scholarly journals The Performance of a Gradient-Based Method to Estimate the Discretization Error in Computational Fluid Dynamics

Computation ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 10
Author(s):  
Adhika Satyadharma ◽  
Harinaldi
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Discretization Error ◽  
Computational Time ◽  
Simulation Data ◽  
Manufactured Solutions ◽  
Grid Convergence ◽  
Gradient Based ◽  
New Perspective ◽  
Grid Convergence Index

Although the grid convergence index is a widely used for the estimation of discretization error in computational fluid dynamics, it still has some problems. These problems are mainly rooted in the usage of the order of a convergence variable within the model which is a fundamental variable that the model is built upon. To improve the model, a new perspective must be taken. By analyzing the behavior of the gradient within simulation data, a gradient-based model was created. The performance of this model is tested on its accuracy, precision, and how it will affect a computational time of a simulation. The testing is conducted on a dataset of 36 simulated variables, simulated using the method of manufactured solutions, with an average of 26.5 meshes/case. The result shows the new gradient based method is more accurate and more precise then the grid convergence index(GCI). This allows for the usage of a coarser mesh for its analysis, thus it has the potential to reduce the overall computational by at least by 25% and also makes the discretization error analysis more available for general usage.

Richardson Extrapolation-Based Discretization Uncertainty Estimation for Computational Fluid Dynamics

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Tyrone S. Phillips ◽  
Christopher J. Roy
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Convergence Rates ◽  
Richardson Extrapolation ◽  
Local Solution ◽  
Navier Stokes ◽  
Grid Convergence ◽  
Computational Fluid Dynamics Cfd ◽  
Grid Convergence Index ◽  
2D And 3D

This study investigates the accuracy of various Richardson extrapolation-based discretization error and uncertainty estimators for problems in computational fluid dynamics (CFD). Richardson extrapolation uses two solutions on systematically refined grids to estimate the exact solution to the partial differential equations (PDEs) and is accurate only in the asymptotic range (i.e., when the grids are sufficiently fine). The uncertainty estimators investigated are variations of the grid convergence index and include a globally averaged observed order of accuracy, the factor of safety method, the correction factor method, and least-squares methods. Several 2D and 3D applications to the Euler, Navier–Stokes, and Reynolds-Averaged Navier–Stokes (RANS) with exact solutions and a 2D turbulent flat plate with a numerical benchmark are used to evaluate the uncertainty estimators. Local solution quantities (e.g., density, velocity, and pressure) have much slower grid convergence on coarser meshes than global quantities, resulting in nonasymptotic solutions and inaccurate Richardson extrapolation error estimates; however, an uncertainty estimate may still be required. The uncertainty estimators are applied to local solution quantities to evaluate accuracy for all possible types of convergence rates. Extensions were added where necessary for treatment of cases where the local convergence rate is oscillatory or divergent. The conservativeness and effectivity of the discretization uncertainty estimators are used to assess the relative merits of the different approaches.

Combining Computational Fluid Dynamics (CFD) and Flow Network Modeling (FNM) for Design of a Multi-Chip Module (MCM) Cold Plate

2013 ◽  
Author(s):  
John Fernandes ◽  
Saeed Ghalambor ◽  
Akhil Docca ◽  
Chris Aldham ◽  
Dereje Agonafer ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Thermal Analysis ◽  
Computational Fluid Dynamics ◽  
Network Modeling ◽  
Computational Time ◽  
Design Parameters ◽  
Cold Plate ◽  
Original Solution ◽  
Flow Network ◽  
Computational Fluid Dynamics Cfd

The objective of the study is to improve on performance of the current liquid cooling solution for a Multi-Chip Module (MCM) through design of a chip-scale cold plate with quick and accurate thermal analysis. This can be achieved through application of Flow Network Modeling (FNM) and Computational Fluid Dynamics (CFD) in an interactive manner. Thermal analysis of the baseline cold plate design is performed using CFD to determine initial improvement in performance as compared to the original solution, in terms of thermal resistance and pumping power. Fluid flow through the solution is modeled using FNM and verified with results from the CFD analysis. In addition, CFD is employed to generate flow impedance curves of non-standard components within the cold plate, which are used as input for the Hardy Cross method in FNM. Using the verified flow network model, design parameters of different components in the cold plate are modified to promote uniform flow distribution to each active region in the chip-scale solution. Analysis of the resultant design using CFD determines additional improvement in performance over the original solution, if available. Thus, through complementary application of FNM and CFD, a robust cold plate can be designed without requiring expensive fabrication of prototypes and with minimal computational time and resources.

