Continuous Pasteurization of Egg Yolk with Plate Heat Exchangers: Thermal-Hydraulic Performance and Configuration Optimization

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1 Continuous Pasteurization of Egg Yolk with Plate Heat Exchangers: Thermal-Hydraulic Performance and Configuration Optimization J. A. W. Gut, J. M. Pinto,,*, A. L. Gabas 3 and J. Telis-Romero 4 Dept. of Chemical Engineering, University of São Paulo, Brazil, jorgewgut@usp.br Othmer Dept. of Chemical and Biological Sci. and Eng., Polytechnic University, USA, jpinto@poly.edu 3 Dept. of Food Engineering, University of São Paulo, Brazil, gabas@usp.br 4 Dept. of Food Eng. and Technology, Universidade Estadual Paulista, Brazil, javier@eta.ibilce.unesp.br * Corresponding author: J. M. Pinto, Othmer Dept of Chemical and Biological Sciences and Engineering, Polytechnic University, Six Metrotech Center, Brooklyn, NY 0, USA, Tel: , Fax: , jpinto@poly.edu. Abstract: The objective of this paper is to develop an optimization procedure for the configuration design of plate pasteurizers that makes intensive use of thermophysical properties and thermo-hydraulic performance correlations obtained experimentally. This paper addresses the continuous processing of liquid egg yolk in plate heat exchangers. Correlations for predicting friction factors and convective heat transfer coefficients are obtained for diagonal and parallel flow on a 50 chevron plate. Thermophysical properties of egg yolk (non-newtonian, power-law) and cooling fluid (glycol-water, 40/60) are also obtained for a wide temperature range. The mathematical modeling of a plate pasteurizer is presented and an optimization technique is applied for obtaining the optimal configuration of the equipment, for diagonal and parallel flows, subject to equipment design and performance constraints. Keywords: pasteurization; egg yolk; plate heat exchanger; friction factor, heat transfer coefficient, process design. INTRODUCTION Plate heat exchangers (PHEs) are widely used for continuous pasteurization of liquid food ucts because of their high thermal effectiveness, good flow distribution and ease of sanitation. The conventional PHE consists of a stack of corrugated metal plates clamped together in a single frame. Elastomeric gaskets seal the space between plates forming a series of parallel channels, where fluids flow alternatively and exchange heat through the thin metal plates. The embossed patterns provide a substantial increase in surface area, promote turbulence and improve the mechanical resistance of the plate pack. The corrugation geometry determines, to a great extent, the thermo-hydraulic performance of the PHE. However, information available on this issue is mostly proprietary. The corrugated pattern in general use is the chevron (herringbone) design. Previous

2 investigations have shown that the inclination angle of the chevron corrugations (relative to flow direction) has major influence on performance (Focke et al., 985; Muley and Manglik, 999). Moreover, the type of flow inside the channel, which can be diagonal or parallel depending on the gasket type (see Figure c), also influences the PHE performance, especially for wide plates (Bansal et al., 00). The main parts of a plate pasteurizer are the three sections of the PHE (regeneration, heating and cooling), the holding tube, the uct pump and the heating and cooling circuits, as in Figure a. Efficient process design is critical for the pasteurization of food ucts to ensure that the desired level of heat treatment is achieved with minimal damage to their organoleptic characteristics. However, due to the lack of information of the processing of non-newtonian fluids with PHEs, the unit is usually oversized, leading to a poor design with cost implications and deterioration of uct quality. Consequently, rigorous simulation and optimization models with experimental validation are required for predicting and optimizing equipment design and performance. a) b) Pasteurized W hot Product Q H p6 p4 h h Holding Tube d) c cooling c regeneration Q R p p heating p3 c) Q C W cold W Raw Product Figure : Schematic of a plate pasteurizer and PHE