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I PREDICI'ING PM W AND IEI'H'AIITY INHYDKBTATIC REIURI‘S Kathleen Elizabeth Young A THESIS Sunnitted to Michigan State University in partial fulfillment of the requirements for the degree of MAS'I‘EROE'SCIENCE Department of Food Science and Human Nutrition 1981 ABSTRACT PREDICI‘ING Pm TEMPERATURES AND LEI'HALITY IN HYDRCBI‘ATIC RE'I‘OM‘S By Kathleen Elizabeth Young A canputer model was develOped to predict gearetric center tempera- tures in cylindrical containers based on standard heat penetration data (for determination of thean diffusivity) , container dimensions, and factory time-temperature profiles (i.e. , heat distribution data) for a hydrostatic sterilizer. The program utilized a numerical solution of the general differential equation for two-dimensional, unsteady heat conduc- tion in a finite cylinder with time-varying boundary conditions. To test, adapt, and confirm the model, retort time-temperature profiles for a set of hydrostatic simulated, heat penetration tests (a condensed cream soup, 211 x 400 can size) were euployed. The progran-generated product tanperatures correlated well with those measured experimentally. Lethal- ity calculations determined fran the respective temperature profiles also agreed well confirming the applicability of the program to both heating and step-change cooling envirorments. This model has the potential, not shared by conventional themal process calculation methods , of predicting the response of the center-can temperature to normally and abnormally varying environmental temperatures . Dedicated to William E . Perkins my mentor and dearest friend The author wishes to express her appreciation to Dr. James F. Steffe for patiently bringing light to the concept of modeling, and for encour- aging deadlines. Dr. D.R. Heldman and Dr. J.B. Gerrish are acknowledged for their interest and helpful suggestions . AspecialtharflcsisextendedtoJohnIarkinforhiscanputerpro— gramning assistance, and willingness to plot and replot the results. Campbell Soup Ccmpany is recognized for providing the opportunity to learn the technical skills necessary for this study. 'Ihe author also wishes to adamledge Dr. Cash and Dr. Markakis serving, with a nurents notice, on her cannittee. TABIEOFCONTEN’I'S IIS'I‘OFTABIES LISTOFFIGURES WEE m l. 2. Introduction 1.1 General Ianarks 1.2 Objectives Literature Review 2 . 1 Current Industry Practice 2.1.1 The General Metrod 2.1.2 Ball's Formula Method 2.2 Hayakawa's Methods 2.3 The Design of the Hydrostatic Retort 2.4 Factors Affecting Lethality Predictions Daring Cooling 2. 4. 1 Exit Hydro Leg Cooling Water Teuperatures 2. 4.2 The Gradient Pressure of the Exit Hydro 169 Theoretical Developrent Transient Nunerical Heat Transfer Nodal for Cans Least Squares Prediction of Thermal Diffusivity Lethality Evaluation by the General Method WWW c UNH 3. 3 . l The Lethal Rate Concept 3.3.2 Conversion of Initial Temperatures 3. 3.3 Application of the Trapezoidal Rule ii PAGE V1 viii 10 l4 14 15 l7 17 25 27 27 28 3O 4. 5. iii Methods 4 . 1 Heat Penetration Tests in a Hydrostatic Simulator 4.2 4.3 4. 1. 1 Kitchen Batch Preparation 4. 1. 2 Hydrostatic Similator Features 4.1.3 Test Run Procedures 4.1.3.1 Hydrostatic Retort Simulations 4.1.3.2 Batch Retort Tests Developnent of the Hydro Lethality Prediction Nbdel 4. 2. 1 Description of the Temperature Prediction Madel 4.2.2 The General Method Program Confirmation of the Models Results 5.1 5.2 5.3 Effect of Cooling Water Temperature on Lethality Effect of Varying External Pressure on lethality memof theModeltoConventionalandOther 5 3.1 Ball's Formula Method vs. Actual lethality 5.3.2 Hayakawa's Method vs. Actual lethality 5.3.3 The lbdel vs. Actual lethality APPENDD! A Energy cost savings equations APPENDIXB Catputer program to predict the thermal center, product time/temperature profile for a hydro- static or other type retort APPENDIX C Thermal diffusivity estimation program based on the least squares procedure (including a sample output) APPENDIX D Polynanial interpolation function subroutine PACE 32 32 32 35 38 38 43 43 44 48 48 54 54 59 6O 61 62 64 81 83 85 87 93 99 iv PACE APPENDIX E lethality estimation program euploying the .100 general method (including sample output) APPENDIX F Conversion factors: English to S.I. units 104 LIST OF W 105 3.1 4.1 5.1 5.2 LISTWTABLES Summary of rode point solutions employed in the nunerical heat transfer analysis for a finite cylinder Summary of hydrostatic and batch retort experimental tests and cooling conditions Actual (general method) vs. predicted (Ball's formula method, Hayakawa's method, and the model) F0 values Predicting hydrostatic retort lethality values by. Hayakawa' s nethcd using standard heat penetration heating and cooling parameters FAQ: 23 39 57 63 2.1 3.1 3.2 3.3 4.1 4.2 4.3 4.4 4.5 5.1 5.2 5.3 5.4 5.5 5.6 LIST OF FIGURES General schanatic of a hydrostatic retort Finite cylinder rode labeling for numerical heat transfer analysis Square matrix system (10 X 10) for a finite numerical solution . lethal rate curve for anorganisnwitha z of 18°F in 603 X 700 out green beans Schenatic View of hydrostatic simulator Interior view of hydrostatic simulator Typical tine/tetperature profile for a ccumercial hydrostatic retort Nmnerical vs. analytical RT = 250-heating curve Numerical vs. analytical CWI' =- 65 -cooling curve The effect of water tauperature and pressure on product cooling rate Plotting of heating and cooling heat penetration data Batch retort - heating curve CWI‘ = 70 no pressure Batchretort-coolingcurve M=7O nopressure Batch retort - heating curve CWI' = 70 constant pressure Batch retort - cooling curve CWI‘ = 70 constant pressure vi PPGE 12 19 21 29 33 36 49 52 53 55 58 65 66 67 68 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 Hydro sinulaticn - heating curve CWI‘ = 130 gradient pressure Hydro simulation - cooling curve CWI' = 130 gradient pressure Hydro sinulaticn - heating curve CWT = 130 constant pressure Hydro sinulation - cooling curve M = 130 constant pressure Hydro simulation - heating curve CWI‘ = 160 gradient pressure Hydro sinulaticn - cooling curve (.WI‘ = 160 gradient pressure Hydro sinulatim - heating curve CWI‘ = 160 constant pressure Hydro simulation - cooling curve CWI‘ = 160 constant pressure Hydro simulation - heating curve CNI‘ == 190 gradient pressure Hydro simulation - cooling curve CWI' = 190 gradient pressure Hydro sinulation - heating curve CWI‘ = 190 constant pressure Hydro simulation - cooling curve on = 190 constant pressure PACE 69 7O 71 72 73 74 75 76 77 78 79 80 NOW B a processing time (min) CCI' = center can teuperature (°F) CH = can height (in) CW'= can width (in) on = cooling water tenperature (°F) fa = slepe of the logarithmic part.of the cooling curve (min) Poor: finalcentercantemperatureattheendofaheatprocess (°F) fh = slope of the logarithmic portion of the heating curve (min) F value = the symbol used in comparing the relative efficiency of thermal process FO‘Value = the number of minutes required to destroy a specified number of spores at 250°F when 2 = 18°F (Fégo) i = sequence of radial increments j = sequence of vertical increments jc = cooling lag (refer to Fig. 5.2) jh = heating lag (refer to Fig. 5.2) k = thermal conductivity LR.= lethal rate (eq. 3.24) r = radius at any point (r6 = can radius)(in) RT = retort temperature (°F) t = time Cmin) T = temperature (°F) viii Ti = initial product temperature (°F) T(i:j,) = temperature at rode (i,j) (°F) z=reciprocaloftheslopeofathermaldeathtimecurveofan organism (°F) o = thermal diffusivity (inz/min) At = selected time increment (min) Ax = selected element size (in) Ar = RDJCR a radial increment size (in) Ay = ZINCR = vertical incranent size (in) WW 1. 1 General lunarks (he of the most promising and readily implenented strategies for minimizing the themel energy required to calmercially sterilize food productsinthecanningirdustry istotakeadvantageof currentlywasted or unaccounted-for energy. Singh (1977) discussed various steam-retort heat losses, atong the nost critical being energy leaving with product and condensate. In the continuous hydrostatic retort ("hydro") , this dissipated energy could be utilized to raise the tarperature of the water in the discharge leg , thus retarding cooling rates of conduction-heating products enough to permit process time reductions of 10-20%, without con- pronising lethality. These reductions in steau requirenents could mean yearly savings, in fuel costs alone, of approximately $30,000 for a typical 11de (Appendix A) . The substantial contribution that a prograrmed cooling phase can im- part to the inactivation of bacterial spores was first elucidated by Board et a1. (1960). Several efforts to mathanatically predict the center- can teuperature profile for this cooling phase, particularly during the well lawn curvilinear segment characteristic of initial cooling, have been published (Hayakawa, 1970; Griffin et al., 1971; Stumbo, 1973) . These and other authors have tried to improve on the first formula method (Ball, 1923) based on heating studies of canned corn. Ball erroneously assured a constant cooling lag (jc) of 1.41, and a cooling rate (fc) equal to the heating rate (fh). Despite these imperfect assumptions, Ball's method is todaythemostwidelyacceptedprocedureemployedbythecan— hing industry for process lethality evaluation because of its relative simplicity. Ball's formula metlod provides a reasonable, though invariably low, estimate of the overall lethality of a batch retcrted, corducticn-heating product in a typical shelf-size can (nominally 8-19 ounces net weight) that is cooled, without overriding air pressure, in 65-85°F water. This method, honever, grossly underestimates the sterilizing values associated with conduction-heating products processed in hydros due to its inability to take into account the high temperature cooling cycle and gradient water pressure inherently imposed by the discharge leg. In numerous cases, the acmalacornflatedprocesslettialityfortriehydrohasbeenfarotobeas much as two times that predicted "by Ball's fonmla. 1. 2 Objectives The specific objectives of this study were to: l . Develop a computer model for predicting thermal center temperatures in a corduction-heating product based on the heating characteristics of the product (thermal diffusivity), the specified can dimensions, and the factory time-temperature profile of the hydrostatic or other type of retort being evaluated . 2. Test/adapt/confirm the model and its ability to pre- dict center-can temperatures that correlate well with ttose measured during simulated hydrostatic heat penetration tests . 3 . Investigate the influaoe of the inherent character- istics of the hydrostatic discharge leg (high tempera- ture cooling water and gradient overriding pressure) (:1 lethality prediction for conduction-heating type foods. 4. Compare sterility values (F0) carputed from measured and mathematically predicted hydrostatic retort simu- latedtarperaturesusingthismodelandotherprocess calculation methods. 2.1 Currait Industry Practice Foodbornebotulismisasyndroteresultingfromtheactimofa prefomedneurotoxinproducedbyoneorarotherofttefwrsemtypesof Clostridium botulinum tonic for humans (Kautter and Lynt, 1971; Sugiyara, 1980) . These anaerobic, spomlating microorganisms, indigenous to the soil, are of obvious concern to the food industry, particularly the canningindustry, becauseofthenearlyoxygen freeenvironmentprovided byahermeticallysealedcan. T'hetoxinformedby _C_._botulimimisone of the most potent poisons known. Its interference with the passage of stimuliviathemotornewescan, withinthreetotendaysof ingestion, cause paralysis of the diaphragm, and in the absence of mechanical venti- lation assistance, result in death due to respiratory failure (Center for Disease Control, 1979) . The awareness of g; botulinum has locked (the heat sterilization techrology of the food industry and its regulating agencies in a state of safe conservatism. A review of the literature reveals that current in- dustrial metl'ods introduced in the twenties still enjoy the virtually unqualified acceptance of the industry because incidences of spoilage during the nearly six decades of their use have been relatively rare. It is current industrial practice to base canned food thermal 5 process specifications solely on a desired reduction in microbial popula- tion (typically by an arbitrarily-chosen twelve log cycles) . Such reduc- tions are assayed by' one of the following industry-employed protocols (Tomsero et al., 1968) . 1. The experimental pack, which involves inoculating food cmtainers with a set number of selected organisms of known resistance; processing at different levels of time, or temperature, or both; and determining the degree of spoilage after a minimum time period (usually four weeks) by incubating or subculturing. This procedure provides biological verification , and is caiductedfornetvproductlinesorinacaseofa significant process modification (e.g., process reduction, new starch system, etc.) . 2. Mathematical metlods based on two considerations: (a) The thermal death time characteristics of the rmicroorganistettothenmalprocessisinteroedto kill, and (b) the description of the temperature pro- file in the container at its slowest heating point as a function of process time. 2.1.1 The General Method The general method, one of the two most comonly employed mathemati- cal metl'ods in the canning industry, was developed over sixty years ago 6 by Bigelow, Bohart, Richardson, and Ball (1920) . Despite the precision of the method, its utility is limited in that this procedure camot predict lethality values for process times other than ttose tested experimentally. Bigelow et a1. (1920) conceived the idea of a "lethal rate curve" that related time-temperature events with the relative inactivation of spoilage bacteria (Perkins, 1964) . By this classical metlod, the lethal rate for eachslowestheating pointmeasuredduring the course of an entireprocessisplottedonrectangularcoordinatepaper. Thearea beneath this curve represents the sterilizing value of the process in tenmsoftlettermalresistanceofthesporesinquestion. Thisgraphical mettodcanbeappliedtoanytypeproductwhetheritheatsbyconvection, coronation, or a combination of the one (Perkins, 1964) . Siroe 1920, the general metlod has been improved and simplified. Schultz and Olson (1940) developed the use of lethal rate paper (for a 2 value of 18°F only) to decrease the potential of human plotting error. At the same time, these two scientists introduced a formula for simple and rapid conversion from one initial product temperature and/or retort taperature to arother for any set of heat penetration data. Patashnik (1953) reported an additional application of metlod which permits estimation of ultimate lethal rates during the course of the process. Despite the wide applicability of the Bigelow method and its enhance- ments, sterility value calculations using this metlod are still laborious . Before this method can be applied, the actual time/temperature profile for a product experiencing a given thermal process must be generated by tedious factory thermocouple tests . In instances of frequently changing enviromental conditions (e.g., the hydro, with environments of steam, water immersion, and sprays) , accurate time/product temperature profiles beco'te very difficult to obtain. 