Mathematical simulation of microclimate of sub-surfaced in the ground potato storehouses Текст научной статьи по специальности «Физика»

UDC 631.243.42:519.86

MATHEMATICAL SIMULATION OF MICROCLIMATE OF SUB-SURFACED IN THE GROUND POTATO STOREHOUSES

Kondrashov V.I.1, Prusakov G.M.2, Moiseenko A.M.1, Ph.D.

1Orel State Agrarian University, Orel City, Russia

2Quincy College, Quincy, MA 02169, USA E- mail: [email protected]

ABSTRACT

The highest significance in the safekeeping of the biological production has the heat-moister regime in the storehouses and inside of a stored agricultural produce. Existing storage technologies demand certain adjustment in each case, which can be significantly simplified with the computer simulation. The adequate model with realistic conditions can be provided with the complete mathematical description and all basic factors taken into an account. The purpose of this work is the development of the methods of the heat-technical calculation and computer simulation of vegetable storehouses microclimate by solving the conjugate non-stationary heat and moister exchange tasks. The full mathematical model of a heat-exchange is based on the conjugate non-stationary heat-moister exchange task for the whole system construction-equipment-bulk in their heat interconnection, but not for each component separately taking part in the heat-exchange. As a generic math model we consider the heat-moister condition of a semi-sub-surfaced in the ground storehouses, because in this case it’s necessary to take into account the heat interaction not only with air surroundings, but also with the ground, unlike above ground surface storehouses as a particular version of common model. Developed the finite-difference method of calculations which have sufficient enough high-speed and accuracy for engineer practice. These methods allow in short time calculate the temperature and moisture in the storehouses. Software package POSOH (Kondrashov, Kondraschov, Kokin, Tyukov, 2003) was designed for computer modeling of these processes. Examples of the simulation for selection of most appropriate construction and technology parameters for reduction of depreciation of agricultural production during storage are provided. The heat-resistant properties of above surface and semi-sub-surfaced storehouses were compared.

KEY WORDS

Simulation; Finite differences; Agriculture produce; Storehouse; Heat-moister condition.

NOMENCLATURE

• a1: thermal diffusivity of the side barrier [ m2 / s ]

• aE = a(i - p)

• aa: thermal diffusivity of air [m2 / s ]

• an: thermal diffusivity of the cover [m2 / s ]

• aM : thermal diffusivity of the bulk, considering porosity [ m2 / s ]

• ae: thermal diffusivity of the air in the bulk , considering porosity [m2 /s ]

• D: diffusion coefficient [m2 / s ]

• B: temperature coefficient of breathing [1/°C]

• ch: heat capacity of a bulk [J/kg • °C ]

• ci: heat capacity of the side barrier, considering porosity [J/kg • K ]

• d(x, y,x): moisture content of air in the bulk [°C]

• Fh: specific surface of a bulk [m2/m3]

• F(V): aerodynamic resistance, which depends on Reynolds’s number and porosity characteristic of a bulk

• f(Tm) = a + bTm: approximation of equilibrium air moisture content from temperature

ak F

• ki = ki H : constant, where ak is a coefficient of convection heat exchange between

P„c„ 1

a bulk and air [W/(m2 • K) ]

ak Fh

• k2 =—1—: constant, where ca is a heat capacity of air, [J/(kg • K) ] and pa is a

PaCa

density of air [kg/ m3 ]

• p: porosity of the side barrier

• P( x, y, t) : pressure in a bulk [Pa]

• qn: heat of steam creation [J/kg]

• q0: heat of breathing of elements of a bulk [W/t]

• Qt: specific power of heat sources in upper zone [W/m2 ]

• T1(x, y,T) : temperature of side barrier [°C]

• TJx, y,T): temperature in the bulk of production [°C]

• Tab (x, y,T): temperature of air in the bulk [°C]

• Tn(x, y,T) : temperature of a cover [°C]