configuration parameters. The objective of this paper is to develop an optimization procedure for the configuration design of plate pasteurizers that makes intensive use of thermophysical properties and thermo-hydraulic performance correlations obtained experimentally. Results of the experimental investigation of heat transfer and pressure drop of liquid egg yolk in a PHE with 50 chevron corrugation pattern are presented. Correlations were obtained for the diagonal and parallel plates. Correlations for the thermophysical properties of the egg yolk and cooling fluid (glycol-water, 40/60) are also obtained for a wide temperature range. A mathematical model for plate pasteurizers with non-newtonian fluids of the power-law type is adjusted to the experimental data (Gut and Pinto, 003a, 003b). The model is applied to a practical design problem, where a configuration optimization procedure is used and the influence of the flow type is analyzed. EXPERIMENTAL APPARATUS AND PROCEDURE Thermophysical Properties The liquid egg yolk for this study was provided directly from the processing line of an egg breaking plant. The moisture content of the initial batch was determined in a vacuum oven (48 h, 333 K), resulting in

3 54.04 % moisture (wet basis). The ph values of the samples were measured with a phmeter (Marconi, São Paulo, Brazil) and a mean value of 6.4 was obtained. A 40/60 (w/w) mixture of ethylene glycol and water was used as cooling liquid. The methodology for obtaining the thermophysical properties of the egg yolk and the cooling fluid are those described by Gut et al. (003) and Telis-Romero et al. (00), respectively. Experimental Apparatus A schematic diagram of the overall experimental setup is shown in Figure. The PHE has AISI36 chevron plates with 50 corrugation angle (one adaptation of the model M3-FHC, Alfa Laval). The main plate dimensions are: L P = 3 mm, w = 84 mm, D p = 35 mm, e = 5 mm, A plate = 03 m², Φ = A plate /(w L) =.9 (see Figure d). Different gaskets were used for varying the channel gap: b = 3, 5, 8 and 0 mm (Telis-Romero et al., 004). 9 7 Egg Yolk Circuit Glycol/Water Circuit 0 Figure : Schematic diagram of the experimental setup: ) storage tank; ) butterfly valve; 3) positive head pump; 4) flow meter; 5) pressure transmitter; 6) temperature transmitter; 7) data logger; 8) PHE; 9) data acquisition system; 0) centrifugal head pump; ) secondary heat exchanger. The PHE was employed for the cooling of egg yolk using the ethylene glycol / water mixture. A static mixer was placed at the end of the PHE for homogenizing the egg yolk prior to obtaining its mean temperature (the correct determination of the mean temperature is crucial for accurate heat transfer measurements, as it is difficult to mix the flow thoroughly, especially for very consistent fluids). The PHE was configured for single-pass countercurrent flow with 3 channels per pass for the hot and cold sides. A HP data logger model 75,000-B, a HP-IB interface and a HP PC running a data acquisition and control program monitored temperatures and pressures. Statistical analysis was performed using the Origin 5.0 software (OriginLab, MA, USA). The suitability of the fitted correlations was evaluated by the coefficient of determination (R ), the significance level, and residual analysis. Heat Transfer and Pressure Drop Analysis The heat load, Q, is obtained from Eq.(), where C is the average heat capacity, T is the temperature change, U is the overall heat transfer coefficient, A is the heat transfer area, T lm is the logarithmic mean of the temperature difference and F is its correction factor (F.0). The heat transfer area is A = (N C -) A plate, 3

