CALIFORNIA STATE
UNIVERSITY~
NORTHRIDGE
CONTROL SIMULATION OF A SODiut·1 COOLED,
1\
ADVANCED CENTRAL RECEIVER FOR A
SOLAR/ELECTRIC
PO~!ER
PLANT
A graduate project submitted in partial satisfaction of
the requir'ements for the degt·ee of Master of Science in
Engineering
by
William W. Willcox
January, 'l979
The Graduate Project of William W. Willcox is approved:
Timothy Fox
/
I
California State University, Northridge
;i
~··
ACKNO\~LEDGEMENT
The author acknowledges the assistance of Bob O'Neill and Art
Presson in utilizing the Continuous System Modeling Program (CSMP)
and Lyle G·lasgow for providing sodium system and advanced central
receiver design information.
All three are members of the Energy
Systems Group, Rockwell Internati on a 1, v1hose computer facilities were
used in exercising this model.
iii
~·":>'·
~··
TABLE OF CONTENTS
Page
Approval Page
ii
ACKNOWLEDGEt~ENT
iii
NDr~ENCLATURE
vii
ABSTRACT
xi i
Chapter
INTRODUCTION
I
1
A Objectives and Purpose
B Central Receiver System Description
C Model Scope
D Literature Search
MODEL DESCRIPTION
II
9
A CSMP
B Model Features. General Description and Assumptions
C Specific Equations
Thermal
Hydraulics
3 Plant Protection and Control System
4 Boundary and Initial Conditions
1
2
III
IV
V
VI
RESULTS
33
DISCUSSION OF RESULTS
43
CONCLUSIONS AND RECOMMENDATIONS
54
REFERENCES
56
59
APPENDIX
iv
LIST OF FIGURES
Figure
Page
1
Simplified Flow and Control Diagram
2
Advanced Central Receiver Transient Model Schematic
11
3
Overall Proportional Response to Step Flux Change
34
4
South Panel Proportional Response to Step Flux Change
35
5
West Panel Proportional Response to Step Flux Change
36
6
North Panel Proportional Response to Step Flux Change
37
7
Overall P.I.D. Response to Step Flux Change
39
8
South Panel P.I.D. Response to Step Flux Change
40
9
West Panel P.I.D. Response to Step Flux Change
41
10
North Panel P.I.D. Response to Step Flux Change
42
11
Idealized Panel Control Block Diagram
44
12
Process Reaction Curve for Cohen and Coon
Controller Setting Optimization
45
v
6
LIST OF TABLES
Page
Table
I
II
Comparison of Hydraulic and Process
Time Constants
47
Stability Criterion Compar-ison
51
vi
NOMENCLATURE
A
Fluid Flow Area (ft2)
Arr
Node Reradiation Area (ft 2)
B
Measured Receiver Panel Outlet Temperature (°F)
C
Receiver Panel Outlet Temperature (°F)
Cp
Heat Capacity (BTU/lbm-
CVC
Calculated Control Valve Flow Coefficient (GPM/PSI)
CV.1
Design Control Valve Flow Coefficient, Panel i (GPM/PSI)
c1
Receiver Pump Torque and Head Curve Fitting Coefficients
D
Receiver Tube Inside Diameter (ft)
DPCV;
Panel i Control Valve Pressure Drop (PSI)
DP
v
0
0
F)
Drag Valve Pressure Drop (PSI)
E.1
Node Inlet Elevation (ft)
E0
Node Outlet Elevation (ft)
EIR.1
Panel i Outlet Temperature Integral Error (°F)
ET.l
Panel i Outlet Temperature Error (°F)
F
Force ( 1bf)
FH.1
Panel i Friction Head Drop (PSI)
FD 0c
Downcomer Friction Head Drop (PSI)
G
Open Loop Transfer Function
Gc
Controller Transfer Function
Gp
Process Transfer Function
Gt
Product of Valve, Process and Measuring Element Transfer
Function
vii
Gv
Va1ve Transfer Function
HARN
Sodium Film Coefficient Area Product (BTU/°F-SEC)
HAF
Receiver Air Surface Film Coefficient (BTU/Ft 2-SEC-°F)
HRP
Receiver Pump Fractional Head
HRPO
Receiver Pump Steady-State Head (PSI)
Ioc
Downcomer Flow Inertia (PSI-SEC)
If
Riser Flow Inertia (PSI-SEC)
Ifi
Panel i Flow Inertia (PSI-SEC)
IR
Riser Inertia (PSI-SEC)
k
Thel·mal Conductivity (BTU/HR-ft- f)
K
Closed Loop Transfer Function Gain
Kc
Controller Proportional Gain (valve travel/°F)
KF.1
Panel i Steady-state Friction Drop (PSI)
KFHR
Riser Steady-state Friction Drop (PSI)
KRP
Receiver Pump Time Constant- 1 (SEC- 1 )
l
Flow Path Length (ft}
L
Process Dead Time (SEC)
LOGAR
Riser length/(g Area)
M
Mass (lbm)
m
Process Sensitivity (°F/unit valve position change)
!AI
Absolute Value of Mass F)ow (lbm/SEC)
A1
Mass Flow at Node Inlet(s) (lbm/SEC)
~-
Panel i Mass Flow (lbm/SEC)
A10
Panel i Steady-state
A0
Mass Flow at Node Outlet ( 1bm/SEC)
Mf
Fraction of Initial Mass Flow
1
0
(lbf SEC 2/lbm ft 2 )
t~ass
Flow (lbm/SE.C)
Viii
~··
f.1o
Initial Mass Flow (lbm/SEC)
,,, .
Panel i Mass Flow Fraction
MR
Riser Flow (lbm/SEC)
MRO
Steady-state Riser Flow (lbm/SEC)
MfDC
Downcomer Fractional Mass Flow
N
Normalized Receiver Pump Speed
Npp
Normalized Panel Power
Nu
Nusselt Number
Pov
Drag Valve Pressure Drop (PSI)
pf
Axial Panel Power Fraction
pp
Panel Power (BTU/SEC)
PLOGA
Panel Length/(g Area)(lbf-SEC 2/lbm-ft 2 )
PIR
Receiver Inlet Pressure (PSIA)
POCT
Cold Tank Ullage Pressure (PSIA)
POHT
Hot Tank Ullage Pressure (PSIA)
POR
Receiver Outlet Pressure (PSIA)
PO ROT
Receiver Outlet Tank Ullage Pressure (PSIA)
Pr
Prandtl Number
Q
Volumetric Flow (GPM)
Qa
Absorbed Solar Power (BTU/SEC)
Qc
Convective Receiver Losses (BTU/SEC)
Qi
Incident Solar Power (BTU/SEC)
Qr
Receiver Reradiated Power (BTU/SEC)
R
Process Reaction Rate (°F/SEC)
Rsp
Set Point ( F)
fl
0
ix
Re
Reynolds Number
Rp
Receiver Incident Power (BTU/SEC)
S
Laplace Transform Operator
SHoe
Downcomer Static Head (PSI)
SHi
Panel i Static Head (PSI)
T
Node Temperature (°F)
TA
Ambient A·ir Temperature ( F)
TCT
Cold Tank Sodium Temperature (°F)
TDVI
Drag Valve Inlet Sodium Temperature (°F)
TDVO
Drag Valve Outlet Sodium Temperature (°F)
T
9
Ti
Ground Temperature ( 0 R)
TN
Sodium Temperature (°F)
TNI
Receiver Sodium Node Inlet Temperature (°F)
TNO
Receiver Sodium Note Outlet Temperature (°F)
TNR
Riser Sodium Node Temperature (°F)
TNRI
Riser Sodium Node Inlet Temperature (°F)
TRPI
Receiver Pump Inlet Sodium Temperature (°F)
TRPO
Receiver Pump Outlet Sodium Temperature (°F)
T$
Sky Temperature ( 0 R)
TW
Receiver Tube Wall Node Temperature (°F)
U
V
Absorbed Solar Power (BTU/SEC)
Volume (ft 3)
VN
Sodium Node Volume (ft 3)
VP.1
Panel i Actual Control Valve Fractional Position
0
Panel i Sodium Outlet Temperature (°F)
X
VPOX;
Panel i Controller Demand Fractional Valve Position
Y
Temperature Deviation (°F)
Z
Process Time Constant (SEC)
a
Acceleration (ft/SEC 2 )
gc
Gravitation Constant (32.2 ft-lbf/lbrn-SEC 2 )
t
Time (SEC)
v
Velocity (ft/SEC)
GREEK
Tube Absorptivity
Error ( F)
0
n
p
Receiver Pump Fractional Efficiency
Dens·i ty ( 1bm/ft 3 )
Sodium Density (lbm/ft 3)
Water Density (lbm/ft 3)
p
Mean Density (lbm/ft 3)
a
Stefan-Boltzman Constant (BTU/SEC-ft 2- 0 R4)
Panel i, Controller Derivative Time Constant (SEC)
Controller Derivative Time Constant (SEC)
Panel Hydraulic Time Constant (SEC)
Controlle~
Integral Time Constant (SEC), Panel i
Receiver Pump Motor Torque (Normalized)
Receiver Pump Required Torque (Normalized)
Absolute Viscosity (lbm/ft-SEC)
xi
ABSTR1\CT
CONTROL SIMULATION OF
;11.
SODIUM-COOLED,
ADVANCED CENTRAL RECEIVER FOR A
SOLAR/ELECTRIC
PO~JER
PLANT
by
William W. Willcox
Master of Science in Engineering
1\
nun.erical dynamic simulation model of the thermal-·hydraulic
characteristics of a sodium-cooled advanced central receiver solar/
electric power plant has been developed.
The roodel was used to deter-
mine the optimum receiver temperature control system configuration.
Independent feedback control of each of the 24 t'eceiver panels was
found to be an adequate method of receiver outlet coolant temperature
control.
However, integral and derivative control modes, as well as
propoi''tional, are required for satisfactory response speed and accept·-
ab1e temperature offset.
The use of simple independent feedback loops
for contn; 1 does not cause any unusua 1 problems even though the panels
ar·e hydraulically coupled by a common feed and return lines.
The limits of controller stability were explored by increasing
the proportional control constant, Kc, in all the panels simultaneously.
The panels having the highest heat flux experienced
instability first as a result of inherently higher ratios of dead-time
xi i
~·-
to process-time constants.
Inducing instability in one panel does
not, however, affect the operation or control of the other panels.
Xii;
I.
INTRODUCTION
The central receiver solar/electric power plant has often been
identified as the solar power concept with the greatest potential for
commercial application by utilities (l).
This concept consists of a
tall tower surrounded by a large field of heliostats (mirrors) which
redirect the sun•s insolation to a receiver located at the top of the
tov1er.
face~
The receiver is cooled by a flu·id flowing parallel to its surusually contained in banks of tubes.
The receiver geometry can be either of two types.
The cavity type
admits the solar flux through an apperture and utilizes the inside surface of the receiver for energy absot'pt ·1 on ( 2) The extern a1 type uses
the outside of the receiver surface for absorption ( 3).
Several receiver coolants have been proposed for use in central
receivers.
The criteria for fluid selection is based on the power· con-
version system selected as well as economic considerations.
Brayton
Cycle solar/electric systems utilize air or some other gas as the
coolant ( 4 ). For conventional Rankine cycle systems, the natural
choice of receiver coolant is water ( 5).
However, water has several
disadvantages as a coolant in this application.
It is usually
vapor~
ized in the receiver at high pressures requiring thick receiver tubes
and two phase flow capabilities.
In the steam sections of the
receive~
the film-side heat transfer coefficient, which is relatively small, is
controll"ing.
Thet~efore,
precise control of the receiver incident flux
1
2
is required to prevent tube burn-out.
Storing and recovering the
thermal energy in steam is a difficult task usually resulting in low
efficiency conversion during non-solar operating hours.
Finally, high-
efficiency Rankine cycles which use re-heating are impractical due to
the long pipe length of the tower and the requirement to pipe steam
back up to the tower.
Single phase, high-boiling point fluids have been suggested as
alternate candidate receiver coolants in several advanced r'eceiver
studies.
These fluids can be used in the receiver at atmosphereic
level pr·essures, can run reheat cycles directly or from storage and
can accommodate a wider range of flux levels than water. The two
fluids currently under study are molten salt ( 6) and liquid sodium ( 3)
While both fluids are superior to water as heat transfer media, both
suffer from thei1n own disadvantages.
caution in handling.
Both require extraordinary
Both require salt or sodium-to-water heat
exchangers (steam generators).
Sodium and water can react energeti-
cally, requiring great care in their handling when in prox·imity-to one
another'.
Salts are generally very corrosive in the presence of air.
While the heat transfer properties of sodium and salt are superior to
water, both are solid at room temperatures, requiring piping trace
heating.
Regardless of the fluid selected as receiver coolant, the
temperature control of all receivers is critical.
Most central
receivers operate with outlet temperatures in the neighborhood of
1000°F ( 3)(S)(G), necessitating the use of high temperature alloys as
materials of construction.
These alloys usually have relatively low
thel~ma1
conductivities and, unless they are thin, are subject to
severe thermal stress problems, particularly when subjected to thermal
transients.
Also
l~eceiver
downcomer pipes are subject to thermal
shock if the receiver thermal control system fails.
A common flow distribution scheme for centr·al receivers is a
single feed pipe or riser which feeds several parallel flow panels of
many tubes through a distribution manifold ( 3)( 6). The panel flows are
joined in a collection manifold at the receiver exit and from there a
downcomer carries the heated fluid to the base of the tower to the
thermal storage and/or energy conversion subsystems.
A control system
designed to maintain a constant outlet temperature for such a receiver
raises some interesting questions.
The panels and their tubes are configured in parallel and,
therefore, coupled hydraulically but not thermally.
raises some serious questions.
This coupling also
Is it possible that flow perturbations,
due to any cause, in one or more of the panels could feed back to the
other panels and cause limit cycle or unstable behavior? What kind of
control scheme is required to prevent unstable behavior?
Since the
receiver system is non-linear, these questions would be difficult to
answer in an analytically quantitative manner.
Therefore, a numerical
model is proposed to be used as a tool to answer these questions.
As
a side benefit, this model can be used to study other items of interest
such as system transient behavior and stress analysis.
A sodium-cooled system has been selected for specific study for
several reasons:
(1) The relatively high thermal conductivity and
film coefficients of sodium produce rapid thermal equilibrium in the
4
components which contain it.
This greatly simplifies the model by
allowing the use of one-dimensional equations.
(2) This rapid thermal
equilibrium also produces the highest magnitudes of component thermal
shock which solar central receivers might encounter.
(3) The sodium
system will be subjected to the highest solar heat flux of any central
receiver so as to take advantage of its heat transfer properties (l)
For these reasons, the sodium system will be exposed to the most severe
operating environment and is, therefore, of greater interest than a
molten salt system.
A water/steam central receiver has already been
simulated as part of a previous program (S) and is, therefore, not considered here.
A.
Objectives_ and
Pm~pose
The primary objective of this project is to investigate proportional temperature control of a solar-heated central receiver, cooled
by a non-vaporizing fluid.
