Squeeze Film Force Using an Elliptical Velocity Profile
01 Jan 2003-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 70, Iss: 1, pp 137-142
TL;DR: In this article, the authors theoretically predicted the squeeze film force in a circular Newtonian squeeze film by using the elliptical velocity profile assumption in the squeeze films by three different approximation methods and obtained numerical results for the sinusoidal squeeze motion, constant velocity squeezing state, and constant force squeezing state.
Abstract: The squeeze film force in a circular Newtonian squeeze film has been theoretically predicted by using the elliptical velocity profile assumption in the squeeze film by three different approximation methods. As examples, the numerical results for the sinusoidal squeeze motion, constant velocity squeezing state, and constant force squeezing state have been obtained
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TL;DR: In this article, a theoretical study of the non-Newtonian effects on the squeeze film characteristics between parallel annular disks is presented using a small perturbation method, a closed-form solution is derived.
31 citations
TL;DR: In this paper, a theory describing the nonlinear stationary waves of finite amplitude and long wavelength on a thin viscous Newtonian film at high Reynolds numbers and moderate Weber numbers has been developed using the energy integral method (EIM).
Abstract: The theory describing the nonlinear stationary waves of finite amplitude and long wavelength on a thin viscous Newtonian film at high Reynolds numbers and moderate Weber numbers has been developed using the energy integral method (EIM). The linear instability of the uniform flow by EIM has been analyzed and the linear instability threshold has been obtained as cot θ/Re=6/5, which agrees with the classical results of the Orr–Sommerfeld analysis by Benjamin [J. Fluid Mech. 2, 554 (1957)] and Yih [Phys. Fluids 6, 321 (1963)] and verified experimentally by Liu and Gollub [Phys. Rev. Lett. 70, 2289 (1993)]. Further, in the frame of reference moving with the steady wave speed, the second order approximate equations reduce to a third order dynamical system. While wave transitions in real life involve complex spatio-temporal dynamics and many of these transitions lead to chaotic waves that are not stationary traveling waves, bifurcation of stationary traveling waves has been examined as a preliminary study of the more complex transitions. Stability of the fixed points of the dynamical system, parametric regimes of heteroclinic orbits and Hopf bifurcations are delineated. Numerical integration has been carried out in order to study the different bifurcation scenarios as the phase speed deviates from the Hopf-bifurcation thresholds. Four different bifurcation scenarios have been observed and the dependence of bifurcation scenarios on the inclination angle, Reynolds numbers and Weber numbers have been discussed. Although the results obtained by the momentum integral method and EIM exhibit similar bifurcation scenarios, there are quantitative differences which shows that the modeling differences exist in the literature.
26 citations
TL;DR: In this paper, a matched asymptotic expansion approach is used to determine the flow behavior of Casson and Herschel-Bulkley fluids between two parallel plates that are approaching each other with a constant velocity.
Abstract: A matched asymptotic expansions approach is used to determine the flow behaviour of Casson and Herschel–Bulkley fluids between two parallel plates that are approaching each other with a constant velocity. The present study is based on the earlier work of Muravleva (2015), who has analyzed the squeeze flow of a Bingham fluid using the method of matched asymptotic expansions. A naive application of classical lubrication theory leads to a kinematic inconsistency in the predicted plug region - the well known “squeeze flow paradox” for a viscoplastic fluid. The objective of this work is to determine a consistent solution for the aforementioned constitutive equations. Based on the technique of matched asymptotic expansions, the solution is formulated in terms of separate expansions in the regions adjacent to the two plates where the shear stress is dominant, and a central pseudo-plug (plastic) region where the normal stresses become comparable to the shear stress; the two regions being separated by a pseudo-yield surface. In this manner, a complete asymptotic solution is developed for the squeeze flow of both Casson and Herschel–Bulkley fluid models. Using this solution, we derive expressions for the velocity, pressure and stress fields, and the squeeze force acting to retard the plates. The effect of the yield threshold on the pseudo-yield surface that separates the sheared and plastic zones, pressure distribution and squeeze force is investigated.
16 citations
TL;DR: In this paper, the influence of fluid inertia on the ferrofluid squeeze film between a sphere and a plate in the presence of external magnetic fields was investigated, and the results showed that the effects of the fluid inertia forces enhanced the load capacity and prolonged the approaching time of the squeeze film.
