Model simulation based parametric study

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The solution algorithm is the same as given above for the direct model.

3.4 Model simulation based parametric study

The results of the simulation based on the formulation described above have been presented in the form of a parametric study for the constant piston velocity boundary condition. This has been done for comparing the results of transient model with steady boundary condition with the results of quasi static

Rosenfeld (2005), Weng and Oyadiji (2008), Wang and Gordaninejad (2007) and Li (2000)), for the variation of pressure gradient with the velocity. In this section the acceleration of the piston has been considered zero in Eq 3.43. For the transient model simulation for this section, the piston was assumed to start with a given constant velocity and the pressure gradient variation with time is compared with the pressure gradient for the quasi static model. This parametric study is presented to achieve the following objectives:

(1) To establish the stability of the solution over the operating range of yield shear stress developed in MR fluid due to applied magnetic field.

(2) Study of transient effects in MR fluid for the velocity range from 0-1m/s.

(3) To determine the effect of variation of parameters such as velocity, yield shear stress and transients on hysteretic behaviour of the MR damper.

During the operation of an MR damper the velocity of the damper piston varies with time. Therefore in order to apply the quasi static model to predict the variation of damper force with time the researchers such as Kamath et al,(1996), Chooi and Oyadiji,(2008), and Cesmeci and Tehsin,(2010), have considered the piston velocity to be constant during a given time step. In this section the damper piston is considered to start suddenly at a given velocity and variation of pressure gradient with time due to transient effect has been presented for velocities in the 0-1m/s. The range of yield shear stress for the MR fluid has been taken as 10-40 kPa. This model can be called as the constant velocity transient model. The variation for pressure gradient for piston speeds 0.025-0.25m/s have been shown in Fig 3.6-3.7. The Fig 3.7 is the enlarged view of the boxed portion of Fig 3.6. The two figures show that the transient effects are significant at low speeds. The fluctuations of pressure gradient with time are more significant if the time scale is of the order of μ-seconds. If the piston velocity is considered in the range of 0.5-1m/s the transient effect start becoming

very significant when the time scale is of the order of 10 μ-seconds. This can be seen in the Fig 3.8-3.9. The above two sets of figures have the following common observations:

(1) The overshoots of the transient are high at low piston velocity. The overshoots also increase with the in the yield shear stress. This is because the thickness of the plug is higher for low piston velocity. Since the thicker plug has higher inertia therefore the over shoot are higher at lower piston velocities.

(2) The time decay of pressure gradient transient increases with the increase in yield shear stress of MR fluids.

(3) The time of decay of transients increase with the increase in piston.

In this work the transient effects in terms of the variation of pressure gradient with time have been shown. However, it s pertinent to mention that the transient effect also causes changes in the plug thickness of the MR fluid flowing through the channel, till the steady state is reached. It is due to the above reason that some of the results may not be in agreement with the above mentioned observations. Here the results for the variation of the thickness of the plug of MR fluid with time have not been presented as they may be difficult to verify experimentally. During the experiments on the MR damper the measurement of force is usually taken at a sampling rate which is of the order of 5 kHz, as such the transient effect must be taken into account for predicting the force of the damper. Therefore, in order to give an overview of the effect of fluid transients on the pressure gradient, the results of variation of pressure gradient with velocity corresponding to the time at the instance 0.1 m-seconds and the variation of pressure gradient with velocity due to quasi static model have been presented (Fig 3.10). From Fig 3.6 and 3.8 it can be seen that the fluid transients can be significant at the time scale of 0.1m-seconds for some combinations of piston speed and yield shear stress of an MR fluid.

Fig 3.6 Variation of pressure gradient with time for piston velocities 0.025-0.25m/s and yield shear

stress 10-40 kPa.

Fig 3.7 Enlarged view of box A showing transient effects atμ-seconds time scale. A

Fig 3.8 Variation of pressure gradient with time for piston velocities 0. 5-1m/s and yield shear

stress 10-40 kPa.

Fig 3.9 Enlarged view of box A showing transient effects atμ-seconds time scale. A

The variation of plug thickness with the piston speed has been also shown in Fig 3.11 to facilitate the visualisation of change in velocity profile of MR fluid in the channel due the variation of piston speed and due to transient effect.

From Fig 3.10a it can be seen that the fluid transients also significantly contribute to the damper force. Since the fluid transients are non controllable component of damper force therefore they also tend to reduce the dynamic range of an MR damper. To further validate this observation the comparison of the damper force predicted by the transient model has been made with the results of quasi static model and experimental results given in Kamath et al (1996). The results are shown in Fig 3.10b. The transient model results agree very well with the experimental force of the damper. Based on the comparison of the results of transient model with the results of quasi static model it is concluded that the presence of fluid transients can be one of the contributors to such scatters. The error bars show the range of error which is likely to be introduced due to the neglecting of transient effect. The magnitude of error bar is in close agreement with the variation in the experimental and quasi static model results of Kamath et al (1996). The electrotrhological damper used in Kamath et al (1996) has a piston of 1” diameter, annular channel similar to Fig 3.1 with a gap size of 0.1” and the length of flow path is 4”. The operating Reynolds number is much less than the critical Reynolds number and so the laminar flow assumption is valid. The comparison of damper force has been made in a velocity range of 0-0.2m/s. The fluid properties of VersaFLo ER fluid are given in the table 3.1.

Table 3.1 Fluid properties used for results of Fig 3.10b

Electric field strength(KV/mm) Yield shear strength (kPa) Post yield Viscosity (Pa s) 1 0.25 0.16 2 0.4 0.085 3 0.5 0.077

Fig 3.10a Variation of pressure gradient with piston velocity for yield shear stress values