Effect of rolling motion on the expansion and contraction loss coefficients

doi:10.1016/j.anucene.2012.09.019

Annals of Nuclear Energy

Volume 53, March 2013, Pages 259-266

https://doi.org/10.1016/j.anucene.2012.09.019 Get rights and content

Abstract

The sudden expansion and sudden contraction loss coefficients in rolling motion are investigated with CFD code FLUENT. The calculation results are validated with experimental and theoretical results in steady state. The effects of rolling motion on the expansion and contraction loss coefficients are different. The effects of spanwise and transverse additional forces on the expansion and contraction loss coefficients are weak. The effect of velocity oscillation on the contraction loss coefficient is more significant than that on the expansion loss coefficient. The oscillation of local loss coefficient also becomes more and more irregular as the strengthening of rolling motion.

Highlights

► The expansion and contraction loss coefficients in rolling motion are analyzed. ► Effects of rolling motion on the expansion and contraction loss coefficients are different. ► The spanwise and transverse additional forces contribute slightly to the local loss. ► The oscillations of loss coefficients increase as the strengthening of rolling motion.

Introduction

The cross-sectional areas of the fluid inlet and outlet lines to the heat exchanger and component are normally smaller than the cross-sectional area of the fluid channels in the heat exchanger. If the change in channel cross-section is gradual, no flow separation occurs and the change of static pressure may effectively convert to the kinetic energy. However, if there has an abrupt flow area change, it would cause a significant loss due to additional turbulence arising in the connection.

In ocean environment, the thermal hydraulic behavior of ship-based equipment is influenced by different motions such as rolling, pitching and heaving motions (Fig. 1, Yan and Yu, 2011). Oscillations change the effective forces acting on the fluid and induce flow fluctuations, which result in a change in momentum, heat and mass transfer characteristics (Pendyala et al., 2008a, Tan et al., 2009a, Tan et al., 2009b). Isshiki (1966) was the first scholar to analyze the effect of ocean environment on the thermal hydraulic performance of water cooled reactor. Ishida et al. (1990) investigated the effect of heaving and rolling motions on the thermal hydraulic behavior of marine reactors numerically with a modified RETRAN02 code. Muruta et al., 1990, Murata et al., 2002 carried out a series of single phase natural circulation tests in a model reactor with rolling motion was performed, in order to investigate the natural circulation characteristics of a marine reactor in a stormy weather. The heeling and heaving experiments of small Pressurized Water Reactor (PWR) have been carried out by Ishida and Yoritsune (2002) with the deep sea research reactor (DRX). They also analyzed the operational characteristics of DRX in ocean environment with RETRAN02 code. Pendyala et al., 2008a, Pendyala et al., 2008b investigated the effect of axial flow oscillation on the flow and heat transfer in a vertical tube experimentally. Tan et al., 2009a, Tan et al., 2009b have also finished a series of experiments for studying the single-phase natural circulation flow and heat transfer under rolling motion condition. Yu et al. (2008) and Yan et al., 2009, Yan et al., 2010, Yan and Yu, 2009 analyzed the flow and heat transfer characteristic of laminar and turbulent flow in ocean environment by establishing mathematical models. Their results indicate that the ocean environment may affect on the thermal hydraulic behavior of nuclear reactor systems.

Since traditional theoretical models and correlations could not predict the flow and heat transfer behavior in ocean environment correctly, most recent works were done for the frictional resistance coefficient and Nusselt number in channels in ocean environment (Pendyala et al., 2008a, Pendyala et al., 2008b, Tan et al., 2009a, Tan et al., 2009b, Yan et al., 2009, Yan et al., 2010, Yan and Yu, 2009). To the authors’ knowledge, no theoretical or experimental work has been done for the effect of ocean environment on the local loss coefficient and local pressure drop. The simulation of local loss coefficient and local pressure drop in all kinds of components is of great importance in nuclear thermal hydraulic analysis. The local loss coefficient is also a necessary input parameter in nuclear engineering simulation.

In this paper, the expansion and contraction loss coefficients are investigated with CFD code FLUENT. The calculation results are verified with experimental and theoretical results in steady state. The results of present study are hoped to shed some light on the local loss coefficient and local pressure drop in difficult components in ocean environment.

Section snippets

Momentum equation

In rolling motion, the flow field and flowing behavior are influenced by the spatial and temporal variant additional forces. The momentum equation of Reynolds time-averaged equations of turbulent flow should be modified as: $\frac{\partial}{\partial t} (ρ \bar{u_{i}}) + \frac{\partial}{\partial x_{j}} (ρ \bar{u_{i}} \bar{u_{j}}) = - \frac{\partial \bar{p}}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [μ (\frac{\partial \bar{u_{i}}}{\partial x_{j}} + \frac{\partial \bar{u_{j}}}{\partial x_{i}}) - \frac{2}{3} δ_{ij} \frac{\partial \bar{u_{j}}}{\partial x_{i}}] + \frac{\partial}{\partial x_{j}} (- ρ \bar{u_{i}^{'} u_{j}^{'}}) + F_{a}$ where the superscript ^– and ′ denote the time-averaged and fluctuation values, respectively. u stands for velocity, t for time, ρ for density, p for pressure, x_k for coordinates. F_a is the

Sudden expansion

In a pipe line, in addition to frictional loss, local loss is produced through additional turbulence arising when fluid flows through such components as change of area, change of direction, branching, junction, bend and valve. In steady state, the additional force does not exist and the expansion loss that occurs could be estimated by simple theory (Shames, 1992). The schematic of the sudden expansion analyzed in this work is shown in Fig. 2. The channel is horizontally located. The diameters D₁

Sudden contraction

Although a sudden contraction (Fig. 9) is geometrically the reverse of a sudden expansion, it is not possible to apply the momentum equation to a control volume between wide region and narrow region. This is because, just upstream of the junction, the curvature of the streamlines and the acceleration of the fluid cause the pressure at the annular face to vary in an unknown way. However, immediately downstream of the junction a vena contracta is formed, after which the stream widens again to

Conclusions

The prediction of local loss coefficient and local pressure drop produced through additional turbulence arising when fluid flows through difficult components is of great importance in the nuclear thermal hydraulic analysis. The local loss coefficients in pipes and components are also a necessary input parameter in nuclear engineering simulation. In this work, the expansion and contraction loss coefficients in rolling motion are investigated numerically. The calculation results are in good

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Effect of rolling motion on the expansion and contraction loss coefficients

Abstract

Highlights

Introduction

Section snippets

Momentum equation

Sudden expansion

Sudden contraction

Conclusions

Nucl. Eng. Des.

Nucl. Eng. Des.

Nucl. Eng. Des.

Nucl. Eng. Des.

Appl. Therm. Eng.

Ann. Nucl. Energy

Ann. Nucl. Energy

Ann. Nucl. Energy

Nucl. Eng. Des.

Ann. Nucl. Energy