ML19347E109

Orturb:A Digital Computer Code to Determine the Dynamic Response of Fort St. Vrain Reactor Steam Turbines

ML19347E109
Person / Time
Site:	Fort Saint Vrain
Issue date:	04/30/1981
From:	Conklin J OAK RIDGE NATIONAL LABORATORY
To:	NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
References
CON-FIN-B-0122, CON-FIN-B-122 NUREG-CR-1789, ORNL-NUREG-TM-3, NUDOCS 8104240030
Download: ML19347E109 (43)

Text

NUREG/CR-1789 ORNL/NUREC/'Iti-399

• Dist. Category R8 CC Contract No. W-7405-eng-26 Engineering Technology Division ORTURB: A DIGITAL COMPUTER CODE TO DETERMINE THE DYNAMIC RESPONSE OF 1HE FORT ST. VRAIN REACTOR STEAM TURBINES J. C. Conklin e

. Manuscript Completed - March 5, 1981 Date Published - March 1981 NOTICE This document contains information of a prehminary nature.

It is subject to revisicn or correction and therefore does not represent a final report.

Prepared for the U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research Under Interagency ' Agreements DOE 40-551-75 and 40-552-75 NRC FIN No. B0122 Prepared by the OAK RIDGE NATIONAL LABORATORY e Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION

• for the DEPAR'IMENT OF ENERGY S/6t' Moo 3d

Lit CONTENTS

• Page LIST OF SYMBOLS .................................................... v ABSTRACT .......................................................... I

1. INTRODUCTION .................................................. 1-

2. HIGH-PRESSURE TURBINE SIMULATION ..............................- 5

3. REGENERATIVE INTERMEDIATE- AND LOW-PRESSURE TURBINE SIMULATIONS .................................................... 9

4. FEEDWATER HEATER SIMULATION ................................... 13

5. CONTROL ....................................................... 21

6. RESULTS ....................................................... 23 REFERENCES ........................................................ 27.

APPENDIX A. INPUT REQUIREMENTS ................................... 29 APPENDIX B. OUTPUT ............................................... 33 4

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v LIST OF SYMBOLS Nomenclature A a constant Ag crcss-sectional flow area Cp specific heat ge gravitational constant h specific enthalpy k isentropic exponent K ex shape-loss constant fcr extraction flow M mass P pressure T ramperature UA overall heat transfer coefficient multiplied by heat transfer area v velocity V volume W flow W ex extraction steam flow v specific volume p density oP pressure drop Subscripts used in feedwater heater modeling (Eqs. 9 through 34)

A halfway C condensing DC drain cooler f flash fg flash from liquid to vapor FC feedwater in drain-cooler section FW feedwate r FE feedwater in vapor section i feedwater heater inlet Q outlet s extraction flow

l vi sat saturation conditions Sil superheat .

v vapor i liquid

$ feedwater heater outlet 4

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OBTURB: A DIGITAL COMPUTER CODE TO DETERMINE THE DYNAMIC RESPONSE OF THE FORT ST. VRAIN REACTOR STEAM TURBINES

. J. C. Conklin ABSTRACT ORTURB is a computer code written specifically to calcu-late the dynamic behavior of the Fort St. Vrain (FSV) High-Temperature Gas-Cooled Reactor (HTGR) steam turbines. The ORTURB program can be independently exercised but is intended to be used in the overall FSV plant simulator code ORTAP cur-rently under development at Oak Ridge National Laboratory.

ORTURB uses a relationship derived for ideal gas flow in an iterative fashion that minimizes computational time to de-termine the pressure and flow in the FSV steam turbines as a function of plant transient operating conditions. An impor-tant computer modeling characteristic, unique to FSV, is that the high pressure turbine exhaust steam is used to drive the reactor core coolant circulators prior to entering the re-heater.

A feedwater heater dynamic simulation model utilizing seven state variables for each of the five heaters completes the ORTURB computer simulation of the regenerative Rankine cycle steam turbines.

1. INTRODUCTION The Nuclear Regulatory Commission (NRC) Division of Reactor Safety Research has funded a research program at Oak Ridge National Laboratory (ORNL) since July 1974 to analyze the response of the Fort St. Vrain High-Temperature Gas-Cooled Reactor (HTGR) plant to transient conditions (Fig. 1). Owned and operated by Public Service Company of Colorado, this demonstration reactor is the nation's only HTGR and was designed and built by the General Atomic Company of San Diego, California, with financial as-sistance from the U.S. Atomic Energy Commission.

The ORTAP code l was developed under sponsorship from this research program. Individual plant component simulators (i.e., steam generator, reactor core, etc.) were written by different individuals as separate

, computational " modules." The steam turbines with feedwater heaters were identified as the simulator module requiring the most computational time.

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df g y M CIRCULATORS DEMINERALIZER FEED F.W. HEATERS PUMPS F.W. HEATERS Fig. 1. Flow diagram of the Fort St. Vrain Reactor.

3 The computer simulation for dynamic behavior of steam turbine compo-e nents was revised with the objective of maintaining sufficient accuracy while reducing computation time. This present ORTURB simulation uses equations similar to those presented for the steam turbine model l but uses a modeling and iteration scheme that reduces computer time by mini-mizing floating point exponentiation. ORTURB was developad and debugged independently of ORTAP and hence required inclusion of FORTRAN statements in a main driver subroutine to provide the necessary transient input pa-rameters. In ORTAP, these parameters are supplied by appropriate plant component simulations.

The ORTURB program is divided into three main parts: the driver sub-routine; turbine subroutines to calculate the pressure-flow balance of the high , intermediate , and low pressure turbines; and feedwater heater sub-routines. This feedwater heater model is substantially modified from the original ORTAP feedwater heater model as developed by Delene.2 Necessary steam property subroutines, obtained from Ref. 3, were also taken from this same report.

The ORTURB program has two important limitations: (1) the turbine a shaft is assumed to rotate at a constant (rated) speed of 3600 rpm; and (2) energy and mass storage of steam in the high , intermediate , and low-pressure turbines is assumed to be negligible. These limitations, which were also true of the original ORTAP turbine plant model, exclude the use of ORTURB during a turbine transient such as startup from zero power or very low turbine flows. The ORTURB program may be obtained on request frca the author.

