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A mathematical solution for food thermal process design
Full text linkA new mathematical procedure was developed to correlate g (the difference between the retort and the coldest point temperatures in canned food at the end of the heating process), fh/U (the ratio of the heating rate index to the sterilizing value), z (the temperature change required for the thermal destruction curve to traverse one log cycle) and Jcc (the cooling lag factor). These are the four heat penetration parameters of 57 Stumbo's tables (18,513 datasets) in canned food. The quantities fh/U, z and Jcc are input variables to determine the g values, which is used in Ball's formula to calculate the heating process time B at constant retort temperature. The new procedure was based on three equations; the first was obtained by the inversion of the function that expresses the process lethality, F, and hence the fh/U parameter. However, the inversion was possible for a sub-domain of the function. The inverse function g = g(fh/U, z, Jcc ) was then extended to the entire domain (10°C ≤ z ≤111°C , fh/U ≥ 0.3 and 0.4 ≤ Jcc ≤ 2 ) using two polynomials (second and third equation) obtained with articulated multiple regressions starting from the Stumbo's datasets. A comparison between the calculated value of g and desired Stumbo's values of g provided the following values: a determination coefficient R2=0.9999, a mean relative error MRE=0.85±0.91% and a mean absolute error MAE=0.06°±0.09°C (0.11°±0.16°F). The results obtained by applying the mathematical procedure of this work, namely the g values using the three equations and the process time B using Ball's formula, closely followed the process time calculated from tabulated Stumbo's g values (root mean square of absolute errors RMS=0.393 min, average absolute error=0.259 min with a standard deviation SD=0.296 min). The high accuracy and simplicity of the procedure proposed here, make it useful in the development of mathematical algorithms for calculating and controlling, by computer, of food thermal processes. These algorithms replace the 57 look-up tables and 18,513 data sets needed in the Stumbo formula method. As such, this work offers a computerized formula method as an alternative to existing computerized numerical methods for this purpose
Design of the optimized and downsized axial fan for the air carrier orchard sprayers
Full text linkThe new vineyard and orchard installations are made with a high intensity of plants per hectare and therefore with a reduced distance between the rows. The tractors and the air carrier sprayers for plant protection, must therefore have smaller width.
In consequence, a method of design of axial fans for the air carrier sprayer, to get a small diameter without losing the performance required by the agrochemical applications, must also be studied. The new method was found by imposing a law of Compound Vortex for the tangential component of absolute air speed. In consequence the equations for: the axial component of the absolute air velocity, the flow rate, the total specific energy and the invariance of the lift coefficient versus the radius, were found. Then, the method consists in the solution of the system of these four equations to determine the fan design parameters. This new method allows to obtain a reduction of the external diameter of the fan by a factor of 0.8 and a reduction of the lift coefficient because imposed constant vs. the radius. Therefore the new method may allow to further increase the total specific energy. Finally, there was no significant difference between the average speed, relative to airfoils, of the new method (Compound Vortex) and of the traditional method one (Free Vortex) and then there are no downgrades in the fluid dynamic efficiency
The check problem of food thermal processes: A mathematical solution
Full text linkTo calculate the sterilizing value U, and hence, the microbial lethality F in thermal processes of the canned food, starting from the knowledge of heating time B, a mathematical modeling was carried out. Therefore it’s useful to verify the desired microbial destruction (check problem) and it was obtained by reversing the mathematical approach carried out in a previous work [23] for the design problem, namely to calculate the retort heating time B, starting from a desired lethality F and, hence from the fh/U parameter. A comparison between the predicted fh/U, related to the lethality F calculated with the mathematical model of the present work and the desired Stumbo’s values of fh/U, provided the following statistical indices: a mean relative error MRE=1.18±2.11%, a mean absolute error MAE=1.61±11.7 and a determination coefficient R2=0.991, better than ANN models. The mathematical procedure, quickly usable also with a spreadsheet, replaces the 57 Stumbo’s tables and 18512 data sets in the Ball formula method
INGEGNERIA DELL'INDUSTRIA ALIMENTARE
No full textIl volume Ingegneria dell'Industria Alimentare vuole essere un utile strumento per gli studenti, i tecnologi e gli ingegneri, quindi persone di diversa formazione culturale, affinché possano più facilmente comprendere e ottimizzare i processi dell’industria alimentare.
