ࡱ> nLuorsypZZZZZZZZZ""""# ###&#(#.#z#|#####(8(:(~(((Z)^)`)***T/^/00044477 7"7*74787|7777888"8Ľ򦽦mH 5CJmHCJmH CJOJQJ0JmHCJ5CJOJQJ CJOJQJ j[CJOJQJ j[CJOJQJ56CJOJQJ6CJOJQJ5CJOJQJ CJOJQJH*mHmH<|##`)p**T,.{{{99A$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF I@$ w'`08p @ xHP !$`'0*-/2p5@8;=@CPF IC$ & F w'`08p @ xHP !$`'0*-/2p5@8;=@CPF ISub-Sea Fluid Piping Heat Transfer Calculation Procedure for Piping System Optimization BRUNO ALI and NIK`A FAFANDJEL Faculty of Engineering University of Rijeka Department for Naval Architecture and Ocean Engineering 51000 Rijeka, Vukovarska 58 Croatia Phone: ++ 385 51 651453; Fax: ++ 385 51 675 818 E-mail: calic@riteh.hr JULIJAN DOBRINI Faculty of Engineering University of Rijeka Department for Naval Architecture and Ocean Engineering 51000 Rijeka, Vukovarska 58 Croatia Phone: ++ 385 51 651453; Fax: ++ 385 51 675 818 ABSTRACT While transferring fluids through sub-sea piping, those are exposed to changeable surrounding water temperature and sea current velocity. Therefore heat transfer from piping towards outer surrounding water or from outer surrounding water towards piping occurs. The objective is to calculate more precisely total heat energy transfer along sub-sea piping. For better understanding of hydraulic losses over long piping a special mathematical model was defined. The model is based on definition of finite piping segment heat energy transfer. Corresponding computer software for heat energy transfer calculation was developed and tested, mainly intended to solve specific ecology problems influenced by pollutant fluids blocked in sunken vessel tanks. For long vertical piping presented software can be used successfully taking under consideration: predicted or experimental variation of surrounding sea current velocity along piping has to be prepared for cubic spline approximation, predicted or experimental variation of surrounding water temperature along piping has to be prepared for cubic spline approximation, physical properties of water have to be additionally prepared in table form for automatic computer approximation procedure. Changes of pipeline outer fluid temperature and flow speed that are obtained on basis of local environmental properties monitoring are processed by computer using cubic spline method. From those curves, relevant mathematical results are obtained for mean values of outer temperature and flow speed, for every mathematical (finite) segment of the pipeline. Obtained results( analysis enables defining shape (cross sections) and variables such as: dimensions of the pipeline, wall thickness and material, and insulation thickness and material, etc. As conclusion authors suggest that by interactive calculation based on developed software it is possible to perform the analysis of piping heat transfer with the objective of whole piping system optimization. Computer processing results are graphically presented in three dimensions (3D) with the possibility to change any pair of above mentioned variables, that is illustrated on a deep sea piping system example. INTRODUCTION Author of this article has been solved specific problems that correspond to ecology problems influenced by pollutant fluids blocked in sunken vessel tanks. Preparation procedure for extraction of pollutant fluids from sunken vessel tanks Author has been described in [1], as well as theoretical and professional background. For good prediction of extracting power that necessary for pollutant transfer, ntiPollutant software has been developed and tested. Usage possibilities of ntiPollutant software in marine technology has been described in [2]. An overlook to new structures and devices in coastal zone and subsea in tourist offer, has been described in [3]. On that base usage of ecology solar energy can be solved. If solar energy plants are used different solar energy long piping will be exposed to environmental conditions (winds, temperatures). As better understanding of hydraulic losses over that long piping, because of additional heat transfer problem, solved problem for underwater piping is presented. Theoretical and computation background solved for specific underwater use can be very easy adapted for losses prediction in long solar piping. Basic differences are in environmental fluids (water - air), as well as in hydrostatic pressures (depths - highs). SUB-SEA FLUID PIPING HEAT TRANSFER CALCULATION PROCEDURE FOR PIPING SYSTEM OPTIMIZATION Mathematical Model of Heat Transfer Between Pipe Finite Segment and Environment Figure 1 shows geometrical data of pipe finite segments for two heat transfer stages: a) heat transfer into a finite fluid segment from outer environmental fluid, b) heat transfer from a finite fluid segment to environmental fluid. Figure 2 shows qualitative changes of heat transfer temperatures for two heat transfer stages: a) heat transfer into a finite fluid segment from outer environmental fluid, b) heat transfer from a finite fluid segment to environmental fluid.  