4 where N C is the number of channels. The overall heat transfer coefficient is obtained from Eq.(), where h is the convective heat transfer coefficient, λ plate is the plate thermal conductivity and R is the fouling factor. The convective heat transfer coefficient is usually obtained from correlations such as Nu 3 = a Re a Pr or St = a Re a, where St 3 = Nu Re Pr. Q = C T = U A F () T lm U = h hot + h cold e + λ plate + R hot + R cold () For determining the experimental convective coefficients, countercurrent flow was assumed (F = ) because of the single-pass arrangement and the large number of channels per pass. The pressure drop for either side of a PHE section is determined by Eq.(3), where f is the Fanning friction factor, P is the number of passes, ρ is the fluid density, D e is the equivalent channel diameter, W is the mass flow rate, N is the number of channels per pass and g is the gravitational acceleration. The velocity inside a channel is v = W/(N ρ b w). The friction factor is related to the Reynolds number for channel flow a4 with correlations such as f = a Re. f LP P ρ v P = D e 3 P W ρ π D p + ρ g L Reynolds and Prandtl numbers for non-newtonian fluids rely on the generalized viscosity, µ g, which is defined in Eq.(4) for ducts of arbitrary cross-section using the power-law rheological model, where ξ and υ are the duct geometrical parameters (Delplace and Leuliet, 995). µ g = K ξ n v D e n n υ n + ( υ + ) n Parameter ξ is obtained from the Fanning friction factor curve for a Newtonian fluid, f = ξ/re, whereas parameter υ can be approximated by υ = 4/ξ. The geometrical parameters for cylindrical ducts are ξ = 8 and υ = 3 (obtained from the well known Hagen-Poiseuille equation; Darby, 00) and ξ = and υ = for infinite parallel plates. Delplace and Leuliet (995) experimentally obtained ξ = 56.6 for the channel of a PHE with washboard corrugation. For the PHE used in this study, the obtained values are ξ = 33.4 for diagonal flow and ξ = 33 for parallel flow. P (3) (4) EXPERIMENTAL RESULTS Thermophysical Properties Density (ρ), Specific heat (Cp), thermal conductivity (λ) and power-law rheological parameters (K, n) of liquid egg yolk were obtained in triplicate at eight selected temperatures from 4 to 68 C, as reported by Gut et al. (003). The fitted correlations are compiled in Table. Density (ρ), Specific heat (Cp), thermal conductivity (λ) and Newtonian viscosity (µ) of the ethylene glycol / water mixture were obtained in triplicate at nine selected temperatures in the -3 to 78.9 C range. The resulting correlations are presented in Table. 4

5 Density Table : Thermophysical properties of liquid egg yolk (4 < T < 68 C) Property Correlation R Units ρ = T 996 Specific Heat Cp = T.000 Thermal Conductivity 4 λ = T 99 Consistency index (Power-law) * K = exp R T 999 Behavior index (Power-law) * 98 n = 77 T 847 * Valid for shear rate between 7 to 5.4 s - ρ: kg/m 3 Cp: J/kg K λ: W/m K K: Pa s n T: K n: (dimensionless) T: K Table : Thermophysical properties of 40/60 ethylene glycol/water (-3 < T < 78.9 C) Property Correlation R Units Density ρ = -005 T + 30 T Specific Heat Cp = T Thermal Conductivity λ = T T Viscosity µ = exp R T 998 ρ: kg/m 3 Cp: J/kg K λ: W/m K µ: Pa.s T: K Heat Transfer and Pressure Drop Heat transfer data was obtained for egg-yolk at a range of temperatures from 5 to 6.0 o C. At the experimental conditions, varied between 5.4 and 8, with thermophysical properties calculated for the mean stream temperature. Figure 3: Stanton Number and Fanning friction factor for egg yolk flow in the PHE channel Friction factors for diagonal and parallel flows were calculated using Eq.(3) and the results are presented in Figure 3a as a function of the generalized Reynolds number. The convective heat transfer 5

6 coefficients are obtained from Eqs.() and () and the results are presented in Figure 3b. The adjusted correlations for f( ) and St( ) are compiled in Table 3. The results are in good agreement with the correlations presented by Saunders (988) for 50 chevron plates. Table 3: Obtained correlations for friction factor and Stanton number Type of Flow St Correlation R f Correlation R Range Diagonal St = f = < 00 Diagonal St = f = Parallel St = f = < 00 Parallel St = f = CONFIGURATION OPTIMIZATION Configuration Characterization For characterizing the configuration of a PHE section, six parameters are used: N C (number of channels), P I (number of passes at side I, which comprises the odd-numbered channels), P II (number of passes at side II, which comprises the even-numbered channels), φ (determines the feed connection relative location, as in Figure b), Y h (Y h = when the hot fluid is at side I and Y h = 0 otherwise) and Y f (Y f = for diagonal flow and Y f = 0 for parallel flow, as in Figure c). Pasteurizer Thermal and Hydraulic Modeling The heat loads for the regeneration, heating and cooling sections are defined in Eqs.