I processi possono essere visti come il susseguirsi di singole operazioni (unitarie) ciascuna delle quali richiede anche una modellazione fisica e matematica e di conseguenza l’approntamento di strumenti di calcolo e di ottimazione delle relative macchine ed impianti.
Con questi obbiettivi, nel volume vengono richiamati di volta in volta alcuni argomenti base calati nella realtà dell’industria alimentare, come la meccanica dei solidi e dei fluidi, la trasmissione del calore e il trasporto di materia. Quindi vengono affrontate le più diffuse operazioni unitarie: trasporto di prodotti fluidi e semifluidi, estrazione meccanica e per solvente, decantazione statica e centrifuga, flottazione, filtrazione, microfiltrazione, ultrafiltrazione, nanofiltrazione, osmosi inversa, pastorizzazione, sterilizzazione, concentrazione, refrigerazione, surgelazione, essiccazione, liofilizzazione e distillazione. Sono anche presenti varie applicazioni numeriche e molti dati relativi alle proprietà di vari prodotti alimentari.
Didatticamente il testo è destinato agli allievi dei corsi di laurea in Scienze e Tecnologie Alimentari, sia di primo che di secondo livello, ma è organizzato anche con vari paragrafi e appendici di approfondimento per fornire ulteriori strumenti di calcolo ai tecnologi e agli ingegneri operanti nel mondo dell’industria.
Per il livello degli argomenti tipico dei corsi di insegnamento di Ingegneria dell’industria alimentare, di Macchine e impianti dell’industria alimentare e di Operazioni unitarie, queste parti di approfondimento possono essere omesse senza che venga a perdersi la continuità del percorso didattico
INFLUENZA DELLA FORMA E DELL'ESTENSIONE DEI DIAFRAMMI SULLA MISCELAZIONE DI FLUIDI ALIMENTARI CON AGITATORI A GIRANTE RUSHTON
No full textA test bench for performance measurements of the mechanically agitated vessels working in turbolent mixing was assembled.
A comparison between two mechanically agitated vessels with different pattern of baffles was carried-out. The first had four usual laminar baffles and the second had four new baffles with a triangular shape. These baffles was proposed to reduce the fouling and to improve the cleaning.
For both baffles pattern a various tests changing the width were carried-out. So power and mixing time were measured and mixing energy was calculated. For triangular baffles the power was smaller than for laminar baffles, whereas the mixing time was highest and the mixing energy was the same. Finally, the width influence for both baffles pattern showed that power, time and energy, were steady for B/T = 0,10
ANALISI DIMENSIONALE DELLA SEPARAZIONE DI PARTICELLE SFERICHE DA SOSPENSIONI ALIMENTARI DILUITE
No full textPrediction of the settling or rising velocity of particles or bubbles finds application in many processes of food industry (gravitational or centrifugal settling, flottation, ecc.)
In this paper we concern with the simple case of terminal velocity of a single rigid sphere in unbounded volume of the fluid phase (very dilute food suspension).
On the basis of asymptotic analysis, Nguyen et Al. (1997) showed that the terminal velocity of a rigid sphere can be directly predicted on the basis of the physical properties of the solid particle and fluid medium via Archimede number, by a single formula valid for Reynolds number up to 1000.
By a dimensionless number analysis we obtained, in this paper, an improved formula for the terminal velocity. We showed that our equation is careful and simple in the same way, but is valid for Reynolds number up to 10000
STUDIO TEORICO E SPERIMENTALE DI EIETTORI A VAPORE E A GAS
No full textSteam and gas jet ejectors are an essential part in concentration, desalinization, refrigeration and vacuum production of food industries and not only.
The ejector theory saw the contribution of many authors in the time, among them stand out Munday and Bagster. But many experimental studies showed this theory too optimist. In this work some changes at the theory concerning the diffusion fenomena was proposed.
