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Journal ArticleDOI

# Numerical models to predict steady and unsteady thermal-hydraulic behaviour of supercritical water flow in circular tubes

01 Aug 2015-Nuclear Engineering and Design (Elsevier)-Vol. 289, pp 155-165
TL;DR: In this paper, a simple one-dimensional numerical thermal-hydraulic model based on a finite-difference scheme has been developed to predict steady and unsteady thermal hydraulic behavior of supercritical water flow at various operating conditions.
About: This article is published in Nuclear Engineering and Design.The article was published on 2015-08-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Heat transfer & Turbulence.

## Summary (2 min read)

### 1. Introduction

• The THRUST and CFD models are evaluated by comparing the simulation results with the experimental data under various operating conditions.
• Further, both the numerical models are then used to simulate the transient response of the SCWR.
• Subsequently, the step change and periodic variation of various physical variables are introduced with a purpose to assess the capability of the numerical models to predict the heat transfer phenomenon during a transient process.

### 2. Mathematical details of the numerical models

• The mathematical details of the THRUST and CFD models are presented in this section.
• The present analysis is carried out under both steady state and transient conditions.

### 2.1. Mathematical formulations of the 1-D TH model

• After the coefficient and source term are linearized, Eq. ( 6) is discretized with a characteristics-dependent implicit finite-difference scheme where the spatial derivative terms are approximated by a backward or forward difference depending on the sign of the characteristics.
• The resultant discretized equations are then combined together and used for a numerical solution depending on the boundary conditions for the particular problem.

### 2.1.4. Determination of the critical heat flux for DHT

• The above mentioned empirical correlation is based on the mass flux only.
• Therefore, it does not account for other factors that might affect DHT.
• It can predict successfully the occurrence of DHT for the cases under consideration in the present study when comparing with the experimental data.
• But it cannot predict the deteriorated heat transfer zone (DHTZ).

### 3. Results and discussion

• For the purpose of validation of the proposed numerical models and to carry out the intended analysis, 7 different steady state experimental cases are selected.
• The experiments under consideration dealt with supercritical water flowing vertically upwards in bare circular tubes subjected to constant and uniform heat flux in the periphery.
• The selected experimental data sets have broad range of operating conditions in terms of mass flux, heat flux, inlet temperature and operating pressure.
• Cases 4-7 represent the situation where DHT was observed experimentally (q w < q dht ) under low mass flux (Cases 4-6) and high mass flux (Case 7) conditions.

### 3.1. Validation of the numerical models at steady state condition

• The highest average error in the numerical results occurs in Case 7, which is 6.44%.
• In case of CFD simulations, both turbulence models, the RSM and k-ω SST model, are found to comparable to each other for all the cases.
• Therefore, it can be concluded that a good agreement between the numerical results and the experimental data, in general, is obtained; however, the local discrepancies do exist, but generally are confined to a narrow region inside the channel where DHT takes place.

### 3.2. Comparison of the numerical models at the transient condition

• The transient results corresponding to the step change in the wall heat flux rate are shown in Fig. 10 .
• For this transient case study, the mass flux is unchanged and therefore, based on Eq. ( 11) it is also expected that the minimum value of heat flux, at which DHT may take place, also remains the same.
• The outlet bulk temperature, as observed in Fig. 10b , also has similar qualitative trend as the previous case and the initial oscillations are predicted by both CFD model and THRUST.
• The axial variations of the wall temperature and bulk temperature at different time are shown in Fig. 10c .
• Table 5 also confirms the good agreement among the numerical results from the two models.

### 4. Conclusions

• After satisfactory validation of the THRUST and CFD models with 7 different experimental cases of steady state heat transfer, transient simulations under 3 conditions are carried out.
• Out of these 3 conditions, 2 of them involve the step change in the input mass flow rate and heat flux whereas third one is of a sinusoidal variation in the input mass flow rate.
• The THRUST and CFD models are able predict the temporal and axial variations of the wall and bulk temperatures, and the predictions by the THRUST and CFD models are in a good agreement.
• The temporal variation of the outlet mass flow rate and outlet bulk temperature for all the cases obtained by the THRUST and CFD model show the exact value at the final steady state, but the actual time taken to reach to the final steady state is more in the case of the CFD model than the THRUST.

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##### References
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Book
01 Jan 1985
TL;DR: In this article, the physical concepts and methodologies of heat and mass transfer are explained for advanced undergraduate engineering majors, using a systematic method for problem solving and discusses the relationship of heat transfer to many important practical applications through examples and problems.
Abstract: This book, designed for advanced undergraduate engineering majors, explains the physical concepts and methodologies of heat and mass transfer. It uses a systematic method for problem solving and discusses the relationship of heat and mass transfer to many important practical applications through examples and problems. A and significant contribution is the extensive use of the First Law of thermodynamics.

4,113 citations

Proceedings ArticleDOI
06 Jul 1993
TL;DR: In this article, two versions of the k-w two-equation turbulence model are presented, the baseline model and the Shear-Stress Transport (SSn) model.
Abstract: Two new versions of the k - w two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k - w model of Wilcox. but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner SOC7£; of the boundary-layer but changes gradually to the standard k - f. model (in a k - w fonnulation) towards the boundary-layer edge. The new model is also virtually identical to the k - f. model for free shear layers. The second version of the model is called Shear-Stress Transport (SSn model. It is a variation of the BSL model with the additional ability to account for the transport of the principal turbulent shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear-stress is pro­ portional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different fiowfields. The results of the BSL model are similar to those of the original k - w model, but without the undesirable free stream dependency. The predictions of the SST model are also independent of the freestrearn values but show better agreement with exper­ imental data for adverse pressure gradient boundary-layer flows.

2,470 citations

### "Numerical models to predict steady ..." refers background or methods in this paper

• ...(1965) (HTCS), Watts and hou (1982) (HTCW), Jackson (2002) (HTCJ) and Mokry et al. (2011) HTCM) based on experimental data may be limited to specific conitions....

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• ...Later, the k–ω SST model developed by Menter (1993) which combines the strength of k– model in free stream region and strength of k–ω in recirculating regions is used by various researchers, such as Cheng et al. (2007) and Palko and Anglart (2007, 2008)....

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01 Jan 2007

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01 Jan 2002

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### "Numerical models to predict steady ..." refers background in this paper

• ...U.S. DOE NERAC, GIF, 2002....

[...]

• ...…supercritical water cooled reactor (SCWR) has been idenified as one of the six proposed technologies for the generation V nuclear reactors (U.S. DOE NERAC and GIF, 2002) because of ts advantage of high thermal efficiency, compact plant system, voidance from boiling crisis and close proximity to…...

[...]

• ...Introduction The supercritical water cooled reactor (SCWR) has been idenified as one of the six proposed technologies for the generation V nuclear reactors (U.S. DOE NERAC and GIF, 2002) because of ts advantage of high thermal efficiency, compact plant system, voidance from boiling crisis and close proximity to the proven echnology of supercritical fossil power plants....

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, T. Fujii1
TL;DR: In this article, a comprehensive set of data was obtained for pressures from 226 to 294 bar, bulk temperatures from 230 to 540°C, heat fluxes from 116 to 930 kW/m 2 and mass velocities from 310 to 1830 kg/m2s.

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### "Numerical models to predict steady ..." refers background in this paper

• ...…such as water and CO2, at supercritical conditions have been studied extensively since 1950s, such as the experimental research works carried out by Yamagata et al. (1972), Swenson et al. (1965), Jackson (2002) and many more as mentioned in the review papers by Duffey and Pioro (2005), Pioro et…...

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