Mhwp 2000 PDF

MONTENEGRIN ACADEMY OF SCIENCES AND ARTS

Petar V. Vukoslavevi Dragan V. Petrovi

MMUULLTTIIPPLLEE HHOOTT--WWIIRREE PPRROOBBEESS

MEASUREMENTS OF TURBULENT VELOCITY AND VORTICITY

VECTOR FIELDS

Podgorica, 2000

MONTENEGRIN ACADEMY OF SCIENCES AND ARTS

And the array of seeming disorder, always follow some definite order, (Petar Petrovi Njego in the book The Mountain Wreath, 1847)

___________________________________________________________________ MONTENEGRIN ACADEMY OF SCIENCES AND ARTS

Special Editions Volume 39

Section of Natural Sciences Edition no. 21

Petar V. Vukoslavevi, Dragan V. Petrovi

MMUULLTTIIPPLLEE HHOOTT--WWIIRREE PPRROOBBEESS

MEASUREMENTS OF TURBULENT VELOCITY AND VORTICITY VECTOR FIELDS

Editor Milojica Jaimovi

Podgorica, 2000 _________________________________________________________________________________ _________________________________________________________________________________

AUTHORS

Petar V. Vukoslavevi Montenegrin Academy of Sciences and Arts Rista Stijovia 5, PODGORICA, MONTENEGRO E-mail: [email protected]

Dragan V. Petrovi University of Belgrade - Faculty of Agricutlure Institute for Agricultural Technique Chair of Technical Sciences Nemnajina 6, 11080, BELGRADE ZEMUN, SERBIA E-mail: [email protected];

[email protected]

Reviewers: Prof. Simeon Oka, Institute Vina, Belgrade

Academician Vladan orevi, Faculty of Mechanical Engineering, Belgrade

Prof. Svetislav antrak, Faculty of Mechanical Engineering, Belgrade

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TTAABBLLEE OOFF CCOONNTTEENNTTSS

TTAABBLLEE OOFF CCOONNTTEENNTTSS I NNOOTTAATTIIOONN III

11.. IINNTTRROODDUUCCTTIIOONN 1

22.. TTUURRBBUULLEENNCCEE AANNDD IITTSS MMEEAASSUURREEMMEENNTT 4 2.1 Introduction to turbulence 4 2.2 The aims of turbulence research 5 2.3 Basic operational principles of hot-wire anemometers 6 2.4 Basic operational principles of laser-Doppler anemometers 8 2.5 Hot-wire anemometers and laser-Doppler systems: a comparison review

of the operational properties 10 2.6 Hot-wire anemometers and laser-Doppler systems: competitors

and complements 18

33.. CCOONNSSTTAANNTT TTEEMMPPEERRAATTUURREE HHOOTT--WWIIRREE AANNEEMMOOMMEETTEERRSS:: GGEENNEERRAALL PPRRIINNCCIIPPLLEESS AANNDD SSIIGGNNAALL AANNAALLYYSSIISS 20

3.1 General heat-transfer equations 20 3.1.1 Hot-wire cooling mechanism 20 3.1.2 Heat generation the Joules effect 24 3.1.3 Heat balance equation hot-wires cooling law 25 3.2 Basic principles of constant temperature anemometers 27 3.2.1 Development of constant temperature anemometers 27 3.2.2 Basic elements of CTA feedback circuit 28 3.2.3 Basic steps of CTA set-up procedure 30 3.2.4 The operating point of a feedback circuit 32 3.3 Effective cooling velocity 34 3.3.1 The reference coordinate system for fluid velocity vector 34 3.3.2 Effective cooling velocity for a heated wire 36 3.3.3 The generalised law of hot-wire cooling 40 3.3.4 The cosine law and hot-wire effective cooling angle 41 3.4 A typical CTA experimental set-up 44

II P. V. Vukoslavevi and D. V. Petrovi _________________________________________________________________________________________________________________________

44.. MMEEAASSUURREEMMEENNTTSS OOFF TTUURRBBUULLEENNTT VVEELLOOCCIITTYY FFIIEELLDDSS BBYY MMUULLTTIIPPLLEE HHOOTT--WWIIRREE PPRROOBBEESS 47

4.1 Introduction 47 4.2 Basic types of the probes for velocity field measurements 48 4.3 Hot-wire probes design 51 4.4 Directional sensitivity of a finite-length-wire probe 53 4.5 Hot-wire probes for 3-D velocity measurements 57 4.6 Influence of hot-wire probe dimensions and geometry on

the measurement accuracy and uniqueness domain 64 4.7 Special hot-wire configurations the eight sensor probe 69

55.. MMEEAASSUURREEMMEENNTTSS OOFF TTUURRBBUULLEENNTT VVOORRTTIICCIITTYY FFIIEELLDDSS BBYY MMUULLTTIIPPLLEE HHOOTT--WWIIRREE PPRROOBBEESS 77

5.1 Vorticity 77 5.2 Spatial resolution of the probes 80 5.3 Measurement of longitudinal vorticity component 90 5.4 Measurement of two cross-stream vorticity components 101 5.5 Simultaneous measurements of two cross-stream vorticity components 104 5.6 Simultaneous measurements of three vorticity components 107

66.. OOPPEERRAATTIIOONNAALL CCHHAARRAACCTTEERRIISSTTIICCSS OOFF TTHHEE VVOORRTTIICCIITTYY--TTYYPPEE AANNDD HHOOTT--WWIIRREE PPRROOBBEESS SSPPEECCIIFFIIEEDD FFOORR VVEELLOOCCIITTYY MMEEAASSUURREEMMEENNTT 127

6.1 Measurement accuracy of the mean statistical parameters of turbulence velocity field 127

6.2 Relationships between the higher-order velocity moments 140 6.3 Minimisation of the sampling frequency and time 144

77.. GGEENNEERRAALLIISSEEDD NNUUMMEERRIICC PPRROOCCEEDDUURREE 151 7.1 Equations governing the hot-wire cooling 151 7.2 Data reduction for triple and four-wire probes 155 7.3 The algorithm for twelve-sensor probes WP-12+/q(G) 161 7.4 The procedure for two-sensor probes 166 7.5 Possible advances of the generalised numeric procedure 168 7.5.1 General principles 168 7.5.2 Dual directional generalised numeric procedure for quadruple probes 170

88.. CCOONNCCLLUUSSIIOONNSS 177

99.. RREEFFEERREENNCCEESS 180

NNOOTTAATTIIOONN Numbers in brackets indicate sections in which quantities are defined or first used. A, Ai calibration constant (3.1.3-A), constant in a polynomial fit (3.1.3-Ai) a, aT hot-wire overheat ratio [a=R/Rf] (3.1.1-a), [aT =(T-Tf)/Rf)] (3.1.1-aT), half-axis

of an offline contraction that describe hot-wire response (4.4) a1-a5 calibration coefficients of hot-wire cooling law (3.3.3), (6.2) a1H-a5H, a1V-a5V calibration constants for hot-wires placed in a horizontal and vertical

planes, respectively (3.3.3), (7.1) ai1-ai5, ai,j1-ai,j5 calibration coefficients of generalised cooling law of hot-wire no. i

(7.2-ai1-ai5), included in array no. j=1,2,3 of vorticity probe (7.3-ai,j1-ai,j5) B calibration constant of hot-wire cooling (3.1.1), (3.1.3), binormal coordinate

axis in a local coordinate system of hot-wire (3.3.1) B, N, T binormal, normal and tangential axis of wire local coordinate system (3.3.1) b constant in hot-wire cooling law (3.3.2), half-axis of an offline contraction

describing wire response (4.4), channel half-width (5.2) bm, b1-b3, nm, n1-n3, tm, t1-t3 transformation coefficients between the fluid velocity

components U, V, W in a space-fixed Cartesian coordinate system and components Un, Ub, Ut in a local system of hot-wire, where m=1,2,3 (3.3.3)

bn, bin polynomial constants of 3-D generalised cooling law for i-th hot-wire, where n=1,2,3,4,5 (7.1)

bi,jn, bi,j1-bi,j5 polynomial constants of 3-D generalised cooling law for wire no. i=1,2,3,4 included in array no. j=1,2,3 of vorticity probe, where n=1,2,3,4,5 (7.1),(7.3)

