pletely quantitatively. Depending on the gear application, a wide variety of designs can be found. In vehicles, they are used for speed adjustment between engines and drive axle, for speed compensation between axles and wheels or for changing direction in the drive train. Transmissions are typically classified into manual transmissions, automatic transmissions, dual clutch transmissions, axle gears and central hydraulics / steering gear. When selecting an application-specific matching transmission oil, a wide variety of ingredients are used to meet the requirements that are important for each gear type. In addition to “lubrication”, the requirements are: cooling, wear protection, good friction value properties, oxidation stability, foam and air separation behavior, fuel efficiency, good cold switching capability, low cold viscosity, corrosion protection, high friction value stability, high thermal stability, long replacement intervals, noise and vibration damping, high shear stability, compatibility with electrical components, pressure absorption capacity and dissolve contamination and deposits. Aus der Praxis für die Praxis 56 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 Product properties and manufacturing process of lubricants Transmission oil as a functional element in a huge variety of different gear types has manifold requirements to meet. Complex processes in the lubricant and at the contact surfaces of the constructive friction partners must be considered. The underlying chemistry and physics of tribology can often not be described or calculated com- DOI 10.30419/ TuS-2019-0033 Process optimization and scale-up verification of the dispersion process for lubricant production using CFD simulation Daniel Kieser, Thomas Kroth, Emir Sirbubalo, Matthias Zemke, Marc Christmann, Peter Hoffmann, Johannes Ferner, Rebekka Drafz, Torben Fruth* Für eine dauerhaft hohe Produktqualität von Schmierstoffen ist u.a. das Herstellungsverfahren maßgeblich. Anhand einer Scale-Up-Verifikation wird der Einsatz einer CFD-Simulation zur Sicherstellung gleichbleibender Produktgüte für ein Dispergier-System vorgestellt. Dieser Beitrag zeigt eine neuartige Anwendung bewährter Vernetzungstechniken und numerischer Methoden zur Scale-Up Analyse eines Dispergierer- Behälter Systems. Hierbei wurde eine numerische Gesamtbetrachtung des kompletten Systems umgesetzt, welche die simultane Behandlung kleiner Skalen (Dispergierer) und großer Skalen (Behälter) kombiniert. Schlüsselwörter CFD Simulation, OpenFOAM, Scale-Up, Verifikation, Strömungsverhalten, Vernetzungsstrategie, Geschwindigkeitsgradienten, Herstellungsprozess, Schmierstoffe, Entschäumer For a permanently high product quality of lubricants, among other things, the manufacturing process is decisive. By means of a scale-up verification, the usage of a CFD simulation is presented with the goal to ensure consistent product quality for a disperser system. This contribution presents a novel application of established meshing techniques and numerical methods for scale-up analysis of a disperser-vessel system, combining simultaneous treatment of small disperser and large vessel length scales in a single simulation. Keywords CFD simulation, OpenFOAM, scale-up, verification, flow pattern, meshing strategy, velocity gradients, manufactoring process, lubricants, antifoam system Kurzfassung Abstract * Dr. Daniel Kieser FUCHS Schmierstoffe GmbH, 68169 Mannheim Marc Christmann, Technischer Betriebswirt Peter Hoffmann, Maschinenbautechniker Johannes Ferner, Dipl.-Chem. Dr. Torben Fruth Dr. Rebekka Drafz Thomas Kroth, M.Sc. TeSolva l Falk & Hattemer GbR, 55122 Mainz Dr. Emir Sirbubalo Matthias Zemke, cand. Phys. TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 56 Within the scope of lubricant development, a catalogue of requirements is created via a system-analytical view of the tribosystem. This captures the required rheology, load ratios, energy inputs, working temperatures, materials, wear risk, environmental media, and environmental requirements. This results in the basic structure of a formulation which typically contains the following components: base oils and additives for wear, oxidation and corrosion protection, friction value reducers, viscosity improvers and defoamers. From the requirements listed above the rheological and physico-chemical properties of the product from the composition of a green oil mixture based on solvent natural oils, hydrocrackates, polyalphaolefins, esters, polyol esters, complex esters, polyglycols, perfluoroethers and alkylates are derived. On the additive side, a component recipe is created from a large selection derived from the requirements. Depending on the application, typical values for a transmission oil are approx. 