Browsing by Author "Ahmed, Humayun"

Now showing 1 - 3 of 3

Open Access
Modeling lubricants enhanced by finite elasticity polymers
(2023-12) Ahmed, Humayun
Lubrication is essential for the longevity of mechanical and biological surfaces in relative motion and susceptible to friction and wear. A well designed lubricant, for example a base oil enhanced with polymer additives, can effectively reduce both energetic and material losses. However, difficulty arises when modeling these lubricant mixtures exhibiting complex rheological behavior, in particular, a dependence of the viscosity on pressure (piezoviscosity), temperature (thermal thinning), shear rate (shear thinning) and the onset of viscoelasticity. Accurate estimates of the load carrying capacity of the thin lubricating film requires careful modeling of shear thinning. Available models such as the generalized Reynolds equation (GR) and the approximate shear distribution (ASD) have drawbacks such as large computational time and poor accuracy, respectively. In this work, we present a new approach, i.e. the modified viscosity (MV) model. We investigate, for both MV and GR, the load, the maximum pressure and the computational time, for (i) sliding (non-cavitating) contacts, (ii) cavitating and (iii) squeezing contacts. We observe that the computational time is reduced (i) considerably for non-cavitating sliding and rolling contacts and (ii) by several order of magnitudes for cavitating and squeezing contacts. For strongly elastic lubricants, the viscoelastic Reynolds (VR) approach (Ahmed & Biancofiore, Journal of Non-Newtonian Fluid Mechanics, 292, 104524, 2021.) has been shown to be effective in modeling (i) the pressure distribution and (ii) the load carrying capacity of a viscoelastic lubricating film for mechanical contacts for the Oldroyd-B constitutive relation. In this work, we have extended the VR approach to the non-linear finitely extensible non-linear elastic (FENE) type constitutive relations that account for the (i) finite extension of the polymer chains and (ii) shear thinning. We have validated the VR approach against DNS, showing an excellent agreement over a wide range of the Weissenberg number W i, i.e. the ratio between the polymer relaxation time and the flow time scale, and finite extensibility parameter L, using FENE-CR and FENE-P. Following a thorough validation, the pressure distribution and the load carrying capacity of a journal bearing, whose channel height is governed by the journal eccentricity ratio e, is considered. It is observed that the load carrying capacity of the film portrays a strongly non-linear dependence on W i, L and e: while it increases for small values of W i, limited greatly by the capacity of the polymer to stretch, a saturation and a subsequent decline is observed for highly viscoelastic regimes. Additionally, a weakly (strongly) eccentric configuration plays an important role in promoting (hindering) the growth in load versus both W i and L. These effects are significant and have to be considered when modeling thin contacts lubricated with a strongly viscoelastic fluid. Additionally, we have extended the VR approach towards three-dimensional lubricated contacts (in cartesian and cylindrical coordinate systems) for several non-linear constitutive relations and have provided a linearized model in De. Owing to the increase in computational requirements, a globally fully-implicit numerical technique was adopted for the efficient solution of the equations. The load and friction response for an extruded journal bearing e = 0.9 (and parabolic slider) showed a strong variation versus the channel aspect ratio (otherwise zero for a Newtonian lubricant), i.e. a = ℓx/ℓz, the ratio between the channel streamwise and spanwise lengths. The effects of transient surface motion on the response of an elastic polymer have also been examined, with a specific focus on the load carrying capacity and the friction, via a second-order perturbation model and the VR approach. We find, the perturbed models only offer a matching prediction (i) once the motion has proceeded from some time and, (ii) the De is small. A simplified look into the influence of polymer elasticity on the temperature distribution of the film showed a weak dependency versus De. The film heating owing to the fluid dissipation remained largely unaffected unless the De was large.
Open Access
A new approach for modeling viscoelastic thin film lubrication
(Elsevier BV, 2021-03-27) Biancofiore, Luca; Ahmed, Humayun
Lubricants can exhibit significant viscoelastic effects due to the addition of high molecular weight polymers. The overall behavior of the mixture is vastly different from a simpler Newtonian fluid. Therefore, understating the influence of viscoelasticity on the load carrying capacity of the film is essential for lubricated contacts. A new modeling technique based on lubrication theory is proposed to take into account viscoelastic effects. As a result, we obtain a modified equation for the pressure, i.e. the viscoelastic Reynolds (VR) equation. We have first examined a parabolic slider to mimic a roller bearing configuration. An increase of the load carrying capacity is observed when polymers are added to the lubricant. Furthermore, our results are compared with existing models based on the lubrication approximation and direct numerical simulations (DNS). For small Weissenberg number (), i.e. the ratio between the polymer relaxation time and the residence time scale, VR predicts the same pressure of the linearized model, in which is the perturbation parameter ( is the ratio between the vertical length scale and the horizontal length scale). However, the difference grows rapidly as viscoelastic effects become stronger. Excellent quantitative and qualitative agreement is observed between DNS and our model over small to moderate Weissenberg number. While DNS is numerically unstable at high values of the Weissenberg number, VR does not have the same issue allowing to capture the evolution of the stress and pressure also when the viscoelastic effects are strong. It is shown that even in high shear flows, normal stresses have the largest impact on load carrying capacity and thus cannot be neglected. Furthermore, the additional pressure due to viscoelasticity comprises two components, the first one due to the normal stress and the second one due to the shear stress. Afterwards, the methodology used for the parabolic slider is extended to a plane slider where, instead, the load decreases by adding polymers to the fluid. In particular, under the effect of the polymers surface slopes enhance the rate at which pressure gradients increase, whereas curvature opposes this along the contact. Therefore, the increase of the load carrying capacity observed for viscoelastic lubricants is due to its shape close to the inlet, which is steeper than the plane slider.
Open Access
Nonlinear modeling of non-Newtonian hydrodynamic lubrication
(2019-08) Ahmed, Humayun
Lubrication is essential to improve the performance of sliding surfaces. Power transmission in mechanical and biological systems rely on proper lubrication to minimize wear and energy losses. However, most practical applications involve conditions that cause or require the lubricant to exhibit non-Newtonian behavior, namely shear thinning and viscoelasticity. In this study a novel non-linear 1D Reynolds equation is proposed for modeling shear thinning and a 1D viscoelastic Reynolds equation is proposed to model viscoelastic effects. The models are compared with the direct numerical simulation (DNS) of thin films for different geometries. The results are in good qualitative and quantitative agreement indicating the simplified models are valid. The pressure presents strong variations as lubricant elasticity becomes significant, but stagnates as the polymer relaxation time becomes slow compared to the characteristic ow time. The net film pressure is shown to be a superposition of a Newtonian and viscoelastic component. The viscoelastic pressure varies as contact geometry changes. Surfaces with constant slope (plane slider) exhibit a constant decrease in film pressure whereas parabolic surfaces can enhance pressure for low relaxation times.