0b , 0n , 0t unity ort-vectors of B, N, T axes in a local cooridnates of a hot-wire (3.3.1) C calibration exponent (3.1.1) Cij1-Cij6, Cijl calibration constants of i-th sensor in j-th array, where l=1,2,3,4,5,6 (5.6) C0, C0j geometrical centre of a multiple hot-wire probe and its array no. j=1,2,3 (7.3) c sound velocity (3.1.1), specific heat of hot-wire material (3.1.3), half-axis of

an offline contraction that describe hot-wire response (4.4) cp, cv specific heat of a fluid under constant pressure and volume (3.1.1) c1-c6, cjk generalised constants of hot-wire cooling law, where j=1,2,3,4,5,6 denotes

a sequential number of a constant, while k=1,2,3 designates a sensor (3.3.3) D hot-wire diameter (3.1.1), probe sensing volume diameter (4.2) D1, D2, D3 sleeves diameter, prongs diameter and stem diameter (3.3.2) D+,Dq diameter of a front sensing area of plus and quadrate probe (4.7) E, E voltage drop along the hot-wire (3.1.2) and its time-averaged value (3.4) Ei, Eij anemometer output voltage of the i-th sensor of velocity hot-wire probe

(5.6-Ei), or i-th sensor of j-th array of the vorticity probe (7.3-Eij)

IV P. V. Vukoslavevi and D. V. Petrovi _________________________________________________________________________________________________________________________

EQI amplifier offset voltage in constant-temperature anemometer (3.2.3) E0 output electrical voltage of a constant temperature anemometer at flow

velocity (3.2.2) and at zero-velocity (3.3.4) E1, E2 characteristic electrical voltage in the branches of Wheatstone bridge (3.2.2) EAC, EBD characteristic voltage drops of a Kovasznay probe (5.3) e calibration constant in a hot-wire cooling law (3.3.2) e, e0 fluctuating part of voltage drop E along hot-wire (3.4) F convection cooling heat flux from a heated wire to the surrounding flow

(3.1.1), flatness factor (4.7) VF)E,E,E,V(F 321 characteristic criteria function (5.6) 0jj E,W,V,UF characteristic response functions of j-th hot-wire (j = 1,2,3) of a probe specified for measurements of fluid velocity vector (5.6) 001 j,iii E,VF , 003 j,iii E,VF characteristic criteria functions for the hot-wire array no. j=1,2,3 of vorticity hot-wire probe, if the vertical wire no. 1 or no. 3 (respectively) are used (7.3)

Flow(V)F1(V), Fhi(V)F3(V) criteria functions for hot-wire no. 1 or 3 used (5.6) FU, FV, FW skewness factors of probability density distribution functions of longitudinal

(streamwise) U, transversal (normal) V and lateral (spanwise) W velocity fluctuations, respectively (4.7)

fS, fSLIM sampling frequency and its limiting value (6.3) f temporal sampling frequency fS criterion 3Uf (6.3) fS a searching step of sampling frequency in optimisation procedure (6.3) Gr Grashof number [ 232 /TTDg f ] (3.12) GS gain of a bucking-up amplifier (3.4) g gravitational acceleration (3.1.1) h convection heat-transfer coefficient (3.1.1), calibration constant in hot-wire

cooling law (3.3.2) hP, hS prongs separation (4.5- hP), wires separation of a parallel-wire probe (5.2-hS) hi, hij calibration constant of hot-wire no. i (5.3- hi), in the j-th array (5.6- hij) I, I0 intensity of electrical current through hot-wire (3.1.2-I), feedback current of a

constant temperature anemometer (3.2.2-I0) and electrical current passing through the prongs of Kovasznay probe (5.3-I0)

I1, I2 electric current passing through the branches of Wheatstone bridge of a constant temperature anemometer (3.2.2)

i , j , k ort-vectors of x, y, z axis in a space-fixed Cartesian coordinate system (3.3.1) Kn Knudsen number [/D] (3.1.1) Kij1 - Kij6 calibration constants of the sensor no. j in the i-th array (5.6), (7.3) of a

vorticity probe with nine or twelve hot-wires k amplifier gain (3.2.4), calibration constant in hot-wire cooling law (3.3.2) ki,j1- ki,j5, k1,j1,-k4,j5 calibration coefficients of generalised cooling law hot-wire no.

i=1,2,3,4 included in array no. j=1,2,3 (7.3) L, LC, LS active sensing length of hot-wire (3.1.1-L), length over which supports

affects the temperature distribution along hot-wire (3.3.2-LC), sampling length SS fUL 2 (6.3-LS)

M calibration constant (3.1.1), grid mesh dimension (5.6)

MULTIPLE HOT-WIRE PROBES V __________________________________________________________________________________________________________________________

Ma Mach number [U0/c] (3.11) m mass of hot-wire sensor (3.1.3) N calibration constant (3.1.1), measuring error of turbulence parameter (6.3) NCD % of non-converged data (5.6) Nu Nusselt number [ f/Dh ] (3.1.1) P heat-flux induced in hot-wire by Joules effect (3.1.2), pressure (5.1) Pr Prandtl number [ fp /c ] (3.1.1) p, q calibration exponents (3.1.1-p, q), pressure (5.5-p) Q2, Q4 roots introduced in 3-D procedure (7.2), or its 2-D variant (7.4) R, Rf hot-wire electrical resistance at operational temperature T (3.1.1-R) and at

fluid temperature (3.1.1-Tf) RH, RV residual term in the generalised hot-wire cooling law of a sensor placed

in a horizontal and vertical plane (7.1) RK,RP, RT ,RSW resistive elements in a constant temperature anemometer (3.2.2)

resistance of adjustable potentiometer in a Wheatstone bridge (3.1.3), residual in the generalised cooling law of vertical hot-wire (7.1)

Ri residual term in the generalised hot-wire cooling law of a sensor of a probe specified for fluid velocity measurement (7.2)

Ri,j, Ri,jP, Ri,jS residual terms in the generalised cooling law of vorticity probe sensor, where i=1,2,3,4 denotes hot-wire and j=1,2,3 is for array (7.3)

R0 hot-wire electrical resistance at referent temperature T0 (3.1.1) R0 equivalent electrical resistance (3.2.4) R1, R2 resistances of fixed resistive elements in a Wheatstone bridge of a constant-

temperature anemometer system (3.2.2) Re Reynolds number [ /DU 0 )] (3.1.1-Re), defined according to

diameter of a wake cylinder (5.4-Red), grid mesh dimension M (5.6-ReM), boundary layer thickness (5.6-Re), momentum thickness (5.2- Re), friction velocity u (5.2- Re)

S hot-wire surface (3.1.1), prongs separation (3.3.2), skewness factor (4.7) SU, SV, SW skewness factors of a PDFs of U, V W velocity fluctuations (4.7) Sx skewness factor of longitudinal/streamwise x vorticity PDF (5.6) S1 length of hot-wire prongs (3.3.2) s virtual length of hot-wire sensor (4.4) T, T0 operational and referent temperature of a hot-wire sensor (3.1.1) TF, Tf film temperature [TF=(T + Tf)/2] (3.1.1), fluid temperature (3.1.1-Tf) t, tS, tSLIM time (5.1-t), sampling time (6.3-tS) and its limiting value (6.3-tSLIM) tS a searching step of sampling time in optimisation procedure (6.3) U, V, W longitudinal/streamwise, transversal/normal and lateral/spanwise fluid

velocity vector components in the x,y,z-axis directions of a Cartesian space-fixed coordinate system (2.5),(3.3.1), hot-wire inner energy (3.1.3-U)

UN, UNe total normal component of fluid velocity vector 0U , perpendicular to hot-wire axis [ 222 bnN UUU ] (3.1.3-UN), and its effective value (3.3.2- UNe)

UNi,UN1-UN4 fluid velocity components orthogonal to hot-wires no. i=1,2,3,4 (5.3) UN0 component of instantaneous fluid velocity vector in the measuring direction

of laser-Doppler anemometer (2.4)

VI P. V. Vukoslavevi and D. V. Petrovi _________________________________________________________________________________________________________________________

Ub, Un, Ut, binormal, normal and tangential component of an instantaneous fluid velocity vector 0U in a local coordinate system of hot-wire (3.3.1)

Ue, UeG, UieG hot-wire effective cooling velocity (3.1.3-Ue) and its generalised form VWaUWaUVaWaVaUUeG 54321

2222 (6.2-UeG), (7.2-UieG), where indices i denote sensor number (7.4-UieG)

