A Moisture Transfer Model for Drying of Grain

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A Moisture Transfer Model for Drying of Grain by Kurt O. Lund Kurt Lund Consulting 135 Sixth Street, Del Mar, CA 92014. [email protected] Presented at the COMSOL Conference 2009 Boston

Transcript of A Moisture Transfer Model for Drying of Grain

A Moisture Transfer Model for Drying of Grainby

Kurt O. Lund

Kurt Lund Consulting

135 Sixth Street, Del Mar, CA 92014. [email protected]

Presented at the COMSOL Conference 2009 Boston

Single-Kernel Moisture Transfer

Spherical Kernel Model

∂∂∂

=∂

∂r

MDrrrt

M kk

k 22

1 ( )R

kkeqRkm r

MDMMh∂

∂−=−

∂∂

∂∂

=∂∂

ξξ

ξξτmm 2

21

m = (M – Meq)/(M0 – Meq)

02

11 ≈

∂∂

−=ξm

Bim

m

ξ = r/R τ = t/tk tk = dk2/Dk

Bim = hmdk/Dk ≈ 107

Single-Kernel Moisture Transfer

Dk = Akexp(-Bk/Ta)

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1-.05

0

.05

.1

.15

.2

.25

.3

.35

rh

Meq

Meq = Eeq – Feqln[-(T [C]+Ceq)ln(rh)]Chung-Henderson Correlation:

Equilibrium Moisture Content (Meq= EMC)

T = 25 C50 C75 C

τ0.0 0.1 0.2 0.3 0.4 0.5

m ,

dm/d

τ

0.01

0.1

1

10

100

Legend

dm/dtaum

Volume-Average Concentration

scaled time, τ0.0 0.1 0.2 0.3 0.4 0.5

m avg

0.0

0.2

0.4

0.6

0.8

1.0

0011.011.012

++

τβ

)(11 eqkkkkk MMShdtMdV −=− ρρ

hk = βdk/6tk= 2/3 β Dk/dk

mdmd βτ

=−

Single-Kernel Moisture Transfer Correlation

Multiple-Kernel Moisture Transfer

One-Dimensional Mass Transport Equations

)(6)1( eqk

kk

T

mVm MM

dh

VQq −−== ρε

Vmsk qx

MUt

M−=

∂∂

+∂

∂− ρε )1(

Vmaa qx

Ut

=

∂∂

+∂∂ ωωερ

Volumetric Moisture Transfer

Solid-Phase Moisture Transport

Air Humidity Transport

One-Dimensional Heat Transport Equations

Volumetric Heat Transfer

Solid-Phase Heat Transport

Air Heat Transport

)(6)1( sak

a

TV TT

dh

VQq −−== ε

tMhquq

xTCU

tTC

fgsVmmVss

sss

s ∂∂

−−−=

∂∂

+∂

∂− ρερε )1()1(

''

VmmVaa

aaa

a quqxTCU

tTC

+−=

∂∂

+∂

∂ ''ερ

C’a = Ca + ωCm um - um0 = Cm(Ts – Tm0)

C’s = Cs + CmM

Moisture Fraction for Stationary Bed or Bin

Moisture Fraction for Stationary Bed or Bin

Moisture Fraction for Stationary Bed or Bin

M

Meq

ω

Moving Column of Grain

Us = 0.05m/s, Ua = 5m/s

Kernels Moisture Fraction Air Humidity Ratio

ε = 85%

Air Relative Humidity Air Temperatures

Moving Column of Grain

The End