MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF WOOD MATERIALS IN THE HYGROSCOPIC RANGE

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1 INNOVATION IN WOODWORKING INDUSTRY AND ENGINEERING DESIGN, / (5): 9 MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF WOOD MATERIALS IN THE HYGROSCOPIC RANGE Nencho Deliiski University of Forestry, Kliment Ohridski blvd, 797 Sofia, Blgaria, deliiski@netbg.com ABSTRACT A mathematical model of the specific heat energy, which is needed for defrosting of wood materials in the hygroscopic range, q, has been sggested. The specific heat energy q consist of two parts: the energy needed for heating of the frozen wood ntil melting of the ice in it, q wfr, and the energy needed for the melting of the ice formed from the bond water in the wood, q bw. Using the sggested model comptations have been carried ot for the determination of q wfr, q bw, and q = q wfr + q bw dring defrosting of oak, pine, beech, and poplar frozen wood with moistre content from. kg kg - p to the border of the hygroscopic diapason and with initial temperatre in the range from o C to o C, at which the thawing of the ice formed from the bonded water is completed. Key words: modelling, wood defrosting, specific heat energy, wood specie, hygroscopic range INTRODUCTION When sizing the power of the sorces of heat energy, which are sed for the spply of the eqipment for defrosting of wood materials, it is necessary to take into consideration the need for energy both for the heating of the frozen wood and for the thawing of the ice in it dring the winter (Shbin 99, Pervan, Trebla and Klement, Videlov ). In Deliiski (,, ) -,-, and -dimensional models have been created, solved, and verified of the transient non-linear heat condction and energy consmption in frozen wood materials with prismatic and cylindrical shape dring their thermal treatment. The soltion of these models, in which the mechanism for distribtion of the temperatre in the wood materials is described by rather complex differential eqations with partial derivatives, is carried ot with the help of specialized software, developed by the athor. For the calclation of the need of thermal energy for the heating of the frozen wood and melting of the ice in it with the help of non-stationary mathematical models it is necessary to have the mentioned specialized software, whose accessibility however is very limited. The aim of the present work is to sggest an easy for engineering applications mathematical model of the specific heat energy consmption, q, which is needed for defrosting of frozen wood materials in the hygroscopic range. For the achieving of this goal mathematical models of the two consisting parts of q have been also sggested, as follows: of the energy needed for heating of the frozen wood ntil melting of the ice formed from the bonded water in it, q wfr, and of the energy needed for melting of the mentioned ice, q bw.

2 9 NENCHO DELIISKI. MODEL OF THE ENERGY NEEDED FOR HEATING OF THE FROZEN WOOD UNTIL MELTING OF THE ICE IN IT IN THE HYGROSCOPIC RANGE where c T T q.. q is the specific heat energy wfr The specific energy needed for heating of frozen wood ntil melting of the ice in it in the hygroscopic range, q wfr, can be determined according to eqation given in Deliiski (): w wfr w nfw & Tw T needed for heating of frozen wood ntil melting of the ice in it, kwh m - ; w density of the frozen wood in the hygroscopic range, kg m - ; c wfr specific heat capacity of the frozen wood, J kg - K - ; T w temperatre of the frozen wood at the beginning of its defrosting, K; T wood defrosting temperatre, i.e. the temperatre at which the ice formed from the bonded water in the wood is transformed completely into a liqid state, K. The temperatre T is determined according to eqation () given below when. kg kg or according to eqation (7) if ; wood moistre content of the frozen wood, kg kg - ; fiber satration point of a given wood specie, kg kg -. The vale of is determined according to a sggested by Stamm (9) eqation, given in Deliiski (); w b S v 9.5.T, () fiber satration point of the wood at temperatre Т = K, i.e. at t = о С, at which the thawing of the ice formed from the bonded water is completed (Chdinov 9), kg kg -. The vales of are determined according to the eqation given in Deliiski (); nfw content of non-frozen water in the wood at given temperatre T w 7. 5 K, kg kg -. The vale of nfw is determined according to eqation (5) given below. The mltiplier. in the denominator of eqation () ensres that the vales of q wfr are obtained in kwh m - instead of in J m -. For practical sage of eqation () for the determination of q wfr it is needed to have mathematical descriptions of w and c wfr in the hygroscopic range. In Deliiski () the following descriptions of w and c wfr in the hygroscopic range have been nfw & T T, () 9.5 Tw T Tw T nfw c K wfr c, ()

