Speed Comparison of Single Equation Method based on Saturated Steam Water Spaces Models

Transcription

1 Speed Comparion of Single Equation Method baed on Saturated Steam Water Space Model Jacob Philip Simulator Group Nuclear Poer Corporation of India Limited Mumbai, India Faruk Kazi, Harivittal Mangalvedekar Electrical Engineering Department VJTI, Mumbai Univerity Mumbai, India Abtract - -Simulator are extenively ued a a tool for indutrial training, deign and development. The overall improvement in computational peed of imulator i very important and can be improved by redeigning the mathematical imulation model or by uing fater computational platform. Modern day imulator are uing cloud computing platform and other high performance computing ytem. The complex algorithm employed in imulation of team-ater pace and team table reulted in longer computational time. The ue of cloud computing for imulation make eential the optimization of cot of computing and cot of tranmiion. The quai-numerical, quai-teady tate, Single Equation Method baed aturated team ater pace modeling can be employed to improve the peed of computation and to uit the ne computing environment. Thi make the imulator fater and cot effective. Experiment uing differenet computing platform ho that the propoed ingle equation baed quai-numerical, quai-teady tate i around eight time fater than the team-table iteration baed modeling approach. Keyord - imulation; aturated team ater pace; quai-teady tate modeling; team table; performance optimization; cloud computing, performance comparion I. INTRODUCTION Mot of the heavy indutrie ue team for heating purpoe and a a poer fluid. Foil and Nuclear Poer Plant (NPP cycle ue ater & team a their primary proce fluid for generation of electricity. There are many team and ater baed equipment operating at aturated team preure/temperature ued in foil fired poer plant cycle like feed ater heater, team condener, team flah tank and de-aerator. NPP, additionally need preurizer for maintaining high preure in Heat Tranport Sytem (HTS [1] and bleed condener (BCD for bringing don the temperature of preurized HTS ater from C to C[1],[2]. Thee equipment contain team & ater at aturation temperature and may be collectively termed a Saturated Steam Water Space (SSWS ytem. SSWS model heavily depend on the aturated team-table (SST. The SST relate the propertie of pecific volume, denity, pecific enthalpy of team & ater at different temperature[3]. The SST i a large table hich need to be acceed continuouly to match the propertie of team and ater o a to get the bet fit for the operating temperature and preure. Iteration and interpolation i generally carried out to obtain the bet fit of operating temperature and preure. To reduce the amount of iteration & interpolation, large team-table need to be attached to the computer ytem hich involve conumption of computation time and memory[4]. Hence it i prudent to avoid or at leat reduce the ue of team-table to reduce the computation time[11]. Toard thi one effective method i to convert the team-table into a et of equation. Leat quare approximation baed formula for of team denity, pecific liquid enthalpy propertie are ued in[4]. Simple non-linear function for uperheated and ub-cooled ater propertie in the range of to 21.3MPa are ued in [5] International Atomic Energy Agency, IAEA, recommend the ue of mathematical equation for etimating the thermodynamic propertie of light ater & heavy ater including their vapor tate[6],[7]. To increae the computational peed for indutrial application, International Aociation of Propertie of team (IAPS formulation developed an indutrial formulation IAPS-IF97 baed on the computationally intenive IAPS-95 formulation[6]. In a control room operator training imulator, all the calculation pertaining to all the model of all ytem need to be computed ithin the cycle time of computation, ay 100mS or 200mS. In a poer plant imulator, epecially NPP, many SSWS baed model are computed every cycle. Some critical equipment model are computed many time ithin one cycle to improve it accuracy. Therefore, in FPP a ell a NPP, the SSWS equipment imulation form a coniderable imulation load. Cloud computing (cloud i a computing environment offered a a ervice at a cot to the uer. The cot are baed on the conumption of reource like proceor time, netork bandidth/data, torage and memory. Cloud can be conidered a a large et of virtual computing machine (VM orking together acro a netork. To ave cot, cloud computing environment need optimized model to take advantage of the cloud benefit like calability & multiproceing capability and to overcome it limitation in cot of overhead in computing, netork traffic, computation time, and proceor time [8],[9],[10]. A foil poered boiler ytem, including it ub-model, a imulated ith MATLAB a the back-end & LABVIEW baed client on a cloud computing platform. Differential Algebraic Equation ere ued for the ame[11]. Conventional domain pecific model need uitable model adaptation hen thee imulator are ported on a cloud DOI /IJSSST.a ISSN: x online, print