2.1.2 Ball's Formula Metrod Tl‘esecondandonlyothermetlodapprovedbythecanningindustry for process lethality evaluation is Ball's fonmula method, published in 1923. This method was tre first formuh metrod reported in the literature, and in a time before the advent of corputers, a mathematical wonder. An excellent review of the theoretical development of Ball's metrod has been presented by Merson et a1. (1978). Its approach reduced the lethality calculation of a sterilization process to a single fontula by combining the equation for the rate of destruction of bacterial spores (thermal death time curve) with the equaticm describing the heating rate of a canned food. Both of these rates are assured to be logarithmic, a premise that can be validated experimentally within the terperature limits of conventional canned food sterilizers. Themethodisveryversatileinprovidingameans ofpredicting either the time required to obtain a given lethality value or the F value thatvmldbederivedfronagivenprocessingtine. Ineither case, the 2 value (terperatm-e dependence of the destruction rate of a specified organism) , the heating charateristics of the product (the lag (jh) , and the lepe of the heating curve (fh) , the cooling and'heating-media telperatures, and the initial product temperature must be specified. Ball simplified the solution by incorporating several assumptions and erpirical factors into his method. Of these assumptions, four most often curprcmise the accuracy of lethality values . First, Ball "...assumed that the cooling curve is the exact reverse of the heating curve...[which] meant that the two curves had the same slope..." (Ball, 1923, p.13). On the same page, however, Ball notes 8 that "'Ihis is...known to be false in amajority of the cases; but is a cmvenient assumption upon which to base the calculations." Industrial experience verifies Ball's statelents that the slope of the cooling curve (fc) is rarely if ever equivalent to the slope of the heatingcurve (fh)' andtl'usslouldrotbeassmedtobeequalifan accurate lethality value is to be predicted. Despite the modifications introduced by Bell and Olson (1957) for incorporating the actual fc value into Ball's formula metlod, the tedium of computing an fC value by hand, and the corplications of evaluating the cooling slope by computer have precluded the use of such an "Improved Fonmula Metlod" by the industry. The second inaccuracy in Ball's 1923 formula is the etpirical selection of a constant cooling lag factor of 1.41. This value was based by Ball on "...experimentally detennined heating curves...principally those of corn" (p.19), noting later, "... [it was] realized that this [jC] valuestnfldhmrebeenbasedupmcoolingcurvesratherthanheating curves". Ball chose a jc constant in order to simplify the impOSing task of preparing parametric charts and tables for estimating lethality by means of his single equation. The assumption of a constant jC intro- duces an error when the cooling lag factor differs from 1.41 (often true for products with thermal diffusivity values that differ from that of Ball's "canned corn", or for products processed in sterilizers other than batch retorts) , and when the relative sterilizing effect during cooling cannot be neglected (Hayakawa, 1969) . The initial portion of the cooling curve (immediately following "steam-off"was further characterized by Ball as follows (Ball, 1923, p.11) : 9 "Rather than use for the cooling curve the complicated expression [analytical solution] given by Thompson [Thompsom 1919], it has been assumed that, in all cases, the first part of the cooling curve satisfies the equation of a hyperbola until it passes into the logarithmic [part of the] curve...". Depending on the methods of cooling used (e.g., cooling water temperatures and overriding air pressure conditions), the shape of the initial segment ofthecoolingcurvewilltakeonformenotalways approximatedwellbya hyperbola. The last assumption that introduces significant error in calculating lethality values for sterilizing systems other than batch retorts is that ”...the temperature of the cooling water remains constant during the cool- ing of the can." (1923, p.13). Ball's tables and derived fh/U versus log g curves (Townsend et al., 1968), which relate the thermal center temperature at " steam-off" , the heat resistance of the relevant spoilage microorganisms , and the cooling water temperature , provide only for tem- perature difference values (between the cooling water terperature and the retort steam terperaoire) of 130°F, 160°F, and 180°F. Thus, Ball's estimate of cooling lethality relates only to cooling water temperatures between 70°F and 120°]? (for a 250°F steam temperature). No provisions can be made for cooling media temperatures that exceed 120°F. The limitations of Ball's formula method, from the standpoint of efficiency, are particularly evident when evaluating the lethality of a hydro process, where the unique characteristics of the cooling cycle can contribute up to one third of the total process lethality. 2.2 Hayakawa's MetI'ods A catprehensive review of the english language literature revealed no truly versatile metlod for predicting process lethality. Hayakawa ' s 10 etpirical formulas (1970) , the most flexible for constant loating and cooling conditions, can calculate the lethality at the slowest heating point given any experimentally determined jc’ fc' and cooling water tem- perature curbination. However, this metrod has limited use in that it camotgedggfleflienmaloemtercoolingpatternsofprodmtsprocessed under conditions other than tlose measured experimentally. This method is a corbination of the finite cylinder heat-conduction fonmulae proposed earlier by Gillespie (1951) for predicting temperature distribution during heating of conductive canned products and Hayakawa' s own emperically- derived cooling formula. Hayakawa later derived (1971) analytical formulas for predicting transient temperature distributions for conduction-heating canned products subjected to five empirically selected, surface-varying temperature functions. mly two of these temperature functions, however, are applica- ble to standard retort processing, and neither of these is adaptable to the step-change cooling conditions of the hydrostatic retort. 2.3 The Design of the Hydrostatic Retort The hydrostatic sterilizer, standing as high as 60 feet and accomp- dating up to 1200 cans per minute, is the most widely used of continums sterilizers. This machine operates on the hydrostatic principle, with the pressure of the saturated steam exactly balanced by the hydrostatic pressure exerted at the base of the two water legs (Stork-Amsterdam, 1977) . The cans are introduced into the chain at the carrier feed/discharge station, typically by rolling into a canted "T"-shaped carrier in groups of approximately twenty cans (Perkins, 1978) . From this point, the cans ll traverse a series of four-to-five chambers which comprise this ingenious retort system. Initially, the ronsterile product cans are passed through an infeed hydro leg (Fig. 2.1), a water immersion phase where the temperature may range from ambient to just below boiling (altrnigh usually set between 130°F-l90°F) . Products that heat predominately or cotpletely by conduc— tion experience to significant heating while in this phase of the cooker which would, havever, provide sufficient heat to prevent lowering of initial product temperature (Perkins, 1978) . Thecansnextenterthe steamchamber, whichmay contain anywhere from two-to-ten sterilizing passes, depending on the specified processing timeandcanspeed. Thepressureexertedbythewater legsatthebaseof the steamdoredictates thetemperaturein this section (ranging from 230°-265°F) , and may be regulated by raising or lowering the height of the water legs. For example, a ' -nine foot column of water would exert a pressure at its base of 15 psig, resulting in a steam chamber temperature of 250°F. The provision thus made for a continuous can feed in and out of the sterilizing section effects significant energy savings byeliminatingtheneedforrepeatedlyheatingandcoolingthesteam chamber. Reportedly, fifty percent less steam is consumed, and seventy percent less water than in a batch retort (Stork-Amsterdam, 1977) . After leaving the steam date, the containers pass through a two-to three phase cooling section. The first is the exit hydro leg, another immersion phase (Fig. 2.1) , typically maintained at l30°F-l65°F. Cur- rently, thettermalenergyleavingwithproductarocondensate isexpended by one of two hydrostatic designs. In one design, the water build-up in He manometric infeed/exit leg column is conveyed by gravity from near thetopoftleinfeedlegtoacollectiontankandpumpedtothetopof COOLING S PRAYS II I uh I!" IHI IIII IHI I I INFEEDIEE I”! ’ i| .III '1 I“! H II” I] "ll 'I "*I 'I "H 'I IHI ' 'I I“! II II'I I CAN FEED :: d 'I II |I '\/I 'I CAN DISCHARGE U P I 'I \ \ \ \ \ COOLING RESERVOIR -. . J L 3. ,. Fig. 2.1 General schematic of a hydrostatic retort (from Perkins, 1978) . 13 theexithydro legasrequiredtomaintainthenecessarywater level. In doingso, theheatofthecoroensateandthatgivenupbytrecansleaving thesteamisurifonmlydistribrtedbeoeentl'elegs. Inthesecondtype of design, the hydrostatic system pumps water off the base of the dis- chargelegthroughaheatexchanger. Thisprocedureooolstleexitleg water further, and effects an even more rapid and energy dissipating cooling of the containers when the steam cycle is completed. The uninterruped cooling cycle, initiated in the exit hydro leg, is continued in a series of cooling spray toners, where a corbination of freshamdrecirculatedwateriscascadedorsprayedovertkecmtairer- conveyor chain at temperatures of 85-100°F. At the end of the cycle, the canspasuudenmeaththeentiresystemwhereathird, immersion, stage of cooling may if necessary, be effected (e.g., for large can sizes, to bring the slowest cooling point temperature below 110 °F precluding thermo- philic spoilage during storage). Pressure, as well as temperature, is an important variable during cooling. Associated with steam processing at 250°F, the cans are sub— jectedtoagradualincreaseinexternalpressurefromzerotolSpsigin the infeed leg, a constant pressure of 15 psig in the steam done, and a gradualdecreaseinexternalpresairefromlStozerOpsiginthe exit leg. The very precise reverse pressure gradient provided by the discharge hydro leg can be beneficial in preventing buckling during cool- ing of large cans (i.e., exceeding 303x406). Itshouldberotedhere that contrarytocomonbelief, thehydro- static process is effectively a "still process" because of the slow can velocity (typically 2. 5 to 3 induce/minute) through the multiple chain passes and the transitional overbends/uiderbends. Such a steady progres- l4 sicn through the sterilizer induces a measureable convection currents for thickened and/or highly garnished products that heat by conduction. Several types of agitating hydros, manufactured in Europe, are em— ployed primarily for sterilization of milk and infant formula. Their appealislimited,1m1ever,becauseoftleirhighinitialcostand mechanical complexity. 2.4 Factors Affecting lethality Predictions During Cooling The substantial lethality contribution that can be associated with thecoolingphaseofathermalprocessdesigred foraconduction—heating product-was first elaborated on by Board (et al., 1960) . In accurately predicting the potential of. a hydro process in teams of spore inactivation, it is essential to account for the uiique attributes of the exit hydro leg that can perhaps exert a positive influence on lethality. 2.4.1 Exit Hydro leg Cooling Water Temperatures When hydrostatic sterilizers were first introduced over thirty years ago, prototional material suggested possible reductions in steam times as compared with the same product/container combination processed in a batch retort (Perkins, 1978) . The basis for this suggestion was the influence of the hot exit leg water on retarding cooling rates relative to typical retort cooling conditions of 65-85°F. Comprehensive studies of the influence of higher temperature cooling on process lethality have not been published, however, presumably because of the difficulty and expense of performing precise simulations and con- .15 firming factory tests. 2.4.2 The Gradient Pressure of the Exit Hydro leg Heat penetration tests performed in the laboratory still retorts Board et al., 1960; Helmer at al., 1952) have detonstrated that constant pressure during the cooling cycle of a conduction-heating product plays a vital roleinincreasingthelethalitymanifested atthecancenter. This pheumenon is apparently related to internal can pressure associated with the temperature-dependent expansion of the product and of the headspace air during heating (Hersom and Hulland, 1969). This internal pressure, in the absence of applied air pressure, results in "ebullition" (i.e., mixing) of the can contents during initial cooling (Gillespy, 1962) . Turbulence thus created rapidly mixes the cooler-central portion of the product with the totter—peripheral contents , effecting a reduction in the sterilizing value at the can center (Helmer et al., 1952) On the other hand, when pressure is mechanically controlled in the retort, the internal pressure in rormally filled cans is likewise main- tained, and the mixing of the container contents is precluded. Under these conditions, lethality values were found by Helmer et a1. (1952) to be as much as double in the 603 X 700 can size. Similar lethality en- hancements were observed by Board et a1. (1960) as a result of pressure cooling with smaller cans. Thus, the smaller the container size, the lesser the influence of pressure cooling on the F value. The possibility of taking advantage of this sterility-enhancing- effect seete most applicable to the hydro, with its gradient pressure edt leg. If "ebullition" can be prevented by the gradual decrease of 16 external pressure of the hydro leg, the rate of terperature change at tlegeoretricceiterofthecanwouldbegovernedbytheladsoftherela- tively slow process of pure conduction cooling. By retarding the cooling rates, lethality values would increase, and most likely, significant reductions in processing times would be feasible. 3. 