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5

2. HIGH-PRESSURE TURBINE SIMULATION t

The basic governing equation for pressure and flow balance of high-pressure turbines (HPT) is the ideal gas. flow law:

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where k = isentropic exponent, P = pressure, V= specific volume, A = represents a flow constant, and W = flow.

The subscript I refers to an upstream value, and the subscript 2 refers to a downstream value.

Use of this equation allows the effect of a downstream pressure vari-ation to be reflected upstream when the pressure ratio (downstream to up-stream pressure) is greater than critical. This is an important consid-eration in predicting the transient performance of the high pressure tur-bine whose exhaust pressure will be affected by steam turbines driving the four helium circulators (Fig. 2).

The high pressure turbine has been divided into three-stage groups:

the governing stage, including the flow control valve, and two reaction stage groups (Fig. 2). It was necessary to use this detati and suffer the computational expense to properly calculate governing stage shell

, pressure. This shell pressure is a feed-forward signal for the plant feedwater flow controller and is primarily determined by the flow passing

.-- ability of the following reaction stages.

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1 r 1 r 1 r 1 r FWH 6 FWH 6 FWH 3 FWH 2 FWH1 FEEDWATER TO ECONOMlZER UE HIG H-PR ESSUR E UUE m LOW-PR ESSUR E FEEDWATER HEATERS FEEDWATER HEATERS Fig. 2. Fort St. Vrain Reactor turbine generator plant flow diagrata.

7 Shell pressure of the governing stage at 100% power is determined from initial conditions, assuming that the governing stage is designed according to Chap. 8, article 2 of Ref. 4. The most significant part of this assumption is that the ratto of governing-stage wheel speed to theoretical steam velocity is 0.5 for a one-row wheel at design load.

The ratio of published exit pressures to this determined govern:ng-stage shell pressure was found to be less than the critical pressure ts-tio. The following reaction stages were then modeled as two stage groups so that the stage group pressure ratios (Pexit/Pinlet) of each would be greater than critical. This allows downstream exit pressure variations, which affect the flow passing ability of the reaction stages, to be re-flected upstream to the governing-stage shell pressure.

High pressure turbine thermal ef ficiency is calculated from input data at 100% power and corrected for of f-normal conditions by the methods presented in Ref. 6. Two important design factors, the governing-stage pitch diameter (762 mm) and the number of rows of moving buckets of the governing stage (1), were obtained by applying the methods and informa-tion from Ref. 6 to published heat balances 5 at 100 and 25% power.

High pressure turbine flow constants are determined from input data at design load conditions and are assuned to be constant throughout the simulation. The flow control valve is simulated by varying the governing-stage tiow constant during a calculation to control the flow through the turbine.

After initialization calculations, turbine flows are calculated from pressure distribution. Then, mass flows are checked at stage group boundary points to ensure that flows are balanced within a specified tolerance. If flows are unbalanced at one point, pressure at that point is appropriately modified, and a resultant mass flow rata is calculated from one stage group upstream to one stage group downstream of the point in question using Eq. (1). Turbine stage group flows are again checkea, and if all are balanced within tolerance, the turbine iterations are com-pleted. If flows are again unbalanced at any point, pressure is changed and the two stage group flow calculation is again performed. Use of this

. two-stage group technique, instead of recalculation of the ostire turbine,

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minimizes the floating point exponentiation made _ necessary by the ideal .

gas flow equation.

While most minor flows in the turbine were neglected, the packing . .

gland flow from the high pressure turbine exit to the shell of feedwater heater 5 was not ignored because a relat.tvely large amount of energy'is carried by the flow. This flow is determined throughout a transient simu-lation by assuming that pressure drop from the turbine exhaust to the shell of feedwater heater 5 is due to a shape loss, with the proportion-ality constant determined from input data at design load. This flow is calculated after high pressure turbine iterations are complete, and it is subtracted from the exit flow of the high pressure turbine.

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3. REGENERATIVE INTERMEDIATE- AND LOW-PRESSURE TURBINE SIMULATIONS Assumptions and approximations were also made to simplify the calcu-1ation of transient performance of the intermediate and low pressure tur-bines (ILPT).

Figure 2, a schematic of intermediate and low pressure turbines, shows steam extraction points from the turbines and connections to the feedwater heaters. Dynamics of crossover piping connecting the inter-mediate turbine exhaust with the low pressure turbine inlet are ignored.

Volume and mass inventory inside this pipe are quite small compared with the main steam piping or the deaerator, so dynamic response of the cross-sver piping would be essentially instantaneous as compared with the re-sponse of other components. Therefore, the ILPT is considered a single entity.

This analysis assumes that the external conditions experienced by the individual components do not change during a timestep. Each of five feedwater heaters and the deaerator are considered separate components, as are the feed pump turbine and the ILPT.

The ILPT is divided into seven stage groups separated by points rep-resenting the turbine inlet, six steam extraction points, and the con-denser. During initialization calculations, the stage group flow con-stant for the ideal gas flow equation and the stage group thereal effi-ciency are calculated for each stage group. The stage group flow con-stant remains unchanged throughout a simulated transient, whereas the stage group thermal efficiency is corrected for turbine inlet volume flow.7 This stage group thermal ef ficiency correction is necessary because fixed stage losses, such as root and tip interference losses and rotation losses, have less effect on overall stage group efficiency as the steam volumetric flow increases. The correction curve should have a hyperbolic shape but has been linearized for simplicity. This assumption is reason-

- ably accurate for high volume flows but would overestimate stage group thermal efficiency at very low flows.

1. To accurately model ILPT reaction stages, the pressure ratio across each computational grouping of reaction stages should be greater than

10 critical, with the exception of the last stage which (fer condensing tur-

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bines) has critical flow at design conditions. Perturbations of the flow-passing a5111ty of a stage group because of downstream pressure fluctua-tions such as feedwater heater transients can be accounted for with the ideal gas flow equation if the pressure ratio is greater than critical.

The pressure ratios across stage groups for the design power condition are generally slightly less than critical. "his condition means that a downstream pressure increase, such as that caused by stopping extraction flow to a feedwater heater, would have to increase the stage group pres-sure ratio above critical before stage group flow is affected by a down-stream pressure rise.

The ILPT modeling could be made more accurate by an increase in the number of computational stage groups and an assurance that the pressure ratio across each group (except for the last) is greater than critical.

