Steam Turbine Model Research Articles

Thermal Modeling of a Solar Steam Turbine With a Focus on Start-Up Time Reduction

Steam turbines in solar thermal power plants experience a much greater number of starts than those operating in baseload plants. In order to preserve the lifetime of the turbine while still allowing fast starts, it is of great interest to find ways to maintain the turbine temperature during idle periods. A dynamic model of a solar steam turbine has been elaborated, simulating both the heat conduction within the body and the heat exchange with the gland steam, main steam and the environment, allowing prediction of the temperatures within the turbine during off-design operation and standby. The model has been validated against 96 h of measured data from the Andasol 1 power plant, giving an average error of 1.2% for key temperature measurements. The validated model was then used to evaluate a number of modifications that can be made to maintain the turbine temperature during idle periods. Heat blankets were shown to be the most effective measure for keeping the turbine casing warm, whereas increasing the gland steam temperature was most effective in maintaining the temperature of the rotor. By applying a combination of these measures the dispatchability of the turbine can be improved significantly: electrical output can be increased by up to 9.5% after a long cooldown and up to 9.8% after a short cooldown.

6시그마 기법을 적용한 원자력 터빈 시뮬레이터의 발전기 출력 연산오차 저감

This paper describes the improvement of the calculation by using 6σ method on steam turbine simulator in a nuclear power plant. The simulator is essential to not only verification and validation of control logic but also making sure of control constants in upgrading the long time used control system into the new one. And the dynamic model is a key point in that simulator. The model used during the retrofit period of the turbine controller in Kori Nuclear Power Plant makes difference in calculating generator output and control valve positions. That is because such operating data as the main steam pressure, the main steam temperature and control valve positions of Yongkwang #3 are different from those of Kori #4. Therefore, the model parameters must be tuned by using actual operating data for the high fidelity of simulator in calculating the dynamic characteristic of the model. This paper describes that the 6σ method is used in improvement of precision of generator output calculation in the steam turbine model of the simulator.

0602 実機規模蒸気タービン多段静動翼列の非定常流動解析(OS6-1 流体機械のCFD解析最前線,オーガナイズドセッション)

0602 実機規模蒸気タービン多段静動翼列の非定常流動解析(OS6-1 流体機械のCFD解析最前線,オーガナイズドセッション)

F208 NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF UNSTEADY 3-D FLOW THROUGH TWO-STAGE CASCADES IN STEAM TURBINE MODEL(Steam Turbine-3)

Unsteady 3-D flows through two-stage stator-rotor cascade channels in a low-pressure steam turbine model developed by Mitsubishi Heavy Industry (MHI) are numerically investigated and compared with the experiments. The fundamental equations solved in this study are based on the compressible Navier-Stokes equation and the SST turbulence model in general curvilinear coordinates. The high-order high-resolution finite-difference method based on the fourth-order compact MUSCL TVD (Compact MUSCL) scheme and the Roe's approximate Riemann solver are used for the space discretization of convection terms. A parallelized LU-SGS scheme based on the pipelining algorithm is also employed for the parallel-implicit time-integration. Total pressures, static pressures and yaw angles of flow velocity vectors at the outlet of first-stage rotor, second-stage stator, and second-stage rotor obtained from the computation are compared with the corresponding experiments. Finally the reliability of both numerical and experimental approaches is discussed.

Steam turbine model

In order to characterize the transient dynamics of steam turbines subsections, in this paper, nonlinear mathematical models are first developed based on the energy balance, thermodynamic principles and semi-empirical equations. Then, the related parameters of developed models are either determined by empirical relations or they are adjusted by applying genetic algorithms (GA) based on experimental data obtained from a complete set of field experiments. In the intermediate and low-pressure turbines where, in the sub-cooled regions, steam variables deviate from prefect gas behavior, the thermodynamic characteristics are highly dependent on pressure and temperature of each region. Thus, nonlinear functions are developed to evaluate specific enthalpy and specific entropy at these stages of turbines. The parameters of proposed functions are individually adjusted for the operational range of each subsection by using genetic algorithms. Comparison between the responses of the overall turbine-generator model and the response of real plant indicates the accuracy and performance of the proposed models over wide range of operations. The simulation results show the validation of the developed model in term of more accurate and less deviation between the responses of the models and real system where errors of the proposed functions are less than 0.1% and the modeling error is less than 0.3%.

A MINLP model including the pressure levels and multiperiods for CHP process optimisation

In this paper a mixed integer nonlinear programming (MINLP) model for small-scale combined heat and power (CHP) plant synthesis and operation is presented. The model includes also the modelling of pressures levels and part load operation unlike the model presented in earlier work. Also, a detailed model of a back-pressure steam turbine is added to the model, taking into account the efficiency changes in turbine stages and the steam extraction pressure dependence on the steam mass flow rate. The sensitivity analysis shows that the developed model can be solved fairly reliably with commercial local MINLP solvers. The model corresponds well with a simulation model based on an existing plant. The model is able to find improved small-scale CHP designs that have higher efficiencies and that are profitable for wide ranges of electricity prices and fossil CO 2 emission permit prices. The developed model is a suitable decision making tool when evaluating the trade-offs between investments, profits, and fossil CO 2 emissions in small-scale CHP plant synthesis and operation. However, the formulations of the model are not limited to small-scale CHP processes and can be used to model also larger CHP processes and energy systems.

