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E-raamat: Simulation of Industrial Processes for Control Engineers

(City University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Jul-1999
  • Kirjastus: Butterworth-Heinemann Ltd
  • Keel: eng
  • ISBN-13: 9780080517247
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 13-Jul-1999
  • Kirjastus: Butterworth-Heinemann Ltd
  • Keel: eng
  • ISBN-13: 9780080517247

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For full-fledged and student control engineers, Thomas (electrical, electronic, and information engineering, City U., London) demonstrates in two dozen chapters how the laws of physics and chemistry can generate the equations and models for dynamic computer simulations to comprehend and automate the control processes in the chemical, electrical, gas, and oil industries. Such models must address realities undreamt of by design engineers' steady- state models. Includes nine appendices relating to energy terms, calculation of compressible flow, equations and models for control valve flows, measurement of the internal energy of reaction, efficiency formulae for different nozzle types, modeling turbine reaction stages, fuel pin average temperature and effective heat transfer coefficient, and integral desaturation algorithms. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Computer simulation is the key to comprehending and controlling the full-scale industrial plant used in the chemical, oil, gas and electrical power industries. Simulation of Industrial Processes for Control Engineers shows how to use the laws of physics and chemistry to produce the equations to simulate dynamically all the most important unit operations found in process and power plant.



The book explains how to model chemical reactors, nuclear reactors, distillation columns, boilers, deaerators, refrigeration vessels, storage vessels for liquids and gases, liquid and gas flow through pipes and pipe networks, liquid and gas flow through installed control valves, control valve dynamics (including nonlinear effects such as static friction), oil and gas pipelines, heat exchangers, steam and gas turbines, compressors and pumps, as well as process controllers (including three methods of integral desaturation). The phenomenon of markedly different time responses ("stiffness") is considered and various ways are presented to get around the potential problem of slow execution time. The book demonstrates how linearization may be used to give a diverse check on the correctness of the as-programmed model and explains how formal techniques of model validation may be used to produce a quantitative check on the simulation model's overall validity.

The material is based on many years' experience of modelling and simulation in the chemical and power industries, supplemented in recent years by university teaching at the undergraduate and postgraduate level. Several important new results are presented. The depth is sufficient to allow real industrial problems to be solved, thus making the book attractive to engineers working in industry. But the book's step-by-step approach makes the text appropriate also for post-graduate students of control engineering and for undergraduate students in electrical, mechanical and chemical engineering who are studying process control in their second year or later.

Arvustused

"With his book, Professor Thomas has provided a major contribution to the modelling of major unit processes which are found in the chemical, oil-and -gas and power generation industries....the book represents a major achievement and can be strongly recommended." --IMechE - Proc. Inst. Mech. Engrs. October 2001

..highly recommended to anyone involved in mathematical simulation for any purpose..” --Nuclear Energy, October 2000.

"Professor Thomas has produced a much-needed work in the field of modeling and simulation of industrial systems...It is most apparent that a practitioner with many years of experience has written this book....a most valuable addition to any technical library..It is a useful reference not just for control engineers but for mechanical and chemical engineers as well." --Intech (ISA Journal) , August 2000

"Engineers simulating industrial processes commonly found in the chemical, nuclear and oil industries will find this book essential to their work....this book will be of considerable importance to all engineers interested in the mathematical modelling and simulation of industrial processes. The book is clearly the most comprehensive and up-to-date treatise currently available on this important topic." --IEE Computing & Control Engineering Journal, April 2000.

"This is a significant book for those serious about learning how to produce good dynamic simulations of process plant...it shows how to use good science to derive models of the appropriate complexity to suit the particular problem....It is recommended both for those wishing to learn about the subject, and for the experienced who need to find out how to model a particular piece of equipment." --Measurement and Control, Nov. 1999

"Professor Thomas and his publishers are to be congratulated for producing such a useful resource text." --The Nuclear Engineer, Vol. 41, No. 1, 2000

"This book should be of great interest to those addressed in the title...It is difficult to think of a comparable source of explanation and information in this field." --Dr Alex Thompson, HMS Sultan

"it is rare to find a modern engineering textbook which combines theory and practice to such a useful effect. Professor Thomas is to be congratulated on providing such an outstanding work." --Dr Andrew Eadie, Glasgow Caledonian University.

