactions on Modelling and Simulation vol 5, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X

516 Computational Methods and Experimental Measurements

today the skin friction measurement techniques are complex (Winter [1]) andnot used in routine operations. Typically: 1) the Preston method, that iscurrently the most widely used, and the other techniques, based on themeasurement of the boundary layer velocity profile, are intrusive and canprovide measurement only at comparatively small number of points. 2) Thedirect measurement techniques, in addition to the above mentionedshortcomings, need very small floating elements and very accurate straingauges (sensitive to very small forces) and imply complex instrumentedmodels. 3) Oil or liquid tracers techniques overcome the limitation of the finitenumber of measuring points, but are partially intrusive and need some care ofthe test environments. They rely, in fact, on the measurements, by aninterferometric technique, of the oil or liquid film thickness and are rather

qualitative.The purpose of the present paper is to propose an integration of

computation and experimental thermographic (TG) technique as a method forthe measurement of the skin friction coefficient in 2-D, turbulent,incompressible flows that can overcome the above mentioned shortcomings.The method consists in: i) measuring- the Stanton number (St) distributionover the model surface and ii) relating the local Stanton numbers to the skinfriction coefficients (%) by a Reynolds analogy. Three different formulationswere considered to compute the skin friction from the Stanton nurnber.Inorder to select the most suitable one, a computer code, based on a 2-D,incompressible inviscid/viscous flow interaction, was written to implement theReynolds analogy formulations and therefore to compute the local factor St/CpOf course, in order to realize an integrated computational/experimental TGmethod, operating in real time, the code has to run on the same personalcomputer interfaced with the TG equipment. Thus both the solution of theflow field and the Reynolds analogy formulations had to rely on simple andfast computational methods.

Monti and Zuppardi [2] already proved that an unsteady ComputerizedThermographic Technique (CTT) is a powerful tool for the accuratemeasurement of the Stanton number by taking measurements of thetemperature time profile of the model surface during heating or cooling. Thenot-intrusive feature and the high space resolution of CTT enable theproposed method to overcome the shortcomings of the conventional skinfriction measurement techniques.

The paper describes: i) the Reynolds analogy formulations, 11) theexperimental equipment and the test procedure, Hi) the numerical code tocompute the Reynolds analogy factors.


Computational Methods and Experimental Measurements 517

The method has been tested successfully in two flow conditions: 1)isobaric flow fields (i.e. on a flat plate) at Re/L of about 7x10̂ [m"l] and2x1 06 [m'l], in order to check the accuracy and to evaluate the effect of theReynolds number. Both Stanton number and skin friction distributions agreereasonably well with the ones reported in literature. 2) Adverse pressuregradient flow fields, at the same Reynolds number, in order to evaluate theeffect of the pressure gradient. Tests have been performed on a NACA 0012airfoil model in the range of angle of attack 0° - 4° at Rê of about 1.5xl(RUnfortunately comparison data on the airfoil model are not available inliterature at the present experimental test conditions. In any case skin frictioncoefficients by the present method agree with the ones measured by thePreston tube and the ones obtained by processing, by the Spalding "law of thewall", the local mean boundary layer velocity, taken by a hot wireanemometer.

REYNOLDS ANALOGY FORMULATIONS

The Reynolds analogy correlates, in 2-D flows, the Stanton number with theskin friction coefficient. Its classical formulation "St=c/2" refers to: i) laminarflow, ii) unitary Prandtl number (Pr=l), iii) isobaric flow field, iv) isothermaltemperature surface.

There are several formulations of the Reynolds analogy that remove all orsome of the above mentioned assumptions and extend the St(cf) relations toturbulent flows. The formulations by Christoph et al.[3], by Gerhart andThomas [4] and by Tetervin [5] are particularly interesting for theexperimental conditions addressed by this paper. These formulations are basedon quite different theoretical approaches.

1) The Christoph et al.[3] formulation reliqs on the integration of thecontinuity, momentum, and energy balance equations across the boundarylayer. Christoph started from the "mixing length" theory to define theturbulent heat and shear stress and evaluated the following expressions for thelaw-of- the-wall velocity and temperature correlations, respectively:

ay* Ky+

where the symbols have the following meanings:



dpldr\ is the pressure gradient along the flow direction and K is the Von

Karman constant (K=0.4).By means of equations (1) and (2), Christoph integrated the continuity,

momentum, and energy balance equations across the boundary layer, andprovided a system of two total differential equations in the Stanton numberand in the skin friction coefficient, to be integrated along the body surface.This formulation fails as the law-of-the-wall fails, namely when the pressuregradient: i) is favorable (because of a possible flow re-laminarization), and ii)is very strong adverse. This formulation requires the knowledge of theturbulent Prandtl number (Pr̂); a value of 0.9 for P% (Christoph et al.[3]) hasbeen assumed in the following computations. By the integration of theequations (1) and (2), along the direction y normal to the wall, it is possiblealso to compute the boundary layer thickness 5. This equals the integrationvariable y, when the velocity u equals the local inviscid value (u=u@).