(5a) to (5c), respectively, where C is the average heat capacity of the corresponding path (see Figure a). Q Q Q R H C = C = C = C p p p p3 p6 p4 R p p p4 ( T T ) = C ( T T ) = ε min( C,C ) ( T T ) p p p4 h h H p p3 h h ( T T ) = C ( T T ) = ε min( C,C ) ( T T ) p3 p heat h h c c C p6 c c ( T T ) = C ( T T ) = ε min( C,C ) ( T T ) p6 cool c c In order to solve the system of equations in Eq.(5), the thermal effectiveness of the sections are required (ε R, ε H and ε C ). These can be obtained from the steady-state thermal model of the PHE, which is presented by Gut and Pinto (003b) as a function of the configuration parameters and dimensionless thermal coefficients for sides I and II, which are defined as α I = A plate U N I /C I and α II = A plate U N II /C II, respectively (N is the number of channels per pass). The overall heat transfer coefficient, U, is obtained from Eq.(). The thermal model for generalized configurations ε = ε(n C, P I, P II, φ, Y h, Y f, α I, α II ) is developed in algorithmic form. For any given configuration parameters, the algorithm guides the assemblage of the mathematical model and its solution by analytical or numerical methods (Gut and Pinto, 003b). An important thermal parameter for pasteurization is the heat regeneration ratio, which is defined as 6 heat cool p4 h p p c (5a) (5b) (5c)

7 RR = Q R /(Q R +Q H ). Moreover, a temperature drop is assumed for the holding tube, so that T p4 = T p3 - T drop. The pressure drop for either side of a PHE section is determined by Eq.(3). The pressure drop of the uct comprises the summation of the pressure drop contributions along the fluid path, including the holding tube (the last term in Eq.(3) is accounted for only once). The Branching Method The objective of the optimization problem is to simultaneously configure the three PHE sections of the plate pasteurizer for achieving minimal annual pasteurization cost. The optimization variables are the configuration parameters of each PHE section, which yields a very large number of possible combinations, such as 9. 0 configurations for N total C = N R C + N H C + N C C 0 The problem of configuration optimization for multiple section PHEs is presented by Gut and Pinto (003a), where the optimization constraints are grouped in three categories as follows: design constraints (physical connection among plates and sections), thermal performance constraints (bounds on T p4, T p6, ε R and RR) and hydraulic performance constraints (bounds on P and v for the uct and utility streams). Moreover, the problem is also subject to the pasteurizer thermo-hydraulic model. Since the PHE thermal model for generalized configurations cannot be represented in algebraic form (Gut and Pinto, 003b), it is not possible to use mixed-integer nonlinear programming (MINLP) techniques to solve the optimization problem. An enumeration procedure could be used to locate the optimal solution, since the optimization variables are discrete and constrained. However, this procedure would be prohibitive because of the computational time required to evaluate the large amount of elements. Alternatively, a branching procedure is proposed, as described by Gut and Pinto (003a), where the optimization variables are arranged on an enumeration tree and the constraints are applied at its levels as criteria for node generation. A structured search algorithm enumerates the feasible region of the problem with a reduced number of exchanger evaluations (several orders of magnitude in comparison to exhaustive enumeration). In addition to the reduced computational effort, other advantages of the branching method are as follows: ) multiple optimal elements can be located; ) the near optimal elements are also determined and can be further analyzed; and 3) any objective function can be used to explore the feasible region. Moreover, the simplified branching method assumes pure countercurrent flow