Furthermore a modifications of momentum equation and energy equation were proposed to consider the primary and aspirated gas as different fluids.
To evaluate the modified theory, an experimental ejector was assembled and tested and, in comparison with Munday and Bagster theory, an improvement was estimated. In addition the two mathematical models was compared with further experimental data from scientific literature. The values of the average error between the calculated and experimental ejection coefficient was 42,2% and –3,9% for the old and modified theory, respectively
STUDIO DI UN IMPIANTO E PROVE SPERIMENTALI DI STRIPPAGGIO DELL'ANIDRIDE SOLFOROSA DAI MOSTI D'UVA
No full textFor technological and economical reasons, in the grape juices production the long time storage of the must is made by addition of sulphur dioxide (up to 2000 mg/l).
For legal reason, on preparing and packing the juice, the stripping of the sulphur dioxide is necessary (legal limit is 10 mg/l). The available stripping plants date back to a patent of 1955 and they have serious troubles to obtain such a deep stripping with economical productivity.
Therefore a mathematical model was given to predict the sulphur dioxide stripping by the steam generated from the must; in fact it is forbidden to utilise steam of the boiler. This allowed a right design and the construction of a pilot plant.
Experimental results, on different musts, indicated that the new pilot plant is able to stripping with a residual sulphur dioxide under the legal limit. A residual concentration range of 5-9 mg/l was obtained. Also, a high productivity (6000 kg/h) was obtained against about 1000 of old plants
Energy saving with total energy system for cold storage in Italy: Mathematical modeling and simulation, exergetic and economic analysis
Full text linkWith the aim of energy saving in cold storage in Italy, an integrated system (Total Energy System - TES) was considered for production of cold air, obtained by assembling compression system, absorption system and cogeneration unit (CHP) fuelled with methane-gas, in two different plant solutions: 1) TES consisting of the CHP, mechanically coupled with the compression refrigerating machine and thermically with the absorption system both designed to cool the air in the store rooms; 2) TES* characterized by the CHP, mechanically coupled with the compression refrigerating machine, designed to cool the air in the store rooms, and thermically with the absorption system designed to cool the air in a pre-refrigeration plant. A mathematical modeling and a consequent computer simulation of the behavior of both integrated system (TES and TES*) and both related conventional systems (CES consisting of a compression machine to cool the air in the store rooms and CES* characterized by two compression machines, the first cooling air in the store rooms, the second cooling air in a pre-refrigeration plant) was carried out. As an overall results, an energy saving of 21÷16% was calculated. Considering the difficulty of comparing the different types of energy involved, an exergetic analysis was also carried-out, confirming a better exergetic efficiency of TES vs. CES. Finally, an economic evaluation was also conducted with a very attractive profitability index for TES and TES* systems fuelled with natural gas. The economic analysis showed that the use of bio-methane, in the TES system, is profitable up to a bio-methane cost of 0.46 €/m3
A New Mathematical Model for Food Thermal Process Prediction
Full text linkA mathematical model was developed to correlate the four heat penetration parameters of 57 Stumbo’s tables (18,513 datasets) in canned food: g (the difference between the retort and the coldest point temperatures in the canned food at the end of the heating process), fh/U (the ratio of the heating rate index to the sterilizing value), z (the temperature change required for the thermal destruction curve to traverse one log cycle), and Jcc, (the cooling lag factor). The quantities g, z, and Jcc, are input variables for predicting fh/U, while z, Jcc and fh/U are input variables for predicting the value of g, which is necessary to calculate the heating process time B, at constant retort temperature, using Ball’s formula. The process time calculated using the g value obtained from the mathematical model closely followed the time calculated from the tabulated g values (root mean square of absolute errors RMS = 0.567 min, average absolute error = 0.421 min with a standard deviation SD = 0.380 min). Because the mathematical model can be used to predict the intermediate values of any combination of inputs, avoiding the storage requirements and the interpolation of 57 Stumbo’s tables, it allows a quick and easy automation of thermal process calculations and to perform these calculations using a spreadsheet
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