5 . 1 EXP ERIMENTAL ERROR
Whenever any fr eez i ng or thawi ng t ime pred ict ion method is compared wi th experi mental freez i ng and thawi ng dat a , some lack of agreement i s
inevi table. This imprec is ion may ar ise from one of three sources : ( a ) uncerta inty i n th ermal property data for the material be i ng froz en
or thawed ( data error )
( b ) imprec i s e knowledge and contro l of the freezing or thawi ng cond i t i ons ( e xper i mental err or ) and
( c ) inaccuracy ar is ing from assumptions or ap prox imat ions made in the
der i vation of the pred i ct ion me thod ( pred i c t ion method error ) .
Thermal proper ty data uncerta inty depends on the material used for the exper imen ts and is d i scussed in Sec . 5 . 2 . To assess in i solat i on as far as is possible the magn itude of the th ird source of inaccuracy , the aim of any experimenta l procedur e or techn i q ue i s to k eep e xpe r i me ntal errors randomly d istr i buted and small i n s ize.
The f irst of two s ources of experi men tal error i s the err or ar i s i ng from imperfec t control of exper imental condit ions . Many vari ables are controlled to pre-set val ues . There i s cont rol error w i th i n each run as well as control problems in atta in ing the same pre-set value in all s imi lar runs . The abi l i ty to reduce the control error can be measured from the var iab i l i ty of repli cate runs for the same set of nominal e xper imental cond i t ions .
Second ly , there i s the error ar i s i ng from imprec ise knowledge of the experi mental cond i t ions . Hav i ng controll ed the exper i mental cond i t i ons duri ng each run the mean values must be measured . Uncer tainty can ari se as a d ifferenc e between the measured val ue of a paramet er and the unknown true value . The uncertaint y can be reduced by r ep l i cate determinat ions , but measurement s are suspectible to systematic errors which repl icate determ inat ions wil l not d iscern. Systematic error cannot be eas ily quantif ied and can only be minimised by ensur i ng that the measurement techniques used are val id and accurate. Sources of systematic error include ; unwanted edge h eat transfer , i nstrument
Experi mental Procedur e and Dat a Collection 58
cal ibrat ion error s and inhomogenei t ies i n th e phase change mater ia l due to the presence of air voids or thermocouple wir e .
Cle land & Ear le ( 1 98 4 a ) d i scuss the d ifferen t sources o f error commonl y encountered i n phase change experimentat ion and g ive a chec k l is t that enables the most probable sourc es of d i f ferences between exper iments and predict ions other than the pred ict ion method error to be assessed . Exper imental data are most use ful i f systemati c error i s negl igible compared with random errors , and the latter are mi nimised .
5 . 2 CHO IC E OF PHASE CH ANGE MATERI ALS
The materials used for phase change experi mentat ion must meet the cond itions l i s ted in Tab le 3 . 2 , be cheap and easy to use , g ive
reproduc ible results and should have acc urately k nown thermal
propert ies . Food materi als are rar ely homogeneous , each sample can on ly be used experimental ly on ce or twice, and they t end to have a w i de var iat ion in compos i t ion . Consequent ly thermal property data are often i mprec i se . For these reasons analogues have commonly been used ( R i edel 1 960a, Lentz 1 96 1 , Fraz erhurst et al 1 97 2 , Geuz e et al 1 972 , Badari
Narayana & Kr i shna Mur thy 1 975 , Alb in e t al 1 979 ) . " Kar lsruh e t est
substance" developed by Ri edel ( 1 9 60a) is p robab ly the mos t successful
and widely used ( Flem i ng 1 9 67 , Bonac ina & Comini 1 97 1 , Bonac i na &
Comini 1 972 , Bonac ina et al 1 97 4 , Comini et al 1 97 4a , Gorenflo & Mertz
1 975 , Cle land 1 977 , Hayakawa e t al 1 983b ) . Commonly k nown and referred
to as " Ty lose " , it is a 2 3 % methyl-cellulose gel . Tylose is eas i ly
moulded into d ifferen t shapes and i s homogeneous on ce equ i l ibrati on has
occurred . It can be used repet i t ively for exper iments without
deteriorat ion , i t s dens i ty does not alter sign i f ica nt l y as phase change occurs , and it has well character ised thermal propert ies simi lar to
those of many h igh mo is ture foods ( Cleland 1 977 ) . For these reasons
mos t of the exper imental work was done w i th Ty lose . The particular Tylose u sed was MH1 000 � a product marke ted in New Zealand by Hoechst New Zealand Limi ted.
