24th International Colloquium Tribology - January 2024 151 A Novel Mortar Multiphysics Computational Method for Thermal Elastohydrodynamic Lubrication Volker Gravemeier 1* 1 AdCo Engineering GW GmbH, Unterföhring, Germany * Corresponding author: E-mail gravemeier@adco-engineering-gw.com 1. Introduction There are numerous applications of thermo-fluid-structure interaction (TFSI) in engineering and nature, such as airbags, supersonic re-entry from space, hypersonic flight, gas turbines, rocket nozzles, heat exchangers, and quenching, just to name a few. Thermal elastohydrodynamic lubrication (TEHL) represents a specific subfield of TFSI, where the involved fluid domain typically features a drastically reduced thickness in at least one spatial direction. The interaction of contacting structure surfaces separated by a thin fluid film - with or without thermal interaction - is generally of great importance in various engineering as well as biomechanical applications. Due to this importance, improved designs, for which particularly valuable support might be provided by advanced computational methods, among other things, will be instrumental in both enabling substantial energy savings and reducing CO 2 emissions in the future. A comprehensive multiphysics computational method for TEHL and results obtained from applying it to tribosystems will be presented. Taking the multiphysical nature of tribosystems into account when simulating such systems is inevitable in most of the cases for truly reflecting their real-world features. For this purpose, it is typically both mandatory and challenging to consider all (nonlinear) effects of the individual physical fields as well as their mutual interactions. Only this way, though, it is ensured that one obtains reliable simulation results eventually. This is particularly true as soon as one approaches, for instance, the threshold range for dimensioning technical systems such as those prevalent in tribology. Among other things, the proposed new method overcomes typical limitations frequently reported in the literature for existing simulation methods for TEHL, such as (i) restrictions to reduced-dimensional or static/ steady-state problems, respectively, (ii) the availability of merely rather simple material laws (e.g., linear elasticity), (iii) the inevitable avoidance of contact scenarios within boundary and mixed lubrication regimes at all or the use of simplified modeling assumptions (e.g., elastic half-spaces), respectively, (iv) limitations on “code couplings” using commercial or opensource CAE software packages as “black-box” components, and (v) restrictions to node matching or accuracy-reducing interpolation procedures, respectively, at domain interfaces, to name a few. In contrast, the presented advanced computational method, available within a singular CAE software enables predictive, fully-coupled and detailed 3-D resolved simulations along the complete spectrum of the Stribeck curve, which displays the regimes of lubrication, and beyond. 2. Computational Method and Results Our computational method AVM 7 is embedded in our inhouse finite-element-based CAE software AMSE (“AdCo Multiphysics Software Environment”). In the following paragraphs of this section as well as in the first core part of the presentation, it will be introduced, among others, by five of its main (or “m-”) features: multiphysics, mortar, multilevel, multiscale, and multigrid. After the method will have been introduced, computational results obtained with it for various tribosystems featuring TEHL problems, such as bearings and seals, as well as a challenging TFSI application will be shown as the second core part of this presentation. From a computational point of view, TFSI and TEHL are particularly complex coupled multiphysics problems, involving in general four fields to be adequately considered numerically, as depicted in Figure 1: a fluid/ lubrication field, a structural (or solid) field, and two temperature fields, one within the fluid/ lubrication domain and one within the solid domain. Accordingly, there are four couplings or interactions, respectively: on the one hand, the fluid/ lubrication-structure interaction (FSI) and the thermo-thermo interaction (TTI), which occur at the interface between fluid and solid domain as a surface coupling, and on the other hand, the thermo-fluid interaction (TFI) and the thermo-structure interaction (TSI), which occur within the respective domain as a volume coupling. For all of these couplings, both monolithic and partitioned computational coupling approaches as described in [3] are available and may be chosen depending on the respective problem. Figure 1: Fields/ domains and their couplings for TFSI and TEHL Particularly important for successfully simulating coupled multiphysics applications is an adequate numerical consideration of the involved interfaces, both with respect to sur- 152 24th International Colloquium Tribology - January 2024 A Novel Mortar Multiphysics Computational Method for Thermal Elastohydrodynamic Lubrication face and volume couplings. Mortar methods were initially proposed for non-overlapping domain decomposition and later applied to various problem types such as contact (see, e.g., [3]), FSI and fluid flow (see, e.g., [1]). Mortar