A secondary objective is to extend the
study to inc1ude derivative and integral controller action.
The results of this study should be applicable to other parallel
flow, single phase, common feed and return processes, and should provide insight into the transient behavior of such processes.
The purpose of this study is to prove that advanced central
receivers require only simple, easily-understood control schemes, which
will allow safe operation even under extreme solar flux transient
conditions.
<K:0'·
B.
Advanced Central Receiver
~ystem
Description
A simplified flow and control diagram of the conceptual configuration of a 100-MWe Sodium-Cooled Advanced Central Receiver Power
System is shown in Figure l.
In th·is s_ystems liquid sodium is pumped
{P-1) from a cold tank (T-1) through 24 solar receiver panels to a hot
tank (T-·2).
Sodium is heated in the receiver by solar insolation
reflected by a large number of heliostats which surround the receiver
tower.
From the hot tank (T-2), sodium is pumped (P-2) through a
superheater (X-2) and rehcater (X-3), which are configured for parallel
sodium flow, to an evaporator (X-1) and finally back to the cold tank
(. ·r -I- 'J • Under conditions of full solar insolation, the flow through the
steam generators (evaporator, superheater, reheater) is about 2/3 of
the receiver flow.
Thus, 1/3 of the receiver flow accumulates in the
hot tank during the day for use at night.
Steam, generated from
sensible heat released by the sodium in the steam generators, is used
to drive a three-stage steam turbine in conjunction with a conventional
Rankine cycle.
Some of the process values and component sizes are
shown in Figure 1.
A more detailed description of the sodium-cooled
advanced central receiver system is contained in Reference 9.
C.
For purposes of developing
Model Scope
~
meaningful representation of the
Sodium-Cooled Advanced Central Receiver Power System, on1y the normally
active sodium components physically located in the flow stream between
the cold and hot tanks are included in the model.
The large mass
capacity of the hot and cold tanks effectively isolates the receiver
ADVANCED CENTRAL RECEIVER
( 1(JO 11We}
T-1 & T-2
:'-1
II ( 597) 182
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P-MN/m (psi)
1-m {ft)
0 - m (ft)
£ - MH (hr)
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T-341(646}
P-17 {2400)
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X-2
SUPERIIEAHR
538 ( 1000}
15 (2200)
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X-3
REiiEATER
538 ( 1000)
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Hli!-220 (722)
f - 1:3 (20)
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P-2
STORAGE TANKS
RE Gg l \lE R_f!!MP
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F•ftOI'l
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m· /S(l03y}
J- PowH\
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--{X}----l.,._.c~~~~~
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Figure l.
Si•i'f,l~H!ed
flow and Control Olagram
~
7
and its associated components from the steam gener·ation equipment.
Consequently, it is cost effective to cons.ider the receiver and its
equipment separately since the outlet temperature variation of the
hot tank and cold tank are insignificant.
The components comprising the model include the cold tank,
receiver pump, riser check
valve~
riser piping, panel control valves,
24 rece·iver panels and associated manifolding, panel flow controllerss
receiver outlet surge tank, surge tank level controller, downcomer
piping, drag valve, and hot tank.
Minor pressure drags associated
with pipes and valves used for filling or draining receiver equipment
have been omitted from the model for simplicity, but they could be
included in future studies.
Solar flux profiles at the receiver surface were adapted from
Reference 9.
D.
Literature Search
Under contract to the Department of Energy, DOE (formerly
the Energy Research and Development Administration, ERDA), McDonnell
Douglas Co. is developing a water/steam central receiver solar power
plant.
As part of the contract, a detailed modeling effort was under-
taken to simulate the plant using a hybrid digital analog computer (B).
In the McDonnell Douglas study, the controlled variables consisted of
receiver panel outlet temperature and pressure.
Also, only 2 receiver
panels were needed to simulate receiver response since detailed consideration of the receiver and its controller mechanisms were unimportant.
The result of the McDonnell Douglas study indicated that individual-
8
panel, proportional-only control was adequate for a dual phase solar
receiver.
An extrapolation of these results suggests that individual-
panel control may also be applicable to sodium receivers.
II.
MODEL DESCRIPTION
A.
CSMP
The Advanced Central Receiver (ACR) Sodium Cooled Solar Electric
Power Plant was modeled using International Business Machine's Continuous System Modeling Program ( CSMP) (ll).
CSMP is a program designed to
solve coupled sets of ordinary differential equations implicitly.
If
a system of differential equations is expressed in terms of time, then
CSMP will simulate the response of the system to various perturbations
in boundary and initial conditions, much like an analog computer.
A variety of integration routines are available to the CSMP user,
ranging from the single-step trapezoidal method to fourth-order RungeKutta methods and include several multiple-step methods.
Naturally,
the more stable, sophisticated methods require more computer time per
solution and are, consequently, more expensive.
This comnon dilewma
requires that the user trade off model accuracy against simulation
cost.
The size of the ACR model, in terms of finite element nodes,
requires that the integration method be among the most efficient so
that cost-effective runs can be made.
The CSMP format requires th.at the model be expressed in three
parts:
initial, dynamic, and terminal.
Boundary and initial condi-
tions are input directly or calculated in the first section called
11
INITIAL. 11
The coupled differential equations and intermediate calcu-
lations are contained in a section entitled
9
11
DYNAMIC. 11
Solution
10
monitoring, time step changes, and output instructions are located in
the 11 TERMINAL 11 section.
Subroutines, called MACRO•s in CSMP, are
physically located prior to the INITIAL section and can be called from
either the INITIAL or DYNAMIC sections as required.
CSMP also has a
table look-up capability with several interpolation options.
A full
description of CSMP is well beyond the scope of this report.
The
interested reader is referred to Reference 11 for more detailed CSMP
information.
It is hoped that the foregoing discussion will allow a
reasonable understanding of CSMP such that the computer program source
listing in the appendix will be understandable.
B.
Model Features, General DescriQtion and Assumptions
For purposes of thermal analyses, certain large components of
the ACR system, contained within the previously described scope, are
divided into finite elements, and each element represented by a node.
A nodal diagram is shown in Figure 2.
The components which are so
divided include the receiver, the receiver rising piping, and the
receiver downcomer piping.
The hot and cold storage tanks, the re-
ceiver outlet tank, the receiver pump, and suction pipe and the drag
valve, as well as the dischrage pipe, are all treated as single nodes.
The receiver panels are divided into 3 equal-volume sodium
(coolant) nodes and 3 equal-volume receiver tube wall nodes.
As shown
in Figure 2, each sodium node is associated with one tubing node.
The receiver riser pipe is divided into 10 equal axial sodium
nodes which are considered to be ideally insulated.
Each axinl node•s
<7\0'·
11
FLOW FROM OTHER PANELS
---.--•
SURGE
T/\tiK
------,
I
DOWNCOMER
I PIPING
I
SOLAR
-INSOLATION
PAIIEL
FLOW
r..J.._,
l
r -1-l
1
CONTROL~ ...I
LT..J
I
I
FlOW TO OTHER PANELS
I
I
___ .JI
I
PANEL CONTROL
VALVE (typical}
SURGE TAIIK
CONTROLLER
I ~EVEL
I
DRAG VALVE
TO STEAH
GENEHfl iOR
RISER PIPING
CHECK VALVE
~
Figure 2.
HOT TANK
RECEIVER
PUMP
-vt-Q---
PUMP
FROM SHAM
GENERATOR
COLD TANK
Advanced Central Receiver
Transient Model Schematic
12
response is determined by fir·st order dynamics and is subject to
input only from the upstream sodium node. ·
The receiver downcomer is similarly divided into five axial sodium
nodes.
The characteristic time constraints of the riser and downcomer
nodes are variable as the hydraulic conditions of the system change.
The receiver hydraulics section of the model is more complicated.
In the riser and downcomer, flow is considered possible only in one
direction.
However, the receiver panels, each of which is modeled, can
experience flow reversals if the receiver is isolated from the pump and
hot tank.
Thus, each receiver panel model subsection has reverse flow
thermal as well as hydraulic capabilities.
Each panel is considered
to be thermally independent (i.e., ideally insulated back and sides)
along its length, but is hydraulically coupled at each end.
Thus,
panel thermal interaction is due totally to hydraulically-coupled
perturbations.
Each receiver panel is subdivided into three axial sections, each
section consisting of a tubing or wall node and a sodium node.
The
differential equation describing each node's temperature is derived
from an energy balance taken around each node.
Thermal losses from
the wall nodes include reflection, reradiation to ground and sky, and
convection to air.
Conduction lnsses from the sodium and tubing wall
nodes have been neglected in the energy balances for the receiver
nodes.
In spite of the 550°F axial gradiant along the sodium path and
the excellent thermal conductivity of sodium, the calculated magnitude
of heat transferred is less than 0.1% of the convected heat losses due
13
to the limited sodium flow area.
The tubing nodes have even less
available conduction area.
A significant question regarding the receiver concerns the
magnitude of the convective heat loss from the receiver as a function
of 1t1ind speed and direction.
The Reynolds and Prandtl numbers associ-
ated with the wind velocities of interest (0-40 mph) are outside the
normal ranges for which Nusselt numbers and, consequently, film heat
transfer coefficients have been previously determined.
Achenbach
addresses the determination of heat transfer coefficients as a function
of circumferential position on the surface of a cylinder in crossflow
( 12 )
The Reynolds number range of interest vJas 2 x 10 4 to 4 x 10 6 .
However, for the advanced central receiver, the applicable Reynolds
number range is 0 to 6.13 x 10 6 , with a Reynolds number of 4 x 10 6
corresponding to wind velocities of 24 mph.
Consequently, due to the
large diameter of the receiver and the low viscosity of air, overall
heat transfer coefficients as well as local coefficients are difficult
to estimate from the literature. Consequently, a detailed study (l 3)
was undertaken as part of the sodium-cooled advanced central receiver
program to estimate the magnitude of the natural plus forced convection
heat losses from the receiver and, consequently, the heat transfer
coefficient.
The results of this study suggest that for a nominal
wind velocity in the range of interest, an overall film coefficient of
1.5 BTU/HR FT 2°F is reasonable. When this value is adopted, the nominal convected losses are less than 20% of the total losses.
Under the
conditions of interest, the nominal total losses are then about 10% of
14
the incident insolation, including reflective and reradiative losses.
Consequently, it was concluded that the convective losses would be
less than 2% of incident power and, therefore, of marginal magnitude.
Nevertheless, the overall coefficient suggested previously was incorporated into the model for completeness.
As mentioned previously, the synthesization of the receiver flux
profile is considered outside the scope of this model.
However, Raiz
and Gurr give the methodology for obtaining a closed form solution to
the problem of flux profile as functions of heliostat field configuration, time of day and aiming strategy (l 4 ). The actual profile used
in the model simulations was developed as part of the advanced central
receiver program and is documented in References 9 and 15.
The incident receiver flux can also be circumferentially,
axially~
or time varied to simulate heliostat field design variations,
cloud cover passage, or the effect of various aim point strategies.
Panel wall node physical properties are assumed constant, but sodium
properties and film coefficients are allowed to vary within temperature and flow.
Each receiver panel is assumed to empty into the receiver outlet
tank.
The
outlet~
as well as the hot and
cold~
tanks are assumed to
be ideally mixed.
Temperature rises of the sodium due to inefficiencies in the
receiver pump and pressure drop in the drag valve are considered and
included in the model.
Changes in these pressure differentials are
assumed to occur instantaneously.
15
For purposes of hydraulic simulation, three flow sections are
considered.
The first section runs from the cold tank surface to the
receiver inlet header, where the sodium flow splits to each panel.
The second section simulates the sodium flow through each receiver
panel where the sodium is heated.
The third section considers the
sodium flow from the receiver outlet tank to the hot tank.
For each section, the derivative of the flow is determined from
a force balance around that section.
This method can accommodate
reverse flow without methodology modification.
One force balance is
required for each panel as well as the receiver upstream and downstream
sections.
At the interface of the receiver and its upstream section
(i.e., the receiver inlet manifold), no free surface and,
no arbitrary pt·essure exists.
thet~efore,
Therefore, the continuity equation must
be utilized to obtain the pressure at this point.
Pressure drops are
neglected in the receiver inlet and outlet manifolds for simplicity.
For purposes of panel flow and receiver outlet tank level control,
Proportional plus Integral (reset) plus Derivative control schemes are
available.
Any combination of the above can be selected.
The problem
of integral wind-ups wherein the demanded valve position is greater
than open or less than closed is resolved in the model through the use
of appropriate logic.
Valve pressure drop is calculated by means of
standard equations developed by Kern (l 6 ) for subcritical flow.
16
C.
1.
Thermal
Specific Equations
(See Section 3.3 of the computer program listing~
Appendix for detailed implementation and nomenclature)
All nodal temperatures are determined by integr·ating the time
derivative of the temperature developed from a first law or energy
balance equation for each node, generally given by the following
equation:
Accumulation of}
within
{energy
the system
Transfer of
}
}
Transfer of
_ energy out of the
energy into the
{system through
( 17)
{system through
system boundary
system boundary
Energy generaEnergy consurnp-1
- {tion within the
+ {tion within thej
(1)
system
system
=
1
Since there is no significant internal generation or consumption in
any of the nodes, the last two terms are zero.
For a given node, the
term on the left side of the equation becomes:
Accumulat·ion = dMTCp/dt,
(2)
where:
M
= mass
of node (lbm),
T =temperature of node (°F),
Cp
t
=
heat capacity of node (BTU/1 bm -
0
F),
=time (SEC).
In all cases, the Cp of the node is assumed constant for at least each
time step, thus Equation 2 becomes,
Accumulation = CpdMT/dt.
(3)
In most cases, the volume of the node is fixed and the density
assumed to be constant over the time interval of interest.
Hence,
<i'f>'·
Equation 3 becomes:
Accumulation = MCpdT/dt.
(4)
Tanks, which are either draining and filling and, therefore,
subject to changing volume and mass, are simulated by Equation 2 as:
Accumulation
The
right~hand
==
Cp(TdM/dt + MdT/dt)
terms of Equation
1~
( 5)
including energy transfer to
and from the system, depend upon the node location and will be considered on an individual basis below.
a.
~eceiver
Tube Nodes (See Section 3.3.1.1, Appendix)
Solar energy absorbed by the nodes is given by:
Qa
= Qia
- Qr - Qc,
(6)
\vhere:
Qa -
Incident power absorbed (BTU/SEC),
Qi
- Incident power (BTU/SEC),
a
= Tube Absorptivity (constant),
Qr = Reradiated power (BTU/SEC),
Qc = Convect1on power losses (BTU/SEC).
Qi, the receiver incident power, is determined by:
(7)
where:
Pp =Circumferential varying panel power (BTU/SEC),
Pp
= Rp X Npp'
Rp =Total receiver power (BTU/SEC),
N
PP
= Panel power fraction,
Pf = Axial position power fraction.
