Computational Fluid Dynamics Algorithms Research Articles

Application of CFD to modelling of the flow in hydrocyclones. Is this a realizable option or still a research challenge?

The search continues for accurate and efficient 3D computational fluid dynamics algorithms for hydrocyclone flows. A review of recent work and new developments are presented. This contribution is based on the authors' past experience both in creating their own specialized numerical approaches and using commercial packages for simulating swirling flow. In particular, the paper presents the application of the developed 3D finite element code to hydrocyclone modelling. Some important factors in the numerical solution of the model equations, namely proper representation of geometry, imposition of boundary conditions and the choice of turbulence model, are discussed. Numerical results indicate the versatility and the effectiveness of the new approaches. A scheme that utilizes numerical results in the multi-objective design is also suggested. Remaining technical difficulties are highlighted in order to suggest key directions for future work.

Optimization of the geometry of a double-path spray chamber for inductively coupled plasma-atomic emission spectrometry by computer simulation and an evolutionary strategy

Computational fluid dynamics (CFD) is used to investigate the analytical performance of variously sized inductively coupled plasma (ICP)-double-path spray chambers (Scott-type) and for the optimization of the geometry of the spray chamber using an evolutionary strategy. It can be seen from the simulation of the aerosol transport in chambers of various lengths that shorter chambers have better characteristics. This result was confirmed experimentally. A higher mass flow rate at the outlet of the chamber (aerosol yield) is obtained by reducing the diameter of the inner tube and keeping the other dimensions constant. An evolutionary strategy in combination with CFD was applied in order to find the optimum geometry for this type of chamber. For the evaluation of the virtual chambers the development of a quantitative objective function was necessary. The search for the best chamber geometry was then performed by searching for the global maximum of this function. As result, a modified ICP-double-path chamber with a much better analytical performance than that of the initial one was obtained. Replacing the original chamber by the optimized one, in the same inductively coupled plasma-atomic emission spectrometry instrument, resulted in the detection limits being lowered by a factor of 2–6 depending on the element. The combination of CFD and evolutionary algorithms can be used as a new and powerful tool for the optimization of various analytical flow systems.

Development Of A Smoke Transport Model To Enhance The Certification Process For Cargo Bay Smoke Detection Systems

Current regulations require that aircraft cargo compartment smoke detectors alarm within one minute of the start of a fire and at a time before the fire has substantially decreased the structural integrity of the airplane. Presently in-flight and ground tests, which can be costly and time consuming, are required to demonstrate compliance with the regulations. A physics based Computational Fluid Dynamics (CFD) tool, which couples heat, mass and momentum transfer, has been developed to decrease the time and cost of the certification process by reducing the total number of both in-flight and ground experiments. The tool would provide information on smoke transport in cargo compartments under various conditions, therefore allowing optimal experiments to be designed. The CFD based smoke transport model will enhance the certification process by determining worst case locations for fires, optimum placement of fire detector sensors within the cargo compartment, and sensor alarm levels needed to achieve detection within the required certification time. The model is fast-running to allow for simulation of numerous fire scenarios in a short period of time. In addition, the model will be user friendly since it will potentially be used by airframers and airlines not expected to be experts in CFD. Following verfication of this CFD code, full-scale experiments will aid in the validation of the code and will gauge the reliability of using such a formulation to increase the efficiency of the aircraft fire detection system certification process by decreasing the total number of ground and flight experiments. This document includes a description of the CFD model and simulation studies developed to test the modeling strategy and numerical implementation of the CFD algorithm. Copyright © International Association for Fire Safety Science

Numerical Reconstruction of Ejector Rocket Experimental Tests

Air ejector rocket systems, typical of combined cycle engines for space propulsion applications, have been studied within the ESA Future European Space Transportation Investigations Program. The description and validationof the computational fluid dynamics (CFD) algorithm that has been tuned to simulate the behavior of these systems, and the numerical rebuilding of the ejector rocket experimental tests that were carried out at TNO in The Netherlands are given. The computational developments being presented target the problem of turbulent mixing layer simulation, which is one of the leading phenomena that govern flow behavior inside an ejector rocket. Comparison between experimental and CFD data is given for two validation test cases: a two-dimensional turbulent mixing layer and an axysimmetric ejector in cold flow. Then, the numerical rebuilding of the ejector rocket experimental tests is presented, and the results are discussed with regard to the comparison between numerical and experimental data.