Figure 1 Geometrical data of pipe finite segments  Figure 2 Qualitative changes of heat transfer temperatures Figure 1 and Figure 2 have been used as base for defining of mathematical model that will be described later on. Main heat power equations consist of heat transfer in an outer region (q), over a pipe wall surface (qp), heat transfer in an inner region (qi), and finally heat transfer between inlet and outlet pipe finite segment surfaces (qc): q = qp = qi = qc, where, ( SEQ ( \* ARABIC 1) q = hn Ao (TBE - TO1), ( SEQ ( \* ARABIC 2) qp = ks AM (TO1 - T2), ( SEQ ( \* ARABIC 3) qi = hni Ai (T2 - Ti1), ( SEQ ( \* ARABIC 4) qc = (o ( Dio2 uo cp (Ti1 - TB1)/2. ( SEQ ( \* ARABIC 5) Figure 3 shows heated fluid piping in solar plants exposed to environmental conditions as base that can be used for heat looses calculation in solar plants piping/channels.  Fig. 3 Heated fluid piping in solar plants Corresponding heat transfer energy can be expressed by equations: Wq = Wqp = Wqi = Wqc, where, ( SEQ ( \* ARABIC 6) Wq = q t; Wqp = qp t; Wqi = qi t; Wqc = qc t. ( SEQ ( \* ARABIC 7) Known values: TB1, hf, Dio, ts, ks, (Lo, (T, (T1 Additionally necessary data: TBE, ums Data that have to be computed: TB2, to1, T2, ti1, Tf Determination of initial conditions while computation has to start with a new pipe finite segment: to1 = TBEq = 0T2 = TBEand,qp = 0ti1 = TBEqi = 0qc = 0 Starting iteration procedure position and conditions necessary for determining of average fluid temperature at a pipe computation segment. Defining of heat transfer orientation depends on: (T = to1 - TB1. ( SEQ ( \* ARABIC 8) (T < 0 - negative heat energy - outcome heat energy (loosed energy) in pipe finite segment, (T > 0 - positive heat energy - income heat energy to pipe finite segment, (T = 0 - there is no heat energy exchange in a correspond pipe finite segment, except that heat energy which is transforming from hydraulic losses, and has reflection to making higher thermal energy level in computed pipe finite segment. Average temperature on an outer pipe finite segment wall surface is computed: to1 = to1 + |(T |, if (T < 0, and, ( SEQ ( \* ARABIC 9) to1 = to1 - |(T |, (T > 0. Environmental fluid film temperature is calculated by equation: Tf = (TBE + to1)/2. ( SEQ ( \* ARABIC 10) Reynolds number for pipe finite segment cross flow: Reo = (Dio + 2 ts) ub / Nop, ( SEQ ( \* ARABIC 11) Nop - is computed over subprograme CSPLINE1(BUT%,9) on TF base, and ub - is computed over subprograme CSPLINE1(BUT%,2) on hf base. Friction coefficient is computed over subprogram "KOTRENJA" on base of preliminary compute Reynolds number: Cf = (1.82 ln(Reo) - 1.64)(-2). ( SEQ ( \* ARABIC 12) Nusselt number calculation preparation:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  where: Pr - over subprograme CSPLINE1(BUT%,3), on TF base, Pe = Pr Reo, (b - over subprograme CSPLINE1(BUT%,7), on TBE base, (iw - over subprograme CSPLINE1(BUT%,9), on to1 base. Nusselt number:  EMBED Equation.3   EMBED Equation.3  ( SEQ ( \* ARABIC 13)  EMBED Equation.3  Heat-transfer coefficient: hv = Ns Kp / Doo, where Doo = Dio + 2 ts. ( SEQ ( \* ARABIC 14) Heat power: q = hn Ao (Tbe - to1), where, Ao = (Dio + 2 ts) ( (Lo1. ( SEQ ( \* ARABIC 15) From equation qp = q changes of temperature on an inner pipe wall surface is given: (q = q ts (ks Am), where ( SEQ ( \* ARABIC 16) Am = (Doo2 - Dio2) ( (Lo1 / (2 Dio ln(Doo/Dio). Finally average temperature at an inner surface is: T2 = to1 + | (q |, for q < 0, and T2 = to1 + | (q |, for q > 0. ( SEQ ( \* ARABIC 17) Initial value of inner fluid average bulk temperature is ti1 = T2, and average temperature in first computation step will be: ti1 = ti1 + (T1, for T2 > to1, and ti1 = ti1 - (T1, for T2 < to1 ( SEQ ( \* ARABIC 18) Reynolds number that correspond to pipe a finite segment inner fluid flow is: Reo = uo Dio / (op, ( SEQ ( \* ARABIC 19) where, (O = uPI(Dip/Dio, environmental pipe inlet speed. Fluid physical value that necessary for computing of Nusselt number: (OP - over CSPLINE1(BUT%,9), on ti1 base, Pr - over CSPLINE1(BUT%,3), on ti1 base, (IB - over CSPLINE1(BUT%,7), on ti1 base, (IW - over CSPLINE1(BUT%,7), on T2 base, and cp - over CSPLINE1(BUT%,5), on ti1 base. Friction coefficient CZ is given from subprograme "KOTRENJA", on same manners as before. Exponent n is chosen in relation to Reynolds number: n = 0.14, for Reo < 2300 and for heating and cooling, n = 0.25, for Reo >= 2300 and for q < 0, n = 0.11, for Reo >= 2300 and for q > 0. Now on base of flow type, that is known against REP% value: 1 - laminar flow; 2 - mixed flow, and 3 - turbulent flow, Nusselt number for fluids can be defined:  EMBED Equation.3   EMBED Equation.3  FR for mixed flow,  EMBED Equation.3  polynomial regression is used, for  EMBED Equation.3 ,  EMBED Equation.3  ( SEQ ( \* ARABIC 20)  EMBED Equation.3  (suggested B. ali)  EMBED Equation.3  by  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Computation of Nusselt number for air:  EMBED Equation.3  ( SEQ ( \* ARABIC 21) Heat-transfer coefficient on an inner pipe finite segment wall surface:  EMBED Equation.3  ( SEQ ( \* ARABIC 22) Heat-transfer over a pipe finite segment inner surface:  EMBED Equation.3 , where ( SEQ ( \* ARABIC 23)  EMBED Equation.3  Heat Transfer Iteration Procedures a) qi = qp = q, Fig. 1 b) qc = qi = qp = q, Fig. 2 Heat-transfer accuracy determination, qi ... qp ... q: qi = p1 q ; RO4 = p2 (q Accuracy of p1and p2 coefficients can be defined as input data, too. Real difference between heat powers qi and q:  EMBED Equation.3 , ( SEQ ( \* ARABIC 24) if q1 <= qi , iteration procedure on qi ... q, relation is finished, and if q1 > qi, iteration procedure is started again: If POC% = 1: ti1 = q (ti1 - T2)/qi + T2; ti1s = ti1; qias = qi If POC% > 1, and if q < 0: ti1 = (q - qi) (TB1 1.2 - ti1)/(qias - qi) + ti1 and if q > 0: ti1 = (q - qi) (TB1 1.2 + ti1)/(qias - qi) + ti1. If iteration procedure a) is finished, than iteration procedure b) is started that mean first step of qc computation. Temporary qc is filed as qcp: If POC% = 0, than first heat-transfer power is:  EMBED Equation.3  ( SEQ ( \* ARABIC 25) qc is computing by equation:  EMBED Equation.3  ( SEQ ( \* ARABIC 26) Real heat power difference between qc and q is:  EMBED Equation.3  ( SEQ ( \* ARABIC 27) If qr1 <= RO4, iteration procedure is finished, If qr1 > RO4, iteration procedure is not finished, a new iteration step is coming, with new: to1 = TBE, and  EMBED Equation.3  Computer processing of average inner fluid bulk temperature in pipe finite segment:  EMBED Equation.3  ( SEQ ( \* ARABIC 28) Now flow type has to be controlled: if is the same as at start position, a new pipe segment can be computed, if not, procedure has to be repeated with higher fluid flow type. Fluid flow type is achieved over Reo that is computed as before: Reo = (Uo Dio)/(OP. Now, from subprograme "KOTRENJA" is a real friction coefficient calculated, if Reo > 300000. If Reo < 2300 friction coefficient is computed by formula: FO3 = 64/Reo. For Reo <= 20000, FO3 = 0.184 Reo (-0.25), and for Reo <= 300000, FO3 = 0.184 Reo (-0.2). Pressure losses at a pipe finite segment is:  EMBED Equation.3  ( SEQ ( \* ARABIC 29) In former formula have been used data for (OP and (OS, given from subprograme CSPLINE1(BUT%,9) and CSPLINE1(BUT%,4), and on base of fluid average bulk temperature in a temporary pipe finite segment, ti1. Total pressure losses in environmental fluid pipe by last included computed pipe segment is:  EMBED Equation.3  ( SEQ ( \* ARABIC 30) After computation procedure with environmental pipe is finished, on same manners can be started procedure with computation procedure with pollutant fluid pipe. Pressure loses in a pollutant fluid pipe segment is:  EMBED Equation.3  ( SEQ ( \* ARABIC 31) Total pressure losses in pollutant fluid pipe with a latest computet pipe segment included is:  EMBED Equation.3  ( SEQ ( \* ARABIC 32) Total pressure loose in both pipes is:  EMBED Equation.3  ( SEQ ( \* ARABIC 33) Total necessary pump hydraulic height, for resistance, density differences and heights support, is:  EMBED Equation.3  ( SEQ ( \* ARABIC 34) Total necessary power for fluid transfer is:  EMBED Equation.3  ( SEQ ( \* ARABIC 35) Differences Between Underwater and Surface Piping