'HIBOREI'ICAL W 3.1 Transient Nurerical Heat Transfer Lodel for Cans Whei a terperature gradient exists between a canned product and its immediate ewiroment, there is an eergy transfer from the high- temperature region to the low-temperature region (Holman, 1972) . Accord- ing to Fourier's Law of heat conduction [eq. 3.1], energy transfer is by cmduction and the heat-transfer rate per unit area is proportional to the temperature gradient. q = -kA aT/Bx [3.1] Here, q is the heat-transfer rate, aT/Bx is the existing terperature gradieit, and k is the thermal conductivity of the material. The negative sign indicates that the heat flux is in the direction opposite the tem- perature gradient. When investigating the rate of heat transfer into a can of product during the course of a sterilization process (heating and cooling) , the differential equation defining two-dimeisional , unsteady-state heat con- duction in a finite cylinder is etployed [eq. 3.2] (Carslaw and Jaeger, 1959) . This equation represeits a composite of the solutions for an infinite slab and an infinite cylinder: 17 l8 air/29::2 + (1/r) (ET/8r) + aZ'r/ay2 = (l/a) (er/at) [3.2] Where: T = temperature at any point, at any time (°F) r = radial distance from the ceiterline (in) y = vertical distance from the mid-plane (in) . a = thermal diffusivity of the food product (inz/min) t=time(min) Figure 3.1depictstheplacerentofrandywithrespecttothecerterlire and mid-plane (Orlowski, 1979) . Wen boundary conditicns vary with time, analytical solutions to equation [3.2] are very ouplex, not available, or overly simplified to be useful. For these special cases, the solution to equation [3.2] is best handled using numerical methods and the aid of a compiter. The following terms in equation [3.2] can be rewritten in a finite differeice form using central difference operators (Fig. 3.1) (Orlowski, 1979): 2 I 2 32W"? = [Tu-lo) ‘ 2T(i,j) + T(i+l.j)]/Ar [3'3] 2 ' 2 BZT/ay = [Tug-1) ‘ 2T(i,j) + T(i.j+l)]/AY [3'4] W3" = [Tu-Li) " TIi+LjIV2Ar [3'5] (t+At) t 8T/3t = [T(i,j) - T(i,j) ]/At [3.6] and rearranged to obtain the general algebraic equation [3.7] for the temperature at a selected point after a selected time interval in terms of tie temperatures at surrounding points at the beginning of the given time interval (Teixeira et al. , 1969) . Heice, the general solution to i,j-1 i—1,j ii i+1,j LI” ’1 mid-plane :- <-—--DI KN 1 center lune ¢ Fig. 3.1 Finite cylinder node labeling for nurerical heat transfer analysis (from Orlowski, 1979) . equation [3.2] is: (TI-At) _ t 2 __ "(i,j) - Tun) + [Mt/Ar ”Tu-1.3“) ”(i,j) t ' t + T(i+l.j)] + (“At/2r“) [Tu-1,3) ‘ Ti+1.jI 1 2 t + ("WAY ”Tun-1) ‘ 2T(i,j) + T(i.j+l)] [3'7] Where: i = radial element sequence j = vertical eletent sequence At = a selected time incretent (min) Ax = a selected element size (in) T(i,j) = tetperature at rode (i,j) (°F) eiperscript t = at time t subscriptt+timeincretent (At) =attimet+At mdifications (required because of geotetrical considerations) in equation [3.7] result in three separate solutions that can be used in cotbinaticn with this equatim to predict the temperature distribution profile for me quarter of a canned product (Arpaci, 1966) . me to the symmetry of the cylindrical coordinate system (typical matrix - Fig. 3.2), oily one quarter of the can was evaluated. At the ceiterline, equation [3.7] is incorrect since the fourth term is not defined when r equals zero. However, by using L'Hospital's Rulethe (l/r)(3T/3r) termcanbe corputedbytakingthe limits as r approaches zero, and rewrittei as (Arpaci, 1966): Jim aT/Br = 3% [3 8] r + 0 r 311 . Since T(‘i+1,j) = T (i-1,j) When I? = 0 [3.9] 0 Boundary Te!perature Nodal Points $ Matrix Center Temperature Nodal Points BMid—Plane Temperature Nodal Points [Boenterline Temperature Nodal Points G Geozetric Center Temperature Nodal Points M r1 r1 r1 Syrmetry fl n ('1 f'l L=I/2 O I. UJ LJ Lu LI; .1 . .s r a: LA (1:11) ZR {K 1h {R fix (a {H t {-x rt \1 \J’ \l \J VJ \J‘ W/ \J \J A\ rs I‘K re re ("a 4% 1L As at (1,9) I: \1 VJ \J V] \f \1 \r VJ \/ A In /\ rx H (H r-x 1R ta (a \M \ \J V \J \{ flu \J \l ZN JN [K A (A [L r5 fix rx Ix (1 ,7) r \ NJ \f \J \l/ \J H} W/ \ A r‘ R (L _1‘H r'\ ft in r-x rh sly VJ VJ \J \J \J \J \I/ A J" / A5 r'\ / rH [K j'\ (“N (1 , 5) ‘ w w .1 \. \f .1 \l \J x f 1 Z\ rs rx 5 an rm {'1 rs rm ms 9 \J \J \J \J \J J \J \J \I/ A rs xx A [a AK r-\ 1 In (L ‘(l:3) Mr \ \J \J \J \/ VJ ‘T' W r h (H fix 3 \I \ L=0 -- (1,1) (11:1) (9:1) (7:1) (5,1) (3,1) (1,1) F0 , ‘ i Fig. 3.2 Square matrix system (10 X 10) for a finite nurerical solution - 21 22 temperature at the ceiterline (excluding the geotetric ceiter of the can) can be defined by a centerline solution, which, after substituting equa- tion [3.3] for the fourth term in equation [3.7] become: '1' (t+At) _ t 2 (i,j) ' T(i.j) + ”AW/Ar ”21' t (i-Lj) ' 2T 0 T(r,O,t) = f(t) for t > 0 t(r,L,t) = f(t) for t > 0 Where: r r =canradius o y=OorL, referringtocanbottomandtop, respectively T(r,y,t) = tetperature at T1 = initial product tenperatire (°F) In summary , the mathematical heat conduction model involved the [3.14] [3.15] [3.16] [3.17] solution to the general differential equation for a finite cylinder (equa- tion [3.21) with the initial condition stated in equation [3.14], and the boundary corditions stated by equations [3.15], [3.16], and [3.17]. In applying the model, the tenperatures related to the time dependent bounda- ry conditions are nuterically specified from measured heating or cooling media temperatures. Assumptions made in the construction of this model were: 1. Negligible heat transfer resistance at the can surface (possible influence of headspace void on 25 heat transfer ignored), i.e,, infinite convective heat transfer coefficient. 2. Constant thermal diffusivity over the temperature ranges under consideration (heating and cooling) . 3. No internal heat generation. 4. Conduction heating and cooling only, with no 5. Internal volume unaffected by changing external pressure. 6. Homogeneous, isotropic material. 7. No circumferential heat flow. 3.2 least Squares Prediction of Thermal Diffusivity The thermal diffusivity of a food product plays a preeminent role in the prediction of tetperature distribution during food processing (equa- tions [3.7], [3.10], [3.12], and [3.13]). For this sttdy, a computer program (Larkin, 1981) was employed for estimating thermal diffusivities of conduction-heating food products based on actual time/ temperature heat peietration profiles measured under laboratory conditions . Using an initial diffusivity estimate (based on the moisture content of the food; if unknown, the program estimates it at 50%), a three point grid of diffusivity values is produced to determine the direction of the minimmmsumof squarederror (SSE). SSEis camputedasthedifference 26 between the actual heat penetration points and the calculated temperature data points. New grids are then created until the difference between the diffusivity is smaller than an error factor set at 1.0E-5. lodetenmimflEpredictedterperaturesusedinthisleastsquares procedure, analytical solutions of an infinite slab and infinite cylinder were employed. Equation [3.2], subject to the initial (eq. [3.14]) and following boundary conditions constituted the mathematical model. T(ro,y,t) = R1‘ for t> O [3.18] T(r,O,t) = RP for t> 0 [3.19] T (r,L,t) = RP for t>0 [3.20] Where: R1‘ = retort temperature (°F) 'Ihe solution of this problem may be represented as the analytical solution for the temperature distribution in an infinite slab and an in— finite cylinder given similar boundary conditions (Myers, 1971) . The solutim for the infinite slab is: co ', 2 2 T(x,t) - RP _ A Z sin((2n + DEX/L) -(2n + l) m at T1 - RI' - 1r n==o 2n+1 exp L2 [3'21] Where: L = length of the can (in) a a thermal diffusivity (inz/min) t = time (min) T(y,t) = surface temperature at point y at time t (°F) :1 n initial temperature (°F) axial position or slab thickness where the ‘< ll bottamofcan=0.0,top=L ’I’i 27 and the infinite cylinder solution is: co T(r,t) - HP :3 Ti _ m 2m;- (JO(er)/[(lmro) JleerH eXP {-(Ukmro) 2 at)/r02] [3.22] Where: Jo (Amro) 0 for m= 1,2,3,... r a radial position where 0.0 = center and roasurface Jo = Bessel function of the first kind of orderzero J =Besse1functionofthefirstkindof l orderone In solving for actual temperatures in the finite cylinder, the product solution is used, i.e., T(r,y,t) - Rr = mm) - RT) (mm) - Hr) Ti - RI' (Ti - RP) (Ti - KP) [3.23] Equatim [3.23] was used to determine predicted temperatures in campiting thermal diffusivity values fram standard heat penetration data (refer to Section 4.2.1.). 3.3 Lethality Evaluation By The General Method 3.3.1 The lethal Rate Concept lethality is the integrated spore inactivation potential of a thermal process (including heating 31g cooling). By convention, it is usually 28 expressed (for low acid processes) as equivalent mnintes at 250°F. The symbol for lethality, the F value, permits comparisons of the relative efficaci'es of varying processes. If the sterilizing effect of a thermal process is evaluated for a 2 value of 18°F (2 representing the relative resistance of microorganism eqaressed in terms of the number of Fahrenheit degreesrequiredforthethenmaldeathtimecurvetotraverseonelog cycle) and a reference temperatnnre of 250°F, the sterilizing value (Fégo)isreferredtoastheFovalue. ‘ The procedure used in applying the general method (Bigelow et al., 1920) requires the conversion of thermal center product telperatures measuredorpredicted atvarioustimeintervals throughoutaprocessto lethal rates (LR): LR = 10 (T " Tref)/z [3.24] Where: T = thenmal center product temperature (°F) Tref = reference temperature (e.g. 250°F or 212°F, respectively, for low acid and high acid products) A curve resembling that presented in Fig. 3.3 results when the lethal rates determined by equation [3.24] are plotted as a function of time. The area under this curve represents the lethality of the total process in terms of equivalent time (mnin) at the reference temperature . 3.3.2 Conversion of Initial Temperatures To compare lethality values determined from various sets of heat penetration tests , all initial product temperatures were converted to 29 u 5 J < E u d 121‘161820222‘262030323‘ TIME min Product: Cut anon buns. No. 5 sim. bunch“ 1V2 minutes at nso-F. Can sits: 603 by 700. Fm: 75 ounce of burns. Cans film: mm 2% salt brim. Thomas“ caution: Va“ 150'. cotton: on Iongitudinal axis. Como-«o time: 10”: minutes. Rom tumour-tun: 250$. Process time: 29 minutes. HEAT PENETRATION DATA Lcthal Rita HEAT PENETRATION DATA Lathli Rah “fl (I. ' ms. min on! mm. mm xcmocntun. ‘ 0 60 (IT) 19 243% 0.402 1 60 20 243% 0. 2 59 21 244% 0.512 3 60 2651/- C. 4. 70 23 24516 0530 5 35 246% 0 620 6 108 27 2461‘s 7 133 2‘7 0 661 8 156 9 175 Slum off and coon-nu mun 10 192 at 30V: minutes. 11 207 0.004 30% 247 0.601 12 217”: 0.018 31 247 0.651 225 0.041 32 2 0.660 14 2301/: 0.063 33 233% 0.121 15 234% 0.138 34 2171/: 0 016 16 238% 0.222 35 03 0 002 17 200 0.278 36 189 18 2411/: 0.337 Fig. 3.3 lethalratecurveforanorganismwithazof 18°Fin 603 X 700 cut greenbeans (from, Townsendet al., 1968). 30 150°F by the following equation (Schultz and Olson, 1940): Ncr=m'-[(Rr-NIT)/(RI'-AIT)](Rr-ACI‘) [3.25] Where: R1‘ = retort temperatures (°F) AIT = original initial temperature (°F) NIT = new initial temperature = 150°]? PCI=cantetperauireoftheactualsetofheat penetration data (°F) wr=newcanterperatureccrrespondingtoAcr (°F) Use of equation [3.25] assures that product heating is by conduction and/ or convection (Ball and Olson, 1957) . 3.3.3 Application of the Trapezoidal Rule The nnmerical integration metrod employed in this study for oorputing the area under the lethal rate curve was the well-known Trapezoidal Rule: Area = (1/2) [(b-a)/n] [f(xo) + f(xl)] + (1/2) [(b—a)/n] [f(xl) + f(x2)]+...+(l/2) [(b-a)/n][f(xn-1) + f(xn)] (1/2)[(b-a)/n][f(xo) + f(xl) + f(xl)+f(x2) + f(xz) +...+f(xn) + f(xn)] [(b-a)/2n][f(xo)] + [(b-a)/n][f(xl) +...+f(xn-l)] + [(b-a)/2n] [f( )] Kn [3.26] Where (as applied to lethal rate curves): 31 [(b-a)/n) = At = time between successive temperature measurements f(xo), f(xl), f(xz),...f(xn) = lethal rate of each measured thermal center product temperature Patashnik (1953) pointed out that if the first and last ordinates of the lethality curve are equal to zero, equation [3.26] can be simpli- fied to: area = At(f(x1) + f(x2)+...+ f(xn-l)) [3.27] The lethality values calculated by this method were considered the "acmal" geotetric center F0 values. The error estimate for this "general method" calculation is a function of the unit trapezoidal width, of the order of 1' 0.10% (Cedar and Outcalt, 1977). 4. MEIHOIE 4.1 Heat Penetration Tests In A Hydrostatic Simulator To properly characterize the influence of a high temperature cooling cycle and a gradual pressure diminution (inherently imposed by the dis- charge leg of a hydro) on overall process lethality, heat penetration tests were conducted in the hydrostatic simulator represented in Fig. 4.1. The tests were perfonmed at the pilot plant scale to permit variable separation and precise monitoring. The main purpose of these simulations was to provide an erpirical basis for conparison of the mathematical terperatinre predicting model developed in this study. 4.1.1 Kitchen Batch Preparation rllnemodel food system selectedwasacondensedcream soup. Itwas chosen because of its highly reproducible corduction-heating/cooling characteristics and its relatively few ingredients . The product contained (in order of concentration): water, mushrooms, wheat flour, partially hydrogenated vegetable oils (soybean oil, palm, or cottonseed oil), cream, salt, modified food starch, dried dairy blend (whey, calcium caseinate) : margarine (partially hydrogenated soybean oil, nonfat milk, water, natural flavoring, vitamin A palmitate) , whey, monoscdium glutamate, soy protein isolate, natural flavoring, yeast extract, and dehydrated garlic. The 32 33 mm>am> dogmgueoou 8083 steam 8.33m HOHEOO Hmowuuowam gag game, 93> Hoods figuwmmm 9nd . Egon uoo 935 women who :80me Hmumznowuooeou OHEEV “Sega 6338.6»: Hung .580me . . d” 83350308 Hmong . wig xenon mos . $803 Edam e8. . £883 5958 . gang H303 OHS . guided . 5de Samoa . .3 madam ”Ema . (vie-mun boo HN no em? oflmgm as .3... 34 thickners (wheat flour and modified food starch) were increased 15% to represent the least favorable factory product in terms of lethality evaluation. Each heat penetration test employed .copper-constantan, needle-type thermocouples (Ecklund, 1978) , positioned at the geometric center of the 211 X 400 can (standard condensed soup can size). Four additional retort ttermocoupleswerewiredatttetoparflthebottomofthehydrostatic simulator, as well as immediately above the tlnermocouple can area, to measure the ambient temperatures throughout the simulator during proces- sing. The thermocouple wires were connected to a high-sensitivity data- logger, which compensated, linearlized, and digitized the type T analog millivolt signal arnd simnltaneously printed the temperatures at selected intervals, recording them on tape for subsequent computer analysis (Doric Scientific, 1980) . The overall measuring error for this system was ap- proximately i 0.5°F. The cans were filled to a constant weight (315 grams), and sealed at about 160°]? to achieve an actual minimum factory MIT (minimum initial temperature) of 150°F at the start of the process. The thermocouple cans were placed in a tray situated at the midpoint of the lower half of the hydro simulating vessel (Fig. 4.2). The can level in the tray was marked on the water gauge sight glass on the side of the retort (Fig. 4.1) for use as a reference point to track conversion from immersion to spray. 35 4.1.2 Hydrostatic Simulator Features Because of the obvious complexities of moving a thermocouple equipped can successively through water imersion/steam/water inmtersion/water spray , the cans were fixed in a 60-inch diameter, 31-inch deep, modified FM: ”Steritort" (Figures 4.1 and 4.2) in which the enviromrent was smcessively changed. Theinfeed legbirmmersionphasewasrotpartofthesirmlations due to its negligible effect on lethality (during this phase of the hydro- static process, the center-can temperatures are less than 200°F; by equation [3.24], the lethal rate is less than 0.002). Accurate simulation of the hydrostatic process required a heated water reservoir (held at 10°F above actual exit leg temperatures) with constant temperature control (themostatically controlled steam sparger) , and a high capacity transfer/recirculation) pump to effect an almost instantaneous transition from the steam phase to the hydrostatic exit leg phase of a commercial sterilizer. The heated water reservoir had a capacity (approx. 