US3588265A - System and method for providing steam turbine operation with improved dynamics - Google Patents

System and method for providing steam turbine operation with improved dynamics Download PDF

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US3588265A
US3588265A US722790A US3588265DA US3588265A US 3588265 A US3588265 A US 3588265A US 722790 A US722790 A US 722790A US 3588265D A US3588265D A US 3588265DA US 3588265 A US3588265 A US 3588265A
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turbine
steam
rotor
temperature
strain
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William R Berry
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Westinghouse Electric Corp
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01K—STEAM ENGINE PLANTS; STEAM ACCUMULATORS; ENGINE PLANTS NOT OTHERWISE PROVIDED FOR; ENGINES USING SPECIAL WORKING FLUIDS OR CYCLES
    • F01K7/00—Steam engine plants characterised by the use of specific types of engine; Plants or engines characterised by their use of special steam systems, cycles or processes; Control means specially adapted for such systems, cycles or processes; Use of withdrawn or exhaust steam for feed-water heating
    • F01K7/16—Steam engine plants characterised by the use of specific types of engine; Plants or engines characterised by their use of special steam systems, cycles or processes; Control means specially adapted for such systems, cycles or processes; Use of withdrawn or exhaust steam for feed-water heating the engines being only of turbine type
    • F01K7/22—Steam engine plants characterised by the use of specific types of engine; Plants or engines characterised by their use of special steam systems, cycles or processes; Control means specially adapted for such systems, cycles or processes; Use of withdrawn or exhaust steam for feed-water heating the engines being only of turbine type the turbines having inter-stage steam heating
    • F01K7/24—Control or safety means specially adapted therefor
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D19/00—Starting of machines or engines; Regulating, controlling, or safety means in connection therewith
    • F01D19/02—Starting of machines or engines; Regulating, controlling, or safety means in connection therewith dependent on temperature of component parts, e.g. of turbine-casing

Definitions

  • ABSTRACT A programmed digital computer control system for an electric power plant steam turbine responds to turbine impulse chamber steam temperature and other input variables to control turbine inlet steam flow within constraint limits that prevent excessive rotor loading and allow controlled accumulation of turbine rotor plastic strain fatigue according to (inquired) predetermined fatigue accumulation standards.
  • the present invention relates to elastic fluid turbines and more particularly to systems and methods for determining the dynamic operation of steam turbines.
  • each of the various types of steam turbines generally involves the application oflimits to the rate at which turbine steam flow and/or inlet steam enthalpy can be changed for speed, load or other end variable control because of thermal and mechanical turbine response considerations.
  • the turbine casing design is determined largely by steam operating pressure and temperature, and the turbine rotor design is determined largely by rated steady state centrifugal loading forces at maximum speed and rated full power torque with appropriate consideration for other factors including lateral stiffness and critical speeds of rotation.
  • the turbine casing and rotor also must perform under transient and cyclic changes in steam conditions such as those involved in effecting a turbine speed change and/or a turbine load change.
  • the rotor must also perform under transient centrifugal force loading conditions such as those involved in cold startups and the like. Rate or dynamic limits placed on turbine operation largely reflect considerations of thermal expansion and contraction loading associated with inlet steam condition changes and considerations of centrifugal force loading associated with transient speed changes.
  • steam condition it is meant herein to refer to steam temperature, pressure and other steam characteristics including steam flow.
  • Thermal loading limits have particular significance because rates of change of turbine operating level nearly always or at least quite frequently result in temperature gradients which cause portions of the turbine metal parts to expand and contract in excess of their elastic limit in most applications across the steam turbine art.
  • the turbine structural material, and particularly the turbine rotor structural material undergoes a developing history of transient and cyclic plastic strain with continued turbine operation.
  • the combined considerations of turbine operating characteristics required to meet even the minimum needs of turbine users, operating steam thermodynamic properties, turbine size, and turbine structural material thermal and mechanical properties work together to make plastic strain of turbine materials a virtually unavoidable consequence of turbine operation.
  • Plastic strain resulting particularly from temperature cycling is significant to supervised or controlled turbine operation because of fatigue damage and eventual fatigue cracking which determines the turbine operating life. Fatigue damage accumulates most rapidly at locations most exposed to the widest and most frequent steam temperature variation. It is potential fatigue damage to turbine material at these locations which ordinarily figures most prominently in placing dynamic constraints on turbine operation.
  • Transient centrifugal force loading is typically of greatest concern at turbine rotor locations of highest steady state centrifugal loading such as in the intermediate pressure section of a large steam turbine system. In the latter case; steady state centrifugal force loading eventually causes creep cracks and these are to be distinguished from plastic strain cracks.
  • Turbine life and efficiency and economy of turbine operation have thus been adversely affected by the limited prior art capability for dynamic turbine supervision and control with respect to large electric power plant turbines as well as turbines across the turbine art as a whole.
  • limited steam turbine dynamic capability has resulted in limited plant capability to meet changing electrical load level demands.
  • the steam temperature determining means is combined with means for determining a predetermined thermally caused rotor condition and preferably for determining rotor surface stress or strain in the predetermined rotor portion as a function of the determined steam temperature.
  • the monitored steam flow region is that where steam temperature variation is the greatest, such as the impulse chamber.
  • rotor surface strain it is herein intended to refer to strain occurring at or near the rotor surface including at or near rotor surface structural features such as at or near the base of blade or other rotor grooves.
  • rotor surface stress is correspondingly defined.
  • function of a certain variable it is herein intended to refer to a function in which that variable is a significant determining variable but not necessarily the only determining variable in the function.
  • the steam temperature is determined in the predetermined region, the rotor thermal condition is determined, and a limit is placed on the rate at which the turbine operating level is changed in order to limit predetermined turbine conditions including the extent of the rotor thermal condition while meeting end controlled variable demand.
  • the control system including the necessary determining means provides automatic end variable control under automatic closed loop dynamic constraint control. In electric power plant turbines, load and speed changes are constrained within the rotor thermal condition limits. More accurate, more efficient and more economic turbine operation is realized by application of the invention.
  • control system includes a digital computer system. It is programmed to determine end variable control actions during transient and steady state operation with dynamic constraints computed as a function of steam temperature in the predetermined steam flow region.
  • Another object of the invention is to provide a novel method and system for operating a steam turbine with greater accuracy, efficiency and economy.
  • a further object of the invention is to provide a novel method and system for operating a steam turbine with both extended turbineoperating life and better satisfaction of turbine operating level demand.