2 platform. A very good example for domain pecific model adaptation i the development of polynomial multiplication of the order of million uing FFT algorithm for cloud and multiproceor architecture. Thi a developed epecially for higher order polynomial ued in imulation of aero-pace, ignal proceing and image proceing [12] SSWS modeling uing combined propertie of team & ater a employed in [13] greatly implifie the SSWS modeling and reduce the overall turn around time for SSWS modeler. Fater model computation, to a great extent, can reduce the overall computational cycle-time of imulator. Reduced cycle time may be ued in increaing the accuracy, depth or idth of imulation [13][14][15]. Thi paper propoe a numerical approach ith polynomial approximation function to replace each team & ater propertie of SSWS. Thee polynomial approximation function can be directly ued in modeling of SSWS in quai-teady tate. Thi make the model uitable for imulation in normal a ell a cloud computing environment. We had conducted extenive imulation experiment for comparing the performance of team table baed iteration and approximation method. The methodology adopted in avoiding error in comparion i alo explained. Reult of the experiment for time performance comparion of team table iteration baed approach and propoed quai-teady tate approach i alo dicued. The paper refrehe the baic equation ued in SSWS from [15]. Final enthalpy equation of SSWS along ith the approach to derive the approximation equation are reproduced from [15] in Section-II. Performance comparion in virtual and phyical machine i given in Section-IV along ith detail of imulation experiment methodology adopted. II. SINGLE EQUATION BASED SSWS MODEL Conider a tank of volume v operating at aturation temperature T and preure P. Let ma in Kg of team & ater be denoted by m & m, pecific enthalpy by h & h, denity by d & d, and volume of team and ater by v & v. Let the total ma m in kg i m=m + m and total SSWS volume i v=v + v Then total enthalpy (heat H in the tank/ssws hall be [13],[14],[15] H = mh mh (1 Further v =m /d and v =m /v. Subtituting and rearranging, e get after eliminating m, m, v, & v H ( d d md h vd d h (2 vd d h md h mdh vddh vddh md (3 h H ( d d = 0 Equation (3 i termed a the Single Equation a thi decribe the hole SSWS in one equation. The propertie d, d, h, & h are ome function of the aturation temperature T. The temperature at hich (3 i atified hall give the aturation temperature. Here H, m, v are knon quantitie, d, d, h, & h are dran from SST a per the reultant aturation temperature of the SSWS [3][14][15]. A. Relation beteen propertie and temperature Steam table provide the team/ater propertie at different temperature. Each property ha a different range. The relationhip of d, d, h, & h a a variation of temperature in degree centigrade are hon in Fig-1. Propertie d, d, h, & h h can be conidered a function of SWSS temperature though their relationhip are complex and different[4],[3],[13],[14],[15]. Reriting (3, d, d, h, & h ith a function of temperature T (Kelvin or Degree Centigrade e get H = [ md( T h ( T vd( T d( T h ( T vd( T d( T h ( T md( T h ( T ] (4 [ d ( T d ( T ] Propertie Variou Propetie V Temperature Water Enthalpy kj/kg Steam Enthalpy kj/kg Water Denity kg/m3 Steam Denity kg/m3 0 Temperature FIGURE 1: ACTUAL STEAM/WATER PROPERTIES VS TEMPERATURE[15] B. Deriving Approximation function Conider the property, ater denity d and it behavior repect to T. No by normalizing temperature T in the range of 20 to C range to normalized temperature T N (an N in the uffix denote the variable i normalized. T N =(t-20/(360-20, here T N i normalied in Per Unit (PU range. Similarly the aturated liquid denity d decreae from 998 to kg/m3 a temperature varie from 20 to C. Normalizing d = (d N -998/( The a relationhip beteen T N and d N can be decribed uing a fourth order polynomial of T N (derived uing Leat Square Method a 4 dn( = dn(,4 = ( T ( T N 1 N ( T Here (T N,m repreent an m th order polynomial k m = k = 1 A T k k here A k are contant. N DOI /IJSSST.a ISSN: x online, print

