**Abstract**

Supercritical pressure water (SCW) has been widely used in many engineering fields and industries, such as fossil fuel-fired power plants, newly developed Gen-IV nuclear power plants and so forth. Heat transfer characteristics of SCW are of great importance for both design and safe operation of the related systems. Many heat transfer correlations have been developed in the history for predicting the heat transfer characteristics of SCW. However, the prediction accuracy of the existing correlations is less than satisfactory, especially in the cases with deteriorated heat transfer (DHT) because of the severe and quick variation in thermal physical properties of SCW in the vicinity of the fluids' pseudo critical point. It is very necessary to develop new correlations for the heat transfer of SCW to meet the engineering requirements for satisfactory prediction of the heat transfer behavior of SCW. In this chapter, experimental data on heat transfer of SCW are extensively collected from published literatures, and the performance of the existing heat transfer correlations for SCW are reviewed and quantitatively evaluated against the collected experimental data, and then a new heat transfer correlation for SCW with high prediction accuracy is proposed.

**Keywords:** supercritical water, enhanced heat transfer, deteriorated heat transfer, correlation, smooth tube

### **1. Introduction**

Supercritical pressure fluids (SCFs) have been widely used in many engineering fields and industries, such as fossil fuel-fired power plants, newly developed Gen-IV nuclear power plants, chemical processes, and so forth. Heat transfer characteristics of SCFs are of great importance for both design and safe operation of the related systems. As one of the most popular SCFs, supercritical pressure water (SCW) has been selected as the ideal working fluid in nuclear power plants and fossil-fired power stations, and the heat transfer behavior of SCW has attracted more and more attention from both scholars and engineers in these fields [1, 2].

As well known, most of the newly designed thermal power plants are operated at supercritical pressures, and the operating parameters of future fossil-fired power plants have been suggested to raise to even higher levels to gain higher thermal efficiency, and at the same time, to obtain effective gains in reduction of the

pollution products emission. For example, the U.S. Department of Energy has ever proposed a research program (AD 760), in which the operating parameters of the future fossil-fired power plants are suggested to raise to 37.9 MPa/732°C/760°C with an efficiency of up to 47%. A program similar to AD 760, i.e., the AD 700 thermal program, has also been proposed in Europe, and planned to build the ultrasupercritical steam condition at 720°C and 35 MPa in the future thermal power plants so as to obtain a cycle efficiency up to 50% [2]. There is no doubt that the heat transfer characteristics of SCW is an important issue for the thermal power plants with high level parameters. The higher the operating parameters, the higher the thermal efficiency, and as well, accordingly, the more important is the precise prediction of heat transfer characteristics of SCW. It should be noted that deteriorated heat transfer (DHT) is one kind of special heat transfer phenomena of SCW that might happen in the heat transfer tube and even lead to the burst of heat transfer tube or other failure accidents in the plants. On the other hand, the supercritical water-cooled reactors (SCWRs) has been selected as one of the six most promising reactors concepts presented at the Generation IV International Forum due to its high thermal efficiency and other features [3]. Similar to the situation in supercritical pressure thermal power plants, the heat transfer of SCW is an important issue for SCWRs as well. Furthermore, due to the possible risks in release of radioactive medium under conditions with tube or vessel failures, the heat transfer of SCW is of much more concern for the safe operation of SCWRs than that of thermal power stations, and as a result, precise knowledge about the heat transfer characteristics of SCW is one of the major tasks for the design and operation of SCWRs [3, 4]. Besides, heat transfer of SCW is of significance for other applications with SCW as the working fluid, such as SCW gasification system [5].

Dittus-Boelter et al.'s correlation [10]. Under supercritical pressure conditions, there exists no phase change of the fluid, but the thermophysical properties of the SCW experience dramatic change in the vicinity of pseudocritical point which might have great impact on the heat transfer behavior of the SCW. In view of this fact, a few correction terms consisting of the fluid thermophysical properties, such as *ρ*w/*ρ*b, *μ*w/*μ*b, *λ*w/*λ*<sup>b</sup> among the others, were introduced to the first type correlations, resulting in the emerge of second type heat transfer correlations for SCW. With the deepening research on heat transfer phenomena of SCW, buoyancy effect and thermal acceleration were considered to be the main reasons for DHT of SCW and then two special correction terms, i.e., **Gr\*** and *q*<sup>+</sup> proposed by Jackson [11] and were added to the second type correlations, yielding the third type heat transfer

*Heat Transfer Correlations for Supercritical Water in Vertically Upward Tubes*

*DOI: http://dx.doi.org/10.5772/intechopen.89580*

Pioro et al. [8, 12] have conducted a comprehensive review of the existing heat transfer correlations for SCW and argued that none of the existing correlations could predict the heat transfer of SCW accurately under all heat transfer regimes. Lei et al. [2] ever put emphasis on the deterioration heat transfer of SCW by analyzing the physical mechanism of special heat transfer behavior of the SCW and tried to build new correlation for SCW, and found that most of the existing correlations for heat transfer of SCW focused mainly on the enhanced heat transfer (EHT) regimes of SCW, and these correlations were not capable of providing satisfactory prediction accuracy when it was applied to the DHT regime of SCW, and he thus suggested that excluding DHT data in the development of heat correlations should be responsible for the distinct deviations between the calculated heat transfer values and the experimental data of SCW in the DHT regimes. Another reason for the unsatisfied prediction accuracies of the existing correlations for heat transfer of SCW might be, to some extent, attributed to old thermophysical properties data adopted in the development of some of the existing heat transfer correlations [13]. Therefore, a new and accurate correlation for heat transfer of SCW is expected to be effectively accurate under both the DHT and EHT regimes of SCW, and special emphasis should be directed onto the DHT phenomena, which is the most dangerous situation to not only thermal power plants but also to the Gen-IV SCWRs and other heat transfer equipment with SCW as the working fluid. In this chapter, experimental data on heat transfer of SCW are collected, including both the EHT regimes and the DHT regimes. Existing heat transfer correlations for SCW are well reviewed. Detailed assessments of prediction accuracy of the existing correlations are also conducted against the collected experimental data. On the basis of the evaluation of the prediction behavior of the existing heat transfer correlations for SCW, a new correlation is proposed for the heat transfer of SCW to cover both the EHT regime and the DHT regime. The prediction capability of the new correlation is also assessed against the collected experimental data.

