Elrod Adams Model Research Articles

Numerical solution of a hydrodynamic model with cavitation using finite difference method at arbitrary meshes

In this paper, we investigate the implementation of the finite difference method on arbitrary meshes in conjunction with a fixed-point algorithm for the lubrication problem of a journal bearing with cavitation, considering the Elrod-Adams model. We establish numerical properties of the generalized finite difference scheme and provide several illustrative examples.

Cavitation in oscillatory porous squeeze film: a numerical approach

PurposeThis study aims to present a numerical model to investigate cavitation effects on oscillatory porous squeeze film. This effect is able to cause considerable damage to the lubrication mechanisms, mainly in the form of surface erosion. The erosion process is caused by surface spalling due to alternating positive and negative contact stresses imposed by bubble collapse. If the process continues uncontrolled, the performance of the contact will rapidly deteriorate.Design/methodology/approachThe study is conducted numerically using Elrod–Adams model for the modified Reynolds equation coupled with the Darcy’s law for the lubricant flow through the porous medium. The governing equations are numerically discretized and iteratively solved.FindingsThe numerical results show that frequency, amplitude and permeability have a significant influence on the generation of cavitation. A comparison of the present numerical results against available literature experimental data in particular case proved a good agreement.Originality/valueThe present paper is to develop a more realistic and efficient model. Indeed, the consideration of cavitation phenomena in this model will lead to a more accurate prediction of the squeeze film characteristics. The results of this paper are based on original work and have practical value.

The effect of fluid viscoelasticity in lubricated contacts in the presence of cavitation

In this work we study the influence of fluid viscoelasticity on the performance of lubricated contacts in the presence of cavitation. Several studies of viscoelastic lubricants have been carried out, but none of them have considered the possibility of the presence of cavitation. To describe the effect of viscoelasticity, we use the Oldroyd-B model. By assuming that the product between ϵ, i.e. the ratio between vertical and horizontal length scales, and the Weissenberg number (Wi), i.e. the ratio between polymer relaxation time and flow time scale, is small, we can linearise the viscoelastic thin film equations, following the approach pioneered by "Tichy, J., 1996, Non-Newtonian lubrication with the convected Maxwell model." Consequently, the zeroth-order in ϵWi corresponds to a Reynolds equation modified to describe also the film cavitation through the mass-conserving Elrod-Adams model. We consider the flow of viscoelastic lubricants using: (i) a cosine profile representing a journal bearing unwrapped geometry, and (ii) a pocketed profile to model a textured surface in lubricated contacts. The introduction of viscoelasticity decreases the length of cavitated region in the cosine profile due to the increasing pressure distribution within the film. Consequently, the load carrying capacity increases with Wi by up to 50% in the most favorable condition, confirming the beneficial influence of the polymers in bearings. On the other hand for the pocketed profile, results show that the load can increase or decrease at higher Wi depending on the texture position in the contact. The squeeze flow problem between two plates is also modeled for viscoelastic lubricants considering an oscillating top surface. For this configuration a load reduction is observed with increasing Wi due to the additional time needed to reform the film at high Wi. Furthermore, if viscoelastic effects increase, the cavitation region widens until reaching a value of Wi for which a full-film reformation does not occur after the initial film rupture.

An extended Elrod-Adams model to account for backpressure and blow-by inception

Abstract The Piston-Ring-Liner system is the main tribological component of internal combustion engines. Hydrodynamic models are customarily used to numerically assess the performance of different ring designs and liner surface treatments. However, available models do not properly incorporate the backpressure boundary condition, which corresponds to the combustion chamber pressure and is quite significant. A new model is proposed here that imposes the combustion-chamber pressure in a mass-conserving and physically realistic way, together with an effective algorithm for its numerical approximation. The new model incorporates the pressure difference across the ring, which is shown to have a substantial effect on the predicted friction force and film thickness. The model is further elaborated so as to provide a criterion for predicting blow-by inception.