Foreword xv
Notation xvii
Introduction
1(4)
Fundamental concepts of dynamic simulation
5(16)
Introduction
5(1)
Building up a model of a simple process-plant unit: tank liquid level
5(2)
The general form of the simulation problem
7(1)
The state vector
8(1)
Model complexity
9(1)
Distributed systems: partial differential equations
10(2)
The problem of stiffness
12(3)
Tackling stiffness in process simulations: the properties of a stiff integration algorithm
15(1)
Tackling stiffness in process simulations by modifications to the model
16(1)
Solving nonlinear simultaneous equations in a process model: iterative method
17(1)
Solving nonlinear simultaneous equations in a process model: the Method of Referred Derivatives
18(2)
Bibliography
20(1)
Thermodynamics and the conservation equations
21(11)
Introduction
21(1)
Thermodynamic variables
21(1)
Specific heats of gases
22(1)
Relationships between the principal specific heats for a near-ideal gas
23(1)
Conservation of mass in a bounded volume
23(1)
Conservation of energy in a fixed volume
24(2)
Effect of volume change on the equation for the conservation of energy
26(1)
Conservation of energy equation for a rotating component
26(1)
Conservation of mass in a pipe
27(1)
Conservation of energy in a pipe
28(2)
Conservation of momentum in a pipe
30(1)
Bibliography
31(1)
Steady-state incompressible flow
32(9)
Introduction
32(1)
The energy equation for general steady-state flow
32(1)
Incompressible flow
33(1)
Magnitude of the Fanning friction factor, f
34(1)
Frictionally resisted, incompressible flow through a real pipe
35(1)
Pressure drop due to level difference
36(1)
Frictional pressure drop
36(1)
Pressure drop due to bends and fittings
37(1)
Pressure drop at pipe outlet
37(2)
Pressure drop at pipe inlet
39(1)
Overall relationship between mass flow and pressure difference
40(1)
Bibliography
40(1)
Flow through ideal nozzles
41(9)
Introduction
41(1)
Steady-state flow in a nozzle
41(4)
Steady-state flow through a nozzle with constant specific volume
42(1)
Steady-state flow through a nozzle for a gas undergoing a polytropic expansion
43(1)
Isentropic steady-state flow
44(1)
Steady-state flow through a nozzle for a gas undergoing an isothermal expansion
44(1)
Maximum mass flow for a polytropic expansion
45(1)
Sonic flow
45(2)
Sonic flow for a polytropic expansion
45(2)
Sonic flow for an isentropic expansion
47(1)
Sonic flow during an isothermal expansion
47(1)
Comparison between flow formulae
47(2)
Bibliography
49(1)
Steady-state compressible flow
50(10)
Introduction
50(1)
General overview of compressible pipe-flow
50(1)
Frictionally resisted, adiabatic flow inside the pipe
51(4)
Deriving a second equation for the Mach number at station `2'
51(2)
The ratio of specific volumes at pipe entrance and outlet, v3/v2
53(1)
The pipe outlet pressure, p3: the effect of choking
53(2)
Solution sequence for compressible flow through a pipe
55(1)
Determination of the friction factor, f
56(1)
Determination of the effective length of the pipe
56(1)
Sample calculation
56(1)
Explicit calculation of compressible flow
57(1)
Example using the long-pipe approximation
58(1)
Bibliography
59(1)
Control valve liquid flow
60(8)
Introduction
60(1)
Types of control valve
60(1)
Pressure distribution through the valve
61(1)
Liquid flow through the valve
62(1)
Cavitation and choking in liquid flow
63(1)
Cavitation
63(1)
Choking
63(1)
Relationship between valve capacity at part open and capacity at full open
64(1)
The valve characteristic
64(1)
Velocity-head loss across the valve
65(2)
Bibliography
67(1)
Liquid flow through the installed control valve
68(6)
Introduction
68(1)
Liquid flow through an installed valve
68(1)
Choking during liquid flow
69(1)
Cavitation during liquid flow
70(1)
Example: calculation of liquid flow
70(4)
Control valve gas flow
74(16)
Introduction
74(1)
Representing the first section of the control valve as a nozzle
74(2)
The relationship between throat ratio and the valve pressure ratio at high valve pressure ratios, p2/p1
76(1)
Deriving a value for throat area, At, from the limiting gas conductance, Cg
77(1)
Correlation of the friction coefficient at high-pressure ratios with the cavitation coefficient
77(1)
The relationship between throat and valve pressure ratios when the valve pressure ratio is low