80 - 95 % base oil mixture and 5 - 20 % additives. These are developed using a multifunctional approach through appropriate laboratory and testing bay expertise. An important component of every transmission oil is the defoamer system. Its main task is to avoid foam on the oil surface. For this purpose, highly surface-active and deliberately oil-insoluble substances are used, which stick to the foam bubbles and cause them to burst in the shortest possible time (see Figure 1). Similarly, the defoamer droplets also settle on dispersed air bubbles with in the oil. This undesirable effect can lead to a poorer air release behavior and thus to a lower total density of the oil. This, in turn, can negatively impact the application in terms of cavitation tendency, reduced wear protection or increased oxidation. In principle, a lubricant is produced by mixing the base oils and additives in the correct proportions. Process parameters like temperature and mixing conditions must be observed carefully. Depending on the type of antifoam system used, it is advisable to disperse the antifoam droplets as finely as possible for optimum values in terms of foaming, air release and storage stability of the transmission oil. This is achieved by the usage of a highspeed dispersing system delivering the needed shear forces on the disperser. Scale-up of a production plant In the development phase, magnetic stirrers and handheld high-speed mixers are used in the laboratory to stir and disperse the defoamer. Aus der Praxis für die Praxis 57 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0033 Figure 1: Defoamer mode of action: (above) Foam on the surface, (below) Defoamer destabilizes and decomposes foam bubbles Figure 2: Process sketch of manufacturing unit TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 57 Due to the simulation results, the technical functionality of the larger system could be ensured in advance. The goals were defined as follows: The verification of the scale-up had to be done by comparing the results of a working small system vs. a planned new large system with the following parameters: • Flow pattern in the whole vessel • Pumping capacity and velocity gradients of the disperser Looking at these requirements, two major challenges became apparent which had to be considered and solved in the simulation strategy: 1. Differences in Scale The entire vessel has a diameter of 1600 mm, whereas the geometrical details of the disperser are in the range of only 1 mm, as can be seen in Figure 3. This is an important aspect regarding mesh generation, convergence and computation time, which must be considered during the modelling process. 2. Rotating components CFD simulations usually simulate the flowing medium, not the solid structures. In this case, suitable numerical formulation for rotating motion of disperser components must be selected, considering grid quality and computation time. The geometrical data, the process-related boundary conditions and the challenges described above, formed the basis for developing and implementing a suitable simulation strategy. Aus der Praxis für die Praxis 58 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 Until a formulation is ready for series production, different scale-up stages are usually passed through, from laboratory blends of different sizes to pilot plant blends (>200 - 800 kg) to production blends on a multi ton scale. The topic of defoamer dispersion described above is an important process variable. The transfer from the laboratory to the production process is classically scaled by the energy input of the disperser. In the manufacturing process sketch (see Figure 2), the important step is carried out in a 500 kg premix vessel and transferred to the 100 m 3 batch. According to growth of business we planned an upscaling with a batch size of 500 m 3 , the scaling factor results in a premix vessel of 2.5 t/ batch defoamer dispersion. Regarding the dimensioning of the disperser system for such a plant, an estimation for the extrapolated shear energy is conventionally performed using empirical equations. But the determination of further process-side important data, such as the homogeneity of the mixture and the required mixing time are currently only accessible by experiments. Due to technical advances, the usage of numerical simulation in many different fields of engineering is on the advance. Therefore, the aim was to determine whether such scale-up could be validated via a flow simulation. Support for Scale-Up through CFD simulation Support of the day-to-day work of engineers through computer-aided calculation techniques is more and more commonplace in the industrial environment, especially with today’s hardware and software capabilities. Numerical simulations enable the analysis of processes and products in a time-effective, cost-effective and hazardfree manner. Thereby the investigated system can be designed optimally, and the profitability margins can be increased significantly. To examine fluid mechanical problems, the Computational Fluid Dynamics (CFD) simulation is generally used. With CFD, the behavior of systems with liquid and gaseous media can be calculated and thus parameters, such