Casting computational fluid mechanics into a convex quadratic optimization framework

Implicit subiteration algorithms for time-accurate Navier-Stokes flow solvers for moving body and deforming applications have been investigated. Several example calculations are computed to demonstrate the performance of these algorithms for solving unsteady Navier-Stokes problems. A set of relatively simple two-dimensional validation cases has been identified to assess the performance of unsteady CFD solvers. These cases demonstrate the advantages of second order time derivatives and subiterations for unsteady flow simulations. This investigation also indicates that the same level or a reduced level of numerical error relative to a baseline calculation using a smaller time step can be achieved with large time steps using subiterations when a highly convergent inner algorithm is used. here currently exists a great interest in performing calculations using Computational Fluid Dynamics (CFD) for high Reynolds number unsteady flows. Researchers are beginning to apply the new hybrid RANS/LES class of turbulence models to a host of unsteady high Reynolds flows containing large-scale coherent turbulent structures. Applications involving moving and deforming bodies are also becoming more common. Validation and verification of CFD codes becomes much more difficult for these unsteady flows than for traditional steady state CFD problems. Grid convergence studies do not address all of the relevant dimensions of a problem. Often refining the results in resolution of smaller scale structure in the unsteady flow, and hence a grid resolved solution does not exist except in the Direct Numerical Simulation (DNS) limit. In many cases convergence can only be judged in a statistical sense. The choice of time step can have a tremendous effect on the time-accuracy of a solution. The high frequency spectral regime will be under-resolved if the chosen time step is too large. Large time steps can introduce error in the solution if no means are provided to locally converge (i.e. convergence in both time and space at each time step) the solution. If the time step is too small a tremendous number of iterations will be required in order to adequately resolve the low frequency spectral regime. Hence the selection of a time step for a typical CFD problem is an exercise in the art of compromise and often requires some a priori knowledge of the unsteady nature of the flow. Much of the numerical technology for the solution of the Navier-Stokes equations over the last three decades has been focused on obtaining steady-state solutions. These algorithms generally provide large amounts of numerical dissipation in order to damp out spurious numerical fluctuations rapidly. Excessive numerical dissipation can cause the unsteady structures in the flow to be over-damped. This study focuses on subiteration strategies that allow for large time steps and local convergence at each step. Large time steps are useful in problems that require assembly or remeshing at each time step since it minimizes the number of these operations required for a simulation. This effort outlines the basic implicit numerical algorithms required for unsteady flow applications using large time steps including moving and deforming body applications. Simple two-dimensional example cases are provided that allow numerical algorithms to be assessed for unsteady flow applications. The test cases were chosen based on the availability of analytical solutions to the Navier-Stokes equations and/or a regular periodic behavior of the flow. This allows the user to evaluate the ability of a flow solver to provide a locally converged solution in time and to