These changes, however, would entail an increased computation cost due to the increased amount of floating point exponentiation required to repre-sent the ideal gas flow equation. Present ILPT modeling is sufficiently accurate for use in an overall steam plant dynamic simulation, considering the accuracy of existing turbine design data available. ,

Pressure at an extraction point determines extraction flow to the shell side of a feedwater heater. Pressure loss in the extraction pipe is assumed to be a shape, or form, loss as expressed by AP ex v2 "K (2) p ex 2ge -

Multiplying both sides by the square of the der.sity, and the right-hand side (RHS)by(Af/Af),

K ex (pAgv)2 pap = , (3)

A2 2gc and the mass flow Wex is .

Wex " PAf v . (4) .

11 Substituting Eq. (4) into Eq. (3), collecting constants, and rearranging:

PAP W ex"j[gjx (5) where I

Ke 'x = DI2 (6)

We x,1 and i represents initial conditions at the extraction point. Substituting Eq. (6) into Eq. (5)

PAP W ex =W ex,i 3p (7) or Ap Nex *W ex,1 ,3[ yvi (8) api Since steam property subroutines used in ORTURB calculate specific volume rather than density, Eq. (8) is used. Equation (1) can be shown to reduce to Eq. (8) for small pressure drops.

During turbine iterations, if feedheater shell pressure is greater than extraction point pressure, extraction flow is set to zero (no reverse flow) until the extraction pressure is again greater than shell pressure.

The feed pump system for Fort St. Vrain consists of three pumps, two d' riven by steam turbines and one by an electric motor. The steam enth21py drop across the feed pump turbines is added to the enthalpy of feedwater flowing through the pumps. Energy imparted to the feedwater by electric feed pump is ignored. This, in effect, assumes that feed pump thermal efficiency is 66.7%. These results agree well with published heat bal-ances.5 For simplicity, the feed punp system for the steam side is mod-eled as one steam turbine-driven pump. Feedwater flow through the pump is determined by the plant controller simulator and not turbine steam con-ditions. This simplification could be modified by substituting a feed-water pump computer simulation.

The feed pump turbine has been modeled as one stage group, meaning that entrance and exit pressures are used as upstream and downstream

12 pressures in the ideal gas flow equation. Inlet pressure is set equal to pressure at the second ILPT extraction point (point 3 of Fig. 2), and exit .

pressure is set equal to main condenser pressure. No flow control device is modeled for the feed pump turbine, which means that the flow is depen- -

dent on inlet steam conditions and outlet steam pressure if flow is less than critical. A steam-flow control device could easily be added if necessary.

Turbine flows resulting from the previous-time pressure distribution are all calculated initially for a timestep. The turbine flow upstream from an extraction point is then compared with the turbine flow downstream and the extraction flow. If the flows do not balance, extraction pressure is modified accordingly, and the two stage group flow calculation is re-peated (as described for the ilPT) until convergence is obtained. Test cases were run in which the entire turbine flow distribution was recalcu-lated when only one pressure changed during the iteration process. No significant differences in converged flows from the two point case were noticed, but computer time was greatly increased.

Low pressure turbine exhaust loss is calculated according to the pro-cedure in Ref. 6. This loss is a unique function of steam velocity at the

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discharge of the last-stage bucket. Empirical data are used for this pro-cedure and were developed from known dimensions (851 mm active length on the last-stage bucket) and published exhaust losses 5 at 100 and 25% power.

As the pressure-flow iteration advances through the turbine, recaired i steam properties of temperature and specific volume are obtained from steam property subroutines originally written for the ORCENT code3rather than the ASME 1967 steam table equations.8 The ORCENT subroutines have fewer iterative loops, thus consuming less computer time than AS!!E equa-tions, ar.d are of sufficient accuracy for transient analysis of steam turbines.

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4. FEEDWATER HEATER SIMULATION The feedwater heater model used in the simulator is shown in Fig. 3.

There are five such feedheaters in the simulated turbine plant, located as shown in Figs. I and 2.

Steam from the turbines enters the shell of the feedwater heater. If this steam is superheated, the assumption is that it will first lose this superheat to the feedwater by means of a simple heat balance. If the steam is wet, it is divided into a saturated steam part and a saturated liquid part. The liquid falls into a liquid stream on a tray or partition within the feedwater heater. Liquid from a previous feedwater heater may also enter this stream. Because its temperature is usually hotter than the saturated vapor temperature, part of it flashes; this vapor goes into the vapor space. Steam in the vapor space condenses on the tubes con-

taining the feedwater and falls into the liquid stream. This liquid eventually flows into the drain-cooler section of the feedwater heater and loses additional heat to the feedwater as it flows through the drain cooler.

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Fig. 3. Feedwater heater.

'14 Feedwater enters the-feedwater heater tube bundles and flows counter to the direction of the drain coolant flow. After leaving the drain ..

cooler,- feedwater enters tube , bundles in the vapor space where it gains additional heat as steam is condensed. Before leaving the heater, feed-water 'in the tube bundle passes. through a superheat section where any

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superheat in the turbine extraction steam is removed.

In the simulation, the . drain-cooler section of the feedwater heater is treated as a .counterflow heat exchanger. - The feedwater heater section in which feedwater tubes' pass through the vapor space is treated as a tube-in-shell heat exchanger with a uniform shell side temperature.- The superheat section heat balance is W s,i h3;g = Wpg ahpg , (9)

The steam flowing into the feedwater heater shell dividestinto two I

streams, Ws *WV + Ug , (10) such that Whs s " Wvhy + Wght. (11)' -

The liquid entering from a previous drain cooler divides into two

streams, WDC,1 " WDC,f + WDC,t . (12) such that WDC,1 hDC,1 = WDC,f hfg + WDC,1 hDC ,1 , _ (13) where hfg and hDC,1 are evaluated at the vapor temperature Ty.

The vapor condensing rate We is calculated by We =

(UA)EV y -- TFE,$) + .(UA)gy-(T (T y -TFE,A) . (14) .

h fg hgg (UA)EV is the heat transfer. coefficient multiplied by the area over one-1

15 half the evaporator length. (UA)DC is the heat transfer coefficient mul-tiplied by the area over one-half the drain-cooler length. These coefft-cients are assumed to be constant in the simulation.

