Measurement and Calculation of Preform Infrared Heating a first approach

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Heating a first approach

Yannick Le Maoult, Fabrice Schmidt, V Laborde, Mouna El-Hafi, Philippe

Lebaudy

To cite this version:

Yannick Le Maoult, Fabrice Schmidt, V Laborde, Mouna El-Hafi, Philippe Lebaudy. Measurement and Calculation of Preform Infrared Heating a first approach. 4th International Workshop on Advanced Infrared Technology and Applications, Sep 1997, Florence, Italy. �hal-02056160�

MEASUREMEN TAN DCALCULATION OFPREFORMIN FRARED HEATIN G:AFIRSTAPPROACH

Y. LE MAOULT (*), F. M. SCH MIDT (*),

V. LABORDE (*) , M. EL H AFI (*) , P. LEBAUDY (**),

Abstract

In a first step , the goal of the w ork is to obtain an accu rate characterisation of the heat sou rce of the infrared em itter. In a second step , the com p u tation of the view factor betw een the lam p and the p reform has been p erform ed u sing a Monte-Carlo m ethod . Then, an exp erim ental valid ation of the view factor com p u tation u sing qu antitative infrared therm ograp hy has been d evelop ed . This w ork is a first contribu tion to the stu d y of rad iative heat transfer w hich are involved in infrared heating of p reform related to the injection stretch -blow m old ing of therm op lastic bottles.

N omenclature

Bi Biot nu m ber  total Absorp tivity of a sheet

cp Sp ecific H eat of cop p er t Em issivity of tu ngsten

F12 View factor  Wavelength

I Intensity of the cu rrent  H eat flu x

m m ass of a sheet  Resistivity of tu ngsten

Nt Total generation of c Density of cop p er rand om nu m bers

R Resistance  Variance

S Su rface of a sheet  Therm al tim e constant

T Tem p eratu re k therm al cond u ctivity of cop p er U Su p p ly of a lam p h global heat transfer coefficient V Volu m of a sheet

(*) _{ÉCOLE DES MINES d'ALBI, Campus universitaire Jarlard, Route de Teillet, 81013 ALBI CT}

CEDEX 09 (FRANCE)

1. Introduction

Form ing p rocesses of therm op lastic su ch as PET, PVC or PP (injection stretch -blow m old ing, therm oform ing,..) need a heating stage [1, 2]. A tu be -shap ed or sheet-shap ed p reform is heated in an infrared oven above the glass transition tem p eratu re (for PET Tg # 80 °C) in ord er to p rovid e a ru bber -like state before the inflation step . The op tim isation of the heating stage is cru cial. The final thickness d istribu tion of the p rod u ct is d rastically controlled by the initial tem p eratu re d istribu tion insid e the p erform . Besid es, the op tim isation of the oven w ill p erm it to m inim ise the cost of energy. So the p relim inary w ork p resented here d eals w ith tw o p articu lar p oints :

- The characterization of the infrared lam p u sed to heat the p reform (tem p eratu re, sp ectral, and d irectionnal asp ects)

- The interaction betw een the lam p and the p reform (view factor), this last p oint is n ot obviou s w hen the em ission of the lam p is strongly d irectionnal and w hen the rad iant energy interact w ith a sem i- transp arent m ed ia [3].

A typ ical oven w ith blow ing p rocess is show n in figu re 1

2. Characterization of the heat source : the infrared emitter

2.1 p hysical d escrip tion of the lam p

w e u sed a p hilip s lam p w hich is com m only p lu gged in ind u strial ovens. The nom inal p ow er of this sou rce is 300 W. The d ifferent com p onents of this lam p are :

- a sp ecificic d ou ble sp iraled filam ent contained in a tu bu lar enclosu re in qu artz.

- A reflector (p olished alu m iniu m ) fitted on the back sid e of the qu artz, its m ain role is to increase the efficiency of the em itter in the forw ard d irection.

A view of the lam p is show n in figu re 2 :

figure 2

2.2 Tem p eratu re of the tu nsten filam ent.

An electrical setu p has been realized to m ake tem p eratu re m easu rem ent of the filam ent. A variation of the su p p ly U of the lam p is necessary to p lot a cu rve of U versu s I(am p ), this grap h is easily converted to a list of valu e of the resistivity (T) from a w ell-know n relationship

R(T) (T).L(T)

Where L and S are the length and the cross section resp ectively. The variation of the term L/ S versu s T is very w eak com p ared to (T) and can be assu m ed as a constant, then an inverse p olynom ial interp olation based on the d ataset of r from [4] give T = f() w ith T in Kelvins :

T = -5.723e-22

+ 36.58+115.3 (2)

at nom inal Pow er (P=300 W), w e find : T = 2030±50°C

This ap p roach has been also valid ated w ith an op tical p yrom eter. The absolu te u ncertainty of 50 °C is not a d eterm inant factor becau se of a w eak

variation of em issivity betw een 2000 and 2100 °C.

