**7. References**

316 Computational Simulations and Applications

In this study, the way to evaluate the cross-section averaged pressure distribution in a single subchannel has been developed. If we assume that cross flow has minor effect on the pressure distribution in each subchannel, we can evaluate the pressure differences between subchannels by axial pressure distribution for each subchannel. In this way, the prediction of differential pressure by the model is compared to that obtained from the numerical simulation as shown in Fig. 32. It can be seen that the prediction of this model may reproduce the results of numerical simulation generally. For the time of 0.22 or 0.27, cross flow may have not negligible effect on inter-subchannel differential pressures and thus

To perform thermal hydraulic design of the boiling water reactor (BWR) without actual size tests, we have been developed a new design method for BWRs. In this design method, the two-phase flow correlations for fluid mixing phenomena must be modified or created based on results of large scale numerical simulations. Then, we developed an innovative two-phase flow simulation code TPFIT and an advanced interface tracking method. In the advanced interface tracking method, gas and liquid mass conservation equations are solved, to treat compressibility of gas and to keep high volume conservation

In the second step, to verify and validate the TPFIT with the advanced interface tracking method, the TPFIT was applied to some experimental analyses including three the 2-channel fluid mixing tests, and comparisons between measured and predicted result were carried out. By these results, it was concluded that the TPFIT can be applied to the two-phase flow

In the next step, the TPFIT was applied to the numerical simulation of fluid mixing between subchannels on a current BWR and FLWR that is one of innovative water reactor concept developed in JAEA. The existing two-phase flow correlation for fluid mixing was evaluated using detailed numerical simulation data. When inlet quality ratio of subchannels is relatively large, evaluated mixing coefficients by existing two-phase flow correlations for fluid mixing were different from those of the detailed numerical simulation data. And new

In the fourth step, we tried to develop new two-phase flow correlations related to the fluid mixing phenomena. Differential pressure fluctuation between subchannels dominates the fluid mixing phenomena. We considered that the differential pressure fluctuation is induced by difference of axial pressure distribution in each subchannel. Then we developed new correlation for axial pressure distribution. In this correlation, a hydrostatic gradient, acceleration and frictional gradients are taken into account in the liquid slug, and no pressure gradient exists in the slug bubble. New correlation was validated by numerical results of the TPFIT, and it was concluded that predicted results of this correlation almost agree with the simulation results. Furthermore, differential pressure fluctuation based on predicted axial pressure distribution in subchannels can predict differential pressure by the TPFIT. We thought that the method to create new twophase flow correlations by results of large scale numerical simulations is effective. However, there is issue such as required computational resources or validation of

correlation based on large scale numerical simulation results are expected.

predictions deviate from the simulation results.

**5. Conclusion** 

of gas and liquid.

fluid mixing phenomena.

prediction accuracy of created correlations.


**14** 

*Canada*

**Numerical Simulations of Unsteady Fluid Forces** 

Heat transfer is the main concern in designing shell and tube heat exchangers. Flowinduced vibration (FIV) is also a major concern while designing shell and tube heat exchangers. Fluidelastic instability (FEI), turbulence, periodic instability, and acoustic resonance are the FIV mechanisms that could cause to vibrations in heat exchanger tube bundles. FEI is the most dangers mechanism, since it can cause to tube damage in short time when the flow velocity exceeds the critical flow velocity (Ucr). Therefore, intensive researches have been undergoing in the last five decades to predict and under stand this mechanism. Different theories and models are in use to predict the FEI thresholds as function of mass damping parameters (MDP). These theories and models rely on some coefficients and parameters. Experimental approaches are used to predict these parameters for some tube arrays geometries. The experimental approach is expensive and a time consumer. Computational Fluid Dynamics (CFD) is an alternative approach proposed in this study to predict these parameters. This study utilized the CFD model to simulate the unsteady flow and the resulting fluidelastic forces in a tube bundle. Numerical simulations of in-line square tube arrays with a pitch-to-diameter (*P/d*) ratio of 1.33 utilizing a 2 dimensional model are presented. In this model, a single tube was forced to oscillate within an otherwise rigid array. The numerical model solves the Reynolds-Average Navier-Stokes (RANS) equations for unsteady turbulent flow, and is cast in an Arbitrary Lagrangian-Eulerian (ALE) form to handle mesh motion associated with a moving boundary. The fluidelastic instability was predicted for both single and fully flexible tube arrays over a mass damping parameter (MDP) range of 0.1 to 200. Fluid forces acting on the oscillating tube and the surrounding tubes were estimated. The predicted forces were utilized to

Fluidelastic instability is the most destructive excitation mechanism leading to rapid failure by fatigue or tube-to-tube clashing if the stability threshold is exceeded. Due to this potential for catastrophic failure intensive research has been ongoing for several decades on the topic of predicting and mitigating FEI effects. This has resulted in a vast amount of literature on the topic. Much of the research has been directed towards obtaining a reliable estimate of the critical flow velocity for the purpose of design. There are several models available to analyse FEI problems and the associated critical velocity. These models range from analytical approaches such as the models of Lever and Weaver (Lever & Weaver, 1982) and Païdoussis and Price (Païdoussis & Price, 1984) to the empirically-based unsteady flow

**1. Introduction** 

calculate fluid force coefficients for all tubes.

**in Heat Exchanger Tube Bundles** 

H. Omar, M. Hassan and A. Gerber

*University of New Brunswick* 

