**3. Identification of thermal boundary conditions in heat exchangers of fluidized bed boilers**

Circulating fluidized bed (CFB) boilers burning coal or biomass are in use for several years. Fluidized bed combustion is widely used in power boilers due to its impressive environmental performance and also its fuel flexibility. Therefore, the studies of combustion and heat transfer are the subject of many recent investigations aimed at improving the design and operation of CFB boilers. Sun et al. [35] applied wide size biomass and investigated its combustion, heat transfer, and emission characteristics in CFB [35]. They found that co-firing wide screening crushed biomass pellets in CFB may reduce emissions and enhance heat transfer. Sundaresan and Kolar [36] conducted experiments to determine the total surface-average heat transfer coefficients from the tube to suspension for vertical tubes of different heights, which were placed in the core of a square cold CFB riser.

Superheaters and reheaters are the surfaces that achieve the highest temperatures in a boiler and for this reason require a lot of attention in the design, fabrication, operation, and mainte‐ nance to ensure that the permissible metal temperatures are never exceeded. A standard method for hydraulic calculation and design of boilers is described in [37]. The hydraulic calculation of superheater aims to provide the safe temperature of superheater tubes, efficient flow arrangement, and determination of pressure losses. Considerable attention has been given to hydraulic maldistribution in steam superheater tubes. A standard method for thermal design of steam boilers, including superheaters, was developed in [38]. Although the boiler standards are extensively used by manufacturers of boilers, they adopt for the calculation of the superheaters procedures which are used in design or performance calculations of usual heat exchangers assuming constant physical fluid properties [37–40]. For superheated steam, a constant value of the specific heat cannot be assumed because of the strong dependence on temperature. The specific heat of the water steam can decrease even twice over the length of the superheater tube.

The basic superheater and reheater design principles are discussed in detail by Rayaprolu [39]. Thermal and flow process in large steam boilers are the subject of the book [40]. Design and performance procedures for calculating of coal-fired boilers were described. Much attention has been paid to analyzing start-ups of steam boilers. Approximately 40% of all boiler failures are caused by damage of steam superheaters due to the overheating of the tube material [41]. Because of this, steam superheaters are modeled mathematically or monitored to avoid overheating of tubes. CFD simulations and optimization results of a 300 MW lignite-fired power boiler are presented by Tzolakis et al. [42]. A heat recovery steam generator (HRSG) was optimized by Behbahaninia using the genetic algorithm [43]. The results show that the thermodynamic optimization is not capable of decreasing significantly the total cost of the HRSG. Mathematical modeling of the boiler superheater was presented in not many publica‐ tions despite a great interest of boiler manufacturers. This is mainly due to the difficulty of the description of complex flow and heat transfer processes taking place in the steam superheaters both in pulverized coal and fluidized boilers. A numerical method for modeling of the superheaters in pulverized coal-fired boilers was developed in [44, 45]. Much trouble causes the flue-gas temperature unevenness in a duct where a superheater is situated. A thermal load deviation model for the superheater and reheater in a utility boiler is presented by Xu et al. [46]. Many failure analyses on the superheaters were carried out to reveal the causes of tube overheating or tube rapture. The unevenness of the steam temperature is one of the main reasons for boiler tube failures. The 320 MW natural gas-fired boiler was simulated using the CFD code by Rahimi et al. [47]. The main goal of the computational analysis was to detect the reason for the tube rupture inside the boiler. A new procedure for determining heat flux in superheater and reheater tubes based on the empirical formulas and the finite element modeling is presented by Purbolaksono et al. [48]. The finite element simulations were performed by Othman et al. [49] to find the main reason for superheater tube deformations. It was revealed that the failure of the tubes occurred due to the restriction of the tube deforma‐ tions. Local short-term overheating of the tubes due to concentrated flue-gas flow was the primary cause of superheater tube failure [50]. A failure analysis was carried out using visual inspections and in situ measurements of hardness the experimental examination was supple‐ mented by finite element analyzes. The rate of corrosive wear in superheaters of supercritical boilers was presented in the paper by Pronobis and Wojnar [51]. The slagging and fouling processes in superheaters influence the efficiency and lifetime of the boiler. Harding and O'Connor used the ten-year database to determine the lost generated through forced outages due to the coal quality or slagging and fouling issues [52]. A computer system for monitoring slagging and fouling of superheaters is described in [24].

performance and also its fuel flexibility. Therefore, the studies of combustion and heat transfer are the subject of many recent investigations aimed at improving the design and operation of CFB boilers. Sun et al. [35] applied wide size biomass and investigated its combustion, heat transfer, and emission characteristics in CFB [35]. They found that co-firing wide screening crushed biomass pellets in CFB may reduce emissions and enhance heat transfer. Sundaresan and Kolar [36] conducted experiments to determine the total surface-average heat transfer coefficients from the tube to suspension for vertical tubes of different heights, which were