250 gallons) more than double the volune required to immerse the test cans in the simulator. The tempered "exit leg" water i was recirculated during the pre-heat and processing period through the 4-inch line connecting the reservoir tank to the steam vessel to mninimize convection and radiation heat loss during the transfer at the end of the steam process (Perkins, 1978) . Regulation of the simulated exit leg temperature was accomplished by steam or cold water injection into the immersion water (Fig. 4.1) , which was mixed by continuous recirculation through a centrifugal pump (referred to as the steritort pump). The residence time in the discharge hydro leg was based on a typical factory ratio of hydro exit leg-hot spray capacity (Fig. 2. l) , to steam water spray header thermocouple outlet thermocouple wire water level-immersion cooling ,r' 1r nr‘ n. I II 'I 1’ / at. --a---------- -...-.---.--..--..--—----.-----.---a' A ‘\\\\\\\\ —— water level-spray cooling ,’— / _ _ — canned product can 511 open tempered W810? Fig. 4. 2 INTERIOR VIEW OF THE HYDROSTATIC SIMULATOR 37 chamber capacity and process time calculated as follows: # carriers in exit leg. +- #1 carriers in- l'nort--spra}§1 Process [ J[ tine ] # carriers in steam # minutes in immersion phase (exit leg) [4.1] Applying typical values : (45 carriers in exit leg + 160 carriersin rot-sprays) (65 min) = 1265 carriers in steam 10.5 min Make-up hot water for the hydrostatic system is continuously circu- latedtoanifromafeed—balancetankarxiirrtroducedthroughaspray headeratthetopoftheexithydro legtower. Theresultisrnear— equilibration between the leg-immersion water and the initial spray cool- ing water temperatures. Therefore, the mmrber of carries in the dis- dnargelegusedforthisestimateincluiedtroseintteareabetweenthe water immersion/spray interface: and fine overbend between the hydrostatic exitlegtowerandthesprayccolingtover. The hydro leg pressure gradient was simulated by compressed air introduced into the Steritort headspace above the immersion water level (Fig. 4.2) . The pressure was diminislned from the process steam pressure of 15 to zero psig at a rate corensurate with that experienced by the can in a factory hydro leg. It was essential to control this pressure gradient accurately, since an abrupt loss of external pressure would cause unaccountable, ronconductive heat transfer due to induced movenent of the food in the can (Board at al., 1960). The final three mninute passageofthecansthroughthecascadinghydro, hotwater supplytothe top of the hydro tower was simulated by eliminating overriding air 38 pressure, but maintaining the same immersion water temperature. At the appropriate time for entering the cooling spray towers (for this experimental system, 10.5 minutes after "steam-off") the water level was rapidly dropped to the spray cooling level, and the cooling water spray header was activated (Fig. 4.2) . The spray phase was continued until the thenmal center reached a ton-lethal temperature . The environmental tetperatures chosen for each simulated hydrostatic phase were based on themooouple records collected from actual factory tests by an Acurex-mdel 6000 Data Retriever System (Acurex Corporation, Antodata Division, 1978) . 4.1.3 Test Run Procedures A summary of the eight tests perfomed and their conditions (six hydrostatic tests simulating varying exit leg temperatures (130°F, 160°F, and 190°F) with gradient or constant external pressure, and two batch retort runs) can be found in Table 4.1. A description of the procedures (Fig. 4.1) involved in conducting these tests follows. 4. l. 3 . 1 Hydrostatic Retort Simulations A. Gradient Pressure 1. The cans were held in pure steam for 65 minutes, timed from "steam-up" . 2 . The bottom bleeders were closed 20-30 mninutes before the end of the process (to permit con- densate build-up necessary to prime the Steri- Table 4.1 Summary of hydrostatic and batch retort experimental EMU-{WWW HYDKBTATIC SIMJLNI'ICNS Test Cooling Time and Tlenperature (min/°F) 3 Conditions after a in Each Processing Phase ,5 65 min Process at 250°F 'g 3 Steam Water Spray Water +3 Process Imm. Cool Cooling 5 53} SW Batch 0-65 65-76.2 '— mtort Heat Penetration E Test - 65-70°F Immersion o Cool, No Pressure 250 55"7 "' h Batch Retort - 65-70°F 0-65 65-79-1 '- nmnersion Cool, Constant g 250 65-7 -- " (15 psig) 13012°F Immersion Cooling 3 For 10.5 Min, Gradient Pressure (15 to 0 psig) \g 45 160C? (S) 66-76.5 76.5-82.9 A for 10.5 than, Gradient 1’3 Pressure (15 to 0 psig) g 9515°F Spray Water Cooling 250 130 95125 :3 13032°F Immersion Cooling 0-66 55-34 .. A Constant Pressure (15 psig) / / g2 N0 Sprays 250 130 - SC} + . . l60-2‘°F Immersion Cooling 66-76.5 75.5-37 No Sprays 2 01 m 190 190CP 95t5°F Spray Water Cooling 250 160 1601-2”? Immersion Cooling 0-66 66-90 .. A Constant Pressure (15 psig) / g2 No Sprays zsq 160 - ‘3. . + . 190-2°F Immersion Cooling 0-66 66-76.5 76.5-88.1 :5 For 10.5 Min, Gradient V Pressure (15 to 0 psig) + g 9515? Spray Water cooling 250 190 95-5 2 19012:": Immersion Cooling o-ae 66-101 -- i Constant Pressure (15 psig) / / E 5. 40 tort-centrifugal pump) . Cneminmtepriortotheerioftheheatprocess: a. b. Digital temperature recorder converted to continuous scan (readings taken every four seconds). Tank water recirculation turned off . Twenty seconds before cooling: a. b. Ce Top bleeder closed. Air pressure controller set to 15 psig. Steamn turned off. 65 minutes (end-of-process) : Tempered tank water (pre-set at 115i2°F, 14oi’2°r, annd 18032°F for respective hydro exit leg simulations of 130i2°F, 16012°F, annd 19oi2°m was immediately transferred from the water reservoir to the hydro simulator. Steritcrt vessel vented as needed (cracking open top vent) when first bringing in the .tank water to prevent pressure from rising above the proces- sing steam pressure (15 psig) . As soon as the water appeared in the sight glass (ca. 10 seconds), recirculation of the "exit leg" water was started within the Steritcrt by activating the Steritcrt pump (bottom circulation only , no sprays , for best 41 temperature control). d. When the cans were immersed (water level slightly above reference mnark on sight glass) , the tank water valve was closed. One minute was allowed for temperature equilibration (transferred tank water contacting 250°F vessel) before making any tenperature adjustments. a. The high side of the simulated exit leg tempera- ture range (132°F, 162°F, or 192°F) was approximated inthe immediate post-steamminutes tomimic the higher leg temperatures actually experienced at the steam exit leg interface. b. 'nne simulated exit leg temperature of l30i2°F, 160:2°F, annd 19012°F for the first 10.5 minutes of cooling was maintained by injection of steam or cold water into the immersion water. A retort thermocouple, positioned at the bottom of the retort, was used as a reference (digital tenperature printout) to predict any necessary temperature adjustments. For the tests modeling actual hydro simulations, the external overriding air pressure was steadily dropped from 15 to zero psig in the first 7.5 minutes of the 'l3oi2°F, 160i2°F, and 19oi2°m immersion cooling phases. For the last three minutes of this high tempera- ture immersion phase, the pressure was held at 0 psig (simulating the conditions the can would etperience from the immersion/ spray interface to the top of the 8. 9. 10. 11. 42 spray cooling leg tower). Tables of actual cooling times and proportional pressure regressions were pre- paredassoonastheexact"steam—off" timewasknom. After tenminutes intothecooling cycle (halfminute prior to the simulated spray cooling leg): a. M water was rapidly drained below the cans (water level under the tray mark on sight glass) . b. Thiswaterwasthendirected fromtheSteritort pump to the Steritcrt spray (valve 7 open, valve 8 closed - Fig. 4.1). This resulted in full sprays concentrated at the center of the tray or thermo- couple area of tie simulator vessel (Fig. 4.2) . At the end of the simulated immersion phase: a. Cold citywaterwasrushedintothevesselby lnolding valve 4 open. b. T‘ne drain was worked simultaneously with the cold water valve to keep the water level below the cans. c. Step 9b. was continued until the thermocouple at the bottom of the vessel dropped to 80°F. After 10.5 minutes of cooling: a. Spray water temperature was equilibrated to 95i5°F. b. Tie digital printouts of the two retort thermo- couples wired in the thermocouple can area were constantly referenced for 9515°F readings. Termination of the spray phase occurred when the product thermal center reached 200°F. 43 B. Constant Pressure StepslthronghGa.werethesareasinA. However, forthese tests, the pressure was maintained at 15 psig (employing nno sprays) until tl'e center-can product temperature was approximately 200°F. 4.1.3.2 Batch Retort Tests A. Constant Pressure 1. At 65 minutes (end-of-process) , 65-70°F cooling water (city water supply) was rusted into the vessel. 2. Process steam pressure was maintained unntil the center-can temperature reacted 200°F. B. No Pressure 1. Sane as A.l. 2. Overridingairpressurewasdroppedtozero psig by opening the top vent wide immediately at the start of cooling. 3 . Immersion cooling continued until all product thermocouples read 200°F. 4.2 Development Of The Hydro lethality Prediction Model A computer program was developed to predict the temperatures at any point within one quarter of a can, at any time, given the thenmal dif- fusivity of the product, the initial product temperature, the dimensions of the can, and the time-varying bounndary conditions of the sterilizer being evaluated (Appendix B). The center-can temperatures from this 44 analysis were saved for later conversion to lethal rates , which were integrated over the entire heating and cooling period to yield a lethality value (F0) for tie thermal process in question. 4 . 2.1 Description of the Temperature Prediction model Onequarterofthecanwassubdivided intoanumber ofvoluneelenents of small but finite size (Fig. 3.1) that were defined by can height (4.00 innches), can width (2.6875 inches), and tie size grid selected. For the 211 X 400 can size, a 10 X 10 matrix, as defeded by Telxeira et al. (1969), was found nmore accurate ad precise in predicting thermal center temperatures than a 5 X 5, 15 X 15, or 20 X 20 matrix system. Using odo- dimensional Cartesian geometry (to account for radial and vertical teat transfer only: circumferential teat transfer was disregarded), the grid evaluated by the program was identical to that depicted in Fig. 3.2. If one considers this grid to represent the right lower quarter of the can, tie remaining three quarters (i.e., lower left, top right, and top left) are, by symmetry, mirror images of each other. Therefore, it is possible to generate the entire cylindrical container temperature profile on the basisofeventsinonequarterofthecontainer. If oe were to use this model to evaluate nutrient degradation during a theomalprccess, itwouldbenecessarytoretainall the temperatures generated for each time interval through-out the container (Teixeira et al., 1969) . But, for purposes of estimating thermal center lethality, the basis for the comparisons reported here, conpltation of the nodal point temperatures in a 10 x 10 matrix comprising one quarter of the container was sufficient (Fig. 3.1) . Because of the symmetry of the 45 four half-height quadrants , the geometric center temperature profile during heating and cooling could be accurately estimated on the basis of a single quadrant. ‘nneintersectionsofthenetworksdranminf‘ig. 3.2, calledncdal points, aredefinedintheprcgran (AppendixB) bytwosubscripts, iand j, to indicate the row and the column of the point, respectively. For example, the descriptor (11,11) (i.e., with the boundary values set at one, the geometric center represents the eleventh nodal point from the can end andside)would identify the geometric center of the can. Each nodal point tenperature was classified according to its location as inte- rior or boundary nodal points, and calculated by a series of numerical operations (equations [3.7], [3.10], [3.12], and [3.13]) that approximated the general differential equation for two-dimensional, unsteady-state Mat condmtion in a finite cylinder (eq. [3.2]) using a finite dif- ference technique (eq. [3.6]). At the beginning of the process (identified as either a hydrostatic or batch retort simulation) , all interior nodal points (identified in Table 3.1) were set to the initial product tenperature, while the bonndarymdesweresettotheretorttenperaunreatthestartcf proces- sing ("steam-up") . 'Ihe drop below factory minimum initial temperature (150°F) , due to unavoidable delay in transporting the cans from the closingmadninnetotheSteritort, wasaccounnted forbyextendingthe commercially prescribed process time from 65 minutes to 66 minutes for the hydro simulations only. The batch retort tests, conducted primarily for the determination of thermal diffusivity, were processed for 65 nminutes. As a basis for numerically predicting temperatures , it was necessary to determine two factors: (1) the diffusivity constant (on), and (2) the 46 time interval (At) between each temperature prediction. 'Ihe thermal diffusivity values were computed by a least squares program developed by Larkin (1981) (equations [3.21] to [3.23]), which enployed the measured center—can temperatures of only the heating cycle of each simulation. The program, together with a sample output, is presented in Appendix C. The thermal diffusivity values calculated for each experiment showed excellent agreerent among themselves (0.0169in2/ min 12.5%) , and with those cited by Lenz and Lund (1977) (e.g., pureed peas - 0.0169in2/min, and pureed lime beans - 0.0167in2/mirn) . The thermal diffusivity employed by this numerical heat transfer model for all the hydro temperature profile predictions was based on the mean value derived from the ban standard batch, heat penetration tests - 0.0166in2/min- The numerical stability of the can model is dependent on the size of the container (can height and width), the corresponding selected elenent size (Ax, based here on a 10 X 10 matrix), the thermal diffusivity of the food product, and the specified time increment. The following stability equation for a two-dimensional system (Holman, 1972) limits ttemagnitudeofthetimeincrenentthatmaybeusedrelativetothe elenent size : aAt/(Ax)2 5 2 [4.2] If the time inncrenenrt is large (e.g., 0.20 minute with a radial increnent (Ar) of 0.173 in. annd a height increment (Ay) of 0.457 in.), the system becones unstable and unacceptable oscillation (i.e. , heat flowing in the direction of the temperature gradient) occurs (Orlovski,. 