An Assessment of Computational Fluid Dynamics Cavitation Models Using Bubble Growth Theory and Bubble Transport Modeling

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Michael P. Kinzel ◽  
Jules W. Lindau ◽  
Robert F. Kunz
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Analytic Solutions ◽  
Cfd Modeling ◽  
Computational Time ◽  
Cavitation Model ◽  
Modeling Framework ◽  
Homogeneous Models ◽  
Bubble Transport ◽  
Computational Fluid Dynamics Cfd

This effort investigates advancing cavitation modeling relevant to computational fluid dynamics (CFD) through two strategies. The first aims to reformulate the cavitation models and the second explores adding liquid–vapor slippage effects. The first aspect of the paper revisits cavitation model formulations with respect to the Rayleigh–Plesset equation (RPE). The present approach reformulates the cavitation model using analytic solutions to the RPE. The benefit of this reformulation is displayed by maintaining model sensitivities similar to RPE, whereas the standard models fail these tests. In addition, the model approach is extended beyond standard homogeneous models, to a two-fluid modeling framework that explicitly models the slippage between cavitation bubbles and the liquid. The results indicate a significant impact of slip on the predicted cavitation solution, suggesting that the inclusion of such modeling can potentially improve CFD cavitation models. Overall, the results of this effort point to various aspects that may be considered in future CFD-modeling efforts with the goal of improving the model accuracy and reducing computational time.

scholarly journals Acceleration of a CFD Code with a GPU

2010 ◽  
Vol 18 (3-4) ◽  
pp. 193-201 ◽  
Author(s):  
Dennis C. Jespersen
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Graphics Processing Unit ◽  
Computational Time ◽  
Processing Unit ◽  
Graphics Processing ◽  
Work Done

The Computational Fluid Dynamics code OVERFLOW includes as one of its solver options an algorithm which is a fairly small piece of code but which accounts for a significant portion of the total computational time. This paper studies some of the issues in accelerating this piece of code by using a Graphics Processing Unit (GPU). The algorithm needs to be modified to be suitable for a GPU and attention needs to be given to 64-bit and 32-bit arithmetic. Interestingly, the work done for the GPU produced ideas for accelerating the CPU code and led to significant speedup on the CPU.

Multi-Objective Optimization of a High Specific Speed Centrifugal Volute Pump Using Three-Dimensional Inverse Design Coupled With Computational Fluid Dynamics Simulations

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Luying Zhang ◽  
Gabriel Davila ◽  
Mehrdad Zangeneh
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Design Method ◽  
Three Dimensional ◽  
Inverse Design ◽  
Computational Time ◽  
Specific Speed ◽  
Meridional Shape ◽  
Inverse Design Method ◽  
Blade Geometry

Abstract This paper presents three different multiobjective optimization strategies for a high specific speed centrifugal volute pump design. The objectives of the optimization consist of maximizing the efficiency and minimizing the cavitation while maintaining the Euler head. The first two optimization strategies use a three-dimensional (3D) inverse design method to parametrize the blade geometry. Both meridional shape and 3D blade geometry are changed during the optimization. In the first approach, design of experiment (DOE) method is used and the pump efficiency is obtained from computational fluid dynamics (CFD) simulations, while cavitation is evaluated by using minimum pressure on blade surface predicted by 3D inverse design method. The design matrix is then used to create a surrogate model where optimization is run to find the best tradeoff between cavitation and efficiency. This optimized geometry is manufactured and tested and is found to be 3.9% more efficient than the baseline with reduced cavitation at high flow. In the second approach, only the 3D inverse design method output is used to compute the efficiency and cavitation parameters and this leads to considerable reduction to the computational time. The resulting optimized geometry is found to be similar to the computationally more expensive solution based on 3D CFD results. In order to compare the inverse design based optimization to the conventional optimization, an equivalent optimization is carried out by parametrizing the blade angle and meridional shape.

