Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case
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François Vilar↗
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Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case
Explore the source record for details and available documents.
François Vilar↗
Multi-material swept face remapping on polyhedral meshes
Remapping is a conservative interpolation of a discretized intensive quantity between two meshes. In this article, we propose a novel multi-material flux remapping method that avoids the geometric computation of mesh-mesh intersections needed for an accurate intersection based remap. The flux remap is applicable to scalar quantities such as material density describing the multi-material flow between meshes with the same connectivity but small mesh displacements. Herein, the method is described for two- and three-dimensional polygonal/polyhedral meshes as it is implemented in Portage. Another open source library, Tangram, is used to calculate material interfaces in cells containing more than one material. Performance and accuracy of the flux remap are discussed with respect to Arbitrary Lagrangian-Eulerian simulations and compared to an accurate intersection based remap. In particular, cyclic remapping shows that the accuracy of the flux remap is limited to first order on material boundaries while maintaining second order accuracy in pure material regions.
97 MATHEMATICS AND COMPUTING↗
Next Generation Co-Molded One-Piece Automotive Parts
The purpose of this project was to determine the feasibility of co-molding Class A Sheet Molding Compound (SMC), structural SMC, and continuous fiber prepreg materials to produce a single piece co-molded automotive part, such as a hood. The combination of the three molding materials and the incorporation of selective design features (ribs, flanges, corrugations) was expected to eliminate the need for inner reinforcement panels, significantly reducing tooling costs and simplifying the manufacturing process. A multi-material solution would also result in significant weight savings. The scope of this project included the material characterization of the three materials, development of cure and flow simulation models, and validation of the models against parts molded with different combinations of the materials on an 11”x11” plaque tool with rib features. The intent of this project was to apply the learnings obtained from co-molding a part with simplified geometry to a Phase 2 project that would produce a single piece hood, co-molded with the same materials. Resins from INEOS Composites were provided to IDI to produce SMC and continuous fiber prepregs. Purdue University and INEOS Composites characterized the rheological and curing behavior of the different materials as well as the mechanical properties of the co-molded parts. This data was used by Purdue University to create simulation models. Models were created to predict both flow patterns and predict mechanical properties of different laminate constructions in and around the ribs. Michigan State University - Corktown validated Purdue’s models by co-molding the three materials in different combinations on a tool containing rib features provided by Century Tool. The co-molded parts were evaluated against the simulation models by Purdue, Corktown and INEOS. The project team demonstrated the following: • The ability to obtain a cohesive co-molded structure made up of Class A SMC, Structural SMC, and continuous fiber prepreg. • The ability to obtain a co-molded part with a Class A surface • Modeling of flow and fiber orientation • Modeling to predict mechanical properties of multi-material co-molded structures The predicted flow behavior and fiber orientation from simulations were then compared with the molded samples. Exact local orientation state was difficult to compare between microscopy and flow simulation, but captured general trends. Multi-material flow behavior was generally modeled well with SMC materials, but the introduction of woven material sheets requires further model development. Purdue compared the predicted versus actual mechanical properties, and INEOS Composites evaluated the surface appearance of unpainted and painted co-molded parts. The models developed by Purdue demonstrated that the mechanical properties can be predicted for parts with varying material configurations. The resulting models can be applied to future co-molded part design, tooling design, and molding conditions.
36 MATERIALS SCIENCE↗
Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods
A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.
97 MATHEMATICS AND COMPUTING↗
An extension of the localized artificial diffusivity method for immiscible and high density ratio flows
The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.
Artificial diffusivity↗
A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part II: linesweep ALE rezoning for nonconformal block-structured AMR meshes
The simulation of flows presenting contact discontinuities, vorticity, and large variations in spatial scales can be performed in a framework coupling Arbitrary Lagrangian Eulerian (ALE) algorithms and Adaptive Mesh Refinement (AMR). This coupling requires adaptation of ALE rezoning techniques to meshes containing nonconformal nodes arising from both the AMR topology and the junction of mesh blocks. Here, in this paper, we present an ALE rezoning strategy that is compatible with such meshes, and that can also act as a disentangling algorithm. Emphasis is put on an algorithm that respects intrinsic Lagrangian mesh properties in order to preserve accuracy around discontinuities. To that end, we adapt the weighted linesweep algorithm to nonconformal block-structured AMR meshes. Then, we present control parameters introduced in the method for it to be applicable in practical situations. Notably, the method is coupled to a specific metric optimization in order to palliate some shortcomings of the linesweep method. Finally, numerical test cases are presented that feature the capabilities of the ALE-AMR algorithm for flows that present discontinuities, vorticity, and a variety of scales. Notably, we show that our ALE-AMR algorithm gives results at least similar to Euler-AMR, but provides better accuracy in cases where discontinuities are involved, thanks to a method that respects the Lagrangian features of the mesh. Additionally, it enables Euler-AMR-like computations on domains with temporally varying domain boundaries.