There are three basic differences: Underwater environment Surface/land environment Environmental fluids salt/fresh water air Environmental flows sea currents winds speed Hydrostatic pressure environmental water/ warm water, air pressure pollutant neglected Conclusion Described computer tested mathematical model is mainly intended for computation in underwater vertical pipes. If there is not in use environmental pipe, computation procedure is adequately reduced. In cas of land piping under consideration, main part of presented software can be used very successfully with some adaptation: variation in pipe height along piping has to be prepared for a cubic spline approximation, predicted or experimental (statistic) variation of wind speed along piping has to be prepared for cubic spline approximation, predicted or experimental (statistic) variation of ear temperature along piping has to be prepared for cubic spline approximation, physical properties of ear, as well as heater transported water has to be additionally prepared in table form for automatic approximation procedure. In case that no circular pipes are used, it is necessary that additional data have to be prepared for heat loses. NOMENCLATURE A0m2Heat transfer surface of outer pipe finite segment surfaceAMm2Heat transfer surface of average logarithmic pipe finite segment surfacecpJkg-1K-1Thermal conductivity by constant pressureDiomPipe finite segment inner diameterDoomPipe finite segment outer diameterEPP1Nm-2Total environmental fluid pressure related to reference computational densityEPP2Nm-2Total pollutant fluid pressure related to reference computational densityhfmMiddle depth of a pipe finite segment;hnWm-2K-1Heat-transfer coefficient on pipe finite wall segment outer surfacehniWm-2K-1Heat-transfer coefficient on pipe finite wall segment inner surfaceKpWmK-1Thermal conductivityksWmK-1Thermal conductivity of a pipe finite wall segment;NUD-Nusselt numberPe-Pecklet numberPPWNeeded power for pollutant fluid pumpingPr-Prandtl numberPTWTotal necessary power for fluid transferqcWheat flow through the pipe finite segmentqiWheat flow on pipe finite wall segment inner surfaceqpWheat flow in pipe finite wall segmentReo-Reynolds numberT01C(Average temperature at a pipe finite wall segment outer surfaceT2C(Average temperature at a pipe finite wall segment inner surfaceTB1C(Average bulk temperature at pipe finite segment inlet cross sectionTBEC(Average inner fluid bulk temperature at half height of a pipe finite segmentTfms-1Average environmental fluid flow speedsTi1C(Average inner fluid bulk temperature at a computation finite segmenttsmPipe finite segment wall thicknessumsms-1Average environmental fluid flow speedsUPIms-1Average speed of pollutant flow at the pipe outletWqJHeat transfer energyWqcJHeat transfer energy through pipe finite wall segment WqiJHeat transfer energy through pipe finite wall segment inner surfaceWqpJHeat transfer energy through pipe finite wall segment outer surface(0 kgm-3Environmental fluid density(IB kgm-1s-1Average fluid dynamic viscosity of pipe finite segment(IWkgm-1s-1Average film fluid viscosity(L0mPipe finite segment length(opm2s-1Average fluid kinematic viscosity of pipe finite segment(OPkgm-3Pollutant fluid density(P-Pump efficiency coefficient (PSkgm-3Pollutant fluid density of pipe finite segment(T-Initial step of a pipe finite wall segment outer surface temperature variation ACKNOWLEDGMENTS The authors wish to express gratitude to the Faculty of Engineering University of Rijeka and specially to the dean Prof. Bernard Frankovi, D. Sc. for their understanding and support to the research and development activities in field of naval architecture and ocean engineering. Herewith, authors also express their gratitude to the Government of the City of Rijeka and specially to the major Mr. Slavko Lini for their help and comprehension to enable participation to IOA(99 conference in IMARI. The authors also acknowledge the help and participation regarding performed experiments with the prototype of the "Ecology Underwater Device" developed on basis of Mr. Calic invention to the "Brodospas" Towing and Salvage Company from town Split. Special thanks goes to the Shipyard "Uljanik" Pula for their participation in construction and testing of mentioned device prototype. REFERENCES B. ali, Prilog metodama rjeaavanja ekologije voda primjenom specijalnih autonomnih sustava za