• TH(x, y,T): temperature of surroundings [°C]

• Ta: temperature of air in upper zone, °C;

• Tc: average temperature of air in a bulk [°C]

• tn: average temperature value of ground surface [°C]

• ta: half of a common interval of changes in temperature in surface, or an oscillation amplitude of temperature on the surface of the ground [°C]

• V : module of velocity filtration in a bulk [m/h] V = -^u2 x + u2 y

• Wx: velocity of infiltration through the side barrier [m/s]

• w: volume moister of ground (0< w < 1)

• ux: x-component of velocity of filtration in a bulk [m/s]

• uy: y-component of velocity of filtration in a bulk [m/s]

Greek symbols:

• ak : coefficient of a convection heat exchange of air between surfaces of a bulk and a cover [W/( m2 • K) ]

• ah : coefficient of a ray heat exchange between surfaces of a bulk and a cover [W/(

m2 • K) ]

• ah: coefficient of a convection heat exchange between an external surfaces of a barriers and surroundings [W/(m2 • K) ]

• p : coefficient of moisture exchange [kg/ (m2 • Pa • s) ]

• P0: coefficient of volume expansion [1/°C]

• sh: evaporation ability of elements of a bulk <<1

• 0X: temperature of ground under a bulk [°C]

• A,1: thermal conductivity of the side barrier [W(m-K)] XE = A(i - n)

• Aa: thermal conductivity of air [W(m-K)]

• XH : thermal conductivity of a bulk [W(m-K)]

• Xn. thermal conductivity of a cover [W(m-K)]

• ph: density of a bulk product [kg/ m3 ]

• p: side barrier density [kg / m3 ], considering porosity;

• p: ground density [ kg / m3 ]

• pwtr: water density [ kg / m3 ]

• O: relative humidity (moisture) of air in a bulk [%]

• t : time

• t0 : phase of temperature oscillation.

A heat-moisture condition of semi-sub-surfaced at the ground storehouses is presented as an example of generic approach to simulation of microclimate in stored agricultural produce, because it’s necessary to take into an account interaction not only with air surroundings, but also with soil.

The semi-sub-surfaced and sub-surfaced storehouses are commonly enough used in the climate zones with low or high temperatures during the storage period. Additionally, besides the permanent storehouses, collapsible semi-sub-surfaced constructions with active ventilation have gained popularity for storage of potatoes and vegetables, which in 10-20 times cheaper then fundamental constructions. One of these storehouses, which combine low cost, simplicity of manufacture and assembly with high safety and good quality of produce, is the large dimension clamp (Kondrashov VI 1997). The capacity of these clamps is up to 400 t. of potatoes and 320 t. of forage beets. The construction elements of the these clamps can be manufactured in small enterprises, and be assemble without lifting crane in 2-

3 days in prepared in advance a trench of 3 m deep. The ventilation module is placed in the center part of the construction. Thus for any whether conditions, a forced air of specified temperature is blown into the bulk of the produce, using the uses heat-generation of stored potatoes and vegetables. The height of the bulk can be up to 4m. A cover of loaded produce is a multi-layer material, which composed of packages of pressed straw and air-impenetrable pellicle.

The complete embedding is used for storage for example in small and medium size trenches. The heat-exchange plays a significant role here and therefore losses of moister are small and the results of storage are good. Small trenches are usually used without multilayer of sand and soil.

The microclimate in the bulk of agricultural produce in the storehouse mainly depends on heat regime of the walls, where is direct contact to the production.

The heat regime of external walls of the storehouse has been determined by the regularities of internal and external heat influences and the conditions of the heat interactions with the ground.

We have to note that many publications (Beukema, Bruin, Schenk 1982, Jia, Sun, Cao 2000, Nganhou 2004, Tashtoush 2000) are dedicated to simulation of heat and mass exchange at the bulk, but as it was mentioned in annotation - the models for the system: bulk-wall-ground are practically absent.