  • An additional object of the invention is to provide a novel method and system for operating a steam turbine with better control over turbine speed and load change rates.
  • Another object of the invention is to provide a novel turbine plant instrumentation package capable of determining real time turbine rotor stress or strain and thereby enabling turbine operation in both existing and new turbine installations to be supervised more efficiently, more economically and more accurately within dynamic constraints.
  • FIG. I shows a schematic diagram of a large electric power plant steam turbine supplied with steam by a steam generating system and operated in association with certain sensor and control devices in accordance with the principles of the invention
  • FIG. 2 shows a schematic diagram of a programmed digital computer control system operable with the steam turbine and its associated devices shown in FIG. I in accordance with the principles ofthe invention
  • FIG. 3 shows an enlarged portion of a longitudinal section through a high pressure section of the steam turbine of FIG. 1 and certain sensor devices placed therein;
  • FIGS. 4A and 4B show further enlarged portions of the section view of FIG. 3 which illustrate typical locations at which rotor plastic strain fatigue cracking might develop;
  • FIG. 5 illustrates the manner in which turbine inlet steam pressure and temperature and impulse chamber steam temperature are related with the use of typical specific electric power plant steam turbine data
  • FIG. 6 shows typical temperature transients for various locations in a large electric plant steam turbine as the turbine is brought up to the synchronous speed value and placed under steady state load operation;
  • FIG. 7 shows a typical rotor surface temperature cycle for an electric power plant steam turbine
  • FIG. 8 shows a typical thermal plastic stress-strain cyclic capacity chart corresponding to cyclic operation like that of FIG. 7 for a 3600 rpm. electric power plant steam turbine rotor having a geometric design of high thermal duty cycle capacity;
  • FIG. 9 shows a supervisory and control logic flow diagram employed in part of a programming system which operates the computer system of FIG. 2 in accordance with the principles of the invention
  • FIG. 10 shows a turbine dynamics supervisory and control portion of the diagram of FIG. 9 in greater detail.
  • FIG. 11 graphically illustrates one manner in which turbine steam enthalpy and/or flow changes and in turn impulse chamber steam temperature can be controllably constrained as a function of rotor strain.
  • FIG. I a large single reheat steam turbine 10 constructed in a well-known manner and operated and controlled in accordance with the principles of the invention as part of a fossil fuel fired electric power plant 12.
  • Other types of steam turbines such as extraction turbines, reactor turbines, back pressure turbines, etc. can also be controlled in accordance with the principles of the inven' tion.
  • the turbine is provided with a single output shaft l4 which drives a conventional large alternating current generator 16 to produce three phase (or other phase) electric power as measured by a conventional power detector 18.
  • the generator 16 is connected (not shown) through one or more breakers (not shown) per phase to a large electric power network and when so connected causes the turbogenerator arrangement to operate at synchronous speed under steady state conditions. Under transient electric load change conditions, system frequency may be affected and conforming turbogenerator speed changes would result.
  • power contribution of the generator 16 to the network is normally determined by the turbine steam flow which in this instance is supplied to the turbine 10 at substantially constant throttle pressure.
  • the turbine 10 is of the multistage axial flow type and includes a high pressure section 20, an intermediate pressure section 22 and a low pressure section 24.
  • Each of these turbine sections may include a plurality of expansion stages provided by stationary vanes and an interacting bladed rotor connected to the shaft 14.
  • turbines operated in accordance with the present invention can have other forms with more or fewer sections tandemly connected to one shaft or compoundly coupled to more than one shaft.
  • the constant throttle pressure steam for driving the turbine 10 is developed by a steam generating system 26 which is provided in the form of a conventional drum type boiler operated by fossil fuel such as pulverized coal or natural gas. From a generalized standpoint, the present invention can also be ap' plied to steam turbines associated with other types of steam generating systems such as nuclear reactor and once through boiler systems.
  • the turbine 10 in this instance is further of the double ended steam chest type, and turbine inlet steam flow is directed through a plurality of throttle valves and a plurality of governor valves designated as inlet valves 25.
  • the double ended steam chest type and other steam chest types such as the single ended steam chest type or the end bar lift type may involve varying numbers and/or arrangements of throttle valves. More detailed description on a particular throttle and governor valve arrangement is presented in the aforementioned Birnbaum and Giras copending application.
  • the preferred turbine startup method is to l raise the turbine speed from the turning gear speed of about 2 r.p.m. to about 80 percent of the synchronous speed under throttle valve control and then (2) transfer to governor valve control and raise the turbine speed to the synchronous value, close the power system breaker(s) and meet the load demand.
  • Similar but reverse practices are involved.
  • Other transfer practices can be employed, but it is unlikely that transfer would ever be made at a loading point above 40 percent rated loading because of throttling efficiency considerations.
  • the reheater system 28 After the steam has coursed past the first stage impulse blading to the last stage reaction blading of the high pressure section 20, it is directed to a reheater system 28 which is associated with the boiler 26.
  • the reheater system 28 might typically include a pair of parallel connected reheaters coupled to the boiler 26 in heat transfer relation as indicated by the reference character 29 and associated with opposite sides of the turbine casing.
  • reheated steam flows from the reheater system 28 through the intermediate pressure turbine section 22 and the low pressure turbine section 24. From the latter, the vitlittcd steam is exhausted to u condenser 32 from which water flow is directed (not indicated) hack to the holler 26.
  • reheat valves 33 include one or more normally open check or stop valves and one or more intercept valves operable to provide reheat steam flow cutback modulation under turbine overspeed conditions.
  • the boiler control system controls boiler operations so that steam throttle pressure is held substantially constant.
  • a throttle pressure detector 38 of suitable conventional design measures the steam throttle pressure to provide assurance of substantially constant throttle pressure supply. and, if desired as a programmed computer protective system override control function, turbine control action can be directed to throttle pressure control as well as or in place of speed and/0r load control if the throttle pressure falls outside predetermined constraining safety and turbine condensation protection limits.
  • An impulse chamber steam pressure detector 40 develops signals for use in programmed computer control of turbine load and ultimately power plant electrical load.
  • Respective hydraulically operated valve actuators indicated by the reference character 42 are provided for the throttle and governor inlet valves 25. Hydraulically operated actuators indicated by the reference characters 44 are also provided for the reheat stop and intercept valves 33.
  • a computer sequenced and monitored high pressure fluid supply 46 provides the controlling fluid for actuator operation of the valves 25 and 33.
  • a computer supervised lubricating oil system (not shown) is separately provided for turbine plant lubricating requirements.
