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