On mix i ng of the powdered material w i th water , rap id hydration of the gel meant that ini t ially i t was non-homogen eous and some a ir entra inment occurred in the f inal moulds . The water content of the gel
Experimental Proc edur e and Data Collect ion 59
equ i l ibrat ed over a per iod of several day s lead i ng to a homogeneou s mater ial . Air pock ets with in the gel tended t o b e very small ( less than 1 mm in d iameter ) and evenly d istr i buted. B y a v i sual examinat ion of the f i nal gel , the voids volume was est i mated as less than 0 . 5 % , whi lst br eak i ng the j o i n of the Tyl ose wi th flat metal and plasti c
surfac es showed an almost complete and even contact . The pos s ible
effects on heat transfer of i mp erfect con tac t are d iscussed i n Sec . 5 . 4 . 3 . I t would be expected that other reseachers usi ng Tylose have had s i mi l ar problems w i th a ir entra i nme nt , y et no dev i at i ons from
the reported thermal proper t i es have been noted . Therefore i t was
cons i dered that the uncerta inty in thermal proper t i es for Tyl ose was not s i gn i f i cantly increased by the presence of the a ir bubbles .
Errors in measur i ng components led to a mo i s ture content of 7 7 . 0 ± 0 . 2 % i n the gel . D irect measurement of the moi stur e i n the ge l a fter
exper imenta l work showed that dur i ng freez i ng or thaw i ng by
except l iqu i d
where l iquid ingress occurred immers ion ( d i scus sed in later
sections for shapes wher e th is was a problem ) , the f i nal mo i s ture was wi th i n 0 .5 % of the or i g inal value.
Cleland & Earle ( 1 984a) g ive the thermal conducti v i ty and apparent volumetric spec if i c heat c apac ity versus temperatur e dat a for Tylose based on the data of R iedel ( 1 9 60a) and Com i n i et al ( 1 97 4 a ) . Other vers ions of the thermal property dat a have been u se d . Cleland & Earle ( 1 979b ) used a " flat tened" version wh ich enabled substanti al sav ings i n computa t i on t imes for numeri cal pred i c t ion methods , at a s l i gh t cost i n terms of loss of accuracy as large t ime steps could b e used wi thout " j ump i ng " of the latent heat peak . Cleland et al ( 1 9 82 ) tested a hypothe t i cal volume tr i c spec if i c heat capac ity c urve wh ich had some supercoo l i ng effects i ncorporated into i t . The Tylos e thermal property data u sed in Group I I ( numerical ) me thods in the present work are g i ven
i n Table 5 . 1 . Compar i sons with the or i g inal data from R iedel ( 1 960a) and dat a for minced lean beef are shown i n Fig. 5 . 1 and 5 . 2 . Val ues i n Table 5 . 1 were chosen t o b e an accurate representat i on o f R iedel ' s data , but the shape of the volumetric spec i f i c heat capac i ty curve was altered so that when i ncorporated into the f in i t e d ifference method and f in i t e element me thod programs , "jump i ng" of the latent heat p eak was less l i kely and large t i me steps st i ll gave good heat balanc es . Most
Expe r i mental Procedure and Dat a Collect ion 60 simple freez ing and thawing t i me predict ion methods need values of the therma l pr operty dat a for on ly the parts of the overal l t emp erature range where the change in thermal propert i es with temperature is small . The therma l property dat a for Tylose used by Cleland ( 1 977 ) were adopted for Group I ( s i mple) methods . These are g iven in Tab le 5 . 2 and are cons istent w i th Tabl e 5 . 1 .
To show whether experimental results obtained usi ng Tylose were typica l of the freez i ng and thaw i ng of real foods , exper i men ts were also conducted wi th mi nced lean beef . Mul t iple fat and mo i s ture determi nat ions gave the compos i tion of the minced lean bee f as 7 4 . 9 ± 1 . 9 % water and 3 . 1 ± 1 . 1 % fat . Meat as a material i s less homogeneous than Tylose , so publ i shed therma l property data var y s ign i f i cant ly and are not cons istent w i th each other ( Mor ley 1 972 ) . The thermal property data used were der i ved from R iedel ( 1 957 ) , Mor l ey ( 1 9 72 ) and from the compos i tion factors of Comini et al ( 1 97 4 a ) by Cleland & Earle ( 1 9 82a ) . These are shown i n Tables 5 . 1 and 5 . 2 and Figs . 5 . 1 and 5 . 2 . They are probab ly less prec ise than the Tylose data.
5 . 3 TEMPER ATUR E ME ASUR EM ENT AND CON TROL
Al l temperature measurements were made wi th 24 Standa rd W ir e Gauge ( SWG) copper/ cons tantan thermocouples ( 0 . 5 mm wire d iameter , 0 . 9 mm d iameter inc l ud i ng plas t i c i nsulat ion) connect ed to ei ther a 1 2 po i nt Taylor Ins truments "Mult i-Scan Recorder" potentiometer operat i ng on a 60 second print c ycle or a 1 2 po int Honeywell-Brown r ecord i ng potent iometer operating on a 1 00 second print cycle with an optional i ntermi ttent 1 5 m inut e del ay between cycles . Bo th o f these mach ines were calibrated w i th the abov e thermocouple wire to w i th in 0 . 3 °C in the r ange -50 °C to 50 °C .
