Integral assessment of the effects of electric field on the

speed of the drying process

 

Nikolaev N.S.

Dr. Ph. Of Technical Sciences, Professor,

Burlev M.Ya.

Dr. Ph. Of Technical Sciences, Academic IAR,

Uruypin M.A.

Dr. Ph. Of Technical Sciences,

Moscow State University of Food Industry,

Russian Federation

 

 

Introduction. The results of experimental research and mathematical modeling of the process of drying of skim milk in a thin layer with the application of an electric field. Implemented an integrated assessment of the impact of the electric field at the speed of the drying process. Graphically shows the dependence of the electric field effect on the drying process of its key features.

Keywords: skimmed milk, drum (roller) dryer, mathematical modelling, electrical field, convective drying, drying in a thin layer, intensification

 

         Many products to dehydration are the convective drying in a thin layer. To do this, often use drum (rolling) dryer. The efficiency of the drying process in a drum dryer is associated largely with the processing time. In addition, it is directly related to, including, and the size of the drum [1]. In this regard, the intensification of the process of drying of skim milk in a thin layer is an urgent task that will reduce the size of equipment, reduce processing time and thus reduce capital investment and increase energy efficiency. To accomplish this, used the influence of electric field [2].

 

         Figure of convection drying process in a thin layer with the electric field presented in Fig. 1.

 

 

 

6

 

 


5

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

3

 

 

 

 

 

2

 

 

 

1

 

 

 

 

 

 

 

 

7                                     8

 

 

 

 

 

 

 

Fig. 1. Drum (roller) dryer milk using an electric field:

1 – screw conveyor; 2 – product (skim milk); 3 – scraper; 4 – nozzle;

5 – extractor hood; 6 – drums; 7 – electrodes; 8 – pneumatic transport

 

 

Method of Integral assessment:

         Remove moisture under the action of the temperature field.

To describe the first period of drying mass transfer (constant speed), can use a known mass linear equation:

 

         -dW/dτ = const = β (Wequil. – Wavrg.)                                                       (1)

 

         W      – the moisture content of the material, kg/kg;

Wequil – equilibrium moisture content of the material, kg/kg;

Wavrg. – the average amount of body moisture content material, kg/kg;

τ        – time, sec;

β       – the mass transfer coefficient, 1/sec.

To describe a mass transfer of the second period (the period of the falling speed) using diffusion equation (2-nd Fick's law):

 

         ∂W/∂τ = D (∂2W/∂x2 + ∂2W/∂y2 + ∂2W/∂z2)                                     (2)

 

D - the diffusion coefficient, which takes into account a number of internal mass transfer, m2/sec;

x, y, z – spatial coordinates, m.

It was for drying layer of skim milk on the substrate assumed, that is a lot smaller than the thickness of the substrate, and physical properties of the material are constant throughout the substrate. In this case, from a three-dimensional spatial diffusion equation can be one-dimensional equation:

 

         ∂W/∂τ = D (∂2W/∂h2)                                                                      (3)

 

h        – is the only axis-height in a layer on a substrate, m.

The initial condition:

τ = 0,          0 <h <H,              W = WB,

H       – layer thickness, m;

WB       – the initial moisture content of the material, kg/kg.

Boundary conditions:

 

τ ≥ 0,          h = 0,                   ∂W/∂h = 0,           τ → ∞,       h = H,         W = Wequil ,

 

The exact analytical solution of this equation generally get fails, but using numerical methods [3], you will get a solution for any given option.

Family of functions W (h) moisture distribution in the thickness of the thin layer at regular intervals is shown in the following graph (τ = 0, the initial moisture content W (h) = WB = const):

Wí,%

100

 

 

 

 

 

 

 

 

 

 

 

  75

 

 

 

 

 

 

 

 

 

 

  50

 

 

 

 

 

 

 

 

 

 

  25

 

 

 

 

 

 

 

 

 

 

   10

 

 

 

Wequil

 

 

 

 

 

 

 

 

 

 

0          10        20           30        40           50        60           70        80           90  100 h/H/%

 

Figure. 2. Family of graphs the distribution of moisture content W in thickness of a thin layer of skim milk on a substrate at regular intervals.

        

         Remove moisture under the action of the electric field.

 

         In order to get closer to the understanding of the influence of electric fields on the process of removing moisture from the product and to quantify this impact in the form of a supplementary member of the equation obtained experimental data have been processed, are listed below.

         Focused on the experimental data of drying thin layer of skim milk on the substrate.

 

         Variants:

À0 – without electric impact

 

À1 - frequency of impulses f1 = 150 Hertz, duty cycle Q = 3

 

À2 - frequency of impulses f2 = 200 Hertz, duty cycle Q = 3

 

À3 - frequency of impulses f3 = 300 Hertz, duty cycle Q = 3

 

À4 - frequency of impulses f4 = 400 Hertz, duty cycle Q = 3

 

Â1 - duty cycle Q1 =  2, frequency of impulses f = 200 Hertz

 

Â2 - duty cycle Q2 =  3, frequency of impulses f = 200 Hertz

 

Â3 - duty cycle Q3 =  5, frequency of impulses f = 200 Hertz

 

Â4 - duty cycle Q4 = 10, frequency of impulses f = 200 Hertz

 

Voltage (amplitude) U = 600 Volt

Note: Variants À2 and Â2 are the same and are for illustration purposes only.