Implicit subiteration algorithms for time-accurate Navier-Stokes flow solvers for moving body and deforming applications have been investigated. Several example calculations are computed to demonstrate the performance of these algorithms for solving unsteady Navier-Stokes problems. A set of relatively simple two-dimensional validation cases has been identified to assess the performance of unsteady CFD solvers. These cases demonstrate the advantages of second order time derivatives and subiterations for unsteady flow simulations. This investigation also indicates that the same level or a reduced level of numerical error relative to a baseline calculation using a smaller time step can be achieved with large time steps using subiterations when a highly convergent inner algorithm is used. here currently exists a great interest in performing calculations using Computational Fluid Dynamics (CFD) for high Reynolds number unsteady flows. Researchers are beginning to apply the new hybrid RANS/LES class of turbulence models to a host of unsteady high Reynolds flows containing large-scale coherent turbulent structures. Applications involving moving and deforming bodies are also becoming more common. Validation and verification of CFD codes becomes much more difficult for these unsteady flows than for traditional steady state CFD problems. Grid convergence studies do not address all of the relevant dimensions of a problem. Often refining the results in resolution of smaller scale structure in the unsteady flow, and hence a grid resolved solution does not exist except in the Direct Numerical Simulation (DNS) limit. In many cases convergence can only be judged in a statistical sense. The choice of time step can have a tremendous effect on the time-accuracy of a solution. The high frequency spectral regime will be under-resolved if the chosen time step is too large. Large time steps can introduce error in the solution if no means are provided to locally converge (i.e. convergence in both time and space at each time step) the solution. If the time step is too small a tremendous number of iterations will be required in order to adequately resolve the low frequency spectral regime. Hence the selection of a time step for a typical CFD problem is an exercise in the art of compromise and often requires some a priori knowledge of the unsteady nature of the flow. Much of the numerical technology for the solution of the Navier-Stokes equations over the last three decades has been focused on obtaining steady-state solutions. These algorithms generally provide large amounts of numerical dissipation in order to damp out spurious numerical fluctuations rapidly. Excessive numerical dissipation can cause the unsteady structures in the flow to be over-damped. This study focuses on subiteration strategies that allow for large time steps and local convergence at each step. Large time steps are useful in problems that require assembly or remeshing at each time step since it minimizes the number of these operations required for a simulation. This effort outlines the basic implicit numerical algorithms required for unsteady flow applications using large time steps including moving and deforming body applications. Simple two-dimensional example cases are provided that allow numerical algorithms to be assessed for unsteady flow applications. The test cases were chosen based on the availability of analytical solutions to the Navier-Stokes equations and/or a regular periodic behavior of the flow. This allows the user to evaluate the ability of a flow solver to provide a locally converged solution in time and to

Fluidized bed CFD using simplified solid-phase coupling.

In this paper, an emerging alternative computational technique, the lattice Boltzmann method (LBM), was used to study indoor airflows. Emphasis was placed on low-Reynolds-number indoor airflow fields in a model room with a partition. The predicted results by LBM are compared with available experimental data and results predicted by traditional computational fluid dynamics (CFD) with the RNG k-∊ turbulence model. For the model room case, it is found that the computational results of LBM agree very well with the experimental data in terms of airflow velocities. The unsteady-procedure-based LBM has the capability to capture more detailed airflow structures than the traditional steady CFD method, which tends to smooth out the flow fields. LBM is further demonstrated through simulation of airflow in a relatively more complex environment, a model ward with 10 beds. The improved resolution in flow field prediction by LBM comes with a moderate increase in computational time requirement.

Experimental results of a hypersonic flow over a flat plate are compared with a CFD simulation. Slip boundary conditions are employed in the CFD simulation, with the accommodation coefficient being varied between 0.5 and 1.0. Detailed velocity profiles in both the x- and y-directions are compared with the experimental data, as well as slip velocity at the wall. A brief comparison is also made to similar simulation results using DSMC. I. Introduction The design of hypersonic vehicles requires accurate prediction of the gas flow around the vehicles surfaces. During it's trajectory through an atmosphere, a hypersonic vehicle will experience vastly different flow regimes due to the variation of atmospheric density with altitude. In addition, the high temperatures encountered due to the high velocities cause dissociation and ionization of the atmospheric gases. Reproduction of these varied flow conditions in ground-based laboratory facilities is both expensive and technically challenging. Hence, there is an extremely important role for computational models in the development of hypersonic vehicles. In the continuum regime flows around hypersonic vehicles can be accurately simulated using traditional Computational Fluid Dynamics (CFD) by solving either the Euler or preferably the Navier-Stokes (NS) equations. These continuum methods assume small perturbations from local thermodynamic equilibrium. In the rarefied flow regime the flow can be computed using the direct simulation Monte Carlo (DSMC) method. 1 The DSMC method does not depend on assumptions involving a small perturbation from equilibrium and hence is more accurate than CFD methods for non-equilibrium flows. Generally speaking, CFD methods for solving the NS equations are about an order of magnitude faster than the DSMC method. Note that in continuum regimes, locally a flow may behave like a rarefied flow if the local characteristic length scale is very small. Previous work by the authors comparing CFD and DSMC focused purely on numerical results, with CFD simulations being compared directly to DSMC simulations. 7-10 In particular, the walls were assumed to be fully diffusive; that is, the gas molecules colliding with the wall were assumed to accommodate fully to the wall conditions. Hence, an accommodation coefficient of unity was used for the CFD slip boundary conditions. In this paper, two-dimensional CFD solutions are compared with experimental measurements of a hypersonic flow of nitrogen over a flat plate. 4 Several different values for the accommodation coefficient are evaluated. In addition, the CFD solutions are also indirectly compared to DSMC solutions of the same flow. 11 Thus, the relative accuracy of CFD and DSMC can be evaluated against a realistic flow.