1979) . A time increment should be selected which maximizes accuracy, and minimizes digital conputer running time. The most appropriate 47 value for the 0.134 in. radial and 0.201 in. height increnent employed for these stndiesvasttetimeincrenentcftherecordedcoolingewiment, 0.0625 minutes, donble tl'e incrementsfiminute recommended by Teixeira (et al., 1969) . Since retort telperatures were only recorded every minuteduringtheprocessingphaseoftrepilotplanttests, apolynomial interpolation function subroutine is called by the program to "create" additional data points for this phase only (Appendix D). After the program initializes the boundary and interior nodes, time (At) isinncrementedbyo.0625minmntes, andtneboundaryncdesaresetto anewenvironmental tenperature. The interiorncdalpointsarethenpre- dicted in the seqnence: matrix center and midplane nncdes (equations [3.7] ad [3.121), centerline nodes (equation [3.101), and finally the single geometric center nodal point (equation [3.13]), which is retained by the program in a file for later lethality analysis (Fig.3.2 and Table 3.1) . The calculation of each successive node temperature is based on the previous time inncrenent temperature of its surrounding nodes (Fig. 3.1) . The new tenperature distribution replaces the initial temperature distribution, and the procedure is repeated to predict tenperature dis- tribution after another time interval.' The program reads from appropriate tapes (Appendix B) tie time/ retort tenperature profiles as measured, in the case of a hydro simula- tion, for each of tre three phases, processing, immersion cooling, and spray cooling (the environmental temperature profile for spray cooling was not needed for the batch-retort control tests). As time is incre- mented, all boundary coditions are changed to the surface condition equivalent to the enviroment under investigation. This method , which accounts for the several temperature transitions which occur in the 48 factory, was the most appropriate for testing the applicability of the model to hydrostatic processes . A typical tenperature hydrostatic pro- file is illustrated in Fig. 4.3. 4.2.2 The General Method Program Fvalneswereestimatedbyageneralmethodprogram (AppedixB). This program (Perkins, 1980) reads the center-can, temperatures for each process phase, and calculates the lethal rate (equation [3.24]) for a given z value (e.g., 18°F), and reference temperature (e.g., 250°F). lethality is integrated using a simplified Trapezoidal Rule (equation [3.27]) for a specified initial temperature (150°?) and retort tenpera— ture (250°F) to yield an P value. 4.3 Confinmation of the models The numerical series of solutions (equations [3.7], [3.10], [3.12], and [3.13]). employed in the transient heat transfer model (Appendix B) were verified by conparison with: 1 . Coduction-heating product center tenperatures measured in cans subjected to precisely controlled tenperature and pre$sure conditions (Table 4.1, and Fig. 5.3 - 5.17). a. Heating profiles (Figures 5.3, 5.5, 5.7, 5.9, 5.11, 5.13, 5.15, ad 5.17): Coordinate plots of actual center-can temperatures versus those predicted mathematically by the model 49 nmeL H P ~81 E R U T A R E P M .8... E T .81 me _ — d H _ e 8 .3 . 8 8 .8 .8 4.323.26dmm. own. a. w €59... Em\§dmnm§ Madmen—m mom m guinea sandman—En Boon? 2. 50 developed in this study showed essentially perfect agreerent during the heating phase. Cooling profiles (Figures 5.4, 5.6, 5.8, 5.10, 5.12, 5.14, 5.16, and 5.18): Similar coordinate plots for cooling manifested exceptional agreenent for conditions of constant overriding pressure (Figures 5.6, 5.14: particularly Figures 5.10 and 5.18). In simulations with no or gradient overriding air pressure (respectively, Fig. 5.4 - a batch retort test: and Figures 5.8, 5.12, and 5.16 - hydro simulations), the correlation between actual and predicted thermal center tenperatures was acceptable in the critical area of highest lethality (i.e., above 240°F). The curves, unfortunately, do nottracteadnotheraswellbelow 240°thenthe ecternaloverridingairpressurewasdroppedtozero (after 7.5 minutes). Thermal center temperatures predicted by heating and cool- ing condition simulations using tre analytical solutions described in equations [3.21], [3.22], and [3.23]. The initial and boundary conditions assured for these two profile predic- tions were: a. Heating profile (Fig. 4.4): (1) Retort tenperature = 250°F (2) Initital product temperature = 150°F (3) Thermal diffusivity = 0.0166 inZ/min 51 b. Cboling profile (Fig. 4.5): (1) Cooling water tenperature = 65°F (2) (Final center can.temperature = 245°F (3) Thermal diffusivity = 0.0166 inZ/min The two sets of profiles generated by the analytical and numerical solutions demonstrated essentially perfect agreement . ‘Ihe lethality estimation program (Appendix E) was verified by hand calculations utilizing equations [3.24], [3.25], and [3.27]. 52 as mas o . m=a~e o.om oo.m~ oo.wa p ...4 oo.oo oo.»o oo... o p p #5:».Ezo N goo—outaz . X m>ozu ozeeom: ommupo Josefidozo .m> homeomzoz 53 oo.mm mo .oE 72:: U2: om.wb oo.m> om.mb co.mh cm.¢m co.mww 0 M03. 03 I... 21 nooZSozo > £3 goo—ouzaz + . N mound m 3.3 m0 5 s tau 0.: re 0 .0 0 w>o30 ozeaoou mmuezu nooop>nozo .w> nouoomzoz 5.RESULTS Tlne influence of coolingwater terperature andpressureonthecooling rate of cylindrical containers of a coduction-heating food is depicted in Fig. 5.1. Tre measured thermal center temperatures plotted versus time oncoordinatepaperforastadardbatdnretorttest (asdescribedin Sec. 4. 1. 3. 2. B.) and a hydrostatic retort simulation (Sec. 4. l. 3. l. A.) illustrates the degree to which the tenperature and pressure patterns that are characteristic of hydrostatic retorts retard the decline of center-can temperature (refer to section of plot circled in Fig. 5.1) . Men, for example, the exit hydro leg water is maintained at 190°F, tie thermal center product temperature remains above 245°F for about eight minutes . The center tenperatnne in this canned product heated identically to (as nearly as possible) the sane final center can tempera- ture (FCCT) , and cooled in 70°F water with no overriding pressure, stays at 245°F or above for less than three mu'nutes. The five minute tempera- ture discrepancy represented by the more precipitous center temperature decline under retort cooling conditions is equivalent, in terms of minutes at 245°F, to 2.6 F0 unnits (62%) of unnrealized cooling lethality. 5.1 Effect of Cooling Water Temperature on lethality The indepedent effect of cooling water temperature on process lethality was examined in this study by means of four control simulations: 54 PRODUCT TEMPERATURE (°F) 55 Q) HYDROSTAT (190°F) O RETORT (65-70°F) 250 e A A O O 0 ° 0 o o 240 ° o o o o 230— o o o 220- 0 o o 210-— o o zoo—i 0*: 1 l T T 5 10 15 20 TIME (MINUTES) Fig. 5.1 The effect of water temperature and pressure on product cooling rate. 56 all with constant pressure (15 psig) during the entire water'immersion cooling phase (no Sprays): and with independently varying cooling water tenperature of, respectively, 70°F, 130°F, 160°F, and 190°F (illustrated in Figs. 5.6, 5.10, 5.14, ad 5.18). Progressive Fo valnne increases were observed as tle cooling water temperature was increased (Table 5.1) . The 160°F simulations, the first tests conducted, were carried out before tle procedures described in Sec. 4.1.3.1 were fully mastered. Tl'erefore, the negligible difference denonstrated between the F 0 values obtained during cooling for the l30°F ad 160°F constant pressure control simulations may not be accurate. Tlereisnoevidentrelationshipbeoeeneither individualsorpairs representing the mo conventional slope-characterizing factors, jc ad fc (Fig. 5.2) finat suggests a means for predicting the relative effect of cooling water tenperature on thermal center lethality, (i.e., neitler value varies consistently with respect to. increasing cooling tenperature) . Thus, cooling paraneters measured at one tenperature (e.g., 70°F) , can- not be applied to predict cooling lethality when a significantly higrer cooling media temperature is employed. This limits the practical applications of Hayakawa's (1977) process calculation metlod, which corpntes cooling lethality by means of a system of equations utilizing experimentally determined jc/fc values. Hayakawa's method can only confirm the general method lethality of a given experi- mental cooling condition. It cannot predict, on the basis of this experi- ment, the lethality that would accrue under other cooling coditions. . groom 8d «a A; canon. 5 con: 0.52 and? gang a 57 tog ofl oz «.3 o.«« S: «.2 or. 5. o.o« o.«« o.«« \ \ \ \ $5.93 o.: to o...« on; «or . «6: on« res «.oo . «.o«\ tea Lu: 5. 3. o.: «.3 n.«« . \ \ .882: or: 8 on« \SA \2. a «.na o3 o3 o mm o.«« a: 93 so o.o o.: o.o o.«« \ \ \ 82:92 . o.«« 8 on« o: o: . no: on; no: . You «.o« o.o« 9: or. «.o a: «.2 «.«a \ \ 6.88: on: 3 on« :4 be; 3.: o2 o2 «a... «.o« v.5 «.2 do «.o «.3 d: «.«a \ \ 62:82 or: 8 om« a: «o« . o6: o3 {.2 or»... o o« a: o.: no n; «.o «.3 o.«« \ \ Groom «.2 on om« ««« s: «.3 on« no «.2. s o« «.2 o.: on «.o «.2 «.2 a: \ \ \ 62. o.: no on« 2a 2: 1oz, o3 no as. «o« «.3 has «.o n.« o.o« «.3 o.«a \ \ \ .22 o.«« no om« boa s: .68 856: on e6 8 6 .38 859. «as \ gnu» Ensures: 333 o E 3 5 u also... on :88. no in 6938. cilia: data: «:38 9:8. Bog .u> .33.! «dunno. «and... «.m Sons. 58 pin—.30 a $5.30 Cerf—.30 .mumo «Eggnog some 3280 one oedema no «tenuous « .m .oas m2; ME; co—lhm ( .LMO-lOO) 90'] cplhm plhm (.LOO‘iH ) 901 59 5.2 Effect of Varying External Pressure on lethality To determine the effect of the imposed gradient pressure of the hydro- static exit leg on the rate of cooling, tests comparing gradient ad constant air pressure were performed for three discharge leg cooling water temperatures: 130°F, 160°F, ad 190°F. The effects of these pressure coditions are reflected in the jc ad fc values cited in Table 5.1 Men a control codition of constant pressure during cooling was maintained, the cooling lag (jc) significantly exceeded that in a gradient pressure environment. The exact reason(s) for this retarded cooling can onlybeconjecturedintheabsenceoftransducer-measured internnalcan pressures during cooling. During the heat process, expansion of product-entrained gases and leaispaceairretainedaftersealingisapprodmatelybalaeedbytleex- ternal steamn pressure. When cooling is initiated, without external pres- sure control, this counter-balance is instantly dissipated, ad the can eds are free to buldge. This allows rapid product expansion and attendant in- ternal turbulence , which circulates tie coolest product away from the geonetric center (exaggerated in Fig. 5.4 for a "blow down" retort test). The effect of dropping pressure at the start of cooling proved, in the extrene case (70NP - Table 5.1), to reduce the spore inactivation potential of tle cooling process phase 47% (i.e., cooling cycle F0 values for 70 NP ad 70C? were, respectively, 2.5 and 4.7). Whether sore convection currents also result from the external gradi- ent pressure (as experienced in the exit hydro leg; Figs. 5.8, 5.12, ad 5.16) , cannot be deduced in the absence of internal pressure measurerents during heating ad cooling. The lag values (jc) of the gradient - 60 pressure cooling curves are, however, consistently smaller and the slope values (fc) , larger than the respective lag ad slope parameters associated with constant-pressure cooling. As a result, the cooling F0 values were generally smaller during gradient, relative to pressure cooling, although the 160°F test data are again equivocal, in that the gradient cooling pressure test indicated more lethality than the constant pressure test. An enanination of the gradient versus constant pressure cooling curves (Figs. 5.7-5.18), within any of the temperature groups, reveals no obvious terperature-related basis for predicting the corbined effects of terperature and pressure on cooling rates in a viscous, conductive- heating liquid food (i.e., a codensed cream soup). Process calculation uethcds (Ball adplson, 1957; Hayakaaa, 1977) enrplcying constant jc ad fc values _can__n£_t, therefore, be used to predict the effect of a pressure codition other than that used experimentally. 5.3 OonparisonOfThebbdelToConventionalAndOtherMethods The reliability of the mathematical process evaluation method developedinthisstndywastestedbyanalyzingthedegreeofaccordance betweenthemathenatically predictedFva'lues andthe trueFvaluesbased on measured tennperatures. Sterilizing parameters calculated by a general method program (Appedix E) fronn measured geometric center tanperatures (Sec. 4.1.3) ad fron center-can temperatures (Sec. 4.2.1) predicted by the mathenatical unodel are conpared in Table 5.1. Heating, cooling, and consolidated F values predicted by this model are also coupared (Table 5.1) with "total" P values computed from the sore ecperinental temperature data by Ball's formula method (1923); 61 generally employed by industry) ad Hayakawa's (1977) analytical nethod (the most recently developed technique for process lethality evaluation) . Represented also in this table (5.1) are the slope/intercept characteristics of each experinrental heating (jh/fh) and cooling (jc/fc) cycle, the initial product temperature (mathématically stadardized at lSO’F: Schultz ad Olson, 1940), the retort temperature, ad the cooling water teuperatures for the hydro simulations . 5.3.1 Ball's Foruula Method Vs. Actual lethality PredictionofaanaluebyBaJl's fomnlamethodrequiresthatthe following paraneters be knom : retort temperature , initial product tenperatmre, cooling water temperature, processing tine, fh, jh, and the 2 value. The lethality values estimated by Ball's formula (Table 5.1) , slightly understated the lethality (5.5% lower than actual general method values) for the stadard retort test , with a significant variation identi- fied for the retort test applying constant pressure (20% lower). In predicting lethality values for the hydrostatic simulations , a cooling water teperature of 120°F was assured (highest cooling water tenperature permitted by Ball's charts). The estimated sterilizing values varied insignificantly with changing cooling water tetperature ad pressure coditions because of the constraints imposed by Ball's assump- tions of a constant jc of 1.41 (jc range in these tests: 1.17-1.59) , and mirror image heating and cooling slopes (experinental heating ad cooling slope temperature discrepancy range: 16.8-55.3°F, with fc in- variably exceeding fh) . A Ball equation lethality estimate for the hydro simulation testing 62 an exit leg teperature of 190°}? was, for example, 30% lover than the actual general method value. This method does not, therefore, account well for hydrostatic retort cooling coditions . 5.3.2 Hayakava's beard Vs. Actual Lethality The following information was employed in the application of Hayakova' 5 heat process evaluation program for purposes of critical point lethality estimation: initial temperature , constant cooling and heating media teperatures, z, fin, jh, fc, jc, ad the final thean center tauperatureattheedof theheatinngphase. This lastvaluewasset equivalenttotheFCITI‘determinedbythegeneralmethod (AppendixE) for an initial product telperature of 150°? (eq. [3.25]). The total lethality values predicted by Hayakava's method shoved fair agreetent. F values for the standard heat penetration test (70NP) and the batch retort test with controlled pressure cooling (70C?) were, respectively, 5.5%annd 2.0% lower than the general method values. T'he sterility values detemnined by this method for the hydrostatic simulations were less accurate: 7.6-9.0% lower for the constant pressure tests and as much as 16% lower for the gradient pressure tests (i.e., 130GP(S)). As a method of estimating lethality from known heat penetration tests, Hayakawa's method accounts fairly well for varying cooling water temperature and gradient pressure (i.e. , characteristics of hydro cooling) by incorporating actual jc and fc values into his lethality computation. But, in predicting hydro retort lethality on the basis of stadard heat penetration data alone (Table 5.2) , Hayakawa's empirical approach is not much better than Ball's formula method. 63 Table 5 . 