2) The Gerhart and Thomas [4] formulation provides an analyticalcorrelation between the Stanton number and the skin friction coefficient. It isbased on the so called "surface renewal and penetration" model. This modelassumes that vortical macroscopic elements of fluid (eddies) move, in anintermittent way, from the turbulent core in the boundary layer to the wall.The heat is exchanged by diffusion, as the eddy is in contact with the wall. Theeddy transport process is governed by the unsteady, one-dimensional (alongthe direction y normal to the wall) momentum and energy equations. Theseare integrated by assuming that: i) convective transport is negligible, ii)unsteady molecular transport occurs when the eddy is in contact with the wall,iii) the properties of the fluid are constant in the eddy, iv) the eddy is semi-infinite in the transverse direction.

The Reynolds analogy formulation reads:

a-^-i(3)

where: K = -vlpjldpldr\.Computation of the Stanton number requires an independent evaluation of

the skin friction coefficient.3) The Tetervin [5] formulation is quite general because it can be used

both for incompressible and compressible flows. It relies on the integration ofthe total enthalpy balance equation across the boundary layer. Energy transfer



is due only to conduction and viscosity. It is computed as the sum of theproducts of: i) conductivity and temperature gradient and, ii) the local velocityand local shear stress. Integration of the enthalpy equation yields an analyticalexpression of the Reynolds analogy factor. To obtain numerical values for theReynolds analogy factor, the shear stress, the energy transfer and the velocitydistribution laws across the boundary layer must be known. Tetervin assumed,in dependence of the pressure gradient sign, different expressions for theabove said distributions. More specifically, for zero and adverse pressuregradient flows (that are of concern for the present test conditions): i) both theshear stress and the energy distributions are approximated by a third degreepolynomial, and ii) the velocity profiles are approximate by power profiles, allof them as a function of the distance from the wall.

The Reynolds analogy factor is computed by:

(4)

where:p = 8lt^dpldr\\ A = (H-V)/2...H. is. the. boundary, layer, shape, factor.

MATHEMATICAL MODEL FOR THE STANTON NUMBERMEASUREMENT

In incompressible regimes the Stanton number is defined by:

St = 2fi (5)

•The convective heat flux on the outer surface of the wall (%) is computed

by the energy balance equation for a thin skin model of thickness V (Fig.l).If the curvature effects are negligible, this equation reads (Monti and Zuppardi

By assuming that:1) the skin is thermally thin, i.e. the skin is smaller than the characteristic



thermal thickness sj:

(7)

where t is the heating or cooling process time. If, furthermore, the skinmaterial is isotropic, then the derivatives in equation (6) can be consideredconstant throughout the skin thickness;

2) The heat flux is negligible over the inner wall surface (g,=0);3) The test Mach number is very low; the adiabatic wall temperaturepractically coincides with the ambient temperature and with the streamtemperature;equation (6) reads:

The Computerized Thermographic Technique is able to compute % in apre-selected time interval At by the measurement at a distance (by athermographic equipment) of the outer model surface temperature distribution(To) at two times t and t+ At, and by the knowledge of the thermophysicalproperties of the skin material (s, k, c, p). Monti and Zuppardi ([2], [6])describe the details of the numerical approximation to solve equation (8).

This technique can be implemented in two ways according to whether theadiabatic wall temperature (T%w) is higher or lower than the local walltemperature at initial time. In the first case the model, initially at roomtemperature, is injected into a hot air flow. In the second case, considered inthis paper, the model is positioned in the air flow and heated by means of anappropriate heat source: the thermographic observation of the outer wallsurface, after the heat source is switched off, gives the TQ distribution.

