# Modeling the Response of Magnetorheological Fluid Dampers under Seismic Conditions
## 5 Conclusions  
In this study, a numerical model was developed to simulate the behavior of magnetorheological (MR) fluid dampers by utilizing a computational fluid dynamics approach in conjunction with the magnetohydrodynamics model. [PERSON]'s law and [PERSON]'s equations were coupled with the Navier-Stokes transport equations through the inclusion of the Lorentz force as a source term. The simulations in this study were conducted based on a two-dimensional axisymmetric MR fluid damper geometry with a magnetized area representing the annular orifice. Three test cases were conducted to investigate the capability of the present model, including a constant pressure case, a sinusoidal pressure case, and a seismic pressure case. Various plots of pressure and velocity were generated against time and displacement, and the model was found to accurately capture the macroscopic characteristics of MR fluids. In the constant pressure case, the MR fluid was found to have a lower velocity when the damper was in the on-state. In this state, it was also observed that the MR fluid decelerated after entering the annular orifice and then accelerated after exiting the annular orifice. This was due to the increased apparent viscosity and viscoelasticity of the fluid created by the resisting Lorentz force in the annular orifice. It was found that MR fluids were most effective at damping constant pressure profiles with the highest pressure drop measured across the annular orifice. However, this was due to the high frequency of the sinusoidal profile and it is expected that the performance of the MR fluid between the two cases would be similar in real world conditions where the frequency of the load would be reduced. Despite this, in both the sinusoidal and seismic pressure cases, there were large pressure variations measured before the magnetized annular orifice, followed by significantly smaller ones after the annular orifice, signifying that the MR fluid dampers were effective at damping these pressure profiles. In conclusion, the presented numerical methodology and simulations in MR fluid modeling is beneficial in reducing the time and cost required in optimizing the design and performance of such devices. The present model is advantageous over the microscopic computational models, such as the discrete phase model, as it is significantly less computationally expensive to effectively model the behavior of MR fluid dampers in their full scale. Some limitations of the present study include the two-dimensional simplification of the MR fluid damper geometry. However, the underlying physical principles are identical between two-dimensional and three-dimensional simulations, thus the present study provides a solid foundation for larger-scale, three-dimensional simulations. The focus of the present model was the fluid behavior within a MR fluid damper when subjected to pressure and external magnetic fields. It may be combined with structure-focused computational models, such as the finite element method [47; 48], to form a fluid structure interaction (FSI) study for further examinations of the effectiveness of MR fluid dampers in protecting various structures against vibration. Lastly, in order to further validate the computational model presented, physical experiments are to be conducted in the future for direct quantitative comparison. Conceptualization, D.D.L., K.H., and G.H.Y. ; methodology, D.D.L., K.H., and G.H.Y. ; numerical simulations, D.D.L. and K.H. ; formal analysis, D.D.L., D.F.K., and Q.N.C. ; writing--original draft preparation, D.D.L. and D.F.K. ; writing--review and editing, A.C.Y.Y., Q.N.C., and V.T. ; visualization, K.H. and D.D.L. ; supervision, V.T., C.M., and G.H.Y. ; project administration, D.D.L. and A.C.Y.Y. ; funding acquisition, V.T. and G.H.Y. This research was supported by the Australian Research Council (ARC Project ID DP150101065 and DP160100021). The support of NVIDIA Corporation with the donation of the Titan Xp and Quadro P6000 GPUs used for this research is also gratefully acknowledged.