2.3 Sp ectral em issivity

In ord er to m od elize the sp ectral intensity em itted by this kind of lam p , w e have to know accu rately the sp ectral em issivity of the tu ngsten w ire and the transm ittivity of the qu artz tu be. This can be d one by u sing sp ectral d at a of tu ngsten [5].Unfortu nately, to fit a com p lete sp ectra at the right tem p eratu re, (beyond 2.5 µm ), it w as necessary to u se the Dru d e ap p roach w hich is based on electrom agnetic theory. The p articu lar exp ression of this m od el is :



 )0.5464 (T )

 (3)

This relation becom es accep table w hen the w avelength > 3 µm . The figu re 3 show s the the com p ilation of d ifferent characteristics, esp ecially intensity inclu d ing the effect of the qu artz w ind ow :

2.3 Directional em ission

A very im p ortant p oint in oven d esign : an IR sou rce w ith a very strong

d irectionality w ill p rod u ce overheating (hotp oints) on the p reform (w e have to keep in m ind that p olym ers have a very low therm al cond u ctivity, a typ ical valu e is # 0.2 W/ m .K). Another sp ecific exp erim ental setu p has been u sed to stu d y this p roblem : a Si(IR) sensor (p hotod iod e) d escribes a half circle arou nd the lam p and give the integrated intensity for several d irections. The sp ectral resp onsivity of su ch op tical com p onent is lim ited to the sp ectral d om ain 750 to 1100 nm . The resu lts are p resented on figu re 4 for d ifferent cases. It ap p ears that the rep rod u ctibility of the sp atial d istribu tion of intensity is affected after reassem bling the reflector.

This p oint highlights the fact that an op tical op tim ization is necessary to heat p rop erly a p rod u ct:

0 0,2 0,4 0,6 0,8 1 1,2 1,4 -0,5 0 0,5 qualitativ e emiss ion with reflector without reflector with reflector (after reassembling) Lambertian (ideal case) 90° 0° 45° 45° 90° figure 4

3. Interaction betw een the lamp and the preform : Computation of the view factor (first approach : lambertian case)

3.1 Assu m p tions : the su rfaces are gray and u niform . These su rfaces are consid ered as d iffu se em itter s and the geom etrical configu rations are sim p le (rectangu lar sheets) as show n below (figu re 5) :

 O X Z Y S1 S2 a(1) b(1) a(2) b(2) zo xo Emitter : size of the lamp

Receiver the “preform” P2 P1 n(P1) 1 2 r n(P2) n figure 5

The know led ge of the view factor F12 (d im ensionless p aram eter) is a fu nd am ental p oint in rad iative transfer to com p u te the therm al p ow er absorbed by the receiver (2) from the em itter (1); so w e have :

abs F12 emis (4)

bibiliograp hic search [6 / 7] show s that, excep t for sim p le cases w here analytical solu tions are available, m ost configu rations m u st be treated w ith nu m erical m ethod s. As w e show , the Monte Carlo m ethod has been chosen for this test compared to Nusselt’s sphere results. The principle of Monte Carlo m ethod is based on statistical ap p roach ap p lied to integral calcu lation. A generation of rand om nu m bers is p erform ed accord ing to a p articu lar

d istribu tion fu nction. The im p lem entation ru n s on a variou s set of d ata and the p rogram generates p oints belonging to the d ifferent su rfaces (the d istibu tion can be isotrop ic or not for each su rfaces). At least the estim ation of the error is m ad e by variance calcu lation. The resu lts are gathered in a table w hich p resents a com p arison w ith analytical solu tion if p ossible or another nu m erical m ethod s. We tested the follow ing sizes for the com p u tation : Em itter : (8 cm * 1 cm ) / Receiver (3 cm * 20 cm ). At first, w e have tested a non -centered configu ration (Receiver shifted resp ect to the Em itter). The com p arison w ith an analytical solu tions show s that the relative error rem ains w eaker than 2 %; bu t a m ore interesting case is the follow ing : configu ration w here the receiver is inclined resp ect to the em itter (no analytical solu tion available):

 (°) _x0 _z0 d F12 N u sselt’s sp here F12 Monte Carlo rel. error in % 15 0 0 10 0,12034 0,12169 1,1 15 0 0 20 0,04017 0,04005 0,3 30 0 0 10 0,12677 0,12709 0,2 30 0 0 20 0,03918 0,03818 2,6 15 5 5 10 0,07455 0,06482 13 15 8 0 10 0,05043 0,04950 1,8 15 0 5 10 0,11802 0,09765 17,3

The nu m ber of elem ents for the em itter (N u sselt m ethod ) is 150 *150 and N t (statistical generations for Monte Carlo) is 3000 . The Agreem ent is good excep t in tw o cases w here a hid d en su rface p roblem ap p ears.