behavior for the PHE sections. Since this assumption requires only a system of algebraic equations for obtaining ε, instead of a system of differential equations, the simplified branching can be used for rapidly obtaining an estimate of the optimal solution. OPTIMIZATION RESULTS AND DISCUSSION The branching procedure is applied for the configuration design of the studied plate pasteurizer, targeting minimal annual pasteurization costs for processing 00 L/h of egg yolk (inlet at 5 C). The utility streams are 4000 L/h hot water at 63 C and 4000 L/h cooling fluid (40/ 60 glycol/water) at 0 C. Fouling factors are obtained for utility streams according to Marriott (97) and for egg yolk according to Lallande et al. (979) for milk pasteurization. Temperature drop assumed for the holding tube is.0 C. Thermophysical 7

8 properties of water were taken from Gut and Pinto (003b). The thermal constraints are: RR 60 %, ε R 60 %, 60 T p4 6 C and T p6 5 C. The minimal channel velocities are 05 m/s for the egg yolk and m/s for the utilities. The maximum pressure drops are 00 psi for the egg yolk (pressure drop in holding tube not considered) and 5 psi for the utilities. Design constraints are detailed in Gut and Pinto (003a). The maximum allowed number of channels is The parcel of the pasteurization cost that depends on the PHE configuration, PC ($/yr), is obtained through Eq.(6), with cost coefficients according to Wang and Sundén (003). PP = W P/ρ is the pumping power (Watts) and Q is the heat load (Watts). total 85 H C ( N ) + 7 ( PP + PP + PP ) + ( Q Q ) PC = C heat The simplified branching method was used for enumerating the feasible region of the design problem, for diagonal and parallel flows using the correlations on Table 3 for the egg yolk and the correlations from Saunders (988) for the utilities. The results are presented in Figure 4 and Table 4. cool (6) 7,600 7,400 Diagonal Flow (Y f = ) 490 elements 7,600 7,400 Parallel Flow (Y f = 0) 68 elements Pasteurization cost ($/year) 7,00 7,000 6,800 6,600 6,400 Pasteurization cost ($/year) 7,00 7,000 6,800 6,600 6,400 optimal configuration 6,00 optimal configuration 6, Total number of channels 6,00 6, Total number of channels Figure 4: Feasible designs for diagonal and parallel flows Table 4: Optimal configurations selected by the branching method Section Diagonal flow (Y f = ) Parallel flow (Y f = 0) N C P I / P II Y h φ N C P I / P II Y h φ Regeneration 40 5 / / Heating 30 5 / / 0 4 Cooling 4 3 / / 4 The optimal and near optimal solutions can be observed in Figure 4. Moreover, it can be noted that the minimum pasteurization cost corresponds to the minimum number of channels, which indicates that the fixed cost plays an important role. The optimal solution for diagonal flow has 94 channels and PC = 665 $/year, while the solution for parallel flow has 0 channels and PC = 6484 $/year. The fact that diagonal flow yields slightly higher convective coefficients and friction factors, as can be seen in Figure 3, influenced significantly the optimization solution, as can be concluded from the parameters in Table 4 for both types of flow. 8

9 CONCLUSIONS Correlations for predicting the friction factor and convective coefficients for PHE with diagonal and parallel plates were determined for egg yolk processing. Moreover, thermophysical properties of the egg yolk and cooling fluid were determined for a wide temperature range. A proposed branching method was used for optimizing the configuration of a plate pasteurizer, using the experimental data, targeting minimal annual pasteurization costs for egg yolk. Different solutions were obtained for diagonal and parallel flow, where the former resulted in lower costs. A heat transfer area, m A plate plate heat transfer area, A plate = L w Φ, m a model parameter b mean channel gap, m C heat capacity, C = W Cp, J/kg C Cp specific heat at constant pressure, J/kg ºC D e equivalent diameter of channel, D e = b/φ, m D p plate port diameter, m e plate thickness, m F correction factor for T lm f Fanning friction factor g gravitational acceleration, g = 9.8 m/s h convective heat transfer coefficient, W/m C K consistency index, power-law