odstranjivanje polutantnih fluida iz potopljenih spremnika (Contribution on Solving Water Ecology by Special Autonomous Systems for Extracting of Pollutant Fluids from Sunken Vessel Tanks), Tehni ki fakultet Sveu iliata u Rijeci (Faculty of Engineering University of Rijeka), Rijeka, 1994., 122 str., Doktorski rad (Dissertation). B. ali, Usage Possibilities of the  AntiPollutant Software in the Marine Technology, Adriatic Coastal Zone and Subsea - Real Challenge for Croatian Tourism, Proceedings, International Conference, Opatija 1995., Croatian Academy of Sciences and Arts & Faculty of Engineering University of Rijeka. B. ali, Nova sredstva u priobalju i podmorju u turisti koj ponudi - New Devices in Coastal Zone and Subsea in Tourist Offer, Adriatic Coastal Zone and Subsea - Real Challenge for Croatian Tourism, Zbornik izlaganja/Proceedings, International Round Table, Opatija 1994., Croatian Academy of Sciences and Arts & Faculty of Engineering University of Rijeka. 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Average temperature on an outer pipe finite segment wall surface is computed as: to1 = to1 + |(T |, if (T < 0, and, ( SEQ ( \* ARABIC 9) to1 = to1 - |(T |, (T > 0 Environmental fluid film temperature is calculated by equation: Tf = (TBE + to1)/2 ( SEQ ( \* ARABIC 10) Reynolds number for pipe finite segment cross flow is: Reo = (Dio + 2 ts) ub / Nop, ( SEQ ( \* ARABIC 11) where: Nop - is computed over subprogram  CSPLINE1(BUT%,9) on TF base, and ub - is computed over subprogram  CSPLINE1(BUT%,2) on hf base. Friction coefficient is computed over subprogram "KOTRENJA" on base of preliminary compute Reynolds number: Cf = (1.82 ln(Reo) - 1.64)(-2) ( SEQ ( \* ARABIC 12) Nusselt number calculation preparation is as follows:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  where: Pr - over subprogram  CSPLINE1(BUT%,3) , on TF base, Pe = Pr Reo, (b - over subprogram  CSPLINE1(BUT%,7) , on TBE base, (iw - over subprogram  CSPLINE1(BUT%,9) , on to1 base. Nusselt number is:  EMBED Equation.3   EMBED Equation.3  ( SEQ ( \* ARABIC 13)  EMBED Equation.3  Heat-transfer coefficient is: hv = Ns Kp / Doo, where Doo = Dio + 2 ts ( SEQ ( \* ARABIGHHHH^NNNN}@$ w'`08p @ xHP !$`'0*-/2p5@8;=@CPF IA$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF IC 14) Heat power is: q = hn Ao (Tbe - to1), where, Ao = (Dio + 2 ts) ( (Lo1 ( SEQ ( \* ARABIC 15) From equation qp = q changes of temperature on an inner pipe wall surface is given by: (q = q ts (ks Am), where ( SEQ ( \* ARABIC 16) Am = (Doo2 - Dio2) ( (Lo1 / (2 Dio ln(Doo/Dio) Finally, average temperature at an inner surface is: T2 = to1 + | (q |, for q < 0, and T2 = to1 + | (q |, for q > 0 ( SEQ ( \* ARABIC 17) Initial value of inner fluid average bulk temperature is ti1 = T2, and average temperature in first computation step will be: ti1 = ti1 + (T1, for T2 > to1, and ti1 = ti1 - (T1, for T2 < to1 ( SEQ ( \* ARABIC 18) Reynolds number that corresponds to inner fluid flow within a pipe finite segment is: Reo = uo Dio / (op, ( SEQ ( \* ARABIC 19) where, (O = uPI(Dip/Dio, represents environmental pipe inlet speed. Fluid physical values that are necessary for computing of Nusselt number are: (OP - over  CSPLINE1(BUT%,9) , on ti1 base, Pr - over  CSPLINE1(BUT%,3) , on ti1 base, (IB - over  CSPLINE1(BUT%,7) , on ti1 base, (IW - over  CSPLINE1(BUT%,7) , on T2 base, and cp - over  CSPLINE1(BUT%,5) , on ti1 base. Friction coefficient CZ is obtained from subprogram "KOTRENJA", based on procedure presented above. Exponent n is chosen in relation to Reynolds number: n = 0.14, for Reo < 2300 and for heating and cooling, n = 0.25, for Reo ( 2300 and for q < 0, n = 0.11, for Reo ( 2300 and for q > 0. Next, on basis of flow type which is known against REP% value: 1 - laminar flow; 2 - mixed flow, and 3 - turbulent flow, Nusselt number for fluids can be defined as follows:  EMBED Equation.3   EMBED Equation.3  FR for mixed flow,  EMBED Equation.3  polynomial regression is used, for  EMBED Equation.3 ,  EMBED Equation.3  ( SEQ ( \* ARABIC 20)  EMBED Equation.3  (suggested B. ali)  EMBED Equation.3  by  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Computation of Nusselt number for air is:  EMBED Equation.3  ( SEQ ( \* ARABIC 21) Heat-transfer coefficient on an inner pipe finite segment wall surface is:  EMBED Equation.3  ( SEQ ( \* ARABIC 22) Heat-transfer over a pipe finite segment inner surface is:  EMBED Equation.3 , where ( SEQ ( \* ARABIC 23)  EMBED Equation.3  Heat Transfer Iteration Procedures There are two different heat transfer directions: a) qi = qp = q, presented in Figure 1, and b) qc = qi = qp = q, presented in Figure 2. Heat-transfer, qi ... qp ... q, accuracy determination: qi = p1; q ; RO4 = p2 (q Accuracy of p1 and p2 coefficients can be defined as input data, too. Real difference between heat powers qi and q is:  EMBED Equation.3 , ( SEQ ( \* ARABIC 24) if q1 ( qi , iteration procedure on qi ... q relation is completed, and if q1 > qi, iteration procedure is started again, as follows: If POC% = 1: ti1 = q (ti1 - T2)/qi + T2; ti1s = ti1; qias = qi If POC% > 1, and if q < 0: ti1 = (q - qi) (TB1 1.2 - ti1)/(qias - qi) + ti1 and if q > 0: ti1 = (q - qi) (TB1 1.2 + ti1)/(qias - qi) + ti1 If iteration procedure a) is completed, than iteration procedure b) is started which means first step of qc computation. Temporary qc is filed as qcp: If POC% = 0, than first heat-transfer power is:  EMBED Equation.3  ( SEQ ( \* ARABIC 25) where qc is computing by equation:  EMBED Equation.3  ( SEQ ( \* ARABIC 26) Real heat power difference between qc and q is:  EMBED Equation.3  ( SEQ ( \* ARABIC 27) If qr1 ( RO4, iteration procedure is completed. If qr1 > RO4, iteration procedure is not completed, and new iteration step follows with new values: to1 = TBE, and  EMBED Equation.3  Computer processing of average inner fluid bulk temperature in pipe finite segment is:  EMBED Equation.3  ( SEQ ( \* ARABIC 28) Now, flow type has to be controlled: if it is the same as at start position, a new pipe segment can be computed, if not, procedure has to be repeated with higher fluid flow type. Fluid flow type is achieved over Reo that is computed as before: Reo = (Uo Dio)/(OP. Now, from subprogram "KOTRENJA", if Reo > 300000, a real friction coefficient is computed. If Reo < 2300, friction coefficient is computed by formula: FO3 = 64/Reo. For Reo ( 20000, FO3 = 0.184 Reo (-0.25), and for Reo ( 300000, FO3 = 0.184 Reo (-0.2). Pressure losses at a pipe finite segment is:  EMBED Equation.3  ( SEQ ( \* ARABIC 29) In former formula data for (OP and (OS, given from s# 0&P . A!n"n#$%za9C_iyuU( ww /2ure > 0 is)> 0Isare ureandure ((((computed case kinematics 10 """###|#};A$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF IA$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF I@ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF Iubprogram  CSPLINE1(BUT%,9) and  CSPLINE1(BUT%,4) , and on base of fluid average bulk temperature in a temporary pipe finite segment, ti1, have been used. Total pressure losses in environmental fluid pipe with last included computed pipe segment are:  EMZZZZ""w5A$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF IA$ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF IC$ & F w'`08p @ xHP !$`'0*-/2p5@8;=@CPF I"8X8^8b88889<9d9h9|998:<:>: @@@@\AAAAB*BNBBBC CCCCvCCCCXD\D`DbDDDDDEpEEEEEFNFlFtFFFFGGGGH̷̷㪲㲤 5OJQJ6CJOJQJOJQJ j]CJOJQJ56CJH*OJQJ6CJOJQJCJ0JmH CJOJQJ CJOJQJ5mHmH5CJOJQJ CJOJQJ? completed can be startedare sare sss in both pipes are between underwater and surface piping Hydrostatic pressure 8 10 A,>Light upward diagonal(G  c PA,>Light upward diagonalGGZB   S D>(ZB   S D>(GGZB   S DBED Equation.3  ( SEQ ( \* ARABIC 30) After computation procedure with environmental pipe is completed, computation procedure with pollutant fluid pipe can be started. Pressure loses in a pollutant fluid pipe segment are:  EMBEDs: presented in , presented in .,, ; iscompleted, as follows completedwhichs where completed.completedndfollows values is ,it ,is omputed, , have been usedwithare Equation.3  ( SEQ ( \* ARABIC 31) Total pressure losses in pollutant fluid pipe with latest computed pipe segment included are:  EMBED Equation.3  ( SEQ ( \* ARABIC 32) Total pressure losses in77088>:CD2DDZEjEfGG@$ w'`08p @ xHP !$`'0*-/2p5@8;=@CPF I@ z(`0h8p @ xHP !$`'0*-/2p5@8;=@CPF I   lB   0D>  ZB   S D   x  0~G x  0~GGd x  0J   <R    &!B S  ?O@{P& 4 }U 494*+  HJMP[^57?BEGKNQSWZ]_ :=?BHKMOFILODGKNSUWY\_ NVowx~ " ! # % ( + . 8 : > A F H M P !"!%!)!.!1!7!:!;!=!>!A!B!E!!!!!""a"d"g"j"|""""""""&#)#,#.#/#2#q#t#y#|### $$$$$"$;$C$D$J$Q$T$b$d$m$u$v$|$$$$$$$$$$$$$$$$$)%1%%%%%&&[&_&&&''B(I(!*"*Y*Z*******=+>+++++++,,',*,2,5,=,>,F,J,M,P,S,V,Z,[,`,d,x,{,,,,,,,,,,,,,,,,,,,,,,,,,,,----.... / ///p/s/v/y/*1-1J1M1Q1S1T1W1t1|1111111122 222"2%272:2E2H2S2V23333%3-3.343330?2?5?8?i?l???????