New Evolutionary Techniques for Optimization of Energy Systems Utilizing Computational Fluid Dynamics

2003 ◽  
Author(s):  
Douglas S. McCorkle ◽  
Kenneth M. Bryden
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Evolutionary Algorithms ◽  
Computational Cost ◽  
Solution Space ◽  
Optimization Techniques ◽  
Computational Time ◽  
Feed Forward Neural Network ◽  
Thermal Fluids ◽  
Fluid Systems

Optimization techniques that search a solution space without designer intervention are becoming important tools in the engineering design of many thermal fluid systems. Evolutionary algorithms are among the most robust of these optimization methods because the ability to optimize many designs simultaneously makes evolutionary algorithms less susceptible to premature convergence. However application of evolutionary algorithms to thermal and fluid systems described by high fidelity models (e.g. computational fluid dynamics) has been limited due to the high computational cost of the fitness evaluation. This paper presents a novel technique that combines two technologies used in the optimization of thermal fluids systems. The first is graph based evolutionary algorithms that are implemented to help increase the diversity of the evolving population of designs. The second is an algorithm utilizing a feed forward neural network that develops a stopping criterion for computational fluid dynamics solutions. This reduces the time required for each future evaluation in the evolutionary process and allows for more complex thermal fluids systems to be optimized. In the system examined here the overall reduction in computational time is approximately 8 times.

scholarly journals Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2438 ◽  
Author(s):  
Vojtěch Turek
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Direct Calculation ◽  
Steady State Solution ◽  
Computational Time ◽  
Process Equipment ◽  
Successive Overrelaxation ◽  
Lower Upper ◽  
Cfd Models ◽  
Relaxation Factors

The ability to model fluid flow and heat transfer in process equipment (e.g., shell-and-tube heat exchangers) is often critical. What is more, many different geometric variants may need to be evaluated during the design process. Although this can be done using detailed computational fluid dynamics (CFD) models, the time needed to evaluate a single variant can easily reach tens of hours on powerful computing hardware. Simplified CFD models providing solutions in much shorter time frames may, therefore, be employed instead. Still, even these models can prove to be too slow or not robust enough when used in optimization algorithms. Effort is thus devoted to further improving their performance by applying the symmetric successive overrelaxation (SSOR) preconditioning technique in which, in contrast to, e.g., incomplete lower–upper factorization (ILU), the respective preconditioning matrix can always be constructed. Because the efficacy of SSOR is influenced by the selection of forward and backward relaxation factors, whose direct calculation is prohibitively expensive, their combinations are experimentally investigated using several representative meshes. Performance is then compared in terms of the single-core computational time needed to reach a converged steady-state solution, and recommendations are made regarding relaxation factor combinations generally suitable for the discussed purpose. It is shown that SSOR can be used as a suitable fallback preconditioner for the fast-performing, but numerically sensitive, incomplete lower–upper factorization.

Improving Computational Fluid Dynamics Simulations for the Spallation Neutron Source Jet-Flow Target

2016 ◽  
Author(s):  
C. Barbier ◽  
E. Dominguez-Ontiveros
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Neutron Source ◽  
Jet Flow ◽  
Computational Time ◽  
Spallation Neutron Source ◽  
Mean Flow ◽  
Cfd Simulations ◽  
Flow Measurements ◽  
Piv Measurements

A liquid mercury target is used at Oak Ridge National Laboratory’s (ORNL [1]) Spallation Neutron Source (SNS [2]) to generate neutrons. The mercury is flowing in a stainless steel containment vessel for neutron spallation, but also to cool the vessel itself. Computational Fluid Dynamics (CFD) simulations have been used to estimate the temperature and pressure fields needed for the thermal stress analysis. Because of the geometry complexity, the high turbulence number, and the computational time requirements, generating a quality mesh that can accurately capture the flow and heat transfer has always been a challenge. However, with today’s High Performance Computing (HPC) advances, larger and larger meshes can now be used and better accuracy can be achieved. In this study, two meshing methods were used for the SNS jet-flow target: automatic tetrahedral method (ANSYS meshing) and manual hexahedral meshing (ICEM-CFD). Both methods are compared in terms of quality, size, ease of generation, convergence, and user-friendliness. Both meshes were used with ANSYS-CFX to simulate the steady, Newtonian, single phase, isothermal, incompressible and turbulent flow in the target. The Shear Stress Transport (SST) k-ω model developed by Menter [3] was used for turbulence modeling. The accuracy of the CFD simulations are tested against experimental data presented in the current paper. An in-depth series of Particle Image Velocimetry (PIV) measurements performed on a “visual jet-flow target”, an acrylic replica target running with water, are presented in the paper. Since flow measurements in mercury are difficult, a water loop was built to investigate the flow in the target and a potential gas injection in the flow to mitigate the pressure wave [4]. A PIV system on a precise translation stage was setup on the water loop to perform detailed and accurate PIV measurements. Mean flow velocity fields were used to validate the CFD simulations. The paper concludes on the choice for mesh generation for future target analysis, and the path forward for CFD simulations for the future SNS targets.