Adaptive mesh refinement↗
Fluid dynamic and thermal performance of a slotted cylinder at low Reynolds number
The fluid dynamic and thermal performance of a circular cylinder with a slot parallel to the flow is numerically investigated. The study utilized the semi-implicit finite volume multi-material algorithm MPM-ICE, a component of the Uintah framework. The normalized slot width s/D ranges from 0.1 - 0.3, introducing an additional heat transfer surface area between ~ 10 and ~ 50%, and a mass reduction between ~ 13 and ~ 38% in the cylinder. We assumed two-dimensional incompressible flow and simulated a Reynolds number Re D between 100 and 1000. The slotted cylinders are found to have a total drag force reduction up to ~ 45%, compared to a solid cylinder despite the additional viscous drag force in the slot. Convection heat transfer is enhanced up to ~ 70%. Further, the slotted cylinder performance index, defined as the ratio of the heat rate to the drag force, increases up to maximum of ~ 3, indicating better overall thermal fluid performance. An entropy analysis showed the best performance index occurs at the highest Re D . Correlations for drag coefficient and Nusselt number are proposed along with an entropy optimization method.
42 ENGINEERING↗
Thermal Analysis of Magnetically-Coupled Pump for Cryogenic Applications
Magnetically-coupled pump is under evaluation at Kennedy Space Center for possible cryogenic applications. A major concern is the impact of low temperature fluid flows on the pump performance. As a first step toward addressing this and related issues, a computational fluid dynamics and heat transfer tool has been adopted in a pump geometry. The computational tool includes (i) a commercial grid generator to handle multiple grid blocks and complicated geometric definitions, and (ii) an in-house computational fluid dynamics and heat transfer software developed in the Principal Investigator's group at the University of Florida. Both pure-conduction and combined convection-conduction computations have been conducted. A pure-conduction analysis gives insufficient information about the overall thermal distribution. Combined convection-conduction analysis indicates the significant influence of the coolant over the entire flow path. Since 2-D simulation is of limited help, future work on full 3-D modeling of the pump using multi-materials is needed. A comprehensive and accurate model can be developed to take into account the effect of multi-phase flow in the cooling flow loop, and the magnetic interactions.
Senocak, Inanc↗
A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows
The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.
Discontinuous Galekin↗
A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part I: Lagrangian and indirect Euler AMR algorithms
Many applications of physics and engineering involve wide ranges of time and spatial scales. The numerical simulation of localized small scales such as shock waves and material interfaces requires a large number of computational cells in these regions. For these applications, Lagrangian and Arbitrary-Lagrangian-Eulerian (ALE) related methods are engaging since the moving mesh feature naturally brings mesh cells on shock discontinuities and material interfaces are carefully captured. In addition, Adaptive-Mesh-Refinement (AMR) strategies aim to optimize computational resources by concentrating finer mesh cells only in areas of interest while using coarser cells elsewhere. A key but challenging AMR requirement consists in efficiently distributing the computational effort to achieve high accuracy without the prohibitive computational costs associated with uniformly fine grids. Here, in this document, the coupling of the p4est AMR library with a cell-centered Lagrangian scheme is presented with the goal to perform reliable 3D Lagrangian-AMR and indirect Euler-AMR multi-material simulations. In particular, it is shown that starting from a 3D indirect ALE code, the memory management and load balancing requirements can be delegated to an external library (here the p4est library) to unlock ALE-AMR capabilities. First, we present a strategy to transcribe the octant-based connectivity of the 3D AMR framework with that of an unstructured mesh of polygonal cells used in Lagrangian hydrodynamics. Then, we show how refinement and coarsening operations must be adapted to the particular Lagrangian framework to ensure the conservation of volume during those steps. Finally, several numerical test cases are presented that demonstrate the capabilities of the Lagrangian-AMR and indirect Euler-AMR algorithms.