Blood flow patterns in an anatomically realistic coronary vessel: influence of three different reconstruction methods

Many clinical studies suggest that local blood flow patterns are involved in the location and development of atherosclerosis. In coronary diseases, this assumption should be corroborated by quantitative information on local hemodynamic parameters such as pressure, velocity or wall shear stress. Nowadays, computational fluid dynamics (CFD) algorithms coupled to realistic 3-D reconstructions of such vessels make these data accessible. Nevertheless, they should be carefully analysed to avoid misinterpretations when the physiological parameters are not all considered. As an example, we propose here to compare the flow patterns calculated in a coronary vessel reconstructed by three different methods. In the three cases, the vessel trajectory respected the physiology. In the simplest reconstruction, the coronary was modelled by a tube of constant diameter while in the most complex one, the cross-sections corresponded to the reality. We showed that local pressures, wall shear rates and velocity profiles were severely affected by the geometrical modifications. In the constant cross-section vessel, the flow resembled to that of Poiseuille in a straight tube. On the contrary, velocity and shear rate exhibited sudden local variations in the more realistic vessels. As an example, velocity could be multiplied by 5 as compared to Poiseuille's flow and area of very low wall shear rates appeared. The results obtained with the most complex model clearly outlined that, in addition to a proper description of the vessel trajectory, the section area changes should be carefully taken into account, confirming assumptions already highlighted before the rise of commercially available and efficient CFD softwares.

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

A numerical method is tailored for the solution of a reduced set of model equations developed for the description of reactive flows in chemical reactors. The numerical method synthesis intends to utilize experience both in chemical engineering solving dispersion models containing complex reaction kinetics, phase equilibria and non-ideal thermodynamics, and in fluid dynamics applying classical numerical algorithms constructed for pure flow calculations. The two types of model equations involved in reactive flow simulations reflect very different physics. A modular method is therefore suggested enabling a split between the flow- and chemistry model parts. In this way more optimal solution methods can be adopted for each operator, in contrast to more traditional computational fluid dynamics (CFD) methods where all equations (and operators) are normally solved by the numerical solvers originally intended for pure flow calculations. In addition, emphasis has been put on modularity enabling the same model framework to be used both for the more traditional 1D and 2D dispersion models with simple 1D flow calculations, as well as for the more elaborate 2D and 3D reactive flow calculations. In the flow part of the algorithm a fractional-step algorithm is constructed for the simulation of dynamic reactive flows in chemical reactors. The numerical scheme is based on the compressible transport equations in the low-Mach-number limit. The method can handle real gas (and liquid) mixtures with variable density as well as constant density fluids. The velocity field is advanced using a projection scheme, which consists of a partial convection–diffusion update followed by a pressure correction step with an intermediate an-elastic filter. A variable density corrector step is implemented for variable density systems in order to couple the evolution of the density and the velocity fields. In the chemistry part of the model all scalar fields are updated using Strang-type operator-split integration steps that combine several explicit convection and semi-implicit diffusion transport operators with a suitable solver tailored for non-linear sink/source terms. Diffusion terms are discretized with a second order central difference scheme in space. Convection terms are discretized with a second order TVD scheme in space. The temperature advection is discretized using a second order upwind scheme. The chemical reaction part of the model is discretized by an implicit Euler approximation, and the resulting set of algebraic equations is solved using a Broyden subroutine. The other source terms are solved using an explicit Euler approximation. The performance and behavior of the operator-split scheme are assessed based on simulations of two industrial chemical processes (i.e. the synthesis gas and methanol production processes) performed in multi-tube fixed bed reactors. These processes are important parts of the Statoil methanol plant at Tjeldbergodden in mid Norway. Both 1D and 2D pseudo-homogeneous dispersion models (i.e. heat and mass balances) with prescribed velocity, mixture density and total pressure profiles are used describing the reactor performance. The predicted profiles for both the methanol and synthesis gas processes were in accordance with results reported in the literature. An oscillatory radial void fraction distribution was then implemented in the 2D model. It was found that the non-uniform void fraction distribution had no significant effect on the temperature and mole fraction profiles. A 1D CFD simulation was performed to evaluate the effect of the variations in velocity, pressure and mixture density on the reactor performance. The changes in these variables significantly effect the composition and conversion in the reactor. A 2D CFD model was then developed for further studies of the multi-tube fixed bed reactor for the synthesis gas process, analyzing the influence of non-uniform void fraction distributions on the flow and chemical conversion. The non-uniform void fraction distribution induces a significant reduction in axial pressure drop and a much higher fluid velocity close to the wall. However, the influence on the temperature and mole fraction profiles was hardly noticeable. Mass- and enthalpy budgets were implemented for the heat and mass quantities in the program. These budgets show that the enthalpy and both the mixture and component mass balances are fulfilled in the simulations. The numerical CFD algorithm developed in this paper has been found to be both computationally stable and accurate. Computational efficiency analysis shows that the Poisson solver requires about 75% of the total computational time. The computational time spend on the chemistry part of the model is about 15% of the total time. About 10% of the cost used on the chemistry part is spend on the chemistry solver.