Computational Fluid Dynamics Modeling of a Self-Recuperative Burner and Development of a Simplified Equivalent Radiative Model

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Haytham Sayah ◽  
Maroun Nemer ◽  
Wassim Nehmé ◽  
Denis Clodic
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Computational Time ◽  
Dynamics Modeling ◽  
Gas Combustion ◽  
Experimental Database ◽  
Transfer Mode ◽  
High Temperature Processes ◽  
Burner Model

The solution for dynamic modeling of reheating furnaces requires a burner model, which is simultaneously accurate and fast. Based on the fact that radiative heat transfer is the most dominant heat transfer mode in high-temperature processes, the present study develops a simplified flame representation model that can be used for dynamic simulation of heat transfer in reheating furnaces. The first part of the paper investigates, experimentally and computationally, gas combustion in an industrial burner. Experiments aim at establishing an experimental database of the burner characteristics. This database is compared with numerical simulations in order to establish a numerical model for the burner. The numerical burner model was solved using a commercial computational fluid dynamics (CFD) software (FLUENT 6.3.26). A selection of results is presented, highlighting the usefulness of CFD as a modeling tool for industrial scale burners. In the second part of the paper, a new approach called the “emissive volume approach” is established. This approach consists of replacing the burner flame by a number of emissive volumes that replicates the radiative effect of the flame. Comparisons with CFD results show a difference smaller than 1% is achieved with the emissive volume approach, while computational time is divided by 40.

Accelerating Computational Fluid Dynamics Simulations of Engine Knock Using a Concurrent Cycles Approach

2020 ◽  
Author(s):  
Daniel Probst ◽  
Sameera Wijeyakulasuriya ◽  
Pinaki Pal ◽  
Christopher Kolodziej ◽  
Eric Pomraning
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Direct Injection ◽  
Turbulent Flame ◽  
Sampling Rate ◽  
Operating Conditions ◽  
Gasoline Direct Injection ◽  
Simulation Data ◽  
Low Frequencies ◽  
Operating Points

Abstract Knock is a major design challenge for spark-ignited engines. Knock constrains high load operation and limits efficiency gains that can be achieved by implementing higher compression ratios. The propensity to knock depends on the interaction among fuel properties, engine geometry, and operating conditions. Moreover, cycle-to-cycle variability (CCV) in knock intensity is commonly encountered under abnormal combustion conditions. In this situation, knock needs to be assessed with multiple engine cycles. Therefore, when using computational fluid dynamics (CFD) to predict knock behavior, multi-cycle simulations must be performed. The wall clock time for simulating multiple consecutive engine cycles is prohibitive, especially for a statistically valid sample size (i.e. 30–100 cycles). In this work, 3-d CFD simulations were used to model knocking phenomena in the cooperative fuel research (CFR) engine. Unsteady Reynolds-Averaged Navier Stokes (uRANS) simulations were performed with a hybrid combustion modeling approach using the G-equation method to track the turbulent flame front and finite-rate chemistry model to predict end-gas autoignition. To circumvent the high cost of running simulations with a large number of consecutive engine cycles, a concurrent perturbation method (CPM) was evaluated to predict knock CCV. The CPM was based on previous work by the authors, in which concurrent engine cycles were used to predict engine CCV in a non-knocking gasoline direct injection (GDI) engine. Concurrent cycles were initialized by perturbing a saved flow field with a random isotropic velocity field. By initializing each cycle with a perturbation sufficiently early in the cycle, each case yields a distinct and valid prediction of combustion due to the chaotic nature of the system. Three operating points were simulated, with different spark timings corresponding to heavy knock, light knock, and no knock. For all the operating points, other conditions were based on the standard research octane number (RON) test specification for iso-octane. The spark timing of the heavy knock case was the same as that of the RON test. The in-cylinder pressure fluctuations were isolated using a frequency filtering method. A bandpass filter was applied to eliminate high and low frequencies. The knocking pressures were calculated consistently between the experimental and simulation data, including the sampling frequency of the data. The simulation data was sampled to match the sampling rate of the experimental data. The knock intensities were compared for the concurrently obtained cycles, the consecutively obtained cycles, and experimental cycles. Knock predictions from the concurrent and consecutive simulations compared well to each other and with experiments, thereby demonstrating the validity of the CPM approach.

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