(8)
- --- - """"'
--
---
-
----- - -
-~---
--
--
-
18
Qr, the receiver
power, is given by the equation:
4
4
Qr = [aoArr([T + 460] - Tg 4 ) + '{[T + 460] - Ts 4 )]/2,
rel~adiated
(9)
where:
= Stefan-Boltzman Constant (BTU/SEC-ft 2-oR4 ),
= Node reradiation area (ft 2 ),
=Ground temperature ( R),
0
=Sky temperature ( 0 R).
The factor of l/2 in Equation 9 is the view factor used for sky
and. ground radiation. Qc' the receiver convection loss, is given by
Equation 10:
Qc = HFA x Arr (T- TA),
( 10)
where:
HfA = Receiver outside surface film coefficient
(BTU/ft 2-SEC-°F),
· TA
= Ambient Air Temperature
(oF).
Energy transferred from the tube nodes to the sodium is given by the
following:
Energy transferred= HARN (T- TN)'
(11)
where:
HARN
= Sodium film coefficient (variable) (calculated from
Seban-Shimizaki correlation in a macro) x tube
sodium side area (BTU/°F-SEC),
TN
= Sodium temperature (°F).
Combining Equations 4, 6, and 11 yields the equation for the
derivative of tube wall temperature:
---~~-
19
dTw/dt = [Qa- HARN (TW- TN)]/(MCp),
( 12)
where:
Tw = Temperature of the tubing wall (°F).
b.
Receiver Sodium Note Temperature_ (See Section 3.3.1.2, Appendix)
The energy transferred to a receiver sodium node is equal to the
energy transferred from the adjacent receiver tubing node and is
described by Equation ll.
Enet~gy transfet~red
from the sodium node by sensible heat gain of
the sod·ium leaving the node is given by the following:
Energy transfer-red fl~om system= 1~11 Cp (TNI- TNO),
(13)
where:
IMI
= Absolute value of fl ov1 of sodium through node
(lbm/SEC),
Cp = Sodium heat capacity (BTU/lbm- °F),
TNI = Sodium node inlet temperature (°F),
TNO =TN= Sodium node outlet temperature (°F).
If the fluid flow in any panel reverses, the physical inlet to
the node changes.
To accommodate this, the inlet temperature of each
sodium node is selected by an input switch function depending on the
fluid flow direction.
Each sodium node is assumed to mix
ide~lly,
resulting in a uniform node temperature equal to the outlet temperature.
Utilization of the absolute value of flow keeps the sense of
direction of energy flow correct since the inlet-outlet temperature
difference provides the driving potential and energy direction sign.
20
Combining Equations 4, 11, and 13 yields the expression for the
derivative of a receiver sodium node:
where:
')
VN
c.
(ft...~),
PN
=Volume of the sodium node
= Sodium density (lbm/ft 3),
Cp
= Sodium heat capacity (BTU/1 bm -
TN
~Sodium
0
F},
temperature (°F).
Riser Pi,2·ing (See Section 3.3.2.2, Appendix)
The equation describing the derivative of the outlet temperature,
TNR' of each riser piping node follows:
dTNR/dt
=
1~11/M (TNRI - TNR),
( 15)
where:
TNR =Riser node sodium outlet temperature (°F).
TNRI =Riser node sodium inlet temperature (°F).
This is the classical equation describing a first-order lag-type
dynamic situation; however, the time constant is allowed to vary with
the flow.
d.
This provides a more accurate picture of the riser dynamics.
R~ceiver Pum~
(See Section 3.3.2.3, Appendix)
The temperature rise due tQ viscous heating is assumed to be a
quasi-steady-state phenomenon.
The equation describing the outlet
temperature is as fo 11 ows:
TRPO = TRPI - [HRP/pCp](l - l/n)(l44/778)HRPO;
(16)
21
where:
TRPO = Receiver pump outlet temperature (°F),
TRPI =Receiver pump inlet temperature (°F),
n
=Receiver pump hydraulic efficiency (fractional),
HRP = Receiver pump head fraction,
HRPO = Steady-state receiver pump head (PSI).
The receiver pump efficiency is assumed to be .75 of the normali zed pump sodi urn fl O\'J.
e.
Col1-T~nk-to-Receiver
Pump (See Section 3.3.2.4, Appendix)
The cold-tank-to-receiver pump piping temperature dynamics are
similar to the riser dynamics.
The equation
describing the dynamics
is similar to equation 15.
f.
f9ld Tank (See Section 3.2.1.1.3, Appendix)
Since the level of the cold tank is variable, the changing mass of
the cold tank must be accounted for, as noted in Equation 5.
The
equation for the cold tank outlet temperature derivative is as follows:
( 17)
where:
TCT = Cold tank temperature (°F),
M.1
=Cold tank sodium inlet flow (lbm/SEC),
T.1
= Cold tank sodium inlet temperature (°F),
M0
= Cold tank sodium outlet flow (lbm/SEC).
The derivative dM/dt is determined from the continuity equation (see
Equation 37).
22
g.
Downcomer Pipi!Ul (See Section 3.3.2.6, Appendix)
The downcomer piping node temperature· equations are the same as
the riser equation.
h.
Pr~ssure
See Equation 15.
Reducing Device (See Section 3.3.2.7, Appendix)
The viscous heating of sodium due to pressure drop across the
drag valve is assumed to be a quasi-steady-state process similar to
the rise across the receiver pump.
However, in this case, all of the
pressure drop is converted to heat by the following equation:
TDVO = TDVI + PDV x l44/(778pCp),
(18)
\'/here:
Tovo = Drag valve outlet temperature (°F),
TDVI = Drag valve inlet temperature (°F),
Pov = Drag valve pressure drop (°F).
i.
Ho1_l~~k
(See Section 3.2.1.9, Appendix)
The hot tank temperature derivative equation is similar to the
cold tank equation.
j.
See Equation 17.
Pressure-Reducing Device to Hot Tank (See Section 3.2.1.8, Appendix)
The hot tank inlet temperature piping equation is similar to the
cold tank equation.
k.
Sodium
~1m
See Equation 15.
Coefficients and Properties (See Section 3.1, Appendix)
The sodium film coefficients for all sodium convective heat
transfer in the receiver is determined by the Seban-Shimazaki carrel at ion:
~
---~----·-
-----
C';0'·
---~
---- -- ---·----
------· -------
23
Nu = 5.0 + 0.025(RePr)· 8 ,
Ct 9)
where:
Nu = Nusselt Number,
HD
Nu = K'
H = Film coefficient (BTU/HR-ft 2-°F),
D =Tube diameter (ft),
k
Re
Pr
. I
= Sodium thermal conductivity
= Reynolds Number,
= Prandtl Number.
{BTU/HR-ft-°F),
This corre·lation includes thermal conductivity and is useful at low
flows.
Sodium properties are determined from correlations supplied by
Yunker (lB).
The correlation for heat capacity follows:
Cp = 0.364 - 0.792 X 10-4 (T + 460) + 0.341 x l0- 7(T + 460) 2 .
{20)
The correlation for thermal conductivity is:
k = 54.306- 0.01878(T + 460) + 2.09 x l0- 6(T + 460) 2 .
(21}
The correlation for viscosity is:
lnll
=
1.0203 + 397.17/(T + 460)- 0.4925 ln (T + 460).
(22)
All of the above correlations are handled as macro statements, which
are called as required from the DYNAMIC sections.
These macro state-
ments are physically located in program Section 1.0.
2.
Hydraulic~
(See Section 3.2, Appendix)
The fluid flow in a given flow channel is determined by integrating fluid acceleration as determined by a force balance between
two points in the flow path.
The general equation is:
Z::F
= Ma,
(23)
24
where:
r.F
= Summation of the forces exerted on the fluid (lbf),
M = Mass of Sodium between Points 1 and 2 (lbm),
a = Acceleration of fluid between Points l and 2, which
is given by:
a= dv/dt
(ft/SEC 2 ).
(24)
Instantaneous velocity is given by:
v
= M/pA,
(25)
noting that the mass of the fluid accelerated is given by:
M = pAl,
(26)
where:
v =fluid velocity (ft/SEC)~
A - Flow area (ft 2 ),
l
= Flow path length (ft),
and combining Equations 23, 25, and 26 yields:
pAld(M/pA)/dt
= r.F.
(27)
p and A are assumed constant and Equation 27 becomes:
ldM/dt = r.F.
Dividing (28) by gcA to convert to
fo1~ce
(28)
per unit flow area and lbf to
lbm yields the expression for flow acceleration:
dM/ dt
= ( gA/ 1 ) r. F.
(29)
where,
gc =acceleration due to gravity (32.2 ft/SEC 2).
It is often numerically convenient to express the flow referenced to
steady-state as a fraction:
25
(30)
where:
~f
~O
= Fraction of reference
= Reference flow.
flow,
Substituting Equation 30 into 29 and dividing through by
M
yields the form of Equation 29 used in the model:
d~f/dt
= (gA/LM0)EF,
(31)
g, A, L and M0 are constants or initial conditions and are lumped
into a term called the flow inertia:
( 31 a)
where,
If
a.
= Flow
inertia.
Receiver Panel and Riser Flow (See Section 3.2.1.1, Appendix)
For any receiver panel, the inlet pressure is the same as any
other panel since all panels start from a common point and manifold
losses are assumed to be negligible.
outlet pressure.
The same is true for the receiver
The equation for the ith panel is as follows:
dMf./dt
1
= (PIR-
POR - FH.1 - DPCV.1 - SH.)/If
.,
1
1
where:
PIR = Comnon panel inlet pressure (PSIA),
POR
= Common
FH.1
=
Panel i friction head (PSI),
OPCVi
=
Panel i control valve head (PSI),
SH.1
=
Panel i static head (PSI),
Mfi
::::
Panel i flow fraction,
panel outlet pressure (PSIA),
(32)
I
26
Ifi =Panel i inertia (PSI-SEC).
POR is determined from the static head in the receiver outlet
tank.
Each panel friction head is approximated by the following:
FH.1
(33)
where:
KF.1 =Steady-state flow friction drop (PSI).
The absolute value function causes the sign of the friction drop to
automatically change during panel flow reversal.
The expression for control valve head is given by:
2
DPCVi = tw Q!QI/CVC ,
(34)
where:
pfpw
= Specific gravity of sodium,
Q =Sodium volumetric flow (GPM),
CVC
~
Control valve flow coefficient (GPM/PSI),
(See control model description).
The equation for panel static head follows:
(35)
where:
Panel outlet elevation,
E
=
E.
= Panel inlet elevation,
p
= Average panel sodium density.
0
1
The riser flow equation is written in a manner similar to the
panel flow equations,
However, only one equation is required.
The
equation is as follows:
dMf _
-dt -· (POCT - PIR + (E.1
(36)
- --
-
-
-"-
. ~-'.'.:
-
-
- - -
27
where:
POCT
~
E1
- Cold tank level elevation {ft),
E0
=Receiver inlet elevation (ft),
Ullage pressure of cold tank (PSIA),
KFHR = Steady-state riser friction drop (PSI),
= Receiver pump
= Riser inertia
HRP
IR
b.
Receive~
head (PSI),
(PSI-SEC).
Outlet Tank, Cold Tank, and Hot Tank (See Sections
3. 2. 1 . l . 2, . 3 and
.7, Appendix)
In these sections, the time varying inventories and levels are
determined by integration of the continuity equation:
dM/dt = t:~l.1 - t:M0 .
c.
gecei~~_p~m£
(37)
(See Section 3.2.1 .1.4, Appendix)
The receiver pump speed is determined by integr·ating Equation 38:
(38)
KRP
= Receiver pump speed (normalized),
= l/receiver pump inertia (1/PSI-SEC),
Tm
= Receiver pump motor output torque (normalized
N
to steady-state_ torque),
TP
= Receiver
pump torque required (normalized to
steady-state torque).
The expression for required receiver pump torque was determined
by fitting the speed-torque-flow curves for a typical sodium pump.
The
expl~ession
follows:
28
(39)
where:
c1 , c2,
and
c3
are the coefficients required to fit the
speed-torque-flow curve.
Similarly, the expression for
receiver pump head is as follows:
2
•
• 2
HRP = c1N + C2NMf + C3Mf ,
(40)
where:
c1 , c2 ,
and
c3
are the coefficients required to fit the
speed-flow-head curve characteristics of the modeled
receiver pump.
The receiver pump head is limited to 120%
of the design head.
d.
Ris~r
Pressure (See Section 3.2.1.1.5, Appendix)
Determining the riser outlet/receiver inlet pressure is critical
to the solution of Equations 32 and 36.
This pressure is determined
from the derivative of the continuity equation:
24
= L:mi,
r\
(41)
i =1
where:
MR
.
m.
1
= Riser flow (lbm/SEC),
= Panel i flow (lbm/SEC).
Taking the derivative of Equation 41 yields:
24
24
dMR;dt- d(L:m.)/dt = L:dm./dt.
1. = 11
. 1 1
1=
(42)
The left side of Equation 42, when expanded, is similar to
Equation 36.
When expanded, the right side of Equation 42 is similar
to Equation 32.
The differences are due to Equations 32 and 36 being
29
f:•
expressed as normalized flow.
by
When Equations 32 and 36 are multiplied
the reference flow and substituted into· Equation 42, the result has
this appearance:
(POCT + [E; - E0 )p/l44- MfiMfiKFHR; HRP)/LOGAR +
24
E(PIR • POR- FH. - DPCV. - SH.)/PLOGA,
i=l
1
1
1
(43)
where:
LOGAR = IRMRO,
(44)
PLOGA = IfiMiO.
(45)
Solving Equation 43 for the receiver
24
PIR ~ [(24 x POR + LSH.1 +
i=l
inlet pressure yields:
24
24
EFH.1 + ~DPCV.)/PLOGA
+
1
i=l
i=l
(POCT + [Ei - E0 ]p/144- Mf!Mf!KFHR + HRP/LOGAR]/
(24/PLOGA + l LOGAR),
which is the form used in the model.
(46)
Equation 46 is not used at very·
low or zero riser flow due to numerical methods considerations.
At
low flow, Equation 46 is simplified to the following form:
24
PIR = L[(FH. + SH. + DPCV.)]/24 + POR.
i==l
1
1
1
3.
(47)
Downcomer Flow (See Section 3.2.1. 1.6, Appendix)
The force balance used to describe the downcomer flow is taken
between the receiver outlet tank surface and the hot tank surface.
expression follows:
where:
The
'
30
I'
\</here:
MfDC = Downcomer fractional flow,
POROT = Receiver outlet take ullage pressure (PSIA),
POHT = Hot tank ullage pressure (PSIA),
FHoc = Downcomer friction head (PSI),
DPov = Drag valve head (PSI),
SHoe = Down comer static head (PSI),
Inc
= Dmmcomer inertia (PSI-SEC).
The equations describing the friction, static and drag valve
heads are the same as those used in the panel friction, static, and
control valve heads.
3.
Plant Protection and Control System (See Section 3.4, Appendix)
The plant protection and control model consists of receiver panel
controllers and a drag valve controller.
Each controller model has
the capability of simulating any combinations of all three control
modes {proportional, integral, or derivative).
a.
Recejve~
Panel Controllers (See Section 3.4.1, Appendix
The valve position demanded by a given controller is fundamentally
expressed as a function of receiver outlet panel temperature error.