as flow velocities, can be determined in a spatially resolved manner. This provides a better understanding of fluidic systems and can reduce and sometimes eliminate the need for costly and time-consuming experiments. Especially in the design of production facilities, such as the production of lubricants, the possibilities offered by CFD simulations can help to verify the functionality of new plants or to optimize existing plants. This article describes the scale-up verification of a disperser system by factor five using a CFD simulation. DOI 10.30419/ TuS-2019-0033 Figure 3: Completely meshed vessel with disperser in the centre TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 58 Definition and implementation of a suitable simulation strategy The quality of a numerical simulation depends essentially on the modelling and the associated simulation strategy. It is important to understand the real processes and to know what kind of simplifying assumptions can be made for the boundary conditions of the simulation model and where it is important to map the reality as accurately as possible. The calculation software uses model equations which in most cases only represent an approximation of the physical processes and thus cannot exactly reproduce the behavior. Nevertheless, these models can be selected and parameterized in a way that the obtained results provide statements of the required quality. In the case presented here, a literature research was carried out first and articles about the topic of simulation of disperser systems were analysed, such as the papers by Feldmann [1], Lindahl [2] or Derrik [3]. These references present important contributions to computational study of rotor-stator, high-speed mixers in general. They are mostly concerned with simulations of laboratory, small-scale devices and systems, for which experimental data is available in form of integral parameters (power and flow numbers) and velocity fields obtained from laser doppler anemometry (LDA) or particle image velocimetry (PIV) measurements. Unlike the studies reviewed in mentioned literature sources, this study presents an attempt at comparative simulations of laboratory and production scale facilities, selecting meshing strategies and numerical methods that proved their fidelity in validation studies of small-scale laboratory systems. Basic settings for the simulation The simulation presented here were performed using the open-source software OpenFOAM [4]. Being opensource, OpenFOAM allows implementation of custom numerical methods and simulation workflows tailored for specific applications, which makes it extremely flexible and versatile. As presented in the previous sections, lubricant mixture of base oil and additives is characterized by complex physical properties. In order to simplify the initial scaleup study of disperser-vessel system, in the simulations presented here, liquid is assumed to be homogeneous single-phase Newtonian fluid with physical properties (density and viscosity) of the mixture. For calculation of turbulence properties, the widely used k-epsilon turbulence model (Launder and Jones [5], Wilcox [6]) was used. It describes the evolution of the turbulent kinetic energy k and the isotropic dissipation rate ϵ with two partial differential equations. Standard wall functions [7] are used to compute turbulence quantities near solid walls. Solution for scale issue In order to achieve an efficient computation time and good convergence behavior, it is reasonable to create a mesh with as many hexahedral volume elements as possible (hex-dominant). However, continuous changes of element sizes in the mesh can only be implemented with tetrahedral elements, which should be avoided as far as possible. In the present case, scale disparity between the overall size of the vessel and small length scales dictated by disperser geometries requires careful selection of grid structure in different parts of the system. Small scales and high velocity gradients in the near field of the disperser require highly resolved computational mesh. Additionally, the periodic and regular geometry of the disperser components lends itself to structured meshing which should in principle enable accurate computation of flow and power numbers of the disperser. On the other hand, bulk flows in the vessel, comparatively large length scales involved, and irregular curved geometry of vessel walls, make it a good candidate for unstructured hex-dominant meshing strategy. After an analysis of various meshing approaches for different parts of the computational domain the following meshing strategy was selected: (1) disperser and its near field have been meshed using structured grid approach and (2) vessel geometry has been meshed using an automatic unstructured hex-dominant mesh generator. Structured disperser mesh is characterized by gradual refinement of cell sizes in wall-normal directions, uniform mesh spacing in wall-parallel directions, and gradual cell size