Pr ior to thawi ng or freez i ng the obj ects of Ty lose or minced l ean beef were kep t in temperature controlled rooms for l ong enou gh t o attain a uniform temperature throughout . To reduce the variation i n i n i tial temperature dur i ng the time from removal o f obj ects from the constant t emperature areas to the start of the freezi ng or thawing proces s , the objects were i nsulated . Excep t for the slab shapes where sheets of 0 . 05 m thi ck polystyrene foam board were u sed , the obj ects were wrapped
Exper i mental Procedur e and Data Collect ion 61 Table 5 . 1 Thermal Property Data U sed In Catcula t i ons By Numer i ca l
Methods 1 T k T c H 2 ( oc ) (W m- 1 oc-1 ) ( oc ) (MJ m-3 oc- 1 ) ( MJ m-3 ) Tylose - 40 .o 1 . 6 7 - 40 . 0 1 . 88 0 . 0 - 30 . 0 -20 . 0 1 .6 7 1 . 66 -30 . 0 1 . 92 1 9 . 0 -20 . 0 1 . 9 5
�
8 . 3 - 1 5 . 0 1 .6 4 - 1 8 . 0 2 . 00 2 . 3 - 1 0 . 0 -9 . 0 1 . 6 3 1 . 6 1 -1 6 . 0 2 . 20 46 . 5 - 1 4 . 0 2 .�
0 5 1 . 0 -8 .0 1 . 60 -1 2 . 0 2 . 0 56 . 1 -7 . 0 1 . 58 - 1 0 .0�
. 70 62 . 6 - 6 . 0 1 . 5 6 -�
.0 . 20 66 . 6 -5 . 0 1 .5 2 - • 0 5 . 00 7 1 . 2 - 4 . 0 1 . 46 -l
.o 5 . 90�
6 . 6 -3 . 0 1 . 35 - . 0 7 . 20 3 . 2 -2 . 5 1 . 28 -�
.0 1 1 • 00 92 .�
- 2 . 0 1 . 1 8 - . 0 1 7 . 00 1 06 . -1 . 5 1 . 04 -3 . 0 25 . 00 1 27 .g
- 1 . 0 0 . 82 - 2 . 5u
3 . 00 1 41 . -0 . 8 0 . 6 6 -2 . 0 5 . 00 1 61 • 3 -0 . 7 0 .55 - 1 . 5 70 . 00 1 90 . 1 - 0 . 6 0 . 49 -1 .6
1 00 . 00 207 . 1 0 . 0 0 . 49 -0 . 1 00 . 00 2J
1 . 1 20 . 0 0 . 5 6 - 0 . 5 1 9 . 9 3 2§
. 1 4 0 . 0 0 .6 2 0 . 0 3 . 7 1 2 8 . o 1 00 . 0 0 . 6 2 1 00 . 0 3 .7 1 660 . 0Minced Lean Beef
- 40 . 0 1 . 5 8 -40 . 0 1 . 89 0 . 0 - 2 4 . 0 1 .5
�
-30 . 0 1 . 9 1 1�
. o -1 2 . 0 1 . 4 -25 . 0 2 . 0 2 2 . 8 -8 . 0 1 . 4 0 -20 . 0 2 .7 0 40 . 6 - 4 . 0 1 . 28 -1 5 . 0�
. 5 8 56 . 3 - 2 . 0 0 . 98 - 1 0 . 0 . 55�
6 . 7 -1 . 0 0 . 48 -8 . 0 5 . 26 6 . 5 o . o 0 . 4 9 -6 . 0 7 . 7 1 9�
. 4 1 00 . o 0 .50 -5 . 0 1 0 . 40 1 0 . 5 - 4 . 0 1 5 .7 0 1 2 1 . 5 - 3 . 0 3 1 . 20 1 45 . 0 -2 . 0 53 . 1 0 1 aA
. 1 -1 . 5 73 .70 21 . 8 -1 . 3 25 5 . 00 251 . 7 -1 . 2 25 5 . 00 277 . 2 - 1 . 0 3 . 65�
0 3 . 1 1 00 .0 3 . 65 7 1 . 71 L i near interpolat ion was use d .