This is the equation:
t
VPOX. = JEIR; x Kc;f-r; dt + KCT 0 .dT;fdt + KcET.,
1
0
1
.
1
(49)
where:
VPOXi = Valve position demanded by controller· for panel i
(fraction of open),
.
EIR; = integral error of Panel i (oF),
ET for O<VPOX.<l,
:::
1
=
0 for l<VPOX.<O,
1
(prevents integral windup)
Kc.1
= Proportional
constant for Panel i controller (valve
openingrF),
= Integral time (1/reset rate) Panel
T·
1
TO.
i controller (SEC),
= Derivative time, Panel i controller (SEC),
1
T.1
- Panel i outlet temperature (°F),
ET i
= Panel i outlet temperature error ( 0 F).
In addition to Equation 49, the outlet temperature of each panel
is processed by
lag.
fii~st-order
dynamics to simulate thermocouple signal
Also, the demanded valve position is also processed by first-
order dynamics to simulate the valve actuator.
The flow coefficient
for each va 1ve is determined from the fo11 owing equation:
eve= .025e( 3· 67 x VP;)ev.,
(50)
1
where:
VP.1
=Actual valve position, Panel i (fraction open),
ev.1 = Design valve flow coefficient, Panel
Equal percentage valves are used, and Equation 50
i (GPM/PSI).
i~
a curve fit
from Reference 19 describing flow coefficient as a function of valve
position.
b.
Pressure Reducing Device
Controlle~
(See Section 3.4.2, Appendix)
The equations describing the drag valve controller response are
similar to those describing the panel valve controllers.
The only
32
difference is that the error is provided by the level of the receiver
outlet tank.
4.
Boundary and Initial Conditions (See Section 2, Appendix)
This section inputs known constants and calculates boundary and
initial conditions.
Initial conditions used in integrals in the
dynamic section are calculated using equations similar to the various
differential equations but with the time derivatives set to zero.
For
example, a typical receiver tubing node temperature, Tw, is
TW = Qa/HARN =TN
(51)
The steady-state sodium node temperatures, TN' must be calculated
implicitly.
Guesses of sodium node temperatures are input and the true
values are determined by converging on the correct value of Qa' using
the method of successive substitution.
v!hile the method of successive
substitution is not guaranteed to converge, it is rapid when the initial guesses are accurate.
In most cases, iterative processes are not
required to determine boundary and initial conditions since the required inputs have been previously determined.
The numbering system
of the initial section is keyed to that of the dynamic section.
Hence,
the boundary and initial conditions required by Section 3.3.2.6 are
contained in Section 2.3.2.6.
A listing of the model followed by a
variable and function index, defining all variable and function names
and units, is located in the Appendix.
Inputs of all initial and
boundary conditions were obtained from Reference 9.
I I I.
RESULTS
The response of the previously described model, configured for
proportional-only individual
t~eceiver
panel control, to a 10% step
decrease in incident receiver flux is shown in Figures 3-6.
The step
was initiated subsequent to 5 seconds of steady-state operation.
The
duration of the run was 100 seconds.
Figure 3 shows the overall receiver input and response.
CRT
Frames 1 and 2 show the overall incident and absorbed solar power, QI
and QA, as functions of time.
The overall receiver response is repre-
sented by the time histories of total· receiver flow, WN, and receiver
outlet tank temperature, TNRO, in the last two frames.
The five curves
of each frame in this transient represent five values of prop6rtional
controller gain, Kc.
Curve 1 represents the smallest gain while
Curve 5 represents the largest.
Curve 3 represents the optimum.
Figures 4-6 show representative panel responses for the South,
West, and North panels, respectively.
The West panel response is also
a valid representation of the East panel response since the circumferential flux distribution is symmetric about the North-South diameter
of the receiver.
Frame l of Figures 4-6 shows the incident panel power, PP(i),
versus time.
Frame 2 is the fractional control valve position, VP(i).
Frame 3 is the normalized panel flow, WNR(i).
33
Panel outlet
34
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Figure 3
Overall Proportional Response to Step Flux Change
35
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Figure 4
South Panel Proportional Response to Step Flux Change
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North Panel Proportional Response to Step Flux Change
r
38
temperature, TNR3(i), as a function of time is shown in the last frame
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Figures 7-10 show the overall and individual panel response of a
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Figures 3-6.
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and time constants has been used.
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IV.
DISCUSSION OF RESULTS
The search for the optimum controller mode, gain, and time constants was initiated by simulating the simplest control mode first.
A
control system which used only proportional control was selected by
disabling the integral and derivative functions of the controller in
the model.
A trial-and-error search routine could have been used to determine
the optimum ga·in for each controller.
been extremely time-consuming.
Cohen and Coon ( 20)
However, this method would have
An alternative method is suggested by
The Cohen and Coon method arrives at the optimum gain by subjecting each panel feedback loop to the following procedure.
1.
The loop is opened thereby eliminating feedback control.
2.
A small step change in demanded valve position is applied
to the loop, initially at some equilibrium condition.
3.
The measured response of the system is monitored until the
response reaches some new ultimate value.
A representative block diagram of the measured system is shown in
Figure 11 .
If the open loop behavior is sufficiently similar to a firstorder response with a transportation lag, the response of the system
will be similar to Figure 12.
to this test
~imultaneously
Each of the panel loops, which subjected
showed reaction curves similar to Figurel2.
43
~···
44
u
~-4-
R
sp--
Gp
B
Rsp = Set point, °F
C = Receiver panel outlet temperature, °F
°F
ET
= En·or,
B
=Measured
U
= Absorbed solar power, BTU/SEC
Gc
- Controller transfer function
Gv
= Valve
receiver panel outlet
temper~ature,
transfer function
Gp = Process transfer function
H
- Measurement element transfer function
Figure 11
Idealized Panel Control Block Diagram
°F
45
t
y
t
----
Y = Deviation from set point (°F)
R = Reaction rate of system (°F/SEC)
t
= Time
(SEC)
m = Overall process sensitivity (°F/unit valve position change)
L = Dead time lag (SEC)
Z = Process time constant (SEC)
Figure 12
Process Reaction Curve for Cohen and Coon
Controller Setting Optimization
46
Thus, the optimum gain for each panel was readily calculated using
the equation derived by Cohen and Coon ( 20 ):
Kc
= 1/RL (1.03 + 0.35 RL/m),
(52)
Kc is the optimal controller proportional gain from Cohen and Coon.
This criteria is designed to give stable response at any frequency
and an amplitude ratio of 0.25.
The fact that each panel behaved as an independent first-order
system, even while interacting hydraulically with all the other panels,
hints that each receiver panel may be treated as an independent firstorder system.
Additional evidence for panel response independence is provided
by a comparison of the overall process time constant, Z, with the
hydraulic
tiw~
constant, THi' of each panel given by:
(53)
THi = IfJPIR,
1
where:
THi = Panel hydraulic time constant (SEC),
If. = Panel i flow inertia (PSI-SEC),
1
PIR = Receiver inlet pressure (PSIA).
The comparison is shown in Table I for the South, East-West,
and North panels.
than .04.
For each of these panels the ratio of THi/Z is less
Therefore, the hydraulic time constant is less than 4% of
the overall process time constant for near steady-state operation.
This indicates that individual panel response should be relatively
independent in this range.
The optimum gains of equation 52 were loaded into the program and
the receiver subjected to a uniform 10% step flux decrease.
While a
Table I
Comparison of Hydraulic and Process Time Constants
Hi Hydraulic Time
Ifi
Constant,
Inlet Pressure, PIR
PIR
(PSIA)
(SEC)
T
Panel
South
If.
Inertia, 1
(PSI-SEC)
Process Time
Constant,Z
.
(SEC)
TH/Z
5.7
69.4
0.1
39.0
0.002
East/West
14.0
69.4
0.2
16.8
0.01
North
26.6
69.4
0.4
8.6
0.04
~
.....:
48
uniform step decrease in flux is not credible as a real transient (due
to retrograde motion of the earth and finite cloud velocity), it is a
widely recognized controller test in that the square corner of the
input subjects the controller to all frequencies of transient input.
If the system is unstable, this test will usually show it.
The results of this run are shown by Curve 3 in Figures 3-6.
The
panel response in terms of outlet temperature is shown for each of
three representative panels in Figures 4-6.
TNR3(1), the south panel,
is the slowest of the three to respond since it is the panel with the
longest process time constant.
TNR3(6) represents an east-west panel.
Its response is faster, due to a shorter process time constant.
TNR3(12) represents the temperature response of the north panel.
This
is the panel with the shortest time constant and, therefore, the
fastest response.
The question as to whether or not the gains supplied by the
methodology of Cohen and Coon are truly optimum is answered by this
run.
In addition to the gains determined as optimum, gains both higher
and lower were also input.
The response due to these gains is repre-
sented by Curves 1, 2, 4, and 5.
north panel (the most unstable
(C~rve
As can be seen in the curve for the
panel)~
increasing the gain by 20%
4) starts to induce sustained limit cycle behavior.
Increasing
the gain by 50%, as shown in Curve 5), induces classical instability
in the response of the panel.
Conversely, decreasing the gain to 80
and 50% respectively, lengthens the response and increases offset.
The phenomenon of instability occuring in the north panel first as
gain is increased can be explained in terms of stability theory.
It
49
has been shown ( 22 ) that for process reaction curves similar to
Figure 12, the valve, process, and measurement element transfer
function pr-oduct can be rep res en ted by:
Gt
= me-LS/(ZS
+ 1),
(54)
where:
Gt
~
GvGpH (See Figure 11),
m =Overall
pl~ocess
sensitivity (°F/unit valve position
change),
L -Dead time (SEC),
Z - Process time constant (SEC),
S
= Laplace operator.
The characteristic equation of the panel control feedback loop is:
1 + G(s)
= 0,
(55)
where:
G ~ Open loop transfer function,
G = GcGvGpH
(56)
G = Kcme -LS(
1 ZS + 1 ) ,
(57}
where:
Kc = Controller proportional gain.
Therefore, the characteristic equation becomes:
1 + Ke-LS/(ZS + l)
= 0,
(58)
where:
K ::: Kern.
1ags 1't· 1. s common. t o approx1ma
. t e e-LS by:
.
F-or t ranspor t a t 1on
e-LS ~ (1 - LS/2)/(l + LS/2). ( 2l)
(59)
50
The characteristic equation then becomes:
= 0.
(60)
Equation 60 becomes:
ZLS 2 + S(L/2 + Z- KL/2) + K + l = 0.
(61)
1 + K(1 + LS/2)/(ZS + 1)(LS/2 + 1)
Simplifying~
Equation 61 can be expressed in terms of the coefficients of S:
A S2 + A1S + A2 = 0,
0
(62)
where:
A
0
= ZL,
A
1
= L/2
+ Z - KL/2,
A -· 1 + K.
2
For control "loop stability under all conditions, A0 , A1 , and A2 must
be greater than 0. Since A0 and A2 are always positive, the stability
criteria for each panel becomes:
A1 = L/2 + Z - KL/2 > 0,
(63)
solving for K yields:
K < 1 + 2Z/L.
(64)
Table II compares the K for the south, east/vJest$ and north
panels.
Since K = KcM, the ratio of Kc to the value of Kc which
causes instability is given by the following equation:
Kc, optimum/Kc,unstable = Kc, optimum/[(1 + 2Z/L)/~1]
This ratio is also given in Table II.
north panel.
This ratio is largest for the
Therefore, when the controller gain of all panels is
multiplied by successively larger values, the north panel should
exhibit instability first.
verifies this observation.
(65)
Curve 5 of the last frame of Figure 6
- . - ! -
51
Table II
Stability Criterion Comparison
Process Time
Dead Time,
L (SECL
(°F/v~lve chang~
K, unstable
Kc~ Optimum
Kc, unstable
South
39.0
2.5
32.3
0.42
East/West
16.8
1.6
21.9
0.50
8.6
1.4
12.9
0.52
Panel
Constant, Z(SEC)
--------
North
52
Comparison of Curves 5 in the three panels shows that the limit
cycle behavior induced in the north panel 'does not reflect back into
the other panels.
For all panels, the response shown in Curve 3 was
accepted as optimum since it had the most acceptable overall response
to a new equilibrium flux level.
While the response to the test step flux decrease of Curve 3 may
be considred optimum for a proportional-only control system, it is by
no means optimum from a system standpoint.
Overall offsets of 6°F,
l2°F, and l5°F were recorded for the south, east/west, and north
panels, respectively.
changes also.
These offsets would have been the same for ramp
While the magnitudes of these offsets are acceptable
for a 10% step change, larger magnitude changes, step or otherwise,
would result in unacceptable offsets from a power-plant-operation
standpoint.
The use of a surge tank does not mitigate this problem
as the offset there is 12°F.
(See Figure 3).
Consequently, integral (reset) control was added to the system.
Integral control will eliminate offset but has the undesirable side
effect of inducing sluggish response.
To decrease the overall re-
sponse time, derivative control was added. Again the methodology
suggested by Cohen and Coon ( 20) was applied and optimum controller
gain and time settings obtained .. The equation for optimum gain, Kc,
is the following:
Kc = (1.35 +
RL/4t~)/RL.
(66)
The equation for optimum integral time, TI (1/reset rate) is:
TI = [(1.35 + RL/4M)L]/(0.54 + RL/3M).
(67)
53
The equation for optimum derivative time constant, TO, is:
TO= l/2(1.35 + Rl/4M).
(68)
The values were obtained for these controller settings from the
same process reaction curves used to obtain the optimum proportionalonly gain setting.
The criteria for optimum P.I.D. system response is
a 0.25 response amplitude ratio and dominant critical damping modes.
The optimum control settings were loaded into the controller model and
the receiver subjected to the same 10% step flux decrease as the
proportional-only system.
The results are shown in the CRT's in
Figures 7-10.
The south panel effectively recovered from the perturbation in
40 seconds with a maximum undershoot of 8°F.
0°F,
The ultimate offset is
The north panel recovered in 20 seconds and had a maximum under-
shoot of 12°F.
Again the ultimate offset is 0°F.
Close examination
of the north panel reveals that it is slightly overdamped since the
amplitude ratio is less than 0.25.
Compari£on of the proportional-only and P.I.D. controller
responses reveals that the addition of integral function increases the
s1uggishness of the response, especially in the south and east/west
panels.
This sluggishness is in spite of the presence of the_ deriva-
tive function in controller algorhythm. · A comparison of the overall
receiver temperature response represented by the surge tank outlet
temperature, TNRO, and the north panel suggests that the north panel
exerts a great deal of influence over the system by virtue of the flux
and flow bias inherent in the system.
V.
CONCLUSIONS AND RECOMMENDATIONS
Consideration of the results and the system response to standard
test inputs leads to the conclusion that one simple feedback loop per
leg which utilizes proportional plus integral plus derivative control
can satisfactorily control a sodium-cooled, advanced central receiver
which is hydraulically, but not thermally, coupled.
The validity of
this conclusion is limited, in this study, to the normal operating
ranges of the receiver.
For emergency start-up or shut-down opera-
tions, additional control methodologies may be required.