Uei, Ueij effective cooling velocity of i-th wire (4.5-Uei), in j-th array (5.6-Ueij) Ue1-Ue4 effective cooling velocity of wire no. 1,2,3,4 of quadruple probe (4.5) Uk, Ui fluid velocity components in tensor notation, where k = 1,2,3 for U, V and W

component in a Cartesian coordinate system (5.1-Uk), (5.5-Ui), respectively Ui, Vi interpretted values (in a 2-D generalised numeric procedure) of U, V

velocity components, which correspond to i-th iteration cycle (7.4) U0, V0, W0 magnitude of a fluid velocity vector 0U (3.1.1-U0), components U, V, W of

the flow velocity vector at probe centre (5.3-U0,V0,W0) Uij, Vij, Wij components U, V, W of the flow velocity vector at the centre of hot-wire no.

i=1,2,3,4 of j-th array, where j=1,2,3 (7.3) U1-U4, V1-V4, W1-W4 magnitude of a fluid velocity 0U (3.1.1-U1-U4), components U, V, W

of a flow velocity at the centre of hot-wire no. 1,2,3,4 (5.3) U1eG-U4eG, Ui,jeG, U1,jeG-U4,jeG generalised effective cooling velocity of hot-wire no. 1,2,3

and 4 of a quadruple probe (7.2-U1eG-U4eG) and of sensors no. i=1,2,3,4 included in array no. j=1,2,3 of vorticity probe (7.3-Ui,jeG, U1,jeG-U4,jeG)

U0s orthogonal projection of an instantaneous fluid velocity vector 0U in a plane of the hot-wire prongs (3.3.1)

U0i,V0i,W0i longitudinal/streamwise, transversal/normal and lateral/spanwise velocity component at the centre of i-th array (i=1,2,3) of vorticity probe (7.3)

U01, U02 longitudinal/streamwise component of a fluid velocity, calculated using different sensor combinations of four hot-wire probe (5.3)

U free-stream (undisturbed flow) velocity (5.3) u, v, w instant fluctuations of velocity components in Reynolds decomposition (5.2) u0, v0, w0 instant fluctuations u, v, w at the centre of hot-wire probe (5.3) u1, u2, u3 instant fluctuations u, v and w in tensor notation (5.2) u friction velocity [ wu ] (5.2) U, u velocity difference between two normal parallel hot-wires, separated at y

(5.2), characteristic velocity difference across a free shear layer (5.4) Ui,jP, Vi,jP, Wi,jP differences between fluid velocity components U, V, W acting on the

probe measuring volume centre C0 and that at the centre of i-th (i=1,2,3,4) sensor included in array no. j=1,2,3 (7.3)

Ui,jS, Vi,jS, Wi,jS differences between components U, V, W acting on the j-th array centre C0j and that at the centre of wire no. i=1,2,3,4 in the same array (7.3)

0U instantaneous fluid velocity vector (2.4) X, Y, Z calibration constants (3.1.3-X,Y), force vector components (5.1-X,Y,Z) x, y, z coordinate axis (or coordinates) in a space-fixed Cartesian system (3.3.1) xi Cartesian coordinates in tensor notation, where i=1,2,3 for x, y and z (5.1) x1, x2, x3 Cartesian coordinates x, y, z in tensor notation (5.2) yi,jP, zi,jP y and z coordinate of the centre of i-th (i=1,2,3,4) sensor of a j-th array

(j=1,2,3) with respect to the probe centre C0 (7.3)

MULTIPLE HOT-WIRE PROBES VII __________________________________________________________________________________________________________________________

yi,jS, zi,jS y and z coordinates of i=1,2,3,4-th sensor centre with respect to the centre of array no j=1,2,3 of multiple vorticity probe (7.3).

y+ non-dimensional distance from the wall [y+ = u/u] (3.3.1) y, y* sensors separation y and its normalised value y*=y/=hS/] (5.2) , i temperature coefficient of electrical resistance (3.1.1-), geometrical angle of

hot-wire (3.3.1-), where indices i denote hot-wire number (5.3-i) e,ei,eij,e1,e2 effective cooling angle of hot-wire (3.3.2-e), no. i=1,2,3,4 (5.3-ei), in

array no j=1,2,3 (5.6-eij), effective cooling angles of X-wires no. 1,2 (3.3.4), 2T coefficient of volume expansion (3.1.1-), uniqueness cone angle (4.4-2T) molecular free path (3.1.1) ijk alternating tensor, where i,j,k = 1,2,3 (5.1) REP(U),REP(V),REP(W) reproduction errors of induced velocity components (7.5.2) Ui, Vi difference between velocity components in two successive iterations (7.4)x measuring error of longitudinal/streamwise x vorticity component (5.3) , I mean kinetic turbulent dissipation rate and its isotropic value (5.2) micro-scale of Kolmogorov [ 413 / ] (3.1.1), (5.2) momentum thickness (5.2), jaw angle (5.6)

0 angle between normal fluid velocity component nn UnU 0

(in a local hot-

wire coordinate system) and component sU 0 in the prongs plane (3.3.1) effective value of angle 0 (3.3.2) f fluid thermal conductivity (3.1.1) , , fluiddynamic (3.1.1), kinematic viscosity (3.1.1) and density (3.1.1) , pitch calibration angle of hot-wire probe (2.5) and its step (3.3.4)

0 angle between a fluid velocity vector 0U and its component

000 bUnUU bns in the plane of hot-wire sensor prongs (3.3.1)

angle between a fluid velocity vector 0U and normal (i.e. its total normal component NU ) to hot-wire axis of symmetry (3.1.1), (3.3.1)

e effective hot-wire cooling angle (3.3.4) w wall shear stress (5.2) i vorticity components in tensor notation, where i=1,2,3 for x, y, z (5.1) x, y, z vorticity components in a space-fixed Cartesian coordinate system (5.1) x+,y+,z+ normalised non-dimensional vorticity components (5.6)

x y z mean (time-averaged) components of vorticity vector (5.1)x, y, z fluctuating parts of a vorticity vector components x, y and z (5.1) (tS,fS) general designation of a turbulence statistical parameter (6.3)

VIII P. V. Vukoslavevi and D. V. Petrovi _________________________________________________________________________________________________________________________

11.. IINNTTRROODDUUCCTTIIOONN

NNooww II tthhiinnkk hhyyddrrooddyynnaammiiccss iiss ttoo bbee tthhee rroooott ooff aallll pphhyyssiiccaall sscciieennccee,, aanndd iiss aatt pprreesseenntt sseeccoonndd ttoo nnoonnee iinn tthhee bbeeaauuttyy ooff iittss mmaatthheemmaattiiccss.. ((WWiilllliiaamm TThhoommssoonn -- LLoorrdd KKeellvviinn,, 11882244--11990077))

The object of present textbook is the measurement methodology of turbulent velocity and vorticity fields by multiple hot-wire anemometer probes. A detailed general review of scientific contributions in the area of interest is given. Well-known complexity of turbulence and complicated measurements of its parameters limited the manuscript to non-compressible isothermal flows. Within these borders, the influences of hot-wire probe configuration and characteristic dimensions, as well as the influences of numeric signal interpretation procedure and sampling parameters, on the measurement results of turbulence statistical parameters are analysed. The text contains nine chapters, including the list of references, in order to achieve higher comprehend and readability.

General description of the textbook represents the object of the 1-st (current) chapter. It provides short basic information on the books content.

Complex nature of turbulence and basic principles of the two most popular contemporary methods for measurement of its parameters, hot-wire anemometer and laser-Doppler system, are generally described in the 2-nd chapter. In addition, a short comparison review of operational properties of these instruments is provided, together with general recommendations for their application.

The 3-rd chapter describes hot-wire cooling mechanism and functional principles of the constant-temperature hot-wire anemometer, which is the most commonly used for turbulent velocity and vorticity fields measurements. An adequate mathematical background, necessary for clear understanding of this complex phenomenon, is also provided.

From the origin of thermal anemometry, functional characteristics of hot-wire probes have been enormously advanced, especially during the last decade. Primarily, the probe configurations, designed for measurement of turbulent velocity field, became more complex and sophisticated. The old models with two

2 P. V. Vukoslavevi and D. V. Petrovi _________________________________________________________________________________________________________________________

and three hot-wires are substituted with the new generations of quadruple probes with four sensors and quintuple configuration containing five hot-wires. A comprehensive review of existing multiple hot-wire configurations and supporting numeric procedures, specified for fluid velocity measurements, is provided together with information on their applicability ranges in the 4-th chapter. Special attention is paid to four-sensor anemometer probes, which seem to be the most popular configurations for investigation of isothermal turbulent flows of higher turbulence levels. The own configuration with eight wires, which enables direct reliable checking of its spatial measurement resolution, is also presented.