A stable numerical strategy for Reynolds-Rayleigh-Plesset coupling

Abstract The coupling of Reynolds and Rayleigh-Plesset equations has been used in several works to simulate lubricated devices considering cavitation. The numerical strategies proposed so far are variants of a staggered strategy where Reynolds equation is solved considering the bubble dynamics frozen, and then the Rayleigh-Plesset equation is solved to update the bubble radius with the pressure frozen. We show that this strategy has severe stability issues and a stable methodology is proposed. The proposed methodology performance is assessed on two physical settings. The first one concerns the propagation of a decompression wave along a fracture considering the presence of cavitation nuclei. The second one is a typical journal bearing, in which the coupled model is compared with the Elrod-Adams model.

An Elrod–Adams-model-based method to account for the fluid lag in hydraulic fracturing in 2D and 3D

An efficient method to model the fluid lag in hydraulic fracturing has been developed based on the Elrod–Adams model. The main feature of this method is the absence of the need to explicitly track the free end of the fracturing fluid, but rather, the fluid front is obtained by solving the pressure field (zero for the lag) and an auxiliary field for the entire fracture. An important advantage of this method is that no change of formulation, and hence no contact detection, is needed when the fluid reaches the fracture tip. Moreover, the method works for both the injection phase and the liquid withdrawal phase. Based on the latter case studies can be developed to investigate the quantity of the remaining fluid after the fracturing process in order to assess the environmental impact of fracturing. The method applies to both 2D and 3D problems.

Investigation of surface texture influence on hydrodynamic performance of parallel slider bearing under transient condition

Although surface texture has been becoming an attractive technique for improving hydrodynamic performance in lubrication system, the study of surface texture mainly focus on the steady-state load conditions. This investigation evaluates the effect of surface texture on hydrodynamic performance under transient lubrication in parallel bearing. In the case, considering cavitation phenomena in liquid lubricating film, a mass conserving formulation based on Elrod–Adams model with JFO conditions is then employed. The implementation of numerical simulation is discretized in spatial and time domain for calculating the pressure distribution. The effect of different geometrical configurations of lubricated contact on hydrodynamic performance is evaluated. The results show that surface texture in parallel bearing yields a great improvement in terms of friction force and friction coefficient.

A computationally efficient mass-conservation-based, two-scale approach to modeling cylinder liner topography changes during running-in

In an internal combustion engine, the surface topography of the cylinder liner changes continuously during running-in. The wear rates at different locations of the cylinder liner can vary greatly. These changes will significantly affect the lubrication and localized wear rate within the piston ring pack-liner system. In this paper, a computationally efficient, two-dimensional, two-scale homogenized mixed lubrication and wear model is developed to predict cylinder liner surface topography evolution during running-in. It takes cavitation effects into consideration by the mass-conservation-based Elrod-Adams model. To reduce computing costs, the Fischer-Burmeister-Newton-Schur (FBNS) algorithm was used to solve the cavitation model. To the author's knowledge, for the first time, this approach accurately predicts the wear rates at different locations along the stroke of a cylinder liner which has been divided into thirteen zones. The effects of the surface topography evolution on the lubrication, friction and wear properties are analyzed. The simulated wear results seem to be consistent with experimental results obtained by other researchers.

INCORPORATION OF BACK-PRESSURE EFFECTS IN THE MODELING OF THE PISTON RING/CYLINDER LINER

The piston ring/cylinder liner system is responsible for about 5% of the energy lose due to friction in a passenger car (Holmberg et al., 2012). Consequently, automotive industry and academy have made efforts seeking for designs that diminish both friction and wear. During the last year, several numerical and experimental studies have shown that texturization can have favorable or detrimental effects on the tribological characteristics of lubricated mechanisms. However, few studies have included the effects of the gas pressure in the combustion chamber, which variates rapidly in the compression stroke and can reach values as high as 60[atm]. Reynolds equation with zero-pressure Dirichlet conditions is mainly adopted in numerical works along with Elrod-Adams cavitation model. This cavitation model only admits a constant cavitation pressure, in spite it is known that cavitation pressure can variate according to the operational conditions (Shen et al., 2013). This work is devoted to the study of the effects that the combustion chamber pressure can have on both the mechanical dynamic of the rings end the cavitation pressure pcav. Keywords: Hydrodynamic lubrication; Friction force; Back-pressure effects; Elrod-Adams model

