Watch Your Adjoints! Lack of Mesh Convergence in Inviscid Adjoint Solutions

AIAA Journal ◽  
2019 ◽  
Vol 57 (9) ◽  
pp. 3991-4006 ◽  
Author(s):  
Carlos Lozano
Keyword(s):  
Mesh Convergence ◽  
Adjoint Solutions

Effect of mesh on CFD aerodynamic performances of a container ship

2020 ◽  
Vol 20 (3) ◽  
pp. 343-353
Author(s):  
Ngo Van He ◽  
Le Thi Thai
Keyword(s):  
Water Surface ◽  
Reference Model ◽  
Full Scale ◽  
Scale Model ◽  
Container Ship ◽  
Ansys Fluent ◽  
Remarkable Effect ◽  
Aerodynamic Performances ◽  
Mesh Convergence

In this paper, a commercial CFD code, ANSYS-Fluent has been used to investigate the effect of mesh number generated in the computed domain on the CFD aerodynamic performances of a container ship. A full-scale model of the 1200TEU container ship has been chosen as a reference model in the computation. Five different mesh numbers for the same dimension domain have been used and the CFD aerodynamic performances of the above water surface hull of the ship have been shown. The obtained CFD results show a remarkable effect of mesh number on aerodynamic performances of the ship and the mesh convergence has been found. The study is an evidence to prove that the mesh number has affected the CFD results in general and the accuracy of the CFD aerodynamic performances in particular.

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

scholarly journals Numerical Approximation of a Compressible Multiphase System

2014 ◽  
Vol 15 (5) ◽  
pp. 1237-1265 ◽  
Author(s):  
Remi Abgrall ◽  
Harish Kumar
Keyword(s):  
Dual Problem ◽  
Conservative System ◽  
Model Description ◽  
Multiphase System ◽  
Discontinuous Solutions ◽  
Glimm Scheme ◽  
Conservation Principles ◽  
Difficult Challenge ◽  
Limit Solutions ◽  
Mesh Convergence

AbstractThe numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the “dual” problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme.

scholarly journals EXPERIMENTAL AND FINITE ELEMENT ANALYSIS OF NONAXISYMMETRIC STRETCH FLANGING PROCESS USING AA 5052

2021 ◽  
Author(s):  
Sachin Kumar Nikam ◽  
◽  
Sandeep Jaiswal ◽  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Sheet Metal ◽  
Element Analysis ◽  
Maximum Percentage ◽  
Element Simulation ◽  
Stretch Flanging ◽  
Explicit Dynamic ◽  
Mesh Convergence

This paper deals with experimental and finite element analysis of the stretch flanging process using AA- 5052 sheets of 0.5 mm thick. A parametrical study has been done through finite element simulation to inspect the influence of procedural parametrical properties on maximum thinning (%) within the stretch flanging process. The influence of preliminary flange length of sheet metal blank, punch die clearance, and width was examined on the maximum thinning (%). An explicit dynamic finite element method was utilized using the finite element commercial package ABAQUS. Strain measurement was done after conducting stretch flanging tests. A Mesh convergence examination was carried out to ascertain the maximum percentage accuracy in FEM model. It is found through finite element simulation that the width of sheet metal blanks has a greater impact on the maximum percentage of thinning as compared to preliminary flange length, and clearance of the punch dies.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

Numerical investigations of 2-D planar magnetic nozzle effects on pulsed plasma plumes

2021 ◽  
pp. 1-20
Author(s):  
J. D. Burch ◽  
D. Han ◽  
S. N. Averkin
Keyword(s):  
Plasma Plume ◽  
Three Dimensional ◽  
Pulsed Plasma ◽  
Coil Current ◽  
Numerical Investigations ◽  
Magnetic Nozzle ◽  
Plasma Plumes ◽  
Discharge Parameters ◽  
Convergence Study ◽  
Mesh Convergence

Abstract This paper presents a study of a novel type of magnetic nozzle that allows for three-dimensional (3-D) steering of a plasma plume. Numerical simulations were performed using Tech-X’s USim® software to quantify the nozzle’s capabilities. A 2-D planar magnetic nozzle was applied to plumes of a nominal pulsed inductive plasma (PIP) source with discharge parameters similar to those of Missouri S&T’s Missouri Plasmoid Experiment (MPX). Argon and xenon plumes were considered. Simulations were verified and validated through a mesh convergence study as well as comparison with available experimental data. Periodicity was achieved over the simulation run time and phase angle samples were taken to examine plume evolution over pulse cycles. The resulting pressure, velocity, and density fields were analysed for nozzle angles from 0° to 14°. It was found that actual plume divergence was small compared to the nozzle angle. Even with an offset angle of 14° for the magnetic nozzle, the plume vector angle was only about 2° for argon and less than 1° for xenon. The parameters that had the most effect on the vectoring angle were found to be the coil current and inlet velocity.

Development of Parametric Kelvin Structures will Closed Cells

2016 ◽  
Vol 254 ◽  
pp. 49-54 ◽  
Author(s):  
Dan Andrei Şerban ◽  
Emanoil Linul ◽  
Sorin Sărăndan ◽  
Liviu Marşavina
Keyword(s):  
Mechanical Properties ◽  
Cell Wall ◽  
Relative Density ◽  
Material Properties ◽  
Cell Diameter ◽  
Rigid Polyurethane Foam ◽  
Loading Direction ◽  
Convergence Study ◽  
Simulation Results ◽  
Mesh Convergence

This work presents the design of a parametric Kelvin structure in which the relative density of the geometry can be varied by adjusting three parameters: cell diameter, cell wall thickness and cell chamfer radius, the structure consistsing of a tessellation of hollow truncated octahedral. The developed model was evaluated in terms of compressive stiffness for the case of a rigid polyurethane foam of 0.256 relative density. Three models were analyzed in order to determine the influence of geometric characteristics on mechanical properties: a model that presented no chamfer a model that presented a medium-sized chamfer and a model that presented a large chamfer. A mesh convergence study was performed which analyzed the results in terms of accuracy and time expenses for three element sizes for both linear and quadratic elements. Due to the orthotropic nature of the model, its response on both possible loading directions was investigated. Simulation results were compared with experimental results and yielded accurate results for one loading direction, when using the material properties for solid polyurethane described in literature.

Interpretation of Adjoint Solutions for Turbomachinery Flows

AIAA Journal ◽  
2013 ◽  
Vol 51 (7) ◽  
pp. 1733-1744 ◽  
Author(s):  
Andre C. Marta ◽  
Sriram Shankaran ◽  
Qiqi Wang ◽  
Prem Venugopal
Keyword(s):  
Adjoint Solutions
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