  • the respective actuators 42 and 44 are of conventional construction, and the actuators 42 and the actuators 44 associated with the intercept valves are operated by respective stabilizing position controls indicated by the reference characters 48 and 50. These controls each include a conventional position error feedback operated analog controller (not indicated) which drives a suitable known actuator servo valve (not indicated) in the well-known manner. Reheat intercept valve position control is imposed typically only when reheat steam flow cutback modulation is required. Stop valve operation requires no feedback position control and instead is manually or computer directed with conventional trip or other suitable emergency operation.
  • steam valving position is controlled to produce control over steam flow as an intermediate variable and over turbine speed and/or load as an end controlled variable(s).
  • Actuator operation provides the steam valve positioning, and respective valve position detectors PDIV and PDRV are provided to generate respective valve position feedback signals for developing position error signals to be applied to the respective position controls 48 and 50.
  • the position detectors are provided in suitable conventional form, for example they can make conventional use of linear variable differential transformer operation in generating negative position feedback signals for algebraic summing with respective position setpoint signals SP in developing the respective input position error signals.
  • the combined position control, hydraulic actuator, valve position detector element and other miscellaneous devices form a local hydraulic-electrical analog valve position control loop for each throttle and governor inlet steam valve.
  • the position setpoints SP are computer determined and supplied to the respective local loops and updated on a periodic basis. Setpoints SP are also determined for the intercept valve controls.
  • a speed detector 52 is provided to determine the turbine shult speed for speed control. for centrifugal stress determination and turbine constraint operation, for frequency participation control purposes, and preferably also for rotor surface heat transfer conductance computation associated with rotor thermal strain control.
  • the speed detector 52 can for example be in the form of a reluctance pickup (not shown) magnetically coupled to a notched wheel (not shown) on the turbogenerator shaft 34.
  • the process sensor equipment further includes an impulse chamber steam temperature detector 54 and easing temperature detectors 56 all of which are employed in programmed computer loading and thermal strain determination as subsequently described more fully.
  • Analog and/or pulse signals produced by the speed detector 52, the power detector 18, the pressure detectors 38 and 40, the temperature detectors 54 and 56, the valve position detectors PDIV and PDRV and other sensors (not specifically shown) and status contacts (not specifically shown) are all applied to i a digital computer control system 60 (FIG. 2) which provides turbine steady state and transient operation control on an on line real time basis and further provides system monitoring, sequencing, supervising, alarming, display and logging functions.
  • the programmed digital computer control system 60 operates the turbine 10 with improved dynamic performance characteristics, and can include conventional hardware in the form ofa central processor 62 and associated input/output interfacing equipment such as that sold by Westinghouse Electric Corporation under the trade name Prodac 50 (PS).
  • Prodac 50 Prodac 50
  • use can be made of a larger computer system such as that sold by Westinghouse Electric Corporation and known as the Prodac 250 or separate computers such as P50 computers can be employed for the respective controlled plant units. In the latter case, control process interaction is achieved by tying the separate computers together through data links and/or other means.
  • the P250 typically uses an integral magnetic core 16,000 word (16 bit plus parity) memory with 900 nanosecond cycle time, an external magnetic core l2,00() word or more (16 bit plus parity) memory with 1.1 microsecond cycle time and a mass 375,000 word or more 16 bit plus parity) random access disc memory unit.
  • the P50 processor typically uses an integral magnetic core 12,000 word l4 bit) memory with 4.5 microsecond cycle time.
  • the interfacing equipment for the computer processor 62 includes a conventional contact closure input system 64 which scans contact or other similar signals representing the status of various plant and equipment conditions. Such contacts are generally indicated by the reference character 66 and might typically be contacts of mercury wetted relays (not shown) which are operated by energization circuits (not shown) capable of sensing the predetermined conditions associated with the various system devices. Status contact data is used in interlock logic functioning in control or other programs, protection and alarm system functioning, programmed monitoring and logging and demand logging, functioning of a computer executed manual supervisory control 68, etc.
  • the contact closure input system 64 also accepts digital load reference signals as indicated by the reference character 70.
  • the load reference 70 can be manually set or it can be automatically supplied as by an economic dispatch computer (not shown). In the load control mode of operation, the load reference 70 defines the desired megawatt generating level and the computer control system 60 operates the turbine 10 to supply the power generation demand.
  • lnput interfacing is also provided by a conventional analog input system 72 which samples analog signals from the plant 12 at a predetermined rate such as 15 points per second for each analog channel input and converts the signal samples to digital values for computer entry.
  • the analog signals are generated by the power detector 18, the impulse pressure detector 40, the valve position detectors PDIV and PDRV, the temperature detectors 54 and 56, and miscellaneous analog sensors 74 such as the throttle pressure detector 38 (not specifically shown in FIG. 2), various steam flow detectors, other steam temperature detectors, miscellaneous equipment operating temperature detectors, generator hydrogen coolant pressure and temperature detectors, etc.
  • a conventional pulse input system 76 provides for computer entry of pulse type detector signals such as those generated by the speed detector 52. The computer counterparts of the analog and pulse input signals are used in control program execution, protection and alarm system functioning, programmed and demand logging, etc,
  • Information input and output devices provide for computer entry and output of coded and noncoded information. These devices include a conventional tape reader and printer system 78 which is used for various purposes including for example program entry into the central processor core memory. A conventioual teletypcwriter system 80 is also provided and it is used for purposes including for example logging printouts as indicated by the reference character 82. Alphanumeric and/or other types of displays 81, 83 and 85 are used to communicate current rotor strain, accumulated rotor strain fatigue, and other information.
  • a conventional interrupt system 84 is provided with suitable hardware and circuitry for controlling the input and output transfer of information between the computer processor 62 and the slower input/output equipment.
  • an interrupt signal is applied to the processor 62 when an input is ready for entry or when an output transfer has been completed.
  • the central processor 62 acts on interrupts in accordance with a conventional executive program. In some cases, particular interrupts are acknowledged and operated upon without executive priority limitations.
  • Output interfacing is provided for the computer by means of a conventional contact closure output system 86 which operates in conjunction with a conventional analog output system 88 and with a valve position control output system 90.
  • a manual control 92 is coupled to the valve position control output system and is operable therewith to provide manual turbine control during computer shutdown and other desired time periods.
  • Certain computer digital outputs are applied directly in effecting program determined and contact controlled control actions of equipment including the high pressure valve fluid and lubrication systems as indicated by the reference character 87, alarm devices 9d such as buzzers and displays, and predetermined plant auxiliary devices and systems 96 such as the generator hydrogen coolant system.