A lumped parameter model was constructed using seven differential equations to describe the dynamics of a single feedwater heater unit (Fig. 4). All seven differential equations are for temperature. '

Feedwater temperatures in the drain cooler section are represent 4 by Eqs. (15) and (16), which were derived from a time-dependent energy balance:

dTFC 4 2Wpg 2(UA)DC dt

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!!FC , A - DC, &) + (MCp)FC ,A - D C,M e M dT FC'A 2Wpg 2(UA)DC dt "M FC , ,A) + (MCp)FC * '^ '

Equations (17) and (18) represent feedwater temperatures in the evapora-tor, or vapor section:

2Wpg 2(UA)EV dTyg dt 4"M , A - DE, $k + (MCp)FE " '

, FE '

dTFE A 2Wpg 2(UA)EV dt "M FE , FE,A) + (MCp)FE # '^ '

s Temperature of the coolant in the drain cooler is represented by Eqs.

(19) and (20):

dTDC 4 2WDC 2(UA)DC dt "H DC DC,A - D C,d + (MCp)DC '^- '

dTDC A "

2WDC 2(UA)DC dt MDC , A) + (MCp)DC ' '^ '

,. The seventh differential equation for T , the y saturation temperature of vapor in the feedwater_ heater shell, depends on mass flow rate into and

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OR N L-DWG 72-12012R Wy (EXTRACTION STEAM VAPOR)

I f PREVIOUS W oc.F MV DRAIN ----------TV lSUPERHEATl COOLER g I f

+ T F E.A Z I F E.c w Tpwp VAPOR SECTION CONDENSE D WC

• VAPOR cn I

DRAIN COOLER T FC.c c T FC.A m Tpw; (FEEDWATE R)

SECTION l l i l (PREVIOUS DRAIN W DC.L COOLER) r T DCA T oc.&

(EXTRACTION w t_ _

L Tt 2 1 C STEAM LlOUID)

I W DC Fig. 4. Flow diagram of simulated feedwater heater.

17 out of the'shell in the following manner:

d sat sat sat ( I}

The shell vapor mass rate of change dM/dt is the net flow into the feedheater shell,

=Wy+WDC,f - W e. (22)~

Combining Eqs. (22) and (14) with Eq. (21), the seventh differential equation is dTv dT dP 1 dt dP sat dp sat V

'(UA)E7 Wy+WDC,f - h-fa

• ( *T y -TFE,A - TFE,$) ' * ( )

Saturation derivatives are reevaluated at the beginning of each time-

, step using the previous timestep value of pressure and density. Shell pressure is determined from the saturation temperature, T y.

The value T g in Eq. (20), representing the temperature of the liquid going from the shell to the drain cooler, is obtained from an energy bal-ance of shell liquid flow and enthalpy with condensation flow and energy using the previous timestep values. Since flashing of this shell liquid back to stean is not represented, the value of Tg should be monitored dur-ing a simulated transient to ensure that it does not rise significantly above the saturation temperature T y.

Flow f rom the drain cooler WDC'is assumed to be constant during a timest ap and is calculated at the beginning of each timestep by WDC " WDC,1 + W1+WC* (24)

The set of seven dif ferential equations (15-20, 23) are solved each

) timestep using the matrix exponential method,9 as discussed in Ref. 10.

18 in initializing steady state calculation, the various' masses (MDC.

PfFC, MFE) are calculated, using a holdup time supplied as an input. Dur-

• ing a transient, these masses are corrected for changes in saturated water density caused by temperature changes from initial conditions. Tempera-ture input data include inlet and outlet feedwater temperatures (Tyy,i and Tyg,4) and drain cooler inlet and outlet temperatures (TDC,1 and TDC,$)*

The saturated vapor temperature T y is determined from input shell vapor pressure. Flow rate input data include steam flow rate Ws , feedwater flow rate (Wpg), and the drain cooler flow rates WDC and WDC,i. From this data, two of the seven state variables for each feedwater heater (TFE,4 and TDC,4) are known. The temperature of feedwater leaving the drain cooler region TFC,4 may be calculated from the following heat balance:

Wpg (hFC,4 - hyg,1) = WDC (hg - hDC,4) . (25)

The feedwater temperature halfway through the evaporator, TFE,A 18 determined as shown on the following schematic.

r Ty T FE,9 T FE,A T FC,$

From a heat balance, Wpg

• Cp (TFE,9 - TFC,$) = 2(UA)EV ATim , (26) where ATim is the log mean temperature difference:

Ty-T ATim - f(Ty-TFC , $) -- (Ty-TFE,$) In FC'$ . (27)

-T44 Substituting Eq. (27) into Eq. (26) and rearranging, (UA)EV 1 Ty - TFC,4 (28)

= - in WWp FC 2 Ty - TFE,)  ;

19 i

I Analogous reasoning will yield the following expression for TFE,A*

(UA)EV

, TFE,A = Ty - (T y-TFC,4)exp -- W C p ,. (29) where all terms on the RHS are known.

FC,A and T DC,A are chosen as the tem-In the drain-cooler section, T peratures halfway along the feedwater coolant pipe and the drain cooler, respectively. Following the analysis presented by Giedt,Il which is the classic NTU (number of transfer units) analysis for heat exchangers, these temperatures are obtained by solving two simultaneous equations, TDC,A = TDC,1 - Eh (TDC,1 - TFC,A) , (30)

TDC,4 = TDC,A Eh (TDC,A - Tyg,1) , (31) where the heat exchanger-heating effectiveness Eh is

• ! (CA)og (WCp )DC (WCp )DC (UA)DC (WCp )DC \

Eh " I - '"P _.

i_ , xp _

i- 1. (32) g (wcp )oc (WCp )rw (wcp )rw ( (WCp )Dc (Wcp )rw j The deaerator (feedwater heater 4) is treated as a large mixing tank.

Mass and enthalpy inventory calculations are performed at each timestep and resulting equations are solved by Euler's method. The resulting homogenous liquid is assumed to be at saturated conditions.

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5. CONTROL ,

As ORTURB is intended . to be used as a part of an overall Fort St.