Hot-wire probes, specified for turbulent vorticity field measurements, are presented in the 5-th chapter, as well as the adequate supporting numeric algorithms and fundamental principles of fluid vorticity vectors measurement. Besides the short historical review of their development, starting from the first configuration with four sensors (Kovasznay 1950), the newest configurations containing nine and twelve hot-wires are described in detail. The problem of estimating the probe spatial resolution is also analysed, as well as the existing methods for its resolving.

Although achieve lower measurement accuracy, hot-wire probes designed for fluid velocity measurements are more operationally suitable then the vorticity probes with larger number of sensors and extremely complex signal-interpretation procedures needed to account the gradients over the sensing volume. A comparison review of the most important operational properties of the vorticity probes and configurations specified for fluid velocity measurements is presented in the 6-th chapter. The anemometer probes with twelve, four and two hot-wires are compared, enabling analysis of the influence of neglecting the velocity gradients and/or one of three fluid velocity components on the mean statistics of turbulent velocity field. Thus, information on the influence of probe geometry and number of hot wires on the measurement results of turbulent velocity field is provided. An algorithm for direct estimating the influence of sampling time and frequency on the measured values of mean statistical parameters of the turbulence velocity and vorticity fields is also presented. It reduces the computation time, in comparison to the total-search method of the time-frequency domain, but achieves the same evaluation accuracy of sampling parameters.

The 7-th chapter explains physical and mathematical background of the own unique procedures for evaluation of the calibration constants and signals interpretation of the twelve, four and two hot-wire anemometer probes.

Conclusions, remarks, recommendations and plans for future research work in the area of interest are, as usual, left for the last chapter.

Such sophisticated and voluminous scientific area is covered by analysing results originating from the leading world aerodynamics laboratories, published contributions of other researchers, as well as own experiments performed in the three laboratories: at University of Maryland (USA), University of Montenegro in

MULTIPLE HOT-WIRE PROBES 3 __________________________________________________________________________________________________________________________

Podgorica (FR Yugoslavia) and Friedrich-Alexander University of Erlangen-Nrnberg (FR Germany). Our experience, acquired during extensive collaboration that resulted in Ph.D. thesis of Petrovi 1996a, has also contributed to the content of the textbook. However, this textbook has primarily benefited from the experimental results and research work done in the Fluid dynamics laboratory at the University of Maryland (USA), together with Prof. James M. Wallace.

Laminar separation on a thin ellipse. Source: Bradshaw 1970.

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2.1 INTRODUCTION TO TURBULENCE

Turbulence is an important physical phenomenon. Its name originates from the Greek word "turbo", meaning vortex. Analysis of turbulent flows is very difficult, because they contain the most possible complex forms. The application of ordinary hypothesis (two-dimensionality, stacionarity, non-vorticity), effective in other flows, is not possible here. This is the main reason why turbulence is still one of the very rare problems in fluid dynamics that has not been completely resolved yet.

Turbulence is a rather well known term that characterises a special class of fluid motions. It is not easy to formulate its definition that could cover all details of flow characteristics. Following Hinze 1959, according to Websters "New International Dictionary" turbulence denotes agitation, disturbances, boiling, etc. Unfortunately, this definition is too general and is not quite precise to be completely acceptable. The most of researches believe that completely adequate definition of turbulence does not exist. Even more, some of them claim that this phenomenon can be only described by reviewing its main properties.

Tennekes and Lumley 1978 explained the most important physical properties of turbulence that enable clear recognition of such flows toward the other existing classes of fluid motions. They are listed and shortly discussed in the following text and illustrated in fig. 2.1 by photograph of turbulence initiation, development and dissipation in a free round jet, produced by a flow visualisation technique.

Irregularity. Behaviour of turbulence can be described as accidental in space and time. This is one of the main motives for applying the statistical methods for analysis of turbulent flows.

Diffusivity. Caused by intensive fluid velocity fluctuations, it increases fluid mixing and transfers of impulse, heat and mass.


High values of Reynolds number. Turbulence usually initiates at high Reynolds numbers, as the instability of the laminar flows described through the interaction of the viscous and non-linear terms in the equations of motion. Furthermore, these type of flows fully and the most clearly manifest some of their characteristic properties only at high enough values of Reynolds numbers.

Three-dimensional vortex fluctuations. High-levels of vortex fluctuations represent a typical characteristic of turbulent flows. They can not exist in two-dimensional flows, because the crucial mechanism of vortex generation known as vortex stretching is three-dimensional by its nature. The importance of this property becomes even more clear, having in mind the origin of term turbulence from the Greek word turbo meaning vortex.

Dissipation. In opposite to accidental gravitational and sound waves, turbulence is naturally highly dissipating phenomenon. Viscous tangential stresses are responsible for deformation work that increases the inner fluid energy on the count of kinetic energy of turbulent fluctuations and the mean flow. Consequently, turbulence needs continual supply of energy to the flow, which compensates viscous looses enabling its maintenance. Otherwise, the intensity of turbulence decreases and the flow becomes laminar.

Continuum. Turbulence is a phenomenon of continuum mechanics with typical spatial scales, much greater in comparison to typical dimensions of the molecules and their characteristic scales.

Primarily, turbulence is not a property of fluid, but a property of its flow. At high values of Reynolds numbers, dynamics of turbulence is basically the same for all fluids. General behaviour of turbulence does not depend on the fluid, but on its environment and flow conditions.

2.2 THE AIMS OF TURBULENCE RESEARCH

Extremely complex structure of turbulent flows demands application of sophisticated methods for their research. The chances for final success in resolving any specific problem can not be easily predicted in advance, before detailed analysis is performed. However, the investigation of turbulent flows is of great

Fig. 2.1: Turbulent free round jet.

Source: Van Duke 1982.


scientific and practical interest, because turbulence causes strong changes of the integral flow characteristics. They result in a great increase of the coefficients of mass, impulse and energy exchange. Nowadays, the importance of turbulence researching is recognised worldwide. Turbulent flows are frequently present not only in the nature, but also in the engineering practice.

In some cases turbulence effects are negative, like energy dissipation, heat losses, generation of pressures and aerodynamic forces by turbulent velocity fluctuations, etc. In some other situations, turbulence represents the main source of many useful effects, such as the turbulent transport of heat, mass and impulse, contaminants dispersion, water circulation in nature, etc. These effects usually have not the reversal influence on turbulence, as is the case for a turbulent transport of passive contaminants (temperature, solid particles, etc.). However, interactions between the turbulence and its consequent effects are also present. The effects caused by turbulence sometimes directly influence intensifying or depressing of turbulent flows. The most common examples are heat and mass transfer during the intensive burning that extremely changes physical properties of the fluid, which (from the other side) change characteristics of turbulent flow.

The aim of turbulence researching is to provide information that could enable or improve its control. In some cases, it is useful to initiate turbulence or even amplify its fluctuations, to suppress it in the processes where its effects are negative and balances its influences in the cases where turbulence has mixed effects. Typical illustration of the last case is a thermal apparatus, which needs intensive heat transfer and low energy dissipation.

The most popular theoretical approaches in the area of turbulence research are turbulence modelling and direct numerical simulation. However, using these methods it is not possible to resolve completely the existing problems without direct support of experimentally verified information. Unfortunately, in spite of extensive measurements performed in aerodynamic laboratories worldwide for many years, theoretical methods still suffer from the lack of empirical data, motivating the researches to perform new experiments. 2.3 BASIC OPERATIONAL PRINCIPLES OF HOT-WIRE ANEMOMETERS

At present, only two instruments for true quantitative measurement of the non-stationary fluid velocity fields exist: hot-wire and laser-Doppler anemometer. Hot-wire anemometer is an electronic instrument, primarily designed for measurement of velocity and temperature fluctuations in the non-stationary flows. Its sensors are very thin metal wires of tungsten, platinum, iridium, platinum-rhodium, platinum-iridium alloys, etc., 0.25-10 m in diameter and 0.3-5 mm in length. As it is the case with all conductors of electric current, hot-wire resistance is a function of its temperature. Anemometer probes are most frequently designed with one or two hot-wires, although the last probe versions with larger number of sensors also exist.