Experi mental Procedure and Data Co llect ion 62 Tab l e 5 . 2 Thermal Pr operty Data U sed In Calculat ions By Simple Formulae
Property Tylos e Minced Lean Beef
ks ( W m-1 oc- 1 ) 1 . 6 5 1. 55 kl (W m-1 oc - 1 ) 0 . 55 0 . 50 CS ( MJ m-3 oc- 1 ) 1 . 90 1 . 9 0 cl (MJ m-3 oc- 1 ) 3 . 7 1 3 . 6 5 L (MJ m-3 ) 209 .0 209 .0 tJi (MJ m - 3 ) 226 .0 23 0 . 0 T i f ( oc ) -0 .6 -1 . 0 T i fave ( oc ) -2 . 1 -2 . 5 kave (W m-1 oc- 1 ) 1 . 2f 1 • o t
1 �H = enthalpy d i ffer ence between 0 °C and - l 0 °C , kave = average thermal conduc t i v i t y dur i ng the phase change pr ocess , T ifave = mean freez i ng or thawi ng temperature .
?
�
�
>- - ·s; :;: (J-d
c 0 u � E � � ..c:. I- 2 1.5 0.5Ex periment al Proc edure and Dat a Coll ec t i o n
··· ·· •· ·· ·· · ·· • ·· ·• ··· ··· ···· ·· . •• • . . ·. . • • . • • . . • • • Legend A B . ...• -20 -15 -10 -5 0
Temperature (•c)
5 10 F i g . 5 . 1 Th e r ma l Conduc t i v i t y Da t a For Ty lo se ( A ) a nd M i nc e d L e a n Bee f ( B ) . 1,000�
� � 100 >-1
I
u ; ucl
-20 -15 -10 -5 0 Ter11*'oh.r•(•c)
5 10 Legend A. a ···-·-·- c ...F i g. 5 . 2 A pparent Volu met ric S pec ific Heat Capac it y Data Fo r T ylos e ( A , C ) and Minc ed Lean B eef ( B ) .
A , B - dat a from Tab le 5 . 1 , C - data from R i e de l ( 1 9 60 a) .
Exper imental Procedure and Data Col l ec t i on 6 4
i n insulat ion materi a l and transported i n containers l ined w i th 0 . 0 2 m th i ck po lystyren e foam . Though the del ay s we re as long as 1 0 m i nu tes , usi ng th is method the max i mum measured d ifference i n the i n i tial temperature of the obj ects from the mean value was found to b e 2 . 0 °C . For slabs , bec ause the i nsulat ion could b e app l i ed and hel d more d irec tly onto the sur faces , the temperature var iations were only ±0 . 5 °C about the mean value .
For var iati ons i n temperature of up to 1 0 °C on e i ther side of a mean ini tial temperature the d ifferen ce in pr ed i cted freez i ng t i me for slab s was found t o b e less than 0 . 5 % ( Cleland 1 97 7 ) . Wh ilst th is analy s i s was carr i ed out us i ng f in i t e d i fferenc e simulat ion very s imi l ar resul ts would be expected if an exper imenta l invest igat ion was carr ied out , as f ini te d i fferenc es prov id e a suf fic i en t l y ac curate s i mulat ion of the freez ing process .
shapes other than
Errors of s i mi lar magni tude would slabs . For thaw i ng the error
be expected for due to i n i t ia l temperature non-un i form i ty would b e expected to be smaller because the enthalpy change for a 1 °C variat ion in i n i t ial temperature is a lower percentage of the total enthalpy change , compared wi th that for a 1 °C var ia t i on i n ini t ia l temperature in fr eez i ng . The need to u se a mean i n i t i al temperature to represent a non-uni form i n i tial temperature therefore introduced negl ig ible error .
The amb ient heat i ng or cooling med ium was e i ther water or 29 % calc ium chlor ide b r i ne held i n a 1 m3 i nsulated tank ( F i g . 5 . 8 ) . The med ium temperature was measured by two th ermocouples ; one pr ior to and one after the exper imental sec t ion. External c ir c ulation of the med ium was used for slab thaw i ng exp er i men t s , in wh ich case an add i t i onal thermoco uple was locate d i n the return stream to the tank . In all experi men ts there was no measurabl e d ifferenc e in temperature b etween the thermocouples because the c irculat ion rate of the med ium wi th in the p i p i ng and around the tank was suff ic i ently h ig h .
The t ank t emperature was c ontrolled b y a RKC PN- 4 1 " Bl i nd Control ler" act ivati ng both refr i g eration and heati ng systems. Th e thermal capaci t y of the tank contents was l arge c ompared w i th the heat loss or ga in from the env ironment and from the obj ect be i ng frozen or thawed .
Exper imental Procedure and Dat a Collec t i o n 6 5 Th i s mean t that the med ium t emperature wou l d change onl y slow l y wi th t ime if left uncontrolled dur i ng the exper i ment . The control system