increase as the distance from the disperser increases to mesh the meshing scale in the vessel region. Cell sizes in the vessel region have been volumetrically refined to match the sizes in the disperser region, and gradually increased with the distance from the disperser. The individual mesh regions in the area of the disperser are described in Figure 4. On the left side, a bridging re- Aus der Praxis für die Praxis 59 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0033 Figure 4: 3D View of mesh regions near by the disperser TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 59 This approach is advantageous in that it is possible to simulate the flow in a steady manner which makes it less computationally intensive. The disadvantage of the approach is that the relative position of the rotor and stator teeth is fixed (Figure 6) and therefore the unsteady pulsating effects in jets in stator teeth gaps cannot be resolved. On the other side of the spectrum lies the sliding mesh technique, in which the mesh for the rotating region is dynamically moved during the simulation. In principle, this approach offers better accuracy at the expense of increased computational intensity due to a high temporal resolution required in order to resolve the unsteady effects. The simulation approach selected in this study is to use the steady MRF approach for the relatively fast initialization of both gap flow fields in the disperser region and bulk flow fields in the vessel. These results are used as initial conditions for the subsequent unsteady simulation using the sliding mesh approach, in which the pump blades and the rotor teeth were turned. Due to the fine network, only very small-time increments could be applied. In total, about half a turn was simulated. The function Arbitrary Mesh Interface [8], which is available in OpenFOAM, was particularly used for the calculation of the moving parts. This function had been developed especially for the simulation of the sliding interfaces. Among other things, temporary overlaps of faces belonging to mesh elements moving against each other are considered in the equations and corrected by implicit coupling of the equation systems via matrix coefficients. This is much more stable and accurate than the consideration through boundary conditions with weighted averages. After the final development of the simulation model, the solution was calculated with the unsteady solver pimpleFoam. For the first 100 - 1000 iterations of the steady simulation, the rotation rate of the MRF zone was linearly increased to the specified rotation rate, within a Aus der Praxis für die Praxis 60 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 gion from the coarse mesh in the vessel towards the finer mesh at the disperser is indicated. This cylindrical area can also be seen in Figure 3, represented by the gray discs. The nearfield of the disperser is the area in which the socalled jets spread, caused by the flow rate of the disperser. Thus, this is an area that requires fine mesh resolution. The finest solution is needed directly at the disperser itself, in the gaps between the stator and rotor teeth. In this region, the narrow stator-rotor gap of 1 mm is divided radially into 10 elements and tangentially into 40 elements (on 5 mm stator, or 8 mm rotor). The gaps between the teeth in the peripheral direction are divided into 20 elements in each case, as shown in Figure 5. This meshing strategy has enabled simulation tractability in terms of computational resources, and, at the same time, very good mesh resolution and mesh regularity in the regions of high velocity gradients where highly accurate results are desired. The generation of the mesh was performed iteratively and after each modification test calculations were initiated to analyze computation time and convergence behavior. Also, for the combined simulation of the global flow behavior in the vessel and the finely resolved areas in the disperser, this procedure was the decisive factor. It was the most time-consuming step of the entire simulation project. Solution for rotating components Coupling of rotating and non-rotating regions in a single CFD simulation is possible at various levels of accuracy and complexity. On one side of the spectrum, there is a multiple reference frame (MRF) technique, in which both regions of the geometry are simulated on a static mesh, and where cells in the rotating region are supplied with Coriolis and centrifugal forces for a virtual handling of rotation effects. DOI 10.30419/ TuS-2019-0033 Figure 5: Top view of mesh regions stator-rotor-stator-nearfield TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 60 computation time of approximately 1.5 - 2 days by using a multicore high-performance computer system. After that, the unsteady simulation, which included the half rotation of the rotor, was carried out in a computation time of approximately 3 days. Verification of the Scale-Up of a disperser system The results