2 Predicting hydrostatic retort lethality values by Hayakova ' 3 method using stadard heat penetration heating and cooling paraneters . Test Conditions Total lethal Value (F0) 130 GP(S) 12.6 130 CP(NS) 160 @(S) 13.5 160 CP(NS) 190 GP(S) 14.7 190 CP(NS) The jh,jc,fh,fc, ad FCCI‘ values used for the above computations were, respectively, 1.77, 1.06, 38.5 min, 70.6 min., and 246.4%". The innitial temperature was set equal to 150°F, and the cooling water tenperature was assured to be equivalent to the specified immersion cooling temperature . 64 5.3.3 The Dbdel Vs. Actual lethality Sterilizing values derived from the model's predicted center-can temperatures are cited in Table 5.1 for the individual Mating/cooling phasesoftreexperimentaltestscoductedinthisstudy, andforthe total process. The predicted temperatures were based solely ona stadard heat penetration thermal diffusivity value for a codensed cream soup (0.0166 inZ/min) , and simulated factory, sterilizer-surface temperatures. These center-can tanperatures demonstrated (in every case but the 160°F tests and the "blow-down" cooling batch-retort test) excellent agreement with actual cooling temperature profiles (Figs. 5.3-5.18) . lethality calculations determined from the respective model-generated temperatures also correlated well with F values based on measured tempera- tures (again, with the exception of the 701an test, and the 160°F set of hydro simulations). F0 values for conditions of constant overriding air pressure during cooling were 2.6% higher for the batch-retort test (70C?) ad 0-1. 1% higher for the hydro simulations. The lethality values predicted by the model for the gradient pressure hydro simulations showed the best agreenent of any of the process calculation methods evaluated in this study (0-7.5% higher). These results confirmn the unique applicability of the model developed herein to both heating ad step-chage cooling environments (e.g. , hydro- static retort processes). Using this mnodel, lethality values may be pre- dicted for any set of processing coditions once the rate of heat penetra- tion (thermal diffusivity) for the canned, conduction-heating food has been determined. 65 m.m .mE 72:: m2: oe.mm oe.em oc.nv oo.mm oc.w~ oa.wr cube—omen. x .ano 4 mozwwmoo oz ooupzo m>e2o ozoeomz .. Heepmo zubom 66 oo.mm ed.¢E 72:: m2: oo.mb cc.m~ co.wb oo.mm - — oo.mm owho _ ammo w: Joshua .4 moawwwoo oz Obnezo w>oao 027.com .. Hooemo Iueom oo.m 67 md.Er . MZHH ...ae 8. mm 8. mm 8. 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X dozhoo .0 wmzwwmeo pzmoooeo owfiuezu m>mzu ozopomr .. zooeonszom coo»: a can 84% 8dr 8.? m .0 0 00'092 74 mom .mE A. 2:: of h 86m. 8.4m. 8.2. 84. oo.oo co.mm oo.NQ r I . p .1. '4 ,4 '4 p ouho _ omen. N Joshua O .4 ,4 .1. monwwwmo Hzmooooo owflupzu m>ezu ozoqooo zoepodzzew coo»: 75 00. NR. oo.cm co. me p - hm - owe”: ammo a. .53th mozwwmmo pzoewzoo omfinezu m>o2u ozopowr .. zooeooazom coo»: 76 3:“. .93 . A.z~:. meek oo.om co.mo oc.~e co.mp eo.ae oc.pe oo.m coho H ouoo N Joohoo oooowmoo Hzoewzco coonpzo m>ooo ozoocco .. zcoeooozow coo»: oo-ooé° 0) dHBl 133 I 00' 032 77' ma.m .maa 72:: oz: OO.NP Day-cm DD.DV OO.mm DOJVN OO.N— oo.n~l .l . . p p .7 0 onto a ouoo X ASH—co e A moowoooo »z.n:oooo coonpzo m>ooo ozoboo: .. zcoeooozoo coo»: 78 ma.m .maa A.z_zc use» 8.8 8.8 8.8 8.8x. 8%. 8.2. 88 p p b oo~ooé° U) c4143.]. 133 I 00' 033 owpo _ ouoo N .5on: meammmma ezmaoqmo omluezc u>mac ozlnooo n zoieenszcw Dee»: 79 5H.m .mam 72:: oz: oc.Nb oc.cm oc.ov oc.om oo.¢N cc.N— oo.P. P p p — h p owhouomoo G Joohoo + oooowmoo Hzo»ozco cofwézo m>ooo ozohom: ... zcohooozoo coo»: 80 35 6E A. 2:: oz. _ 8.8m 8.8 8.8 84.8 88%. 8.8 86 bl 83.8.: M dB 838 a .u ooomomoo Hzopozoo coHHHZQ m>ooo ozoocco .. chZZDer coo»: l. 6 . CCNCLUSICNS The higher the cooling water temperature, the greater the spore inactivation.contribution of the cooling cycle. Such an effect could not.be reliably evaluated by the empirical cooling curve lag (jc) and slope (fc) values, which demonstrated no obvious trends when plotted from.varying cooling water heat penetration data. Thus, cooling parameters measured at one temperature (i.e., a standard retort test cooled at a constant 70°F), cannot be applied to predict cooling lethality when a significantly hotter, step-changing cooling (hydrostatic retort) environment is employed. F values calculated from heat penetration data associated with gradient pressure and a range of cooling water temperatures were l5% and 7% lower (l30°F and 190°F, respectively) than those determined.frtmlconstant pressure tests. The reason for these discrepancies is unclear without a better understanding of the exact pressure changes occurring within a canned conductionr heating product during heating and cooling. Ball's formula method predicted F values that were as much as 30% lower than F values determined by the General Method using 81 5. 82 experimnentally measured product temperatures . Hayakawa's mettnod provides reasonable lethality estimates when the tneating ad cooling product profiles fora thennnal process canbecharacterized. Incaseswheretheheatpeetrationdata are not available (e.g., converting a batch retort process to a hydrostatic retort process), Hayakawa' s empirical estimates are no better than ttese projected by Ball's formula netted. Thermal center temperatures associated with conduction product cooling can be accurately predicted by the model developed in this stndy for varying boundary and external pressure conditions. These predictions can be based solely on standard retort, heat penetration tests (i.e., cooling water temperatures of 65-85°F) , and simulated factory, sterilizer-surface temperatures. Complicated process deviations involving multiple environmental temperature changes presently can be evaluated only by tedious ad expensive physical simulations . The results of this study (Table 5.1) indicate that the model currently developed has the potential, not shared by any other ttnennal process calculation method, of predicting the response of the center-can temperatures to normnally ad abnonnally (i.e., during process irregularities ) varying environments . Subjects for future study are: To validate ttne computer metted developed in this project with mnicrobiolcgical tests (e.g. , inoculated tests). To evaluate the potential of applying the model to process irregularity lethality predictions. By changing the tune/tenetatnme sterilizer profile read bythe program to the actual titre/tamerature, surface profile experienced during the aberrant process (indicated on the process-recording chart) , the lethality value may be accurately omputed, and net "guess estimated" , as unfortunately is frequently the case today. . To quantify the effect of varying external pressure conditions on the cooling rate of codnction- heating/cooling food products, and to develop compensating constants for use in the model designed in this stndy. To measure the influence of high cooling water temperature ad varying external pressure coditions for a wide variety of container sizes and food products. 83 84 5. To investigate possible means of utilizing the model developed herein to optimize the ttnermnal process design of hydrostatic retort sterilizers, thus, reducing the energy requireennts per can. APPENDICES APPENDIXA ENEMY COST SAVINGS EQUATICNS 85 Appendix A - Energy Cost Savings Equations (Using Typical Values for a Single Hydrostatic Retort) 15% . . . ( . ) (66 mun process) = 9.9 min reduction lbduction or a 56.1 min process 1265 carriers in steam _ . at 20 / ier - 25,300 cans in steam a. 25,300 cans __ . 66 min - 383.33 cans/min b. 25,300cans _ ' . 56.1 min — 450.98 cans/mun c. 450.98 - 383.33 = 67.65 cans/min improvement . [80% line efficiency ] (67.65) = 54.12 cans/min improvement (capacity of the line relative to stops ad starts) Converting to pounds of product: 10.75 oz. in a typical can __ 16.0 oz/lb ‘ 0'67 lbs So: (0.67 lbs) (54.12 cans/min) = 36.36 lbs of product/min inprcvenent Converting to lbs of product/year: (60 min/hr) (16 hrs/day) (260 working days/year) = 249,600 min/year So: (36.36 lbs of product/min) (249,600 min/year) = 9,075,456 lbs/year improvement 86 7. Converting extra lbs of product to conserved lbs of steam: 448.22 BTU's /lb product for a hydro retort Since: 368.18 BTU's/lb product in an agitating cooker (Singln et al., 1980) And: 56 (Factor for a hydro) 1 _. n [46 (Factor for a continuous sterillfizerJ 968°”) " MMB'ZJgthrS Ilbflm (Singh, 1977) So: ' 9 Saved (9,075,456 lbs/year) (448.22 BTU s/lb)= 4.07 X 10 31.0.3/ 8. In dollars: Since: 1 million BTU's/7.2 Gal Fuel Oil (Nadler, 1980) (4.07 x 109 BTU's) (7.2 Gal Fuel Oil/1 million B'I'U's= 29,304 Gal of Fuel Then: (29,304 Gal Fuel) ($1.20/Gal Diesel) = $35,165 9. If based on one quarter natural gas (typical for American industry): (7.2 Gal) ($1.20/Ga1) lOGBTU' s = $8.64finillion BTU's for Fuel Oil Estimated $4.00/mnillion BTU's for Natural Gas: Then: (.75) (8.64) + (.25) (4.00) = $7.48/mi11ion BTU's SC: (4.07 x109 BTU's) ($7.48/nmillion BTU's) = $30,445 per typical hydro per year in fuel costs alone. APPENDIXB WPKERAM'IOPREDICI'TFE 'IHERJALCENI'ER,PmTfldE/TMERA'IURE PWFORAHYDKJSMICOROHIERTYPEW 87 130:Ce..........c...........o................ceooccecvct 110:6 120:6 133:6 140:6 150:6 TRANSIENT NUMERICAL HEAT TRANSFER PODEL FOR FOOD PRODUCTS HEATING BY CDNDUCTION ADAPTED TEIXEIRA ET AL. €1969) BY KATHLEEN E. YOUNG 160=c.....................12....ct.c.o.......c..c....... 170:6 153:6 190: 20086 21386 220:6 236:6 240:6 256: 262:6 270:6 266:6 230:6 360:6 313:6 320:6 333:6 340:6 336:6 36086 3 6:6 350:6 390:6 351:6 400:6 A13: 426:6 430:6 446:6 430:6 460:6 470:6 472:6 486:6 490:6 566:6 510:6 52:: 530:6 350:6 360:6 370:6 330:6 596:6 600:6 610:6 620:6 THIS PROGRAM PREDICTS THE-TINEITEHPERATURE PROFILE AT ANY POINT UITHIN ONE QUARTER OF A CAN. AT ANY TIPE. FOR A CONDUCTION°HEATING FOOD PRO- DUCT PROCESSED IN A BATCH OR HXDROSTATIC RETORT. THF DATA REQUIRED ARE THE THERHAL DIFFUSIVITY OF THE FOOD PRODUCT. THE INITIAL PRODUCT TEN- PERATURE. THE DIHENSIONS OF THE CAN. AND THE TIRE-VARYING BOUNDARY CON -DITICNS OF THE STERILIZER BEING EVALUATED. THE GEONETRIC CENTER TEN- PERATURES ARE THE ONLY TEMPERATURES RETAINED BY THIS PROGRAP (TAPEB). ZHICH ARE LATER CONVERTED TO LETHAL RATES BY A SEPARATE GENERAL METHOD PROGRAM (GENHZI. TO DETERRINE NUTRIENT DEGRADATION DURING A THERMAL PROCESS. IT UOULD BE NECESSARY TO SAVE ALL THE TEMPERATURES GENERATED FOR EACH TINE INTERVAL THROUGHOUT THE CONTAINER (REFER TO TEIXEIRA ET AL. (1969)). ONE QUARTER OF THE CAN IS SUBDIVIDED INTO A NUNBER OF VOLUME ELENENTS THAT ARE DEFINED BY THE CAN HEIGHT. CAN UIDTH. AND GRID SIZE (10 X 10 HATRIX). THE INTERSECTIONS OF THIS NATRIX NETHORK. CALLED NODAL POINTS ARE DEFINED IN THE PROGRAH BY THO SUBSCRIPTS. I AND J. TO INDICATE THE RON AND THE COLUHN OF THE POINT. RESPECTIVELY. FOR EXAMPLE. THE DES. CRIPTOR (11.11) IDENTIFIES THE GEOHETRIC CENTER OF THE CAN. EACH NODAL POINT TEMPERATURE IS CLASSIFIED ACCORDING TO ITS LOCATION AS INTERIOR OR BOUNDARY NODAL POINTS. AND CALCULATED BY A SERIES OF NUHERICAL OPERATIONS THAT APPROXIHATE THE GENERAL DIFFERENTIAL EQUATION FOR THO- DIMENSIONAL. UNSTEADY-STATE HEAT CONDUCTION IN A FINITE CYLINDER USING A FINITE DIFFERENCE TECHNIQUE. AT THE BEGINNING OF THE PROCESS. ALL INTERIOR NODAL POINTS ARE SET TO INITIAL PRODUCT TEMPERATURE. UHILE THE BOUNDARY NOOES ARE SET TO THE RETORT TEMPERATURE. AFTER THE PROGRAN INITIALIZES THE BOUNDARY AND IN- TERIOR NODES. TIHE IS INCRENENTED BY A CHOSEN TIME. AND THE BOUNDARY NODES ARE SET TO A NEU ENVIRONHENTAL TENPERATURE. THE PROGRAH READS FROH APPROPRIATE TAPES (TAPEI.TAPE2.TAPE3D THE TIRE/RETORT TEHP. PRO- FILES AS MEASURED. IN THE CASE OF A HYDRO SIHULATION. FOR EACH OF THE THREE PHASES. PROCESSING. INNEPSION COOLING. AND SPRAY COOLING (A TEMPERATURE PROFILE FOR SPRAY COOLING FOR A BATCH RETORT UOULD NOT EXIST). AS TINE IS INCREHENTED. ALL BOUNDARY CONDITONS ARE CHANGED TO THE SURFACE CONDITION EQUIVALENT TO THE ENVIRONHFNT UNDER INVESTIGATION. FOR CASES UHERE THE SURFACE PROFILES HAS NOT RECORD. ED EVERY 0.0625 HIN. A POLYNOMIAL INTERPOLATION FUNCTION SUBROUTINE IS CALLED BY THE PROGRAH (TERPI) TO "CREATE“ ADDITIONAL DATA POINTS. THE INTERIOR NODAL POINTS ARE PREDICTED IN SEQUENCE: HATPIX CENTER! HIDPLANE NODES. CENTERLINE NODES. AND FINALLY THE CENTER NODAL POINT. THE CALCULATON OF EACH SUCCESSIVE NODE IS BASED ON THE PREVIOUS TIRE INCREHENT TEHPERATURE OF ITS SURROUNDING NODES. THE NEH TEHPERATURE DISTRIBUTION REPLACES THE INITIAL TEMPERATURE DISTRIBUTION. AND THE PROCEDURE IS REPEATED TO PREDICT TE‘PERATURE DISTRIBUTION AFTER ANOTHER TIHE INTERVAL. ‘5303c......ceccceoot99......veceoctccctecceottvecettecot 646:6 650:6 563:6 670:6 685:6 696: 700:6 713:6 VARIABLE LIST - nanpthnnunt onsnnnaunnon pnsoncnnon TDIFF:THERHAL DIFFUSIVITY VALUE (CHZIHIN) CH=CAN HEIGHT (INCHES) CU3CAN VIDTH (INCHES) R=RADIUS AT ANY POINT RTOT:RADIAL DISTANCE FROH THE CENTER LINE ZTJT:VERTICAL DISTANCE FROM THE HIDPLANE 88 720: RINCR:RADIAL INCREMENT SIZE 66!) 733: ZINCR:VERTICAL INCREMENT SIZE (CH) 740:6 RT=RETORT TEMPERATURE. F 750:6 ARTsAVERAGE RETORT TEMPERATURE. F 76?:6 CUTI=CODLIVG HATER TEMPERATURE - IPNERSION PHASE. F 770:6 ACHTI:AVERAGE COOLING HATER TEMPERATURE - IHHERSION PHASE. F 780:6 CUTs=COOLING HATER TEMPERATURE - SPRAY PHASE. F 790:6 ACUTS:AVERAGE COOLING HATER TEMPERATURE - SPRAY PHASE. F 863:6 TI:INITIAL PRODUCT TEMPERATURE. F 310:6 TINCR:TIME INCREMENT CHIN) 820:6 NH:NUPBER 0F VERTICAL INCREPENTS 332:6 NR:NUMBEP 0F RADIAL INCREMENTS 940:6 I:SEOU£NCE OF RADIAL INCRENENTS :50: 035500210: or VERTICAL INCREPENTS 960:6 TA:0LD TEMPERATURE AT EACH POINT 876:6 TB:NEU TEHPERATURE AT EACH POINT 886: PR06ESS=PROCESSING TIME FROM STEAM UP TO BEGINNING COOL (MIN) 890:6 COOLI=TIHE 0F IMMERSION COOLING (MIN) ' 960:6 CODLS=TINE 0F SPRAY COOLING (HIM) 910:6 CCT:CENTER CAN TIME\TEHPERATUPE PROFILE (SEC/C OR F) 920:6 ICUT.IPROCESS.ICOOLI.ANO ICOOLS ARE COUNTERS 933:6 INT:NUHBER 0F REQUESTED INTERPOLATIONS 940:(tttcttvcccceceet'teetceconcoct..9....ec......oceoee 930: PROGRAM TMPPRED6INPUT.OUTPUT.TAPEI.TAPEZ.TAPE3 966: 9.TAPE6:OUTPUT.TAPE8.TAPES) 970:6 966: DIMENSION TA(25.25).TB(23.25).TC25.25) 990: DIMENSION TIMEITSD).TEHP(750).CCTI1000.2) 1000: CHARACTER CTYPE*3.0NE'1.THO*1 1010: DATA ONEI'I'I.TUOI'2'/ 1920: IGNOTI=0 1030=C 1040=C READ IN CONSTANT VALUES 1350:C 1160: URITEC6.50) 1070:50 FORMATI'I'.II.' IS THIS A BATCH RETORT 0R HYDROSTATIC COOKER' 1360: 9.’ SIMULATION?’.I.' (1=BATCH.2:HYOROSTATIC)') 1090: PRINT 60 1130360 FORPAT(1(I)) 1110: READ(¢.'(A)°) CTYPE 1120: URITE(6.70) 1130:70 FORMATT' './.' ENTER THE TIME INCREMENT (MIN) FOR EACH OF THE' 1140: .,O FOLLOUING PROCESS PHASES:'.I.' PROCESSING. '. 1130: O'IMfltRSION COOLING. AND SPRAY COOLING'.I.' (SUBSTITUTE 0 FOR' 1166: 0.’ PHASES OHITTED)') . 