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Multiple-Effect Evaporators in the Food Industry: Fundamentals, Design, Simulation, Control, and Applications

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Abstract

Evaporators are one of the most important equipment in the food process industries such as sugar, fruit juices, dairy products, edible oils, tomato paste, and coffee. They need a lot of energy in the form of steam from boiler and it is necessary to minimize their energy consumption. One of the best strategies for this purpose is the design and application of multiple-effect evaporators (MEEs), in which the vapor from one stage (effect) is the heating medium for the next stage. There are various configurations and designs for MEEs and they can also be equipped with vapor compression systems and steam ejectors to further reduce the energy consumption and increase their economic efficiency. This article is covering the fundamentals, design, simulation, control, and application of MEEs in various food industries for the first time with discussing recent advances in this field.

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Abbreviations

A :

Heat transfer area

A E :

Equal heat transfer area for all effects

B :

Boolean matrix

°Bx:

Degrees Brix

Cp :

Specific heat capacity

D(i) :

Function of mass flow rate of heating medium

H :

Total enthalpy

h L :

Boiling convective coefficient

h V :

Condensing convective coefficient

i :

Index of effect in a MEE sequence

F :

Mass flow rate of liquid in a MEE

f(x,y):

Particular function for the mass balance

G :

Dimensionless mass rate of the falling-film

G C :

Dimensionless mass rate of condensing vapor

G(i) :

Function for the flow direction of the liquid

g:

Gravity acceleration

g(i) :

Function related to flow direction

j :

Index of effect in a MEE sequence

k :

Index of effect in a MEE sequence

L :

Mass of liquid that leaves one effect

LT :

Length of the tube

M:

Mass charge into the evaporator

M(x,t):

Mass of the falling-film

M Evap(x,t):

Mass evaporated from the falling-film

N T :

Number of tubes per effect

Nu:

Nusselt number

n :

Number of effects in a MEE

P :

Pressure of vapor

P M :

Pressure of discharge vapor

P S :

Pressure of motive steam

P T :

Pressure of input vapor

Pr:

Prandtl number

Q :

Heat flow rate

q :

Heat flux

R :

Vapor ration

Re:

Reynolds number

S :

Mass flow rate of motive steam

T :

Temperature of effect

T Film :

Temperature of the falling-film

Ts :

Temperature of heating medium

T sat :

Temperature at saturation

T wall :

Temperature of the wall

U :

Overall heat transfer coefficient

V :

Mass flow rate of vapor in a MEE

V T :

Mass flow rate of vapor from the effect that feeds the thermo-compressor

v :

Velocity of descent for a falling-film

W :

Dimensionless evaporated mass rate of water from the falling-film

W C :

Dimensionless condensate mass rate of water

X :

Dimensionless mass fraction of solids

x :

Mass fraction of solids

Y :

Matrix of fraction of liquid that leaves j-effect to enters into i-effect

y:

Fraction of liquid that leaves j-effect to enters into i-effect

Z:

Parameter of correlation

z:

Direction of flow for a falling-film

L:

Liquid phase

V:

Vapor phase

F:

Condition of feed stream

Γ:

Wetting rate

Δ:

Boiling point rise

ΔT i :

Difference of temperature

ε :

Calculated error

ε A :

Calculated error of heat transfer area

ε T :

Calculated error of temperature

ε U :

Calculated error of overall heat transfer coefficient

ε x :

Calculated error of mass fraction of solids

η :

Dimensionless parameter

η C :

Dimensionless parameter

η T :

Dimensionless parameter

κ :

Thermal conductivity

λ :

Specific condensation enthalpy

μ :

Dynamic viscosity

ρ :

Density

σ :

Surface tension

Φ:

Function of correlation

ϕ T :

Diameter of the tube

ϕ U :

Upper diameter of frustum

ϕ F :

Lower diameter of frustum

ξ :

Thermal resistance of the fouling

CFD:

Computational Fluid Dynamics

CIP:

Cleaning in place

MEEs:

Multiple-Effect Evaporators

MEFFE:

Multiple-Effect Falling-Film Evaporators

PID:

Proportional-Integral-Derivative control

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Acknowledgements

First author, Christian Díaz-Ovalle, appreciates the financial support by CONAHCYT México. Last author acknowledges the Chinese Ministry of Science and Technology "the Belt and Road" Innovative Talent Exchange Foreign Expert Project (Grant Number DL2021003001 and DL2021014003L).

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  1. Departamento de Ingenierías, Tecnológico Nacional de México/I.T. Roque, km 8.0 Carretera Celaya-Juventino Rosas, 38124, Celaya, Guanajuato, Mexico

    Christian O. Díaz-Ovalle

  2. Department of Food Materials and Process Design Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

    Seid Mahdi Jafari

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Díaz-Ovalle, C.O., Jafari, S.M. Multiple-Effect Evaporators in the Food Industry: Fundamentals, Design, Simulation, Control, and Applications. Food Eng Rev 15, 691–717 (2023). https://doi.org/10.1007/s12393-023-09350-6

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