A novel Infrared Thermography (IRT) based experimental technique for distributed temperature measurements in hot gas flows

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Lorena Walker
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1 QIRT th International Conerene on Quantitative InraRed Thermography July 7-3, 1, Québe (Canada A novel Inrared Thermography (IRT based experimental tehnique or distributed temperature measurements in hot gas lows by M. Gallo*, J. P. Kunsh and T. Rösgen Institute o Fluid Dynamis, ETH Zürih, Zürih 89, Switzerland. *Corresponding author. gallo@id.mavt.ethz.h, tel.: , ax: Abstrat A new experimental tehnique is being developed to overome the drawbaks exhibited by existing tehniques used to perorm temperature measurements in low ields. It requires the insertion into the low o a high porosity grid ormed by a thin eletrially ondutive wire. By measuring the grid temperature distributions with an inrared (IR amera, one an alulate both, the distribution o the onvetive heat transer oeiient and the loal luid temperature. In this paper the physial priniples o the tehnique, the alibration o the IR amera and the experimental proedure will be desribed. As a initial test ase the tehnique is used to measure the luid temperature proiles in a heated ree jet. 1. Introdution The knowledge o the temperature distribution in a low ield an be o undamental importane to understand the underlying physial proesses. Currently, there are several tehniques available whih an be used or suh investigations. Unortunately all o these tehniques are aeted by dierent drawbaks. The temperature distributions in a low ield an or example be reorded by thermoouples. While they are apable o providing quite aurate measurements, the surveys an be quite time onsuming and intrusive. Non-intrusive temperature measurements an be arried out by laser-based tehniques (LIF/PLIF whih are aeted by high equipment ost and general omplexity o operation. The use o inrared thermography to perorm diret temperature measurements in a gas low provides reliable results only in ases o high emissivity suh as in yellow lames or or hot ombustion produts ontaining substanes (CO and H O whih emit in a suitable inrared band. The tehnique to visualize and to measure temperature distributions o a gas low using IR thermography and a high emissivity mesh inserted into the low, was initially proposed by Anderson et al. [1] and Burh et al. []. More reently Cehlin et al. [3] have suggested a variant o the tehnique. They plaed into the low a paper sreen to investigate the temperature ields by means o IR thermography. Although it provides a global view o the temperature ield, the tehnique annot be employed or the exploration o a hot gas low ield. Neely [4] deined the physial and geometri harateristis o a mesh so as to render it resistant to high temperatures. In addition, he investigated under whih onditions the mesh surae temperature depends only on the loal gas temperature. Despite its small upstream inluene, a transverse mesh is responsible or a strong downstream impat resulting both in the ormation o wake strutures and in the alteration o the turbulene levels. In order to make the sensors (meshes desribed in the previous studies less intrusive, a new tehnique has been developed using a planer array ormed by a meandering wire. This wire, whih represents several loops, allows the mapping o the temperature o a hot gas low with an aeptable spatial resolution. Following the basi idea originally proposed by Gartenberg and Roberts [5], the tehnique desribed in the present paper may also be used to measure the distribution o the veloity omponent normal to the plane o the grid. An objetive o the present work is to desribe the basi physial priniples whih govern the new experimental tehnique. Subsequently the alibration proedure o the IR amera and the experimental proedure will be desribed. In order to validate the new experimental tehnique, temperature proiles were aquired in a ree hot jet using the new tehnique and a onventional rake o thermoouples at the same loations.. Heated grid tehnique This tehnique allows to perorm measurements in a plane o both the temperature and the main veloity, i. e. the veloity normal to the plane. It requires the insertion into the low ield o a very high porosity grid (the sensor, normal to the main low diretion, ormed by a thin eletrially ondutive wire having high thermal emissivity. The sensor surae temperatures are measured by means o an inrared (IR amera.

QIRT 1 http://dx.doi.org/1.1611/qirt.1.45.1 Governing equations Eq. 1 represents the energy balane or an annular element o a long solid ylinder (L>>r with internal heat generation (Fig. 1. In this ase the heat is generated as the result o the urrent passage in the wire o the sensor (Joule eet.