Wires are heated by electric current (the Joules effect), and simultaneously cooled mainly by fluid flow of lower temperature (heat convection). Difference between generated and convective cooling heat flux is balanced by the inner hot-wire thermal energy that is directly dependent on its temperature, i.e. electric resistance. Basically, hot-wire anemometer detects heat transfer from a heated element placed in the flow toward its environment. It is sensitive, virtually instantaneously, to any change of the flow conditions that affects the heat exchange between the heated wire and its environment. Therefore, hot-wire anemometry can be successfully applied for measurement of the fluid velocity and temperature, concentration changes in fluid mixtures, phase changes in multiphase flows, etc. Furthermore, some additional important flow properties, like vorticity, can be also measured by sophisticated hot-wire techniques. Following the mathematical definition, vorticity vector components can be evaluated using values of fluid velocity vector components, measured in the proximate flow locations.

Hot-wire anemometers operate in two modes, depending on the way of control-ling the electrical heating current through the sensor. If this electrical current is maintained constant, hot-wire operates in the so-called constant-current mode. In this case, variations of the sensor temperature caused by the flow generate corresponding changes of the wire resistance and voltage drop along its length. Establishing the suitable functional form between the flow properties and sensor resistance enables evaluation of fluctuating flow properties through monitoring the fluctuations of voltage drops along the hot-wire. The constant-current (CC) mode of hot-wire anemometer is used primarily for temperature measurements, when a low-intensity electric current is supplied to the sensor. Under these conditions, hot-

wire sensitivity toward fluid velocity is negligible and hot-wire sensor functions as a simple resistance-temperature device, usually denoted as cold wire.

In the constant-temperature (CT) mode (fig. 2.2), sensor is connected in the electrical feedback circuit that maintains its resistance nearly constant. Having in mind dependence of wire resistance on its temperature, it follows

Fig. 2.2: Constant-temperature anemometers, designed

in the Turbulence Flows Laboratory at the University of Montenegro in Podgorica: - CTA-12, containing twelve channels (up) and - CTA-4ex, possessing four low-noise

electronic measuring circuits (down).


that sensor temperature is also nearly constant. Fluctuations of hot-wire cooling flux are registered as variations of the wire heating current, by monitoring the corresponding voltage drops. The constant-temperature anemometer possesses higher frequency response in comparison to constant-current mode: nearly constant wire temperature in the constant-temperature mode decreases its thermal inertia. In addition, it provides high wire sensitivity to the velocity variations and low sensitivity to temperature changes if the temperature difference between wire and flow is maintained high enough. Therefore, constant-temperature anemometer, as more appropriate, is used almost exclusively for fluid velocity measurements.

The simple measurement principle, together with small measuring volumes of the probes and low costs of these systems, make the hot-wire anemometer very suitable and popular instrument, especially for fluctuating air/gas velocity and temperature measurements. From its origin, estimated to be at the beginning of this century (Comte-Bellot 1976), hot-wire anemometer characteristics have been enormously improved. Sophisticated electronic components with high signal-to-noise ratio, fast dynamic response and high stability toward the changes of environmental temperature (that are not discussed here) have been developed. Anemometer probes are also greatly advanced: in opposite to the first configurations with a single sensor to measure only one (of three) fluid velocity component, the last generation of the probes with nine and twelve hot-wires is capable of simultaneous measurement of three-dimensional fluid velocity and vorticity vectors. Besides these complex configurations, a variety of other hot-wire probes exists, with different dimensions of measuring volumes, numbers of sensors, their dispositions, applied materials, fabrication technologies, etc. 2.4 BASIC OPERATIONAL PRINCIPLES OF LASER-DOPPLER ANEMOMETERS

Laser-Doppler anemometer measures indirectly the non-stationary gas and liquid flow velocities. This instrument registers the phase change of monochrome laser-light, reflected from the tracer that is currently passing through its measuring volume. Term tracer assumes various types of optical inhomogenity within the fluid that trace the flow and provide the reflection of monochromatic laser light of high enough intensity to be registered. In the liquids, the ordinary present impurities can be used as tracers. However, researching of gas flows is more complex, because the introduction of specially prepared liquid or solid tracers is needed. In these cases serious problems may occur. The necessity of tracer presence in the fluid flow which velocity field is measured is one of the main disadvantages of laser-Doppler anemometer. This measuring principle results in the logical question about the reality of fluid velocity representation by the tracers. Also, it suffers from the problems of choosing tracers material, technique for their introducing in the flow, dimensions, quantity, etc.

The velocity of fluid flow and its tracer is very small in comparison to light velocity of 300 000 km/s. This makes impossible direct registration of Doppler


shift of laser-light, caused by tracers movement. The problem was resolved by introducing the indirect differential method in the operational practice. Two laser-beams simultaneously illuminate tracer, while the difference of Doppler shifts is detected on the photo-detector. The resulting frequency is low, and can be registered easily. Furthermore, it is proved that connection between this frequency and fluid velocity is linear in the defined direction.

This connection represents theoretical base of the measurement method of laser-Doppler anemometer. Generation of the characteristic Doppler signal, which is registered by the photo-detector, is usually visualised by the model of interference bars (fig. 2.3b). If the wavelength of both beams is equal, the stationary dark and light bars arise in the intersection zone. They are orthogonal to the plane of the laser beams. The tracer travels through the measuring volume, producing the variations of the intensity of reflected laser light. These variations are registered on the photo-detector as characteristic Doppler signal.

Typical scheme of laser-Doppler anemometer with two beams is sketched in fig. 2.3a. The basic element of the anemometer is laser (1). It generates polarised monochrome light (2). Optical prism (4) forms two laser beams of equal intensities, which are separately modulated in defined frequency by a pair of Brags cells (5). Prisms (6) set-up beams diameters in front of the output lenses (7), which form the elliptical measuring volume (8) (fig. 2.3b). The light-stop mask (9) is mounted in

front of the focusing lens (10). Photo-electric converter (12) and its mask (11) are in the common housing (13). Converted signals are forwarded in the processing unit. Described system measure one component of velocity in the defined direction. Including the additional pairs of differently coloured (in comparison to the first pair) laser beams enable measurement of other components.

9

13

TRACER

U0UN0

U0 tracer velocity UN0 - component in the measuring direction

U0UN0

(a)

(b)

113 4 1

2

6 7 8 10 125

Fig. 2.3: Laser-Doppler anemometer (LDA): (a) a functional scheme,

(b) the measuring principle. Adapted from: Matovi 1988.


2.5 HOT-WIRE ANEMOMETERS AND LASER-DOPPLER SYSTEMS: A COMPARISON REVIEW OF THE OPERATIONAL PROPERTIES

Although the laser-Doppler anemometer is a newer and presently very popular instrument, hot-wire anemometry still represents a very attractive measurement technique for fluctuating flow properties. The last version of quadruple and quintuple hot-wire probes (containing four and five hot-wires respectively) can be successfully applied even in the flows with higher turbulence levels. According to Dobbeling, Leuckel and Lenze 1990a, quadruple configurations enable velocity field measurements of turbulence levels up to about 38%. Furthermore, Holzapfel, Leuckel and Lenze 1994 claimed that their quintuple configuration enables velocity field measurement in the flows of turbulent levels up to around fascinating 66%.

Following Bruun 1995, it is likely that hot-wire anemometer still remains the principal research tool for most of air/gas-flows studies. In addition, for measurements in the flows of low and moderate turbulence levels below ~25%, it seems that hot-wire technique is superior in comparison to laser-Doppler anemometer. Detailed comparison analyses of the typical operational and other technical properties of hot-wire anemometers and laser-Doppler systems is presented in the next few paragraphs of the present section.

Cost. Hot-wire systems are cheap in comparison with corresponding laser-Doppler systems, especially if the latter have to be accompanied with tracers dozing apparatus (air/gas flow studies).

Frequency response. Most of contemporary constant-temperature hot-wire anemometers have flat frequency response from 0 Hz to around 20-50 kHz, except for very low velocities. Furthermore, it is generally accepted worldwide that reliable measurements of up to several hundred kHz (Bruun 1995), and even up to 1 MHz (in supersonic flows, for example) can be performed. However, this general belief was little shaded by recent studies of Saddoughi and Veeravalli 1994, 1996, who pointed out non-adequate hot-wire anemometers response at very high frequencies. Fortunately, this problem originates from the electronic circuits, not primarily from hot-wire measurement principle, and therefore can be resolved by using advanced electronic components and improved anemometers design. In contrast to hot-wire method, their main competitor laser-Doppler anemometer is usually restricted to less than 30 kHz.