The model
in its current configuration is capable of simulating these abnormal
conditions and in a separate study, completed as part of the Advanced
Central Receiver Program ( 22 ), the validity of the control methodology
suggested here has been extended down to the point where the receiver
pump is inoperative.
It can· also be concluded that the methodology outlined by Cohen
and Coon for determining optimum control settings is valid for certain
types of parallel-flow, hydraulically-coupled, single-phase, non-linear
systems.
This method is, therefore, extremely valuable for use as a
deterministic method of setting controllers in complex systems.
Under normal circumstances, it has been shown that induced limit
cycle or unstable behavior of the panel with the highest flux does not
force the system to go unstable since the unstable panels represent
less than 22% of the total system energy received.
54
55
The final conclusion concerns the controller mode requirement.
As a result of power plant operating requirements, a sodium-cooled
central receiver requires integral and derivative control modes as
well as proportional modes.
As mentioned previously, the model is capable of simulating a
wider range of operating conditions than was simulated here.
Ques-
tions concerning natural circulation of the receiver in the absence
of pumped flow, the response of the receiver during cloud
transients~
and emergency flux excursions were not considered under the scope of
this project.
These topics are recommended for further study.
'ilo/3'·
VI.
REFERENCES
1.
Caputo, R. S., and Truscello, V. C., Proceedings of the Eleventh
Inter_?ociety Energy Conversion Engineenng Conference~ Volume II,
i 216-1223, paper 76213, State1 i ne, Nevada, September 12-17, 1976.
2.
Tracey, T. R., Blake, F. A., Royere, C., and BrO\'In, C. T.,
Proceedir~ of the Twelfth Intersociety_lnergy Conversion
Enginee~~onference, Volume II, 1224-1230, paper 779198,
Washington, D.C., August 28-September 2, 1977.
3.
Johnson, T. l.., and Thomson, W. B., Proceedings of the Twelth
ety En~J:: Conversion Eng·i_!1eeri ng Conference_, Vo 1ume II,
1203-1208, paper 779194, Washington, D.C., August 28-September 2,
Int~r_?oc i
1977.
4.
Grosskreutz, J. C., McBride, E. J., and Gray, D. C., Proceedings
5lf the Twelfth Intersociety Energy Conversion Engineering Conference, Volume I I, 1209-1217, paper 779'195, Washington, D.C.,
AUgust 28-September 2, 1977.
5.
Hallet, R. W. and Gervais, R. l.., 11 Central Receiver Solar Thermal
Power Syst!:~m Phase 1 CRDL Item 2 Pilot Plant Preliminary Design
Report,n Volume I, pp. 2-4 through 2-6, DOE Report No. SAN-110876-8~ McDonnell Douglas Report No. MDC G6776, McDonnell Douglas,
Huntington Beach, California, October 1977.
6.
"Conceptual Design of Advanced Central Receiver Power System-Phase I Dallas, Texas Semiannual Review, 11 Oral presentation by
Martin t~arietta Corp., Dallas, Texas, September 20, 1978.
7.
Spr·inger, T., 11 Conceptual Desigr. of Sodium-Cooled, Advanced Central Receiver Power System, Sl\ND78-8015, Semi-Annual Review of
Solar Thermal Central Pm>Jer Systems, NTIS, April 1978.
11
8.
Ha.llet, R. W., and Gervais, R. L., 11 Central Receiver Solar
Thetmal Power System Phase I CRDL Item 2 Pilot Plant Preliminary
Design Report:' Volume II, pp. 4-82 through 4-115, SAN-1108-76-8,
MOC G6776, ~1cDonnell Douglas, Huntington Beach, California,
October 1977.
56
57
9.
"Draft Final Report, Conceptual Design of Advanced Central
Receiver Power Systems, Sodium-Cooled Receiver Concept, 11
Volume II~ Book 1, Conceptual Design PP. 1~1 through 1-6, 2-4
through 2-7, 3-30 through 3-34, and 4-1 through 8-96, Rockwell
International, September 1978.
10.
Riel, E., "Central Receiver Plant Control Simulation Model, 11
SAND78-8015, Semi-Annual Review of Solar Thermal Central Power
Systems, NTIS, April 1978.
ll.
SH19-7001-5, 11 Continuous System Modeling Program III (CSMPIII)
Program Reference Manual,'' IBM Program Number 5734-X59, September
9' 1972.
12.
Achenbach, E., 11 Heat Transfer from Smooth and Rough Surfaced
Circular Cylinders in a Cross-Flow, 11 Proceedings of the Fifth
International Heat Transfer Conference, Volume II, pp. 229-233,
Tokyo, Japan, 1974.
13.
Mouradian, E. M., 11 Draft Final Report, Conceptual Des~gn of
Advanced Central Receiver Power Systems, Sodium-Cooled Receiver
Concept," Volume II, Book 2, Appendix F, Rockwell International,
Canoga Park, CAlifornia, September 1978.
14.
Raiz, Mq and Gurr, T., Solar Ene.!:.QY, Volume 19, pp. 185-194,
Pergamon Press, 1977, Great Britain.
15.
"Liquid Metal Cooled Solar Central Receiver Feasibility Study
and Heliostat Field Analysis," ORO 5178-78-1, October 1977,
pp. 5-32, University of Houston.
16.
Kern, R.s Chemical Engineering, April 14, 1975, pp. 85-93,
McGraw Hill, New YOrk.
17.
Himmclblau, D. M., Basic Principles and Calculations in Chemical
Third Edition, p. 288, 1974, Prentice Hall, New
Jersey.
~ngil}_~el~ing_,
"i8.
Yunker, W. H., "Standard FFTF Values for the Physical and Thermophysical Properties of Sodium," TOT. 12083, (WHAN-D-3), Hestinghouse Electric Corporation, Richland, Washington.
19.
~asoneilan Handbook for Control Valve Sizing, Fifth Edition,
·Masoneilan company, 1975.
20.
Cohen, G. H., and Coon, G. A., "Theoretical Considerations of
Retarded Control," Transactions of the ASME, July 1953, f.i.rnerican
Society of ~lechanical Engineers-;- New York. -
58
21.
Coughanowr, D. R., and Koppel, L. B., Process Systems Analysis
anQ_Con1rol, pp. 312-315, 1965, McGraw Hill, New York.
22.
Willcox, W. W., 11 0raft Final Report, Conceptual Design of
Advanced Central Receiver Power Systems, Sodium-Cooled Receiver
Concept, 11 Volume II, Book 2, Appendix L, Rockwell International,
Canoga Park, California, September 1978.
APPENDIX
Model Listing
59
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">'~U
~O~Vl~~C
RHtlHT Q:FH;:J>;A { T'!>< T0 l
- -l .. l"T (•"'"'"'A>"T 0 I 'lt;,]H T (J /C AHT
. -------··-- ____________ OC.UC 1 b\)1)
0000 l c Ill
L~OTo:~hPOTO/~MODCO/C.Q81
OUOQIC>2U
lHJoJOJt,]O
ll;<IJDCO:I<><Il>Jl ( T'lR~O l
·----'=s..,ocT:i c(.:~u1 o-+E %ooT -Liii.H r o-1
*"'Hiloc •iTsl"sF'r _____________________ uuout t>'-'u
KF~Ot:~FMOC~•~~0**2
OP~Vl~SWDC!•KF~OC
Oh0UI~50
OCIIDit>bU
SGDV:RM0DCO/b2,U
UOuDI~7U
OlO(:w~D•L~SGP~/SGO•
IJiji/Cl~bO
______ _ERSGDII.:SGRU SGCJ {) ______ ______ ------
-----CiiVOlt><IC _
CVCDv:QJOC•~~SGuVtSORT(DPOVll
O;)OOI7uu
VPD~l=t.O~Obt>+.272o5!•ALOG(CVCDV/CVD\)
00i>Oi71L·
. -Oiluul72u
ouoo 17 .Hi
SUUlU~ ~lLM COEFFI[I~NTS
.J0cl\11711U
----------·-·-------·-- - - - - - - ___ IJI).Jtll7~v. _
--lF\,.ll: ,2535---,oiiTudt.:, 0511Z
, ~1>-Pl :]27 • ~5
O~fJ(I I 7t>IJ
u..ovvl770
ullOill~~u
9 I __________ RECEl_¥_ER PAI\:EI.__FLD"--- _
-·--·--- _I<[J1'\o<Z..l3. ""'-0
CONST
--•~.z.t.l
CONST
l~wO:Q,Q
,L~SGP~:7,1<12c
,Rrl:55,<l~
ilUO\llr'SII
•••• Pt1HOlhoO
________QN~j__,_QJ_ _____Ajl f!_F_::__. <I
LBSGPH:Co'lvE?SIO~
R~=RECEIVER P~NEL
•
Lb~/SEC
W~IG~T
.UJiiLOll\7.0 __ _
TO
00001~'1U
(FT)
. SINSFT:C(J"''iEt<SID'~ F I.CTP'l SO 1" 1(1 SG fT
PlR:P~ES5URE ~T RECEivER !NLEl
(PSIA)
•
-~E-Kfl,Tt l,;-q~-;BE·0-~~;(?1:-o~sG-f.:-o-LI;
__
ui)Q()IOBO
GIL/~lN
i<<'H\3 l='~.t3E•Oll
OiiQUl<IOU
!10001'1\0
uouut'I2U
_il9_1~1) j .. ~~~--
KFH{II)~~~'1bf•OII,~F~(5):~,71E•0a,•FH(t>):@,3'1E•OU
, •• ,;,onot <;uv
, ••• OOOO!QSD
-· ______KFH(7):8,o?E•Q:! 1 KFM{I\):b,tlE•i,£1,1\~H(Q):B,fJ3E•ull
·' . . . OOCo!ql:>(o
KFH(10}:7,Q2E•ull,aFrl(11l=7,85f•D4,KFHI\2):7,blE•C4
,,,,DOUC\<170
KF~(13l=7.~5E·u~,~•H(t4l=7,Q2E•oa,~rH(J5l=e.o3e-oa
•••• ooootq8o
- KF~ (It> l :I) ,.11 E •01.1 1 o<'_FH (I 7): "' ~ ~·J( • J'4 1 •,_> H_( 18) =i\..J<l( ~Jlll ________ ..__._u lHlC 01 '19.(>
------KI'H(Tqf:,6·. 71 E•oa, d'>< ( ?i• i:t'. 'H,F.•-)G, ~<f "'< 21 J :<l .t3t.-vu
, •. oi!OC02000
~Fri{22}:q,5oE•04,"FH(2]):<1,bbE•04,~FH(24):Q,b6~-0ll
TABLE
C-'¥(i;zpi;?o-7o,-,CV(1•5)::3•!:B,,CV(o)::?2U,;Cv(7.;,'1)::3*1.11S,
__ _
00~02010
,,.,
oovo2o20
OOI•U2V'~
CV(!O•J0):5•oDO,,CV(I'j•t7):]•Ut5,,CVI!f):22U,
•••• OU~C2uUU
-------~.Y(J_<l_...2i.J ~-*-U 3 ,, C_'/_\22.-.2l.lj_E.J•_L.,..___ __________________ (L0Jl02050 __ ·TA~LE
•2,2,!,1,2
. ·•
ooco?.oeu
~NRo(l•?.Ul=?D*l•O
RECEIVE~
UUTI.ET
TAN~
Ollli02070
0VOU2120
63
oouOZilo
I~CUN
OOOQ21~ll
0_1!_~02_1 ~0
00002\bli
00002171)
OUOOZibU
I.IOC021'11J
oouonoo
_! 2 • 2 • 1 • I ._J,_ _ _ _ _.....C.:.OL!L.IA NK__
----------"Ou.nw•• 112Z!...IJ- ..
00t.02<;20
IN COt~
u~oo223u
---~-----
CONST
--------------- ----------------- ______ l)ll1JU2240
-~---
CAC1:7854.
~CTl=l.O,
VU0022':>0
ooou2i'bu
_ _!l_.j_._L_j_.__I!_ _ _ _ _ _ _R_~(;_El_yJ__Ji_£_\J~P:__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _-:--"U..OU221.11 __
IIII0022Bv
STQ:.c;;>bb,
RT0=.021t>
Ollv(l2ii'lt>
__TA2: • t>3333, ___ P 3=• • 2222 2 _________ ---------- __ IID£•1i2300
CONST
COIIIST
_1 A1: • 51'.!!11'1, _
CONST
CONS T
~•t=lo22b'14,
I< iH': • I '15 b ,
Hi?=.c~Q25,
C000231U
Cu 0 (123 Z l'
HA3:•.211o1'1
TP T: I 0 C0 •
_l_NCO~-~-Q~._O
~1/C.2JJfJ_
01J01i23ij(l
Ollu023~U
.oovu?3ou
(10VOZ37l•
oouo23~<u
_JI_Q H~2 3 'UL__
ooooz~ov
COIIISl
L"I=ob3,o,
lRPSP:\00,0 1
-·- ----- -·· HRPo=.5t S • 2q 1
L~RP:1100,,
Go:3z.;>,
RPSPCA=I\75, 7,
_KF >1PPP:3
POROT:I5.7
~~P(A:35'1
0
04
•••• 0000?4\IJ
\S'I(,wi)b_ ------------.1..• • o0UUQ242Q _.
OOu021I30
00Cil2<~40
_1 .,,,:_>IN~ !_1. ~-Q_P/_GO /Pi<PCA • .,,,0 ~~PS.£1~~ /R.£S_~C~ _
- - - - - - f;;;-P.i>s: .. r-10 •L><Ps"-/GO/f<PS"C A
·
__________ __!!.llllJI2<15Q _
000024t>O
I..O:;AF:I.,N/111"\l
00(>(12<170
___________ ------------- __ OII002LI81)
onuo2<~'~u
oouo2~ou
_ _ _ _ _ _ _ _ _ _ _ _ _ __..u.uo.25L'L_
uoou2Scu
-
110002':>30
__ VOOQ2SilU
-
LRrCP~IIOQ,,
LRDVDP:too.o,
~~~DCR~7.oo5E•Ob,CVDV:Ju~5.,
PDCCA:?bO,'I,
DVDPCA:2t>D.'I
'•••
EbRU1:71Po5
OU~D255u
U0~~25bu
·-··-------------------------------t•OO_o2S7t•
- iNi:UN--;il)N.(i: 1, C1
ouoo25ilu
*2.Z,1.1,7
00002~'1(.'
OOCQ2cOu
lNCON
ouco2td 'J
tioi;o?e20
__t_o~~;~w-~HJ;: 1 .•.!4---
.. ,.quR:::wcrtP.