  • Computer digital information outputs are similarly applied directly to the tape printer and the teletypewriter system 80 and the display devices 8t, 83 and 85.
  • the turbine high pressure section 20 includes a casing or cylinder wall 100 within which a rotor 102 is supported for rotation.
  • Casing strain at predetermined casing locations is based on conventional outer and inner wall temperature thermocouple probes 104 and I06 which form a part of the casing temperature detectors 56.
  • a suitable steam temperature sensor (not specifically shown but included as a part of the analog sensors 78) can also be employed in the intermediate pressure section 22, such as in the inlet steam pipe but preferably in the [P inlet steam chamber (not shown). I? steam temperature data is used in the computation of rotor bore thermal stress in the intermediate pressure section 22.
  • a conventional thermocouple probe 1 I4 is appropriately supported by the casing 100 to measure the im pulse chamber steam temperature.
  • a dummy section 6 includes spring backed seal rings I13 and seal strips ll3A (FIG. 4A) which provide sealing action against excessive axial steam escape through the interface between the rotating rotor shaft and the surrounding stationary turbine structure.
  • FIGS. 4A and 48 further enlarged views ofareas H5 and 117 of HO. 3 show circumferential labyrinth seal grooves H8 and 120 and a circumferential rotor blade groove 122 and typical respective fatigue cracks 124, I26 and 128 which may develop at the base of the grooves 118, 120 and 128 after prolonged thermal plastic strain cycling caused by impulse chamber steam temperature variation.
  • the blade support grooves could be axial rather than circumferential.
  • the significance of the rotor grooves or other similar structural features at or near the rotor surface is their stress concentrating effect, i.e. greater thermal stress at these locations is associated with greater likelihood of plastic strain fatigue cracking at these locations.
  • Rotor surface thermal stress and plastic thermal strain are most significant near the impulse chamber region in the high pressure section because this is where they are the largest as a result of the widest ambient steam temperature variations.
  • To determine the HP rotor surface stress and/or strain it is necessary to determine the rotor surface temperature near the impulse chamber region.
  • the HP rotor surface temperature is determined as subsequently described from the impulse chamber steam temperature T, and the heat transfer conductance at the HP rotor surface. Because the heat transfer conductance between the ambient impulse chamber steam and the rotating rotor surface is very high for elevated turbine speeds, the rotor surface temperature T,,- is substantially equal to the impulse chamber steam temperature T, except during startup and shutdown under conditions of relatively low steam flow and pressure and low rotative speed. lmpulse chamber steam temperature T, in turn can vary widely with inlet steam flow changes even if inlet steam enthalpy is held constant.
  • the heat transfer conductance at the rotor surface is less than that in the high pressure section 20 at various turbine speeds because of reduced steam density and pressure.
  • determination of the rotor surface temperature in the inlet steam region of the intermediate pressure section 22 is based on the measured lP inlet chamber steam temperature and the variable and lower heat transfer conductance at the lP rotor surface.
  • the IP heat ill transfer conductance is a predetermined function of the turbine speed similar to the function subsequently indicated for the HP heat transfer conductance at the HP rotor surface.
  • Suitable steam flow and steam pressure sensor devices are employed in block 78 to provide lP flow and pressure data needed for the computation of the IP rotor surface heat transfer conductance K,,,.
  • the relationship between the impulse chamber steam temperature T, and the inlet steam conditions is illustrated in FIG. 5 for the high pressure section ofa large steam turbine designed for 2400 p.s.i. inlet steam pressure and l000 F. inlet steam temperature.
  • the impulse chamber steam temperature T is read from the intersection of the steam enthalpy and steam flow values.
  • Rotor surface stress can be determined with reasonably good approximation as set forth in the aforementioned Berry and Johnsson paper. Briefly, the step transient heating and cooling functions and the linear transient heating and cooling functions of ambient steam temperature change are of primary interest since these are the most commonly encountered ones and since principles of superposition can be used to construct special transients from these. Further, the surface thermal stress is proportional to the difference between the rotor surface temperature T,, and the rotor volume-average tern perature T. As subsequently described more fully, programmed computer control preferably involves computation of rotor surface strain E, and it is likewise proportional to the difference between T, and T.
  • the linear transient process terminates at a final level of steady ambient steam temperature when the desired load change has been accomplished.
  • termination of the transient occurs before the quasi-steady state is reached.
  • the difference between T, and T is greatest at the usual liner transient terminating point to define the maximum surface thermal stress for the transient. Maximum stress depends on both the magnitude and the rate of change of the ambient steam temperature, and for very rapid rates of change the limiting case of the step transient is approached.
  • FIG. 6 a time plot of the throttle steam temperature, the impulse chamber steam temperature T,, the rotor surface temperature T,, the rotor bore temperature T,, and the rotor volume-average temperature T covering the starting and loading of a typical large 23 inch diameter 3600 rpm. electric power plant steam turbine.
  • the rotor is initially at 400 F. with 750 F. throttle steam made available at the starting time. After throttling and expansion, the inlet steam reaches the impulse chamber at 525 F., and the rotor is subllll jected to a step heating transient with a followup linear heating transient during the startup period.
  • the impulse chamber steam temperature T drops because of a changeover to partial admission as control is transferred from throttle valves to governor valves. If control of synchronization and initial loading is by turbine throttle bypass valve, the steam temperature drop occurs later with more pronounced effect on rotor surface temperature at changeover to partial admission.
  • throttle steam temperature may rise rapidly with increased steam flow and firing rate as five percent load is applied to the turbine unit.
  • the rotor surface temperature T at this time nearly equals the impulse chamber steam temperature T, with the increased surface conductance associated with higher steam flow and pressure and higher rotor speed.
  • percent load is held until the rise in throttle steam temperature stabilizes and load is then applied at approximately a uniform rate as throttle steam is brought to rated temperature.
  • the load increase accordingly applies a linear heating transient to the turbine rotor. in this case, the rotor temperature response reaches the guasi-steady state condition during the loading period.
  • FIG. 7 there is shown a typical daily flat top" cycle of the impulse chamber steam temperature T,, the rotor surface temperature T and the rotor volume-average temperature T in a large electric power plant steam turbine as a result of turbine load changing such as that caused by full load day operation and fractional load night operation.
  • the rotor surface fibers undergo stress-strain hysteresis cycling dependent in part on the properties of the rotor material which may be for example the conventional Cr- Mo-V alloy steel rotor material.
