Diagrams of the moist air extended by equilibrium moisture of dried materials

Transcription

1 Diagrams of the moist air extended by equilibrium moisture of dried materials Ivan Vitázek, Zuzana Mikulová, and Janko Klúčik Citation: AIP Conference Proceedings 1768, (2016); View online: View Table of Contents: Published by the American Institute of Physics Articles you may be interested in X-ray spectroscopy study of local microstructures in CdSe quantum dots prepared by UV photolithography AIP Conference Proceedings 1764, (2016); / Transition metal distribution in the brain and spinal cord of a dysmyelinated rodent model AIP Conference Proceedings 1764, (2016); / Mechanical properties of slag treated by a thermal plasma system AIP Conference Proceedings 1768, (2016); / Deformation correction algorithm for PIV data AIP Conference Proceedings 1768, (2016); / On aerodynamic forces physical mechanism AIP Conference Proceedings 1768, (2016); / Contribution to investigation of turbulent mean-flow velocity profile in pipe of circular cross-section AIP Conference Proceedings 1768, (2016); /

2 Diagrams of the Moist Air Extended by Equilibrium Moisture of Dried Materials Ivan Vitázek 1, a), Zuzana Mikulová 1, b) 1, c), Janko Klúčik 1 Department of Transport and Handling, Slovak University of Agriculture in Nitra, Nitra, Slovakia a) ivan.vitazek@uniag.sk b) mikulovazuzana@centrum.sk c) xklucik@is.uniag.sk Abstract. Drying of cereals is an essential procedure in post-harvest processing. For long-term storage of cereals, it is necessary to know their sorption properties and equilibrium moisture. In the research at the Slovak University of Agriculture, the new i-w-x diagram of moist air and moist material is already applied. Moreover, the method of the immediate depiction of the moist material condition in particular environment in the i-x-w diagram is presented. The authors used Henderson s relation for equilibrium moisture of moist air and completed the i-x-w diagram with graphic representation of equilibrium moisture of the given material in the whole displayed area of nonsaturated moist air for maize, wheat, rye, barley and oats. The new characteristic parameter, drying potential xp is proposed. It is calculated from the state variables derived from the i-x-w diagram. The examples of depiction of the drying process course for maize seed by the means of i-x-w diagram with drying medium temperature of 40 o C and depiction of the process with cyclic changes of drying medium flow are also provided. These new methods will enable considerably more precise modeling of various drying modes and will also improve the evaluation of control measurements at the dryers. INTRODUCTION Agricultural products harvested with high moisture content, such as cereals and fodder crops, have to be dried to the required (normalized) moisture, which will enable long-term storage. Drying therefore becomes an essential procedure in post-harvest processing ( 14 ). Heated atmospheric air is the most used drying environment. Crops are hydroscopic capillary-porous materials. Their heat and sorption properties are so complex that they are determined almost exclusively by the means of experiments ( 10; 5 ). To observe the changes of the atmospheric air conditions in the process of drying, methodology of thermodynamics of moist air with demonstrative i-x diagram of the moist air is available for use ( 3 ). Only selected tabular values of equilibrium moisture of the dried materials are provided in the scientific literature, along with sorption isotherms exclusively for one given temperature. However, this information is not sufficient. Therefore we developed the methodology ( 11 ) for depicting the values of the equilibrium moisture of a given material in the i-x diagram of the moist air. This type of diagram was called i-x-w diagram of the moist air and given moist material and was designed for various materials ( 12; 15 ). This paper introduces the mathematical part of the method of this modification of i-x diagrams, as well as the method of immediate depiction of the moist material condition in this modified diagram. As an example of application of such diagram, the method of the drying potential Δx P determination is proposed. The Meeting of Departments of Fluid Mechanics and Thermomechanics (35MDFMT) AIP Conf. Proc. 1768, ; doi: / Published by AIP Publishing /$

3 MATERIAL AND METHODS Applied Concepts Relative air humidity φ is defined by the ratio of partial vapour pressure in the air p p to the saturated vapour pressure p (from tables) at the same temperature: p p (1) p Relative humidity of saturated air is φ = 1 (100 %). Relative humidity of nonsaturated air is lower than 1 (lower than 100 %). Moisture content dry basis u of the material is defined by the ratio of moisture weight in the material M w to the weight of the dry matter M MS : MW u (2) M MS Moisture content wet basis w of the material is defined by the ratio of moisture weight in the material M w to the whole weight M M of this material: M W M W w (3) M M M M MS Reciprocal dependences of u and w are described by the relations: 100 u w 1 u (4) w u 100 w (5) In practice, it is common to express the moisture of a material by the means of the moisture content wet basis w. On the other hand, the theory of thermodynamics of drying works exclusively with the moisture content dry basis u. Sorption isotherm (Figure 1) is a graphic illustration of the course of the equilibrium moisture of the material in w r dependent on relative air humidity r, at the given temperature t. Along with the graphical illustration we also use a chart expression w r = f ( r ) t=const and analytical expression with the help of the relation r = f (t, u r ). Equilibrium moisture (w r, u r) is the moisture of the material relevant to the state of the thermodynamic equilibrium between the material and the environment. Analytical Relation Equilibrium Moisture In order to calculate the equilibrium moisture for the purposes of our paper, Henderson s analytical relation, which is cited in ( 2 ), was used: n 1 r exp( a T ur ) (6) where: r relative equilibrium air humidity, T absolute temperature, u r absolute equilibrium material moisture, a, n constant factors, individual for each material Authors transformed Eq. (6) for linear regression. They multiplied first logarithm of Eq. (6) with -1: W