@ @#@%@s@u@@@@@@@@@GAIALAOAhAjAmApAAAAAAAAABBPBRBBBBBBBCCCC=D?DpDsDDDDD]E_EzE}EEEF FZF]F~FFFFFFFFGGcGfGGGHHHHIIIIII-J0JBJGJJJKKqKxK|KKKKKKKKKLLLLLL L!L,L-L7L8L?L@LBLCLQLRL]L^LdLeLgLhLsLtL}L5M;M>MDMFMIMXM]M}MMN&NzNNNNNNNNNNNNNNNNNNNNO O_OeOOOOOOOOOP%PP1Fs2s /D qbx g } !!!""K#a#''y(())~))u++--J.`...>0T022,4B4'5=555B6X666V7l7PP P P!P!P#P#P%P'P(P*P+P6P8PBPJPOPQPSPTPVPWPYPZP]P_PbPdPgPiPkPmPpPrPuPwPzP|P~PPPPPPPPPPPPPPPPPPPPPPPPPPPPZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.doc <PSzܿ, xvC {IK)]\*CJOJQJo(. @[]hh5o(.hh5o(.hh5o([]hh5o(.@.hh.hh.hh.hh.@.,JM<EnyEny*CJOJQJo(nz`n@.z`m@[]*CJOJQJo(nx`n@.`m@[]M @[]P@.TP @.P @856>*CJOJQJo(n Q`n@.\Q`m@[]Q @[]   @zzXzzzO  5OJQJ 0  $%:;@z   DE01BC uw  z | !!!!""^#`#'''((())))++--]._...Q0S022?4A4:5<555U6W666i7k7>>>>>>>&?'?0?>?i?q?????@@@(@i@j@s@z@@@@AGARAhAsAAAAAAABBB&BPBWBBBBBBBCCOCWCCCCC3D4D=DGDpDyDDDDDE)E]EdEzEEEEFFTF`F}FFFFFFG"G]GiGGGGGGGH.H/H:H;HLHKKKLXMXNXOPPPPP P!P"P#P$P%PPPPNPRBRpnLTrntnxV\]^`bd~nunvnvnwnwn\zn{n nnnnnn nn"nnnn:nn2n nnnnnnn|nrnʹnnnм(*,.>FHZv$4| 2J>XJZz 8F v*<`btx6Ln~&> H`VXnp n268PRTVXGTimes New Roman5Symbol3& ArialuCRO_Avant_Garde-NormalTimes New Roman9CG Times5& zTahoma;WingdingsKUniversalMath1 BT A V 999J A ! $V 0dPXIMPLEMENTATION POSSIBILITIES OF  AntiPollutant SOFTWARE IN LONG SOLAR PIPING - CHANNALSDaliborZavod za brodogradnju$$$$$$G Zbjbjَ rP]zzz4dTdTdThTV'h$Y^^^^MOOOOOO$s z[^sa^^.Ybaaan*^z^Mh|Maan.@:z9^$YlI'N-dT': Root Entry Gv$G F@xmjiICData/G   B1C;DE4ЩWordDocument t|5 j *U;1 @    lr^ObjectPoolH<@KѼ WҼ   MO !"#$%&'()*+,-./013456789:;<=>?@ABCDEHGNFL2RPKJSTUVWXYZ[\]^_`abcdefghijkmtwvq xEquation Native  1TableSummaryInformation(DocumentSummaryInformation8      !"#$12345678>?@ABCMNOPQR]^_`abcdefghijklmnopqrstuvwxyz{+CompObj j0Table2j0 QDaliboraliioa_paper1.doc.dotIZavod za brodogradnjuLI14oMicrosoft Word 8.0j@<.@v<@N@  A ՜.+,D՜.+,D hp  %TFRiN!P  YIMPLEMENTATION POSSIBILITIES OF AntiPollutant SOFTWARE IN LONG SOLAR PIPING - CHANNALS Title 6> _PID_GUIDAN{7FF67BE0-6288-11D2-BD69-9DA6EDB4104A}  FMicrosoft Word Document MSWordDocWord.Document.89q FMicrosoft Equation 3.0 DS Equation Equation.39q Oh+'0$@ `l    YIMPLEMENTATION POSSIBILITIES OF AntiPollutant SOFTWARE IN LONG SOLAR PIPING - CHANNALSOMPL  %*,-.3456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_defghijklmnopqrstuvwxyz{|}~ 4 N /pv$     }B/C/DEFJA,..H q &/8,P&l)*#'*#,#/*)'%#h7  xxU %"$@               `Light upward diagonal  FB CDE(FjJ / 2vWTGV @     $  NB CDE(FjJ / 2vWTGV @    $  FB CDE(F  / 2vWTGV @    o$OrB  6D p GlB  0D Gv$GlB B 0D/G   B1C;DE4FjJ t|5 j *U;i(1 @     ^v$   B1CDE@F jJ xUk  =z=xx5.1 @      2v$@~B  BDg xx`B  c $4D+,`B  c $Dg~  6  N 7   ~  6"{# ~  6|  5 ~  6-3i   H ?.   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Footnote Text&)@1& Page Number8YB8 Document Map-D OJQJ."@.Caption xx5%,/25:?DHMRW[`ejorw|sPT  x  0T Gd TB  C DX"x  0s  TB  C D%TB  C DG%GxB  <DGx  0   x  0  v  ~B  BDg      c PA,>Light upward diagonal(G  c PA,>Light upward diagonalGGZB   S D>(ZB   S D>(GGZB   S D  lB   0D>  ZB   S D   x  0~G x  0~GGd x  0J   <R    &!B S  ?O@rWP& 4 }U 494?A.0VXILGJ+*,*******,, / /w/z/\1d1j1m111r3u3OOXP % ( )))--8.G...n/s///0!0333444495:55555M777777OOOOOOOOOOOOOOOOOOOOOOOOOOOOPPP P PPPPPPPPP!P$P&P(P)P,P.P1P3P5P6P8P9PBPDPGPIPLPNPSPXPZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnju+C:\Temp\AutoRecovery save of ioa_paper1.docZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dotZavod za brodogradnjuC:\ ali\ioa_paper1.doc.dot <PSzܿ, xvC {IK)]\*CJOJQJo(. @[]hh5o(.hh5o(.hh5o([]hh5o(.@.hh.hh.hh.hh.@.,JM<EnyEny*CJOJQJo(nz`n@.z`m@[]*CJOJQJo(nx`n@.`m@[]M @[]P@.TP @.P @856>*CJOJQJo(n Q`n@.\Q`m@[]Q @[]   @M7Xzb{V hFOJQJC$EƀOJQJb'C$Eƀb'$C$Eƀb' & F??OJQJ$ & F??OJQJVC$Eƀb' hC$Eƀb'FC$Eƀb' $OJQJ$ & F?? & F?? & F??6 & F??C$Eƀ6b'' Hhklm   , / F     ! " # $ ; _ n   % + X n 9 A  !yCH%;<[g}~Z_wz)*+,-TZ[s,-023TUD^u  &"-EFI^bj%,/25:?DHMRW[`ejorw| sP "   `#W)2;EsPGl< /XYZz2IZ tv , 9  !yzEwx1 ,MNlC A3K+Cw  | !D!y!!^""##`###&$X$$$$U%%%%%&&&&'/'k''''((0(Z((()W)))))*F*y**+F++,Y,,,---._...