  • compressive thermal stressing occurs in the plastic strain range during heating cycle portion H36
  • residual thennal stressing occurs during cycle portion 133
  • tensile thermal stressing in the plastic strain range occurs during cooling cycle portion M0
  • new residual thermal stressing occurs during cycle portion 142.
  • the width of the stress-strain hysteresis loop so formed represents the plastic strain for the cycle.
  • the material elastic stress limit is likely not caused to be exceeded by steam temperature variation and rotor surface plastic strain then probably nearly vanishes.
  • most turbine operation level cycling does involve plastic strain.
  • cyclic thermal rotor surface temperature causes similar hysteresis looping and corresponding cyclic rotor surface plastic strain.
  • another typical cyclic rotor surface temperature pattern is a substantially sinusoidal pattern caused by sinusoidally applied frequency control action.
  • FIG. 8 there is shown a cyclic fatigue capacity chart for flat top rotor surface temperature cycles like that of FIG. 7.
  • This chart shows the number of plastic strain cycles required under varying duty characteristics to produce groove cracking in a 3600 r.p.m. and 23 inch diameter rotor of high thermal duty cycle capacity geometric design. Larger diameter rotors involve larger thermal inertia and therefore involve a more extended time scale than that shown in FIG. 8.
  • the flat top rotor surface temperature cycle pattern associated with the illustrated fatigue capacity chart is represented by the idealized one that is shown in the upper part of FIG. 8.
  • linear heating occurs over a At period from a first steady state rotor surface temperature
  • equalizing and holding occurs at a second steady state rotor surface temperature equal to the beginning steady state rotor surface temperature plus AT linear cooling occurs over a time period AI, and equalizing and holding occurs at the first steady state rotor surface temperature.
  • Heating and cooling amounts and rates are made equal for simplicity although in the general invention application case these quantities can be variable.
  • the rotor surface temperature change AT,- and the heating and cooling intervals A! are determined and the number of cycles N required to produce rotor fatigue cracking is then read from curves 144.
  • N can be determined from locus curves 146 when the rotor surface temperature change rate is known and applied over the interval Ar.
  • fatigue damage is determined by first identifying the type of cycle, i.e. flat top, sinusoidal, etc., and then determining the cycle fatigue capacity N from corresponding cycle fatigue capacity charts on the basis of particular values of rotor surface temperature change and change rate and temperature transient duration or their equivalents. Next, the damage per cycle UN is determined. Cumulative fatigue damage equals the sum of the values for UN through the course of turbine use. When the cumulative value reaches the value one, rotor surface fatigue cracking is theoretically expected to occur. Fatigue cracking thus might result from relatively few large fatigue damage cycles, from a large number of small fatigue damage cycles, or from any of various combinations of varied fatigue damage cycles.
  • Typical prior art practice involves determining the desired turbine plastic strain fatigue life and determining some fixed supervisory or control program restriction on cyclic turbine operation such that resultant cumulative rotor fatigue damage as predictively calculated from cycle fatigue capacity charts and the planned restricted turbine cycling would likely conform to the desired turbine operating life to be met. As already indicated, that procedure has been too approximate with resulting shortcomings in accuracy, efficiency and economy of turbine operation.
  • a programming system is employed to operate the computer system 60. It includes control and related programs as well as certain conventional housekeeping programs directed to internal control of the functioning of the computer system itself. The latter include the following:
  • the highest bidding program or interrupt routine is determined and allowed to run when a change is to be made in the programmed instructions undergoing execution. Some interrupt routines run outside the priority structure as already indicated, particularly where safety and/or expensive equipment protection are involved.
  • Analog Scan Periodic execution for the entry of predetermined analog inputs which have been converted by the analog input system 72 and stored in the analog input system buffer register.
  • the programming system control and related programs include the following:
  • Alarm Periodic and process interrupt execution for operating the alarm devices 94 and other system devices and for supervising and/or disabling the valve position and other control programs.
  • the present invention primary involves the functioning of the turbine rotor loading and strain constraint subprogram and further specific programming system description herein will accordingly be limited to the valve position control program and the included rotor constraint subprogram.
  • Flow charts including certain algorithms are shown in FIGS. 9 and 10 as a representation of the basic logic content of the steam valve position control program indicated by the reference character M and the constraint subprogram indicated by the reference character 156.
  • Actual programs entered into the computer system 60 are coded in machine language from more detailed flow charts which are in turn derived from the illustrated flow charts.
  • the turbine Prior to startup, the turbine is motor driven at the turning gear speed of about 2 r.p.m. to minimize "breakaway torque and to maintain shaft straightness.
  • a start signal is applied to the computer 62 as by operation of the manual control 68.
  • Startup is allowed by programming system operation if the predetermined interlock logic permissives are satisfied including for example steam generating system functioning normally, steam throttle pressure at required value, power breakers open, turbine steam valves in starting positions, high pressure fluid system functioning normally, etc.
  • the steam valve position control program 145 is periodically executed such as at the rate of once per second to develop steam valve positioning actions directed first to bringing the turbine 10 to the synchronous speed and then to controlling the turbine load.
  • the program 145 is preferably like that described in the aforementioned Birnbaum and Giras application, and program description more detailed than the description to be presented here can be obtained by reference to that application.
  • feedback turbine speed correction d is determined from the product of gain g and AS which is the difference between a reference speed w and the actual turbine speed w
  • the speed reference w approximately provides for turbine speed changing within predetermined dynamic limits, and it is determined from a computer stored startup (or shutdown) ramp curve of turbine speed versus time.
  • the gain g corresponds to the speed regulation desired for the system.
  • the speed regulation 8 might for example be 3 percent, i.e. 3 percent overspeed at full turbine load results in full closure of the turbine inlet steam valves 25.
  • the numerical form of the speed correction d thus is in percentage form, and it provides advantages in the load control operating mode as more fully described in the Birnbaum and Giras application.
  • program block 148 directs the program execution to block I50 which determines a maximum speed change valve position demand D which dynamically characterizes the control system with a constraint on the rate at which turbine inlet steam flow can be changed for turbine speed control.
  • the constraint demand D effectively acts as a feedback trim on the speed ramp w which involves feedforward but only approximate dynamic constraint. If desired, speed constraint operation can be imposed only on startup and the conventional coastdown procedure can be used on shutdown. The program is appropriately modified when coastdown operation is selected.
  • Block M8 directs the program execution to block 152 where speed calibrated load demand is determined from the load reference 70 or D
  • Block 154 next determines a maximum load change valve position demand D, which dynamically characterizes the control system with a constraint on the rate at which turbine inlet steam flow can be changed for turbine load control.