Cirular ylinder with internal heat generation d dt r = k r dr dr q G (1 When the solid ylinder is immersed in a luid having a temperature T, the boundary onditions require that the heat lux by

2 QIRT 1 Governing equations Eq. 1 represents the energy balane or an annular element o a long solid ylinder (L>>r with internal heat generation (Fig. 1. In this ase the heat is generated as the result o the urrent passage in the wire o the sensor (Joule eet. Fig. 1. Cirular ylinder with internal heat generation d dt r = k r dr dr q G (1 When the solid ylinder is immersed in a luid having a temperature T, the boundary onditions require that the heat lux by ondution rom the ylinder equals the rate o the onvetion and radiation lux at the surae: k dt dr r = r = h ( T T ; ( r = r T T = Here, h and T are the heat transer oeiient and the temperature at the speiied surae r = r, respetively. By using the boundary onditions above, it is possible to obtain the temperature distribution in the ross setion o the wire: The ratio h r k T qgr = 4h hr + k r 1 r T(r. ( represents the Biot number (Bi whih aptures the relative importane o the ondutive thermal resistane R` = r k and the onvetive resistane R = 1 h. I the Biot number approahes zero, the solid an be onsidered isothermal in the setion normal to the longitudinal axis o the wire and the temperature hange ours primarily at the luid-solid interae. When the Biot number is signiiantly smaller than one, eq. an be rewritten 1. 1 Eq. 3 an be equally obtained by perorming an overall energy balane: q ( π r L = h(πr L(T T G

3 QIRT 1 Fluid Dynamis & Energetis qgr = h(t T. (3 The heat transer oeiient h inludes both, the onvetive (h and radiative (h r heat transer ontributions, Substituting eq. 4 into eq. 3 and imposing h (h + h r = (4 T = leads to Twh qgr = h (T T + h (T T (5 wh r wh with h r σε 4 4 ( T T wh amb =. (6 ( T T wh The temperature T amb is the ambient temperature in ase o unonined lows, while or the onined ones T amb is the bulk temperature T b. Taking into aount the expression o h r (eq. 6, eq. 5 beomes q 4 wh wh amb Gr In absene o heat generation (q G = eq. 7 an be written by setting 4 = h (T T + σε(t T (7 T = Tw 4 4 = h (Tw T + σε(tw Tamb. (8 Subtrating eq. 7 rom 8 the onvetive heat transer oeiient h an be evaluated using the ollowing equation: 1 qgr 4 4 ( T T h = σε wh w (9 ( Twh Tw The sensor temperature distributions obtained by the IR amera relative to the heated ase (q G >, T=T wh and to the un-heated ase (q G =, T=T w allow to evaluate the onvetive heat transer oeiient distribution (h by means o eq. 9. One h is known, eq. 7 or 8 yields the luid temperature distributions T. This inormation an then be used to obtain a distribution o the loal Nusselt number that is urther linked, through King s law, to the loal distribution o the Reynolds number and ultimately the mean low veloity.. Experimental set-up The experimental layout is depited in Fig.. A single Cu-Ni wire with a diameter o.4mm and oated with a very thin layer o high emissivity paint is employed to measure the luid temperature proiles o a ree hot jet. The wire is onneted to a stabilized DC power supply, and the power input to the wire is monitored by preisely measuring voltage drop and urrent. The hot jet is generated by a heater-blower whih reates a jet having a ore with temperatures up to 7 C. The temperature o the heated jet is kept onstant during the tests by means o a PID ontroller that uses the signal o a thermoouple to ontrol the power supplied. A seond PID unit ontrols the blower whih supplies the eletri heater with air. It reeives the input signal rom a volumetri low rate sensor and keeps the volume low rate o the old air supply onstant.

QIRT 1 http://dx.doi.org/1.1611/qirt.1.45 A irular pipe with a diameter (D o 6m is mounted immediately behind the heater in order to reah a ull homogenization o the low onditions at the exit setion.

A 5mm lens is used during the test at a distane o about 1.3m.