of the simulation were analysed by visual representation as well as calculation of integral numerical parameters. For several interesting results and in order to gain an understanding of the large-scale flow fields, it is instructive to visually compare plots of flow fields of smalland large-scale disperser systems. Contour plots were compared on several horizontal and vertical cross section planes as well as streamlines on combined cross section planes (exemplified in Figure 7) and interpreted with regard to the respective flow patterns. All figures show a comparable flow behavior in both vessel sizes. The average velocities in the large vessel are slightly higher than those in the small vessel. Furthermore, the velocity gradients were plotted as a measure for the shear rates in horizontal contour plots in the area near the disperser, Figure 8. These figures also show a comparable pattern in the two vessel sizes. In both cases there is a local concentration of the gradient Aus der Praxis für die Praxis 61 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0033 Figure 6: Disperser as 3D CAD drawing (left), stator-rotor-stator horizontal cross section (right) Figure 7: Streamlines with contour plot of the velocity magnitude in a combined horizontal/ vertical cross section: Small vessel (left) / Large vessel (right) TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 61 Both results show, that the planned new large system has higher performance than the already working small system. It legitimizes the statement that the proposed system will work fine. In summary, challenges in form of scale differences and rotating components had to be overcome in this flow simulation and this was achieved by an advanced simulation strategy. Both, the visual and the numerical comparison, based on the simulation results, show that the larger disperser system is dimensioned sufficiently. Thus, the scale-up could be verified by means of a numerical CFD analysis, so that the new plant could be implemented in the planned manner. As described, the production of high-quality lubricants is extremely complex. The selection and composition of the individual components and the design of the manu- Aus der Praxis für die Praxis 62 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 at the stator edge, where pressure of the fluid is increased through the rotor movement. Other than the visual comparison, two numerical key figures were determined, based on the simulation results, which verify the scale-up. The first value is the specific flow rate of the dispersers based on the total volume. For this purpose, the volume flow was calculated via defined surfaces in the disperser near field (see Figure 9) and divided by the respective vessel volume. The resulting numbers show that the specific pumping capacity of the disperser in the large vessel with 2.68 (m 3 / min)/ m 3 is twice as large as in the small vessel with 1.33 (m 3 / min)/ m 3 . The second measure is the maximum velocity gradient grad(U) at the stator-rotor slot. Also, for this key figure, the value for the large tank (97000 1/ s) is significantly greater than that for the small tank (67000 1/ s). DOI 10.30419/ TuS-2019-0033 Figure 8: High resolution plots offer detailed view of disperser teeth Figure 9: Calculation of the total flow from the velocity fields TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 62 facturing process must be strictly monitored and meet high standards. In this article should be shown, that the numerical simulation is a useful tool for the verification of such requirements. For the described plant scale-up it was possible to ensure the functionality of the disperser system without looking at experimental lab tests. Literature [1] O. Feldmann, „Dispergieren in begasten Rührkesseln,“ Technische Universität München, München, 2003. [2] A. Lindahl, „Fluid Dynamics of Rotor Stator Mixers,“ Lulea University of Technology, Lulea, 2013. [3] D. Ko, „Computational Fluid Dynamics SImulations of an In-Line Slot and Tooth Rotor-Stator Mixer,“ University of Maryland, Maryland, 2013. [4] H. Weller, C. Greenshields und C. de Rouvray, „OpenFO- AM Official,“ The OpenFOAM Foundation, [Online]. Available: https: / / openfoam.org/ . [5] B. E. Launder und W. P. Jones, „The Prediction of Laminarization with a Two-Equation Model of Turbulence,“ International Journal of Heat and Mass Transfer, Nr. 15, pp. 301-314, 1972. [6] D. C. Wilcox, Turbulence Modeling for CFD, Anaheim: DCW Industries, 1998. [7] B. E. Launder und D. B. Spalding, „The Numerical Computation of Turbulent Flows,“ Computer Methods in Applied Mechanics and Engineering, Nr. 3, pp. 269-289, 1974. [8] C. Greenshields, „OpenFOAM 2.1.0: Arbitrary Mesh Interface,“ The OpenFOAM Foundation, 19 th December 2011. [Online]. Available: https: / / openfoam.org/ release/ 2-1-0/ ami/ . Aus der Praxis für die Praxis 63 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0033 TuS_6_2019.qxp_T+S_2018 28.11.19 14: 54 Seite 63