  • the constraint demand D effectively acts as a feedback dynamic constraint on the load control loop which in its preferred form is a feedforward control loop.
  • Blocks and 154 contain some common execution steps and form the turbine rotor loading and strain constraint subprogram 156 which is shown in greater block detail in FIG. 10.
  • total steam valve position demand D is detennined in a closed speed feedback loop and it is made equal to a predetermined function of d or it is constrained by D under predetermined rotor loading or thermal strain conditions.
  • D may or may not be a numeric variable, and in this case it preferably either allows ramping of w or disallows such ramping when speed change constraint is to be imposed.
  • the steam valve movement is then determined by speed error based on a fixed reference speed value until the constraint action is released.
  • a determination that D is to constrain D in effect means making Dy equal to the predetermined function ofd, with w held constant.
  • total steam valve position demand D is determined in block 157 from D or it is constrained by D under predetermined rotor changing or thermal strain conditions, specifically when D is greater than D during or less than D during unloading when D in effect acts as a minimum constraint.
  • Determination of D is preferably made from a static characterization in the feedforward load control loop and it is then load calibrated to D on the basis of impulse chamber pressure error in block 158 as more fully explained in the Birnbaum and Giras application.
  • the static characterization in the block 157 defines the total steam valve positioning required to satisfy the demand D or D if D, is under constraint.
  • the block 158 corrects for any minor characterization or other error by its trim action.
  • Total valve position demand D or D is distributed among the inlet steam valves 25 in block 160 according to a predetermined schedule.
  • the respective digital inlet valve position setpoint values are then determined in block 162 just before the program run is ended.
  • surface thermal strain E be the determined HP rotor thermal condition upon which supervisory or control 5 action is to be taken in the turbine operation because this is the fundamental variable involved in cumulative fatigue damage.
  • other HP rotor thermal conditions such as the rotor thermal stress can be determined and processed in computing supervisory or control data.
  • the HP rotor surface temperature T,- can be made equal to the detected impulse chamber steam temperature T, under certain justifying operating conditions, i.e. when the heat transfer conductance K at the HP rotor surface has an adequately high value. This can be the case for most of the typical electric power plant steam turbine cycles such as that shown in FIG. 7 and for most of other like cycles.
  • the HP rotor surface temperature T can be automatically determined as a function of variables including the impulse chamber steam temperature and the steam ambient to rotor heat transfer conductance K HP.
  • the HP rotor surface heat transfer conductance is determined as a predetermined function of the rotor speed, i.e. (K, f(u and the rotor surface temperature is calculated from the measured ambient steam temperature T, and from the computed value for (K, in the manner subsequently described.
  • the block I64 provides for determining the rotor volumeaverage temperature T. This operation is based on standard cylinder thermal gradient transient analysis as set forth in a text by G. M. Dusenberry entitled Numerical Analysis of Heat Flow” and published in 1949 by McGraw-Hill. Generally, the rotor is mathematically divided into a preselected number of successive rings having equal radial extent and being numbered radially inwardly. The respective rings have respective heat capacities C 1 Cu and interring heat flow transfer conductances K K Kml l8 1) (n) associated with them.
  • Equations involving the ring heat capacities are set up for heat flow between the ambient steam and the rotor surface ring through the surface (film) thermal conductance (l(, and between the first and second and successive ingoing rotor ring pairs through the respective interring conductances in terms of the steam and ring temperatures at time 1,, and the ring temperatures after a time interval A! or at (I,,+Al).
  • the ring temperature at the present time (1 is solved in terms of the other equation quantities.
  • the computed value for T is the value used for T in block I64.
  • Present rotor volume-average temperature T is computed from present ring temperature values as follows:
  • T is subtracted from T and the difference is multiplied by the thermal expansion coefficient a and a concentration factor n which makes the computation lib applicable to the groove base where thermal strain and stress are concentrated.
  • the resulting quantity is next divided by lv where v is Poissons ration to give the HP rotor surface strain E if surface thermal stress S rather than surface thermal strain E is the computed quantity, the equation in block l64 is modified by including the modulus of elasticity E as an additional multiplier of the difference quantity (T T ln addition, the concentration factor 1; is modified to reflect the fact that stress rather than strain is being calculated.
  • the determined HP rotor surface strain E is stored as indicated by block 166, and the successive strain values 5, from successive program runs are tracked to determine strain cycle activity.
  • the successive strain values 5, from successive program runs are tracked to determine strain cycle activity.
  • block l68 calculates rotor plastic strain fatigue damage associated with each identified cycle. The damage calculation is made by determining N (previously defined) from stored cycle fatigue capacity chart data once the type of rotor strain cycle and the cycle duty characteristics are ascertained.
  • Block acts as a HP rotor surface fatigue damage accounting system since it adds successively determined damage values to provide a running rotor fatigue damage total.
  • the display devices 81 and 83 can show the current computed HP rotor surface strain E,- and the accumulated rotor surface fatigue damage by programmed scheduling or by operator demand.
  • the effectiveness of the fatigue accumulation procedure in following actual rotor fatigue damage depends on the standards employed in identifying strain cycles. i.e. the kind of screening used in determining which cycles are to be damage counted and which cycles are not to be damage counted. For example, in electric power plant steam turbines, identified cycles could be as few as one per day with very coarse screening and in these and similar applications blocks 168 and 170 would function infrequently.
  • a closed constraint control loop (not shown) can be applied to the basic control in a long term supervisory sense based on the accumulated HP rotor strain fatigue damage of block H70.
  • the subsequently considered strain limit E of the block R84 might be modified with time passage as a function of the computed damage total.
  • the impulse chamber steam temperature detector 54 and the arrangement for determining HP rotor surface strain E and if desired for recording and accumulating cycle fatigue damage can be provided separately in the form of an instrumentation system or package useful for supervisory turbine operation where closed loop dynamic strain constraint control is not desired.
  • the impulse chamber steam temperature sensor output and the turbine speed detector output are coupled to suitable computing means capable of performing the programmed operation described for block 164 and if desired blocks 166, 168 and 170.
  • the instrumentation computer can be a special purpose analog, digital-analog, or digital computer.
  • the instrumentation combination is especially useful for older installed turbines where improved operating supervision can be realized by operator knowledge of actual rotor strain operating conditions and actual rotor strain fatigue damage. Similar instrumentation packages can be employed for determining thermal stress and/or strain conditions in intermediate pressure sections of large turbines as well as in turbines other than large electric power plant turbines.
  • a HP rotor surface strain limit E is determined in block 172.