3 Thi approximation polynomial introduce a maximum error -1.51% at C. Fig-2 ho the comparion of fourth order polynomial & imple (T N 2 approximation of normalized ater denity ith the SST baed normalized ater denity for a normalized temperature of 20 to C. Here fourth order polynomial approximation provide a very accurate repreentation of actual ater denity[14],[15]. 1.2 Water Denity V Normalied Temperature ytem during the time of computation and the ytem ha attained aturation condition. Fig-3 ho the SSWS total enthalpy value obtained uing approximation function and enthalpy value obtained from the team table (SST for temperature in the range of 100 to C. It i clear that the trend of calculated enthalpy uing approximation function and actual enthalpy computed ith team-table iteration-interpolation are imilar ith limited error [13],[14],[15] Actual & Calculated Heat V SSWS Temperature Normalied Water Denity Liquid Denity Simple Quadratic 4-th Order Polynomial Enthalpy Actal H KJ Calculated H KJ Normalied Temperature FIGURE 2: WATER DENSITY, POLYNOMIAL AND QUADRATIC FIT[15] C. Approximation function for Simulation of Steam/Water Propertie Specific enthalpy of ater can be expreed a h =A*h N (T N,4+B ith maximum error of 0.75% at 360OC here 4 3 hn(,4 = ( Similarly h N can be expreed a h N (T N,6 and that of d N a d N (T N,4. III. SIMULATION OF SSWS ENTHALPY USING APPROXIMATED EQUATION Each property term d, d, h, & h in SSWS equation a decribed in (3 i a function of SSWS temperature T. Therefore a explained in Section-2.2, d NS, d NW, h NW, & h NS are function of T N. No expanding each term d, d, h, & h a a function of SSWS normalied temperature T N [15] [ m * d h v* d d( h v* d d h (6 m* d ( T h ( T ] N N [ H *( d d( ] = 0 Conider an SSWS ith volume v in =12m 3 and ma of light ater m=1200 kg. The Enthalpy H in kj of the SSWS for the temperature from C i calculated uing(4. Thi conider that no ma i added to or removed from the Temperature FIGURE 3: APPROXIMATE &ACTUAL HEAT VS TEMPERATURE[15] In a real life SSWS modeling cenario, it i important to compute the aturation temperature of an SSWS, hen a diturbance in ma, volume or enthalpy i applied to the ytem[15]. Thee diturbance are introduced by: Diturbance in ma m: team or ater i added to or removed from the SSWS Diturbance in volume v: change in hape/ize of the SSWS volume or due to expanion in pipe Diturbance in enthalpy H: heating or cooling by external heat ource. Thi diturbance can alo occur hen ma or team i added/removed from the ytem. The diturbance in ma m, volume v or enthalpy H can be computed and appropriately applied to the SSWS equation(6. After computing and accommodating the diturbance, (6 can be olved for ne normalized temperature T N. SSWS temperature T can be computed from T N [15]. IV. SPEED COMPARISON, RESULTS AND ANALYSIS A. Comparion of Computing Speed in Virtual Machine Simulation experiment ere conducted to compare the peed of computation of SSWS equation uing ingle equation baed, quai-normalied quai-numerical approach and the olution obtained uing Saturated Steam Table iteration and interpolation. Simulation ere carried out uing variou peronal computer (PC a ell a virtual machine (VM. The VM ere created uing VMWare Player (VMW & Windo Virtual PC (WVPC. In general GNU Compiler Collection (gcc compiler a ued for compiling C program. In Microoft Windo, to environment ere ued, firt uing mingw (Minimalit GNU for Windo and econd ith DOI /IJSSST.a ISSN: x online, print

4 CYGWin (a Unix-like environment & command-line interface for Microoft Windo platform. Define max_repeat = 5 Define max_iter = 900 Million START For num_repeat 1 to max_repeat Print cur_time Call Function polynomial approx( Print cur_time Call Function team_table_iteration( Print cur_time End num_repeat FOR END Function polynomial approx( For num_iter 1 to max_iter Compute SSWS T by Polynomial_approximation Function Steam_Table_iteration( For num_iter 1 to max_iter Compute SSWS T by Steam Table iteration FIGURE-4 PSUEDO-CODE FOR SPEED COMPARISON ROUTINE B. Methodology Adopted for Simulation Experiment For experiment intead of uing a full fledged team table, a team-table of jut 14 ro ( C, at interval of 20 0 C in an array form a ued. The fit of temperature a derived uing continuou iteration & interpolation ithin the 14 ro SST. We employed Neton-Raphon baed olution ith four iteration for quai-numerical approach. Four iteration