4 Vrain plant simulator code (ORTAP), certain parameters must be supplied to ORTURB to execute it independently. These time-dependent parameters are desired turbine loading, high pressure turbine inlet steam pressure and enthalpy, intermediate turbine inlet pressure and enthalpy, and feed-water flow through each feedheater and into the steam generator. These parameters are supplied by the appropriate ORTAP simulator to the version of ORTURB presently implemented in ORTAP. 'However, to execute 0RTURB by.

itself, these parameters are written into coding of its main program.

Coding modifications to the main driver subroutine must be made to, repre-sent any other transient.

Feedwater flows of the tube-side of heaters 5 and 6 and the outlet flow of the deacrator are set to the desired steam generator flow rate.

Feedwater flaw of the tube-side of feedheaters 1 through 3 is set so that the deaerator has a constant fluid level. No attempt is made to balance flow in the condenser.

- The drain coolant flows (shell-side only) from feedheaters 1, 2, 3,

. 5, and 6 are controlled so that the flow into the drain cooler equals the flow out (i.e., constant liquid level).

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.6. RESULTS 4 ..

A simulated turbine runback from 100 to 25% electrical power' achieved

• very good agreement in steady state with the 25% power heat balance s

( Appendix B and Fig. 5). 'The values in parentheses lin Fig.'5 are calcu-

. lated results from ORTURB. A small portion af the information presented in the 25% power heat balance was used during' turbine initialization -

(low pressure turbine leaving loss and high pressure turbine exit steam conditions needed to calculate thermal. ef ficiencies). However, all tur-bine flows, enthalpies, and pressures were in very good agreement with the heat balance at 25% power (Fig. 5) when initialization was done with the information representing 100% power (Fig. 6).

Transients representing loss-of-condenser, loss-of-feedwater heater, and high pressure turbine exit pressure fluctuations were also simulated.

The turbine model indicated appropriate responses for all simulated tran-sients. Comparisons with actual plant data can easily be made when the information becomes available. >

.During the modeling for the loss-of-condenser transient, convergence dif ficulties were noted for the ILPT segments close to the condenser. The subroutine ZER01, a slightly modified version of the subroutine ZEROIN,12 was then used to bring the pressure-flow distribution into convergence.

The mass flow convergence tolerance also required modification during simulation of this severe transient.

The ORTURB turbine model uses approximately 0.05 s of IBM Model 360/91 computer time for each computational timestep. This value is sub- i ject to the transient being modeled and will increase as the severity of the transient increases. However, this reduced computer time is a sig-nificant improvement as compared to the earlier turbine model in ORTAP.I J

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- a 3 / N-:

1 2=

q2 3sp 54: (c) (D) 33s (5.38)

TR' (2.4s) / @

FT

\ (1177 1152 9H) OH UEEP = 1133 OH Q (1130.1H)

@ @ @ @ @ @ " 'E'8m4 i13P bb WP 40 6P 212P / OP 3 bP 1. /P 167la 3019F (713P; 268 2F (43 6P) / (23'2PI 1718F (7 8P) 143 9F (4 IP) 114 4F 1186P) 114 4F 2 M M M' '.* M A/V - M 1310 5F) (277 2F) ,

3 SF (183 5F; (1b4 6F > (123 9F) 11118F) r5 5 278 2F w 746 6F 153 9F S [ 124 4F % [ 124 4F 79=

(278 6F 6 (244 9F1 (157.3F ) (126.2F) (1119F) (86s) w 236 6F (243 3F) s - FLOW (ib,/s) P = PRESSURE (psw) H = E NTHALPY (8tullb,) F = TEMPERATURE ( F)

ORTURB CALCULATED RESULTS ARE IN PARENTHESES Fig. 5. Turbine conditions at 25% power heat balance.

e , ., . , .

l 1

l i

t l

l i l 8

M O REHEATER e

l fE, 3 :A i

"'1 g

{ r 8 cn l

N w

' = h w 893.3P 1358.5H '~

g

~

m.

\ '

a #

T y 2 e 8

~

a & &

9

' e "

4 C 3 T e"

} 5 s

/N z -

o" g g

• N

- a e S U is ~

• A h m k

O E

n e .

O

o. 27' W

t' m

2 O

g 268 BP 1426.4H '

E 2 e S

u 2

hE S T

- ~ $'

" 5D.

5 s m u

- $ I " * "

o cr 8".

G h ~

\ ~

m '

c

$ \

e 9 g 19Sa \

13.9P 1159 OH C

9 M g g 39 3 \4 83 2P 1302.7H

o. = 4 =

' m (D D N g -4 co O'

E \ "

H $ -

b

=

D o

@I' 27.3P 1207.2H 25.9 i

2 -

g 6.19P 1107.9H 3 '

i 8 8 . .

' m C

h ,

7 i .' ,, y l

{- bii ~~ o

'sa i

8 I n . es cn a m~a s Eh 9 0 o

l l

SZ

27 REFERENCES

~

1. J. C. Cleveland et al. , ORTAP: A Nuclear Steam Supply System Simula-tion foe the Dynamic Analysie of High-Tempemtune Gas-Cooled Reactor Transients, ORNL/NUREG/TM-78 (September 1977).

2. J. G. Delene, A Digital Computer Code for Simulating the Dynamics of Demnstration Siae Dual-Purpose Desalting Plants Using a Pressurined Vater Reactor as a Feat Source, ORNL/TM-4104 (September 1973).

3. H. I. Bouers, ORCENT: - A Digital Computer Progmm for Satumted and Lor > Superheat Steam Turabine Cycle Analysis, ORNL/TM-2395 (January 1969).

4. J. K. Salisbury, Steam Turbines and Their Cycles, Robert E. Krieger Publishing Co., Huntington, New York, 1974.

5. F. 2. Swart, Public Service Company of Colorado, letter to J. C.

Conklin, Oak Ridge National Laboratory, Feb. 8,1977.

6. R. C. Spencer, K. C. Cotton, and C. N. Cannon, A Method for Predict-ing the Performance of Steam Turbine Generators..16,500 kW and Larger, General Electric Co., GER-2007C (July 1974).

7. H. Hegetschweiler and R. L. Bartlett, " Predicting Performance of Large Steam Turbine-Generator Units for Central Stations," Trans.

ASVE 79,1086 (1957).

. 8. C. A. Meyer, R. B. McClintock, G. J. Silvester, and R. C. Spencer, Thermodynamic and Transport Properties of Steam, Am. Soc. of Mech.