Elrod–Adams cavitation model for a new nonlinear Reynolds equation in piezoviscous hydrodynamic lubrication

In previous studies, different cavitation models have been incorporated into the classical Reynolds equation in piezoviscous regimes. The advantages of the Elrod–Adams cavitation model compared with the Reynolds model have been demonstrated in this classical framework. Recently, a new nonlinear Reynolds equation was rigorously justified [15] for lubricated line contact problems by introducing the piezoviscous Barus law into the departure Navier–Stokes equations before passing to the thin film limit. In addition, the corresponding nonlinear first order ordinary differential equation (ODE) has been proposed.In the present study, we incorporate the Elrod–Adams model for cavitation and we pose the free boundary problem associated with the nonlinear first order ODE, which involves a multivalued Heaviside operator for the relationship between the lubricant pressure and saturation. After analyzing the qualitative properties of the solution, we propose suitable numerical techniques for solving the problem as well as obtaining the lubricant pressure, saturation, and viscosity. Finally, we give some numerical results to illustrate the performance of the proposed numerical methods as well as comparisons with alternative models.

Equilibrium analysis for a mass-conserving model in presence of cavitation

We study the existence of equilibrium positions for the load problem in Lubrication Theory. The problem consists of two surfaces in relative motion separated by a small distance filled by a lubricant. The system is described by the modified Reynolds equation (Elrod–Adams model) which describes the behavior of the lubricant and an extra integral equation given the balance of forces. The balance of forces allows to obtain the unknown position of the surfaces, defined with one degree of freedom.

A Universal Model for Both Flooded and Starved Lubrication Regimes and Its Application in Ring–Liner System

ABSTRACTThis article presents a new flow continuity model by modifying the traditional Elrod-Adams model. Both fully flooded lubrication and starved lubrication can be predicted using the universal model. In particular, for the starved lubrication problem, the inlet and outlet boundaries of oil film can be automatically determined. The discontinuity of the convection flow (or lubricant transport velocity) at the interface between the full lubricant film region and the partial lubricant film region is overcome by introducing a transition region. In addition, the two-dimensional version of the presented model is deduced. Furthermore, using the presented model, the results are presented to gain insight on the influence of starvation on the friction for the textured ring–liner system.

Mixed lubrication problems in the presence of textures: An efficient solution to the cavitation problem with consideration of roughness effects

In order to consider the effect of the local surface properties, such as textures and roughness, a mass-conserving model is specifically developed based on the Elrod–Adams model. The classic flow factor methodology is incorporated in this model to deal with the roughness scale. Meanwhile, by reformulating the cavitation conditions according the Fischer–Burmeisster equations, the system of discretized equations for this model is changed to be unconstrained. The computational efficiency of the developed model is similar to that when cavitation is not considered. Finally, this model is evaluated in the predicting the performance of the textured ring/liner system under the start-up process.

Regularised cavitation algorithm for use in transient rotordynamic analysis

Journal bearings are still widely used, and – in combination with the omnipresent trend of light weight construction – there is an increasing focus on transient behaviour. Therefore, the structure, or more precisely, the aspect of rotordynamics has to be considered in conjunction with the hydrodynamics. Existing tools either address rotordynamics accurately while simplifying the bearings, or they model the bearings profoundly, including cavitation, but oversimplify the rotor to a point mass. The paper at hand addresses an approach to close the gap between both worlds. Therefore, a cavitation algorithm for the use in transient rotor dynamic applications is developed based on a regularised formulation of the Elrod–Adams model. Due to the achieved smoothness of the cavitation boundary, the solution of the hydrodynamic task yields to a more robust and faster calculation with respect to the classical approach. Therefore an application in transient simulations including rotor or multibodydynamic interactions under arbitrary conditions is realizable. For validating purposes, other approaches as well as experimental data were considered. The comparison shows an excellent agreement and additionally underlines the numerical advantages. As a result, the influences of rotordynamic aspects like the shaft's time dependent skew positioning can be considered and lead to a more precise representation of the system's behaviour, e.g. bearing damping or minimal fluid film gap.

