Modeling the Effect of Headspace Steam on Microwave Heating Performance of Mashed Potato

Size: px

Start display at page:

Download "Modeling the Effect of Headspace Steam on Microwave Heating Performance of Mashed Potato"

Julie Williams
5 years ago
Views:

1 Modeling the Effect of Headspace Steam on Microwave Heating Performance of Mashed Potato J. Chen, K. Pitchai, D. Jones, J. Subbiah University of Nebraska Lincoln October 9 th, 2014 Session : Electromagnetic Heating 1

2 Microwave Heating Convenient but Non-uniform 2

3 Microwave Heating Models Computer model use science based approach for : product formulation design product layout design package develop cooking instructions 3

4 Novel Food Product Development Café steamer 4

5 Objectives Develop a comprehensive multiphysics model that includes: Electromagnetic heating Heat and mass transfer Phase change of water evaporation Laminar flow and heat transfer in headspace Evaluate the headspace steam on microwave heating performance 5

6 Model Development 6

7 Problem Description in Food Sample Vapor convection Liquid pumping Microwave heating Internal heating Internal water vaporization Food sample Microwave heating J. Chen, K. Pitchai, S. Birla, M. Negahban, D. Jones, J. Subbiah Heat and mass transport during microwave heating of mashed potato in domestic oven model development, validation, and sensitivity analysis. Journal of Food Science. DOI: /

8 Problem Description in Headspace Outlet flow Vapor inlet Vapor inlet Vapor inlet 8

9 Geometric Model Coaxial feed Oven cavity Waveguide Lid with slit Turntable Mashed potato 9

10 Assumptions Frequency 2.45 GHz Moisture condensation in headspace was ignored. The radiation from the hot steam to the food product was ignored. EM field and heat source was calculated using room temperature dielectric properties. 10

11 Governing Equations Electromagnetics Maxwell s Equations µ r 1 EE 2πf c 2 ε r iε EE = 0 QQ = πfε 0 ε EE 2 f Microwave frequency c Speed of light ε r Dielectric constant ε Dielectric loss factor µ r Permeability Q Power dissipation density Food sample 11

12 Governing Equations Phase Change (Water Vaporization / Condensation) I= K Mw (p v,eq p v ) R T K p v p v,eq R T Mw Evaporation rate constant Vapor pressure Equilibrium water vapor pressure Ideal gas constant Temperature Molecular weight of vapor/water Food sample 12

13 Governing Equations Momentum Conservation Darcy s Law u i = k in,i k r,i μ i P u i Darcy s velocity, k in,i Intrinsic permeability k r,i Relative permeability µ ii Dynamic viscosity P Total pressure Food sample 13

14 Governing Equations Mass Conservation c i + D i c i + uu c i = ± I/Mw Diffusion Convection Phase change c D I u Concentration of the species Diffusion coefficient Evaporation rate Darcy s velocity Food sample 14

15 Governing Equations Energy Conservation ρc p eff + ρc puu = k eff λii + Q Food sample ρ C p u (ρc p ) eff k eff λ I Q fluid density fluid heat capacity fluid velocity field effective heat capacity effective thermal conductivity latent heat of evaporation evaporation rate heat source 15

16 Governing Equations Laminar flow of vapor Navier-Stokes Equation ρ u t + (ρu) = 0 + ρ u u= [ pi +μμ u + u T 2 3 μ u I] + F p Pressure μ Viscosity 16

17 Governing Equations Heat transfer of fluid ρcp T t + ρc pu T= k T ρ C p u K T Fluid density Fluid heat capacity Fluid velocity field Thermal conductivity Temperature 17

18 Meshing Tetrahedral and prime elements

19 Simulation Strategy EM field at 12 locations Averaged heat source Heat from 4 C for 90 s Laminar flow of vapor Heat transfer in fluid of vapor Heat and mass transfer Phase change of water evaporation Darcy s velocity Fully coupled 19

20 Results and Discussion 20

21 Velocity in Headspace Animation 21

22 Spatial Temperature on Top Surface The headspace steam increased the temperature on the top surface Time, s C C C Without headspace C C C With headspace 22

23 Total Moisture Evaporation The headspace steam increased the total moisture evaporation Total moisture evaporation, g Without headspace steam With headspace steam Time, s 23

24 Heating Nonuniformity The headspace steam increased the heating uniformity on the top surface by 8%, but not for the whole food product. Heating nonuniformity, % Without headspace steam With headspace steam Time, s Whole food product Heating nonuniformity, % Standard deviation / average temperature Without headspace steam 10 With headspace steam Time, s Top surface 24

25 Conclusions A comprehensive model of microwave heating coupled with heat and mass transfer in food product and headspace was developed. The headspace steam increased the temperature on the top surface and the total moisture evaporation. The headspace steam increased the heating uniformity on the top surface by 8%, but not for the whole food product. The model needs to be further refined and validated before it can be used by the food industry to assist food development. 25

26 Thank you very much! Jiajia Chen 26

Multiphysics Modeling of Microwave Heating of Food Undergoing Heat, Mass and Momentum Transport

Multiphysics Modeling of Microwave Heating of Food Undergoing Heat, Mass and Momentum Transport J. Chen 1, K. Pitchai 1, S. Birla 2, R. Gonzalez 2, D. Jones 1, J. Subbiah 1 1 University of Nebraska Lincoln