provided accurate olution up to four decimal for quai-numerical approach[15]. The tructure/peudo-code for the program i given in Fig-4. A in Fig-4, to function ere created, one for finding out the reult in array format ith team table iteration & interpolation method and the other for finding out the reultant temperature uing Polynomial approximation- Neton Raphon method. Before the actual peed comparion experiment ere conducted, the to function ere teted for accuracy of reult ith ingle iteration. Thi a obtained by uing print function (printf function in C program. Thi program a enhanced to call the to function, team-table-iteration & polynomialapproximation function, to be executed in to loop to compare their peed. The number of time each loop executed a equal and the to function ere executed one after the other equentially. Any variation in computing peed affected the to function together, team table iteration and polynomial approximation in a imilar manner. Thi helped in reducing the error ariing from variation in peed of computation of a machine. We ued imple time function (ctime available in C library to meaure the time. For each loop, time a printed before and after the loop. The ctime function a ued up to the level of econd and thi neceitated to overcome the inaccuracie of time bunching, the number of iteration needed to be increaed, epecially for the polynomial-approximation method function in fat proceor. Therefore to increae the reolution of computation time, both module ere executed for 900 million time in a ingle program equentially. Here alo, a to pronged approach a ued; in firt one, ithin the ame program executing the to loop multiple time a in Fig-4 and in the econd, the to function executing only once. tart_time, STEAM_TABLE, Thu Jan 29 23:28: , End_time, STEAM_TABLE, Thu Jan 29 23:31: tart_time, SSWS_APPRX, Thu Jan 29 23:31: , End time, SSWS_APPRX, Thu Jan 29 23:32: tart_time, STEAM_TABLE, Thu Jan 29 23:32: , End_time, STEAM_TABLE, Thu Jan 29 23:35: tart_time, SSWS_APPRX, Thu Jan 29 23:35: , End time, SSWS_APPRX, Thu Jan 29 23:35: tart_time, STEAM_TABLE, Thu Jan 29 23:35: , End_time, STEAM_TABLE, Thu Jan 29 23:38: tart_time, SSWS_APPRX, Thu Jan 29 23:38: , End time, SSWS_APPRX, Thu Jan 29 23:39: tart_time, STEAM_TABLE, Thu Jan 29 23:39: , End_time, STEAM_TABLE, Thu Jan 29 23:42: tart_time, SSWS_APPRX, Thu Jan 29 23:42: , End time, SSWS_APPRX, Thu Jan 29 23:42: tart_time, STEAM_TABLE, Thu Jan 29 23:42: , End_time, STEAM_TABLE, Thu Jan 29 23:45: FIGURE-5 SAMPLE EXPERIMENT RESULT FROM MINT LINUX VM TABLE-I PROCESSED SAMPLE RESULT FROM MINT UNIX VM PC/VM Enviro nment/ Compi ler Experiment equence number Steam- Table Iter time (S Polynomial apprx Time (S Speed Up (% gcc gcc gcc gcc gcc gcc gcc gcc From the final program, all the print function ithin the loop for printing the reult ere removed to avoid the load on the Input/output ytem. Since the program ere already DOI /IJSSST.a ISSN: x online, print

5 validated and only comparion of computational peed of the to function a of prime concern, the print tatement for reult ere avoided. Fig-5 ho the ample reult obtained from a machine by continuouly running the to function equentially for five time. Table-I ho the detail of reult obtained from a ample experiment conducted on one machine. Simulation experiment ere conducted randomly in different machine, either in batche of five or a iolated ingle experiment. The reult ere later proceed to find the SpeedUp imilar to Table-I and average SpeedUp and tandard deviation a in Table-II. The SpeedUp a calculated a SpeedUp (% = (SteamTable_time/PolynomialTime*100 Table-2 ho the comparion of average computational peed-up in % obtained uing Polynomial approximation method againt team-table iteration method. The detail of the variou virtual machine & PC here the experiment ere carried out are alo given in the Table-II.. The minimum average SpeedUp oberved a and the maximum average SpeedUp obtained a a een in Table-II. Thu approximation function baed model for SSWS are around 7 to 10 time fater than team-table iteration- interpolation model a evident from Table-2. Standard deviation of SpeedUp i alo hon in Table-2. Thi variation in SpeedUp in a particular machine may be attributed to the then tate of the machine ith repect to computational and other Input-Output operational load on the proceor & machine at that point of time. TABLE Machine Detail Machine Type, Operating Sytem, Virtualization Platform PC, FX core, Windo-7, 4GB RAM, mingw PC, FX core, Windo-7, 4GB