Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Lagrangian approach”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes

Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the Eulerian and Lagrangian modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.

Adeniji-Fashola, A.↗
NASA NTRS1993

Supersonic gasdispersional jets and jet noise

This paper examines the potential for controlling jet noise radiation using methods developed for modifying jet infra-red thermal radiation. The control of jet noise may be possible by properly adding different solid and liquid particles into the jet flow and by using special nozzle shapes to change the jet exhaust flow structure. The numerical methods used to achieve these objectives are outlined in this paper. A combined Lagrangian-Eulerian approach is used to numerically simulate a Jet flow with particle addition. The unsteady behavior of jet impingement is examined. The techniques for grid and boundary condition definition are discussed as related to the accuracy of the calculations. Preliminary comparisons to experimental data are presented.

Gilinsky, M. M.↗
NASA NTRS2012

Determining Wheel-Soil Interaction Loads Using a Meshfree Finite Element Approach Assisting Future Missions with Rover Wheel Design

A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.

Contreras, Michael T.↗
NASA NTRSDate not supplied

A Comparison of Trajectory Refinement Schemes for GlennICE

A requirement of computational ice accretion solvers is the ability to predict the water impingement on a geometry of interest. This portion of the tool is typically implemented in an Eulerian or Lagrangian methodology with both approaches having various pros and cons. GlennICE utilizes a Lagrangian framework. For this approach to be tractable in an engineering sense, the trajectories simulated must be chosen in a more intelligent fashion than naïve uniform refinement. This paper investigates a new refinement methodology implemented in GlennICE and compares it to the previous implementation.

Computational↗
NASA NTRS1993

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Felici, Helene M.↗
DOE OSTI2021

Realism of Lagrangian Large Eddy Simulations Driven by Reanalysis Meteorology: Tracking a Pocket of Open Cells Under a Biomass Burning Aerosol Layer

An approach to drive Lagrangian large eddy simulation (LES) of boundary layer clouds with reanalysis data is presented and evaluated using satellite (Spinning Enhanced Visible and Infrared Imager, SEVIRI) and aircraft (Cloud-Aerosol-Radiation Interactions and Forcing, CLARIFY) measurements. The simulations follow trajectories of the boundary layer flow. They track the formation and evolution of a pocket of open cells (POC) underneath a biomass burning aerosol layer in the free troposphere. The simulations reproduce the evolution of observed stratocumulus cloud morphology, cloud optical depth, and cloud drop effective radius, and capture the timing of the cloud state transition from closed to open cells seen in the satellite imagery on the three considered trajectories. They reproduce a biomass burning aerosol layer identified by the in-situ aircraft measurements above the inversion of the POC. Entrainment of aerosol from the biomass burning layer into the POC is limited to the extent of having no impact on cloud- or boundary layer properties, in agreement with the CLARIFY observations. The two-moment bin microphysics scheme used in the simulations reproduces the in-situ cloud microphysical properties reasonably well. A two-moment bulk microphysics scheme reproduces the satellite observations in the non-precipitating closed-cell state, but overestimates liquid water path and cloud optical depth in the precipitating open-cell state due to insufficient surface precipitation. A boundary layer cold and dry bias occurring in LES can be counteracted by reducing the grid aspect ratio and by tightening the large scale wind speed nudging towards the surface.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Abstract Quantum annealing is a promising method for solving hard optimization problems by transforming them into quadratic unconstrained binary optimization (QUBO) problems. However, when constraints are involved, particularly multiple inequality constraints, incorporating them into the objective function poses challenges. In this paper, the authors present two novel approaches for solving problems with multiple inequality constraints on a quantum annealer and apply them to the set cover problem (SCP). The first approach uses the augmented Lagrangian method to represent the constraints, while the second approach employs a higher‐order binary optimization (HUBO) formulation. The experiments show that both approaches outperform the standard approach for solving the SCP on the D‐Wave Advantage quantum annealer. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but its scalability in terms of embeddability in the quantum chip is worse. The results demonstrate that the proposed augmented Lagrangian and HUBO methods can successfully implement a large number of inequality constraints, making them applicable to a broad range of constrained problems beyond the SCP.