Superheaters and reheaters are the surfaces that achieve the highest temperatures in a boiler and for this reason require a lot of attention in the design, fabrication, operation, and mainte‐ nance to ensure that the permissible metal temperatures are never exceeded. A standard method for hydraulic calculation and design of boilers is described in [37]. The hydraulic calculation of superheater aims to provide the safe temperature of superheater tubes, efficient flow arrangement, and determination of pressure losses. Considerable attention has been given to hydraulic maldistribution in steam superheater tubes. A standard method for thermal design of steam boilers, including superheaters, was developed in [38]. Although the boiler standards are extensively used by manufacturers of boilers, they adopt for the calculation of the superheaters procedures which are used in design or performance calculations of usual heat exchangers assuming constant physical fluid properties [37–40]. For superheated steam, a constant value of the specific heat cannot be assumed because of the strong dependence on temperature. The specific heat of the water steam can decrease even twice over the length of

The basic superheater and reheater design principles are discussed in detail by Rayaprolu [39]. Thermal and flow process in large steam boilers are the subject of the book [40]. Design and performance procedures for calculating of coal-fired boilers were described. Much attention has been paid to analyzing start-ups of steam boilers. Approximately 40% of all boiler failures are caused by damage of steam superheaters due to the overheating of the tube material [41]. Because of this, steam superheaters are modeled mathematically or monitored to avoid overheating of tubes. CFD simulations and optimization results of a 300 MW lignite-fired power boiler are presented by Tzolakis et al. [42]. A heat recovery steam generator (HRSG) was optimized by Behbahaninia using the genetic algorithm [43]. The results show that the thermodynamic optimization is not capable of decreasing significantly the total cost of the HRSG. Mathematical modeling of the boiler superheater was presented in not many publica‐ tions despite a great interest of boiler manufacturers. This is mainly due to the difficulty of the description of complex flow and heat transfer processes taking place in the steam superheaters both in pulverized coal and fluidized boilers. A numerical method for modeling of the superheaters in pulverized coal-fired boilers was developed in [44, 45]. Much trouble causes the flue-gas temperature unevenness in a duct where a superheater is situated. A thermal load deviation model for the superheater and reheater in a utility boiler is presented by Xu et al. [46]. Many failure analyses on the superheaters were carried out to reveal the causes of tube overheating or tube rapture. The unevenness of the steam temperature is one of the main reasons for boiler tube failures. The 320 MW natural gas-fired boiler was simulated using the

placed in the core of a square cold CFB riser.

236 Numerical Simulation - From Brain Imaging to Turbulent Flows

the superheater tube.

Direct and inverse problems in a platen superheater situated in the combustion chamber of a CFB boiler were studied in [2].

The review of the state of the art in the field of superheaters shows that published papers on the superheaters present mostly experimental results and relate to search for the causes of failures of superheater tubes or analyze ash fouling.

In this work, the finite volume modeling of a platen superheater is presented. The fluidized bed boilers steam superheaters are placed in the combustion chamber and are made of tubes with non-circular cross sections, to avoid erosion and slagging (**Figure 17**). Due to the complex shape of the cross section of superheater tubes (**Figure 18**), numerical modeling has been applied to correctly determine the temperature distribution of steam and tube wall. Accurate calculating the superheater tube wall temperature is necessary because of the high prices of alloy steels used in superheater manufacturing.

A CFD simulation will be carried out for the platen superheater located in the combustion chamber of the CFB boiler. The second stage superheater is situated in the upper part of the combustion chamber of a circulating fluidized bed boiler (CFB boiler) with the capacity of 425 · 103 kg/h steam. The steam boiler with a live steam temperature equal 560°C and a pressure of 16.1 MPa has an atmospheric circulating fluidized bed furnace. The superheater is a threepass heat exchanger. The water steam flows inside the tubes while the flue gas with a constant temperature flows upwards in a perpendicular direction to the tube axes. Two inverse problems will be solved. First, the flue-gas side heat transfer coefficient *hg* will be determined using temperatures measured at the outlet and inlet of the heat exchanger. This coefficient is essential for the proper design of superheaters in fluidized bed boilers. In the second inverse problem, in addition, to the heat transfer coefficient *hg* will also be searched the steam tem‐ perature at the inlet to the superheater based on the measured steam temperatures at three points located at the ends of the superheater passes. Such inverse problem is encountered in a superheater steam temperature controllers.

**Figure 17.** The arrangement of heating surfaces in circulating fluidized bed boiler with a steam capacity of 425·103 kg/h.

On modern large steam boilers, the temperature must be held close to design values since excessive temperatures have a serious effect on the metal lifetime of all parts of a boiler which are subject to it. The inlet steam temperature will be determined from the solution of the inverse problem. Based on this temperature, a correct flow rate of cooling water to the spray-type desuperheater (attemperator) is calculated. Despite the great practical importance, this type inverse heat transfer problems have not yet been analyzed.

Solving Inverse Heat Transfer Problems When Using CFD Modeling http://dx.doi.org/10.5772/63807 239

**Figure 18.** Platen superheater made from "omega" tubes; (a) cross section of omega tube, (b) platen superheater crosssection.

**Figure 17.** The arrangement of heating surfaces in circulating fluidized bed boiler with a steam capacity of

inverse heat transfer problems have not yet been analyzed.

238 Numerical Simulation - From Brain Imaging to Turbulent Flows

On modern large steam boilers, the temperature must be held close to design values since excessive temperatures have a serious effect on the metal lifetime of all parts of a boiler which are subject to it. The inlet steam temperature will be determined from the solution of the inverse problem. Based on this temperature, a correct flow rate of cooling water to the spray-type desuperheater (attemperator) is calculated. Despite the great practical importance, this type

425·103

kg/h.