The microclimate of a premise of potatoes storehouse and the heat condition of stored production mostly depends on the following heat influences: internal air with the temperature regulated by technological demands; external surroundings, which temperature have been determined by natural climate conditions; internal heat secretions of juicy farm produce, that have been determined by biochemical processes.

A common task of investigation of the heat regime of juicy agricultural produce in storehouses has been concluded in determination of dependences between external and

internal heat sources and base characteristics of temperature fields of the barrier constructions and the bulk of product.

Often the recommended methods of calculation of heat regimes are based on simplified scheme of heat and mass transfer (Beukema, Bruin, Schenk 1982, Jia, Sun, Cao 2000, Tashtoush 2000). This approach reduces the reliability of results and leads to significant misrepresentations of temperature’s fields.

For the development of a methodology of heat-technical calculation for vegetable-potato storehouses it is required to build a mathematical model with conjugate (i.e. for the whole system of construction-equipment-bulk in their heat interconnection, but not for each separate part which is taking part in heat exchange) and non - stationary setting of a problem and investigate it with this model of heat-moisture transfer processes.

MATHEMATICAL MODEL

A task of investigation of heat interaction of the storehouse’s external walls with ground and production is based on the following prerequisites: the soil layer (ground) is considering as a continuous environment; the ground surface outside of the building is located above the storehouse floor level (Fig. 1).

Figure 1 - The Storehouse with subsurface at the ground: 1 - subsurface part of external wall; 2 -surface part of external wall; 3- bulk of production; 4- upper zone; 5- cover 6 - ground.

H - height of bulk; Huz - height of an upper zone; Hcov - height of a cover; T - temperature of air; V -

velocity of air; O - relative air moisture.

There is a periodical heat current in the upper layer of ground surface as a result of daily and annually repeating variations of temperature (Chudnovskiy 1987, Jadan 1976). Temperature of ground surface is satisfactory described by the low of harmonic oscillation:

T1 W = tn + ta c°s(W12(r-ro)), (1)

Let tr (y,r) is temperature of ground. Assume that at the first moment in time the linear low of temperature distribution is by y, and on surface of ground is a periodical low of temperature changes (1).

For determination of tr (y,r) we have the boundary value problem:

d1 = ai d? (2)

dr dy

tr (y, o) = By + c (3)

tr (h1,r) = Ti W (4)

dtr (o, r)

dy

= 0,

(5)

where b and c are constants in the linear low of initial temperature changes.

Coefficient of heat conductivity of ground a1, which has dimension m2 /c in equation (2) dependents on the soil type and can be determined by following empiric formula (Kondrashov, Kondraschov, Kokin, Tyukov, 2003):

a1 =

m1

Y

w----

V P

10 — m4

+10 3m2p + m3

10—

(6)

The coefficients mt (i = 1,2,3,4) dependent on the soil type. Their values for different soil types are showed in the table 1.

Table 1 — Empiric coefficients mi for different soil types

Type of ground 1 2 3 4

Regular Chernozem(black earth) -0,013 3,1 1,21 20

Dark-brown -0,017 2,2 1,90 18

Gray -earth -0,0062 2,7 0,20 18

South-earth -0,0104 2,4 0,68 20

The Finite Integral Transformation method is used to solve task (3) - (5):

(2m1 — \)ny

tm1 (l)= jtr (y,l)c0S-

2h

dy

where the formula of conversion is:

( \ 2 / \ (2m1 — 1)^y

tr (y, r) = -T- Z tm1 (r)co^ 2h

h1 m1 =1 2h1

Then the solution of the boundary value problem (3) - (5) is in form of the series:

r\ tf)

<r (y-r)= J I

ri1 m1 =1

fm, (l) + Fm1 eXP

^(2m1 — 1)2^2 a1 4h2

cos

(2m1 — 1)ny

2h

where:

(7),

- +

2(2m1 — l)wa1h1t r \ , 2 1

——[a1^ (2m1 — 1)cos®r + 4h1®sm®rJ

"1

;r(2m1 — 1) (2m1 — 1)4 a12 +16®2 h

7

F =

m1

4h12 e + 2h1 (2m1 —1)^[(— 1)”1 1 (h1, e + d) — tn J 2(2m1 — 1)3 n3 a12 h1ta

(2m1 —1)

22

n

(2m1 — 1)4n4 a12 +16®2 h14

With known temperature of ground the heat and mass transfer in the storehouse is determined by the full mathematical model, which is based on setting of task as conjugate task.

This model includes the following equations and boundary conditions (Kondrashov 1997).

The equation of thermal conductivity for the side barrier:

dT1

dr

+ Wx

P aC a dT1

(PC)1 dx

= aE

fd 2t d 2t1 ^ 1 + 1

dx dy2

(8)

The equation of energy for the bulk of the product:

dTM = 1 q ebTM

dr c„

fiq-F-S-E (f( Tu ) — d)

PhCh

+

dy2

— k1 (TM — Tab )

(9)

The equation of energy for air in bulk of the product:

dTab , u dTab , u dTab L

----------+ ux-------------+ uv-----------= aLab

x v ^ ab

dr dx dy

+ k 2 (TM — Tab )

V

dx 2 dy

(10)

2

,

y

The equation of diffusion of moister:

dd dd dd D fd2d dd^

----+ ux----+ uy — = — —— +--------—

dr dx dy s Vdc dy y

+ PF^ (f ( Tu ) — d)

Pet

,

(11)

The equation of thermal conductivity for the cover:

dTn

dr

dx

(12)

The equation of air movement in the bulk for mixed convection:

dux dux dux 1 dP ux

—- + ux—- + uy—- =-----------------------—F (V); (13)

dr dx dy pe dx peV

du

du

du

cu cu cu 1 dP u . ,

—- + u —- + u —- =----------------------------------— F (V ) —

dr x dx y dy pe dy peV

— PoS(Tab — Tc )

(14)

Vestnik OrelGAU, 3(48), June 2014 The equation of continuity:

du du

(15)

du du

x- + —^ = 0

dx dy

The initial conditions are (r = 0):

T1 (x, y,0) = T10 ; TM (x, y,0) = TM0 ; Tab (x> y,0) = Tab0 '; d(x> y,0) = d0 ; Tn (x> y,0) = Tn0 '; ux (x, y,0) = ux0 ; uy (x, y,0) = uy0 (16)

The boundary conditions on the x-axis. The thermo exchange on the boundary surrounding - side barrier (x = 0) is:

A

T

dx

= a,

' (T1 L=o — T ); a« =a - +a- .( y - h1) (17)

T1 = t1 , under y < h1 The thermo exchange on the boundary surroundings - side barrier (x = l1) is:

2 dTM

Am ~

dx

= a

d

dx

; T

’ 11

x=l

= T \ = T

x=l1 M\x=l1 s

(18)

The conditions on an axis of symmetry (x = l2) are:

dTM dTae = T cd

dx l dx x=l2 l dx x=l2 l dx x=l2

= 0

(19)

The conditions of a moister - impenetrability of the side barrier is:

dd

dx

= 0

(20)

The boundary conditions on the y-axis:

The conditions with y = 0 are:

711 o = T(x) ; T2| = T20;

1 I y=0 1 v ' ’ 2 I y= 0 20 ’

on the exit from the ventilation canal are:

(21)

T

= TaK ; d\

ab I y=0 ab1 ’ I y=0

f (Tab, o) ; (22)

for the rest part of bottom boundary of bulk are:

x

2

X

T \ — ft &d

ab\y=0 1 ’ dy

— 0

y—0

The heat exchange on the boundary of bulk of product - the storehouse upper zone (y=H) is:

-AT

%

3 )+C2 (Tw|y—H Twly—Hj )’