ADVANCED SIMULATION OF OPTICAL FIBER DRAWING PROCESS

Precise modeling of the optical fiber drawing process is extremely important for identifying optimum drawing conditions in a furnace that would produce high-quality fibers at a low cost. In this study, a numerical approach for detailed simulation of thermal transport in an optical fiber drawing furnace is developed by implementing a primitive variable computational fluid dynamics algorithm. To accurately simulate the underlying fluid dynamics, the complete Navier–Stokes equations are solved for both glass and external gas, which are coupled by the conjugate boundary conditions at the interface. The governing equations are discretized by a finite volume approach and the solution algorithm for the discretized equations is based on the semi-implicit method for the pressure linked equations revised (SIMPLER) method instead of the traditional streamfunction approach. Radiative heat transfer is the most dominant mode of heat transfer during optical fiber drawing and it is modeled by the finite volume method. The gas-preform interface is treated as a Fresnel surface instead of a diffuse surface. To validate the present numerical approach and to examine the effects of the Fresnel interface condition on the preform temperature, a benchmark optical fiber drawing problem containing a prescribed neck-down profile is investigated with various fiber drawing speeds, furnace wall temperatures, and preform diameters. For the diffuse interface, the present prediction in temperature is found to match the available other solution very well. For the Fresnel interface, the present prediction is usually higher in comparison with that of the same approach with the diffuse interface. However, the temperature difference between two interfaces is found to be small, implying that the error caused by the diffuse assumption may be not significant.

Aerodynamic Shape Optimization Using Computational Fluid Dynamics and Parallel Simulated Annealing Algorithms

Aerodynamic shape design using stochastic optimization methods, such as simulated annealing method to optimize objective functions evaluated by modern state-of-the-art computational fluid dynamics solvers, normally requires enormous computation time to search for the global optimal design. Aerodynamic shape optimization of internal flow systems is studied using Euler/Navier-Stokes solvers and parallel simulated annealing algorithm, which is implemented on parallel computing platforms. A variety of inverse and direct design of internal flow systems are carried out to examine the efficiency and speedup of the parallel simulated annealing algorithms

Application of coupled solver technology to CFD modeling of multiphase flows with CFX

Over the past ten years the use of Computational Fluid Dynamics (CFD) in chemical engineering has increased at a significant rate. Most of the large chemical engineering companies now use CFD daily in their design process, in problem solving and in improving performance of plants and equipment. The complexity of the problems tackled by CFD is increasing dramatically as the CFD technology advances and is delivered to users in an accessible and user friendly format. Multiphase flows are involved in almost all of the processes in chemical engineering, for examples: gas bubbles in liquid columns, solid particles in mixing vessels, liquid droplets in spray dryers. Multiphase flow problems are inherently very complex. Many of the physical processes (heat, mass and momentum) are linked and coupled between the phases. Despite the difficulties, many successful CFD calculations have been reported in the literature. In most of the current CFD algorithms for multiphase flows such as Spalding's IPSA method, a segregated solution method is used. The momentum, continuity and other equations are solved in separate steps. The whole calculation sequence must be iterated many times (typically thousands of iterations) for the solution to address all the coupling tenns properly and converge to the final solution. For single-phase flows, convergence speed can be improved by using what is known as a coupled solver technology. Within this technique the governing transport equations are all solved simultaneously. This strategy has been implemented in CFX-5 to model two-phase flows. In this paper we will describe the coupled solver technology implemented in the CFX-5 software and examine the advances of this technology in tenns of CFD performance on a real twophase example with published experimental data.

Buoyancy-driven flow through a stairwell

The present work concerns the measurement and the computational fluid dynamics (CFD) modeling of buoyancy-driven air flow through a stairwell that connects the two individual floors of a residential building. A series of experiments was performed in order to study the mass and heat transfer between the two floors. Air flow rates through this stairwell were measured using a single tracer gas decay technique. The analysis of results provided relations which can predict the mass and heat flow rate as a function of the interzone average temperature difference. These results were compared with values estimated by using validated CFD algorithms and showed very good agreement.