78(2)
Relating throat and exit pressure ratios throughout the pressure ratio range
80(1)
Flow at partial valve openings
81(1)
Summary of the nozzle-based model for gas flow through the control valve
82(1)
Worked example using the nozzle-based calculational model
83(2)
Other models for gas flow
85(3)
The Fisher Universal Gas Sizing Equation (FUGSE)
85(2)
Approximate calculation of valve gas flow through modifying the liquid-flow equation
87(1)
Bibliography
88(2)
Gas flow through the installed control valve
90(18)
Introduction
90(1)
Gas flow through the installed valve -- Velocity-Head Implicit Method (VHIM)
90(4)
VHIM without choking
90(1)
Detecting the onset of sonic flow in the valve using VHIM
91(1)
Calculating the flow and pipe conditions when valve flow is sonic in the VHIM
92(2)
Gas flow through an installed valve -- Smoothed Velocity-Head Implicit Method (SVHIM)
94(3)
SVHIM without choking
94(2)
Allowing for sonic flow in the valve using SVHIM
96(1)
Gas flow through an installed valve -- Average Specific Volume Approximation Method (ASVAM)
97(1)
Example: calculation of gas flow
98(8)
SVHIM
99(2)
VHIM
101(2)
ASVAM
103(1)
Simplified Average Specific Volume Method with constant bo: SASVAM
104(2)
Discussion
106(2)
Accumulation of liquids and gases in process vessels
108(9)
Introduction
108(1)
Accumulation of liquid in an open vessel at constant temperature
108(1)
Accumulation of gas in a vessel at constant temperature
108(2)
Use of kilogram-moles in modelling the accumulation of a mixture of gases
110(2)
Application to the accumulation of gas in a vessel of constant volume
112(1)
Gas accumulation with heat exchange
112(2)
Liquid and gas accumulation with heat exchange
114(3)
Two-phase systems: boiling, condensing and distillation
117(18)
Introduction
117(1)
Description of single component boiling/condensing: boiling model
117(3)
Functions used in the modelling of vapour-liquid equilibrium
120(1)
Application of the boiling model to a steam drum and recirculation loop
120(2)
Continuous distillation in a distillation column
122(1)
Mathematical model of the distillation plate
123(7)
Functions used in the modelling of the distillation plate
130(2)
Modelling the distillation column as a whole
132(2)
Bibliography
134(1)
Chemical reactions
135(17)
Introduction
135(1)
The reaction at the molecular and kilogram-mole levels
135(1)
Reaction rate relationship for the different chemical species in the reaction
136(1)
Reaction rates
137(1)
Generalization for multiple reactions
137(1)
Conservation of mass in a bounded volume
138(1)
Conservation of energy in a fixed volume
139(1)
The internal energy of reaction and the enthalpy of reaction
140(2)
The effect of temperature on ΔU and ΔH
142(1)
Continuous reaction in a gas reactor
143(3)
Modelling a Continuous Stirred Tank Reactor (CSTR)
146(5)
Bibliography
151(1)
Turbine nozzles
152(20)
Introduction
152(1)
Velocity and enthalpy relationships in a turbine nozzle: nozzle efficiency
152(1)
Dependence of the polytropic exponent on nozzle efficiency
153(2)
Effect of nozzle efficiency on nozzle velocity
155(1)
Using the concept of stagnation to account for non-neglible inlet velocities
156(1)
Sonic flow
157(1)
The convergent-only nozzle
158(3)
Estimating nozzle efficiency for a convergent-only nozzle
158(1)
Outlet velocity and mass flow in a convergent-only nozzle
159(1)
Nozzle efficiency in choked conditions for a convergent-only nozzle
160(1)
Nozzle efficiency over the whole range of pressure ratios for a convergent-only nozzle
160(1)
The convergent-divergent nozzle
161(10)
Relationship between the throat pressure and the discharge pressure for a convergent-divergent nozzle
161(4)
Nozzle efficiencies for a convergent-divergent nozzle
165(2)
Nozzle efficiency in off-design, choked conditions for a convergent-divergent nozzle
167(1)
The efficiency of a convergent-divergent nozzle down to just below the design pressure ratio
168(1)
Discharge velocity and mass flow in a convergent-divergent nozzle
168(1)
Nozzle efficiency at discharge pressure ratios substantially below the lower critical ratio for a convergent-divergent nozzle
169(1)
Calculating the effciency of a convergent-divergent nozzle over the full pressure range
169(2)
Bibliography
171(1)
Steam and gas turbines
172(18)