Size. Typical hot-wires are 5 m in diameter by 1.25 mm in length, although wire elements as small as 0.25 m by 0.1 mm can be produced using commercially available materials. Typical measuring volume of laser-Doppler anemometer is much greater, around 75 m in diameter by 0.25 mm in length. Sensors of multiple hot-wire probes have to be spatially separated and adequately oriented toward the mean flow, in order to provide directional information, what increases the space needed for their placing. Therefore, sensing volume of multiple wire probes has to


be increased. For example, a typical dimensions of measuring volume of quadruple hot-wire probe, with four 2.5 m tungsten sensors, is 0.5 mm x 0.5 mm x 0.25 mm. Although these dimensions still satisfy the spatial criteria of Wyngaard 1969 (based on Kolmogorov 1941 micro-scale of the smallest structures in turbulent flows) in the most cases of practical interest, in some rare occasions the smaller probes are needed. Recent technological advances enabled fabrication of the quadruple probe with 0.8 m platinum-alloy hot-wires, which sensing volume is much smaller. However, smaller probe dimensions simultaneously increase the sensor and probe fragility, demanding for the probe to be carefully manipulated by the skilful and experienced persons.

Accuracy. Both laser and hot-wire systems, if properly applied, can provide very accurate results. In the carefully controlled experiments, measurement errors can be limited even to 0.1 0.2 %. However, in the practical applications, 1 % accuracy is usually quite acceptable.

Signal-to-noise-ratio. Hot-wire system generates low-noise output signals. A resolution of 1:10000 can be easily achieved. With laser-Doppler anemometer, even 1:1000 is difficult to achieve by present technology (Fingerson and Freymuth 1983). Laser-Doppler measurements sometimes may also suffer from the bias problems.

Range of velocity measurements. Both laser-Doppler and hot-wire systems are effective in a wide fluid velocity range, from very low up to high-speed and supersonic flows. However, in contrast to laser system, compressibility effects may influence the measurement results of hot-wire probe (see Durst, Launder and Kjelstrom 1971 for example).

Simultaneous three-dimensional velocity measurements. From the operational point of view, simultaneous three-dimensional measurements of fluid velocity vectors by laser-Doppler systems are very complicated. Practically, a pair of laser beams is needed for measurement of any fluid velocity component in a specified direction. Simultaneous measurement of two components is possible by two differently coloured pairs of laser beams. They can be initiated by the same emitter unit and easily focused through the same lens to the same measuring location (volume). However, the third velocity component normal to the plane of the first two components needs application of an additional pair of laser beams. They have to be emitted from a different (emitter) position, in the direction orthogonal to directions of the first two pairs of beams, and focused to the same point in order to provide a common measuring volume for all three fluid velocity components. Unfortunately, this can be very complicated to achieve accurately and the most researches simultaneously measure only the longitudinal and transversal components, while lateral (which is usually of less importance) is measured separately, i.e. non-simultaneously with the first two.

Temperature measurements and simultaneous measurements of fluid velocity and temperature. An important advantage of the laser-Doppler technique originates


from its non-sensitivity to changes of fluid temperature. Positive consequences of this laser property are explained in the next paragraph (velocity measurements in the flows with variable temperature). However, its negative side is that laser-Doppler systems do not provide a possibility of temperature measurement. In contrast, it can be successfully measured by hot-wire anemometer operated in the constant-current mode and equipped with hot-wire sensor usually designated as cold-wire or resistance-wire.

Hot-wire technique also enables simultaneous measurement of fluid temperature and velocity fluctuations. In such situations special hot-wire probes are used (see fig. 2.4). Besides the velocity sensors, usually operated in the constant-temperature mode, they contain an additional sensor operating in the constant-current mode (cold-wire). In the case of laser-Doppler system, simultaneous measurement of fluid temperature and velocity is impossible. However, it seems that recently developed technique for in-city collaboration of cold-wire probe with laser-Doppler anemometer (see Heist and Castro 1998) overcomes this problem. Unfortunately, this approach may not be sometimes reliable, because of the cold-wire contamination by naturally occurring particles in the water/liquid measurements, or by seeding particles that have to be introduced in the air/gas flows.

Velocity measurements in the flows with variable temperature. In general, hot-wire readings depend both on the fluid velocity and temperature. If a classic hot-wire probe is applied for velocity measurement it is necessary to maintain nearly constant fluid temperature. Even small temperature changes, of only few degrees centigrade, may produce significant measurement errors of turbulent velocity field, especially if the higher-order statistics is analysed. If these changes are very slow, special probes with elements for automatic temperature compensation of the wire readings are commercially available (see the catalogues of AUSPEX 1994, DANTEC 1996 and TSI 1997, etc.). The other possibility is to measure flow temperature by classic thermometer and using this information digitally correct anemometer output

Fig. 2.4: Triple hot-wire probes,

designed for simultaneous fluid velocity (two constant-temperature sensors) and temperature (a resistance-wire) measurements.

Source: Fiedler 1978.


voltages in the procedure of their interpretation. However, existing correction formulas may not be sometimes reliable, especially in the case of the miniature multiple hot-wire probes. This is the main reason why each of them should be checked carefully for any specified probe configuration and experimental conditions before direct application. Many researchers have extensively studied a variety of different expressions (see Collis and Williams 1959, for example). Among many of them, an expression of Kaneve and Oka 1973 seems to be very suitable for practical applications. However, both automatic and digital compensations of temperature variations are not appropriate for the flows with simultaneous frequent fluctuations of the fluid velocity and temperature. In such cases, special hot-wire probes, each of which contains an additional cold-wire for temperature sensing, have to be used. These hot-wire probes specified for simultaneous velocity and temperature measurements demand an extremely complex and time-consuming calibration: besides the velocity (and directional for the probes with two or more velocity measuring wires) calibration, a temperature calibration is also needed. In contrast to hot-wire anemometers, laser-Doppler readings of fluid velocity are independent on the fluid temperature, what represents an important advantage of this technique in the situations when only flow velocity measurements (without temperature) are needed.

Near-wall measurements. Both hot-wire and laser-Doppler measurements in the vicinity of solid surfaces may be followed by problems. In the case of laser anemometer, tracers may settle down on the wall, especially when they are artificially introduced in the air/gas flow, as is usually the case. When hot-wire anemometer is used close to the wall, two additional effects of wire cooling arise. Besides the heat convection mechanism, which is assumed to be the main process of the heat exchange with environmental flow and included in the wire response equation and calibration coefficients, a radiation between the hot-wire and wall may become significant. This phenomenon changes the wire calibration characteristics, what can produce significant measurement errors. In addition, presence of the sensor in the wall vicinity produces local acceleration, because of the locally decreased free cross-section of the flow. A variety of appropriate methods for digital corrections of the wall influence on hot-wire readings are available (Oka and Kosti 1972, Bhatia, Durst and Jovanovi 1982, etc.). However, all of them include the coefficients that have to be evaluated experimentally, what represents an additional time-consuming process besides the calibration of hot-wire probe.

Air/gas flows a seeding problem. It is likely that hot-wire systems are superior for air/gas flow measurements, in comparison with laser-Doppler anemometers, if the corresponding turbulence levels are below the limits that enable proper application of the chosen hot-wire configuration. The main disadvantage of laser systems is connected with seeding (see Matovi 1988 and Oka and Baki 1996 for example). It originates basically from the velocity difference between a fluid control volume and a tracer that represents its velocity. These differences are


always present to some extent. However, although many extensive experimental studies have been performed in the best aerodynamic laboratories worldwide, an accurate and confident general answer has not been found yet. This problem is important in the air/gas flows, especially if higher-order statistics is analysed, because of the high accurate velocity measurements needed. An additional seeding problem expressed through the non-uniform concentration of tracers (especially in the mixing and recirculation zones) also influences the measurement results. However, it has been established that accuracy of the tracer representation of the flow velocity increases at higher fluid viscosity. Therefore, it follows that measurement accuracy of laser-Doppler increases in the liquid flows. In addition, it also raises in the high-temperature air/gas flows, because the viscosity of gases increases with raising their temperature.