4 QIRT 1 A irular pipe with a diameter (D o 6m is mounted immediately behind the heater in order to reah a ull homogenization o the low onditions at the exit setion. The wire temperatures required to evaluate the luid temperature are measured using an inrared amera with a mid-wave inrared (MWIR InSb sensor (3 5μm and 3x4 pixel resolution. A 5mm lens is used during the test at a distane o about 1.3m. To validate the present tehnique the temperature proiles are ompared with those aquired at the same positions and low onditions using a onventional rake o thermoouples o type K..3 Calibration proedure Fig.. Experimental setup The goal o the alibration proedure is to determine a parametri mapping untion whih relates the wire surae temperature to the orresponding Digital Levels (DL o the IR amera. Owing to the small wire diameter and to the distane between the grid and the amera the single wire only partially overs the pixel surae (Fig. 3. The diagram presented in Fig. 4 shows the proile o the DL o the wire heated by the power supply in quiesent air. The dashed line represents the wire DL distributions obtained by reording the maximum digital levels (DL max seen in the pixels rossed by the wire. Although the wire temperature is onstant, the urve exhibits an osillating signature with a onstant period. This behaviour is due to a slight misalignment o the wire with respet to the pixel rows o the sensor. The portion o a pixel overed by the wire hanges with a period dependent on the angle ormed between the wire and the sensor pixel rows. A better (near onstant trend is obtained by summing the DL in the pixel rossed by the wire and the two DLs o the vertial neighbours (see solid line Fig. 4. So a unique value o the DL an be assoiated to eah value o the wire temperature. DL pix Fig. 3. Wire position relative to the pixels o the IR sensor Fig. 4. DL proiles o the heated wire in quiesent air: proile o the maximum DLs (dashed line; proile o the sum o the DLs provided by three neighboring pixels vertially oriented (solid line For the alibration proedure the wire has to be positioned at about 1m rom the nozzle exit, lose to the thermoouple that while providing the signal or the PID ontroller measures the luid temperature (T _TC immediately behind the nozzle exit. The mass low rate is kept onstant by the PID ontroller whih drives the blower used or the air supply to

5 QIRT 1 Fluid Dynamis & Energetis the heater. During the alibration proedure it is neessary to vary the luid temperature while the mass low rate must be onstant. For eah value o the temperature, the DL o the unheated (Q= and heated wire (Q> have to be aquired (Fig.5. The alibration proedure relies on a parametri model (quadrati polynomial with oeiients p k or the relationship between DL and wire temperature T w, ( DL, { } T = (1 w p k An iteration sheme is implemented whih minimizes the error (eq. 11 between the true low temperature T _TC as measured by the thermoouple and the estimated value T _IR, as obtained with the temperature model desribed in setion.1. Indeed the wire temperatures or the old T w and heated ase T wh, evaluated by eq. 1, are used to alulate the onvetive heat transer oeiient h (eq. 9 and by using eq. 7 or 8 the luid temperature n (i (i = ( { } T _TC T p _IR min ε k i = 1 T _IR. (11 (i The individual alibration wire temperatures T w are obtained by averaging the DLs over the uniormly heated setion o the wire. An example o the resulting DL alibration urve is shown in Fig. 6. DL DL T =11ºC, Q=W T =13ºC, Q=W T =15ºC, Q=W T =11ºC, Q=18W T =13ºC, Q=18W T =15ºC, Q=18W pix Fig. 5. Examples o DL proiles aquired during the alibration proedure T (ºC Fig. 6. Example o alibration urve.4 Experimental proedure or the luid temperature measurements To measure the luid temperature proile it is neessary to aquire the DL distributions or two dierent heating levels o the wire immersed into the low ield. In the ollowing igures both the thermal images (Fig. 7 and the orresponding DL proiles (Fig. 8 are reported. The DL proiles shown in Fig. 8 an be onverted into temperatures by using the alibration urve reorded with the same integration time as the one used or the image aquisition during the atual tests. In this ase the integration time was 6μs, with an assoiated temperature range rom 185 to 5 C. The wire temperature proiles orresponding to the two heating levels are used to evaluate the onvetive heat transer oeiient distributions h (eq. 9 and by eq. 7 or 8 the luid temperature proile is obtained (Fig. 9.