Introduction
172(1)
The turbine stage
172(1)
Stage efficiency and the stage polytropic exponent
173(1)
Reaction
174(2)
Mid-stage pressure; nozzle discharge velocity; stage mass flow
176(1)
Design conditions in an impulse blade
176(2)
Off-design conditions in an impulse stage: blade efficiency and stage outlet velocity in the absence of blade and nozzle inlet loss
178(1)
Loss of kinetic energy caused by off-design angles of approach to moving and fixed blades
179(2)
Loss of kinetic energy at the entry to a moving blade
179(1)
Recovery of kinetic energy at the entry to a fixed blade (nozzle)
180(1)
Off-design conditions in an impulse blade: typical corrections for kinetic energy losses
181(1)
50% reaction stage: the design of the fixed blades (nozzles) and the moving blades
181(2)
Blade efficiency at design conditions for a 50% reaction stage
183(2)
Blade efficiency at off-design conditions for a 50% reaction stage
185(2)
The polytropic exponent for saturated steam
187(1)
Calculation sequence for turbine simulation
187(2)
Bibliography
189(1)
Steam and gas turbines: simplified model
190(14)
Introduction
190(1)
The effect of neglecting interstage velocities in modelling a real turbine stage: the approximate equivalence of kinetic energy and enthalpy at nozzle inlet
190(1)
Stage efficiency for an impulse stage
191(1)
Stage efficiency for a reaction stage
192(1)
Evaluation of downstream enthalpies following isentropic and frictionally resisted expansions
193(3)
Evaluation of the entropy integral for steam
193(1)
Evaluation of the entropy integral for a real gas
194(1)
Evaluation of the entropy integral for an ideal gas
195(1)
Analytic functions linking entropy and enthalpy for saturated and superheated steam
196(3)
Integrating into the superheated region
197(1)
Integrating into the wet-steam region
198(1)
Examples of analytic approximating functions
198(1)
Specific volume at stage outlet
199(1)
Simplifying the calculation of mass flow
199(2)
Calculation sequence for the simplified turbine model
201(2)
Bibliography
203(1)
Turbo pumps and compressors
204(17)
Introduction
204(1)
Applying dimensional analysis to centrifugal and axial pumps
204(3)
Pump characteristic curves
207(2)
Pump dynamics
209(1)
Calculating the flow pumped through a pipe
210(1)
Rotary compressors
211(1)
Compressor characteristics based on polytropic head
212(4)
Isentropic efficiency and isentropic head
212(1)
Polytropic efficiency and polytropic head
213(2)
Dimensional analysis applied to the polytropic head: the use of a characteristic curve and the affinity laws
215(1)
Compressor characteristics based on pressure ratio
216(2)
Dimensional analysis applied to compressor pressure ratio
216(2)
Applying the pressure ratio and efficiency characteristics to estimating flow and section power
218(1)
Computing the performance of the complete compressor
218(2)
Bibliography
220(1)
Flow networks
221(18)
Introduction
221(1)
Simple parallel networks
221(1)
Liquids
221(1)
Gases
222(1)
Simple series network
222(1)
Liquids
222(1)
Gases
223(1)
Complex networks
223(1)
Strategy for solving flow networks using iterative methods
224(1)
Modifying the flow equations to speed up the Newton-Raphson method
225(4)
Solving the steady-state flow network using the Method of Referred Derivatives
229(1)
Outline of the method
229(1)
Determining the initial conditions for the implicit variables: Prior Transient Integration and Extended Prior Transient Integration
229(1)
Worked example using the Method of Referred Derivatives: liquid flow network
230(5)
Avoiding problems at flow reversal with the Method of Referred Derivatives
235(1)
Liquid networks containing nodes with significant volume: allowing for temperature changes
236(2)
Bibliography
238(1)
Pipeline dynamics
239(17)
Introduction
239(1)
Dynamic equations for a pipeline: the full equations
239(1)
Development of the equation for conservation of mass
239(1)
Development of the equation for conservation of momentum
240(1)
Applying the Method of Characteristics to pipeline dynamics
240(3)
Interfacing the Method-of-Characteristics pipeline model to the rest of process simulation: boundary conditions
243(7)
Constrained pressure at the inlet to a liquid pipeline
243(1)
Constrained flow at the outlet of a liquid pipeline
244(1)