         Results and discussion.

Table. 1. Drying speed-changes per 60 sec. mass fraction in drying thin layer of skim milk on a W [%/60 sec]

 

60

120

180

240

300

360

420

480

540

600

660

720

780

840

900

960

1020

1080

Variants.

18

11

9

9

9

9

9

9

9

8

8

7

7

6

5

4

2

1

À0

18

11

10

10

10

10

10

10

10

9

8

7

5

4

4

2

2

0

À1

20

25

18

22

21

11

8

10

2

3

0

 

 

 

 

 

 

 

À2

19

12

9

9

10

9

10

10

10

9

8

8

4

5

4

2

2

0

À3

18

12

10

11

10

9

9

9

9

8

10

8

7

5

2

2

1

0

À4

20

12

16

12

16

17

15

10

7

6

3

4

1

1

0

 

 

 

Â1

20

25

18

22

21

11

8

10

2

3

0

 

 

 

 

 

 

 

Â2

18

17

20

17

19

16

13

3

6

3

2

2

2

1

1

0

 

 

Â3

18

12

12

11

11

11

11

11

10

9

7

4

5

3

2

3

0

 

Â4

 

Table. 2. Change the speed of drying thin layer of skim milk on a W [%/60 sec] due to the electrical effect.

 

.

60

120

180

240

300

360

420

480

540

600

660

720

780

840

900

960

1020

The average value of [%/60sec/600V]

Interval comparison [sec.]

The value of the argument function

À1-À0

0

0

1

1

1

1

1

1

1

1

0

0

0

-2

-1

-2

0

1,0

180-600

f = 150 Ãö

À2-À0

2

14

9

13

12

2

-1

1

-7

-5

 

 

 

 

 

 

 

10,0

120-360

f = 200 Ãö

À3-À0

1

1

0

0

1

0

1

1

1

1

0

1

-3

-1

-1

-2

0

0,6

180-720

f = 300 Ãö

À4-À0

0

1

1

2

1

0

0

0

0

0

0

1

0

-1

-3

-2

-1

0,5

180-720

f = 400 Ãö

Â1-À0

2

1

7

3

7

8

6

1

-2

-2

-5

-5

-3

-6

 

 

 

6,2

180-420

Q = 2

Â2-À0

2

14

9

13

12

2

-1

1

-7

-5

 

 

 

 

 

 

 

10,0

120-360

Q = 3

Â3-À0

0

6

11

8

10

7

4

-6

-3

-5

-6

-5

-5

-5

-4

 

 

7,7

120-420

Q = 5

Â4-À0

0

1

3

2

2

2

2

2

1

1

-1

-3

-2

-3

-3

-1

 

1,8

120-600

Q = 10

        

         Analysis of experimental data has shown that in the investigated range during constant speed the drying effect of the electric field at a rate of close to zero. In this range, the process of evaporation of moisture from the free product is a determining and little depends on the influence of the electrical impulse actions.

         For the second period of drying, the situation is different. From the table. 2 shows that the difference between the speeds of almost constant drying. Within the limits of the physical process, described by Fick's equation, which is in the table. 3 designated as "Interval comparison". A simple (not depending from W) can describe the effect an additional member on the right side of the equation for the derivative W by time:

 

∂W/∂τ = D (∂2W/∂h2) – kï(f, Q) U                                              (3)

W      – moisture content, %

t        – time, sec;

h        – height in a layer of dried material, m;

D       – coefficient of molecular diffusion, m2/sec;

U       – voltage (amplitude), Volts;

kn           – coefficient of influence of electric field on drying process of a flat layer, which is a function of many parameters, including:

f        – frequency of impulses Hertz;

Q       – duty cycle.

 

Table. 3. The coefficient kn in units of [1/sec/V] for drying of skim milk on the substrate:

 

Q \  f, Hertz

150

200

300

400

  2

 

1,7 10-6

 

 

  3

0,28 10-6

2,8 10-6

0,16 10-6

0,14 10-6

  5

 

2,1 10-6

 

 

10

 

0,5 10-6

 

 

 

 

 

 

         Two-dimensional surface coefficient kn for drying of milk on the substrate as a function of frequency f and duty cycle Q is shown in Fig. 3.

 

 

 

Fig. 3. Dependence of the coefficient kn from frequency f and duty cycle Q.

 

         Modelling of drying process in a thin layer with the electric field can be the basis for its intensification in a drum dryer and the results as a basis for the development of more efficient equipment.

 

 

 

 

 

 

 

 

 

 

 

 

Literature.

1.     Ilyukhin V.V., Burlev M.Ya., Zhukavets E.V. / Drying milk using electric fields // Dairy industry – 2011. – ¹ 8. - P. 11 - 12.

2.     Burlev, M. Ya. Use of the drying with influence electricity potential in medicine and pharmaceutics industry // Biomedical and Biosocial Anthropology official Journal of the International Academy. National Pyrogov Memorial Medical University. Vinnitsa, Ukraine. December 2011. – ¹ 17. – P. 267 – 269.

3.     Guzev O.Yu. "Development of a high-tech process of fluidized bed dryer with heat pump”. Diss. of Ph. Tech. of Sciences. M. – 2008. 148 pages.