scholarly journals Experimental Investigation and Mathematical Modelling of Pressure Response for Steam Generator

2018 ◽  
Vol 7 (4.19) ◽  
pp. 960
Author(s):  
Mishaal A. AbdulKareem
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Water Temperature ◽  
Void Fraction ◽  
Steam Generator ◽  
Time Constant ◽  
Heating Power ◽  
Operating Pressure ◽  
Initial Water ◽  
Set Point

Cold startup of boiler is the process of boiler operation with water at ambient temperature and pressure with all intake and discharge valves are fully closed to permit fast development of pressure.  A mathematical model is developed to estimate the pressure response during cold startup of a perfectly insulated steam generator unit. A commercial type pressure switch is used in this unit to control and maintain the desired set point of the steam operating pressure. This mathematical model assume that the thermal properties of the supplied liquid water are temperature dependent. It is based on a novel Pressure Marching Technique that is coded using a FORTRAN language computer program. The maximum percentage error of (8.24 %) was obtained when comparing the predicted results of the mathematical model with the measured values obtained from the experimental test that was done using a (2 kW) electric steam generator unit with a volume of (30 litter) and maximum operating pressure of (8 bar). In addition, the same behavior of the predicted results was obtained when compared with results of a previously published article. It was found that the time constant of the pressure control system is directly proportional with its operating pressure set point and with the volume of the steam generator and its void fraction. A (50%) increase in the pressure set point will increase the time constant by (66.16%). Increasing the boiler volume by (166.667%) will increase the time constant by (166.677%) and increasing the boiler void fraction by (150%) will increase the time constant by (23.634%). The time constant is inversely proportional with the heating power of the steam generator. A (100%) increase in the heating power will decrease the time constant by (50%). The time constant is independent of the initial water temperature. Also, it was found that the time delay to start water evaporation is directly proportional with the volume of the steam generator. A (166.667%) increase in boiler volume will increase the time delay by (166.65%). The time delay is inversely proportional with the initial water temperature and with the heating power and void fraction of the steam generator. A (38.889%) increase in the initial water temperature will decrease the time delay by (8.882%). Increasing the heating power by (100%) will decrease the time delay by (50%) and increasing the boiler void fraction by (150%) will decrease the time delay by (16.665%). The time delay is independent on the operating pressure set point.  

Improving the Boiler Efficiency by Optimizing the Combustion Air

2015 ◽  
Vol 787 ◽  
pp. 238-242 ◽  
Author(s):  
R. Pachaiyappan ◽  
J. Dasa Prakash
Keyword(s):  
Heat Transfer ◽  
Water Temperature ◽  
Steam Generator ◽  
Air Temperature ◽  
Flue Gas ◽  
Maximum Heat ◽  
Air Preheater ◽  
Hot Air ◽  
Boiler Efficiency ◽  
Efficient Combustion

Air pre-heater and economizer are heat transfer surfaces in which air temperature and water temperature are raised by transferring heat from other media such as flue gas. Hot air is necessary for rapid combustion in the furnace and also for drying coal in milling plants. So an essential boiler accessory which serves this purpose is air pre-heater. The air pre-heater is not essential for operation of steam generator, but they are used where a study of cost indicates that money can be saved or efficient combustion can be obtained by their use. The decision for its adoption can be made when the financial advantages is weighed against the capital cost of heater. The efficiency of the boiler increases with the increase in the temperature of the combustion air used in the furnace. This is achieved by the increased temperature of the flue gas in the air preheater and economizer zone. This paper deals with the different ways to obtain the maximum heat from the flue gas travelling through the air preheater and the economizer zone to improve the boiler efficiency.

scholarly journals Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Media Coverage ◽  
New Product ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Significant Difference ◽  
Form Theory ◽  
The Difference ◽  
The Stability

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

scholarly journals Formulated Mathematical Model for Delayed Particle Flow in Cascaded Sub-Surface Water Reservoirs with Validation on River Flow

2018 ◽  
Author(s):  
Ombaki Richard ◽  
Kerongo Joash ◽  
Okwoyo M. James
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Surface Water ◽  
Discrete Time ◽  
River Flow ◽  
Water Reservoir ◽  
Point Sources ◽  
Water Reservoirs ◽  
Discrete Time Delay ◽  
Mixing Problem