Djidjev, Hristo N.↗
DOE OSTI2021

Scalable In Situ Computation of Lagrangian Representations via Local Flow Maps

In situ computation of Lagrangian flow maps to enable post hoc time-varying vector field analysis has recently become an active area of research. However, the current literature is largely limited to theoretical settings and lacks a solution to address scalability of the technique in distributed memory. To improve scalability, we propose and evaluate the benefits and limitations of a simple, yet novel, performance optimization. Our proposed optimization is a communication-free model resulting in local Lagrangian flow maps, requiring no message passing or synchronization between processes, intrinsically improving scalability, and thereby reducing overall execution time and alleviating the encumbrance placed on simulation codes from communication overheads. To evaluate our approach, we computed Lagrangian flow maps for four time-varying simulation vector fields and investigated how execution time and reconstruction accuracy are impacted by the number of GPUs per compute node, the total number of compute nodes, particles per rank, and storage intervals. Our study consisted of experiments computing Lagrangian flow maps with up to 67M particle trajectories over 500 cycles and used as many as 2048 GPUs across 512 compute nodes. In all, our study contributes an evaluation of a communication-free model as well as a scalability study of computing distributed Lagrangian flow maps at scale using in situ infrastructure on a modern supercomputer.

Sane, Sudhanshu↗
DOE OSTI2024

Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems

Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.

Cheng, Tianle↗
NASA NTRS1972

Stability of orthotropic stiffened composite plates.

It is pointed out that the buckling problem of a plate with restrictions resulting from boundary conditions is suited for an application of Lagrangian multipliers. An approach used by Budiansky and Hu (1946) is extended to the study of orthotropic stiffened plates. The variations of the total energy with respect to the three deformation components are considered. The equilibrium equations and the boundary conditions are obtained. It is shown that the deflection functions must satisfy the equilibrium equations. The Lagrangian multipliers are then used to solve stability problems on the basis of the total energy involved, the equilibrium equations, and the boundary conditions. The theoretical analysis is supplemented by an experimental investigation.

Chiu, K. D.↗
DOE OSTI2025

3D mesh regularization within an ALE code using a weighted line sweeping method

The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.

42 ENGINEERING↗
DOE OSTI2020

An augmented Lagrangian filter method

Here, we introduce a filter mechanism to enforce convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows for equality-constrained quadratic programming steps to accelerate local convergence. We also include a feasibility restoration phase that allows fast detection of infeasible problems. We provide a convergence proof that shows that our algorithm converges to first-order stationary points. We provide preliminary numerical results that demonstrate the effectiveness of our proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Nonlinear simulation of a flexible aircraft in maneuvering flight

A mathematical model integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics is examined; the equations of motion for an elastic aircraft in accelerated flight are developed using Lagrangian mechanics. This approach is used to construct a simulation model of an F/A-18 (configured with tip missiles) which includes angular/elastic inertial coupling (IC). In general, the elastic modes significantly affected by IC were aerodynamically decoupled from the rest of the model. The affected modes were those which induced changes in total aircraft mass distribution. The elastic effect is noticeable if deformation-induced mass distribution changes are significant with respect to modal mass and modal frequencies. A modal parameter is presented which characterizes the level of IC between elastic momentum and rigid-body angular momentum.

Buttrill, Carey S.↗
NASA NTRS2011

CFD Model of Water Droplet Transport for ISS Hygiene Activity

The goal of the study is to assess the impacts of free water propagation in the Waste and Hygiene Compartment (WHC). Free water can be generated inside the WHC in small quantities due to crew hygiene activity. To mitigate potential impact of free water in Node 3 cabin the WHC doorway is enclosed by a waterproof bump-out, Kabin, with openings at the top and bottom. At the overhead side of the rack, there is a screen that prevents large drops of water from exiting. However, as the avionics fan in the WHC causes airflow toward the deck side of the rack, small quantities of free water may exit at the bottom of the Kabin. A Computational Fluid Dynamics (CFD) analysis of Node 3 cabin airflow made possible to identify the paths of water transport. The Node 3 airflow was computed for several ventilation scenarios. To simulate the droplet transport the Lagrangian discrete phase approach was used. Various initial droplet distributions were considered in the study. The droplet diameter was varied in the range of 2-20 mm. The results of the computations showed that most of the drops fall to the rack surface not far from the WHC curtain. The probability of the droplet transport to the adjacent rack surface with electronic equipment was predicted.