3D cell-centered Lagrangian numerical scheme↗
Hierarchical Composites Patterned via 3D Printed Cellular Fluidics
Additive manufacturing of freeform structures containing multiple materials with deterministic spatial arrangement and interactions remains a challenge for most 3D printing processes, due to complex fabrication tool requirements and limitations in printability of some material classes. Here, in this paper, a versatile method is reported to produce architected composites using the concept of cellular fluidics, in which lattices of unit cells are used as templating scaffolds to guide flowable infill materials in a programmed spatial pattern, upon which they are cured in place to produce a deterministically ordered multimaterial solid. The lattice design relies on the unit cell size, type, strut diameter, surface wetting, and distribution of cellular structures to control liquid flow and retention. Individual unit cells are tuned to achieve reliable infilling and combined into higher-order architectures to achieve multiscale composite materials with disparate mechanical properties, including those considered non-printable. Lattice design considerations for leveraging capillary phenomena and demonstrate several methods of patterning polymers in 3D-printed cellular fluidic structures are presented. The concept of tuning the compressive response of an architected composite using a flexible-elastomer as the lattice and a stiff-epoxy as the infill material is illustrated.
36 MATERIALS SCIENCE↗
Laser powder bed fusion of Inconel 718 on 316 stainless steel
The joining of Inconel 718 and 316 stainless steel has notable industrial importance. However, traditional arc-welding has many issues. In particular, the formation of the detrimental Nb-rich Laves phase in the heat affected zone can promote crack initiation and propagation, which leads to poor mechanical properties. The small heat input and the rapid solidification of laser powder bed fusion (PBF) has the potential to suppress this problem. Despite the infancy of the multi-material PBF, it is of interest to investigate the relationship among the process parameter, the microstructure at the materials joining point, and the mechanical performance. In this study, we used high-speed x-ray imaging to in-situ monitor the printing of Inconel 718 tracks on a 316H SS substrate via laser powder bed fusion, followed by post-build characterization and testing with SEM, XRD and nanoindentation. We observed that a higher linear energy density resulted in a more diffused interface and a smaller compositional gradient, but as a trade-off, generated more keyhole pores and thermal cracks. Furthermore, we also showed that the built layer exhibited chemical inhomogeneity at two length scales: a tens-of-mu m-scale compositional vortex due to the melt flow, and a sub-mu m-scale Nb-rich dendritic structure due to the non-equilibrium solidification that led to the formation of the Laves phase. It was inferred that the chemical inhomogeneity may benefit the mechanical properties at the interface by providing more interlocking between the two materials and also by limiting the effect of the brittle Laves phase to potentially short range.
36 MATERIALS SCIENCE↗
Electrostatic powder spreading for metal powder bed fusion applications
Typical powder bed fusion processes spread each layer of powder by pushing it across the build area with a spreader bar or roller. While simple, these methods require good flowing powder and do not have the ability to place more than one powder type per layer. This naturally limits the ability to incorporate more than one material onto each powder layer in powder bed additive manufacturing processes. Here we demonstrate electrostatic powder spreading, a method to deposit a powder layer without mechanical contact with the previous layers. Electrostatic powder spreading (ESPS) uses an electric field formed between a powder container and a counter electrode to move powder particles from the container to the powder bed. We show that the rate at which powder is deposited can be controlled by adjusting the strength of the electric field. Correspondingly, the deposited layer thickness is controlled by the strength of the electric field and the recoating speed. To demonstrate the feasibility of ESPS for laser powder bed fusion powder spreading, nearly fully dense (> 99.8%) coupons were built in a commercial L-PBF machine using the ESPS setup. Finally, we achieve 2D patterning of a single layer by using an array of electrodes and switching the applied electric field on and off. ESPS represents a method to produce an arbitrary patterned multi-material powder bed without complicated powder removal steps and easy implementation into existing L-PBF machines. Furthermore, ESPS presents an opportunity to build parts with 3D gradients in material properties.