QIRT 1 http://dx.doi.org/1.1611/qirt.1.45 DL Q=W a Q=1W Q=W Q=1W b Fig. 7.Thermal images o the wire: a unheated ase; b heated ase pix Fig. 8.

6 QIRT 1 DL Q=W a Q=1W Q=W Q=1W b Fig. 7.Thermal images o the wire: a unheated ase; b heated ase pix Fig. 8. DL proiles relative to the unheated (solid line and heated ase (dotted line T (ºC m Fig. 9. Temperature proile 3. Fluid temperature measurements The easibility o the heated grid tehnique is demonstrated by measuring the temperature ield o a ree hot jet. The axis o the jet is vertial to ensure ull symmetry w.r.t. its axis. The Reynolds number, based on the diameter D o the exit setion, is 3 and the gas temperature is 3 C. The wire used or the heated grid tehnique is plaed at our dierent heights rom the exit o the nozzle, i.e. at x/d = 3.33, 5., 6.67 and A rake o thermoouples is plaed at the same loations x/d rom the nozzle exit in order to obtain temperature data or reerene. A single integration time is not suiient to establish a alibration urve valid or the whole temperature range o the jet. Hene, the thermal images o the wire have been aquired or dierent integration times depending on the maximum temperature o the jet and thus on the distane rom the nozzle. By means o the dierent alibration urves, orresponding to dierent integration times, luid temperature proiles, with temperatures ranging rom 75 C to 5 C, ould be reonstruted. The results are summarized in Fig.1 showing the temperature proiles obtained using the heated grid tehnique (solid lines and thermoouples (points. The latter are shown or validation purposes. In addition, a urve it using a Gaussian proile was applied to the thermoouple measurements to extrat the basi data haraterizing the aero-thermodynami eatures o the jet. It is learly visible rom Fig.1 that the maximum temperature measured at the enterline o the jet dereases with inreasing distane rom the nozzle exit, while the width inreases. It an be observed or eah x/d that the proiles aquired with the rake o thermoouples and the heated grid tehnique are in good agreement in the region lose to the jet axis, where the temperatures exeed 1 C. In proximity to the jet boundaries the disrepany between both measuring tehniques beomes more apparent, inreasing with the distane rom the nozzle exit. The long integration times required or low temperature measurements and the orresponding redution in the signal-to-noise ratio may be one reason or this disrepany.

7 QIRT 1 Fluid Dynamis & Energetis x/d=8.33 x/d=6.67 x/d=5 x/d=3.33 y/d Fig. 1. Temperature proiles aquired or x/d=3.33, 5, 6.67 and 8.33: heated wire tehnique (solid line; thermoouple measurements (irular dots; Gaussian it o the thermoouple measurements (dashed line..

8 QIRT Conlusions In the present paper a new experimental tehnique or temperature measurements in a hot gas low was introdued. The physial priniples were outlined, and the alibration and experimental proedures were desribed in detail. The temperature ield o a ree hot gas jet was investigated utilizing the new tehnique and onventional thermoouple measurements. The new tehnique ould be validated suessully omparing the temperature proiles obtained by both tehniques. In partiular, or gas temperatures higher than 1 C the maximum error is less than 3%. REFERENCES [1] Anderson R., Hassani V. and Kirkpartik. A., Visualizing the air low rom old air eiling jets, ASHRAE Journal, vol. 33, p. 3-35, [] Burh S., Hassani V. and Penney T., Use o inrared thermography or automotive limate ontrol analysis, SAE paper no Soiety o Automotive Engineers, Warrendale, 199. [3] Cehlin M., Moshegh B. And Sandberg M., Measurements o air temperatures lose to a low-veloity diuser in displaement ventilation using a inrared amera, Energy and Buildings, vol. 34, p ,. [4] Neely A. J., Mapping temperature distributions in lows using radiating high-porosity meshes, Experiments in Fluids, vol. 45, p , 8. [5] Gartenberg E., Roberts S. A., Mapping low ields with a heated wire and inrared imaging system, J. Airrat, vol. 8, p , 1991.

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