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CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg. Francisco J. Trujillo and Q. Tuan Pham University of New South Wales Sydney 2052, Australia. Objective 1.

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cfd modeling of heat and moisture transfer on a 2 d model of a beef leg

CFD Modeling of Heat and Moisture Transfer on a 2-D Model of a Beef Leg

Francisco J. Trujillo and Q. Tuan Pham

University of New South Wales

Sydney 2052, Australia

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

objective 1
Objective 1
  • To report on problems encountered while trying to model simultaneous heat and mass transfer in both air and solid phases during beef carcass chilling, using the CFD package FLUENT 6.0

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

objective 2
Objective 2
  • To report preliminary results on a simple shape

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

why we must model heat and mass transfer
Why we must model heat and mass transfer

During chilling of beef carcasses, cooling and evaporation influences

  • meat temperature
  • surface water activity
  • microbial growth
  • weight loss
  • tenderness
  • other quality factors

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

transport equations

In the solid

Change = Diffusion

  • where  may be
  • temperature
  • moisture concentration
Transport equations

In the air

Change = Convection + Diffusion + Source

  • where  may be
  • 1 (continuity)
  • velocity components u, v
  • turbulent kinetic energy k
  • turbulent dissipation rate 
  • temperature
  • water vapour concentration

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

turbulence model
Turbulence model

k-model:

effective viscosity calculated from turbulent intensity k and turbulent dissipation 

RNG modification:

RNG (Re-Normalization Group) : includes analytical formula for effective viscosity that is valid across the full range of flow conditions, from low to high Reynolds numbers

Enhanced wall treatment

  • Viscosity effects near wall is completely resolved all the way to the viscous sub-layer (y+ 1)using very fine mesh.
  • Enhanced wall functions: smoothly blend linear (laminar) and logarithmic (turbulent) laws-of-the-wall.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

why is it difficult to model simultaneous heat and mass transfer in meat
Why is it difficult to model simultaneous heat and mass transfer in meat
  • Moisture diffusion is mostly near the surface, while heat conduction takes place over the whole body
  • Due to steep moisture profile near surface, a very fine mesh is required

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

problem related to fluent s capabilities
Problem related to FLUENT’s capabilities

In the meat, the heat and mass transfer could not be solved using FLUENTs standard heat and mass transfer equations because:

  • FLUENT cannot solve mass transfer equation in a solid. Thus the meat had to be defined as a “fluid” phase.
  • Once the meat was defined as a fluid, FLUENT requires the physical properties (cp, , D, k, ) be the same in all parts of the solution domain (i.e. both air and meat phases are modelled as the same substance).
  • Since these properties were in fact different in the two phases, new field variables must be defined and solved in the meat.
  • FLUENT6.0 “ready-made” boundary conditions of the mass transport equations can only be zero flux or a fixed value.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

details of special fluent procedures
Details of special FLUENT procedures
  • Define new field variables called UDS (User Defined Scalars) which represent the moisture concentration and temperature in the meat. These new fields must be tied to those in the air using equilibrium and conservation laws...

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

udf1 b c for mass transfer in meat

Write user-defined functions in C++ to calculate the boundary condition of mass transfer equation in meat:

    • (the mass flux at the meat surface is calculated from the water vapour gradient in the air cell next to the surface)
UDF1: B.c. for mass transfer in meat:

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

udf2 b c for heat transfer in meat

(convective heat flux is calculated from T gradient in the air cell next to the surface.)

(evaporative heat flux is calculated from mass flux calculated earlier)

UDF2: B.c. for heat transfer in meat:
  • Write user-defined functions to calculate the boundary condition of heat transfer equation in meat:

(the heat flux from the meat at the surface is calculated from the convective, evaporative and radiated heats), where

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

udf4 b c for mass transfer in air
UDF4: B.c. for mass transfer in air:
  • Write user-defined functions to calculate the boundary condition of mass transfer equation in air:
  • where
  • aw(meat surface) is calculated from meat surface moisture content using measured isotherm on right
  • aw(air surface) is the relative humidity in the air at the interface

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

slide13

Write user-defined functions to calculate the boundary condition of heat transfer equation in air:

UDF3: B.c. for heat transfer in air:

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

solution procedure for each iteration
Solution procedure for each iteration

For each time t

Iterate

  • Solve linearized momentum equation in the air phase.
  • Solve energy equation in the air phase.
  • Solve mass equation in the air phase.
  • Solve turbulent kinetic energy in the air phase.
  • Solve eddy dissipation in the air phase.
  • Solve energy equation in the solid phase.
  • Solve mass equation in the meat phase.
  • Update all properties
  • Check convergence.

until results have converged (no more change in field variables)

Advance to next time t+t

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

cfd grid
CFD Grid
  • air side: 29033 nodes
  • meat side: 6487 nodes

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results velocity profile

Bound. layer

detachment

Impingement

(stagnation point)

Recirculation

Results: Velocity profile

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

result temperature profiles
Result: Temperature profiles

at 30 minutes

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

result temperature profiles18
Result: Temperature profiles

after 5 hours

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

result moisture profiles in meat
Result: Moisture profiles in meat

after 5 hours

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

result moisture profiles in meat20
Result: Moisture profiles in meat

after 20 hours

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results temperature history
Results: Temperature history

Comparison of ellipse model with “equivalent” real beef leg:

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results temperature profile along surface
Results: Temperature profile along surface

Front of ellipse

Back of ellipse

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results average surface water activity history
Results: Average surface water activity history

Note surface rewetting

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results water activity profile along surface
Results: Water activity profile along surface

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results moisture profile in the meat
Results: Moisture profile in the meat

Note diffusion depth  20mm

Note surface re-wetting

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

results variation of htc and mtc along surface
Results: Variation of htc and mtc along surface

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

how long did it take
How long did it take?

CFD calculation is time consuming because

  • Grid is very fine on both sides of interface:
    • air side (29033 nodes): for enhanced wall treatment
    • meat side (6487): because of small scale of mass transfer
  • Must iterate at each time interval to satisfy 2 equilibrium equations and 2 flux conservation equations at meat-air interface

 160 CPU hours (on a 1.5GHz Pentium 4) to simulate 20 hours of real time.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

conclusions
CONCLUSIONS
  • Even though FLUENT 6.0 is a very powerful CFD software, special techniques have to be used to deal with simultaneous heat and mass transfer in two different phases
  • Solution is very time-consuming - not yet practical for routine industrial calculations.
  • The model gave reasonable predictions of local variations in temperature, moisture and water activity

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003

acknowledgments
ACKNOWLEDGMENTS

This work was carried out under a grant by the Australian Government via the Australian research Council. Francisco Trujillo is supported by a Postgraduate scholarship funded by the grant.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003