3 MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF 97 nfw K c Tw T.75.., () 9.5.T.75exp.57T. w nfw. ln where is the fiber satration point of the wood at temperatre Т = 9.5 K, i.e. at t = о С, whose vales for separate wood species are given in the specialized literatre, kg kg - ; b basic density of the wood given in the specialized literatre, kg m - ; S v volme shrinkage of a given wood specie given in the specialized literatre, %. nfw. kg.kg nfw, (5), (), (7) The calclated according to eqations () to 9.5 () change in,,, S ) and in 9.5 wfr, w ( b v c, Tw for oak, beech, pine and poplar wood with t w o C in the range from. kg kg to are shown on Fig.. The calclated according to eqation () change in q f ( ) for the stdied wfr for wood species with t w o C are shown on Fig.. t w o C and 9 Wood density w, kg.m ,,,,,,,,,, Specific heat capacity c wfr, J.kg -.K ,,,,,,,,,, Wood moistre content, kg.kg - Wood moistre content, kg.kg - c Figre : Change in ρ w (left) and in wfr (right) dring defrosting of wood with t w = o C depending on and on the wood specie

4 9 NENCHO DELIISKI Specific heat energy q wfr, kwh.m -,5,5,5,5,5,5,7,9,,,5,7,9 Wood moistre content, kg kg - Specific heat energy q wfr, kw h.m ,,,,,,,,,, Wood moistre content, kg.kg - Figre : Change in q wfr dring defrosting of wood with t w = o C (left) and with t w = o C (right) depending on and on the wood specie. MODEL OF THE ENERGY NEEDED FOR MELTING OF THE ICE IN FROZEN WOOD IN THE HYGROSCOPIC RANGE The specific energy needed for melting of the ice formed from the freezing of q c T T.. w bw w nfw where qbw is the specific heat energy needed for melting of the ice, formed from the bonded water in the wood, kwh.m - ; c bw specific heat capacity of the ice formed from the freezing of the bonded water in the wood, whose vales (in J kg - bonded water in the wood, q bw, can be determined according to the eqation given in Deliiski (b) & T 7. 5K, () w K - ) in the ranges nfw & T K can be calclated according to the following eqation, given in Deliiski (): Tw T exp c T bw. (9) The meaning of the other variables involved in eqations () and (9) are given The calclated according to eqation () change in q bw, sing also eqations () above when clarifying eqations () to (7). and (), for frozen wood with t w o C The calclated according to eqation (9) change in c bw for the stdied for wood and t w o C depending on is shown species with t C and on Fig.. w o t w o C depending on is shown on Fig..

5 MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF 99 Specific heat capacity c bw, J kg - K -,5,7,9,,,5,7,9 Wood moistre content, kg kg - Specific heat capacity c bw, J kg - K ,,,,,,,,,, Wood moistre content, kg kg - Figre : Change in c bw dring defrosting of wood with t w = o C (left) and with t w = o C (right) depending on and on the wood specie,5 Specific heat energy q bw, kwh m -,5,5,5,5,5,7,9,,,5,7,9 Wood moistre content, kg.kg - Specific heat energy q bw, kwh m - 7 5,,,,,,,,,, Wood moistre content, kg kg - Figre : Change in q bw dring defrosting of wood with t w = o C (left) and with t w = o C (right) depending on and on the wood specie. MODEL OF THE ENERGY NEEDED FOR DEFROSTING OF WOOD MATERIALS IN THE HYGROSCOPIC RANGE The specific energy, which is needed for defrosting of the wood in the hygroscopic range, q, is eqal to the sm of the energy needed for heating of frozen wood ntil melting of the ice in it in the hygroscopic diapason, q wfr, and of the energy needed for the melting of the ice formed in the wood from the freezing of the bond water in it, q bw, i.e. q can be determined according to the eqation q qwfr qbw. () The calclated according to eqations (), (), and () change in q for the stdied for wood species with t w o C and t w o C depending on is shown on Fig. 5.