  • the strain limit E can be a value determined by a predetermined function or it can be a value selected from a table of values with each table value corresponding to some predetermined computer determinable set of conditions.
  • rotor strain fatigue damage can be automatically escalated for various operating conditions for which it is prejudged that the overall gain from faster turbine adjustment is worth the cost of increased rotor fatigue damage.
  • Block 178 supplies a combined loading limit which is a predetermined fixed value, or as in the block 172, a table of hierarchical values corresponding to allowed loading under different computer determinable sets of operating conditions.
  • high pressure casing wall strain is computed in block 180 on the basis of temperature readings from the easing temperature detectors 56.
  • a fixed or other casing strain limit is provided by block 182.
  • an allowed maximum rate of change of T is determined in block 184 as a predetermined function of the surface strain E computed in block 164.
  • the inlet steam enthalpy variation rate and/or, as in this case the inlet steam fiow change rate is ultimately limited. in this instance, the allowed maximum change rate (d- T,/dr),, is made equal to a function of the percent ratio of the actual surface strain E to the limit strain E from block 172.
  • maximum cooling may be permissible if the rotor surface is undergoing compressive strain from a previous heating transient and likewise max imum heating may be permissible if the rotor surface is undergoing tensile strain from a previous cooling transient. If the rotor surface is in compression, the extent of that compression determines whether the maximum heating rate of change in T, or some lesser rate is required. if the rotor surface is in tension, the extent of that tension determines whether the maximum cooling rate of change in T, or some lesser rate is required.
  • solid curve 186 allows the highest value of (KL/d1) for heating or increasing values of T, for all tensile strain percent ratios and up to the 50 percent compressive strain ratio. Between 50 percent and 100 percent compressive strain ratio, the allowed increase rate of change of T, drops linearly to zero.
  • dashed curve 188 allows the highest value of (JD/d!) for cooling or decreasing values of T, for all compressive strain percent ratios and up to 50 percent tensile strain ratio. Between 50 percent and 100 percent tensile strain ratio, the allowed decrease ratio of change of T, drops linearly to zero.
  • curves 186 and 188 overlap in region 187.
  • the linear proportional portions of the curves 186 and 188 in effect involve a prediction in a generalized sense that existing rotor strain level, although not yet excessive, probably requires a cutback in steam temperature change rate.
  • Such functions can of course be employed in determining the allowed rate of change of impulse chamber steam temperature T,.
  • Such functions may or may not have a flat top like that at 187 and further may or may not have a fixed highest rate of change value for T, like that at 187, i.e. the highest allowed rate might be made to have different values under different sets of operating conditions.
  • the control system is in the loud operating mode on determined in block 190 and if after comparing the result of block 180 and 182 the casing strain is determined to he too high in block 192, the maximum value (dT,/dl),,, determined in block 184 is reduced a predetermined amount in block 194.
  • the actual present change rate of T is then determined from sensed temperature and time data and it is compared to the computed allowed maximum value in block 196. if the actual value of (IL/d! is equal to or greater than the allowed maximum value, the block 196 computes the maximum steam valve load position demand D If casing strain is within limits, program execution goes directly from block 192 to block 196.
  • Bore loading computation is included in the speed control operating mode because it has special significance during cold startups and the like. lf either bore loading or casing strain is excessive, the maximum value (a'T,/d!),,, determined in block 184 is reduced a predetermined amount in block 200.
  • the actual present change rate of T is computed and compared to the computed allowed maximum value (aT,/dr) in block 202, if the actual temperature change rate is equal to or greater than the allowed maximum value, the block 202 determines D i.e. in this case stops the ramping of w,, in block 147.
  • program execution goes directly from block 198 to block 202.
  • the on line bore loading determination in the block 198 can be eliminated altogether and the program is appropriately adapted to the use of this prior art startup technique.
  • the maximum steam temperature change rate (a'l",dt) is converted into a maximum steam valve position demand which will cause the steam valves 25 to be positioned from the present positions at a rate which causes steam flow change at a rate no greater than that corresponding to the maximum value (Jl,/T),, That is, with inlet steam temperature and pressure and therefore inlet steam enthalpy held substantially constant in this application, the steam valve positioning rate is limited to prevent the rate of change of steam flow from exceeding any value which would cause the rate of change of impulse chamber steam temperature T, to exceed maximum value (d- T,/d!),,,.
  • the inlet steam valves 25 are desirably positioned to setpoint values with slightly over-critical gain as described more fully in the Birnbaum and Giras application, and for this and other reasons it is preferable that impulse chamber steam temperature change rate of dT,/dr be limited by limited the position demand levels D or D made on the positioning control loops as the present case has already been indicated to be.
  • loop gain control can, as one example, be employed in the local analog valve position control loops or in direct digital computer valve position control loops (not shown) for the purpose of imposing direct dynamic constraints on steam valve positioning and in turn on turbine speed changing and/or loading when the temperature change rate dT,/dl is to be constrained.
  • Extended turbine life is made possible by more accurate rotor plastic strain fatigue supervision and/or control. This economy is realized along with improved efficiency in turbine operating control directed to meeting load, speed or other end controlled variable demands. Dynamic constraint operation is better tailored to allowing optimum or near optimum turbine dynamic operation particularly in electric power plant and like applications where it is likely that the significant turbine operating level changes will often require constraint application. Achieved optimization is tied in a relative sense to opera tor standards for accumulation of rotor plastic strain fatigue. Bore loading and casing strain constraints are compatibly combined with the rotor strain constraint in the dynamic constraint control.
  • a system for operating a steam turbine comprising means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, means for determining a representation of at least one predetermined thermal condition of the rotor portion as a predetermined function of the steam temperature representation and the stress concentration of grooves or similar rotor surface structural features on the preselected rotor portion, means for controlling the turbine steam conditions in the predetermined turbine region, and means for operating said steam condition controlling means as a predetermined function of the thermal condition representation.
  • a system for operating a steam turbine comprising means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, means for determining a representation of at least one predetermined thermal condi tion of the rotor portion as a predetermined function of the steam temperature representation, means for determining cyclic rotor thermal plastic strain fatigue damage in accordance with a predetermined function of the one rotor thermal condition representation, means for controlling the turbine steam conditions in the predetermined turbine region, and means for operating said steam condition controlling means as another predetermined function of the thermal condition representation.