Eng., New York (1967).

9. S. J. Ball and R. K. Adams, MATEXP, A General Purpose Digital Com-puter Program for Solving Ordinary Differential Equations by the Matrix Exponential Afsthod, ORNL/TM-1933 (August 1967).

10. J. G. Delene and S. J. Ball, A Digital Computer Code for Simulating Large Multistage Flash Evapontor Decatting Plant Dynamics, ORNL/

IM-2933 (September 1971).

11. W. H. Giedt, Principles of Engineering Heat Transfer, D. Van Nostrand Co., Inc., Princeton, N.J. (January 1957).

12. G. F. Forsythe, M. A. Malcolm, and C. B. Moler, Computer xtethods for Mathem2cical Computations, Prentice-Hall, Englewood Clif fs, N.J.

(1977).

29 I

Appendix.A

(, INPUT REQUIREMENTS 4

Refer to Figs. 2 and 6.

4 Cards No. 1 (FORMAT 20A4)'

l Two title cards j Card No. 2 (FORMAT 15)

N0SCS -- number of steam generator modules feeding the- high pressure turbine (for FSV set equal to .12).

Card No. 3.(FORMAT 2E10.3, 110) ,

TSTRT -- starting time

, DT -- t ime s te p ,

NTMSP -- desired number of time steps -

Card No. 4 (FORMAT 2E10.3)

P -- desired precision of the A-matrix for feedwater heater calcula-tions. Experience with different values of this parameter will be necessary to evaluate the trade-offs of computational accuracy.

and computer time (recommend 10-6 for IBM computers).

ATOL -- desired fractional change of each of the seven calculated state variables of the feedwater heater calculation before up-dating the A-matrix.' Again, experience is necessary to evalu-ate the trade-offs of computer accuracy and time (recommend 0.01).

j Card No. 5 (1615)

IND(I), I=1 through 16 set to zero except the following.

l IND(3) -- desired number of time steps between printouts.

l IND(4) -- *et not equal to zero if A-matrix information is desired output wherever updated (for debugging).

! IND(5) -- set not equal to zero if the forcing function vector. is desired during printouts (for debugging).

Card No. 6 (2E10.3)

- ABSTOL -- absolute tolerance (1bm) i RELTOL -- relative tolerance (f raction)

.J 1

p. - ag&4,- sa+ -&- . y- g

~

T 30 The actual tolerance used by ORTURB during the pressure-flow itera-tions for both the !!PT and ILPT is of the form: -

TOL = ASBTOL + Wupstream RELTOL.

Card No. 7 (6E10.3)

• WIIP100 -- inlet flow to high pressure turbine (llTP) at 100%.

power (Ibm /s).

PHPTO -- inlet pressure to itPT at 100% power (psia)

PHPEXO -- exhaust pressure f rom HPT at 100% power (psia) tillP100 - inlet enthalpy to HPT at 100% power (Btu /lbm) tillPEXO -- exha'ust enthalpy from HPT at 100% ~ power (Btu /lbm)

WilPLKO - packing gland leak flow rate f rom flPT exhaust to the shell of feedwater heater 5 (1bm/s)

Card No. 8 (FORMAT E10.3)

IICON -- condenser outlet enthalpy (Btu /lbm)

Card No. 9 (FORMAT /E10.3)

WILP(I), I=1 through 7 - 100% power mass flow in each of the interme-diate- and low pressure turbine (ILPT) seg-ments (1bm/s)

Card No. 10 (FORMAT 8E10.3) w ,

PILP(1), I=1 through 8 - 100% power pressure at the beginning of the i ILPT segments (psia)

Card No. 11 (FORMAT 8E10.3)

IIILP(I), I=1 through 8 - 100% power enthalpy at the _beginning of the -

ILPT segments (Btu /lbm)

Card No.12 (FORMAT SE10.3)

PFPTIO pressure at inlet to feedpump turbine (FT) at 100% power (ps )

IIFPTIO -- enthalpy at inlet to FT at 100% power (Btu /lbm)

PFPTO -- exhaust pressure of FT at 100% power (psia)

IIFFTO -- exhaust enthalpy of FT at 1007. power (Btu /lbm)

WFPTO -- flow of FT at 100% power (1bm/s)

Card No. 13 (FORMAT 6E10.3) ,

One card is required for each feedwa:er heater as numbered on Fig. 2 at 100% power. The deaerator is considered feedvater heater 4. L

31 WDC - drain coolant flow-(lbm/s)

I WFW -- feedwater flow (lbm/s)

TFWI -- temperature of feedwater entering heater (*F)-

0 TFWO -- temperature of feedwater leaving heater (*F)

TDC0 -- temperature of liquid leaving drain cooler (*F)

PFHV -- vapor pressure in feedheater shell (psia)

Card No. 14 (FORMAT 4E10.3)

One card is required for each feedwater heater at 100% power.

HFWC -- holdup time of feedwater in drain-cooler portion (s)

IIDC -- drain cooler holdup time (s)

RFWE -- holdup time of feedwater in evaporator portion (s)

IIVFH -- steam holdup time on shell-side of feedwater heater (s)-

)

9

33 Appendix B OUTPUT Output f rom ORTURB is presented in Fig. B.1 for 100% power conditions and in Fig. B.2 for 25% power conditions. An explanation of the informa-tion that is not self evident follows.