10 citations
TL;DR: Han et al. as mentioned in this paper employed the Energy Integral Method with ellipse profile EIM(E) as a weight function and is motivated by the success of EIM in effectively and accurately predicting the squeeze film force in squeeze flow problems and in predicting the inertial effects on the performance of squeeze film dampers.
Abstract: A new model which accounts for energy balance while describing the evolution of a thin viscous, Newtonian film down an incline at high Reynolds numbers and moderate Weber numbers has been derived. With a goal to improve the predictions by the model in inertia dominated regimes, the study employs the Energy Integral Method with ellipse profile EIM(E) as a weight function and is motivated by the success of EIM in effectively and accurately predicting the squeeze film force in squeeze flow problems and in predicting the inertial effects on the performance of squeeze film dampers [Y. Han and R. J. Rogers, “Squeeze film force modeling for large amplitude motion using an elliptical velocity profile,” J. Tribol. 118(3), 687–697 (1996)]. The focus in the present study is to assess the performance of the model in predicting the instability threshold, the model successfully predicts the linear instability threshold accurately, and it agrees well with the classical result [T. Benjamin, “Wave formation in laminar flow down an inclined plane,” J. Fluid Mech. 2, 554–573 (1957)] and the experiments by Liu et al. [“Measurements of the primary instabilities of film flows,” J. Fluid Mech. 250, 69–101 (1993)]. The choice of the ellipse profile allows us to have a free parameter that is related to the eccentricity of the ellipse, which helps in refining the velocity profile, and the results indicate that as this parameter is increased, there is a significant improvement in the inertia dominated regimes. Furthermore, the full numerical solutions to the coupled nonlinear evolution equations are computed through approximations using the finite element method. Based on a measure {used by Tiwari and Davis [“Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface,” Phys. Fluids 21, 102101 (2009)]} of the temporal growth rate of perturbations, a comparison of the slope of the nonlinear growth rate with the linear growth rate is obtained and the results show an excellent agreement. This confirms that the present model’s performance is as good as the other existing models, weighted residual integral boundary layer (WRIBL) by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J: B 15, 357–369 (2000)] and energy integral method with parabolic profile [EIM(P)] by Usha and Uma [“Modeling of stationary waves on a thin viscous film down an inclined plane at high Reynolds numbers and moderate Weber numbers using energy integral method,” Phys. Fluids 16, 2679–2696 (2004)]. Furthermore, for any fixed inclination θ of the substrate, 0 < θ < π/2, there is no significant difference between the EIM(E) and EIM(P) results for weaker inertial effects, but when the inertial effects become stronger, the EIM(E) results for energy contribution from inertial terms to the perturbation at any streamwise location is enhanced. More detailed investigation on the model’s performance due to this enhancement in energy contribution and the assessment of the model as compared to the other existing theoretical models, experimental observations, and numerical simulations, in the inertia dominated regimes, will be reported in a future study.
6 citations
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TL;DR: In this paper, a general theory for the elastic interactions in a composite plate of layers with different relaxed planar dimensions is presented, and the experimental determination of the planar substrate strain is presented as a rigorous test of the correctness of the theory.
Abstract: A general theory is presented for the elastic interactions in a composite plate of layers with different relaxed planar dimensions. Solutions are obtained for the case of equivalent elastic properties and for the case of different elastic properties among the layers. Approximations for the case of thin films on a substrate lead to the governing equations for stresses in multilayered thin‐film systems. Finally, the experimental determination of the planar substrate strain, which is first order in the film/substrate thickness ratio, is presented as a rigorous test of the correctness of the theory.
362 citations
TL;DR: Fluid inertia effects in squeeze films are analyzed in this paper, where the agreement between theory and experiment is very good, and the experimental results are also shown to be very good as well.
Abstract: Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.
141 citations
122 citations
TL;DR: In this article, a theoretical study of the flow behavior of thin Newtonian liquid films being squeezed between two flat plates is made, and solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested.
Abstract: A theoretical study is made of the flow behavior of thin Newtonian liquid films being “squeezed” between two flat plates. Solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested. Particular emphasis is placed on including in the analysis the inertial terms in the Navier-Stokes equations. Comparison of results from the numerical calculation with those from Ishizawa's perturbation solution is made. For the conditions considered here, it is found that the perturbation series is divergent, and that in general one must use a numerical technique to solve this problem.
110 citations