6 NENCHO DELIISKI 9 Specific heat energy q, kwh.m - 7 5,5,7,9,,,5,7,9 Wood moistre content, kg.kg - Specific heat energy q, kwh.m -,,,,,,,,,, Wood moistre content, kg.kg - Figre 5: Change in q dring defrosting of wood with t w = o C (left) and with t w = o C (right) depending on and on the wood specie The calclated according to eqations (), (), and () change in q for frozen wood with. kg kg and the calclated according to eqation (5) change Specific heat energy q, kwh.m - Non-frozen water nfw, kg.kg - in the content of non-frozen water in the wood nfw depending on initial wood temperatre t w is shown on Fig..,,5,,5,,5 I C E W A T E R Temperatre t w, o C, Temperatre t w, o C Figre : Change in q of wood with =. kg kg - (left) and in nfw (right) dring defrosting of wood materials depending on wood initial temperatre t w and on the wood specie. DISCUSSION The analysis of the shown on Fig. to reslts gives the basis for the following conclsions:. The density of frozen wood w in the hygroscopic range increases according to a linear dependence when the wood moistre content increases (Fig. left). A reason for this is the proportionality of the wood mass depending on.. The specific heat capacity of the frozen wood c wfr and the specific heat capacity of the ice formed in the wood from the freezing of the bond water in it, c bw, increase in the hygroscopic range according to a logarithmic dependences when the

7 MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF wood moistre content increases (Fig. right and Fig. right).. The specific heat energy consmption, q wfr, which is needed for heating of frozen wood ntil melting of the ice in it in the hygroscopic range, increases almost proportionally to the wood moistre content (Fig. ).. The specific heat energy consmption, q bw, which is needed for melting of the formed in the wood ice from the bond water in it, increases proportionally to the wood moistre content (Fig. ). 5. The specific energy, which is needed for defrosting of the wood in the hygroscopic range, q, increases almost proportionally to the wood moistre content (Fig. 5).. The specific heat energy consmption q decreases according to a slight crvilinear dependence when the initial wood temperatre t w increases (Fig. left). 7. The content of non-frozen water in the wood increases according to exponential dependence when the initial wood temperatre t w increases (Fig. right).. When the wood contains the maximm possible qantity of bond water, i.e. when (Chdinov 9), for the defrosting of wood, which contains ice formed from the freezing of the mentioned water the following vales for q are needed (Fig. 5): kwh m - at t w = o C and.77 kwh m - at t w = o C for oak wood with. kg kg ; 7.7 kwh m - at t w = o C and. kwh m - at t w = o C for beech wood with. kg kg ; 5.7 kwh m - at t w = o C and.9 kwh m - at t w = o C for pine wood with.7 kg kg ; 5.79 kwh m - at t w = o C and.5 kwh m - at t w = o C for poplar wood with. kg kg. 9. If the increase in q depending on is taken to be flly linear in the range from nfw to at which the thawing of the ice formed from the bond water in the wood is completed, then each increase of by. kg.kg - in this range cases an increase in q for the stdied wood species as follows: by. kwh m - at t w = o C and by. kwh m - at t w = o C for oak; by. kwh m - at t w = o C and by. kwh m - at t w = o C for beech; by.5 kwh m - at t w = o C and by. kwh m - at t w = o C for pine; by. kwh m - at t w = o C and by.9 kwh m - at t w = o C for poplar. This reslts show that the most inflencing factor on q is the basic density of the wood. The obtained above reslts for the increase of q when increases by