4 ln( 1 ) a T (7) n r u r And logarithm of this Eq. (7) is: ln( ln( 1 r )) lna lnt nln u r (8) After the adjustment we obtained a relation, which can be used for linear regression of the tabular values: Y A b X (9) where: X Y ln( ln( 1 )) (10) r A ln a lnt (11) lnu r wr ln 100 w r (12) By the linear regression we obtain the values a, b, from which we derive: n b (13) a exp( A lnt ) (14) FIGURE 1. Sorption isotherms for four materials Depiction of the Material Condition in the i-x-w Diagram Modified diagram for the corn grain was used in this research. Fig. 2 shows the method of depiction of the immediate condition of the moist corn grain in the modified diagram, which is exposed to the air flow of the drying

5 medium, point 1. Temperature of the drying medium t 1 = 40 o C, corn grain with moisture content wet basis w M = 16 %. Corn grain is a moist material; therefore it possesses characteristics of the water level. Condition of the material, point M, is depicted by the construction for the temperature of the marginal adiabatic evaporation in the intersection point of the axis i = constant for point 1 and line w M = constant for given material. By the means of i-x-w diagram, the equilibrium parameters φ Mr = 0.76, t Mr = 22.4 o C, x Mr = 13.4 g/kg are determined. FIGURE 2. i-x-w diagram of moist air and corn grains Drying Potential Specific moisture of the drying medium at the input (output) is defined by the value x 1 (x 2 ). Specific equilibrium moisture of the drying medium for the dried material at the input (output) of the drying medium is given by the value x M1 (x M2). Difference of these values represents the potential of the drying medium to drain away the moisture. This value was defined as the drying potential Δx P, determined by the i-x-w diagram. At the input, the drying potential is: x (15) p1 xm1 x

6 At the output, the drying potential is: x (16) p2 xm 2 x2 The drying potential Δx P allows considerably more precise evaluation of the drying mode design or already monitored course of the drying process. RESULTS AND DISCUSSION Equilibrium moisture content of cereal grains Authors worked with the tabular values of equilibrium moisture content wet basis w r from ( 7 ) for four sorts of cereal grains for temperature 20 C, for relative humidity of the air from 20 to 90 %, for air pressure p = kpa. Regarding the scope of the article, the analytic model and sorption isotherms for wheat, rye, barley and oats are presented. TABLE 1. Equilibrium moisture contents wet basis wr for temperature 20 C % Wheat Rye Barley Oats These isotherms are presented graphically in Fig.1 in coordinates w r, φ r. By linear regression of Eq. (6) were obtained the following equations with the help of the Henderson's analytical relation: Wheat exp T u (17) Rye exp T u (18) Barley exp T u (19) Oats exp T u (20) The equations for rye and barley are nearly identical. For peas have equation (6) this expression: exp T u (21) Constant values a, n were introduced in the Eq. (6) for the calculation of equilibrium moisture contents w r = 8; 10; 12; 14; 16; 18; 20; 24 % course of sorption isotherms in coordinates φ, t. These curves w r = const. are drawn in coordinates φ, t into the i-x diagram of moist air. Figures 4 and 5 show i-x-w diagrams for wheat, rye and barley - considering the scope of the article, diagram for oats is not provided. Moisture content wet basis in the section of permanent rate of drying is higher than the moisture content in the critical point and in all cases (materials) is equal to the relative humidity of saturated air = 1. Moisture content of the material in the section of decreasing rate of drying is lower than its moisture content in the critical point. The moisture content is determined by the sorption properties of the material. This paper proposes the new method of obtaining and depicting values of equilibrium moisture content of a given material in the i-x diagram of moist air

7 The Drying Process Model in the i-x-w Diagram As an example of the benefit of the work with the i-x-w diagram, a model of the course of the drying process of the corn grain with circular change of the air flow direction of the drying medium is presented. Fig. 3 on the left shows the conditions of the drying medium and also conditions of the dried material in the section of permanent rate of drying (φ Mr = 1). Drying medium: Input, point 1: t 1 = 40 o C, φ 1 = 0.14, x 1 = 5.9 g/kg Output, point 2: t 2 = 23.5 o C, φ 2 = 0.66, x 2 = 12.5 g/kg Dried material: Drying medium input, point M 1 : w M1 > 25 %, φ M1 = 1.0, t M1 = 19.3 o C, Drying medium output, point M 2 : w M2 >25%, φ M2 = 1.0, t M2 = 18.9 o C, x M1 = 14.8 g/kg x M2 = 14.4 g/kg Drying potential: FIGURE 3. i-x-w diagram of moist air and corn grains