Pollution of sub-surface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of reservoir pollution using mixing-problem processes that involve single species contaminants such as nitrates, phosphorous and detergents. The concentration  of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. Systems of ODEs generated from principles of mixing problems were refined into a system of DDEs so that the concentration of pollutant leaving the reservoir at time would be determined at some earlier instant, for the delay. The formulated model is a mathematical discrete time delay model which would be used to describe the dynamics of sub-surface water reservoir pollution. The results from the validation of the model were analyzed   to determine how time delays in the mixing processes affect the rate of particle movement in water reservoirs.

scholarly journals Development of condenser mathematical model for research and development of ways to improve its efficiency

2020 ◽  
Vol 18 (4) ◽  
pp. 578-585
Author(s):  
Madina Shavdinova ◽  
Konstantin Aronson ◽  
Nina Borissova
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Water Temperature ◽  
Steam Turbine ◽  
Cooling Water ◽  
Laboratory Research ◽  
Thermal Engineering ◽  
Linear Regression Method ◽  
Cooling Water Temperature ◽  
The Mathematical Model

The condensing unit is one of the most important elements of the steam turbine of a combined heat and power plant. Defects in elements of the condensing unit lead to disturbances in the steam turbine operation, its failures and breakdowns, as well as efficiency losses of the plant. Therefore, the operating personnel need to know the cause of the malfunction and to correct it immediately. There are no diagnostic models of condensers in the Republic of Kazakhstan at the moment. In this regard, a mathematical model of a condenser based on the methodology of Kaluga Turbine Plant (KTP) has been developed. The mathematical model makes it possible to change the input parameters, plot dependency diagrams, and calculate the plant efficiency indicators. The mathematical model of the condenser can be used to research ways for the improvement of the condensing unit efficiency, for diagnostic purposes of the equipment condition, for the energy audit conduction of the plant, and in the training when performing virtual laboratory research. Using static data processing by linear regression method we obtain that the KTP methodology of condenser calculation is fair at cooling water temperature from 20 °C to 24 °C, but at cooling water temperature from 20 °C to 28 °C, the methodology of JSC "All-Russia Thermal Engineering Institute" (JSC "VTI") is used. One of the ways to increase the condenser efficiency has been proposed. It is the heat transfer augmentation with riffling annular grooves on tubes. This method increases the heat transfer coefficient by 2%, reduces the water subcooling of the heating steam by 0.9 °C, and decreases the cooling area by 2%.

Section 5. Tables of Suggested Water Chemistry Targets

2022 ◽  
pp. 28-30
Author(s):  
Keyword(s):  
Water Chemistry ◽  
Steam Generator ◽  
Prime Factor ◽  
Operating Pressure ◽  
Boiler Water ◽  
Water Contaminant ◽  
Internal Water ◽  
Boiler Drum ◽  
The Difference

Consensus water chemistry controls for the six types of steam generator systems are presented in Tables 1 through 7. The tabulated information is categorized according to operating pressure ranges because this is the prime factor that dictates the type of internal water chemistry employed, the normal cycles of feedwater concentration, the silica volatility, and the carryover tendency. The difference between steam and water densities decreases with increasing pressure and temperature; therefore, separating the steam/water phases completely in the boiler drum becomes increasingly difficult to achieve. Since the tendency to carryover is greater at higher operating pressures, it is necessary to maintain lower boiler water contaminant concentrations to meet the same steam purity target.

scholarly journals Influence of the Thermometer Inertia on the Quality of Temperature Control in a Hot Liquid Tank Heated with Electric Energy

Energies ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 4039
Author(s):  
Dawid Taler ◽  
Tomasz Sobota ◽  
Magdalena Jaremkiewicz ◽  
Jan Taler
Keyword(s):  
Water Temperature ◽  
Time Constant ◽  
Temperature Control ◽  
Complex Structure ◽  
Small Diameter ◽  
Hot Water ◽  
Temperature Control System ◽  
Water Tank ◽  
Water Storage Tank

