ANALYSIS OF HYDRAULIC AND HEAT RELATIONS IN HEAT NETWORKS; CALCULATION IN REAL LOCALITY

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1 International Carpathian Control Conference ICCC 00 MALENOVICE, CZECH REPUBLIC May 7-30, 00 ANALYSIS OF HYDRAULIC AND HEAT RELATIONS IN HEAT NETWORKS; CALCULATION IN REAL LOCALITY Michal PRINC, Jarosla BALÁTĚ and Bronisla CHRAMCOV Institte of Information Technologies, Tomas Bata Uniersity in Zlín, Zlín, Czech Repblic, Abstract: The paper deals with heat networks, which are parts of district heating systems. There was created a complex comptational program as a tool for calclation of pressre, flow and temperatre ratios in particlar parts of the defined heat network. The article is mainly focsed on soltion of hydralic and heat relations in real locality. Key words: District Heating, Analysis, Heat Networks, Simlation. Introdction From the point of iew of system approach, we nderstand the district heating systems (DHS) as technological strings heat prodction heat transport + distribtion heat consmption. As regards the strctre, heat networks are inclded in link of this string, i.e. they are means for transport and distribtion of heat energy in direction from the prodcer to the final consmer. In addition to simple radial networks, in practice, more complicated circle heat networks are sed, namely both steam and hot water networks, which may inclde seeral heat sorces and a large qantity of cstomers. The attention of this article is focsed on analysis of behaior sch heat networks. For this prpose there was created a complex comptational program for pressre, flow and temperatre ratio simlations in networks distribting heat. It calclates pressres and temperatres in particlar places in the network as well as flows, speeds, pressre and heat losses in separate pipelines. The practical ale of these calclations shold be appreciated by designers of heat networks and, aboe all, by operators of these networks. 775

2 Principle of calclation. Calclation of hydralic relations To determine hydralic relations it is necessary to diide the piping network into sectors (branches) with an inariable cross section in which the mass flow does not change. For the calclation of the mass flow in the separate branches of a circlar piping system a method called circle flow was sed. It is an analogy with the method of loop crrent, which is ery often sed in electrical engineering. The mass flow corresponds here to the electric crrent, the pressre is proportional to the oltage and the hydralic resistance corresponds to the electric resistance. If we apply the st and nd Kirchhoff s Law to the defined network, we obtain a system of non-linear algebraic eqations. The procedre is shown on a simple network haing for points of jnction and six branches (see Figre.) M 3 M H M Figre. Scheme of sample network We mark the nknown mass flow of the liqid in the i-th branch by symbol x i, the taken away/deliered qantity in the i-th point of jnction by symbol M i and the actie pressre in the i-th branch by H i. From st Kirchhoff s Law it reslts: The sm of all flow qantities for a determined point of jnction eqals zero. Therefore, we can write the following eqations of balance: Poin of jnction x x 4 x 5 + M = 0, (a) Poin of jnction x x x 6 M = 0, (b) Poin of jnction 3 x + x M 0. (c) M x = The pressre losses in branches, p, arising at flowing of the liqid throgh the circlar piping can be calclated according to the following formla 8L 8 p = + = π d ρ 5 d π d ρ log 3.7 k ξ x r.x, () 4 776