____ C.A..Itl:;.J.l'!SIJ • .Q
-------40.C.-.2e.l1!--oocuie"~
ouuv2t>':IO
__QOCD2coiJ
Ollvu2b7v
uuooi'tl'lv
33. Qt;J_,_( 5,, 4 33. Q'IJ ,_US., n 22 .• O~J_, l25~_, l:Qe a32},_,~•-_jJJLi.!u2c 0 -"...
-c3-5:, 38 <~. ~' > , cos., ;) c; 2. 11 1 • c s" •• 3 1 ". o 1 >, <t-'> •• zo 1. :n > ,
• ••
oovv2t o 1
fUNCTION
---------
RPfJ~o;_E_~<_:_ll> ~,_a
(75. 1 223,b1l,(B5.,!~2.c8J,I'IS.,IUU,~O),(I05,,113.3'11,
(115.t8l,'l_l 1 (125,,S'1.5a),·(13S.,LI?,S2lrl1~S.,2<-,:~5),
D~~02~'12
•••
•••--·
t•Ot!V2t-'13
ciss.,tb.'ll,lleS.,II.02l,lt75,,c.li,C185,,u.l
oov02tQu
0001.12t>'l~
- - - - - - - - - - - - - ·____________Q\IJ)Q.i?(V.i/___ _
CONST
ouov271(!
oi.LF'I-IA:::o,'l5
l4=l>ii.
,A5RA:5,Q?E•11 ,TG:7.3lt10
·-
PLOGA:,t5i\U
,&R~IiO,I7
.
,~CPT~~78,~7
,MwbTUS:'IIJB,O~
,rs=7.31E.to
1 PI't:,ll")bU
•••• 00'102720
1 0 , .\IV\1~?730
,RPl:Ll33,(lq
oucc27Uu
:lUlllJ2750
J.Atli..E.
--- -··---
--------------------------
__ j)J!_0027t>.Q __
64
TAbLE
NPP(tl=.Ot7o,NPP(2):,01~7,NPP(]):,o2,~PP(4):,~2~5
N p p ( S ) : o 0 } 1 } r ""' P ( b ) : o \! ~ Q !' 1 t J J' P ( 7 ) : , ~- U Q 3 1 'I p P ( ~ ) :; , 0 5 <; 1
NPP(Q):.coJU 1 NPP(JQ):,Jbb!,NPP(IJ):,c7n5,NP~(l2):,c7]8
NPP(t]l=a0705oNPP(JU):,O&o!oNPP(J5):,Uel~oNP~(t&):,0551
_ _ _ ___,NPJ:>_(l__"l_l_,::_{l_~.3~ NP~__ll <'~=~ Q_3Q_f'._, t;P_!'!.i.'U =-~ 031..!u><.££.( 2.0J
tONST
CONST
=-
0011\12770
,,.,OOC0278U
... ·---~ o. • a [J i/ {! 0 2 7 q 1/ .
o••oUOUO?!CO
,,,,UU002B!U
U2u~---•..-..ollUU0262lL~PP(2t):.o2,NPP(22J=,ot~7,NPPI23J=,Ot7e,~PP((U):,ot7n
OOUu2t3ll
PF2;.oo72
oouo26ao
PFj"::~i9&u-~-----------------------------
t•SLE
TN~tOG(!-2U):2a•e5e,O
TASL£
TNR]JG(t-2a):21l•t!OO,
----··· .vuou2t5o
OOII021lo0
llu\lu2nu
.ILOQ!J}Q~l!._
-Tii>ie. -~1-:~~2\..c.Tt-,:-z(jT:;iq-;<>92.
-·z~l;-t-:2
Ollt•Olr-Su
--------"RtcETvE R"·soD-Iu>~-Nooc rE,.P"E"><"Arui!{s·-----~ ---
-~--
--
OOOOlOoO
UU\103070
--·uoo o3u llu
0\IUO}GQC
NV Ill 1 H:2c_7c....7~,..-:.'5_ _ _ _ _ __
---~OO'J03J
v_o_ __
U000311U
UUOCI}IUO
_..!.~ ._~ • _2__,_!_ ___ --~tU.t~;R_O_JT_L_E:_T_!._ ~~ __TJ."'!'E_;<•_"!..L!R_t_s_~-~ ---~-------Oil IJQ 31 ':>.0.
ouvu:Siou
INC UN
TNROo:ttOl.q
OOC0317tJ
·------"' il..U.C.H tHL_
uouu3l'IC
. ~Q~S_T__ ! A uH~l:!!
TABLE
000032l•(i
u \l I} 03 21 U
.uz___ .-----··------------- -·--· .. -----·- _--------·---· ()000}220
OUOl•323u
t1.9.1/(!)(ll_p __
INC ON
T!oiRli.l=SSO,
_!?_.,)~_2_._11___________C_QJ.I)_11:'1__1S__IP_P.f_:~EJvE:R_ __P_LI .. P_______________
ooo!'325u
uuuo32eo
uOOuHl\1.
uouo3320
CONSl
OOV\l:B3u
!I.JlV 0 3J <IJ)
IN CUll
uuuuHSo
UIH'033ou
- - --·- -· ·-·· .00003370
oono33bu
•z.:s.z.s
COliiST
-----·- --- ----~o~C'TI=t.o,
______
uO<J03)Qu
_uouc.l~oo.
_
__
oouo3•11 u
uouo3<~20
C_ONST_ ._..TAuDC=tJ.2L ..-.-~-----------·. ----·-···-----·----------- ___
ouuo3<~30
00(/tJ)<IIIQ
TAI:lLE
-
-----~=-=c-:--:-:
PRESSUQE RtUUClNG UEVICE TO HUT
01101/31150
________ Q Oll.U 34 b \l __
00003117U
T~N~
00()1)3U!jl)
CONST
. 110'J03ii'IU
oouo35ou
· lNCUN
TNHTIO=llilii.S
Uilu03510
- - - - - - - - - - - - - - - - - - - · · - - - - - - - - - - - - - ---------~------.Q.Ijl,tQ3521J ....
•2.3,2.'1
HOT T•"~~
ouuo353o
0000354\1
lNCl)N
1)1)1){!3;5\J
UJtl'J3':>bi}
CONST
loiHTO=l.O
OO\i0357u
,
Tlu~cv=o~J-----
----- - -------· lluOu35&v
vn.'Jr,359u ..
ouuo3bOO
Ui!\J03oiO
Ktlii=.ntu2,KCI2l=.ot32·•tll1=,0t~.~c<~1=,o!3,K[(5)=,ot
-----"~t.LeJ.=~ 0.1.
J =.cu._,~
~'~ p:. ~ 1
KC t 9) =~ 11, KC t 1 uJ;::. c. 13.
o. C ( t 1 ) ::. • 0 l ll , t>. C ( I ? l :::: , 0 I 5 1 , KC ( I 3 ) "' , () I 4 , KC ( 1 4 l : , 0 I 3
~[(t5):.ttt 1 KC(!e):,nJ0? 1 KC(171~.011rKC{!8):,o1
- KC J .1 Q_)_:.;) 1 'KC ( 21)):. c l 3, K c ( 21 )
\11 5, "c ( 2 2 J 0 I 32
·TABLE
"c.(]
u
oz.,
=.
c
=.
I!OU03t:2U
, ••• ocoo3e3u
.
--··· ---• ·~~ oooc.3el!1. --·
• • • • \1 V0 I! 31> 5 ~
••••~I!OO]t>bL
-
I ....
ou (1 0 3b 7 0
65
llu(JOJe!lo
_!_~BL!_!_AidJJ_!_::~, O}!_T ~U ( 2l
T.ill ( o}:), ~ !>, T All ( 7 }
0(•U03t>'IV
5 ,_li_O?, TAU ( l l :;, ,lj'l, T':II ( ll )_:!J_.to<l,l ~' ( 5) ::; ,;,1_,, • ,J)IJ'Jf;J 7v(l~ _
1, ,
o 2, T Ai I ( 8 ) : ; , 53 1 TAL' (<I
) ; ~, ~ 7
1
TA II (
l v ) ; 3, ~ 3
TAU ( 11 ) ; 3, <I, TA11 ( I 2 :3, 3 Q, TAU ( I j l: 3, u, 1 AU ( l ~);;: 1,, 1.1 ~
l AlH I 5) :: 3, ll 7 , T AU ( I o): 3, 53 , T l ! I ( l 7 ) : :'-, "2 1 T ~II ( I 1\ ) : ! , !; b
, , , , ;I u I• 0 17 I 0
, • , , IHPJ (l3 7 211
_____ , • , , \1 Ot• 0 J 7 3 0
- - - - ti.U( JQ')::u.27, TAUC20 ):Li.RtJ, TA11(21 ):5. 4'# 1 TAU(22):'5.F.
1
TlU(23·2~l=2•o,07
, ,,,Otlv0377U
•••• ooou3780
•••• uuuo37~~
TAUU(S):,~a5,1AUU(b):,§~S,TAUU(7!:,55tTau01R)::,~38
TA (II)( q) ... 53, T A JD ( I 0):. 5 ;:>I.! I T ApD ( l 1 J:. 51:.' I, 1 ~ l•O ( I 2) =.52
·- TAUO I I 3 l: 0 S;> I• T AUl! ( l !i)::, 52 a, TAU(' ( 1 ~ l::, 53 0, 1 Al!O ( I b):, 53 b
=
PIH.SSURE REOUCl><G DEVICE
tiuDv.,3,o,
CONST
0000375~
______,..Lluil3Ho __
-T4dLE TAu0(-;)::-912,r"Ailci(2J:: -;T73";iAUIJ< 3)-;~?-.;-~-TAuD(iil : , 12"
T~U0(J7):.~5,TAUD(!6):,5~5,T~U~(IQ)::,b21rT•U~I20l:,72B
____ _J~_t21l t s 2 ~1_A.i.lil...L2 .2)_::... " I.h LA ui)...i2.3..!"2ll_]_:_2_.!._.9J..2.
•••00llU37l.l(:
•••• oooo:;eo~
,.,,COJ038!0
-------0.11" OJ8 2JL.__ _
000031'!30
CIJNTROLLE~
T AIIDV l:e9, o 3, ~(i>v:o, OC5,
SLRUT:4,50
OV003'12v
·-lA-tiD •In: it:)--
~--,
____ uouv3'131•
•o•
OOCu3<14 0
001103'150
~-~--~----__li.OJHI.J'~_e_v_
(111003<17(1
OYNAH lt SEG><ENf
--------~-----
INPUT AND
---------
----------~--------------_,.....,..__
BOU~DARY
,
ouou!'~l.!~
_110003<1<1\,
0000"00l'
OUOOIIu!Q
------~---------o~~(l~v2v
CONDITiONS
11000"030
001/0i.IO«O
__SOD I_U_!I_F lL~_ COE fF I C JEt< TS
PROCEDURE
_______ ___
·-------. ___________ thliJOIIO'SO
OOOCriiOoO
CP!,HANR!,AHOt,CP2 1 NANP2,RHn2,C~3.~ANA3,~NOJ,~NRA:wANR<~~R,,,.ocu~~u7c
________ _J'_,.._~,_T!"£_2 1 T"<~3_,_UL_Q 1__()~T_<!~E ~~~.il.L'". ~~)
f'I_(JQ"_Vt!~---
ouuouo9~
00 Soo II=!,2U
WNPACIIJ=A~SI•~A(IIJJ•~NPA(J!l
-----·---_XI, Yl_"'l,.I\ECJ ("N><A (I I) 1.TNI< I (I
J J 1 HLOt OPTU!!E1 HARl
CPt(lJ):xt
WANRIIIIl=Yl
zt :fHi(JNA (T~P I
OuOoli!CO
) _______________ OOIJQllll 0 _
00u0~12u
6ooo~13u
_____ (1_1/_Q_Qil)IJ_!i __ _
(II)}
.111"(fiTiTl'iT1~------
. OOU0lll50
OOOOI.ilbU
l2,Y2=LKEg(~NA4(ll),TNR2(ll),AFLU,OWlU~E,HART)
- - - - - CP2 (I J): X 2
HAN~-2 (I Il :Y~-
. ____ ----·-·---·-- ________________ • ___ ------------- _1/UOOII 17 u
OuOOll 180
OCOOli!9U
Z2:~HU~A(T~R2(1l)l
llH02 ( l I)= Z?
-------x>. v-3=·LK-E:i-{-;"N"Ri(If>, T~><·R-3<II >, irLo, D~<Tu~E.
fL(I_\iO'~ i?([Q ____ _
1
HART J
ooOOll21
t<o\NR3 ( l Il: Y3
- - - - - - - Zl:IHiQNA CTN~3 I I
500 IIHU3CliJ=Z3
v
O~Uu~Zzv
CP3Cll):X)
f)
l
_ ------------------- - - - - - - - - - - - - · - - __ 1Hl00ll23u
uuuOII21.1t•
OUOOll25v
ll0.0'<2oli.-_
000011270
JN(.lPRQ(:fDU'<E_____
tP!H:(PNA(TNRl)
RP:~tGEN(RPQ~ER,Tl~E.)
RE.CElVE'l OUTLET TANK
UUQ0~2ev
---
~---
-------------------
~~~~~~~~
OO<i043!0
--~OOuO'I !2l'
oouo<~Hu
t>OQOIJ3110
__ --~---~---- --·------·------~-----OOOOII3'5V
OUOOil3biJ
UU;)Qil37U
\I_O_!L~ 4 )8 U
oooo<~3Qu
OOOOIILIOU
· - - _____ ·-----·----- ----·-----·· ___ --···---~----------·- · - - - - - - - -·--------- ______ OC.OO•Hl I 0
tHiOOllli2U
PRE.SSURE. REnuCING DEViCE
0CrUU"<I3!J
OOOOil'~liU
66
--- ·--------------··-·---
~~UNDV:~HUNA(TNDV!i
oooot~u<;n
CPNDV:CPNA(TNDV!)
uooou~oli
------·-·-·· ----· _____ ...UCI/0~4 70
OUOOI.I~8r1
OUO(I~u'io
~CPI"'T:'1'-4tHT•CPt<l
______.!U!.IJ
---o-..-fi:(Pf..o-i (YNi.<r) - - - - - - - - - -
v11; 0 Q __ _
UlltJ0<15IO
Rr'iuHT=~~"~ONA!TN"T)
111111111.1520
UCII011;3o
IIUUOli<;IIO
HYORAUI.!CS
OOOOiJS"'U
------,---------------------------------~iiJ.l.CilSo.o
~ECEIVtR
SYSTE~
000(11.1"'7U
UUOUIISIIG
.IIOOIJU5QG
01)()0111>0'1
O<JUOilc Ill
___ Jluu!l4o2\l
---------wN~~1fGql<~N~c~D;NR,2~l---
ooooue3u
OuuuuciiO
SN~Rll:PH0'-4&(TNRl)
__________SN_A_RJ_:sr.;JR_Il/oi!..ll__________________________________________ i)O!Jflllc5\l.
FROCCDURE
(i()O()IIet>O
OuCOllo7~
D~'<R:Dw(~J~,PQR,Ft<,DPCV,St<,lRl
_ _ _ _ _QQ _20~.D_..J..J~_L, 2 u __ --------------- ---------_--------------"u.u.O.IIe!hL __
l~OO
D~~h(JJ):[P!R•POR•FH(JJ)•OPLV(JJ)•SH(JJ))/J~(JJ)
IIDOOIIOQU
ENOPROCEDURt
000011700
. _ (IOooa7v'l
PROCtVLtRE SH, i 5'"= 5 UT!C! E~POT, U<l, 0'1><: 1i -, >IH02, RH03~ S INS~-T ,wt<R-, ZERO j
1/0l\011710
TS"'"-ZERO
[l(l~011711
_____,DO 1_2_(l.J__l_L_=_ L• 21.1
-,~--- OJiJJ.Oll 71.2_
ti!Ol
SHCt.Ll=tEb~OT•LRI)*(R"01(LLl+RH021lL)+~HU31LL>)I3.1Sl~SFT
TSH~TSH+SH(Ll)
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OnuObU~O
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---::--- DT><P.l::. ( "~*" NO• TNRPu~'IT': SC: R)
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0000~195
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_ _ _ _ _ _D_!N_R2 (Lt= tt1~~R2 ( 1-)
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ENDPROC~DURE
-
--.
