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Open access

Dawid Taler and Adam Sury

Inverse heat transfer problem in digital temperature control in plate fin and tube heat exchangers

The aim of the paper is a steady-state inverse heat transfer problem for plate-fin and tube heat exchangers. The objective of the process control is to adjust the number of fan revolutions per minute so that the water temperature at the heat exchanger outlet is equal to a preset value. Two control techniques were developed. The first is based on the presented mathematical model of the heat exchanger while the second is a digital proportional-integral-derivative (PID) control. The first procedure is very stable. The digital PID controller becomes unstable if the water volumetric flow rate changes significantly. The developed techniques were implemented in digital control system of the water exit temperature in a plate fin and tube heat exchanger. The measured exit temperature of the water was very close to the set value of the temperature if the first method was used. The experiments showed that the PID controller works also well but becomes frequently unstable.

Open access

Dawid Taler and Paweł Madejski

Thermomechanical CSM analysis of a superheater tube in transient state

The paper presents a thermomechanical computational solid mechanics analysis (CSM) of a pipe "double omega", used in the steam superheaters in circulating fluidized bed (CFB) boilers. The complex cross-section shape of the "double omega" tubes requires more precise analysis in order to prevent from failure as a result of the excessive temperature and thermal stresses. The results have been obtained using the finite volume method for transient state of superheater. The calculation was carried out for the section of pipe made of low-alloy steel.

Open access

Dawid Taler, Sławomir Grądziel and Jan Taler

Measurement of heat flux density and heat transfer coefficient

The paper presents the solution to a problem of determining the heat flux density and the heat transfer coefficient, on the basis of temperature measurement at three locations in the flat sensor, with the assumption that the heat conductivity of the sensor material is temperature dependent. Three different methods for determining the heat flux and heat transfer coefficient, with their practical applications, are presented. The uncertainties in the determined values are also estimated.

Open access

Jan Taler, Dawid Taler and Andrzej Kowal

Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes

The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing four thermocouples on the fire side below the inner and outer surfaces of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The boundary conditions on the outer and inner surfaces of the water flux-tube are determined based on temperature measurements at the interior locations. Four K-type sheathed thermocouples of 1 mm in diameter, are inserted into holes, which are parallel to the tube axis. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. The heat transfer conditions in adjacent boiler tubes have no impact on the temperature distribution in the flux tubes.

Open access

Dawid Taler, Marcin Trojan and Jan Taler

Mathematical modelling of tube heat exchangers with complex flow arrangement

General principles of mathematical modelling of transient heat transfer in cross-flow tube heat exchangers with complex flow arrangements which allow a simulation of multipass heat exchangers with many tube rows are presented. First, a system of differential equations for the transient temperature of both fluids and the tube wall with appropriate boundary and initial conditions is formulated. Two methods for modelling heat exchangers are developed using the finite difference method and finite volume method. A numerical model of multipass steam superheater with twelve passes is presented. The calculation results are compared with the experimental data.

Open access

Jan Taler, Dawid Taler, Tomasz Sobota and Piotr Dzierwa

New technique of the local heat flux measurement in combustion chambers of steam boilers

A new method for measurement of local heat flux to water-walls of steam boilers was developed. A flux meter tube was made from an eccentric tube of short length to which two longitudinal fins were attached. These two fins prevent the boiler setting from heating by a thermal radiation from the combustion chamber. The fins are not welded to the adjacent water-wall tubes, so that the temperature distribution in the heat flux meter is not influenced by neighbouring water-wall tubes. The thickness of the heat flux tube wall is larger on the fireside to obtain a greater distance between the thermocouples located inside the wall which increases the accuracy of heat flux determination. Based on the temperature measurements at selected points inside the heat flux meter, the heat flux absorbed by the water-wall, heat transfer coefficient on the inner tube surface and temperature of the water-steam mixture was determined.

Open access

Dawid Taler and Jan Taler

Abstract

Various methods for steady-state and transient analysis of temperature distribution and efficiency of continuous-plate fins are presented. For a constant heat transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or hexangular fins. At first approximate methods for determining the steady-state fin efficiency like the method of equivalent circular fin and the sector method are discussed. When the fin geometry is complex, thus transient temperature distribution and fin efficiency can be determined using numerical methods. A numerical method for transient analysis of fins with complex geometry is developed. Transient temperature distributions in continuous fins attached to oval tubes is computed using the finite volume - finite element methods. The developed method can be used in the transient analysis of compact heat exchangers to calculate correctly the heat flow rate transferred from the finned tubes to the fluid.

Open access

Dawid Taler

Abstract

This paper presents a numerical method for determining heat transfer coefficients in cross-flow heat exchangers with extended heat exchange surfaces. Coefficients in the correlations defining heat transfer on the liquid- and air-side were determined using a nonlinear regression method. Correlation coefficients were determined from the condition that the sum of squared liquid and air temperature differences at the heat exchanger outlet, obtained by measurements and those calculated, achieved minimum. Minimum of the sum of the squares was found using the Levenberg-Marquardt method. The uncertainty in estimated parameters was determined using the error propagation rule by Gauss. The outlet temperature of the liquid and air leaving the heat exchanger was calculated using the analytical model of the heat exchanger.

Open access

Jan Taler, Marcin Trojan, Dawid Taler, Piotr Dzierwa and Karol Kaczmarski

Abstract

Calculations were performed of the thermal system of a power plant with installed water pressure tanks. The maximum rise in the block electric power resulting from the shut-off of low-pressure regenerative heaters is determined. At that time, the boiler is fed with hot water from water pressure tanks acting as heat accumulators. Accumulation of hot water in water tanks is also proposed in the periods of the power unit small load. In order to lower the plant electric power in the off-peak night hours, water heated in low-pressure regenerative heaters and feed water tank to the nominal temperature is directed to water pressure tanks. The water accumulated during the night is used to feed the boiler during the period of peak demand for electricity. Drops in the power block electric power were determined for different capacities of the tanks and periods when they are charged. A financial and economic profitability analysis (of costs and benefits) is made of the use of tanks for a 200 MW power unit. Operating in the automatic system of frequency and power control, the tanks may also be used to ensure a sudden increase in the electric power of the unit. The results of the performed calculations and analyses indicate that installation of water pressure tanks is well justified. The investment is profitable. Water pressure tanks may not only be used to reduce the power unit power during the off-peak night hours and raise it in the periods of peak demand, but also to increase the power capacity fast at any time. They may also be used to fill the boiler evaporator with hot water during the power unit start-up from the cold state.

Open access

Dawid Taler and Piotr Cisek

Abstract

The analyzed heat accumulator is a key element in a hybrid heating system. In this paper, analytical and numerical models of the ceramic heat accumulator are presented.The accuracy of finite difference methods will be assessed by comparing the results with those obtained from the exact analytical solution.