Investigation Accuracy and Stability of Modified Inter-Particle Interaction Forcing Scheme in Shan and Chen Method for Simulating Stationary Bubbles in Multiphase Flow

Document Type : Research Article

Authors

Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, I.R. IRAN

Abstract

The current study investigated the accuracy and stability of an improved inter-particle interaction force term by incorporating force methods and different equations of state. In order to evaluate, eight schemes for incorporating the force term and five equations of state, Shan and Chen (S-C), Carnahan-Starling, Peng-Robinson (P-R), Van der Waals (VdW), and Soave-Redlich-Kwong (SRK), are utilized. Furthermore, affections of relaxation time and reduced temperature on accuracy, stability, and amount of spurious velocities are considered. Among several methods of incorporating the force term, the exact difference method with an improved model and Carnahan-Starling equation of state is shown to have better accuracy and stability and can give more accuracy with spurious velocities which have been greatly reduced. Compared with existing models, the improved model for the inter-particle interaction force term reduced the error of simulation, The minimum error rate accrued for the improved model with the exact difference method of incorporating force term and Carnahan-Starling equation of state and its value is equal to 0.4% while in the identical condition this error rate for equation (9) inter-particle interaction force term is 3.6%. Subsequently, in different relaxation times, a maximum range of stability and accuracy occurred for the exact different method which has better operation in a range of 0.8 to 1 relaxation time. The minimum error of this method with the Carnahan-Starling equation of state in relaxation time 0.8 and reduced temperature 0.54 is 1.8%. By comparing the variation of spurious velocities in the range of 0.57 to 2 relaxation time is demonstrated spurious velocities are increased when temperature decreased.

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