EXPERIMENTAL EQUIPMENTS

THERMOGRAPHIC (TG) EQUIPMENTThe TG equipment consists of:1) Thermocamera Agema 880 [7]. The thermal detector is a HgCdTe sensorthat is cooled by liquid nitrogen. The measurement accuracy is 0.07 [C].Thewavelength range of the TG camera is 8 - 12 [jum]. The radiated power fromthe model surface in this range is converted into temperatures by anappropriate calibration. The sampling time for each field point (or area) is ofthe order of 5 [jus]. The spatial resolution of the AGA thermocamera dependson the field of view of the optics.2) A/D Converter AVTORADIO 64/12. This electronic device acquires,digitizes and stores the TG pictures in a 128x128 (12 bits) pixel matrix



N(t,I,J). The digitized thermal pictures are transferred to a computer RAM. Inthe present experiments the model surface viewed on the screen was typically28x25 [cm̂ ], so that each digitized pixel corresponds to a surface model area

of 4 [mm̂ ].3) Personal Computer IBM PS/2 that stores two thermal pictures at times tand t +At for subsequent elaboration.

TG equipment is provided with support computer routines allowing theuser to manage the digitized TG matrices and the Stanton number and the skinfriction coefficient matrices: i) recording/reading matrices to/from the disk, ii)displaying the elements of the matrices, iii) plotting the elements of thematrices along a row and a column, iv) plotting both the temperaturedistributions and the footprints of the Stanton or skin friction coefficient on

the model surface.

WIND TUNNEL AND MODELSThe wind tunnel (open, circular test section) is equipped with two nozzles: 1)the length is 2.4 [m], the diameter is 0.3 [m], 2) the length is 1.4 [m], thediameter is 0.75 [m]. The free stream turbulence level (as measured by aDISA RMS unit 56N10 at the exit of the nozzles) ranges from 1.5% to 2%for the two wind tunnel configurations, respectively. As shown later theseturbulence intensity levels are not critical for test accuracy. On the other handthe aim of the present preliminary tests is just to check the feasibility of the

method.The sketches of the experimental setups for the flat plate and the airfoil

model, are shown in Figs.2 and 3, respectively. Flat plate was tested in thefirst wind tunnel configuration: a tempered glass plate (thickness 5 [mm],length 0.5 [m]) is heated by a 3 KW lamp. The NACA 0012 airfoil model wastested in the second wind tunnel configuration. The model is made of a thinskin of stainless steel (thickness 0.5 [mm]). The span (b) is 0.4 [m] and thechord (c) is 0.2 [m]; the geometrical aspect ratio (ARg) is 2. The modelgeometrical blockage was about 2% at zero angle of attack (a = 0°) Themodel upper surface is equipped by 16 static pressure taps. These taps areevenly spaced along the chord and are 1 [cm] apart. The model was heated byJoule effect, being crossed by an electric current.

The effective model aspect ratio (Aiy and therefore the flow two-dimensionality was increased by means of two square fences (h = 33 [cm]).The effective aspect ratio, as computed by the empirical formula (Hoerner [8])

is:

(9)

This value was considered high enough to satisfy the flow two-dimensionality, also in view of the fact that TG measurements have beenperformed close to the model center line. A qualitative check of the flow two-



dimensionality will be shown later by a map of the skin friction coefficientmeasured on the airfoil model surface.

Both models were provided with a carborundum strip to ensure a turbulenttransition on the whole model surface. The size of the carborundum grainswas 0.63 [mm]. The width of the strips was 20 [mm]. The strips were locatedi) on the leading edge of wing section model, ii) at 3 [cm] from the leadingedge on the flat plate. The outer surfaces were black painted to get a value ofthe surface emissivity close to one. The thermophysical characteristics of bothglass and stainless steel are reported in Table I:

Table I Thermophysical characteristics of glass and stainless steel

Glass Stainless Steel

Density p[kgW 2500 7900Specific Heat c [J/(kgK)] 796 500Thermal Conductivity k [J/(smK)J 0.88 14.6

PRESTON TUBE AND HOT WIRE ANEMOMETERThe skin friction coefficients, evaluated by the thermographic technique, arecompared with the ones:1) measured by the Preston tube. This method relies on a relation between the

wall shear stress


y* - u* +A e**-\-i(faQ (ku+y (fa/T

2 6 24

where y+ and u+ have been already defined, A and k are constants. For thepresent measurements A=0.015, k=0.53227 were used. A simple Newton-

Raphson procedure determines the local value of u^ . Then the shear stress

r^, and finally the skin friction coefficient are computed.