1170: PRINT 60 1130: . READ t.TINCR1.TINCRZ.TINCR3 1190: HRITE¢6.80) 1260280 FORMATI' './.' ENTER CAN HEIGHT AND HIDTH (INCHES)') 1210: PRINT 60 ~ 1220: READ P.CH.CU 1230: . , unnn:¢s.nzon 1240:120 FORMATI' './.' ENTER THE THERMAL DIFFUSIVITY VALUE (CHZI' 1250: ' ¢.'MIN)') 1260: PRINT 60 1270: READ *.TDIFF 1280: HRITEC6.130) 1290:130 FORMATT' '.l.' ENTER INITIAL PRODUCT TEMPERATURE (F)') 1300: PRINT 60 1310: READ ..nn 1320=C 89 13303C READ IN TIME/TEMPERATURE ENVIRONMENT PROFILE OF EACH PROCESS PHASE 11608C 1350:C PROCESSING PHASE 1360:C 1370: ICUT:0 1380: IPROCES=0 1390: ICOOLI=O 1900: ICOOLS=0 1410: CALL READ(1.TIHE.TEMP.IPROCES.ICUT) 1420=C 1A30=C'INHERSION COOLING 1.40:6 1450: ICOOLI:IPROCES 1460: CALL READ(2.TIME.TEMP.ICDOLI.IPROCES) 1A70:C 1AFO:C SPRAY COOLING 1Q90:C ISGOS IF‘ETYPEOEQQONE’ 50 T0 21 1310: IFCTINCR3oEDolo0) GO TO 21 1520: ICOOLS=ICOOLI 1513: CALL READ¢3.TINE.TEMP.ICOOLS.ICOOLI) 15403C 1550:C PREDICT CENTER CAN TEMPERATURES FOR EACH PHASE OF THE PROCESS 1560:C . ' 1570:C PROCESS PHASE 1330:C 1390321 CALL TENPDISITIME.TEHP.IPROCES.ART.CCT.ICUT.CU.CH.TDIFF 1600: 9.71.S.TINCR1.TINCR5.IGNOTI) 1610: IF!S.LE.2.0) GO TO 2 1620: HRITEI6.4)S 1630: GO TO 3 164032 CONTINUE 16508C 1660=C INHERSIDN COOLING 1670:C 1680: IGNOTI:1 1690: CALL TEMPDISATIME.TEHP.ICGOLI.ACUTI.CCT.IPROCES.CU 17003 ¢.CH.TDIFF.TI.S.TINCR2.TINCR5.IGNOTI) 1710:C 1720:C SPRAY COOLING 1730:C ‘ 17A0: IF!CTYPE.E0.0NE) GO TO 36 1750: IF!TINCR3.EG.0.01 GO TO 36 1760: CALL TEMPDISCTIME.TEMP.ICOOLS.ACUTS.CCT.ICOOLI.CH 1770: 9.6H.TDIFF.TI.S.TINCR3.TINCRS.IGNOTI) 1730:C ‘ 1790:C RESULTS OF TEMPERATURE DISTRIBUTION AND NUTRIENT RETENTION PREDICTION 1860=C 1?10:C 1520:C HPTTE CENTER CAN TIME/TEMPERATURE PROFILE TO FILE 9 CALLED CCTSAVE 1830:6 1340:36 REUIND 9 1630: IFCICOOLI.GT.ICOOLSD ICOUNT=ICOOLI 1360: IFCICOOLloLToICODLS) ICOUNT:ICOOLS 1370: DO 10 II=1.ICDUNT 1830:10 HRITEI9.B) (CCTIII.JJ).JJ:1.2) ‘ 1390:A 'FORHAT(' STABILITY CRITERION NOT NET. 8: '.F11.J) 19CO=8 FORMATIZFIGoZ) 191033 CONTINUE 1?2C: STOP 1930: END 19A03C 1950:C. 90. 1960=C SUSROUTINE THAT READS IN TIRE/TEMPERATURE STERILIZER PROFILES 1970:C OF THE VARIOUS PHASES OF A PRCCESS 1980:C 1990:C 2000: 2010: 2020: 2030: 2640: 2050: 2060: 2170:10 2080:15 2090:20 2100: 2110: 2120: 2130:C 2100=C SUBROUTINE READAIFILE.A.B.I.IPOS) DIMENSION A1750).B(750) NOBS:0 REUIND IFILE DO ID I=I210750 READ(IFILE.'.END=IS) A(I).B¢I) NOBS:NOBSOI CONTINUE HRITEAE.207 (AIJI.B(J).J=IPOS*I.NOBSOIPOS) FORHAT!2F10.2) I=NOBSOIPOS RETURN END 21303C SUBROUTINE TD CALCULATE THE TEMPERATURE DISTRIBUTION AND SLDHEST 2160=C HEATING POINT TEMPERATURES DURING EACH PHASE OF THE PROCESS 217o=c 2180:C 2190: 22$0: 2210: 2220: 2230:C SUBROUTINE TENPDISITIME.TEMP.ICOUNT.ANEDIUM.CCT¢NPOS.CU POCHQTDIFF.TIOSOTINCR.TINCR5916NDTII DIMENSION TIHEITSD’VTENP(750).CCT(100092) DIMENSION TAIZSOZSIOTBC25.25).T(25923) zzqozc EVALUATE ALL Cousrnurs 2250:C 22603 2270: 2230: 2290: 2300: 23103 2320: 2330: 2300: 2350: 2360: 2370:C NR=ID NH=ID SUHRTSOoD RTOT=CNP2.5G/2.D RINCR=RTDTINR ZTOT:CH:2.64/2.0 ZINCRSZTDTINH NP1:NR01 NR2=NR02 NH13NH¢1 NH2:NH¢2 23803C DETERMINE IF STABILITY CRITERIA MET 2390:C 2900: 2410: 2¢20: 2‘30: 2‘40: 2450: 2460: 2A70:1 2‘50: 2490:C TINCR52000625 D=TDIFF9TINCRSIZINCR932.D P3!TDIFF'2.D:TINCR5)IRINCP*92.D =TDIFFiTINCR5/(2.D*RINCRI =TDIFF9TINCR5/RINCR**2.D U=TTDIFFPZ.D'TINCRSIIZINCR*P2.0 HRITECSOIIOQP.O.SOU FORMATCT o:'.F11.7.2x.'P:'.F11.7.2x.°0='.F11.7.2x.'s:0.F11.7.2x.°U P3'.FII.7) 2500:C PRESET INTERIOR TEHPERATURES 2510:C 2520: 2530: .2540: IFTIGNOTIOEQOII GO TO 15 DO 10 1:20NR2 DD ID J=Z.NH2 91 2550:10 2560:C 2370=C 2180:C GENERATION 0F TEMPERATURE DISTRIBUTION IN ONE QUARTER OF THE CAN 219036 2600:C . 261086 DETERMINATION OF THE NUMBER OF NECESSARY INTERPOLATIONS 2620:C TAII.J1:TI 2630313 IFITINCRoEDo0.5) INT:Q 2660: IF!TINCR.EG.1.0) INT=16 26!0: IF!TINCR.E0.0.333) INT:S 2660: IFITINCRoEO.5.0) INT:80 2670: IF!TINCR.EG.10.0) INT:160 2650: [FITIHCROLEOJOIZSI INT=1 2690:C 27£D:C PDLYNOMIAL INTERPDLATION OF THE ENVIRONMENT TEMPERATURE USING 27103C THE FUNCTION SUBROUTINE TERPI 2720:C 2730: DO 20 K:NPOS¢1.ICOUNT 2140: IFCK.EO.ICOUNT) INT:1 2750: 00 25 L:1.INT 2760: IFtINT.E0.1) 60 TO 26 2770: RT:TERP1(TIME¢K)¢(IIFLOAT(INT)19(L-1).TIME.TEMP.ICDUNT.0.S) 2730: GO TO 27 2790:26 RT:TEMP((K¢L)-1) 2800:C 2210:C SET UP BOUNDARY CONDITIONS 2320:C 2030327 00 30 1:1.NR2 2800: T(I.1):RT 2930:30 TA!I.1):RT 2060: DO 40 J:1.NH2 2870: T(1.J):RT 2800:!0 TA(1.J):RT 2590:C ZGDOSC DETERMINE CENTER AND MIDPLANE NODE POINT TEMPERATURES USING 29103C THE GENERAL EQUATION 2920:C 2930: DO 60 04:2.NH1 2990:C 2930:C RESET INITIAL R FOR EACH NEH J 2960:C 2970: R:RTOT 2980: DO 65 II=2.NR 2990: :R-RINCR 3000: TB(II.JJ):TA(II.JJ)¢S¢¢TA(II-1oni-2.0-TA(II.JJ)¢TA(II¢1.JJ)) 3'10: 0.0/RtCTA(II-I.JJ)-TA(II¢1.J«))¢O*¢TA(11.00-11-2ootTAtII.JJ)o 3020: oTACII.JJ¢1)) 3030:66 CONTINUE 31‘0:C 30$O=C DUE TO SYMMETRY. THE FIRST INCPEMENTS ON EITHER SIDE OF THE BDGCSC CENTER LINE ARE EOUAL 3070:C 3080: TBINR2.JJ):TB(NR.JJ1 3090860 CONTINUE ‘ 3100:C 311D:C DETERMINE CENTER LINE NODE POINT TEMPERATURES (EXCLUDING THE 3120:C GEOMETRIC CENTER) BY THE CENTER LINE EQUATION UITH R:0 3I30:C 3140: DO 70 J3=2.NH 3150870 TB(NR1.JJ)=TA(NR1.J3102650P:(TA(NR.J3)°TA(NR1.J3)1000(TA(NR1. . 92 3160: 003-1D-2.0tTA(NR1.03)OTA(NR1.J3¢1)1 3170:C 3150:C CALCULATE TEMPERATURES IN THE RON ABOVE THE MIDPLANE 3190:C 3250: DO 83 1332.NR1 3210880 TBCI3.NH2)=TD(I3.NH) 3220:C 323036 DETERMINE THE GEOMETRIC CENTER NODE POINT TEMPERATURE 32AO:C 3250: TBANR1oNH113TAINR10NH1)92.0'P'0TAINR.NH1)OTAINR1oNH1319UtlTAINRI. 3260: ONH)-TAINR1.NH1)) 327?:C 3289:C STORE CENTER CAN TEMPERATURE IN CCT VARIABLE FOR EACH TIME 32963C 3::c: CCTA‘KoL)¢1.I):TIMEIK)v(1/FLOATIINT)):(L‘1) 3313: CCTCCKOL)-1.2):TB(NR1.NHI) sszczc sszozc angnr FOR nexr TIME , 33.0:c LET new renpcaarunzs BECOME OLD rznpcanruncs 3350=C 3363: DO 110 14:2.NR2 3370: DO 110 J¢=2.NH2 33308110 TA(IQ.J¢):TB(I99JO) 339D:C 3600:: DETERMINE AVERAGE PROCESS PHASE TEMPERATURE 39133C ' ' 39203115 SUMRTSSUMRTORT 3930325 CONTINUE 3940320 CONTINUE 3450: IFITINCRQEDQIQD) INT316 3‘60: IFETINCROEOQDO333’ INT:S ' 3970: AHEDIUHSSUHRT/(CICDUNT‘NPDSIRINT) 3490: PRINT R.33650'AMEDIUH8'9AMEDIUM 399D: RETURN ‘ 35:0: END APPENDIXC THEHGALDIETUSIVITYESTMTIQ‘IPW BASEDCNTHEIEASTSGIARESPWRE (MUDINGASAMPIECIH‘PUI') IOO:C 110=C 1203C 1303C 1902C 150:6 1608C 1703C 1803C I903C 2003C 2103C 2203C 2308C 2403C 2503C 2608C 2702C 280: 2903C 3008C 310:6 3208C 330=C SAOaC 3308C 3603C 3703C 3803C 3903C noose 4108C Azozc 4302C Q408C 450:6 QSOSC A7086 48086 #9osc 500:6 5108C 5208C :30:c 5403C 5502C 5808C 590: 600: 610: 6203C 630=C 6403C 63036 6603 6703C 6803C 6908 7003100 710: 750: 93 DIFFUSIVITY ESTIMATION PROGRAM HRITEN BY JOHN H. LARKIN (JAN. 1981) FORTRAN PROGRAM THAT HILL ESTIMATE THERMAL DIFFUSIVITY OF A SOLID FOOD PRODUCT FROM TIME. TEMPERATURE.DATA. COLLECTED FOR. ANY POINT IN THE FOOD SYSTEM. THE CALCULATION IS DONE USING A INITIAL ESTIMATION OF THE DIFFUSIVITY FROM THE MOISTURE CONTENT OF THE FOOD PRODUCT. IF THE MOISTURE IS NOT KNOUN THEN THE PROGRAM ESTIMATES IT AS SD (010) BY THE USER ENTERING 0.0 (010). THEN FROM THIS INITIAL ESTIMATION A THREE POINT GRID IS PRODUCED TO DETERMINE THE DIRECTION OF LEAST ERROR. THE ERROR IS CALCULATED FROM THE DIFFERENCE BETUEEN THE ACTUAL AND CALCULATED TEMPERATURE DATA POINTS FOR EACH INPUT TIME DATA POINT. NEH GRIDS ARE CREATED TO FIND THE MINIMUM ERROR UNTIL THE CHANGE IN THE ESTIMATED DIFFUSIVITY IS SMALLER THEN THE 'ERROR' FACTOR - CURRENTLY SET AT I.OE‘5. INPUT IS DONE USING READ UNIT 5. FOR IBM COMPUTERS CARDS CAN BE USED. FOR CDC COMPUTERS THIS MUST BE DIFFINED IN THE PROGRAM STATMENT PROGRAM DIFFUSCINPUToOUTPUToTAPEGQTAPESSINPUT) FOR IBM COMPUTERS THIS PROGRAM STATMENT MUST BE REMOVED. SD THIS CAN BE DONE BY PLACING A 'C' INFRONT OF THIS CARD. THE INPUT ts To BE ENTERED As FOLLOHS: CARD 1 z z - Axrs POSITION UHERE TEMPERATURE UAS HEAsuan: RADIAL POSITION UHERE TEMPERATURE HAs MEASURED (IN CENTIMETERS). NOTE THE 2 - szs ts DIPFINEO As THE MIDDLE BEING 0.0 AND THE TOP BEING THE HALF LENGTH as THE CAN. THE RADIAL POSITION IS DIFFINED As STARTING on THE 2 - AXIS ANO soxnc our To THE RADIUS or THE CAN. CARD 2 : LENGTH or cAH: DIAMETER or CAN (IN CENTIMETERS). CARD 3 3 MOISTURE CONTENT or FOOD PRODUCT IN PERCENT or NET HEIGHT aAsEsz AND (HE INVERSE BIOT NUMBER. CARD A a INITIAL TEMPERATURE: HEATING MEDIUM TEMPERATURE (SAME UNITS AS THAT USED FOR THE DATA INPUT). CARD 5 - N 8 TIMEIHRIT TEMPERATURE. DATA POINTS (ONE CARD FOR EACH DATA POINT). MAXIMUM 3 3°00 DIMENSION TIMECSDDIOTEMPC3DDITTERR(3)oSLABTI3DDoI)QCYLTCDDDQI)QTEM ¢PA(SDO)QHCI) COMMON SLABTQCYLT TIMECSDD) 3 TIME DATA POINTS TEMPCSDD) 8 ACTUAL TEMPERATURE DATA POINTS TEMPACSDD’ 3 CALCULATED TEMPERATURE DATA POINTS TERRIS) 3 ARRAY OF TOTAL SUMMED ERROR OF 3 GRID DIFFUSIVITY VALUES. IUARN=O. UARN IS A VARADLE USED TO LIMIT THE NUMBER FD UARNINGS ISSUED . NOU SET AS 5. SEE CLT SUBROUTINE. URITECGQIDD) FDRMATC'I'QZDXO'ESTIMATION OF DIFFUSIVITY FROM TIME 0.9/9. '935X9'DATA FOR A CAN.) REUIND 5 TEMPERATURE 94' 160: NUM=0 7708C READ POINT HERE TIME. TEMPERATURE DATA HAS COLLECTED. 780: READ(5.0)Z.R 7903C CHANGE TO METERS. BOD: ZMSZ/IDD. BIO: RMSRIIDD. 8208C READ DIMENSIONS OF CAN 8303 READI5.')CANL.CANR BRDaC CHANGE TO METERS AND DIAMETER TO RADIUS. BSD: CANLMSCANLICZfiIOD.) 860: CANRM:(CANRIIDD.)IZ. 8702C READ MOISTURE CONTENT. 980: READCS.')PMD.H 3903 IF‘PMOOEQOUODI PMO=50. 9003C READ INITIAL AND BATH TEMPERATURES. 910: READ(5.0)TEI.TEO 920: 00 10 131.300 9303C READ TIME. TEMPEATURE DATA. 9408 READ(S.'.ENDSZD)TIME(I).TEMPCI) 950:10 NUM8NUM.1 960: HRITEC6.1201 9703120 FORMAT('-'.5X."'fi HARNING 0'0 THIS PROGRAM HILL ONLY HANDLE'. 9803 .9 A MAXIMUM OF 300 DATA POINTS') 99086 ESTIMATE INITIAL DIFFUSIVITY VALUE. 1000320 SDIFF=ESTCtPM01 101036 ' 10203C CALCULATE A CLOSE ESTIMATE OF THE ACTUAL DIFFUSIVITY FROM 10303C A MIDDEL POINT. IDADSC 1050: TIN8.20 10608 NUMHSNUMIZ. 0 I 10708 CALL CALDIF(DIFF.SDIFF.TIME¢NUMH).TEMPCNUMH).TERR.ZM.RM.CANLM.CANR IDBDS OM.TEI.TEO.1.IHARN.H.TINI 10903 SDIFF=DIFF 1100: TIN=.002 1110=C 11208C USING THIS VERY CLOSE ESTIMATE OF THE THERMAL DIFFUSIVITY 1130:: CALCULATE NDH THE oxrrusxvxTv HITH ALL THE POINTS. 11.0:C ' 1150:. CALL CALDIF‘DIFF.SDIFF.TIME.TEMP.TERR.ZM.RM.CANLM.CANRM.TEI.TEO. 11603 ONUMoIHARN.M.TINI 11703C PRINT ALL RESULTS. IIBOSBDD HRITEC6.IJD)CANL.CANR.PMO.TEI.TEO.Z.R 11903130 FDRMATC'1'./.'D'.38X.'INPUT DATA'./."'.3DX.'LENGTH OF CAN3' 12008 *.GZD.5.2X.'(CM)'.I.' '.3DX.‘DIAMETER OF CAN='.GIB.S.2X.'(CMI'./.' 12103 9’93DX. ' 12203 O'MOISTURE CONTENTS..G17.3.2X.'(OID)'./.' '.JDX.'INITIAL TEMPERATUR 1230: 063'. 12003 OG14.5.I.' '.SOR.'BATH TEMPERATURE='.G17.5./.' '.SDX.'Z-AXIS'. 12503 O' POSITIONS'.GIB.5.2X.'(CM)'.I.' '.JOX.'RADIUS POSITION:'.GIB.5.2X 12603 0.'(CM)'.III.'-'.T30. 12708 O'TIME'.T45.'TEMPERATURE'.T60.'TEMPERATURE'./.' '.TSO.'(HR)'.T47.'A 1280: *CTUAL'.TGO. 12908 O'CALCULATED'.II) 12923 HRITE¢6.2) 129632 FORMATC'I'.I) 13008 SEESO. 1310: H(1)32M I320: CALL SLABCSLABT.H.I.TIME.NUM.CANLM.DIFF.H) 1330: H(1)=RM 13903 CALL CYLICYLT.H.I.TIME.NUM.CANRM.DIFF.H.IHARN) 1350: 1360: 1370: 1380390 13903 1900: 101081¢0 1‘20880 10308 1090: 14503150 1.60: 1A7D: 14808160 1490: 1500: 1510:C 1320:C 1530=C 1540: 1550: 1560: 1570: 1580: 1590:C. 1600=C 1610: 1620: 1630: 15402c 1650: 1660:30 1670: 1680: 1690:35 1700:C 1710: 1720: 1730:C 17403C 1750: 1760: 1770:C 1780: 1790: 1800: 18108 1820: 1830:C 1890:C 1850: 1860350 1870:00 18803C 1890:C 1900:C 19103 1920: 1930: 1990: 1950: .Ennoa .95 DO 90 I31.NUM TR:SLA8TII.1)'CYLTII.1) TEMPAII):(TEI-TEO)OTROTEO SEE:(TEMP(I)-TEMPA(I))-(TEMP(I)-TEMPA(IIIOSEE DO 80 I31.NUM URITEI6.190)TIME(I).TEMPCI).TEMPA(I) FDRMATI' '.25X.G12.5.T05.G12.5.T60.G12.5) courrnut sorrrrssotrr.1o.7539 HRITEC6.150!SDIFF.SDIFFF FORMAT!'-'.20X.'CALCULATED oxrrusxvrTv VALUEsv.azo.s.sx.v¢H2/HHTo. . 1.0 '.20!.'CALCULATED DIFFUSIVITY VALUE='.GZD.6.ZX.'(FTZ/HR1') HRITEI6.160)SEE FORMATI' '.T22.'SUM or SOUARED ERROR:0.628.6) sron END SUBROUTINE TO CALCULATE THE DIFFUSIVITY OF THE FOOD PRODUCT. SUDROUTINE CALDIFCDIFF.SDIFF.TIME.TEMP.TERR.Z.R.CANL.CANR.TEI. OTEO.NUM.IHARN.H.TINI DIMENSION TIMECSDD’.TEMPISOOI.TERRl3).SLABT(300.1).CYLTC300.1).H(1 9) COMMON SLABT.CTLT THE DIFFERENCE BETHEEN THE ESTIMATED DIFFUSIVITY VALUES IN THE GRID AT HHICH TIME THE COMPUTATION HILL STOP. NI:1 N533 ERROR=1.0E-5 INITIAL INCREAMENT OP DINC:SDIFF0TIN OIFF:SDIFF OIFFF=OIFF-2*OINC DO 35 I3NI9NS TENNII)3DOO CALCULATE 3 GRID POINTS. DO 40 I:NI.NS DIFF:DIFFF.I-DINC POR EACH TIME DATA POINT CALCULATE NEH TEMPERATURE PROFILE. FIND INFINIT SLAB TEMPERATURE RATIO. H(1):Z CALL SLAB!SLA8T.U.1.TIME.NUM.CANL.DIFF.H) FIND INFINIT CYLINDER TEMPERATURE RATIO. U(133R CALL CYLICYLT.H.1.TIME.NUM.CANR.DIFF.H.IHARN) DO 50 J:1.NUM TR:SLA8TIJ.1)9CTLT(J.1) TE:TEMP(J)-((TEI-TE019TRoTEO) SUM THE SQUARE OF THE DIFFERENCE BETHEEN THE ACTUAL AND CALCULATED TEMPERATURES FOR THE THREE GRID POINTS. TERRII):TECTE¢TERR(I) CONTINUE CONTINUE IF THE ERROR OF THE LOH GRID POINT IS LESS THAN THE MIDDLE GRID POINT THAN MOVE THE GRID SO THAT THE LOHER POINT IS NOH THE MIDDLE AND START THE SEARCH OVER. IFITERRII).GE.TERR(2)1 GOTO 55 SDIFP:SOIFF-OINC TERR(3)3TERR(2) TERR¢2)=TERR(1) NI=1 DIFFUSIVITY USED IN GRID SEARCH. 1960: 1970: 1980=C 1990:C 2000:C 2010355 202D: 203D: 20Q08 20508 2060: 2070: 20803C 2090:60 2100:C 21108C 212036 2130: 21A0: 2150: 21603 2170: 2180: 2190: ' 2200870 2210: 22203 2230: 2290: 2250:900 22603 2270: 2280:C 22903C 2300:C 2310:C 23203C 2330: 2340: 2350: 23608 2370: 2380: 2390: IF 96' NS=1 GOTO 30 THE ERROR OF THE HIGH GRID POINT Is LOHER THEN THAT OF THE MIDDLE GRID POINT THAN MOVE THE GRID SO THAT THE HIGH POINT IS NOH THE MIDDLE AND START THE SEARCH OVER. IF IFITERRI3).GE.TERR(2)) GOTO 60 SDIFF=SDIFFODINC TERR¢1)8TERR(2) TERRI2)8TERR(3) NI=3 NS=3 GOTO 30 THE CHANGE IN DIFFUSIVITY IS LESS THAN THE SET ERROR VALUE STOP . IFCDINC.LT.(SDIFF9ERROR)) GOTO 900 SINCE THE MIDDLE GRID POINT HAS THE LOHEST ERROR CUT THE GRID INCREAMENT IN HALF AND START THE SEARCH OVER NEAREST THE LOHEST ERROR CHANGE. OINC:DINCIZ.0 IPITTERRT1)-TERR(2)T.LT.(TERR(3)-TERR¢2)T) GOTO 70 SOIFF:SOIFF.OINC TERRI1):TERR(2) N132 NS32 GOTO 30 SDIFF330IFF-OINC TERR¢3T:TERR(2) N132 N532 GOTO 30 DIFF30IFP-OINC RETURN END FUNCTION TD CALCULATE THE INITIAL DIFFUSIVITY ESTIMATE FROM THE MOISTURE OF THE FOOD PRODUCT. BY THE USE OF ESTIMATION EQUATIONS FOR SPECIFIC HEAT (CP). THERMAL CDNDUCTIVITY (CON) AND DENSITY (DEN). FUNCTION ESTD‘FMOI CPSPHOIIOO0.0.2.(1000-P"0”1°o. CONZOND'FMO’IDOOPOZZP(IDOO'PMOIIIDD. DEN3P"°’1000.1032.(1°00'PH03’1000 ESTD3‘CON)[(CFPIDEN*1.E33I RETURN END 97 M TIME TEMPERATURE ON ESTIMATION OF 3.10 MM] CCU “‘ 030 ’) cc “ on 65°70 12° .8 O a Go 165 N T : ‘ nuuNN :AE TNCT “In N PCFC N nXL LO" 6. 90 Q5 1.2.. 8 E R U: RUOO ETII PATT MRI... EESS IBZN TEMPERATURE ACTUAL 00022029869552832108NSNSSN613221111596805920869“89367168526787 777795758792859625911105279232195169256887763185173838260‘7036 0.0.0.0...OOOOOOOOOOOOOO0.0.0.0.....0.000000000000000000000000 99999013581582593693692.791N68013567901233.56788900112233‘“Rs-35 NOOQ5.5555566677788899900001111222222233333333333ND.““RONONQN44R 111111.11.11.1.11111111111229.2222222222222222222222222222222222222 DODDDODOOODOODDDDDDOODDDODDDDODODDDDODDDODDODDDODODDDDDOODDOOD 760676232373063337023219M92355307271G6777753296.305171605826936 .ooooooooocoo-6.6.0.6....oooooooooo0.00.0.6...cocoooooooooooo. 98877802531592693603692N792458D235639012345677890011223334R455 934GA.RSSSEEGOTTT889999D00011111222229.2332....3331...:3...4GGORRNQRRRRRR 11111I1111111111111111222222222.4222222222222229.222222222222222 11111 00000 ..... EEEEE DDODDDDDODDDDDDDDDDOODDDDDDDODDODODDDDDDDDDODODDDDDDDOODODDDD DDDDDDDDDDODDODDDDDDDDDDDDDDDODDDDDDDDDDDDDDDDDDDODDDDDODDDDT 0000007307307307307307307307307307307307307307307307307307301 73073013568013568013568013568013568013568013568013568D1356BDD 13368111111222222333333AAAA4#555555666666777777888888999999.. 00.000000000000000...00.00.000.000.00.00.00...0000.00.00.00011 O 98 DDDD 81.37 a o o o: : APPENDIX D POLYMEAL INI'ERPGIATICN FUNCI'IQ‘I SUBMTI'INE 100: 110:C 1208C 130:C 1.0:C 1303C 1603C 170:C 1808C 1908C 210: 220: 2303 240: 250: 260: 2703 2803 2903 3003 3103 3203 3303 3.03 330: 3603 370: 380: 3903 A00: .103 420: A30: 440: 050: A608 470: 4803 .903 300: 310: 320: 330: 3.03 350: 360: 3703 :80: 390: 600: 610: 6203 6303 6.03 6503 12 11 10 15 16 99 FUNCTION TERPI‘X.XI.YI.N.F) X IS THE INDEPENDENT VARIABLE XI IS AN ARRAY OF VALUES OF THE INDEPENDENT VARIABLE YI IS AN ARRAY OF CORRESPONDING VALUES OF DEPENDENT VARIABLE N IS THE SIZE OF THE ARRAYS F IS A FACTOR FOR THE END SEGMENTST BALANCE OF FIRST OND SECOND ORDER INTERPOLATION ALL VALUES OUTSIDE THE LIMITS OF THE ARRAY ARE COMPUTED BY FIRST ORDER EXTRAPOLATION FUNCTION RETURNS INTERPOLATED VALUE OF DEPENDENT VARIABLE DIMENSION XI(N).YI(N).P(2).E(2).IS(Q.2) LOGICAL OUT DATA IS l-1.D.