3 where: L [m] - length of straight sectors of the piping, d [m] - inside diameter of the piping, ρ [kg.m -3 ]- specific mass of the flowing liqid, k [m] - absolte roghness of the inside srface of the piping, ξ [-] - sm of the coefficients of the inside resistance of the piping, x [kg.s - ] - mass of flow throgh the piping, r [Pa.s.kg - ] - hydralic resistance of the piping. For the chosen loops, and 3 (see Figre.) we can write according to the formla () and according to the nd Kirchhoff s Law the following eqations for the pressre losses in branches: Loop r4 x 4 x 4 r5 x 5 x 5 H = 0, (3a) Loop - r x x r3 x 3 x 3 + r5 x 5 x 5 r6 x 6 x 6 = 0, (3b) Loop 3 x x + r x x 0. (3c) r = To sole the system of non-linear eqations represented in or case by eqation () and (3) we shall se the Newton s iteratie method.. Calclation of heat relations Heat losses in the piping are gien by the heat transmission from the heat carrier medim throgh the wall of the pipe and thermal inslation to the otside enironment in which the piping is located. For the piping located in an open area it is possible to determine the heat loss from the following eqation ( t t ) L Q& π z =, (4) d d + s + α d λ d λ d α tr 777 ( d + s) where: d [m] - otside diameter of the piping, d [m] - inside diameter of the piping, s [m] - thickness of the inslation, t [K] - temperatre of the ambient air, t [K] - temperatre of the heat carrier medim, λ tr [Wm - K - ] - coefficient of the thermal condctiity of the piping material, λ [Wm - K - ] - coefficient of the thermal condctiity of the inslation, α [Wm - K - ] - coefficient of the heat transfer on the otside srface of the piping, α [Wm - K - ] - coefficient of the heat transfer on the inside srface of the piping. As the first and second members of the denominator of eqation (4) are smaller in the order of 0 p to 0 4 when compared with the third and forth members, it is possible to neglect them and the whole eqation can be simplified to the following form L( t t ) L( t t) Q& π π z =& =. (5) d + s d λ d α ( d + s) λ d α d The heat flowing off throgh the walls of pipes into the ambient mst correspond to the heat which the flowing liqid is loses. This balance is expressed by the following eqation

4 Mc ( t t ) πl ( t t ) z k =, (6) d λ d α d where: d [m] - otside diameter of the inslation, c [J.kg -.K - ] - specific heat capacity of the flowing medim, t z [K] - temperatre of the flowing medim at the beginning of the piping, t k [K] - temperatre of the flowing medim at the end of the piping. The temperatre of the flowing liqid inside the piping can be expressed as an arithmetic mean of the temperatres at the beginning and at the end of the monitored sector t t z + t k =. (7) After sbstittion to eqation (6) and following arrangement we obtain the final relation for calclating temperatre at the end of the piping located in an open air d t z Mc πl + πlt λ d α d t =. (8) k d π + L Mc λ d α d From the known temperatre in the initial sorce of heat we can gradally calclate the temperatres at the end of the piping (branches) where the end of one part of the piping is always the beginning of another one. Heat losses of separate branches can be determined from the right or left side of eqation (6). 3 Reslts of calclation in real locality The comptational program was applied to the part of the real district heating system EBO Leopoldo, Hlohoec in Sloakia. The topology of the radial heat network is described in the Figre. The calclation of hydralic and heat relations in the network rns on the basis of determined network parameters (piping length, diameter, local resistance, ), sorce deliery (M=76,55 kg.s -, p=800 kpa) and the consmer s demands. As otpt there are calclated: for each branch: hydralic resistance, mass flow, pressre and heat losses, speed of flowing and in steam network also specific olme of steam, for each point of jnction: pressre and temperatre. The reslts of calclation can be shown on the screen in the form of tables or simple colmn graphs as it is shown in the Figres

5 Figre. Scheme of the part of the district heating system EBO Leopoldo, Hlohoec Figre 3,4. Tables of attained reslts 779

6 4 Discssion Figre 5,6,7,8. Attained reslts presented in the graphical form The attained reslts were compared with calclations made by DH designer. After the analysis we hae fond that both reslts are complying and the comptational program is therefore sitable for soling of sch kind of tasks. The practical importance of the program is not only for design of distribting networks, bt aboe all in the operation of district heating systems. The possibility of simlation of the relations in the network for arios operating conditions, i.e. for instantaneos otpt of sorces or for instantaneos consmptions is ery sefl for dispatchers in power and heating plants. This can be a contribtion not only from technical aspects bt also from economic ones. References BALÁTĚ, J. 98. Design of Atomated Control System of Centraled Heat Spply. Thesis of DrSc (Doctor of Science) Work, Technical Uniersity Brno, 98. MICHALEC, P., MEREŠ, B Analysis of Heat and Hydralic Relations in DH System Leopoldo, Hlohoec in Conjction with DH Trnaa. Bratislaa : STU in Bratislaa, 998, 43 pp. PRINC, M., BALÁTĚ, J., CHRAMCOV, B. 00. Soling of Hydralic and Heat Relations of Heat Networks. In International Carpathian Control Conference 00. Krynica, Poland : AGH Krakow, 00, pp ISBN