EXPERIMENTAL PROCEDURE

The measurement of the Stanton number is made through the following six

steps:1) Establish a steady flow field past the model and record, in adiabatic thermalconditions, a TG image of the model surface. This temperature practicallycoincides with the adiabatic wall temperature.2)Turn on the heat source and warm up the model until a steady state thermal

condition is reached (7̂ > 7̂ ).3) Turn off the heat source at time t=0.4) Take two TG images N(t,I,J) and N(t +At,I,J), where t is the time elapsedfrom turning off the heat source. This time is necessary to "stabilize" thetemperature profile inside the model thickness. The choice of At is acompromise between the numerical approximation of Eq.8, that calls for asmall time interval, and the thermocamera sensitivity that calls for a sufficienttemperature (and time) difference.5) Process by means of a calibration curve the TG signal matrices N(t,I,J) andN(t+At,I,J) to obtain the corresponding temperature matrices To(t,I,J) andTo(t+At,I,J).6) Obtain the local value of the Stanton number by means of equations (8) and

(5)For the present tests the elapsed time t between heat source switch-off and

the first TG image was typically 25 [s] and 2 [s] for the flat plate and theairfoil model, respectively. The thermographic test times (At) was 25 [s] forthe flat plate and 7 [s] for the airfoil model, respectively. These times satisfythe assumption, made in the mathematical model about the thermal thickness(ST is about 5 [mm] for both the flat plate and the airfoil model). These valueswere found to be not critical. Results obtained with other values of At (20 -30 [s] and 5 - 10 [s]) were practically the same. The above mentioned valueswere selected to standardize the tests and make successful the repeatability of



NUMERICAL CODE TO COMPUTE THE REYNOLDS ANALOGY

FACTOR

The computer code, written to evaluate numerically the Reynolds analogyfactors, is based on a very simple inviscid/viscous interaction procedure, as

described below:1) the local body tangential inviscid velocity (or the pressure coefficient)distribution is computed by the first order source panels method or Douglas-Neuman method (Losito and Napolitano [12]). As well known, the airfoil issimulated by three source distributions that generate on every panel atangential velocity distribution related to three basic flows: a) a =0°, b) at

ot=90°, and c) pure circulatory flow.2) Both the laminar and the turbulent boundary layers are computed by theVon Karman integral equations for the momentum and energy. A routine byRotta [13] was interfaced to the Douglas-Neuman routine. The closurerelations by Eppler for the laminar boundary layer and by Ludwieg-Tillman forthe turbulent boundary layer were used. The skin friction coefficient byLudwieg-Tillman:

C = 0.246 x 10-**"* Rê (12)

was used to compute the Reynolds analogy factors by the Gerhartformulation, equation (3). The shear stress from the Ludwieg-Tillman skinfriction coefficient and the boundary layer thickness by the Christophprocedure were used to compute the Reynolds analogy factor by the Tetervinformulation, equation (4).3) The inviscid/viscous flow interaction is an iterating procedure (Losito andDe Nicola [14]). It consists in simulating the effects of the boundary layer onthe inviscid flow by a non-uniform velocity distribution normal to the bodysurface. Another source distribution is added to the three basic flows by theDouglas-Neuman method in order to take into account of the presence of theboundary layer induced normal velocity. A new tangential velocity isintroduced. The laminar/turbulent transition was imposed at x/c=0.05. Theiteration process is terminated when the lift coefficient reaches a constantvalue. At this point the Reynolds analogy factors are computed.

RESULTS

Validation tests have been performed on a flat plate at Re/L = 7x10$ [m"*]and 2x10̂ ̂ -li Tests have been performed on a NACA 0012 airfoil modelat Rec = 1.5x10$ in the range of angle of attack 0° - 4°.

The Preston tube accuracy requires relatively high ratios of 5/D and lowenough adverse pressure gradients (Patel [9] and Winter [I]) Low Reynoldsnumbers guarantee thick boundary layers. Low angles of attack were tested to



get "small" adverse pressure gradients.The minimum value of Sat the most upstream Preston tube measurement

point was 2.4 [mm] for the flat plate and 1.8 [mm] for the airfoil model. The

related ratios 5 /D are 3 and 3.6, respectively. The pressure parameter A/

reaches a maximum value of about 0.035 at 5=4° and x/c=0. 15. This value islower than the maximum allowable value 0.05 (Patel [9] and Winter [1]).

All the Reynolds analogy formulations provided, for the flat plate, aReynolds analogy factor (St/ĉ ) of about 0.6. Both the Stanton number byCTT and skin friction distributions agree reasonably well with the onesobtained by Blair [15] in flows characterized by five turbulence intensity levels(T%) ranging from 0.25 to 6, see Fig.4, and also with some theoretical results,reported by Blair in the same plot. Both the Stanton numbers by CTT and theskin friction coefficients by the present method (St/0.6) are shown by solidcircles. Stanton numbers and skin friction coefficients by Blair are shown byopen symbols. Theoretical data are shown by continuous lines.