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0UUVb23~
~UUUDiQU
--- \•I.IUOt>25V
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-
- - - - - - - - - - - - - - - - - - - C_oJ__\1_\1!>27~'- __
PROt~'llTNS"="'DT ( WNN r oH/Ri<, TNP.lr TNRQ)
MTINS"=O.O
DO t50o IJ:t ,2'1
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oouoo~i:'o
RISER PIPING
OOOOoiJ l••
- - - - - - - - " - ' \ ! ( ) lioii"'_V ___ _
oouuc<~Sv
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_______ \IVOOb.47v
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PROCEDURE 0TNRP,OTNAll:oiSER(TNPP 1 KLNW 1 TNRPUOoT~Rl)
--------"-'OO_Q_Q_~ll'!!' __ _
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300 OTNRP(!Kl=~LNA•(TNRF(l~·I)•TNAP(JK))
DTNR!l
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ENDPROCt.OUIIE
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PROCEDURE f T!: I NTC:::JN ( ES, VP[IX 1 ZE RfJ, 'lNE, T Alj 1 KC, STI<, f11NR3 l
-
0JliJ0727~
uooo72t:Ju
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001.'(171100
IIUUU7<11C
----""·0._,\1'-"11
0.1 <I '-!1__-
PROCEDuRE 1/P X, VP(]x:;<CONT ( l fiX, ZE.RII, ONE-; T AIIO-, ~-C, ES, S Hi 1 VP, T4UVLV 1 VP 1, • • •
Oo uo 71.1311
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ET:ES(M)•STP
U00071170
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PROCEDURE
TN~lX=DLAY(TN~J,ES,TAUTC)
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UUU075110
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UUU(.o7e!O
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------
CCOu7e20
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IIOI•U 7t>511
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ll11(HJ77 :!>tJ
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----------------·------~~-------- ----------------------()V_Illl77b5 _
110110"17'10
01.1('076(-(J
CONTROL STATEMENTS
TIMER DELT:0,03o
MET~OO
FlNTlM:.to,
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Fl Nl SH-LR!JT::ZERO,L RU-T::
- - - - - - - - - - - - - ' o r J !i..iJl~Lu_
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001)07'100
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OUT
(luOoH3U
l~STRUCTlONS
PR! rfT_ _ TNC i-;T.,RPIJ I, TI><RF'UU,T~iP 1 ,-(;f~wt.,
IIOOu7'1uo
~", T~;Rrl'; po( -t-},vP(j )-,-.~;;-R ('j)
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lNST~UCTIO~S
uOOull~2o
COI.ii18C:;u
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illUI.OCI.I<IU ___
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LABEL ~UN OG•07 CLOUD CnvER T~kNS!E~T, 7•13•7H, 200 SECilNOS
uouo~ubu
_____________ --------------------- ________________________________ ucu..ot~.o7o
OUTPUT TIME
,TNCT
,TN~PtJl
,TNNPUO
,TNRl
UUDO€U80
UIJilllllO'IO
-~~;_L_LN_C~~J:'"'Ef!_AJVBf:_\l..f__Sr_lQ_I_IL'"
I_~_C:iJLQ_l_A~....JLl
_LA!l_EL
______!llL{>QI:<JQ.!L__
TNPPlJl • H>1PE'<ATURl [lF SL1lll!IM, PfCUVER PtP•P INLEY {F)
OOOOilliO
TNRPliO • Tf"'P(RATUiiE IJF SOOlt•~, t;~CE.lVE.N PUr-P OIJl!..ET (F)
0000812C.
TNRI • __ TE"!PEI\ATURE UF SU['tU•1, i>fCEl vH_ F•LfT (Fl.
U0UQ8130
OUTPUT
Til-lE
LABEL
I.ABt:L
I.IJ
0-'
wN
ll1ilEL
lAt![L
UOUOtll~\1
l_A~El
. TOTAL
c
rYI
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,TNR()
II DOuR !'SO
__j:_QJ)Q!\1 b\1 __
-------------
HlCIDENT SOLAP PU,.;E:R (IH•T)
TOTAL HlSui<PlD SOLAP ru •. EP ( .. ;.T)
TOTAL RECEIVlk I'L(IW (LI:)/SfCl
coooot7(1
OOOU!)J!\0
------
·-·-
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72
LABEL
IIOUIItcliV
0<1 1JO~(I lo
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IIUOQI-23<,
SOUTH PANEL ll'.iC ll'f.NT P[lri~ J.1 (lo<,.l)
St_ll!TH PA...,E.L VALVE PUS!TJI)I'.i HI-'ACT!O'< (!P~~'')
~ S'JUTH PANEL FL. II'" (N(l'I><AL I ZED Tr, 3to.t 7 LH"'/SEC)
Llt:!EL
PP( 1 l
•
lABlL
LABEL
VP(J)
•
I,.A8EL
TNR3!tl •TE"'PER&TURt OF SnDIUM, SUUTH PANEL UUTLET (F)
riW<( I)
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,PP(c)
, VP(b)
,~<'IIR(b)
,TN~3(b)
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• W~ST PANEl, lNCEDE.NT Pft>lfF (M~T)
VP(o) • •EST PANEL V~LVf. PnSJTJ~Y (FFACTIUN nPtN)
LABE~
~NP(b) • •EST PANEL ~LO~ (NUhMALTZED Bb.!5 LH~/SEC)
____I,.ASEl_ _
Tfll_'1_3 ( o) • TEMPER A Tl'£l_E_~lf_S'~Q 1 U"~-~E S T ~"'-'-"f L_fliJTLt_l_( F~>-~ _________
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LABEL
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CIOOV~H<'
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IIOOOI'liiiJ
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OUTPUT
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_JJVO.!U"'I.ll ___ _
ll(lvllU:~o
00011~!0
---··-·------.UOClli.I<'IJ
U0011Ci30
U~OI1U4U
I ~5J.L_
Ohu!
OOOI!voO
OIOC:JNITPL DUwNCO'-'E'I I'"Lfl" lGP>1l
Ul1(l):LOWER AXI•L NU0F, PA~El J, lNCJO[NT PUwEP IBTU/SfC)
012(1 ):"f!f'lCLE AXIAL NfliJ[, "J.N(L I 1 !NC!l'ENi PP~EI< (hlU/SfCl
--~-----·013(!):-lJ:>Pf>l AJIAL '<U:)E, "A'ifL I, l'lClDE.'H PUwER O:<TU/SE.Cl
QAGI:NUDE I RADIATIVE LPSS TU G~OUNO I~TU/SE.C)
00011070
_t)!)JJ It!!.'(!
C!UOIIOqO
00011100
_____IJ"l_G_~=N(l_DJ___('_~_A_Q_I~I.l~VLl.£.1S~_T_I.'_I,>;.:'}t'~Q__Lb_Tv_(_S~.U~--·--------tiUJ.1.1.V_
*
IIRG:;:•JuOf 3 RADIATIVE LOSS l" t;PflL•N(>
YRSt:NOOE 1 ~AO!ATlVE LOSS Tu
I.IRS2:.:NDDE 2 R AOI A Tl VE. LOSS T'.J
S~Y
U\Jt11!120
U:ITU/SECl
lBTU/SEtl
uGOI1!3U
s• Y l I:HU/SEC )_ ____ ---~ ----------~~;)1/HU 40 __ _
gfl$3:0..ooe:- 3 RADIAl !VE LIJSS Til S"Y .(!:lTtJISEC J.
00\lli!SG
!I
~Rl:NQDE I TOTAL R4DJATIVE LUSS (BTU/SEC!
OOUJllbO
..
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!L!i.JI.l.LL!Jl__
QRJ:NOOE J TOTAL RADJATI~E LUSS (PTU/SECJ
OOOlllbV
0001\lqO
RCONT:I<ECEIVER Plr<EL Ct•NTROLLER RC1UTINE
--·---·---·~ ·---··----· C..\JCI12UO.
-. ~--~--RDCC A:oo.-,.~corott_,.( cROss-sEc r I tn4AL APEA- (S~~ fN_)-~ooa 1121 v
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*
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•
REO:REYNOLCS NUHbEil
•
RH:FlECElVEk PANEL "£lG"T
•
RHUClO:INITIAL
UOIJII220
(FTJ
·-.-----f~iot·l;(OLOTT>J-,--soo!u"rEi.-sr
*
·-----~--
*
*
*
*
*
COLD
TA~~
OOCI123D
TV
DENSITY
RHOfJCo=INITIAL DO~<~CO"E" SODl!l~ (;(OjSJTY
FcH(HiT:.HOT
ooiiit2~<·li--
(LEIH/Clle' T)
SODlu~
(L~M/CU•FT)
OU0!125U
(L81'/CU•f'_T_L___ -~----- __ Q_OQlJ2bO_
TANfl\
SODIUM DENSITY -(L8M/CU•FT)
RHQHTO:INITIAL HOT T.l>'" SilviL•~· D£r-.SlTY (Lb"lti!•~T)
RHO~=SOD!U" DE'-'SITY CLf<"/ClJ•F T1
00011270
C.u01121lfl
__ \1_\i_QJJiqj)_
Df_i<sfTY!:1-0uT l"E~>•E
R..0(}NA:SODI0"
RHONDV~DRtG
U(>CI
13Co
V'LYE SOD[U" U~NS!TY (l8M/[U•FT)
00011!10
R>iDNR}:RECE!VE>< !'<LET snO!U>< •"1ENS!TY (U:·M/Ct;•>1l
OUOIJ3t'U
"•
iiHUROT::SOOIU" DENSlH '<ECE:.li;EC Ulrflf1H"I< (l~"'·CuFTJ
.VOOli:HV
IH•ORF>O=lfiiTIAL ~<TSE~'~ PF'E SL•ciJlJ•· llEi<SITY (Lfl''/Ct••FT)
Onvl IJLIO
t1
RHO I I =!'-I T1 AL SOD I l•"_ L""'.E~_,,rAlCOP;Sl_T_'I'_( I._~_"'_IC],.:,.':.._[l____~~--------.1Ul!H.l35C __
---.----Rii[)ii~i>..r.fi~L -SOO-IU~ '"'!DDL~ '•0LlE Df•;S!TY l~i:''"'ICu-riJ
Ollt'l 1301!
P.H03l:JII;I1PL S•:iJIUH IJP;:>fi'' ><t•Dt DE>.SlTY llb'•ICU~'Tl
OU(i! !37\i
rll10l(l):::Ln"Ew •iOCE, PA~-EL i snDill" DO:SlTY {l.~I'/Cl••Fl) _
.111!0113~'0.
-.-------Ri-oozUJ=-IroDL-E 'lODE, PAI'tL r ~uorl'"' DENs!n lL~'''ICt,.FTJ
uol·tt3..,o
t
Rl103(l}:::UPPER NODE, PA~EL I SPD!UM ~E~SlTY (L~I'/CU•fT)
oO~IIUUII
*
*
*
-*----~FIJ ~_E.!!_:_R_I_S.E_E_P
t
RP~TOTAL
i ':L __Tf.I'Pf." A_I_~RL.i:£".1 Y.;..U.VL.Rf.!!.'l.l~
lNClDE~T
*
~PI=INITIAL
t
RTQ::REtEIVER
~EtEIVER
INCIDENT
PU~ER
'IECEIVE~
•!iA11 qjj) __
O~DI!~.?O
~~~T)
PU•ER
(H~Tl
~0~11~30
*
I?PIF-;:p£(.flYE~ ~"U'IP INLET P«fSSU~>E (PSI'}
~------·-------- OOull'l"ll
·-;;,~--------I'II';UP~;P[CEIVER PIJMP l'llTLET P;;ESS•;RF_ (PSJA l
OIICJII~5U
*
RPO~E>I:JNCIDtNT ~ECElVfA PU•EA FUNCTION NAMF
OOUIIUbO
*
11PSPCA:f![CE.JVER PUMP .SIIt:T!Li'• D!PE CPUSSoSfC.l.!'.~".Ai..._AR~LLS..Q."..!_!<_)~QJ)J)l.l~].\1 ___
•
·-RR.Pc-i=~ I -SE-R -pI PIN_G_ c!;Sss-::s-Ec T~ !-,~-,;A L. AR(A- ( 5~81 N)
UIH' II~ 1:10
PUMP
AND
~'OTn'l
NQPMALIZED RUNNJ>,G TOPQUE
_ ~-. _________ -··
--~-------- SGOv:ORlG. VALVE SODIU~ SPECIF"IC GRA.VlTY~
*
,.
•
•
SGNRl=RECEIYER !hLET SPECIFIC GRAVITY
SHiJ(:oDO""lCUr-ER STATIC '"EAD (PSI)
si<-ritr=T'~ffrACi5o;.><cui-iER.
00011~"0
----~-~---
OOUIISOU
OCV11S1U
·ouVJI5~U
.
.
00011539.__
s-iAT )c;:.·Eio-rPsT)------·---------·uoolt5~L'
SH]:INITIAL RECEIVER STATIC
~EA~ (P$1)
00011550
STATIC HEAD (PSI)
--------·---- llUt:t15bU
--.---~-SINSFT:CO~VEPSIDN FACTOP SfjUAPE- I~CHt.S TO SQUAW[ FOOT
.OOUI1570
*
SL~OT=RECEIVEi< OUTLET TAN~ SET LEVEL (FTl
D~Cll5~u
,.
SNAR!:RECflVf'< Jr.L[T SUD!II~ SPfCJFIC GR6VITY
___it_Q.!J.l.J2"Jl~-
*
SH(l):PANEL I
-.--------SNARlT:i.'(CEflit:R-I-NLEf-SOOJU~DE-;:I·Sl
T~<Lto-Hteti;;;T1 l
oo1111 tooo
SNUV:DIHG VALVE S(>DlU" SPECIFIC GRAVITY
OOOllt>.lll
" - - - · - - - - SFlSGDV=SOLIAPE ROOT (IF T~-'E llh'AG vALvE SiJl>IuM SPf_ClF:lC .GI<A_VITY_____ vv~;llt>20
SSRP:RfCE!VER PUMP SPEED s~ITCH
OUUtlo30
*
STATIC:RECEIVEH PANtl ST4TlC ~EAD ROUTINE NA~-'E
OOOlloqo
-"'-~---_§_!Q=_~')_f!_".'~ .lJl~E D_ S~JJ_C _l.Q£1DUf._[lf__lHL~f C.f_l VE!!__ P'.)l'!'._AI\ID__ MllJDfl____ __o O.Hl t> '.ilL ..