Valve at the inlet to a liquid pipeline
244(2)
In-line valve in a liquid pipeline
246(1)
Pump feeding the pipeline from an upstream tank
247(1)
Junction of two or more pipes: liquid or gas
248(2)
Correcting the speed of sound for the elasticity of the pipe material
250(1)
Example of pipeline flow using the Method of Characteristics
251(3)
Finite differences
254(1)
Bibliography
255(1)
Distributed components: heat exchangers and tubular reactors
256(12)
Introduction
256(1)
General arrangement of a shell-and-tube heat exchanger
256(1)
Equations for flow in a duct subject to heat exchange
257(1)
Equation for liquid flow in a duct subject to heat exchange
258(1)
Equation for gas flow in a duct subject to heat exchange
258(1)
Application of the duct equations to the tube-side fluid
259(1)
Application of the duct equations to the shell-side fluid
259(1)
Equations for the tube wall and the shell wall
260(1)
Solving the heat exchanger equations using spatial finite differences
261(1)
The tubular reactor
262(1)
Mass balance for the gas flowing through the catalyst bed
263(1)
Energy balance for the gas flowing through the catalyst bed
263(3)
Solving the temperature and conversion equations using finite differences
266(1)
Bibliography
267(1)
Nuclear reactors
268(14)
Introduction
268(1)
General description of a nuclear reactor
268(1)
The process of nuclear fission
269(1)
Delayed neutrons
270(1)
Reactor multiplication factor, k
271(1)
Absorption of neutrons and the production of prompt neutrons
272(1)
Overall neutron balance
273(1)
The balance for delayed neutron precursors
273(1)
Summary of neutron kinetics equations; reactor power
274(1)
Values of delayed neutron parameters and the problem of stiffness
274(1)
Relationship between neutron density, neutron flux and thermal power
275(1)
Spatial variations in neutron flux and power: centre-line and average reactor flux
276(1)
Flux and power in axial segments of the reactor core
277(2)
Calculating the temperature of the fuel in each of the axial segments
279(1)
Calculating the coolant temperature
280(1)
Calculating the reactivity
280(1)
Bibliography
281(1)
Process controllers and control valve dynamics
282(14)
Introduction
282(1)
The proportional controller
282(1)
The basic operation of the proportional plus integral controller
283(1)
The proportional plus integral plus derivative (PID) controller
284(1)
Integral desaturation
285(4)
Integral desaturation - Type 1
286(1)
Integral desaturation - Type 2
286(2)
Integral desaturation - Type 3
288(1)
The dynamics of control valve travel
289(1)
Modelling static friction: the velocity deadband method
290(1)
Using nonlinearity blocks: the backlash description of valve static friction
291(4)
Bibliography
295(1)
Linearization
296(12)
Introduction
296(1)
Principles of linearization
296(1)
Example of analytic linearization: the response of liquid flow to valve opening in a pumped liquid system
297(1)
Response of flow to valve opening when the differential pressure controller is switched out
298(3)
To find ∂W/∂y
299(1)
To find ∂W/∂Δp
299(1)
To find dΔp/dy
299(2)
Including the effect of the differential pressure controller
301(6)
Δp measurement
301(1)
Comparator
302(1)
Δp controller
302(1)
The response of steam throttle travel to demanded throttle travel, x/xd
303(1)
Steam throttle opening to steam throttle travel, dyt/dx
303(1)
Response of turbine power to steam throttle opening, dPs/dYt
303(1)
The response of turbine/pump speed to turbine power, N/Ps
303(2)
The change in differential pressure with speed, dΔp/dN
305(2)
Using the linear block diagram
307(1)
Bibliography
307(1)
Model validation
308(71)
Introduction
308(1)
The philosophy of model validation
308(1)
The concept of Model Distortion
309(2)
Transfer-function-based technique for model distortion
311(6)
Defining the companion model
311(1)
Estimation of parameter variance needed for model matching
312(3)
Model acceptance for transfer-function-based technique: explainability
315(1)
Model acceptance for transfer-function-based technique: predictability
316(1)
Time-domain technique for the solution of the model distortion equations
317(5)
Finding the parameter variations needed to match the behaviour of all recorded variables
317(3)
Calculating the parameter variations using the Method of Referred Derivatives