Air/gas flows with strong variations of humidity. Hot-wire anemometer is an indirect instrument, which utilises heat transfer information to deduce desired local flow properties. Hence, it has to be calibrated before measurement of the real flow field parameters. However, calibration unit is very often a different device from the test rig where measurements are performed. Therefore, calibration and measuring flow conditions may be different and consequently calibration has to be corrected to account (among other influences) different air/gas humidity. In most of practical applications influence of humidity variations on the measurement results obtained by hot-wire anemometer is negligible. However, in some other situations, when measurements are undertaken in dryers for example, changes of air humidity has to be accounted in the procedure of hot-wire signals interpretation (Schubauer 1935, Larsen and Busch 1980, Durst, Noppenberger, Still and Venzke 1996). In contrast to hot-wire methods, laser-Doppler anemometer do not utilise any heat transfer mechanism but directly measures tracers velocity, which represent a flow velocity at specified location. Therefore, for adequately chosen tracing particles and seeding technique, this instrument is nearly independent on the changes of air/gas humidity in most of practical applications.

Liquid flows. In opposite to laser systems, applications of hot-film probes in the single-phase liquid flows suffer from the several possible problems. Accumulation of deposits on the sensor can be the major disadvantage of hot-wire technique. This contamination problem can be minimised by introducing a filtration unit in the flow. In addition, anemometer probes with larger sensors are less sensitive to contamination mentioned above. A second important problem is temperature contamination by liquid flow, because of the low overheat ratio used. Even small changes of liquid temperature will result in substantial changes of the sensor response characteristics, evaluated by probe calibration. As a direct consequence, a frequent probe calibration has to be done. Following Bruun 1996, most of these hot-wire problems can be resolved by taking special precautions. However, at present, the laser-Doppler anemometer is superior and seems to be more popular for liquid flow studies, especially in the flows where naturally occurring particles can produce the required tracers seeding.


Two-phase flows. Hot-film probes can be used in the flows containing one continuous turbulent phase and distributed bubbles (liquid/gas or liquid/liquid flows). When a bubble hits the film, an interaction will occur between the sensor and the interface between the continuous phase and a bubble. If the bubble is larger than a sensor, this interaction process can be used for signal analysis without serious restriction on bubble concentration. Laser anemometers demand low bubble concentration, due to the requirement of clear optical path. However, in the case of two-phase flows with particles, advantages of laser-Doppler anemometers become clear. Hot-wire systems are not applicable in such situations, primarily because of the probe fragility. Furthermore, very small particles can sometimes produce depositions on the films, which rapidly change their calibration characteristics.

High-temperature flows and combustion. Typical hot-wire probes are specified for application in the cold or weakly heated flows. However, if iridium sensors are used, velocity measurements become possible in the gases which temperature does not exceed 800 0C. For higher temperatures and flows with combustion, the only presently available technique is laser-Doppler anemometry (see Matovi, Oka and Durst 1994, for example).

Measurements in the atmosphere and distant measurements. In opposite to hot-wire anemometers, contemporary laser-Doppler systems enable reliable fluid velocity measurements at distances greater than 1000 m. Typical examples are the atmospheric measurements of air and clouds velocity. However, although hot-wire anemometry does not enable measurement of fluid properties at large distances, if used properly, it also enables sophisticated measurements of the atmosphere air parameters, primarily velocity field fluctuations (Larsen and Busch 1974,1976).

Instruments damage and contamination. Hot-wire probes are very delicate instruments. However, if handled properly (by skilful persons), they can survive within many months or even years. For low-speed airflow studies, the most common case of probe breakage is improper handling by inexperienced operators. Hot-wire breakage can be also caused by its burn-out. This situation arises if the overheat ratio is set (accidentally) too high. Furthermore, this will happen in the ageing process if the sensor works at high overheat ratio setting. In the high-speed flows, probe can be damaged or destroyed due to impact of relatively fine particles. Deposition of impurities, usually present in all flows, on the sensor may change its calibration characteristics. Furthermore, they may reduce the anemometer frequency response. In these situations probe must be re-calibrated or even cleaned and then calibrated. Usually ultra-acoustic agitation is used to remove dust from the sensor. However, all these problems can be avoided by placing the air-filter in the experimental facility. Due to its non-contact measuring principle none of mentioned problems influence laser-Doppler anemometer.

Industrial application. Fragility of hot-wire probes, unstable response characteristics of their sensors and electronic circuits that demand frequent probe calibration, probe sensitivity to dust presence in the flow and variations of fluid


temperature etc., make a hot-wire anemometer not very appropriate instrument for some industrial applications. Of course, some rare exclusions of this rule exist. For example, Durst, Jovanovi and Unger 1997 designed a special flow meter based on hot-wire technique. In opposite to hot-wire anemometer, the most of these problems are not present if the laser-Doppler anemometer is used, making this technique more suitable for most of industrial purposes.

Signals continuity and their analysis. The output of hot-wire anemometer is a continuous analogue signal (electric voltage). Consequently, both conventionally and conditionally sampled signals can be analysed in the time and frequency domain. In opposite this is sometimes a significant problem with laser-Doppler anemometer, which signal is discrete.

Spatial information and measurements of special turbulence properties. Application of two or more spatially separated probes enables measurement of spatial and temporal correlations. If hot-wire rakes are applied in conjunction with conditional sampling, the spatial and temporal development of large-scale structures can be successfully identified within the turbulent flows. Special hot-wire anemometer probes and adequate numerical algorithms for signal analysis enable sophisticated evaluation of turbulent quantities such as intermittence, gradients of turbulent velocity vector components, dissipation rate, vorticity components, etc. In contrast, discrete character of laser-Doppler signals and the problem of accurate positioning of two or more pairs of laser beams at close locations makes its application for measurements of intermittence, vorticity etc., and for providing any spatial information much more complex and sometimes practically impossible. Therefore, in these cases, hot-wire anemometer seems to be more suitable.

Highly turbulent and recirculating flows. The applicability of a typical hot-wire anemometer system with the last version of quintuple stationary probe operated in the constant-temperature mode is limited to non-recirculation flows which turbulence levels do not exceed ~66 %. However, typical hot-wire probes that contain smaller number of sensors are commonly limited more severely: they can be successfully applied for medium or even for low turbulence level flows only. It is evident that any hot-wire probe possesses some critical limit of turbulence level, which define its applicability. Out of this safe area, two possible sources can produce large measurement errors of turbulence quantities. The first source arises if the single-wire or X-geometry probes are applied. These configurations demand neglecting the two or only one (of three) fluid velocity components, what may cause significant decreasing of measurement accuracy. The second type of error, usually designated as rectification error, originates from the axial symmetry of hot-wire sensor. Consequently, the wire element is not sensitive to a reversal of the flow direction, which may easily occur in the flows with high turbulence levels.

Graphical illustration of this hot-wire property, originating from Willmarth 1985, is presented in fig. 2.5. He analysed the response of idealised hot-wire of indefinite length. In such case, only the influence of fluid velocity vector component UN, normal to the wire axis of symmetry, is relevant for its cooling. If the tips of


velocity vectors are fixed in the centre of the (wire) measuring volume, all their tails giving the same wire cooling effect will lie on the cylinder of infinite length (the hot-wire coincides with the cylinder axis of symmetry). It follows that an infinite number of velocity vectors with equal hot-wire cooling effect (giving the same anemometer output voltage) exists. This property restricts the applicability of hot-wire probes. For any number of sensors, signal ambiguity occurs if the attack angle of fluid velocity vector is greater than some critical value of acceptability.

Satisfactory compensation techniques for these errors are not available for stationary probes at the current level of technology development. A flying hot-wire method, analogue to the frequency shift in laser-Doppler systems, may be used for resolving the rectification problem. Various techniques are reported, providing circular hot-wire probe motion (Cantwell 1976, Wadcock 1978, Coles and Wadcock 1979, Cantwell and Coles 1983, Walker and Maxey 1985, Sirivat 1989, Hussein and George 1989 and Hussein 1990). Perry 1982, Hussein 1990 and Panchapakesan and Lymley 1993 generated linear probe motion, while Crouch and Saric 1986 reported flying hot-wire method utilising oscillatory probe motion. Curvilinear bean-shaped motion mechanisms were used by Thompson 1984,1987, Thompson and Whitelaw 1984, Jaju 1987, Al-Kayiem 1989, Al-Kayiem and Bruun 1991, Badran 1993. However, all methods demand complicated traversing mechanisms. Furthermore, corresponding output signal is not continuous (as it is also the case with the laser-Doppler systems). An additional solution for preventing the occurrence of the rectification errors is the pulsed-wire technique. The problem discussed in this paragraph is one of the most serious disadvantages of hot-wire anemometers, in comparison to laser-Doppler systems that are capable of measurement of high-turbulence and recirculating flows.