— C (TM |y—H - TB3 )+ C (TM |y—H - TM \y—Hj

(24)

y—H

The «soft» stabilization conditions of gradients of air temperature and moisture content

are:

d2d

d2T

— 0;

y—H

— 0.

y H

(25)

The thermo exchange on the boundary upper zone - the cover (y — H13 H1 — H + Hu

) are:

-A

%

y—H1

— cc, I T I „ — T

2 I n ly—Hj B3

y—H1

+ ci2 [ TM

y—h - Tn\y—Hj l + Qi (26)

The thermo - exchange on the boundary - surroundings (y = h2).

-A

= c. (Tnly.,2 - TM ) (27)

y—h2

The boundary conditions for the equation of movement with the force convection (Fig.

2) are:

Y

ux=0

uy=0

P=0

ux^0

Uy£0

Ux(x,y,T) TM(x,y,x)

Uy(x,y,x) Tee(x,y,x)

bulk of production

in

ux=0 P=Po 0 =x s

y o ux^0 uy=0

Uy£0

ux=0

Uy^0

Figure 2 - The boundary conditions with the forced convection

The forced air is pumped with pressure through a channel to the bulk. Compare to Fig. 3 with no channel for forced air, but with natural ventilation, considering u=0,v=0.

0

l

4

H

ux=0

uy=0

► uu yx II II o o

ux(x ,y,x) TM(x,y,x) u x = 0

uy(x,y ,t) Tee(x,y,x) uy^ 0

►

0

ux=0 uy=0

I4

X

Figure 3 - The boundary conditions with the natural convection

THE METHODS OF CALCULATION

The Implicit Difference scheme with the various modifications and using a speed converging of iteration processes were used for the solution of a full mathematical problem. Experiments have shown that q0exp(bTm)/cm can be linearized in a sufficient for explored processes temperature range (Savin, Moiseenko, Kondrashov 2004, Shih Tien Mo 1984).

qo exp(bTm )

where A, B, - known physical constants.

The iterative process is organized to solve the problem (1) - (11) numerically:

1. Tm in the equations (3) - (5) is considered known (as the first approximation) from the previous time level. The equations (1), (3) - (5) in view of (6) - (10) are solved by the finite difference method with use of the implicit difference scheme (three-dot symmetric approximation to derivatives with respect to x) and Thomas algorithm (Prusakov 1994, Savin, Moiseenko, Kondrashov 2004).

2. Tm is obtained numerically in accordance with the found Ta, d, Tt, T3 from the equation (2) in view of the boundary conditions (9)-(10) as in the step 1; f(Tm) is approximated by linearization.

3. The iterative process 2. ^ 1. ^ 2. ^ ... repeats (j + 1) times until the condition Tm+1 -rm\ <7 for x e[0,H] will be satisfied. Accuracy check is carried out for Ta, d, Tt, Ti also.

Numerous calculations show that number of the iterations necessary for calculation accuracy does not exceed 3 - 5 usually. It is most of all because temperature and humidity content time variations and variations along x are rather insignificant in processes being investigated.

Extremely economic Thomas algorithm for standard boundary conditions is explained in the known literature (Prusakov 1994, Beukema, Bruin, Schenk 1982, Nganhou 2004). It is extended to include boundary conditions of conjugation (7) as follows.

Let step of grid is h and point 51 corresponds to the mesh point number N. We approximate (7) by finite differences:

T — T T — T

1 J1,N 1,N—1 -n 2,2 2,1

__ — ^2

h

h

T =T

1,N 2,1

(12)

c

m

The solution of the problem is searched as:

T1,z = ai+1T1,i+1 + Pi+1 ’ i = 0,1 •••’ N -1 TX] —a']+lTX]+l +fi’+1, j — 0,1,..., M -1,

where ai+1, Pi+1, aj+1, Pj+1 - «passage» coefficients.