320(1)
Model acceptance criteria for the time-domain technique: explainability
321(1)
Model acceptance criteria for the time-domain technique: predictability
322(1)
Applications
322(1)
Bibliography
322(1)
Appendices
1 Comparative size of energy terms
323(5)
A.1.1 Introduction
323(1)
A.1.2 Bulk kinetic energy
323(1)
A.1.3 The relative size of the potential energy term
323(1)
A.1.4 Vessel filled with liquid or gas
324(1)
A.1.5 Liquid partially filling a vessel
324(1)
A.1.6 Gas partially filling a vessel, contained above a movable surface, e.g. a liquid surface, undergoing a near-adiabatic expansion or compression
325(3)
2 Explicit calculation of compressible flow using approximating functions
328(13)
A2.1 Introduction
328(1)
A2.2 Applying dimensional analysis to compressible flow
328(1)
A2.3 The shape of the dimensionless flow function, f pipe
328(5)
A2.4 Developing a long-pipe approximation to the full compressible flow equations
333(1)
A2.4.1 Deriving an approximate expression for vave
334(1)
A2.4.2 The correction factor b0
335(1)
A2.5 Calculation of b0
336(1)
A2.6 Using polynomial functions to characterize the b0 surface
336(1)
A2.7 Size of errors using approximating functions
337(1)
A2.8 Simplified approximation using a constant value of b0
338(2)
A2.9 Bibliography
340(1)
3 Equations for control valve flow in SI units
341(3)
A3.1 Introduction
341(1)
A3.2 Liquid flow through the valve
341(1)
A3.3 Gas flow at small pressure drops in US units
341(1)
A3.4 Gas flow at very large pressure drops
342(1)
A3.5 Gas flow at intermediate pressure drops: the Fisher Universal Gas Sizing Equation (FUGSE)
342(1)
A3.6 Converting the Fisher Universal Gas Sizing Equation to SI units
343(1)
A3.7 Summary of conversions between SI and US valve coefficients
343(1)
4 Comparison of Fisher Universal Gas Sizing Equation, FUGSE, with the nozzle-based model for control valve gas flow
344(4)
A4.1 Introduction
344(1)
A4.2 Comparison of the Fisher Universal Gas Sizing Equation, FUGSE, with direct data
344(1)
A4.3 Comparison of the FUGSE with the nozzle-based model for control valve gas flow
345(3)
5 Measurement of the internal energy of reaction and the enthalpy of reaction using calorimeters
348(3)
A5.1 Introduction
348(1)
A5.2 Measuring the internal energy of reaction using the bomb calorimeter
348(1)
A5.3 Measuring the enthalpy of reaction using an open-system calorimeter
349(2)
6 Comparison of efficiency formulae with experimental data for convergent-only and convergent-divergent nozzles
351(12)
A6.1 Experimental results
351(2)
A6.2 Theory versus experiment for the convergent-only nozzle
353(2)
A6.3 Divergence ratio for the convergent-divergent nozzles
355(1)
A6.3.1 Keenan's method of estimating divergence ratio
355(1)
A6.3.2 Alternative method of estimating divergence ratio
356(1)
A6.4 Interpreting the experimental results for convergent-divergent nozzles
357(2)
A6.5 Comparing calculated efficiency curves with measured efficiency curves
359(3)
A6.6 Conclusions
362(1)
A6.7 Reference
362(1)
7 Approximations used in modelling turbine reaction stages in off-design conditions
363(6)
A7.1 Axial velocity over the fixed blades at off-design conditions for a 50% reaction stage
363(2)
A7.2 Degree of reaction at off-design conditions for a 50% reaction stage
365(4)
8 Fuel pin average temperature and effective heat transfer coefficient
369(5)
A8.1 Introduction
369(1)
A8.2 Applying Fourier's law of heat conduction to the fuel
369(2)
A8.3 Heat transfer across the gas gap
371(1)
A8.4 Heat transfer through the cladding
371(1)
A8.5 Heat transfer from the cladding to the coolant
371(1)
A8.6 The overall heat transfer coefficient
371(1)
A8.7 Example of calculating average fuel temperatures in a PWR
372(1)
A8.8 Bibliography
373(1)
9 Conditions for emergence from saturation for P+I controllers with integral desaturation
374(5)
A9.1 Introduction
374(1)
A9.2 Type 1 integral desaturation
374(1)
A9.2.1 Size of the error at emergence from controller saturation
374(1)
A9.2.2 Conditions on the rate of change of error at emergence from controller saturation
375(1)
A9.2.3 Summary of conditions for a controller with Type 1 integral desaturation emerging from controller saturation
375(1)
A9.3 Type 2 integral desaturation
375(2)
A9.4 Type 3 integral desaturation
377(2)
Index 379