Hybrid computational fluid dynamic algorithms based on analytic and finite volume methods

Accelerating unsteady aerodynamic simulations using predictive reduced-order modeling

A numerical study of the interactions between viscous flow, transport and kinetics in fixed bed reactors

Simulation of a 3-D Lid-Driven Cavity Flow by a Parallelised Lattice Boltzmann Method

Chapter 8 - Artificial intelligence-based computational fluid dynamics approaches

Compared to system simulations based on low-dimensional mathematical models, physical-field simulations offer broader prospects in the design processes of gas turbine engines. While computational fluid dynamics (CFD) has become a standard practice for evaluating component-level performance, performing three-dimensional (3D) CFD simulations of the full engine, especially for dynamic processes, remains challenging. A key technical issue with existing solvers for these full engine physical-field simulations is that the governing equations, derived using the multi-frame reference method for turbomachinery, do not account for real-time changes in rotational speed. In this paper, the Navier–Stokes (N-S) equation with angular acceleration source term was derived, and the rotor motion equation was introduced to simulate the engine's dynamic process. By comparing the simulation results of the transient state with the steady-state simulation and experimental data, the reliability of the CFD solver based on these improved governing equation was verified. Then, an exploratory simulations were conducted to investigate the transition state of the KJ66 Micro Turbojet Engine, transitioning into a wind-milling state after the fuel was cut off under specific incoming wind speed. The results indicate that dynamic process simulations previously impossible to achieve using traditional unsteady CFD method, such as engine's wind-milling state and fuel cutoff process, can now be successfully conducted based on the improved N-S equations coupled with the rotor motion.

Computational fluid dynamics (CFD) analysis, which solves the full three-dimensional (3D) Navier–Stokes equations, has been recognized as having promise in providing a more detailed and accurate analysis for oil-film journal bearings than the traditional Reynolds analysis, although there are still challenging issues requiring further investigation, such as the modeling of cavitation and the modeling of conjugate heat transfer effects in the CFD analysis of bearings. In this paper, a 3D CFD method for the analysis of journal bearings considering the above two effects has been developed; it employs three different cavitation models, including the Half-Sommerfeld model, a vaporous cavitation model, and a gaseous cavitation model. The method has been used to analyze a two-groove journal bearing and the results are validated with experimental measurements and the traditional Reynolds solutions. It is found that the CFD method which considers the conjugate heat transfer and employs the gaseous cavitation model gives better predictions of both bearing load and temperature than either the traditional Reynolds solution or CFD with other cavitation models. The CFD results also show strong recirculation of the fresh oil in the grooves, which has been neglected in the traditional Reynolds solution. The above results show conclusively that the present 3D CFD method considering the conjugate heat transfer and employing the gaseous cavitation model provides an efficient tool for more detailed and accurate analysis for bearing performance.

Many problems in Computational Electromagnetics (CEM) and Computational Fluid Dynamics (CFD) require millions of grid cells to properly represent the physics. Advances in parallel computing, both in hardware and software, make it feasible to solve such large scale simulations in a timely manner. The objective of this paper is to describe some of the recent work at Rockwell in performing parallel computing for providing quick-turnaround solutions to problems in CFD, CEM and other computational disciplines.