RAM, CYGWin VM, Live Linux Mint-14, 1GB RAM, VMW VM, Kubuntu, 1GB RAM, VMW VM, SUSE, 1GB RAM, VMW VM WinXP Mode, 512MB RAM, WVPC, CYGWin PC Intel Celeron Windo XP, 256MB RAM, CYGWin PC Intel I-5, 4 Core Windo-7, 3GB RAM, CYGWin PC Intel Pentium Dual Core, Windo Vita, 2GB RAM, mingw II: COMPARISON OF SPEED OF COMPUTATION Number of Simulation Experiment Standard Deviation Average SpeedUp (% V. CONCLUSION The imulator of indutrie uing team a poer fluid ue many Saturated-Steam-Water-Space equipment and their imulation model. Thi paper preent the reult of the experiment conducted to compare the computational peed uing the quai-teady tate, quai-numerical ingle equation baed numerical olution method and Steam table baed iteration & interpolation method. From the reult of the tet on different virtual machine & peronal computer, it i evident that the propoed quai-numerical approximation method i around eight time fater compared to team-table iteration baed approach a een from our experiment. Thu the propoed approach may reduce the overall cycle time for imulation, thereby providing increaed depth & idth in the proce imulation. The contribution of thi paper i in opening a ne path in imulation of SSWS to increae the peed of computation of SSWS model uing an efficient a ell computational friendly modeling approach. Thi efficient & computational friendly approach may reduce the computational overhead, penalty of overhead and improving the performance of imulator uing cloud computing. ACKNOWLEDGMENT Thi i a part of the project for Adaptation of Parallel Proceing in Large Phyical Proce Simulation funded by Dept of Atomic Energy of India (DAE through Board of Reearch in Nuclear Science (BRNS ide anction # 2012/36/52-BRNS and World Bank funding under TEQIP-II (Sub-component for Center of Excellence (CoE in Complex & Nonlinear Dynamical Sytem (CNDS. We expre our gratitude for kind funding. [1] CANDU fundamental training coure, Module-15, Heat Tranport Auxiliary Sytem, COG-CANTEACH Canadian Nuclear Safety Commiion Technical Document Library, [2] M MacBeth, Digital intrumentation & control, Work Book-6&7, CANDU Oner Group COG-CANTEACH, Chulalongkom Univerity Technical Document, 2003 [3] MD Koretky, "Propertie of team (SI unit, engineering and chemical thermodynamic", John Wiley & Son, 2004 [4] WJ Garland, JD Hokin, Approximate function for the fat calculation of light ater propertie at aturation, International Journal on Multiphae Flo, pp , 1988, Elevier. [5] WJ Garland and BJ Hand, Simple function for the fat approximation of light ater thermodynamic propertie, Nuclear Engineering and Deign, 1989, pp21-34, Elevier Science Publiher. [6] Thermophyical propertie databae of material for light ater reactor and heavy ater reactor, IAEA-TECDOC-1496, International atomic energy agency, 2006 [7] Thermophyical propertie of material for ater cooled reactor, IAEA-TECDOC-949, International atomic energy agency, 1997 [8] Cloud computing: a practical approach, Tata McGra Hill Education, ISBN , [9] Yahpalinh Jadeja, Kirit Modi, Cloud computing concept, architecture and challenge, 2012 International conference on Computing, Electronic and Electrical Engineering [ICCEET], pp , 2012 [10] Ajith Ranabahu et al, Application portability in cloud computing: an abtraction driven perpective, IEEE tranaction on Service Computing, Iue-99, In Pre DOI /IJSSST.a ISSN: x online, print

6 [11] PS Saikrihna, R. Paumarthy, P.Raman, S, Chakrabarty, L Sivakumar, Simulation of a boiler model in a cloud environment", ACODS, Feb 2012, Bangalore, India. [12] Ganeh Iyer, Bhardaj Veeravalli, SG Krihnamoorthy, On handling large-cale polynomial multiplication, IEEE Tranaction on Aeropace and Electronic Sytem, Vol-48, pp , Jan-2012 [13] Jacob Philip, Faruk Kazi, Harivittal Mangalvedekar, Mathematical modeling of team-ater-vapor-pace ith mfact-vfact approach uing combined team propertie, Aia modeling ympoium (AMS-2013, pp , Hong Kong, 2013 [14] Jacob Philip, Harivittal Mangalvedekar, Faruk Kazi, Modeling of coupled aturated team-ater pace uing quai-teady tate, quai-numerical approach, 2014 Fifth International Conference on Intelligent Sytem, Modelling and Simulation(ISMS-2014, pp , Malaia, 2014 [15] Jacob Philip, Faruk Kazi, Harivittal Mangalvedekar, Quai teady tate, quai numerical modeling of aturated team-ater pace uing normalized team & ater propertie for efficient computing, 2014 Fifth International Conference on Intelligent Sytem, Modelling and Simulation(ISMS-2014, pp , Malaia, 201 DOI /IJSSST.a ISSN: x online, print