Having substituted T1N and T2,2 in (12) after simple transforming we shall find:

«2 =

1

1 + A- (l — «n )

A

2

P = A <Pn

A2

Starting coefficients a1, P1 are determined from boundary conditions (6). Then ai, P are calculated under known formulas (Prusakov 1994, Savin, Moiseenko, Kondrashov 2004) . Then a2, /3’j are calculated as starting coefficients for x] and then aj, P) are

calculated. Values of functions T2, j, j=M - 1, M - 2, ... , 1 and T1, , i=N, N - 1, . , 1 (reverse passage) are calculated at last.

Note that for governed gas medium it is necessary to set in appropriate way breath heat of biological product that is coefficient q0 in the equation (2). For each sort of stored product (potato, onion, apples, etc.) the thermal properties available in numerous reference books are set.

It is the most expedient to use the mathematical model (1) - (11) as the basic part of software for application in practice of storehouses designing and the analysis of storage processes. So it is made in the POSOH software (Kondrashov, Kondraschov, Kokin, Tyukov, 2003) developed by us. Application of known expensive commercial software on hydrodynamics and heat-and-mass transfer is not effectively for simulation of controlled environment in storehouses because they do not take into account specificity of processes in an organic product and because of essential conjugacy of the problem. The compact software based on adequate models is necessary also for crisp logic automatic control system in storages with controlled environment.

This developed method of solution was approved for calculation of heat-moister exchange processes in the real storehouses of different types. There was an experimental verification of received results. (Kondrashov 1997, Kondrashov 2000)

The results of calculated solution are well correlated with experimental data, which had been received using bulk and rows storage of potatoes with a layer bellow 8-9meters in the storehouse with volume of 10000 tons [Russia, Oryol] with high level of humidity (about 100%) of supplied air and possible «fog» creation.

DISCUSSION OF RESULTS AND EXAMPLES OF SIMULATION

Let consider the regime of storing potatoes in winter period using system of active ventilation in case of decreasing an average value of outside temperature from -10C to -20C. Assume that conceivable temperatures for saving production are from 1°C to 4°C. If the temperature is below 0.5 °C - it’s an overcooling, above 4°C - it’s an overheating. There are results of our simulation with POSOH at the figs. 4-8.

A height of a bulk - 5m.

A height of an upper zone - 1m.

A weight of a bulk is 10 m.

A height of a subsurface part at the ground - 3m.

A thickness of a wall is the same as a thickness of a cover and is 0.5 m.

A thermal conductivity of a cover A — 0.18 W / m • grad.

A thermal conductivity of a wall is An — 0.81 W/m • grad.

The velocity of infiltration is 0.0005 m/s.

Coefficient of a heat exchange of a cover with surroundings is 20 W /m2 • °C

Coefficient of a heat exchange of a wall with surroundings is 23 W / m2 • °C

Coefficient of a ray heat exchange of a cover - the upper lie of a bulk is 2.7 W /m2 • °C

Temperature of a ground at the bottom is 5°C.

Temperature of air at the entrance into a bulk is 2°C.

Temperature of upper zone is 2.5°C.

W — tn + ta cosomo- ox tn — — 20 °C « — 5 °C.

A special system of heating a ceiling and upper air layers is created for elimination of condensate. The heaters are set up in the ceiling in order to avoid the sweating of tubers. As a rule, it’s recommended to use sources of a heat with specific power Qt—5, W /m2.

A relative humidity of air at the enter in a bulk, - 0.9 (moisture content 0.0039 kg/kg)

Consumption of air at a bulk is 10 m3 /1.

Initial moister content of air in a bulk is 0.00463 kg/kg. (relative humidity 1.0)

Proposed algorithm and project allows to choose contraction and technology with numerical experimental solutions, which allowing to save production and eliminate damage of production during the process of storage (Kondrashov 2000, Kondrashov, Kondraschov, Kokin, Tyukov 2003).