model, Pa s n L effective plate length for heat transfer, m Lp plate length between port centers, m N number of channels per pass n flow behavior index N C number of channels Nu Nusselt number, Nu = h D e /λ P number of passes PC pasteurization annual cost, $/yr PP pumping power, W Pr Prandtl number, Pr = Cp µ g /λ Q heat load, W R fouling factor, m C/W Re Reynolds number, Re = D e v ρ/µ generalized Reynolds, Re=D e v ρ/µ g RR heat recovery ratio, % St modified Stanton number T temperature, C U overall heat transfer coefficient, W/m C v average velocity inside the channel, m/s W mass flow rate, kg/s w channel width, m Y f binary parameter for type of channel-flow binary parameter for hot fluid location Y h NOMENCLATURE Greek Letters α dimensionless heat transfer coefficient β chevron inclination angle, º P pressure drop, Pa T temperature change, C T lm temperature difference logarithmic mean, C T drop temperature drop at holding tube, C ε thermal effectiveness, % λ thermal conductivity, W/m C λ plate thermal conductivity of the plate, W/m C µ viscosity, Pa s µ g generalized viscosity, Pa s ξ duct geometrical parameter ρ density, kg/m 3 φ parameter for feed location υ duct geometrical parameter Φ plate area enlargement factor Subscripts cold cold side of PHE section cool cooling utility heat heating utility hot hot side of PHE section uct Superscripts C cooling section of the PHE H heating section of the PHE I side I of the PHE section II side II of the PHE section R regeneration section of the PHE 9

10 REFERENCES Bansal, B., Müller-Steinhagen, H. and Chen, X.D., 00, Comparison of crystallization fouling in plate and double-pipe heat exchangers, Heat Transfer Eng,, 3-5. Darby, R., 00, Chemical Engineering Fluid Mechanics, nd ed (Marcel Dekker Inc., New York). Delplace, F., and Leuliet, J.C., 995, Generalized Reynolds number for the flow of power law fluids in cylindrical ducts of arbitrary cross-section, Chem Eng Journal, 56, Focke, W.W, Zachariades, J., and Olivier, I., 985, The effect of the corrugation inclination angle on the thermohydraulic performance of plate heat exchangers, Int J Heat Mass Tran, 8(8), Gut, J.A.W. and J.M. Pinto, 003a, Selecting optimal configurations for multisection plate heat exchangers in pasteurization processes, Ind Eng Chem Res, 4(4), Gut, J.A.W. and J.M. Pinto, 003b, Modeling of plate heat exchangers with generalized configurations, Int J Heat Mass Tran, 46(4), Gut, J.A.W., Pinto, J.M., Gabas, A.L. and Telis-Romero, J., 003, Pasteurization of egg yolk in plate heat exchangers: thermophysical properties and process simulation, AIChE 00 Annual Meeting Conference Proceedings, San Francisco (CA). Lalande, M., Corrieu, G., Tissier, J.P. and Ferret, R., 979, Étude du comportement d un échangeur à plaques vicarb utilisé pour la pasteurisation du lait, Lait, 59(58), Marriott, J., 97, Where and how to use plate heat exchangers, Chem Eng, 5(4), Muley, A. and Manglik, R.M., 999, Experimental study of turbulent flow heat transfer and pressure drop in a plate heat exchanger with chevron plates. J Heat Tran, (), 0-7. Saunders, E.A.D., 988, Heat Exchangers: Selection, Design & Construction (Longman S.&T, Harlow). Telis-Romero, J., Cabral, R.A., Gabas, A.L. and Telis, V.R.N., 00, Rheological Properties and Fluid Dynamics of Coffee Extract. J Food Process Eng, 4(4), 7-3 Telis-Romero, J., Cabral, R.A.F, Telis, V.R.N. E Gabas, A.L., 004, Effect of corrugation on the hydrodynamic and heat transfer behavior of beer flowing through rectangular corrugated channels. Proceedings of the 9 th International Conference on Engineering and Food, icef9, Montpellier (FR). Wang, L. and B. Sundén, 003, Optimal design of plate heat exchangers with and without pressure drop specifications, Applied Thermal Eng, 3, ACKNOWLEDGMENT The authors wish to thank FAPESP (The State of São Paulo Research Foundation) for financial support (grants 0/046-0 and 03/305-0) and Alfa Laval in Brazil for technical and material support. The authors also would like to thank Dr. Vânia Regina Nicoletti Telis and Food Engineer Renato Alexandre Ferreira Cabral for the valuable contribution in the obtaining of the experimental data. 0