Desired load is a variable that must be specified in the driver rou-tine to control electrical output of the turbine. Actual load is the fraction of 100% power calculated by ORTURB. VLVil is that fraction of TIME (SEC) = 0 HIGH PRESSUR E TUR8!NE OUTPUT (MWE) = 69.138 LOW PRESS fat TURBINE ELECTRICAL OUTPUT (MWE) = 274.65 TOTAL CROSS ELE 2TRICAL OUTPUT ( MW E ) = 337.74 DESIRED LOK.D = 1.0000 ACTUAL LOAD = 1.0000 VLVH = 1.0000 HIGH PRESSUME TURBINE EFFICIEhCY .008051 H!CH PRESSURE TUR8!4E DATA PO!47 FLOW TEM PER A TUR E ENTHALPY PR E SS UR E 1 637.46 1000.C; 1461.30 2412.30 2 636.01 970.66 1449.74 2179.28 3 636.02 874.58 1411.69 1536.29 4 633.08 740.93 1358.50 893.30

=

14TERMEDI ATE AND LN PRESSURE TURBINE DATA PotNT FLOW TEM PER ATUR E ENTHALPY PR E SSUR E 1 621.87 1000.09 1517.70 568.20 2 594.39 808.58 1426.40 268.80 3 554.16 681.64 1367.00 157.60 4 514.95 544.24 1302.70 83.20 5 496,11 335.43 1207.20 27.30 6 476.64 228.87 1159.00 13.*0 7 451.11 171.41 1107.90 6.19 8 470.34 105.83 1029.97 1.13 EXHAUST LOSS (BTU /LBM) = 13.3724 FEEDPUMP F14W (LBM/S) = 19.230 FEEDPUMP OUTLET ENTHALPY (BTU / Lum = 1087.1 FEEDHEATER STATE VAR I A B LE S STG TFC0 TFCA TFE0 TFEA 7:r0 TDC A TFHV 1 115.935 112.396 162.803 151.671 120.600 135.060 167.83) 2 165.133 163.720 200.204 191.101 172.800 183.612 205.119 3 201.521 200.840 235.567 224.145 210.200 220.385 240.290 4 0.0 0.0 0.0 0.0 308.980 0.0 0.0 5 318.319 316.696 352.039 342.475 326.000 336.803 358.308 6 360.270 3 ~.9. 3 2 2 394.134 384.401 368.300 378.884 400.912 STG TFWO T DC O TFWI TFH1 WFHC WDVI WFHV WFHL WDLI WFW WDC TFE!

1 162.800 120.600 110.600 167.833 28.171 0.191 24.885 0.650 18.109 600.890 63.800 115.935 2 200.200 172.800 162.800 235.119 21.639 0.099 19.465 0.0 '8.771 600.890 38.300 165.133 3 235.000 210.200 200.200 240.290 20.'36 0.0 14.840 0.0 0.0 600.890 18.870 201.521 4 308.980 308.983 235.000 109.041 0.0 0.0 0.0 0.0 0.0 640.360 640.360 235.172 5 358.300 326.C00 115.900 358.308 25.940 0.339 24.875 0.0 27.211 640.360 48.250 318.319 6 402.900 368.300 358.900 400.912 28.058 0.0 27.485 0.0 0.0 640.360 27.550 360.270 STG HFWI HFEI HFEO HFWO H DC 1 H DC 0 HFHV HFHS WFHS PFHV 1 78.549 83.560 130.690 130.690 135.728 88.529 1133.307 1107.900 25.535 5.700 2 130.690 132.758 167.829 168.191 173.138 140.701 1147.920 1159.000 19.465 12.800 3 168.191 169.146 201.817 203.277 208.631 178.251 1160.623 1207.200 18.840 25.100

= 4 203.277 0.0 0. 0 278.605 296.507 278.605 1192.249 1302.700 39.396 76.537 5 286.016 288.569 323.664 330.382 330.390 296.507 1194.069 1365.505 24.875 149.800 6 331.016 332.520 368.454 378.125 375.975 341.023 1201.081 1426.400 27.485 249.900

$ Fig. B.I. ORTURB output printing Zor initial conditions at 100%

power.

P00R BRIGINAL

34 TIME (SEC) = 200.00 MIGN PRES $URE TUR8!NE OtFs PUT Destl e 24.294 LOW PRESSURE TUR8tNE ELECTRICAL OUTPUT Dest) e 64.138 70"AL GROSS ELECTRICAL OUTPUT DesE)

• 86.215 DES! RED LOAD

• 0.2500 ACTUAL LOAD = 0.2553 VLV4

• 0.1590 - i MIGN PRESSURE TURSINE EFFICIENCY .545972 i

e NIGH PRESSURE TUR8tNE DATA POINT FLOW . TEMPERATURE ENTHALPT PRESSURE 1 362.48 1000.01 1461.30 2412.30 2 163,39 709.04 1360.55 526.36 3 163.48 654.23 1339.11 376.31 4 160.25 600.18 1319.58 236.00 INTEAMEDIATE AND LOW PRESSURE TURSIME DATA .

POINT FLOW TEM PE RATUR E ENTHALPY PR ESSUR E 1 162.69 1000.02 1529.40 150.10 2 159.27 817.55 1438.76 73 09 3 152.66 696.86 1380.26 43.98 4 146.44 564.22 1316.97 24.03 5 144.33 353.98 1219.37 8.07 6 141.07 246.07 1170.34 4.19 7 139.19 135.62 1120.70 1.87 R 144.49 105.83 1130.09 1.13 E AHAUST LOSS (8' ,,68M) a 39.2681 FEf.DPUMP FLOW (LSM/S) - 5.2975 FEEDPU4P OUTLET ENTHALPY (STU/L84) = 1152.9 FEEDHEATER STATE VARIABLES STC TFCO TFCA TFE0 TFEA TDC O TDCA TFHV i 112.413 111.839 123.548 122.511 111.933 - 113.229 123.552 2 127.765 125.027 153.300 150.587 126,171. 131.654 153.560 3 158.480 155.855 181.438 178.442 157.265 . 162.494 181.893 4 0.0 0. 0 - 0.0 0.0 236.073 0.0 0.0 5 246.124 243.914 271.937 248.700 244.913 250.002 272.463-6 279.839 277.702 303.673 300.632 278.555 283.221 304.144 STG TFWO TDC0 TFWI TFH1 WFHC WDVI WFHV WFHL WDLt - - WFts WDC TFE!-

1 123.890 111.933 111.775 124.233 1.771 0.016 1.177 0.0 6.820 150.970 8.591 112.413 2 154.568 126.171 123.890 154.120 3.568 0.012 3.544 0.0 3.312 150.970 6.880 121.765 3 103.507 157.265 154.568 182.502 3.334 0.0 3.330 0.0 0.0 150.970 1.334 158.480 ?

4 236.073 236.073 183.507 309.041 0.0 0.0 0.0 0.0 0.0 167.100 .167.100 235.172 i 5 277.174 244.913 243.195 272.993 4.668 0.029 4.640 0.0 4.324 167.100 8.992 246.124 6 310.478 278.555 277.174 305.123 4.366 0.0 4. 361 0.0 0.0 167.100 4.366 279.839 -

STG NFWI NFEI HFE0 NFWO HDCI HDCO HFMV HFHS WFHS PFHV .