Particle Image Velocimetry Measurements of the Three-Dimensional Flow in an Exhaust Hood Model of a Low-Pressure Steam Turbine

The three-dimensional flow structure inside an exhaust hood model of a low-pressure steam turbine was investigated using a particle image velocimetry (PIV) velocity field measurement technique. The PIV measurements were carried out in several selected planes under design operation conditions with simulated total pressure distribution and axial velocity profile. The mean flow fields revealed a complicated vortical flow structure and the major sources of energy loss. Vortices with different scales were observed inside the exhaust hood: a strong separation vortex (SV) behind the tip of the guide vane, a longitudinal vortex (LV) at the exhaust hood top, a large-scale passage vortex (PV) evolving throughout the flow path, and an end-wall vortex (EWV) in the region adjacent to the front end-wall. Both the SV and the large-scale PV seemed to consume large amounts of kinetic energy and reduce the pressure recovery ability. The results indicate that the steam guide vane and the bearing cone should be carefully designed so as to control the vortical flow structure inside the exhaust hood.

Experimental investigations of rotating flow instabilities in the last stage of a low-pressure model steam turbine during windage

Experimental investigations on two different three-stage low-pressure (LP) model turbines operated on steam during windage are presented. At very low flows, strain gauges identified that the two turbines exhibit different dynamic stress characteristics of the last-stage rotor blades. The first turbine experienced the highest vibrations from aerodynamic excitations at the resonant frequency of the second mode in a narrow operating range around 13 per cent of the design flow, whereas the second turbine experienced no resonance up to the fourth mode and has the highest dynamic loading at zero flow. Specially developed high-response total pressure probes have been used to determine the cause of the aerodynamic excitation from traverses of the unsteady pressure field at three planes in the last stage. The experimental data for both turbines show that unsteady pressure disturbances steadily grow when the flow is reduced below 25 per cent of design flow and that the excitations are strongest in the axial gap between the guide vane and the rotor of the last stage near the outer casing. Detailed analysis shows that high-amplitude disturbances occur at distinct frequencies and that these rotate in the circumferential direction at a fraction of the rotor speed. Comparison of the pressure signals measured at two circumferential locations on the casing of the second turbine confirmed the characteristic frequency pattern to be a so called ‘rotating instability’. This unsteady phenomenon arising from the tip leakage flow has previously been observed in axial flow fans and compressors and is demonstrated for the first time here in a turbine operating at very low flow rates.

Experimental and Numerical Investigation of the Unsteady Surface Pressure in a Three-Stage Model of an Axial High Pressure Turbine

This paper presents the results of a numerical and experimental investigation of the unsteady pressure field in a three-stage model of a high pressure steam turbine. Unsteady surface pressure measurements were taken on a first and second stage stator blade, respectively. The measurements in the blade passage were supplemented by time resolved measurements between the blade rows. The explanation of the origin of the unsteady pressure fluctuations was supported by unsteady three-dimensional computational fluid dynamic calculations of which the most extensive calculation was performed over two stages. The mechanisms affecting the unsteady pressure field were: the potential field frozen to the upstream blade row, the pressure waves originating from changes in the potential pressure field, the convected unsteady velocity field, and the passage vortex of the upstream blade row. One-dimensional pressure waves and the unsteady variation of the pitchwise pressure gradient due to the changing velocity field were the dominant mechanisms influencing the magnitude of the surface pressure fluctuations. The magnitude of these effects had not been previously anticipated to be more important than other recognized effects.

A unified theory for the interpretation of total pressure and temperature in two-phase flows at subsonic and supersonic speeds

This paper presents a unified theory on the interpretation of total pressure and total temperature in multiphase flows. The present approach applies to both vapour-droplet mixtures and solid-particle laden gases, and at subsonic as well as supersonic velocities. It is shown here that the non-equilibrium processes occurring in the vicinity of a stagnation point are important. These processes may be responsible for the generation of entropy and affect the pressure and temperature at the stagnation point. They should be properly considered while inferring, say, flow velocity or entropy generation from Pitot measurements. By proper non-dimensionalization of the relevant parameters, it is possible to find a single (theoretically obtained) calibration curve for the total pressure as a function of the particle size, which is almost independent of the constituents of the multiphase mixture and of the flow conditions. The calibration curve is a plot of a pressure recovery factor versus Stokes number and specifies the total pressure under different non-equilibrium conditions. The total pressure, predicted by the present theory, varies monotonically between the two limiting values: the frozen total pressure (when there is no interphase mass, momentum and energy transfer in the decelerating flow towards the stagnation point) and the equilibrium total pressure (when the dispersed phase, either the liquid droplets or the solid particles, is always at inertial and thermodynamic equilibrium with the continuous vapour phase). The equilibrium total pressure is always higher than the frozen total pressure. It is shown that the equilibrium total temperature, on the other hand, may be higher or lower than the frozen total temperature. In addition, unlike the case of total pressure, the calibration curve for total temperature is not so universal, and the total temperature under non-equilibrium conditions is not necessarily bounded between the frozen and equilibrium values. It is further shown that the entropy of a multiphase mixture has to be carefully interpreted and is not unequivocally related to the total pressure even in steady adiabatic flow.