Son, Chang H.↗
NASA NTRS2013

Combined Experimental and Numerical Simulations of Thermal Barrier Coated Turbine Blades Erosion

A combined experimental and computational study was conducted to investigate the erosion of thermal barrier coated (TBC) blade surfaces by alumina particles ingestion in a single stage turbine. In the experimental investigation, tests of particle surface interactions were performed in specially designed tunnels to determine the erosion rates and particle restitution characteristics under different impact conditions. The experimental results show that the erosion rates increase with increased impingement angle, impact velocity and temperature. In the computational simulations, an Euler-Lagrangian two stage approach is used in obtaining numerical solutions to the three-dimensional compressible Reynolds Averaged Navier-Stokes equations and the particles equations of motion in each blade passage reference frame. User defined functions (UDF) were developed to represent experimentally-based correlations for particle surface interaction models which were employed in the three-dimensional particle trajectory simulations to determine the particle rebound characteristics after each surface impact. The experimentally based erosion UDF model was used to predict the TBC erosion rates on the turbine blade surfaces based on the computed statistical data of the particles impact locations, velocities and angles relative to the blade surface. Computational results are presented for the predicted TBC blade erosion in a single stage commercial APU turbine, for a NASA designed automotive turbine, and for the NASA turbine scaled for modern rotorcraft operating conditions. The erosion patterns in the turbines are discussed for uniform particle ingestion and for particle ingestion concentrated in the inner and outer 5 percent of the stator blade span representing the flow cooling the combustor liner.

Hamed, Awate↗
NASA NTRS2013

CFD Lagrangian Modeling of Water Droplet Transport for ISS Hygiene Activity Application

The goal of this study was to assess the impacts of free water propagation in the Waste and Hygiene Compartment (WHC) installed in Node 3. Free water can be generated inside the WHC in small quantities due to crew hygiene activity. To mitigate potential impact of free water in Node 3 cabin the WHC doorway is enclosed by a waterproof bump-out, Kabin, with openings at the top and bottom. At the overhead side of the rack, there is a screen that prevents large drops of water from exiting. However, as the avionics fan in the WHC causes airflow toward the deck side of the rack, small quantities of free water may exit at the bottom of the Kabin. A Computational Fluid Dynamics (CFD) analysis of Node 3 cabin airflow enable identifying the paths of water transport. To simulate the droplet transport the Lagrangian discrete phase approach was used. Various initial droplet distributions were considered in the study. The droplet diameter was varied in the range of 5-20 mm. The results of the computations showed that most of the drops fall to the rack surface not far from the WHC curtain.

Son, Chang H.↗
NASA NTRS2014

One Dimensional Analysis Model of a Condensing Spray Chamber Including Rocket Exhaust Using SINDA/FLUINT and CEA

Modeling droplet condensation via CFD codes can be very tedious, time consuming, and inaccurate. CFD codes may be tedious and time consuming in terms of using Lagrangian particle tracking approaches or particle sizing bins. Also since many codes ignore conduction through the droplet and or the degradating effect of heat and mass transfer if noncondensible species are present, the solutions may be inaccurate. The modeling of a condensing spray chamber where the significant size of the water droplets and the time and distance these droplets take to fall, can make the effect of droplet conduction a physical factor that needs to be considered in the model. Furthermore the presence of even a relatively small amount of noncondensible has been shown to reduce the amount of condensation. It is desirable then to create a modeling tool that addresses these issues. The path taken to create such a tool is illustrated. The application of this tool and subsequent results are based on the spray chamber in the Spacecraft Propulsion Research Facility (B2) located at NASA's Plum Brook Station that tested an RL-10 engine. The platform upon which the condensation physics is modeled is SINDAFLUINT. The use of SINDAFLUINT enables the ability to model various aspects of the entire testing facility, including the rocket exhaust duct flow and heat transfer to the exhaust duct wall. The ejector pumping system of the spray chamber is also easily implemented via SINDAFLUINT. The goal is to create a transient one dimensional flow and heat transfer model beginning at the rocket, continuing through the condensing spray chamber, and finally ending with the ejector pumping system. However the model of the condensing spray chamber may be run independently of the rocket and ejector systems detail, with only appropriate mass flow boundary conditions placed at the entrance and exit of the condensing spray chamber model. The model of the condensing spray chamber takes into account droplet conduction as well as the degrading effect of mass and heat transfer due to the presence of noncondensibles. The one dimension model of the condensing spray chamber makes no presupposition on the pressure profile within the chamber, allowing the implemented droplet physics of heat and mass transfer coupled to the SINDAFLUINT solver to determine a transient pressure profile of the condensing spray chamber. Model results compare well to the RL-10 engine pressure test data.

Chemical Equilibrium↗