One of effective and reliable methods of defense of near to the walls product from freezing is an implementation of the air-warmth defense at the inner side of the wall (Jia, Sun, Cao 2000).

On Fig 4a,b,c provided a change of moister-content in a bulk in semi-subsurface storehouse without additional thermo insulation of a surface part. A moister-content of a ventilation air is increasing with time and_by a height of a bulk, with x > 1.3 the curves are the same the different x. Disturbances from the external influences are affecting only on certain distance from the external border.

On Fig5 a,b,c the temperatures of production throughout the height of a bulk for the x = 0.88, x >= 1.3 in the moments of time 12, 22 or 32 hours from the beginning of ventilation for the semi-sub-surfaced storehouse without additional thermo insulation of surface part. The curves T(y) at x > 2.038 practically the same with curve T(y) at x = 2.038. This is happening because the external temperature disturbances are influencing the temperature of a bulk only near the wall.

Let’s compare thermo insulating properties of semi-sub-surfaced storehouses with above surfaced one. It was accepted as correct that a wall heat-resistance of above surface storehouse 4 times greater than of a semi-subsurface storehouse wall.

Fig 6a and Fig 6b compares temperatures T(y) of a bulk for the semi-subsurface and the above surface storehouses with thermo-insulation after 32-hours of ventilation for x as

0.9; 1.3; 1.7.

From the comparison follows that the heat regime in the semi-sub-surfaces storehouse is more acceptable especially near the wall. It’s especially noticeable from comparison of super cooling zones in Fig 7a and Fig 7b.

Figure 4a

Ho is.cant.jkg/KG

.4483E-02 :

.4Z20E-02 :

. 3958E-02

.3696E-02 j

.3434E-02 ;

.3171E-02 ;

.2909E-02 j

.2647E-02 :

.2385E-02 ;

.2122E-02 '

. 1860E-02 y,n

.0000 1.250 2.500 3.750 5.000

Sraph DCm>, if x = const. Time 220.000

Figure 4b

hois.cont. kg/KG

.4491E-02 x= x= .8846 1.269

.4231E-02 x= x= 1.654 2.038

.3970E-02 h" X- X- 2.423 2.808

.3710E-02 X- X- 3.192 3.577

.3449E-02 x= x= 3.962 4.346

.3189E-02 x= x= 4.731 5.115

.2928E-02 x= 5.500

.2668E-02

.2407E-02

.2147E-02

.1B86E-02 .0000 1.250 2.500 : y,m 3.750 5.000 Esc

Sraph D ( i j ) if X - const. Tine 320.000 menu

Figure 5b

T7x 3.223 2.339 1.394 .4799 -.4345 -1.349 -2.263 -3 .178 -4.092 -5.007 -5.921

h P ' I j 'N

.0060

1.250

2.500

3.750

y j in .006

iraph T(m)j if x = const.

Time 320.000

x= .8846

x= 1.269

x= 1.654

X= 2.038

X= 2.423

X= 2.808

X= 3.192

X= 3.577

X= 3.962

X= 4.346

x= 4.731

x= 5.115

x= 5.500

Esc

menu

Figure 6b

.500 1.500 z.500

3.500 4.500 5.500

Supercool, and selfheat, zones.

Tine 320.000

supercooling norm

sup.heat

Esc

menu

To minimize the mass of super cooling produce it is possible to increase mass of air forced into a bulk with temperature of 2 °C, i.e. to reasonably increase the velocity of ventilation, but not to cause a produce drying out. Also advisable to increase as much as possible the power of heat sources in upper zone.

In Fig 8a and Fig 8b are compared 2 possible versions of minimization of a mass of overcooled produce. Semi-subsurface storehouse with thermal insulation in above surface part with G = 30 (3 times increase of speed of ventilation) and Q = 12 (2.4 times increase of a power of heat sources in upper zone) looks like the most appropriate version of a storage of agricultural produce.