methods were proven to ensure consistent load and motion transfers at non-conforming interfaces, where collocation methods typically fail. Thus, they represent a key component of our computational method (integrated in three variants, enabling contact, meshtying and meshsliding at various coupling interfaces) for ensuring overall solution quality while enabling discretization flexibility. Among others, its geometric flexibility avoids any of the frequently observed specifications of existing numerical approaches to conformal vs. counterformal contact or point vs. line vs. area contact regions, respectively, in favor of a general approach. In particular, we make use of mortar methods in so-called dual formulation, which allows for condensing the related Lagrange multiplier degrees of freedom in the system of linear equations obtained eventually. Simulations along the complete spectrum of the Stribeck curve and beyond are ensured by a multilevel approach to solving the lubrication/ fluid field, ranging the mathematical formulations with which those levels are governed from (i) the standard Reynolds equation via (ii) the generalized Reynolds equation to (iii) the complete Navier-Stokes equations. Thus, with the third level, a seamless transition to simulating even more general thermo-fluid-structure interaction (TFSI) configurations is enabled. The most adequate resolution level of the fluid field may thus be chosen depending on the problem at hand, particularly the fluid-film thickness to be expected within the respective configuration. Aside from the fact that variational multiscale formulations are used for both fields in the fluid domain, which apply to all lubrication regimes, another multiscale feature of the method enables to address the specific challenge in the context of TEHL posed by boundary and mixed lubrication regimes. First of all, it is of paramount importance to integrate an adequate computational approach to contact mechanics, if it is aimed at a detailed resolution of the contact phenomena occurring within boundary and mixed lubrication processes. Dual mortar methods, as already addressed above for the interfaces in general, in fully linearized formulation and combined with geometrically nonlinear structural mechanics including various nonlinear material laws serve this purpose for our computational method, representing one of the currently most promising computational approaches to “dry” contact mechanics (i.e., irrespective of any additional lubrication effect). Furthermore, the dual mortar method is embedded in a multiscale approach to lubricated rough thermal contact, that is, the physical problem of boundary and mixed lubrication within rough surfaces. In this context, resolved-scale and subgrid-scale surface roughness are distinguished, where the former is resolved, while the effect of the latter is taken into account. A basis of the multiscale approach is a dynamically adaptive computational lubrication/ fluid domain, using an active-set strategy in combination with a semi-smooth Newton solution procedure for this highly nonlinear problem, among others. Multigrid methods are among the most efficient iterative algorithms for solving systems of linear equations associated with partial differential equations, which are typically obtained at the end of the discretization process. Two types of multigrid approaches may be distinguished: geometric multigrid (GMG) and algebraic multigrid (AMG). So-called aggregation-based AMG methods for solving systems of linear equations, originally proposed in [4], are another key component of our computational method, particularly regarding computing efficiency. Typically, they are integrated into our overall procedure as (block) preconditioners and combined with a subsequent Krylov-subspace iterative solver. For enabling their use in combination with the aforementioned (dual) mortar methods at interfaces, be it in condensed or non-condensed form, we developed specific adaptations of the basic procedures underlying aggregation-based AMG methods. 3. Conclusion Benefitting from various features briefly addressed in this abstract, our proposed novel simulation method AVM 7 enables detailed insights into tribosystems beyond the ones having been made possible by existing methods to date, thus contributing to an advancement of the digital transformation in tribology. In this presentation, among others, we will describe the main features of the method in more detail and show computational results obtained with it for various tribosystems. References [1] A. Ehrl, A. Popp, V. Gravemeier, W. A. Wall, A dual mortar approach for mesh tying within a variational multiscale method for incompressible flow, Internat. J. Numer. Methods Fluids 76 (2014) 1-27. [2] V. Gravemeier, S. M. Civaner, W. A. Wall, “A partitioned-monolithic finite element method for thermo-fluid-structure interaction,” Comput. Methods Appl. Mech. Engrg. 401 (2022) 115596. [3] A. Popp, M. W. Gee, and W. A. Wall, “A finite deformation mortar contact formulation using a primal-dual active set strategy,” Internat. J. Numer. Methods Engrg. 79 (2009) 1354-1391. [4] P. Vanek, J. Mandel, M. Brezina, Algebraic multigrid based on smoothed aggregation for second and fourth order problems, Computing 56 (1996) 179-196.