36 MATERIALS SCIENCE↗
Process parameter translation strategies for variable directed energy deposition spot size using 316L, copper, and Inconel 625
Directed energy deposition (DED) is a form of additive manufacturing available across a variety of laser spot diameter values, often referred to as spot sizes. However, there is no method to easily transfer process parameters across discrete spot sizes, leading to DED process parameters that are equipment specific and not widely applicable. In this study, a strategy is proposed and investigated for five spot sizes that keep the areal energy density constant while varying power, feed rate, and powder flow during the deposition of 316L stainless steel. An assessment of trends in hardness and microstructure is possible due to the novel production of components of a single material across several spot sizes using a single nozzle on a single DED system. The proposed strategy was used to nullify the hardness drop during functional grading of Inconel 625 and pure copper, enabling fabrication of multi-material sample that does not compromise desirable properties. This application shows the value in establishing more efficient process parameter development and understanding spot size influences on geometric and material property flexibility, to enable a more diverse powder-based DED design space and to increase the industry adoption of DED systems.
316L↗
Systematic analysis of melt pool dynamics in laser processing of mixed powder feedstocks
Functionally graded materials (FGMs) fabricated via additive manufacturing of blended powders offer the potential to spatially tailor properties for new technologies, such as fusion first-wall systems, turbine blades, and spacecraft. However, processing these materials is difficult due to the multiplicity of processing parameters to optimize, all of which must be changed as substrate material, powder feedstock compositions, and melt pool dynamics evolve. Here, this work systematically evaluates the qualitative and quantitative effects of these variables on the melt pool size, shape, composition, and particle distribution in an exemplar Ti-Ta system, and connects the experimental results to Marangoni flow behavior and phenomena observed in other systems. Increasing laser power linearly increases melt pool size and layer thickness, driving engineering considerations such as part/geometrical tolerances. Decreasing laser velocity changes the melt pool shape from lenticular to convex and reduces chemical homogeneity due to extreme thermal and compositional gradients between the melt pool center and boundaries. Thermophysical property differences between the powder feedstock and substrate material, as well as the directionality of the gradient, affect dilution and melt pool dynamics, which in turn affect the melt pool boundary characteristics, shape, and uniformity. Mixed powder feedstocks of intermediate compositions do not behave according to linear interpolations between single-material endpoints, instead building taller and wider melt pools. As such, it is recommended to quantify process maps for at least one intermediate composition in the FGM or multi-material system of interest to ensure optimized processing parameters, predictable melt pool sizes and shapes, and compositional and spatial precision.
Dissimilar↗
Modeling atomically mixed graded density impactors
Graded density impactors (GDIs) are multi-material composite impactors used in gas gun experiments to tailor the drive conditions imparted to a sample test material. Previous graded density impactors generally rely on thin, but discrete, layers of different materials. The thinner and the greater number of layers will result in smoother compression. Taken to the limit of very thin layers would be pure material 1 at one surface, such as the front surface of an impactor, smoothly transitioning at the atomic scale to pure material 2 on the back surface. Such an impactor can initially shock, then smoothly compresses a material during a dynamic experiment. This type of experiment can serve to explore a larger region of thermodynamic space than a single or even multi-shock experiments. An overview of how graded density impactors are made is reviewed and sample results are given. Additionally, a strategy for modeling these kinds of impactors is presented. The length scales of constituent mixing are given from the experimental build through electrochemical-deposition. Equation of state models for pure constituents and their subsequent mixtures are presented. It is demonstrated that the time scales for pressure and temperature equilibration, for atomically mixed GDIs, are short enough to be a justifiable closure for the resulting multiphase flow. Furthermore, we present simulation results of dynamic shock followed by a ramp compression, utilizing a silver/gold graded density impactor, onto a tantalum sample.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
REYNO: A Reactive Hydrodynamics Modeling Suite
REYNO is a Python library that is primarily designed as a platform for the agile development and testing of novel reactive flow models. Equations of state and multi-step rate laws can be implemented using the provided class hierarchy with different thermodynamic closure conditions. The library includes a one-dimensional Lagrangian hydrodynamic solver to simulate multi-material reactive or inert problems in planar, cylindrical, or spherical coordinates. Custom time-dependent boundary conditions are also available for problems such as ramp compression. This document describes the different numerical methods and algorithms that are included in REYNO.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