1 79.400 80.359 91.471 -

91.515 92.155 79.879 1115.231 1120.701 1.582 1.867 2 91.813 95.681 121.189 122.193 122.009 94.089 1127.556 1170.342 3.565 4.058 3 122.457 126.369 149.357 151.132 150.425 125.154 1138.881 1219.374 3.340 7.832 4 151.432 0.0 0.0 204.323 213.336 204.323 1195.254 1316.971 7.139 23.251 5 213.574 214.544 240.807 245.799 241.886 213.316 1171.381 1351.194 4.647 43.584 6 246.159 248.885 273.373 280.103 274.869 247.571 1180.892 1438.760 4.373 71.286 Fig. B.2. ORTURB output printing for initial conditions at 25%

power.

the flow constant of the HPT governing stage necessary to achieve the actual load.

Points 1 through 4 of the high pressure turbine data are shown on Fig. B.2. Differences in flow for points 1 through 3 indicate how the flow calculated using the ideal gas flow equation is converging for the different segments. Flow at point 4 represents the value of flow at point

~ '

I less the packing gland flow to the shell of feedwater heater 5. Pres-sure at point 2 is shell pressure of the governing' stage, an important g variable for control of the plant ~ feedwater flow.

1

..g. .

7,, $ , .

,'4 ies y

J

'. M

35 Points 1 through 8 of the ILPT data represent information at the

- points shown on Fig. B.2. Exhaust loss is taken from the enthalpy at point 8 before gross electrical output from the ILPT is calculated.

Feedheater state variables are explained as follows; temperatures are in degrees Fahrenheit, enthalpies are in Btu /lbm, and flows are Ibm /s.

Feedwater heater 4 is a deaerator and is modeled quite dif ferently f rom the other feedheaters. As such, certain variables are not applicable and are zeroed.

Acronyms (Figs. B.1 and B.2)

TFC0 - temperature of feedwater at outlet drain cooler section [TFC,$ of Eq. (15)].

TFCA - temperature of feedwater halfway along the drain-cooler section

[TFC,A of Eq. (16)].

TFE0 - temperature of feedwater at the outlet of the evaporator section

[TFE,4 of Eq. (17)].

TFEA - temperature of feedwater halfway along evaporator section [TFE,A of Eq. (18)].

TDC0 - temperature of liquid at the drain cooler outlet (TDC,$ Of Eq. (19)].

TDCA - temperature of liquid halfway along drain-cocler section [TDC,A of Eq'. (20)].

TFIIV - saturated vapor temperature in the feedwater heater shell (Ty of Eq. (23)].

TFWO - te.nperature of feedwater at the outlet of the feedwater heater.

Dif ferences between TFWO and TFE0 represent amount of superheat in the shell inlet vapor flow.

TFWI - temperature of feedwater at the inlet of the feedheater.

TFIII - temperature of liquid in the evaporator section [Tg of Eq. (20)].

As mentioned in the text, this variable should not rise signifi-cantly above TFilV. If it does, flashing of this liquid into steam is occurring and must be accounted for, which requires modifying differential equations.

O WFilC vapor condensing rate in the feedheater shell [W e of Eq. (14)].

36 WDVT - vapor flashing ' rate of previous drain-cooler liquid [WDC,f of Eq. (12)].

WFilV - saturated vapor flow into the feedwater heater shell [W y of ,

Eq. (10)].

WFIIL - saturated liquid flow into the feedwater heater shell [Wg of Eq. (10)].

WDLI - previous drain-cooler liquid flow rate [WDC,g'of Eq. (12)].

UFW - feedwater flow rate out of feedheater.

-WDC - total drain cooler outlet flow rate.

TFEI - temperature of feedwater at the evaporator section inlet.

IIFWI - enthalpy of feedwater at the feedwater inlet.

IIFEI - enthalpy of feedwater at the evaporator section inlet.

IIFE0 - enthalpy of feedwater at the evaporator section outlet.

IIFWO - enthalpy of feedwater at the feedheater outlet.

HDCI - enthalpy of drain-cooler liquid at the drain cooler section inlet ~

[hDC,1 of Eq. (13)].

HDC0 enthalpy of drain-cooler liquid at the drain-cooler s'ection outlet. .

IIFilV - saturated vapor enthalpy at shell pressure [hy of Eq. (11)].

IIFilS - enthalpy of turbine extraction steam [h s of Eq. (11)].

WFHS - turbine extraction steam flow rate [Ws of Eq. (11)].

PFHV - saturation pressure of shell.

User's note on stability: There is a timestep between the printed values of WFilS and WFHV. At a given transient time, these values should be approximately the same for dry extraction steam. If a significant difference exists between the two printed values, a numerical oscil-lation may be occurring. In such a case, either the timestep should be reduced or vapor holdup time (liFVH) increased.

~

i 4i l

37 NUREG/CR-1789

. ORNL/NUREG/TM-399 Dist. Category R8 e

Internal Distribution

1. S. J. Ball 15. J. P. Sanders

2. K. W. Childs 16.- R. S. Stone

3. J. C. Cleveland 17. T. K. Stovall 4-8. J. C. Conklin 18. H. E. Trammell

9. J. G. Delene 19. ORNL Patent Of fice

10. L. C. Fuller 20. Central Research Library

11. P. R. Kasten 21. Document Reference Section'

12. W. A Miller 22-23. Laboratory Records Department

13. F. R. Mynatt 24. Laboratory Records (RC)

14. J. L. Rich External Distribution 25-28. Director, Office of Nuclear Regulatory Research, USNRC, Washing-ton, D.C. 20555

29. Chief, Experimental Gas-Cooled Reactor Safety Research Branch, 3 Division of Reactor Safety Research, Office of Nuclear Regula-tory Research, USNRC, Washington, DC 20555

30. Director, Reactor Division, DOE, ORO, Oak Ridge, TN 37830

31. Office of Assistant Manager for Energy Research and Development, DOE, ORD, Oak Ridge, TN 37830 32-33. Technical Information Center, DOE, Oak Ridge, TN 37830 34-333. Given distribution as shown in category R8 (10 -- NTIS)

)

,-