Flow disturbance. Although very small, hot-wire anemometer probe placed in the fluid modifies the local flow field. However, for aerodynamically well-designed probe, resulting measurement errors should be very small. Also, correctly applied probe calibration procedure mainly incorporates the related flow disturbances in the calibration constants. Still, in some situations even the best hot-

Hot-wire

Tips of fluid velocity vectors

Tails of fluid velocity vectors

Fig. 2.5: Fluid velocity vectors, giving the same

output signal of infinitely long wire (that follows the cosine law), according to Willmarth 1985.


wire probes may significantly modify any flow phenomenon sensitive to disturbances of the flow, such as separation. However, in opposite to any type of hot-wire probe applied, flow disturbance is negligible only if a laser-Doppler anemometer with carefully introduced tracers is used.

Nozzle

Mixing zoneStill ambient air

U0

U

U0

U

V

V

(b) Potential core U0 = const.(a)

Fig. 2.6: A sketch of angular calibration of X-probe: (a) calibration facility; (b)

induced flow velocity vector in the X-probe coordinate system.

Calibration. Hot-wire anemometer is not an absolute instrument, like laser-Doppler system. It has to be calibrated before measurement, in order to evaluate the functional dependence of the anemometer output voltage on the fluid velocity. Inducing fluid velocity fields of known direction and intensity (measured by some absolute instrument such as Pitot dynamic probe with liquid micro-manometer) provides this information. The simplest calibration procedure corresponds to the normal single-wire probe. It assumes only simple velocity calibration - inducing various intensities of fluid velocity vector without changing their direction. Calibration of the probes for two-dimensional or three-dimensional flow fields measurement is much more complex. Besides changing intensity of fluid velocity, the velocity vectors of various directions have to be induced in order to provide the information about the probe directional sensitivity. Simply rotation of hot-wire probe (see fig. 2.6) in the vertical (pitch calibration) and horizontal plane (jaw calibration) simulate various directions of instant fluid velocity vectors. Hot-wire anemometer output voltages are registered for each induced velocity vector. Resulting information pairs (velocity vector and corresponding anemometer output voltages) are used for calibration curve fitting by the least square method, splines, special functions of Bessel, Hermite, Chebyshev, etc. In general, hot-wire probe calibration still introduces some (usually very small) error in the procedure for anemometer signals interpretation. Furthermore, it is a time consuming process, which fortunately can be enormously accelerated if the computer-controlled anemometer circuits are used (see Jorgensen 1996). 2.6 HOT-WIRE ANEMOMETERS AND LASER-DOPPLER SYSTEMS:

COMPETITORS AND COMPLEMENTS Operational characteristics of hot-wire anemometers and laser-Doppler systems,

explained and discussed in the section 2.4, clearly show that these instruments are primarily complementary techniques. Although each method possesses own


exclusive advantages and limitations, a significant number of flows where both instruments can be successfully used exist.

The main hot-wire exclusions, where laser-Doppler systems are easily applicable, are the high-temperature flows with fluid temperature over 800 0C, recirculating and highly turbulent flows and most of two-phase flows with solid particles. However, it should be noted that recirculating and highly turbulent flows could be measured by another two sophisticated methods, known as the flying and pulsed hot-wire techniques. Detailed information of these methods can be found in comprehensive monographs of Freimuth 1992 and Bruun 1995.

Although both hot-wire and laser-Doppler techniques are applicable for liquid studies, laser is usually preferred by researchers because the seeding requirement is satisfied by naturally present fine particles. In addition, problem of the probe fouling in liquids sometimes makes hot-wire anemometry inappropriate in such situations. Laser-Doppler anemometer is also superior for velocity measurements at very large-distances (up to 1000 m and even more, in the atmosphere). However, although represents a newer instrument with many advantages in comparison with hot-wire method, disadvantages of laser-Doppler system (explained in the section 2.4), still make hot-wire anemometers to be more popular instrument for a variety of air/gas flow measurements.

In general, it can be concluded that appearance of the laser-Doppler anemometer has significantly enlarged the area of possible flow measurements. However, in many cases, hot-wire anemometer is still more reliable, accurate and cheaper instrument for real-time measurement of fluctuating characteristics of turbulence, especially in the studies including vorticity, dissipation terms and temperature analysis. These reasons represent the main motives for many researchers in aerodynamic laboratories worldwide to pay special attention for further development of hot-wire anemometers and their probes. Therefore, these two sophisticated techniques are not only direct competitors, but the complementary methods also.

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3.1 GENERAL HEAT-TRANSFER EQUATIONS 3.1.1 Hot-wire cooling mechanism

Operation of hot wire anemometer is mainly based on two mechanisms: hot-wire heating by electrical current (the Joules effect) and convective cooling by surrounding flow. Their physical connection can be established using the important and well known hot-wire property: dependence of the sensors electrical resistance on the temperature. The relation between temperature and electrical resistance can be defined easily for a known wire material, enabling interpretation of fluid velocity fluctuations in terms of fluctuations of voltage drop along the wire, which can be indirectly measured by registration of anemometers output voltages. In the first approximation, which is valid if the temperature difference T-T0 is not too large, hot-wire temperature and electrical resistance can be related by expression

00 T-T+R=R 1 ; = const., (3.1) where R is the wire resistance at current temperature T, R0 represents its resistance at reference temperature T0 and denotes a temperature coefficient of electrical resistance. For the most common wire materials, tungsten and platinum, is approximately 0.004 K-1 in the temperature range 0 - 300 0C.

Characteristic ratio of wire resistance R at temperature T and its resistance Rf at temperature of surrounding fluid Tf is an important operational parameter of hot-wire probe, which determinates the sensor operational temperature T. In the experimental practice it is known as the hot-wire overheat ratio:

fRRa . (3.2)


If the reference temperature T0 is assumed equal to surrounding fluid temperature Tf, temperature difference T - Tf can be directly related to overheat ratio a:

1 aTT f . (3.3)

The higher wire temperature will intensify its cooling flux and therefore increase its sensitivity. However, the wire temperature should be kept under some limit imposed by the oxidation of material used for its manufacturing. For tungsten, this temperature is around 300 0C.

Besides overheat ratio in the form (3.2), it can be also expressed as a function of fluid and wire temperature:

f

fT T

TTa

. (3.4)

In this case, for T0 = Tf,

Tf aTa 1 (3.5) The heat, generated in the wire by the Joules effect, is transferred to its

environment primarily by convection, but also by conduction through the wire supports and radiation. For a sufficient wire aspect ratio (length to diameter quotient L/D), estimated to be around 600, the heat conduction to the wire supports can be completely neglected (Perry and Morrison 1971). Typical hot wires radiate only around 10 % of the energy that would be radiated by the corresponding black body. In the most common operational conditions, radiation flux reaches around 0.1 % of the convective heat cooling flux (Blackwelder 1981). It corresponds to only 0.01 % of the heat generated in the wire by Joules effect (Comte-Bellot 1976) and, therefore, can be also neglected. The only exception of the conclusions based on the previous analysis are the velocity measurements in rarefied gases, where hot-wire convective heat cooling is usually very small. In such cases, as well as in the vicinity of solid surfaces, heat radiation may become dominant in the overall heat exchange flux.

Following the well known Newtons cooling law, convective heat flux from a heated wire toward the surrounding flow can be expressed as

fTTShF , (3.6) where h is the convective heat transfer coefficient, S wire surface that exchanges heat with a fluid of temperature Tf, while T is the wire operational temperature.

Besides the characteristic temperature difference between the heated wire and surrounding flow, convective heat flux depends on the fluid properties, flow regime and hot-wire dimensions. Corrsin 1963 proposed the following general expression


,

cc

,a ,DL Kn, Gr, Ma,Pr, Re,Nu=Nu

v

pT , (3.7)

based on the non-dimensional terms derived by the theory of similarity:

f

DhNu (Nusselt number), (3.8)

DU

Re 0 (Reynolds number), (3.9)

f

pcPr (Prandtl number), (3.10)

cU

Ma 0 (Mach number), (3.11)

2

32

fTTDgGr (Grashof number), (3.12)

DKn (Knudsen number). (3.13)

Formulas (3.7) (3.13) represent some kind of general mathematical model of the hot-wire cooling flux, expressed by convective heat transfer coefficient h, wire diameter D and fluid thermal conductivity f. It is an extremely complex function of many parameters that characterise fluid properties, flow regime and hot-wire sensor. Practically, cooling mechani

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