As shown in Fig.5a, b, the agreement of the results by the present methodwith the ones by the Preston tube and by the Spalding law-of-the-wall issufficiently good and rather independent of the test Reynolds number.

For what concerns the incidence of the flow turbulence level, Blair foundexperimentally, on a flat plate, that the Reynolds analogy factor increases withthe turbulence level, according to:

StlCf =0.5(1.18 + 1.37) (14)

The turbulence level does not affect substantially the results of the presenttests, in fact at the maximum value of T (T=0.02) St/cf should be 0.603.

Distributions of the three Reynolds analogy factors on the airfoil modelupper surface at a =2° are shown in Fig. 6. Computed Tetervin analogyfactors are somehow intermediate between the Christoph and Gerhart factors.

The skin friction coefficients on the airfoil model upper surface at a =0°,a =2° and a =4° from the CTT technique and the ones by the Preston tubeand Spalding "law of the wall" are shown in Fig. 7, Fig. 8 and Fig. 9,respectively. Data by the Tetervin scaling factors better fit the Preston tubedata at increasing values of the pressure gradient. Skin friction coefficientsfrom the Spalding law-of-the-wall are not shown in Fig. 9 because of thefailure of the law-of-the-wall due to large pressure gradients. Fig. 10 shows theskin friction coefficient footprint on a strip of the model upper surface at a=2° (i.e. the overall skin friction coefficient distribution along the chord andspan of the model). Two dimensionality of the skin friction coefficient (i.e. theStanton number) distribution appears to be satisfactory in the central part of



the airfoil model.Analysis of the results clearly shows that, in weak adverse pressure

gradient, and incompressible flows, the accuracy of the present method is thesame both for the Preston tube and for the Spalding 'law of the wall'techniques. Because of the failure of these conventional techniques in strongadverse pressure and/or compressible flows, the proposed method is expectedto be an unique skin friction measurement method at these test conditions. Infact, both the accuracy of CTT, in measuring the Stanton number, and thecomputation of the Reynolds analogy factor, by the Tetervin formulation, arenot strongly affected either by the intensity of the adverse pressure gradient orby the flow field compressibility. Another code, solving the flow field past theairfoil, has to be written to take into account the compressibility effects, andto provide reliable values of the boundary layer thickness and the skin friction

coefficient.

CONCLUDING REMARKS

An integration of computation and experimental thermographic technique hasbeen proposed as a method for the measurement of the skin friction coefficientin 2-D, turbulent, incompressible flows in wind tunnel testings.

The technique consists in measuring the local Stanton number distributionon the model surface by a Computerized Thermographic Technique (CTT)and in evaluating the skin friction coefficient by the Reynolds analogy factor(St/Cf), that is computed at the same test conditions.

The preliminary test results indicates that the basic idea of the proposedmethod is sound; it is a valid alternative to the conventional techniques for themeasurement of skin friction coefficient.

The advantages of the method are: i) it is not intrusive, ii) it is simple touse, iii) it provides good space resolution, iv) it provides the c


2. Monti, R, Zuppardi, G. 'Computerized thermographic technique for thedetection of boundary layer separation', in AGARD CP 429, pp.30-1 to 30-15,Proceedings of the Symposium on Aerodynamic Data accuracy andQuality : Requirements and Capabilities in Wind Tunnel Testing, Naples,Italic, 1987.

3. Christoph, G.H., Lessman, RC, White, F.M'Calculation of turbulent heattransfer and skin friction' AIAA Journal, Vol.11, pp. 1046-1048, 1973

4. Gerhart, P.M., Thomas, L.C. 'Prediction of heat transfer for turbulentboundary layer with pressure gradient', AÎ A Journal, Vol. 11, pp.552-554,1973

5. Tetervin, N.'Approximate calculation of Reynolds analogy for turbulentboundary layers with pressure gradient' AIAA Journal, Vol.7,pp. 1079-1085,1969

6. Monti, R. Zuppardi, G.Detecting 3-D turbulent separation regions usingunsteady'thermographic technique', in ICIASF 91,pp. 49-59, Rockwille

(USA), 1991

7. Agema Thermovision 880, Operating Manual, 1987

8. Hoerner, S.' Fluid-dynamic Drag', published by the author, 1965

9. Patel, V.C. 'Calibration of the Preston tube and limitations on its use inpressure gradients', Journal of Fluid Mechanics, Vol.23,pp. 185-208, 1965