8 - at the drying medium input: - at the drying medium output: x x x g / kg (22) p1 M1 1 9 x x x g / kg (23) p2 M It is possible to determine the drying potential the same way also for the section of decreasing speed of drying. FIGURE 4 i-x-w diagram of moist air and grains of wheat The described method of representation of the drying course in the i - x - w diagram of moist air and moist material, along with the determination of immediate condition of dried material and drying potential by the means of this diagram may be considered as new findings, which were not dealt with in the available scientific works from the field yet. Modified diagram for vegetable seed was published in Vitázek s work ( 13 ), for the corn grain in ( 15 ). Work ( 13 ) deals with modified i-x diagrams and their application, where also diagrams with drawn converter for gas

9 combustion can be found. The research into sorption properties and equilibrium moisture of selected materials is presented in ( 1; 8; 9 ). In the field of drying, experiments with thin layer of parboiled wheat were performed ( 4 ; 16 ). However, other works discuss only sorption isotherms excluding their incorporation into the diagram of moist air ( 10; 6 ). FIGURE 5 i-x-w diagram of moist air and grains of rye and barley CONCLUSION The presented method of depiction of the drying process in the modified i-x-w diagram of the moist air and moist material enables the determination of immediate state conditions of the dried material as well as the determination of drying potential during the whole drying process. The drying potential was defined as the difference of the specific equilibrium moisture of the drying medium for the dried material at the input (x M1 ) from that one from the output (x M2) of the drying medium. The difference of these values indicates the potential of the drying medium to drain the moisture. By the means of the modified diagram, it is possible to obtain more precise information about equilibrium moisture of the materials than when using the values available from the tables of the sorption isotherms

10 The presented method facilitates the research into new drying modes without the need of demanding experiments and enables more accurate evaluation of control measurements at the dryers. These procedures were successfully applied in practice and their further development is planned. ACKNOWLEDGEMENT Supported by the Ministry of Education of the Slovak Republic, project VEGA 1/0337/15 'Research aimed at influence of agricultural, forest and transport machinery on environment and its elimination on the basis of ecological measures application' and project VEGA 1/0786/14 'Effect of the environmental aspects of machinery interaction to eliminate the degradation processes in agrotechnologies of field crops'. REFERENCES 1. L.N. Bell and T.P. Labuza, Moisture sorption: practical aspects of isotherm measurement and use (2nd ed. American Association of Cereal Chemists, St. Paul, MN., 2000). 2. S. M. Henderson, A Basic Concept of Equilibrium Moisture (Agricultural Engineering for January, 1952), pp J. CHYSKÝ, Vlhký vzduch (Wet Air) (SNTL, Praha, 1977), p D. Mohapatra and P. S. Rao, A thin layer drying model of parboiled wheat (Journal of Food Engineering, Volume 66, Issue 4, February 2005), pp doi: /j.jfoodeng W. Mühlbauer, Handbuch der Getreidetrocknung, (Agrimedia GmbH, Clenze (Germany) 2009), p V. Nejtek, J. Los, and J. Fryč, Laboratory equipment for the measurement of cereals drying on Mendelu in Proceedings of International PhD Students Conference, (Mendel University in Brno, vol. 1 Brno, Czech Republic, 2014). pp S. Pabis, Teoria konwekcionogo suszenia produktov rolniczych (Theory of heat conduction drying of agricultural products) (PWRiL, Warszava, 1982), p J. Štencl, Equilibrium moisture content as a control parameter for a meadow grass drying process in a barn, (Acta Technologica Agriculturae, vol.3, No.1, 2000), pp J. Štencl, M. Fajman, P. Sedlák, B. Janštová, J. Klepárník, and J. Štencl Jr., Sorption characteristics of amaranthus stems under storage conditions and water activity prediction (Bioresource Technology, 2010, vol.101, No.23, Brno), pp E. Tsotsas and A.S. Mujumdar, Modern drying technology, (WILEY-VCH Verlag, Weinheim, 2007), p I. Vitázek, Modifikovaný i-x diagram vlhkého vzduchu (Modified i-x diagram of wet air). (Poľnohospodárstvo, vol. 42, No.8, 1996), pp I. Vitázek and J. Havelka, Equilibrium moisture of cereal grains (Acta technologica agriculturae, vol. 14, No. 4, Nitra, 2011), pp I. Vitázek, Tepelné procesy v plynnom prostredí Modifikované i-x diagramy (Heat processes in gaseous medium Modified i-x diagrams) (SUA in Nitre, Nitra, 2006), p I. Vitázek, Technika sušenia v teórii a v praxi Obilniny (Drying Technics in Theory and Practice Cereals) (SUA in Nitra, Nitra, 2011), p I. Vitázek and J. Havelka, I-x-w diagram of wet air and wheat grain (Research in agricultural engineering, vol. 59, special iss., 2013), pp Xin Yu., Investigation of moisture sorption properties of food materials using saturated salt solution and humidity generating techniques, Ph.D. thesis, University of Illinois at Urbana Champaign,