Generalised Pole-Placement Control of Steam Turbine Speed

An application of a pole-placement self-tuning predictive control algorithm is developed to regulate speed of a power plant steam turbine model. Two types of system representation (CARMA and CARIMA) are used to test the control algorithm. Simulation results show that when using a CARMA model produces better results. Two further comparisons are made when using a PI controller and a generalised predictive controller.

BWR steam line and turbine model with multiple piping capability

A new steam line and turbine model for the prediction of flow transients in main steam supply lines has been developed. The major objectives of the new model are to predict transients in an arbitrary steam line and turbine configuration and to calculate with good accuracy and speed. The model is incorporated in the BISON BWR dynamics program, but it can also be executed as a stand-alone computer code. The steam flow model is based on one-dimensional adiabatic (and optionally isentropic) flow, including spatial acceleration and compressibility effects. In the finite difference form we use the nonconservative form for momentum and energy equation. An implicit time integration scheme is used to eliminate a time-step limitation. The main features of the model are: • - ability to analyse steam single-phase flow transients in any piping network, - models for valves, tees, turbine assembly • - control system interface • - consistent steady-state initialization technique, - restart facility • - time step control algorithm for transient and steady-state solutions. The model has been assessed by comparing numerical results with both analytical solution and experimental data.

New approach for the identification of power system economic dispatch parameters

It is well known that the coefficients of the input-output characteristics of the thermal steam-turbine model as well as the network model parameters have a great effect on the optimal economic operation of all thermal-electric power systems. Until today, these coefficients, the loss formula coefficients, theB-coefficients, and the active-reactive power loss models have been estimated using the well-known least-square estimation algorithm.

Thermal tests of a steam-turbine nozzle-chamber model

This paper describes the measurement of thermal strains and temperatures in a 0.25-scale aluminum-filled epoxy model of a double-flow large-steam-turbine nozzle chamber. A temperature gradient was induced by circulating chilled methyl alcohol through the interior. Strain gages and thermocouples were used to determine surface strains and temperatures at various locations for comparison with a finite-element analysis under development. A uniform cylinder was included on the inlet section of the model for calibration. The maximum measured tensile strain on the interior surface was 0.96 αΔT n , where ΔT n was the average temperature difference between the interior surface and the initial temperature. A maximum compressive strain of 0.50 αΔT n was measured on the outside surface of the nozzle-bowl sidewall.

Integrated energy conversion systems: A mathematical model of extraction steam turbine

In some integrated energy conversion systems, automatic extraction steam turbines are used to provide low quality steam from the turbine for process use or district heating and cooling purposes. This paper presents a generalized mathematical model for steam turbine/generator based on the Rankine cycle. Also, simplified linear models are presented for pure condensing, single extraction and double extraction turbine/generators which could be adapted to optimization of integrated energy conversion systems.

Paper 10: The Influence of Moisture on the Efficiency of a One-Third Scale Model Low Pressure Steam Turbine

The rapid increase in blade-tip diameters and peripheral speeds of low pressure turbines in large 3000 rev/min turbo-generators has presented the designer with many difficult mechanical and aerodynamic problems. To assist in the aerodynamic development of such blading, design studies on an experimental low pressure (l.p.) turbine were started early in 1959. Economic and technical considerations limited the choice to a one-third scale model steam turbine capable of running at three times the normal rotational speed to preserve full-scale working Mach numbers on the blading. Overall output and steam consumption were measured on a hydraulic dynamometer and by volumetric tanking respectively. The inlet steam temperature was controlled by a direct injection desuperheater so that the expansion could be kept dry for traversing or reduced to design inlet temperatures for normal wet running. Three multi-stage sets with last row blade diameters corresponding to 90-in, 120-in, and 136-in full-scale turbines have now been tested in the experimental turbine and the wet performance of the largest forms the subject of this paper. The overall wetness losses on the model 136-in diameter turbine have been assessed from a series of seven tests in which the inlet superheat and rotational speed were varied whilst maintaining fixed inlet and outlet pressure levels. To isolate the stage moisture correction factor (α), however, where a stage-by-stage approach was adopted, in which the dry stage efficiencies were initially established from interstage traverses under dry steam conditions. Two wet steam analyses were made, the first assuming equilibrium and the second supersaturated expansion, but the choice seemed immaterial since the moisture correction factor was almost the same for both. In the case of the supersaturated expansion calculation, it was necessary to establish the point of reversion from supersaturated to near equilibrium expansion (the Wilson point) and supplementary water extraction results were used to establish the maximum supersaturation ratio. These suggest that the maximum level is nearer to 3 in the model turbine than to the value of 4–6 quoted for convergent-divergent nozzles.