This paper presents the medium temperature monitoring system based on digital proportional–integral–derivative (PID) control. For industrial thermometers with a complex structure used for measuring the temperature of the fluid under high pressure, the accuracy of the first-order model is inadequate. A second-order differential equation was applied to describe a dynamic response of a temperature sensor placed in a heavy thermowell (industrial thermometer). The quality of the water temperature control system in the tank was assessed when measuring the water temperature with a jacketed thermocouple and a thermometer in an industrial casing. A thermometer of a new design with a small time constant was also used to measure temperature. The quality of water temperature control in the hot water storage tank was evaluated using a classic industrial thermometer and a new design thermometer. In both cases, there was a K-type sheathed thermocouple inside the thermowell. Reductions in the time constant of the new thermometer are achieved by means of a steel casing with a small diameter hole inside which the thermocouple is precisely fitted. The time constants of the thermometers were determined experimentally with a jump in water temperature. A digital controller was designed to maintain the preset temperature in an electrically heated hot water tank. The function of the regulator was to adjust the power of the electrical heater to maintain a constant temperature of the liquid in the tank.

scholarly journals Decoupling Adaptive Smith Prediction Model of Flatness Closed-Loop Control and Its Application

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 895
Author(s):  
Mingming Song ◽  
Hongmin Liu ◽  
Yanghuan Xu ◽  
Dongcheng Wang ◽  
Yangyang Huang
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Time Delay ◽  
Control Method ◽  
Delay System ◽  
Control Performance ◽  
Time Delay System ◽  
Single Loop ◽  
Flatness Control ◽  
Pure Time Delay

Flatness control system is characterized by multi-parameters, strong coupling, pure time delay, which complicate the establishment of an accurate mathematical model. Therefore, a control scheme that combines dynamic decoupling, PI (Proportion and Integral) control and adaptive Smith predictive compensation is proposed. To this end, a dynamic matrix is used to decouple the control system. A multivariable coupled pure time-delay system is transformed into several independent generalized single-loop pure time-delay systems. Then, a PI-adaptive Smith predictive controller is constructed for the decoupled generalized single-loop pure time-delay system. Simulations show that the scheme has a simple and feasible structure, and good control performance. When the mathematical model of the control system is inaccurate, the control performance of adaptive Smith control method is evidently better than that of the ordinary Smith control method. The model is successfully applied to the cold rolling production site through LabVIEW, and the control accuracy is within 5I. This study reveals a new solution to the problem of coupled pure time-delay in flatness control system.

Estimate of mean tissue O2 consumption at onset of exercise in males

1987 ◽  
Vol 63 (4) ◽  
pp. 1578-1585 ◽  
Author(s):  
M. D. Inman ◽  
R. L. Hughson ◽  
K. H. Weisiger ◽  
G. D. Swanson
Keyword(s):  
Mathematical Model ◽  
Cardiac Output ◽  
Time Delay ◽  
Impedance Cardiography ◽  
Work Rate ◽  
Rate Of Change ◽  
O2 Consumption ◽  
Weighted Mean ◽  
Mean Response Time ◽  
The Mean

A mathematical model has been developed that permitted the calculation of the flow-weighted mean tissue O2 consumption (VO2T) at the onset of a step increase in work rate. From breath-by-breath measurements of alveolar O2 consumption (VO2A) and cardiac output (Q) by impedance cardiography and assumptions about the site of depletion of O2 stores, the rate of change in O2 stores (VO2s) was determined. The sum of VO2A + VO2s = VO2T. Six very fit males performed six repetitions of each of two step increases in work rate. STlo was a transition from rest to 100-W cycling; SThi was a transition from 100- to 200-W cycling. For each work rate transition, the responses of VO2A and Q were averaged over the six repetitions of each subject and the model was solved to yield VO2T. The responses of VO2A, VO2T, and Q after the increase in work rate were fit with a monoexponential function. This function included a time constant and time delay, the sum of which gave the mean response time (MRT). In the STlo test, the MRT of VO2A (24.9 +/- 1.1 s, mean +/- SE) was longer than that of VO2T (15.3 +/- 1.3 s) and of Q (16.5 +/- 6.5 s) (P less than 0.05). The MRT of VO2T and Q did not differ significantly. Also for SThi, the MRT of VO2A (34.4 +/- 3.3 s) was significantly longer than that of VO2T (30.0 +/- 3.4 s) (P less than 0.05). The MRT of VO2T and Q (30.3 +/- 5.5 s) were not significantly different at this work rate either.(ABSTRACT TRUNCATED AT 250 WORDS)

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