//0S0[1\22233A44<5556W666)7k777$8R888889F: ;;<p<<q=>>>>>>>>>>&? both pipes are:  EMBED Equation.3  ( SEQ ( \* ARABIC 33) Total necessary pump hydraulic height, for resistance, density differences and heights support, is:  EMBED Equation.3  ( SEQ ( \* ARABIC 34) Total necessary power for fluid transfer is:  EMBED Equation.3  ( SEQ ( \* ARABIC 35) Differences Between Underwater and Surface Piping There are three basic differences between underwater and surface piping: Underwater environment Surface/land environment Environmental fluids salt/fresh water air Environmental flows sea currents winds speed Hydrostatic pressure environmental water/ warm water, air pressure pollutant neglected Conclusion Described computer tested mathematical model is mainly intended for computation of heat transfer in way of underwater vertical pipes. Obtained results( analysis enables defining shape (cross sections) and variables such as: dimensions of the pipeline, wall thickness and material, and insulation thickness and material, etc. It is suggested that with interactive calculation based on developed software is possible to perform the analysis of piping heat transfer with the objective of whole piping system optimization. Obtained results can be graphically presented in three-dimension (3D) with the possibility to change any pair of mentioned variables. In case of land piping under consideration, main part of presented software can be successfully used taking in consideration: variation in pipe height along piping has to be prepared for a cubic spline approximation, predicted or experimental (statistic) variation of wind speed along piping has to be prepared for cubic spline approximation, predicted or experimental (statistic) variation of air temperature along piping has to be prepared for cubic spline approximation, Physical properties of air as well as heated transported water have to be additionally prepared in table form for automatic approximation procedure. In case that pipes of cross sections different than circular are used, it is necessary to use modified heat loses formulas. NOMENCLATURE A0,m2Heat transfer surface of outer pipe finite segment surfaceAM,m2Heat transfer surface of average logarithmic pipe finite segment surfacecp,Jkg-1K-1Thermal conductivity by constant pressureDio,mPipe finite segment inner diameterDoo,mPipe finite segment outer diameterEPP1,Nm-2Total environmental fluid pressure related to referenc'?*?3?]?^?b?d????????? @ @@@_@`@c@e@@@@@@@@@-A.A1A7ALAMAPAVAAAAAAAAAAAAAAAAAAAAA(B)B,B.BXBYB\B^BBBBBBBBBBBBBCC!C$CdCeCiClCCCCCDD DD6D7D;D>DDDDDDDDDDDDDEEE!E6E7E;E=EtEuEyE{EEEEE F FFF1F2F7F@FwFxF|FFFFFFFFFF G GGG,G-G0G2GOGPGTGZGGGGGGGGG IIJxKyKKL?NOOOOOOOOOPPP PPPP P%P*P.P3P8P=PBPEPJPOPRPUP`PePjPtP%%%%%%%%%%%%%%%%%%% %%k2%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%Q%%%%%%%%%%%%%%%%%.$.$.$.$%%%%%%%%%%%%%%%%%%%%%%%%%t;%%%%Q%Q%%%@M %`%%%%Q%%%Q%%%%%%Q%Q%%Q%%Q%Q%%%%%%%%%T%0%|%|%|%|%+%%|%|%%0G%%%%|%|%%%%%%Q%%%0%{%%%%%%%%0%%0%%%%|%k2%'%%0%k2%%|%%0%%|%%|%%0%%%%%%%%%%%%k2%%%%%%%%%%˺˺\˺˺˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺u˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺W\˺V˺W\˺V˺W\˺V˺W\˺u˺˺\˺Ⱥ˺W\˺V˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺Ⱥ˺˺\˺ȺW˺\˺VW˺\˺VW˺\˺VW˺\˺VW˺\˺VW˺\˺VW˺\˺VW˺\˺VW˺\˺u%%%%k2%%%%%%%dTF%TFTFTF˺˺n9n˺˺˺TFTFTFTFTFTFTFTFTFTFTFTFUTFTFTFUTFUTF;TFTFTFTF t , 9  !yzEwx1 ,MNlC A3K+Cw  | !D!y!!^""##`###&$X$$$$U%%%%%&&&&'/'k''''((0(Z((()W)))))*F*y**+F++,Y,,,---._...//0S0[1\22233A44<5556W666)7k777$8R888889F: ;;<p<<q=>>>>>>>>>>&?'?*?3?]?^?b?d????????? @ @@@_@`@c@e@@@@@@@@@-A.A1A7ALAMAPAVAAAAAAAAAAAAAAAAAAAAA(B)B,B.BXBYB\B^BBBBBBBBBBBBBCC!C$CdCeCiClCCCCCDD DD6D7D;D>DDDDDDDDDDDDDEEE!E6E7E;E=EtEuEyE{EEEEE F FFF1F2F7F@FwFxF|FFFFFFFFFF G GGG,G-G0G2GOGPGTGZGGGGGGGGG IIJxKyKKL?NOOOOOOOOOpPqPtP   2222222222222222222222222@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@ $M!#_% &''(),?-/12F4a5y8b;=SCFJiZZ"8HHAJKNQUXZ\]_adegjlnopsu||u -?qG`dj!<"$b%&)Y,f.01H47u<n=>@|B(CDEYGHmJKgQXZZZ"|#.7GHBDEFGHILOPRSTWY[^bcfikmqtvwxy{~ "(X0x:BDFHJKZZCMV`hrz}UnknownZavod za brodogradnjuNiksa Fafandjel.@Bp,.p,>@n/13GI+?ACWY_qtw  d v y !!!!!"""H#Z#]#&&&&'''+'-'R'f'h'k'''''''''''''''((((,(.(Z(n(p(v(((((()))W)k)m){))))))F+Z+\+r+++------.0.2.G.Y.\.......///0#0%0;0M0P0222222344)4;4>44 55$565955555556%6'6?6Q6T6666666)7=7?7S7e7h7sP t t t t t t t t t t t t::::: t: t t t t t t::::: t:::::: : t: t:: t: t: t: t:: t: t: t: t: t: t: t: t !!l,r$9C_iyuUi %"@ .]`-( 4 N /pv$     }B/C/DEFJA,..H q &/8,P&l)*#'*#,#/*)'%#h7  xxU %"$@               `Light upward diagonal  FB CDE(FjJ / 2vWTGV @     $  NB CDE(FjJ / 2vWTGV @    $  FB CDE(F  / 2vWTGV @    o$OrB  6D p GlB  0D Gv$GlB B 0D/G   B1C;DE4FjJ t|5 j *U;i(1 @     ^v$   B1CDE@F jJ xUk  =z=xx5.1 @      2v$@~B  BDg xx`B  c $4D+,`B  c $Dg~  6  N 7   ~  6"{# ~  6|  5 ~  6-3i   H ?.   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