8 NENCHO DELIISKI. kg kg - at t w = o C differs by not more than.% from the reslts for the increase of q wfr at t w = o C. Using the mltiplied by average vales of the obtained above reslts for the increase of q bw for the case of increase of q nfw where is the wood moistre content in the hygroscopic range, kg kg - ; K coefficient eqals to 7. for oak, 9. for beech,. for pine, and 5. for poplar wood; nfw the content of non-frozen water in the wood at given temperatre T K, kg kg -. The vales of w nfw can be easy determined with the help of Fig. (right), which has been drawn sing reslts obtained according to eqation (5). The calclated according to eqation () vales for q differ from their corresponding vales of q on Fig. 5 and Fig. (left) by not more than 5%. This accracy of eqation () is enogh for different technological and/or engineering calclations of q in the whole hygroscopic range when nfw & Tw T by. kg kg - at t w = o C and t w = o C as proportionality coefficient, K, the vale of q can be calclated according to the following eqation: nfw & Tw T, () dring wood defrosting. Eqation () can be sed for calclation of q dring wood defrosting for all wood species. Data for basic density, b, fiber satration point, 9.5, and volme shrinkage of the wood, S v, for separate wood species needed for the determination of participating in this eqation vales of nfw and K can be fond in the specialized literatre (Shbin 99, Pervan, Trebla and Klement, Videlov, etc.). CONCLUSIONS In the present paper easy for engineering applications mathematical model of the specific heat energy consmption needed for defrosting of frozen wood materials in the hygroscopic range, q, has been sggested. The model takes into accont the inflence on q of the following factors: wood moistre content, initial wood temperatre of the frozen wood, basic density of the wood, volme shrinkage of the wood, and for the first time the fiber satration point of separate wood species and the inflence of the temperatre on. For the calclation of q according to the sggested model a software program has been prepared in the calclation environment of Visal Fortran Professional. Using the program comptations have been carried ot for the determination q of oak, pine, beech, and poplar frozen wood with initial temperatres in the range from t = o C to t = о С, at which the thawing of the ice formed from the bond water is completed (Chdinov 9) and with moistre content in the hygroscopic range. kg kg defrosting. dring wood

9 MODELLING OF THE ENERGY NEEDED FOR DEFROSTING OF Based on the obtained reslts, a very simple and easy for se eqation for the calclation of q depending only on the wood moistre content and on the content of non-frozen water in the wood at given initial wood temperatre has been sggested. This eqation can be sed for precise enogh ( 5% ) technological and engineering calclations of varios processes for thermal and hydro-thermal treatment of frozen wood materials aimed at their defrosting. The obtained reslts are of specific importance for the optimization of the technology and for the model based atomatic control (Deliiski, ) of different defrosting and/or frosting processes of wood and other capillary poros materials. The sggested model and the obtained reslts can be of interest also for the edcational process at specialized technical niversities and engineering schools. REFERENCES. Chdinov, B. S., (9). Theory of the thermal treatment of wood. Pblishing Company Naka, Moscow, USSR, 55 p. (in Rssian).. Deliiski, N., (). Modelling and technologies for steaming wood materials in atoclaves. DSc. Dissertation, University of Forestry, Sofia, 5 p. (in Blgarian).. Deliiski, N., (). Modelling and atomatic control of heat energy consmption reqired for thermal treatment of logs. Drvna Indstrija 55: 99.. Deliiski, N., (). Transient heat condction in capillary poros bodies. In Ahsan A (ed) Convection and condction heat transfer. InTech Pblishing Hose, Rieka: 9 7, 5. Deliiski, N., (). Calclation of the heat energy needed for melting of the ice formed from bonded water in the wood. Jornal of Environmental Science and Engineering B, Volme, No: 7.. Pervan, S., (). Handbook for technical drying of wood. Zagreb, Sand, 7 p. (in Croatian). 7. Shbin, G. S., (99). Drying and thermal treatment of wood. Pblisher Lesnaya promyshlennost, Moskow, USSR, 7 p. (in Rssian).. Stamm, A. J., (9). Wood and celllose science. The Ronald Press Company, New York. 9. Trebla, P., Klement, I., (). Drying and hydrothermal treatment of wood. TU Zvolen, 9 p., Slovakia (in Slovak).. Videlov, H. (). Drying and thermal treatment of wood. Pblishing Hose of the University of Forestry, Sofia, 5 p. (in Blgarian).