*
*
77
..
STR:RECEIVER OUTLE1
SET POINT
OllOilboO
(F)
·*
hSODlL'"' H"PERATliR[ (F)
i---- - - TAa:AME\J[NT AI>' TE"P[IHTIIR[
··-------------
0(1l•11117U
.l.ouvllb~V
OOOIIt>QQ
(OfGPJOES <")
TlUDC:On~~COME., FLO~ TIME C8NSTA~T !SEC)
OU01t70b
l ~UD•H=Di<AG v ~L \'[ l)J SCMA;,r.t p 1 PE. T Plt__c:_L•_••_S !_A_ NT _!_gf_) ________ Ut)_1J_t 7_11!___
--,-----f"Au6·v::o·;;-A:c:·--y AL vCll ;..·( cr',i;; T Ai<T·-("sE.C-l
Olrllll'/1 ~
TI<UOVD::r>R~G VALVE CCH-<T•t•LLU' C'~Cl\lTlV!O TIM[ !SFC)
OO•ill721l
*
*
*
*
TAUDVI:D~&G VALVE CONT~~LLE~ lNTE~kaL T!Mf lSECl
-~~~1173C
TAUD(l):Ut.ldVITIVE Ti"£• PAI-.!;:L! Cl••,To<OLLf" lSt.C)
:,tJt,!17~t•
TAUCl)=!l'iTE:GkAL T!ME 1 PA"tL 1 (!l!Cfo.I(";LLEI' (5[C)(JI~t:,E.Tl
0110!17'!>(1
*
T ~ URP.,::i< I SE 'l PI" J .".G 'I(JDE .. T! ~'t ___ CL"S T A._ T..~C"A SS I"''· S S•> LIJ,..,...S£.U___ .liO.U...1.7oO __ _
--,-----·fitJ-RP-S:-~ECE-I'vf;.c- PU-;,·p Sl'(Til"' PIPE liM[ Cn~;STH;T (5£C)
Vll!!i1770
"
TAUlC: PA'V£l T,.,[R"'OCC"'ti"LE Tj~f (lPo.;STANT !SE:Cl
000117"0
*
TAUVLV=PA~EL VALvE ACT~~1U~S T!Mt CO~STANT lSECl
U~U1179L
.---------
* .. --.
-.--------··rAt::RECEJV£;, Pu"" I'IEc.•JJ;>Ei.• H• 0 ~lit CDE>FICH.•·l 1
!!UOIII<Ofo
tt
TA2:kECElVEI'< PU'-'P ~f(;uiPEfl TCi'-'Qil~ CuEFFICHid ?
00\'lllllli
_,._ _ _ _ _T_l.3::_"_H.£LV...E..!'_£'tl .. ~_I'E:Q•Jl •Er:... H•"l•.VE. ~J•E.[f.JC.l.t..t-.13_·_________ Q_u~ll82ll __
*
lEST"C~-'ECY VALvE SI"LILl.lJIIN FIIH:T!Ll"'
~1 U011t'31!
,.
T~'"HCv=SU'"' (1~ PlNEL ((l'ilP.'ll \itLVf fHiflPS lPSl)
OOVI H'<~U
,0__________ TFHR:SU"1 OF' PANEL f R 1 C i I UN H:. AC• { 10 51)
________________ QQv 1 H'SQ
*
lG:i:FF"ECTlVE GRDLINO TE'<~'fPlT!Il;;E (~*•'IJ
0(!1)llb~:oO
*
TILL=RECEII/ER PlJ>"P JNDUT TUPC'U[ F' 1HCTIO~>:
\II!Oile70
___*______:I.I..."'.l.~_v_.._E_______________________________________________ l'J.I.QJ~t<''iv___ _
~
TJMP.P::R£CE!VEP PU"P P£~UIREr TU~JUE (hURMALIZEOI
Puotl~~u
•
TI~NPX:RECEIVE~ PUMP ~E~UlgfC ~0R"AL!ZEU TOR~Ut
OOOll~OU
l!1RP=RECEivER ~>ti"P Mr<TC'R li'JR"~LIZEU TnROUE
________
i>UOtl'lltl
TN.I.:SQOit.J" TE••PH'ATUt><:: (FJ
OQOII<;f!l/
*
TNCT:COLD TA~~ SODIU" TEMPERATURE (f)
OuQil'IJO
ot
l t<C: TI :CQLD lANI( S(lD I l;,. !liLET T E._':'_l'f ~ A_T_l!~E___J_F J
0'l(1 H q<J 0
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1Hu 11 <~solNOCO(l):J,o;JT!AL OU.-INC!J>~ER t1!JDE l TE"'PERATURE (f)
OUIJil'lt>O
"
l>;!)((l)::DDio<;CO"'ER NODE I H.~'~'f:IHT•J~E !Fl
----------~---··-0111Jll'l70
.--- -----TNOV-1=-0>~AG Y~LvE S[IDJI;" !fJLfT TE"DERAlURE CFi
-Oilllll'l!!u
t1
TNOVO::DRlG VALVE SULll\1" i.JUTU. T T[>lPERAltJRE (F l
~OUII<i'lu
1>
T"'MT::HOT TA"JI( SODIU" TfMP[i<ATI;Rf (F'j
.li.Jll!.lZQQ\1 __
,
, N·H"r1:"of"T .\"N-o\st1oTu~ I•:Lrr-·-rE:;;,.,f;:i~ r uRE cn
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t:
lt>:.-ITJO:<fNillAL t•Ol TA'-1~ SDDl""' i'<LtT TE.,PE>HTIIRE !I')
COOI(ll20
,:,
TNt'\T::>::JN!'f!oi.L HOT THJ~ SDPIU"' TEMPE.RATUR£ IF)
____________ VIl0!2\13U
.• ----·.T>IH t::RECEI \Eli. I t•LE T "~'·l" fJL D TE ><PE;;; i. TUI'<E ( F l
Oct.'! 2o<~ o
*
TNRIO=I~ITlAL RfCEIVtP !~LET T£"'P[RATURt (F)
UU~I20~0
*
TNRO:<RECE!VER ("-ITLET TA~." TE<-1_1"1;>ATI.JRt (F)
...QJ.>.J;_l(Vt>O
*______
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--.,-------f~"R-bi):i: i~JTT fA_L_P"ECE 1-vT~- 'JJTLE-T
T i.-,;~
l E~PE~<A T li'<E
(F)
CiH1 12v
io-
lNRPO:R}SEP Pl"l"JG C"'PTLET TE"'PfPATURt (Fl
uO•H2~il0
--"'------- TNRPUJ:RECEJI'ER P!J'"'P SLID!UM !NL<:T TEMPERATURE. (F) ... _ -·---_ ()00120'10
•
INRPUQaPECE.IYER PUMI> nuTLET TEM~ERATURE (F)
00iji210u
*
TNRPU(J):RISE'< PIP!I!G ~OUr. I"'!iTAL TE••PE.RATirF.E (F)
Uv012110
TNRP ( l) :::R J SER PI_!'_! NG ~o~GDE l srcl_Q_!_l_!_~l_T_E_"_i:>f:_P ~L!_i<E Jl..L_ _______ ~_O_I.Ij:_l ;:> 120 __
1t
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lEMP£PATURf
Duut2130
(F)
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OOUl?l~U
l"'R3l:NQOE 3 SUDIUI' lt<LE.l TE"P[QATURE (F)
____________ 0001215U
*
-TNR!(J):;?ECEIVER PA''EL !, N!ll;E 1, SU:>!Ufo' H~-'PfRAT!IRE (F)
VUOI2Ib0
*
TNR2lll"'PfCEivE.P PA~<EL I, '<{l!l£ ~' ~ODIUM TE"'Pt;.ATuRt (F)
00012171:
~"----_j_JIIR} _(.ll_:Rf.C£1 YE. 'LJ' ~!"E.L ..1 ~- !<011£....3 , __ 5Qf).lJ.j1'\.. l£.".!'£KU..iJP.£_t.f.J _ _ _ ....lill.Jl.!.2! eo__
*
TNRlOG(Il=LO•EQ NUCE, PA~EL J, !~lllAL SOD!UP lE~P. GutSS (F)
00r121q0
T~R2UG(ll=~IDDLE NV~E, PA~El 1, l~ITIAL SODIU~ TE~P. GU~SS lFJ DOC\220~
-~---------_TNR30G(1J:!.JPPE.k'NQDE., PA>,E.L I, l'<ITIAL SOf'IU" TU'"• GUESS U'l .. iH'vl221U
t.
TNP.JQ(!):;:>H•EL !,AXIAL ~;nM I P.!TlAL SUQl\1~' TE>''PE~<ilUhE. (F l
vvt'1222U
~
TNR20(}):PANEL !,AXIAL NODt 2 INITIAL SOUill~ TEMP[NilUk~ ( f )
01/Dl22JU
"
TN_~],_QJj_l_E£_~~E.L __t_,_A_!_I_Ai._. ~,uu_c: 3....J '!.lLl~I-._S.QQlL'.':'_Ul'.!:'.E.B~_T_U~LLt..l __ c.O_O_l!.U.iu_o__
"
TPT:Tl"E OF T~E RECEIVER PU"P TRIP !SECJ
00Uii250
1t
lR:SUDlU'"' TEMPEi<A.TURE ('<)
(100122611
•
H!APZr.INTEGRATIU"'_"'ET~'JD
(TkAPAZOID~l.)
_____________ llQ012<:7U
-.----lPW-!lJ:::NQDE I TUBE TE;<PERAH•''E RAISED TU FOU~TH P[J,.E_;; Oil
\10012.?tl0 ..
It
TR~?Q:NODE 2 TUHE TEHPfPATURE RAISED TU F'JUPTH PU~ER !R)
000122Vu
ot
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_llJ!!illJ QQ__
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TRI'Il(!):PANEL I, ><UDE 1 "aLL lE'"'~'ERATUR!: (F)
U0ci2~HI
•
TR,.2(l):PAN[L I, N(IOE: c "ALL TEMP(kATliRE (F)
\I(/UI232ll
*
1NR2}:NOOE 2
SJO!U~
*
*
TR"3(I):PA~E~
1, NUDE 3
~ALL
T£'"1PERATURE
(F)
UU012330
~-··
78
*
TRwtO(l):PANEL Ir AXIAL NODE I INITIAL ~ALL lE~PEPATURE [F)
000123U~
TRN20(J):tPANtL !r ~~]~L NODE 2 TNJTJAL ~ALL TE~PEPA1URE If)
UU~I2]5U
TRw3~~(I_)_:P~'::I_E L J ! _ ,Yl AL __o"iDOE_)_j_t-; I..!J.~~-Al.L!._E_~E RAT l!EJ;._!£J_______Qy.JIJ? ~ bJi~-TS:rfFFECTfvE s>.:r T£HPE•41Ui<l CRuLl)
OUOI2:!>7u
TSH:SUM OF PANEL STATIC H[ADS (PS!l
00012360
TSOD=SOO!U>< TE"P[RATltRE (F l
___
_ __ QI/\i_l23'1V
----- ------ -OCI012li0U
*
*
*
*
*
---~~-------
*
*
~----------------~~--~-------
VPOV:tDRAG VALVE POSITION (FRACTION OPEN)
VPf)J!.l :tJ_.!<~ill_AL _QR_A_G __ v_l.l vE___ ~':'C'S lUQN_~~~_B_<;__Ep,1_D!'.L~l
VPO\IX:tOPAG VALVE P•TE!)"EOIATE Pll&!Tl()N UE"ANG l>RACll!l~'< uP(")
VPI{U:l"'ITIAL VALVE PCSITiilN, PH1C.L l lPfPCENT liF FttLL (JPE"l
*
*
*
. VPOI(J):PANEL
POSITIO~
I CONTRnLLEP VALVE
UE~ANC
!PEPCtNT
.-~~------VPXtl):(ONT~OLLER 1 VALV£ "GSITIOI< SIGNAL (F>.ACT!(lN UPi:"l)
•
VP{J):PA~EL I VALVE POSI1IO~ (FRACTION OPEN)
WCTl"NOP".I.LfZEDCOL~DTA-;.,.-; Sii0lu;:;-1NL~Lrl"' ll;:s-;:;f$:_c)
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*
COLn
~CTIR~REFERE~C~
_! _____ l>iDN:NQI<.,ALlZED
a
WONA:A&SCll.UTE
*
TA~~
l~LET
SODIUM
FLO~
PEFEPE'CE
FLn~
"
*
WHT[lR:kOT TAN~ OUTLET AtFE~fNCE FLU~ lLHM/SECI
l'l':'lO=P<lTPL HUT TAl<~ '-fli<"ALIZEP SCtviU"' l'•Ltl ~LO,.
lol1\i:>ilSEP •:oR><ALIZf i) Sf!CIV"' < U'"
~
NN~::4BSOLOTE
VALUE OF
~!SEg
vOOI2"'1V
vUU1250U
00t'I252U
~UOtcSJU
"
~..,hi' ·r-1>.~-SL'L !ti"
;L(lR
00012"70
~~~-~----U0012510
~Lr•~
O<IT~LET-F'i:~r;;---
1'10NO"I"'!T!AL DflwNcr,,.f:Q NflR"-'LlZEL'
"'"('f(J":•-io-ii:-iiCfzE-o
OOOici.IOU
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ll~H/SECl
"
*
OCOI24~C
OuVl24~v
QPEN)DUC!2~5U
(l~M/SEC)
O(l.,p,(D"ER FL.D"
VALUE (lF NnR"ALilEO ('(lw•JCOMEII FL(Iw
WONII:Oo~NCU~ER
UOG12liiU
QJJ.!Ll242J;_
00012~1.11!
--------oo~ul2sso
U~OI2~t>U
_ OOCI2S7o
UOUI2';)t'u
(L~.,/SEC)
00012~9u
_i. _____.,.lll_:NOio>~H.JZEiLFlSEiLSOLl!.L" f.l..JJl't ___
--------~-~-~
-UU--'-1-2c.uD-l"H! Pf'::(E!VER 'JllTLE T TA><K [lf,~/SECJ
ilOOlcbi{J
I'IN>!A(J):AE'SULUTE \IAL<'E {Jf >"A1<E.l l FLU;. (Ui"/SEC)
UU012t:)O
I<>N~i'I{J):PAN(L 1 RfFE"'U•Ct_!>llf'liJ'' F'LG" (L!:I"'/~tCJ _____
---~--Ouu<?t:<lil_
-~--------;NRO(l ):P-'t-iEL I. Pill!AL NL'"'"'-L IZU· SUfllUI>i ~'L'i"
o<>ut2e70
*
NNR(l):PANEL 1 NUP~ALilED 50UTU~ FLO•
OOQI2o75
*
WNO:J_!:lJ~i,.-~R_I_.'H,:.P,_F_J_(lw {\.Ji/_SEC_l------------------~-Q_\IJ./121>!<_\L_
*
I'NUINT:JN!TIAL RlSt~ FL[I" i<llUTJilE NA'1t
OVOii't:Qu
I'IN!IH:~-;~T
•
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Fl.[l~
*
oout27Qv
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.
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