The lubrication approximation of the friction force for the simulation of measured surfaces

Models of the friction force are assessed by direct comparison with two-dimensional Navier–Stokes results. A three-term formula obtained from asymptotic expansion provides a reasonable estimate of the hydrodynamic friction of rough runners even at sub-micron clearances.Simulations of a measured honed surface are then reported using the conservative time-dependent Elrod–Adams model with spatial resolutions as fine as 0.25μm per cell (4000×800 mesh). Mesh convergence of the numerical method is observed. Cell sizes between 0.5μm and 1μm appear as a reasonable compromise of accuracy and cost for the simulation of honed runners. The significance of each term of the friction formula is discussed, so as to assess the error involved in neglecting terms of the friction formula.

Mass-conserving cavitation model for dynamical lubrication problems. Part II: Numerical analysis

Numerical results are presented for three fully dynamical lubrication devices (piston ring–liner, journal bearing and mechanical seals) based on the Elrod–Adams model for the Reynolds equation and Newmark scheme for the motion equations. For each lubricated system we give the mathematical model, the corresponding non-dimensional problem and numerical results. We give also the full algorithm in the case of the piston-ring–liner system.

Texture-induced cavitation bubbles and friction reduction in the Elrod–Adams model

A thrust bearing consisting of an infinitely wide pad, subject to a constant load and sliding at constant speed on a runner with transverse sinusoidal textures is considered. The analysis method consists of time- and mesh-resolved simulations with a finite volume approximation of the Elrod–Adams model. Friction and clearance contours as functions of the texture depth and wavelength are built by performing more than 10,000 simulations. Conclusions are drawn for bearings of low, moderate and high conformity, unveiling basic mechanisms of friction reduction and global quantitative trends that are useful for texture selection.

Moving textures: Simulation of a ring sliding on a textured liner

Numerical simulations of the ring/liner contact in which the liner exhibits a periodic texture (pockets) are reported. The mass-conservative Elrod–Adams model is used to treat cavitation, and the dynamics of the ring is considered with a linear mass that corresponds to actual engine compression rings. The results, computed at a Stribeck number of 10−3 and thus in the hydrodynamic lubrication regime, show that the ring profile determines whether pocketing is beneficial or not. For strongly non-conformal contacts pocketing is detrimental, but for quasi-conformal contacts friction reductions of up to 73% are predicted. The largest reduction in friction was obtained for textures consisting of close-packed arrays of circular pockets of diameter comparable to the size of the contact.

A new cavitation model in lubrication: the case of two-zone cavitation

A generalization of the Elrod–Adams model of cavitation in lubricated devices is proposed, such that the translation velocity \(V\) for the saturation field \(\theta \) can be given any value between \(S/2\) and \(S\), with \(S\) being the relative speed of the surfaces. The lack of uniqueness of the classical model when \(V\ne S/2\) is explained and a suitable supplementary condition is proposed to fix this issue. The new model is rigorously analyzed, though in the simplified mathematical setting of a one-dimensional problem with a single pressurized region. The main result states the existence of a unique solution globally in time, unless of course the cavitation boundary leaves the domain or disappears. A few preliminary numerical examples are included to illustrate the model.

Conservative one-dimensional finite volume discretization of a new cavitation model for piston–ring lubrication

This paper presents a conservative numerical implementation of a new cavitation model that is well suited for lubrication problems with cavitated regions in which the fluid film is attached to just one of the participating surfaces, as happens for instance in piston–ring assemblies. This new model was recently proposed by Buscaglia et al. (2011) and is the first successful attempt at modifying the Elrod–Adams model considering a physically realistic value for the lubricant transport velocity in the incomplete-film region in those cases. In this work we show first the reasons for previous attempts to have failed, which come from a loss of uniqueness of the associated exact mathematical problem. Then, the new model is briefly recalled and a one dimensional numerical implementation by means of a finite volume scheme is presented together with several test-case results.