The primary objective of this research work is the methodology about the development of a fluid simulation package integrated with the Internet, which will allow the user to perform fluid simulation on the World Wide Web (WWW). The web-based software package is developed using tools like Java, ActiveX and HTML and is accessible over the Internet from anywhere in the work. This work is a part of a project on framework of web-based CAE system, which includes the creation of software packages for other CAE issues such as Computer Aided Design (CAD), Computer Aided Geometry Design (CAGD), Computer Aided Manufacturing (CAM). The framework of web-based CAE system is a set of CAE packages that can be accessed from all over the world. The simulation package is stored on a powerful server located at the Hong Kong University of Science and Technology, and the input/output (text, graphics, and animation) can be viewed and accessed by any computer supporting a web browser. In this paper, the traditional Computational Fluid Dynamics (CFD) problem — Transient Natural Convection in a Cavity is used as the example to show how to build a fluid simulation package integrated with the Internet. At first, we will introduce the prospect of such a research work; then, the transient natural convection problem in a cavity is analyzed based on the stream-function and vorticity-function; at last, two solution of web-based fluid simulation will be compared using the example of transient natural convection in a cavity. Experiments on Transient Natural Convection in a Cavity have shown the feasibility for a networked fluid simulation service via the Internet.

Cavitation is the phenomenon of bubbles growing when the liquid pressure drops below vapor pressure. Cavitation is mostly undesirable and fluid engineering systems are often designed to avoid it, so proper prediction of the cavitation inception point is important. Traditional Computational Fluid Dynamics (CFD) methodologies cannot properly predict it due to either insufficient grid resolution that results in underpredicted minimum pressures in the flow, or in well resolved grids that can better predict the pressure but do not consider the duration or the volume of the low pressure events. With proper modeling of unresolved turbulence in the sub-grid scale (SGS), cavitation event rates in the SGS can be computed using the rates of low pressure fluctuating events and their corresponding duration. This thesis presents a cavitation inception model that includes pressure fluctuations at the (SGS) level in CFD simulations. As turbulence models look to predict the momentum transfer at the resolved scales by approximating the SGS turbulence behavior, the model presented in this thesis seeks to predict the cavitation inception at the SGS level considering the frequency and duration of unresolved low pressure fluctuations in the SGS. The SGS flow field is modeled as homogeneous isotropic turbulence (HIT), dependent on the unresolved turbulence Taylor scale Reynolds number {Re}_\lambda. Direct numerical simulations (DNS) of HIT up to {Re}_\lambda=240 were performed with a pseudo-spectral code, tracking nuclei with sizes between 0.1 and 150 \mu m and solving the Rayleigh-Plesset equation on the time histories of the nuclei to predict bubble cavitation rates at different absolute pressures. The behavior of the pressure experienced by nuclei in HIT was studied, including pressure probability density functions, low-pressure event frequency and duration, and the effect of nuclei size on these parameters. It is found that low-pressure events are more likely as {Re}_\lambda and the nuclei size increase. Solutions of the Rayleigh-Plesset equation along the nuclei trajectories offered cavitation event rates for a defined cavitation criterion. A table providing cavitation rate as a function of {Re}_\lambda, nuclei radius, turbulent kinetic energy dissipation rate, and pressure was generated to use in the prediction of cavitation inception in complex CFD problems. Validation of the model is performed for high {Re}_\lambda HIT turbulence and shear flow behind a backward facing step. As the model uses the nuclei size distribution and concentration, the predicted cavitation frequency depends on the water quality. The model can predict the effect of unresolved pressure fluctuations, typically increasing the cavitation inception number with respect to CFD predictions using the minimum flow pressure to predict inception but can also predict a lower cavitation inception number for highly resolved LES simulations where very low pressure events can be infrequent and of small volume. The model showed satisfactory comparisons with experiments for both HIT and shear flow.