4. Experimental validation of the view factor computation using quantitative infrared thermography.

4.1 Descrip tion of the exp erim ental setu p (figu re 6) :

The p reform is rep resented here by a sheet of cop p er coated w ith a flat black p ainting (Em issivity = 0.92 betw een 0.5 and 20 m ) and the heater is assem bled w ithou t reflector at nom inal p ow er. The cam era u sed in this exp erim ent is a 880 LW (8-12 m band ) / AGEMA. The frequ ency of analysis is equ al to 25 fram es/ s and the d evice is p lu gged on a 12 bits d ata acqu isition board d rive by a real tim e softw are (PC AT).

4.2 Sim p lified m od el of heat transfer in the cop p er sheet

Exp erim ental p roced u re : the cam era observes the back face of the cop p er sheet w hich has been screened from the rad iant sou rce w ith a p olished alu m iniu m p late. The screen is su d d enly rem oved (H eavisid e step of flu x on the sheet) and the tem p eratu re evolu tion of the sheet is p lotted u p to the stead y state. We m ad e the assu m p tion (w hich is valid ated at the end ) that the heat transfer in the sheet can be treated as a lu m p cap acitance m od el (transient asp ect) so Bi m u st be < 0.1. The averaging equ ation is :

c Vcp dT

dt 2 hgS T





The p ow er em itted by the lam p is know n by the electrical m esu rem ents of U, I so for the stead y state Pelec = em is. = U.I, the solu tion of (5) is

T  _Ta  abs 2 h g S 1 e t 















tem p eratu re is equ al to the am biant tem p eratu re. The tem p eratu re evolu tion of the sheet is p lotted hereafter (figu re 7) :

time

FIGURE 7 :

temperature versus time of the sheet



T

Tf

Ta

initial slope =



F12 = 2.



_

UI

Three configu rations w ere tested (resp ect to the heater) : centered sheet, shifted sheet, inclined sheet. A therm ogram is show n on figu re 8 :

selection of the zone figure 8

The zone N °1 has been chosen as a reference for the com p u tation of the view factor (this zone is isotherm al at 3 %). The resu lts are listed below :

Results

distance lamp /sheet =10 cm

centered sheet shifted sheet = 5 cm inclined sheet 15 ° T_a(°C) 28,9 28,2 29,9 T_st(°C) 76,3 68,5 79,2  (seconds) 210 219 217 hg W/ m 2 K





 

the valu e of the Biot nu m ber is # 8.10-5 and the relative error rem ains very low (<5 %). The agreem ent betw een the sim u lations and the exp erim ental resu lts is fair :

centered sheet shifted sheet inclined sheet F₁₂ (experimental) 0,083 0,063 0,087 F₁₂ (numerical) 0,0866 0,062 0,0913 relative error in % 4,2 1,7 4,7

Conclusions and prospects

A first ap p roach of the characterization of the interaction betw een an infrared heating system and a p reform has been p resented . The sp ectral and geom etrical asp ects have been d iscu ssed for a fu rther ap p roach; and a sim p le therm al m od el to p erform a m easu rem ent of the view factor in several configu rations is p resented and easily valid ated w ith the infrared therm ograp hy techniqu e (lam bertian case). The m ost p articu lar p oint of this p ap er is the u sing of the Monte Carlo m ethod ; the m ain interest of this « p hysical com p u tation » (in ou r context) can be su m m arized as follow s :

- the m ethod w ork w ith com p lex geom etry

- a p recise d escrip tion of the rad iative transfer in a sem i-transp arent m ed ia su ch as Polym ers (PET/ PVC..) can be d one

- The introd u ction in the m od el of an anisotrop ic d istribu tion of intensisty is p ossible (a sp ecific lam p w ith reflector for exam p le).

N ow and for next m onths : The com p u tation of the view factor in the anisotrop ic case is being tested and a m ore accu rate exp erim ental setu p has been d evelop ed to stu d y the heat flu xes on a p lastic p late (this p late is instru m ented w ith therm ocou p les). This d evice w ill be u sed to d e scribe m ore realistic situ ations closer to the ind u strial context.

References

[1] G.D enis, Extru sion-sou fflage et injection -sou fflage avec ou sans bi-étirage,

Techniques de l’ingénieur, A3700,1989.

[3] P. Lebaudy, Etu d e et sim u lation d e la rép artition d es tem p ératu res d ans

u n cylind re creu x d e PET sou m is à u n rayonnem ent infrarou ge, thèse d e d octorat, 1989.

[4] Smithells Metals, Reference hand book - Brand es book, 1990.

[5] F. D esvignes , Rayonnem ents op tiqu es - Masson - 1991.

[6] Siegel R. and J.R How ell, Therm al Rad iation H eat Transfer, Mc Graw H ill,

N ew York, 1981

[7] G. Ritoux , Evalu ation nu m ériqu e d es facteu rs d e form es, Revu e d e