10. Bertelrude, A."Preston tube calibration accuracy' AIAA Journal, Vol.14,pp. 98 - 100, 1976

11. Saetran, L.R.'Comparison of five methods for determination of the wallshear stress' AIAA Journal, Vol. 25, pp. 1524-1527, 1987

12. Losito, V, Napolitano, L.G. 'Critical analysis and improvement of thesource panel method. 1'Aerotecnica Missili e Spazio', Vol. 54, pp. 5-12, 1975

13. Rotta, J.C.' FORTRAN IV Rechenprogramm fur Grenzenschichten beikompresssible ebenen und ashsensymmetrichen Stromungen' DFVLR, DLR-FB 71-51

14. Losito, V, De Nicola, C.'A new viscous-inviscid flow interaction method'Proceedings of 1st International conference on numerical methods in laminarand turbulent flows, Swansee, United Kingdom, 1978



15. Blair, M.F 'Influence of free stream turbulence on turbulent boundary layerheat transfer and mean profile development' ASME Journal of Heat Transfer,Vol. 105, pp. 33-40, 1983

LIST OF SYMBOLS

AR: Model aspect ratiob: Model spanc: Specific heat of the skin material or model chordcf Skin friction coefficientCp: Specific heat at constant pressureD: Needle diameterH: Boundary layer shape factor (H = 5 / 0 )k: Thermal conductivity of the skin materialN(t,I,J): Thermographic (TG) output matrixp: PressurePr, Pr̂ : Molecular and turbulent Prandtl numbersq: Convective heat fluxRe: Reynolds numbers, ST. Skin and thermal thicknessesSt: Stanton numbert: Time

T: Temperature or turbulence intensity level (T= Vi? + v^ + ̂ IV)

w,. u^: Local, mean boundary layer and friction velocities

V: Flow velocityx, z: Cartesian abscissas of the model surfacey: Local, normal distance from the walla: Angle of attack8: Boundary layer thicknessAp: Local dynamic pressure£: Emissivity of the model outer surface

£, rj, n: Coordinates of the model surface (see Fig. 1)

6 Momentum displacement thicknessKinematic viscosityStephan-Boltzman constant

Wall shear stress

Subscripts

a: Ambientaw: Adiabatic walli, o: Inner and outer wallw: Wall



Outer surface.

Inner surrace

Fig.l - Model wall coordinate system

TOP VIEW

FLOW

THERMOCAMERA

Fig. 2 - Sketch of the thermographic experimental set up for a flat plate



FLOW

TOP VIEW

SIDE VIEW

FENCE

FLOW

PRESSURETAPS

a& uu

Si

Fig.3 - Sketch of the thermographic experimental set up for a NACA 0012

airfoil model



JUT1.11 * $

10

Fig.4 - Comparison of skin friction coefficient and Stanton numberdistributions on a flat plate from the present method andthe ones by Blair [15]



• b-

1.8Q St / #68# Pmton fuW (Fatal)Preraa

Fis 5 - Skin friction coefficient distribution on a flat plate at*" /-M>«/T ~7Tin5and{b)Re/L = 2xlO^(a) Re/L = 7x10̂ and (b) Re/L



1.28

8.72

8.68.1 .2 .3 .4

Fig.6 - Reynolds analogy factor distributions on the upper surface of aNACA 0012 airfoil model a a =2% Rê l.



IS.8

XZ.0

5.8

68

38

0.8

1

.1

aa«

.2

t ,

.3

^t

4

Hilling

1 :

.5x/

*•*».t t ,

.6c

a en• fnA Prt

t t :

.

r »a»i«to» r.a«0* I*lUinf i

' t :

•toMto (ft*hm


ts.a

12.B

3.8

8.8.1 .2

Fig. 8 - Skin friction coefficient distributions on the upper surface of aNACA 0012 airfoil model at a = 2°, Rec=



15.8

12.8

0 CTT »• Preston Tm&m (?•


[cm I

.5 2.5 4.5 6.5 8.5 18.5 (E-83)

Skin Friction Coefficient Scale

Fig. 10 - Skin friction coefficient footprint on the upper surface of aNACA 0012 airfoil model at a = 2% Rê l.S


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R. Monti, G. Zuppardi, A. Esposito - WIT Press · 2014. 5. 14. · Institute of Aerodynamics 'Umberto Nobile', Naples, Italy ABSTRACT An integration of computation and experimental