**2. Experimental data and existing heat transfer correlations**

Since 1960s, a series of experimental investigations on heat transfer of SCW have been conducted, and a large amount of experimental data have been accumulated. A comprehensive survey of experimental investigations on heat transfer correlations of SCW has been provided by Pioro et al. [4, 8, 14] and showed that most of previous experimental data for heat transfer of SCW focused primarily on the flow of SCW in vertical circular tubes [2]. In the present study, approximately 12,704 data points and 250 experimental cases about the flow and heat transfer of SCW in vertical circular tubes are retrieved and collected from the published

correlations for SCW.

literatures.

**45**

Two methods have been proposed by different scholars to predict the heat transfer characteristics of SCW: the look-up Table [6, 7] and the heat transfer correlations [8]. The look-up table for heat transfer of SCW is based on real experimental data. The prediction accuracy of such look-up table is pretty high; however, the applicable ranges of the operation parameters (e.g., pressures, mass fluxes, and heat fluxes) of the look-up table are limited by the experimental conditions. In the development of ultra-supercritical pressure boilers or other heat exchangers with high operation parameters, the applicability of the look-up table seems to be limited. Unlike the look-up table, heat transfer correlations have been developed on the basis on experimental data, dimensionless analysis, and theoretical analysis of the heat transfer phenomena. The applicability of heat transfer correlations are much flexible than that of look-up tables, and as a result, heat transfer correlations for SCW have found wide applications in related industries and engineering.

In the last few decades, many heat transfer correlations for SCW were proposed (see **Table 3** in the later section of this chapter). Generally, the existing heat transfer correlations could be divided into three categories [9], as listed in **Table 1**. The first type heat transfer correlation for SCW was built on the basis of the


### **Table 1.** *Three types of heat transfer correlations for SCW.*

### *Heat Transfer Correlations for Supercritical Water in Vertically Upward Tubes DOI: http://dx.doi.org/10.5772/intechopen.89580*

Dittus-Boelter et al.'s correlation [10]. Under supercritical pressure conditions, there exists no phase change of the fluid, but the thermophysical properties of the SCW experience dramatic change in the vicinity of pseudocritical point which might have great impact on the heat transfer behavior of the SCW. In view of this fact, a few correction terms consisting of the fluid thermophysical properties, such as *ρ*w/*ρ*b, *μ*w/*μ*b, *λ*w/*λ*<sup>b</sup> among the others, were introduced to the first type correlations, resulting in the emerge of second type heat transfer correlations for SCW. With the deepening research on heat transfer phenomena of SCW, buoyancy effect and thermal acceleration were considered to be the main reasons for DHT of SCW and then two special correction terms, i.e., **Gr\*** and *q*<sup>+</sup> proposed by Jackson [11] and were added to the second type correlations, yielding the third type heat transfer correlations for SCW.

Pioro et al. [8, 12] have conducted a comprehensive review of the existing heat transfer correlations for SCW and argued that none of the existing correlations could predict the heat transfer of SCW accurately under all heat transfer regimes. Lei et al. [2] ever put emphasis on the deterioration heat transfer of SCW by analyzing the physical mechanism of special heat transfer behavior of the SCW and tried to build new correlation for SCW, and found that most of the existing correlations for heat transfer of SCW focused mainly on the enhanced heat transfer (EHT) regimes of SCW, and these correlations were not capable of providing satisfactory prediction accuracy when it was applied to the DHT regime of SCW, and he thus suggested that excluding DHT data in the development of heat correlations should be responsible for the distinct deviations between the calculated heat transfer values and the experimental data of SCW in the DHT regimes. Another reason for the unsatisfied prediction accuracies of the existing correlations for heat transfer of SCW might be, to some extent, attributed to old thermophysical properties data adopted in the development of some of the existing heat transfer correlations [13]. Therefore, a new and accurate correlation for heat transfer of SCW is expected to be effectively accurate under both the DHT and EHT regimes of SCW, and special emphasis should be directed onto the DHT phenomena, which is the most dangerous situation to not only thermal power plants but also to the Gen-IV SCWRs and other heat transfer equipment with SCW as the working fluid.

In this chapter, experimental data on heat transfer of SCW are collected, including both the EHT regimes and the DHT regimes. Existing heat transfer correlations for SCW are well reviewed. Detailed assessments of prediction accuracy of the existing correlations are also conducted against the collected experimental data. On the basis of the evaluation of the prediction behavior of the existing heat transfer correlations for SCW, a new correlation is proposed for the heat transfer of SCW to cover both the EHT regime and the DHT regime. The prediction capability of the new correlation is also assessed against the collected experimental data.