  • a steam turbine operating system as set forth in claim 1 wherein there is further provided means for determining respective representations of thermal loading and centrifugal loading of the rotor bore at least for one predetermined rotor portion, means are provided for determining a representation of rotor bore loading from the thermal and centrifugal loadings, and said operating means operates said steam condition controlling means as a predetermined function of the first mentioned thermal condition representation and the bore loading representation.
  • a method for operating a steam turbine including determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, determining a representation of at least one predetermined thermal condition of the rotor portion as a predetermined function of the steam temperature representation, determining cyclic rotor thermal plastic strain fatigue damage in accordance with a predetermined function of the one rotor thermal condition representation, and using the thermal condition representation and the fatigue determination in determining the steam turbine operation.
  • a control system for a steam turbine having steam valve means for determining the flow of steam through at least one section ofthe turbine, said system comprising means for determining a representation of steam temperature in a predetermined region in heat transfer relation with a preselected turbine rotor portion, means for determining a representation of at least one predetermined rotor thermal condition of the rotor portion as a predetermined function of the steam temperature representation and the turbine speed, and means for position controlling the steam valve means to determine the turbine operating level as a predetermined function of the thermal condition representation.
  • An instrumentation system for making determinations useful in operating a steam turbine, said system comprising means for detecting steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, and means for determining a representation of a predetermined rotor thermal condition of the rotor portion as a predetermined function of the detected steam temperature and the stress concentration of grooves or similar rotor surface structural features on the selected rotor portion.
  • said determining means includes means for determining a representation of turbine speed and means for determining rotor surface temperatures as a function of the turbine speed and the detected steam temperature.
  • An instrumentation system for making determinations useful in operating a steam turbine comprising means for detecting steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, means for determining a representation of a predetermined rotor thermal condition of the rotor portion as a predetermined function of the detected steam temperature, and means for determining cyclic plastic strain fatigue damage as a predetermined function of the rotor thermal con dition representation.
  • said determining means includes computer means, the predetermined turbine region is the impulse chamber, the represented rotor thermal condition is selected from the rotor surface stress and strain conditions, and the rotor surface thermal condition is determined from the quantity where T is the rotor surface temperature, T is the rotor volume-average temperature, a is the thermal expansion coefficient, v is Poisson's ratio nd 1; is a concentration factor.
  • a digital computer control system for a steam turbine having steam valve means for determining the flow of steam through at least one section of the turbine comprising a digital computer system including means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, and means for determining a representation of at least one predetermined rotor thermal condition of the rotor portion as a predetermined function of the steam temperature representation, means including said digital computer system for position controlling the steam valve means to determine the turbine operating level in a predetermined manner, and said digital computer system further including means for determining constraint action for application against the steam valve positioning control as a predetermined function of the thermal condition representation.
  • a digital computer control system for a steam turbine having steam valve means for determining the flow of steam through at least one section of the turbine comprising a digital computer system including means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion. and means for determining a representation of a rotor thermal condition selected from the rotor surface stress and strain conditions as a predetermined function of the steam temperature representation and the turbine speed and the stress concentration of grooves or similar rotor surface structural features on the selected rotor portion, and means including said digital computer system for position controlling the steam valve means to determine the turbine operating level as a predetermined function of the thermal condition representation.
  • a digital computer control system for a steam turbine having steam valve means for determining the flow of steam through at least one section of the turbine comprising a digital computer system including means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, and means for determining a representation of at lest one predetermined rotor thermal condition of the rotor portion as a predetermined function of the steam temperature representation, means including said digital computer system for position controlling the steam valve means to determine the turbine operating level as a predetermined function of the thermal condition representation, the latter function being a function of the ratio of the representation of the rotor surface thermal condition to a predetermined limit representation of the rotor surface thermal condition and further defining a constant maximum turbine heat change rate over a predetermined range between compressive and tensile values of the ratio and defining a maximum turbine heat change rate inversely proportional to the magnitude of the rotor surface thermal condition ratio for greater compressive and tensile values than those defining the constant function range of
  • a digital computer control system for a steam turbine having steam valve means for determining the flow of steam through at least one section of the turbine comprising a digital computer system including means for determining a representation of steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, and means for determining a representation of at least one predetermined rotor thermal condition of the rotor portion as a predetermined function of the steam temperature representation, means including said digital computer system for position controlling the steam valve means to determine the turbine operating level as a predetermined function of the thermal condition representation, and said digital computer system further including means for determining cyclic rotor thermal plastic strain fatigue damage in accordance with another predetermined function of the rotor surface thermal condition representation and for accumulating the determined cyclic rotor plastic strain fatigue damage.
  • a method for operating a steam turbine digital computer control system comprising operating the computer to determine a representation of measured steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, operating the computer to determine a representation of at least one predetermined thermal condition of the rotor portion as a predetermined function of the steam temperature representation and the stress concentration of rotor grooves or similar rotor surfaces structural features on the predetermined rotor portion, and operating the computer to determine a turbine valve control action as a function of the rotor thermal condition representation.
  • a method for operating a steam turbine digital computer control system comprising operating the computer to determine a representation of measured steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, operating the computer to determine a representation of at least one predetermined thermal condition of the rotor portion as a predetermined function of the steam temperature representation and a representation of measured turbine speed, and operating the computer to determine a turbine valve control action as a function of the rotor thermal condition representation.
  • a method for operating a steam turbine digital computer control system comprising operating the computer to determine a representation of measured steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, operating the computer to determine a representation of at least one predetermined thermal condition of the rotor portion as a predetermined function of the steam temperature representation, operating the computer to determine cyclic rotor thermal plastic strain fatigue damage in accordance with a predetermined function of the rotor thermal condition representation, and operating the computer to determine a turbine valve control action as another function of the rotor thermal condition representation.
  • a method for operating a steam turbine digital computer control system comprising operating the computer to determine a reprcnentution of measures steam temperature in a predetermined turbine region in heat transfer relation with a preselected turbine rotor portion, operating the computer to determine a representation of at where T is the rotor surface temperature.
  • T is the rotor volume-average temperature.
  • a is the thermal expansion coefficient
  • u is Poisson's ratio
  • n is a concentration factor.

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CN115659433B (zh) * 2022-11-02 2023-08-18 中国航发沈阳发动机研究所 一种航空发动机转子结构力学特性定量评估方法
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NL6906007A (enrdf_load_stackoverflow) 1969-10-21
DE1919122A1 (de) 1970-09-24
BE731551A (enrdf_load_stackoverflow) 1969-09-15
CA923211A (en) 1973-03-20
CH509502A (de) 1971-06-30
FR2006556A1 (enrdf_load_stackoverflow) 1969-12-26

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