‘2.‘1.D.1.‘1.DI OUT 3 QFALSEO 481 IF (N‘2) 1.12.3 TERP18YIIJ) RETURN KPL:1 KPU:2 DO A J81.N IF (XI(J) - X) 4.1.6 CONTINUE J 3 N GO TO 2 IF (4'2) 12.8.9 KPL :2 GO TO 10 IF (J 0 N) 10.11.2 J32 OUT3.TRUE. KPU:1 AL 3 (X-XI(J'1)) /(XI(J)-XI(J'1)) TERP18ALRYIIJ)O(1.O-AL)'YI(J-1) IF (OUT) RETURN DO 16 KP:KPL.KPU P(KP)=0.D DO 15 K81.3 JoadOKP . K - 4 XO:XI(JD) YO:YI(JO) 413JOISKK.KP) JZSJOIS(K01.KP) P(KP):P(KP)OYO*(X-XI(J1))I(XO-XI(J1)) P(X-XI(J2))/(XO-XI(J2)) IF (KPL .NE. KPU) GO TO 16 I J133-KPL P(J1)=TERP1OF*(P(KP)-TERP1) E(J1):ABS(P(J1)-TERP1) E(KP):ABS(P(KF)-TERF1) IF (E(1):E(2) .EO. 0.0) RETURN TERP1=((E(1)'AL)'P(2)O(E(2)O(1.0-AL))*P(1)) I ((E(1)'AL) 0(E(2)t(1.0-AL)) ) RETURN END APPENDIXE mmmpmm mmmoo (MUDmGASAMPIEwI‘PUI‘) . 100 99:c.09.....tttttcttattc....ctttacc..v............c..§..otootcttctcvtt 133=CPPPPRROO GENERAL METHOD PROGRAM .n....:.....vc....oot 101:c........ EHPLOYING THE TRAPEZCIOAL RULE .c..........t....c... 102:c.........::....uttttttocctvtttttccct....6.9.....c::..t...ot.....t 1033C THIS PROGRAM READS THE CENTER-CAN TEMPERATURES FOR EACH PROCESS 1:.3C 105=C PHASE AND CALCULATES LETHAL RATE FOR A SELECTED Z VALUE. AND REFER- ENCE TEMPERATURE. LETHALITY IS INTEGRATED USING A SIMPLIFIED TRAPE- 1C6=C IOIDAL RULE FOR A SPECIFIED INITIAL TEMPERATURE AND RETORT TEMPERA- 10730 TURE TO YIELD A F VALUE. 1083C 1393C THE FIRST CARD OF THE ENTERED DATA FILE (TAPE1) MUST CONTAIN THE FOL- 1138C LOHING INFORMATION IN THIS ORDER: 1113C 1123C 1) RUN NUMBER (K) 1133C 2) NUMBER OF TIME/TEMPERATURE POINTS IN DATA FILE (J) 11¢=C 3) REFERENCE TEMPERATURE- USUALLY 250F OR 212F (R) 115:C A) Z VALUE (2) 1163C 5) RETORT TEMPERATURE (RT) 117:C 6) INITIAL PRODUCT TEMPERATURE (TI) 1133C 1192C FOLLOHING THE FIRST CARD IS THE NOSEOUENCE TIME/TEMPERATURE 1203C PRODUCT PROFILE(S) TO BE EVALUATED FOR LETHALITY. 1213C 1223C THE POSSIBLE COURSES OF ACTION THAT MAY BE TAKEN ARE: 1238C 0: NO TI OR RT CONVERSION 1293C 1: CONVERT TI 1253C 2: CONVERT RT 1263C 3: PRINT OUT ARRAYS (MIN.CCT.LRIMIN) 127:C A: ENTER A NEH DATA SET 129:C 5: PLOT LETHAL RATE VS TIME 1293C 63 CHANGE Z 1303C 7: EXIT THE PROGRAM 131:c....tocctc.ctittiovcctttit...to....c:oo.cc...to.tcttctttcttctttc 1493c.:...tc9ctttvc:t:c¢::::t.:9:tt.Qt:tivovttvtcttot§fioottottc09...: 1303C SCHULTZ-OLSON IT AND RT CONVERSION OPTIONAL: J=NUM6ER OP COOTDINATES 1603c :REFERENCE TEMPERATURE.Z:SLOPE OF TOT CURVonzELAPSED TIME.T=COLO- 110:0 POINT TEMP..KSET:OATA SET NUMBER.K:CAN NUMBER.RT:ORIGINAL RT.RT2:NEH 133:: RT.TI:ORIGINAL IT.ST2=NEH IT.C=LFTHAL RATE 1°02 PROGRAM GENMETH!INPUT.OUTPUT.TAPE1.TAPE2.TAPE6) 200: DIMENSION XIGSD). Yt630). C(630) 210: DIMENSION AFILE¢650.2).ICXII).ICY¢1).ICP(1).SCXC2).SCY(2) 220: ‘.CHAR(2) 232: EGUIVALENCETAFILEI1.1).xc1)1.(AFILE(1.2).C(1)T 2.2: CHARACTER *8 CHAR 2503C PRINT TITLE AND DIRECTIONS 260: PRINT 5 210:: FDRMATT1H-.36X..6HG E N E R A L M E T H O D F v A L U El! 281: 0!) 299:0 INITIALIZE DATA SET NUMBER 300: KSET : 1 31:: PRINT DATA SET SUB-MEAD 320: PRINT 39.KSET 332:3? FORMATTIHD..6X.12HOATA SET NO..I3.10H PROBLEMS:III) 340: I6 3 3503C REQUEST COURSE OF ACTION 360337 PRINT*.'HHAT NEXT?‘ 370: READ'.X8 383: PRINT R3 390: I2 = 1 ADD: IFCRB.ED.O) GO TO 57 410: GO TO (57.57.77.57.57.63.77).Ka Q2037? IEAKOOEOOTI STOP .30: PRINT*.'ENTER NEH Z' 101 440: READ..Z 653: GO TO 17 963383 FORMAT(I) #70363 IF(I6.LE.1)GO TD 22 9808C IMCREMENT DATA SET #903 KSET 8 KSET 9 1 530:C PRINT DATA SET SUB-HEAD 5153 PRINT39.KSET 526: GO TO 22 5 2:57 IFIK8.EO.5) GO TO 1122 540: IF(I6.GT.1)GO TO 59 550: REHIND 1 563322 READ(1.'.END:77)K.J.R.Z.RT.TI 57":C SET X ARRAY TO '1 58?: DO 1 J2 3 1.630 5908 X(JZ) 3 '1. 6D031 CONTINUE 6103C READ TIME VS. TEMPERATURE COORDINATES 6293 DO 41 N 3 1.d 63D: READ(1.O)X(N).Y(N) 640:41 CONTINUE 6533 16 3 16 P 1 662: IF(KB.LT.1)GO TO 59 6798 IF(N8-O)29.59.37 680359 IF(RB.LE.2)GO TO 29 6903 REHIND 6 750: HRITE(6.52) 7108C PRINT X.Y.C ARRAYS--.X = '1. IS A RECORD FILLER 720:!2 FORMAT(1H .19X.2§HMIN. CT. LRIMIN ARRAYSIIII19X.3HMIN.5X.2HCT.8X. 733: 06HLRIMIN.GX.3HMIN.5X.2HCT.8 7RD: PX.6HLRIMIN.6X.3HMIN.5X.2HCT.7X.6HLRIMINII) 750: D0 58 NA : 1.J.3 760: HRITE(6.71)X(NA).Y(NA).CCNA).X(NA01).T(NAO1).C(NA¢1).X(NA92).Y(NA: 77D: 02).C(NAO2) 780:71 FORMAT(12X.3(5X.F6.2.3X.F6.2.3X.FB.3)) 790858 CONTINUE 3303 PRINT 03 310: GO TO 37 92:32? GT:RT 832: PT:TI 8.0: IF¢K8.GE.1)GO TO 99 350817 DO 65 I3 = 1.J 9608C CALCULATE LETHAL RATE 870: C(13) : 1.IEXP(2.30263(R-Y(13))12) 880: IF(12.GT.1)GO TO 88 395: S : XIIS) 900: T = C(13) 910: A F0 : D. 922:38 A : (X(I3)-S)tTOIXIIS)-S)t(CtI3)-T)/2. =30:c ACCUMULATE LETHALITY 94c: FD : F0 0 A 950: 12 = 12 . 1 960: S = XCIS) 970: T : C(13) 980:65 CONTINUE 9903C OUTPUT RESULTS 1050: PRINT66.K.Z.R.FO.GT.FT 1010365 FORMATIIHPOZSXQAZHFOR CAN NO. 912.3" FIQFOglngQQFSOIOPH) 3 9 13203 *FB.2.19H FOR RT = .F5.1.7h. IT 3 .F501///) 103D: RT36T IOAO: TIzFT 1050: 1:60:99 102 GO TO 37 IF(K8.GT.1) GO TO 33 1072=C INPUT NEH IT 1080: 1390: 11003 1110: 1120: PRINTO.'NEH IT : ' READ'.ST2 PRINT 83' PT : ST2 DO 79 L : 1.J 11308C CONVERT TEMPERATURES FOR MEN IT 1140: 1150379 1160: CALL ITEMP(RT.TI.ST2.Y(L)) CONTINUE GO TO 17 1170=C INPUT NEH RT 1180833 1190: 1200: 1210: PRINT9.'NEH RT : ' READP.RT2 PRINTB3 GT : RT2 - 1220:C CONVERT TEMPERCATURES FOR NEH PT 1230: 12403 125039 1260: 1270:1122 1280: 1290: 1300: 1313: 1320: 1330: 1340:102 1350: 1363: 1370: DO 9 L2 3 1.J CALL RTEMP(RT.TI.RT2.Y(LZ)) CONTINUE GO TO 17 CALL PLOTA(50.50.2.1.6.0.0.0.0.Do0) ICXI1)31 ICY(1)=2 ICP(1)=J CHAR(1):'.' IND:0 HRITE(6.102) FORMAT('1'.26X.' LETHAL RATE VS. TIME') CALL PLOTB(AFILE.CHAR.ICX.ICY.ICP.SCX.SCY.2.1.630.IND) GO TO 37 END 13808C SUBROUTINE ITEMP CONVERTS TEMPERATURES FDR NEH IT 1390: 1400: 1410: 1420: 1430: 1:40: 1450: 1460: SUDRDUTINE ITEMPCRT.TI.STE.Y) X8 : RT - ST2 X7 : RT - TI xs 3 xe I X? _ ’ x9 3 RT - Y ' Y : RT - X6 1 X9 RETURN END 1470=C SUBROUTINE RTEMP CONVERTS TEMPERATURES FOR NEH RT 14503‘ 1490: 15:0: 1210: 1520: 1330: 1540: 1550: SUBROUTINE RTEMP(RT.TI.RT2.Y) xe : RT2 - TI x7 : RT - TI X6 : X8 I X7 x9 : RT - Y Y = RT2 - XS 3 x9 RETURN END 103 ARRAYS: NIH. C70 LRIIIN LRIHIN CT LRIIIN HIN CT LPININ CT PIN 000000139951725519425686680653690110265666880246319276889854942C24604773430 00000009915699952352954114037‘30099085‘SSSQ0‘32197427339629754329 989765544. 00000000000001123345566‘66777777766766‘6666666665555.4322211111100000000000 OOOOOOOOOOOOOO0.000...OOOOOOOOOOOOO0.0.0000000000000000.00....O...00.000... 10952963193755.332221111111111111111111111111111111222533344455566€65677773 334 55 84035717723126.19 8762262‘39‘321120797776654329639 25557423681435826850437 coco-o.oooooooooooooooooouoocoo.oocnooooooooooooocoono...cocooooooooooooooo 885566652833147912345‘fi‘fi‘77377777777“6666666‘6555443109876544311099877654 QQ56739°II22333300 QQ 09. .QQQQO OQQORQQ .QQQQ.QQQQO Q... QQQ031331.3333332222222 IIIIII122222222222222222222222222222222222222222222222222222222222222222222 .00000000000000000000000000000000000000000000000000000000000009000090000300 000000000000000300000024$3.24609135791357,135‘9124680246802467313579135690? on...coco-coco...00.00.000.00...coco.ooooooooooocooaooooooooocoo-cocooooooo as.“703692581.1036928.5gs6“6““77777“558599999000001.111122222233333.Q Q O Q 55 111:22223334‘ .5555‘6‘5‘ 66 6 ‘66‘fi6‘6‘6‘6‘666‘7777777777777777777777777777 0000001264814564236212‘06607555801192355‘688024008‘9‘2639961305736047075C61 00000000012582730‘30735015027751099087‘655444320075294517408653219937755544 000000000000011233435‘S6667777777fifi7566666‘6‘666655544332221111110000000?99 O0.0.0.0000.000.000...0.00.00.00.00.0000IOOIOOOOOOO000.000...00.0000.0000.0 0196307420“"‘543322211111111I1111IIIIIIIIIIIIIIIIII122233304405556666677777 906OP53206 6745615664752723008421130980776654300740569901668138a6169162580 00.00000000000000000000.0000000000000000cocoooooooooooooooooocoo-0.00000... 862 23320626036802345666667700777777766666666666655!43100976554321109977655 445 890112233334444444444444fl4fi4444444444044444044444444333333333332222222 11111112222222222222222222222 2 2222222222222222222222222222222222222222222 000000300000000000000000000000000000000000000000000000000000200000090000?00 0000000000000000000000143791337913579124680240802467913579133791346802.6902 OOOOOOOOOOOOOOOCOOCOOCOOOOOOOCOOOOOCOCOOOOOOOCOOOOIOIOOOOOOOOOOOOOOOOOOO... 147036925014703692501453535666667777700008’99990000001111122222333334444453 111122233344445556666666666666666666666666667777777777777777777777777777 .90....291322074,707,.‘IQ.3.‘55‘.II°1“"5“““.0.9‘05329547795105007735915‘173 0000000001247151741740542471476309909 44421086406318019754319037765544 0000000000000112234450‘66‘6777777‘67‘6‘ 66666fifi6655554332221111110000000000 0......0000......OOOOOOOOOOOOOOOO...OOOOOOOOOOOO00.00.000.000..0...00.0.0000 .10741.53197‘3443222IIIIIM”IIIIIIIIIII11111111111111222333444455556‘6‘67777 0,55301354324759'70d317‘3 47.9‘2112199877765532185270502I°01460274713‘4713 00.000000000000000. O.0000000.o.000.00000000000000.0000.0000000000000000000 0708900974059257013.5‘6‘6667737777777‘666‘66“66655544210.87654431100987665 5455‘3990122233344444444444404444444444444444440444444444333333333333222222 13111113222329.2222:gasgszgzzzzzzzzggzzz 22222222293129.2222 222222 0000.0000000‘00000000000000000000000000000030000000000300000000000000000000 CUOOUDUOOOROUOUOOUOU0.133791246302468024$7,1357913579135‘9024‘5024‘30135791 0....OOOOOOOOOOOOOIO0.0.0.00...OD...OOOOOOOOOOOOOOOOOO0.0000.00.00...0.0... .3‘92581470369250147035555556 6‘7777783888899999000091111122222333334404445 11122233334445536‘6‘66‘66 ‘6666‘666666666666777777777777777777777777777 APPENDIXF W100 mm: ENGLISH TO S.I. UNITS 104 APPENDIX F Conversion Factors English to S. I. Units 1 inch = 2.54 centimeters 1 lb = 0.4536 kilogramgs Fahrenheit (°F) to Centigrade(°C): (°F - 32) (5/9) = °C Diffusivity: . 2 . -5 2 m/mm=l.08x10 m/sec Englishmitsmreusedinthis suflyduetotheconventions of the food industry (e.g., Fahrenheit mentoreters in processing plants are more typical than not) . IIS'I‘OFREFERENCES _ 105 LIST OF REFERENCES Anon. 1977. Continuous in-container sterilization of products. Stork- , 'I’ne Netherlands. Anon. 1978. 0.15th flienncmples. O.F. Ecklund Inc., Cape Coral, FL. Anon. 1978. Model 6000 dataretriever system. Aware: Corp” Autodata Division, Pbuntain View, CA. Anon. 1980. Doric digitrend 220 datalogger. Doric Scientific, San Diego, CR. Arpaci, V.S. 1966. "Carintion Heat Transfer," Addison—Wesley Pub. Co., Inc. Reading, MA. Ball, C.O. 1923. Thermal process time for canned food. Bull., Nat. Research Council. 7-1, No. 37. Ball, C.O., and Olson, F.C.W. 1957. "Sterilization in Food Technology," McGraw-Hill Book Co., Inc., NY. Bigelow, N.D., Bohart, G.S., Richardson, A.C., and Ball, C.O. 1920. Heat penetration in processed canned foods. Bull. 16-L. Natl. Canners ' Assoc., Res. Lab., Washington, D.C. ‘ Board, P.W., Cowell, N.D., and Hicks, E.W. 1960. Studies in canning processes. III. The cooling phase of processes for products heating by conduction. Food Res. 25:449. Carslaw, H.S., and Jaeger, J.C. 1959. "Corxiuction of Heat in Solids," 2nd ed. Oxford University Press, Great Britain. Cedar, J.C., and Outcalt, D.L. 1977. "Calculus," Allyn and Bacon, Inc., Boston, MA. Center for Disease Control. 1979. MR 28:74. Gillespy, T.G. 1951. Estimation of sterilizing values of processes as applied to canned foods. I. Packs Heating by conduction. J. Sci. Food Agri. 2:107. GilleSpy, T.G. 1962.. The principles of heat sterilization. In "Recent Advances in Food Science," Vol 2. Processing. Butterworths, London. Griffin, R.C., Jr., Herndon, D.H.,and Ball, C.O._ 1971. Use of computer-derived tables to calculate sterilizing processes for packaged foods. 3. Application to cooling curves. Food Technol. 25(2):36. 106 . Hayakawa, K. 1969. Estimating the central tanperatures of canned food during the initial heating or cooling period of heat process. Food Technol. 23(11) :141. Hayakada, K. 1970 . Ecperimental fonuulas for accurate estimation of transient tanperature of food and their application to thermal process evaluation. Food Technol. 24(12):1407. Hayakma, K., and Ball, C.O. 1971. Theoretical fornulas for tauperatm'es in cans of solid food and for evaluating heat processes. J. Food Sci. 36:306. Hayakawa, K. 1977. Mathemtical methods for estimating proper thermal processes and their cauputer implementations. Adv. Food Res. 23:75. Helmer, V.H., Alstrand, D.V., Ecklmxd, O.F.,and Benjanin, ILA. 1952. Processing and cooling of canned foods. Sane heat transfer problem. Ing. Eng. Chem 44:1459. Hersan, A.C., and Hulland, E.D. 1969. "Carmed Foods. An Introduction to their Microbiology," 6th ed. J. and A. Churchill Ltd., London. Holman, J.P. 1972. "Heat Transfer," McGraw-Hill, Inc., NY. Kautter, D.A., and Lynt, R.K., Jr. 1971. FDA Papers. Nov. Larkin, J.W. 1981. Unpublished data. Michigan State University, East Lansing, MI. Lenz, M.K., and Lund, D.B. 1977. The lethality-Fourier nunber method: experimental verification of a nodel fcr calculating tenperature profiles and lethality in urination-heating canned foods. J. Food Sci. 42:989. Merson, R.L., Singh, R.P., and Carroad, P.A. 1978. An evaluation of Ball's fonnula method. of thermal process calculations. Food Ted'nol. 32(3):66. Myers, G.E. 1971. "Analytical Methods in Conduction Heat Transfer," McGraw-Hill, Inc., NY. Nadler, A.D. 1980. Taxing energy insteadof income. The New York Times, Sunday, May 25, Sec. K. Orlcwski, J .M. 1979. Energy and quality simulation of thermal processing in cans and retort pouches. Depart. of Agr. Engr., M.S. thesis, Michigan State University, East Lansing, MI. Patashnik, M. 1953. A simplified procedure for thermal process evaluation. Food Technol. 7:1. 107 Perkins, W.E. 1964. Prevention of botulism by thermal processing. In "Bctulism," Environmental Health Series. 0.8. Dept. of Health, Education and Welfare. Public Health Service Publication No. 999-FP-1. Perkins, W.E. 1978. Discontimms and continuous retorts. In "Intro- duction to Rudimentals of Thermal Processing," IFI' Short Course. Institute of Food Technologists, Chicago, IL. Perkins, W.E. 1980. Unpublished data. Moorestown, NJ. Schultz, C.T., and Olson, F.C.W. 1940. Thermal processing of canned foods in tin containers. III. Mcent :improvenents in the general method of thermal process calculations . A special coordinate paper and methods of converting initial and retort tenperatures. Food lbs. 5:339. Singh, R.P. 1977. Energy consunption and conservation in food sterili- zation. Food Technol. 31(3) :57. Singh, R.P., Carroad, P.A., Gunman, M.S., Ibse, W.W.,and Jacob, N.L. 1980. Energy accounting in canned tanato products. J. Food Sci. 45:735. ' Stunbo, C.R. 1973. "'Ihenrobacteriology in Food Processing," 2nd ed. Acadanic Press, NY. Sugiyama, H. 1980 . Clostridium botulinun neurotcxin. Microbiological Reviews. 44:419. ‘I‘trrtpson, G.E. 1919 . Temperature-time relations in canned foods during sterilization. J. Ind. Eng. Chem. 7:657. Tovmsend, C.T., Saners, I.I., Lanb, F.C., and Olson, N.A. 1968. "laboratory Manual for the Gaming Irdustry," Vol 1. AVI Pub. Co., Westport, CT. Teixeira, A.A., Dixon, J.R., Zahradnik, J.W., and Zinsmeister, G.E. 1969. Canputer optimization of nutrient retention in the themal proces- sing of conduction-heated foods. Food Technol. 23(6) :137.