CONCLUSION

The improvement of safekeeping of juicy agricultural produce - potatoes, vegetable, fruits - is tied to maintaining favorable conditions in the storehouses, ensuring thermo-insulating requirements of external protecting construction of facilities for the storing raw agricultural production. Particular complexity arises during storage of potatoes and vegetable close to the walls of the storehouses in winter period because of possible frost penetration of the produce what leads to big losses.

One of the reasons for high losses of produce is insufficient study of heat-moister processes in the storehouses and in a bulk of a raw produce, unsatisfactory the methods for the heat-technical calculation of the storehouses. The purpose of this article was the development of methods for the heat-technical calculation of the potato and vegetable storehouses by the solving the conjunctive tasks of a non-stationary heat and moister exchange.

The goal was achieved by solving the following problems:

- Developed the mathematical model based on conjunctive task for heat-moister exchange processes in the storehouses of juicy agricultural produce;

- Developed the methodology of calculation for heat and moister exchange processes in the above surface and sub-surfaced type storehouses for the juicy agricultural produce;

- Created methodology and software programs for the calculation of thermodynamic system «external air - protecting construction - inner air of storehouse - a bulk of produce ventilated by air».

Simplicity of setting the initial data, fast calculations and convenient presentation of results allows to use this program as means of mathematical simulation of a heat-moister regimes in storehouses for any engineer.

Presented the examples of the simulation to choose the most appropriate constructive and technological parameters to minimize the deterioration of produce during storage.

REFERENCES

1. Beukema KJ, Bruin S, Schenk J (1982) Heat and mass transfer during cooling and

storage of agricultural products. Chem Eng Sci 37: 291-298

http://dx.doi.org/10.1016/0009-2509(82)80164-4

2. Chudnovskiy A.F. (1987) Heat physics of grounds, Moscow, «Nauka», 352.

3. Fletcher CAJ (1988) Computational Techniques for Fluid Dynamics 1. Fundamental and General Techniques. Springer, Berlin Heidelberg New York

4. Jadan VZ (1976) Heat Backgrounds for Cold Storage of Juicy Raw Material at Food

Processing Enterprises. Food Industry, Moscow

5. Jia C, Sun DW, Cao C (2000) Finite Element Prediction of Transient Temperature

Distribution in Grain Storage Bin. J Agric Eng Res 76: 323-330

http://dx.doi.org/10.1006/jaer.2000.0533

6. Kondrashov VI (1997) Controlled environment in biological product (information

technologies and mathematical modeling). Mashinostroenie, Moscow

7. Kondrashov VI (2000) Mathematical simulation of the coupled heat and moisture exchange in storehouses of agricultural production. Heat and Mass Transfer 36: 381-385 http://dx.doi.org/10.1007/s002310000083

8. Kondrashov VI, Kondraschov N, Kokin JA, Tyukov VM (2003) Computersimulation von Mikroklima in Lagerhallen fur landwirtschaftliche Erzeugnisse. Zeitschrift fur Agrarinformatik 2: 32-36

9. Nganhou J. (2004) Heat and mass transfer through a thick bed of cocoa beans during drying Heat and Mass Transfer:40:727 - 735 http://dx.doi.org/10.1007/s00231-003-0424-1

10. Prusakov G.M. (1994) Mathematical models and methods in computer simulation, Moscow, «Nauka», 144.

11. Savin V.K., Moiseenko A.M., Kondrashov V.I. (2004) Analysis of heat-moisture condition of semi sub-surfaced storehouses of agricultural produce, IzvestiyaVYZov. «Stroitelstvo» #7, p 68-72.

12. Shih Tien Mo (1984) Numerical Heat Transfer. Springer, Berlin Heidelberg New York

13. Tashtoush B (2000) Heat-and-Mass transfer analysis from vegetable and fruit products stored in cold conditions. Heat and Mass Transfer 36: 217-221

14. http://dx.doi.org/10.1007/s002310050388