Computational studies of unsteady flows in a centrifugal compressor stage

This paper describes the flow analysis in a centrifugal compressor stage using a three-dimensional computational fluid dynamics (CFD) algorithm. The flow unsteadiness arising from the interaction between the impeller and the diffuser has also been analysed using an algorithm suitable for equal or multiple numbers of rotor and diffuser blades. The multi-block, structured grid CFD code TASCflow which provides an approximate solution to the Reynolds-averaged Navier-Stokes equations was used as a basis and algorithm development was undertaken to provide the required capability of modelling the unsteady interactions of the impeller and the diffuser. The centrifugal compressor stage under investigation consists of 28 radial blades (of which 14 are splitter blades) in the impeller and 27 vanes in the diffuser. The presented results and analysis are for off-design flow conditions where experimental results were available for comparison. The results obtained for the steady-state model show a reasonable agreement with the measurements. In general the unsteady flow field obtained shows a reasonable agreement with experimental data and exhibits considerable differences when compared with the steady-state results.

Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 1: Validation

Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 1: Validation

Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 2: Comparison

Acomputational study is carried out to develop a fully implicit and time-accuratecomputational e uid dynamics code for the analysis of reactive e ow systems. Periodically oscillating shock-induced combustion around a blunt body in a stoichiometric hydrogen ‐air mixture is used as a validation problem of examining various numerical considerations. Euler equations and species conservation equations are used as the governing equations for the chemically reacting e ow. Spatial discretization of the governing equation is based on Roe’ s approximate Riemann solver with a MUSCL-type total variation diminishing scheme for higher-order spatial resolution. The secondorder-accuratetimeintegrationmethodisbasedonalower ‐uppersymmetricGauss ‐Seidelscheme,usingaNewton subiteration method and Steger ‐Warming e ux Jacobian splitting. As a e rst step of the validation procedure, simulations of experimental results were carried out to cone rm the reliability of the baseline method. In the next step, the general aspects of the baseline method were examined, including order of time integration, number of subiterations, and use of approximate e ux Jacobian splitting. Appropriateness of the grid system is also examined by using a grid ree nement study.

Computational fluid dynamics algorithms for unsteady shock-induced combustion. I - Validation

Computational fluid dynamics algorithms for unsteady shock-induced combustion. I - Validation

Computational fluid dynamics algorithms for unsteady shock-induced combustion. II - Comparison

Computational fluid dynamics algorithms for unsteady shock-induced combustion. II - Comparison

Finite elements for CFD—How does the theory compare?

SUMMARY The quest continues for accurate and efficient computational fluid dynamics (CFD) algorithms for convection-dominated flows. The boundary value ‘optimal’ Galerkin weak statement invariably requires manipulation to handle the disruptive character introduced by the discretized first-order convection term. An incredible variety of methodologies have been derived and examined to address this issue, in particular, seeking achievement of monotone discrete solutions in an efficient implementation. The UT CFD research group has participated in this search, leading to the development of consistent, encompassing theoretical statements exhibiting quality performance, including generalized Taylor series (Lax‐ Wendroff) methods, characteristic flux resolutions, subgrid embedded high-degree Lagrange bases and assembled stencil optimization for finite element weak statement implementations. For appropriate model problems, recent advances have led to accurate monotone methods with linear basis efficiency. This contribution highlights the theoretical developments and presents quantitative documentation of achieved high-quality solutions. Copyright © 1999 John Wiley & Sons, Ltd.

Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. A high fidelity computational fluid dynamics (CFD) algorithm modelling the Euler equations is used to calculate the aerodynamic properties of complex three-dimensional aircraft configurations. The design process is greatly accelerated through the use of both control theory and parallel computing. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented in parallel using a domain decomposition approach, an optimized communication schedule, and the Message Passing Interface (MPI) Standard for portability and efficiency. In our earlier studies, the serial implementation of this design method, was shown to be effective for the optimization of airfoils, wings, wing–bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In this work, our concern will be to extend the methodologies such that the combined capabilities of these new technologies can be used routinely and efficiently in an industrial design environment. The aerodynamic optimization of a supersonic transport configuration is presented as a demonstration test case of the capability. A particular difficulty of this test case is posed by the close coupling of the propulsion/airframe integration.

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

The Acoustic Analogy and the Prediction of the Noise of Rotating Blades

The acoustic analogy was introduced into acoustics by Lighthill in 1952 to understand and predict the noise generated by the jet of an aircraft turbojet engine. The idea behind the acoustic analogy is simple but powerful. The entire noise generation process is mathematically reduced to the study of wave propagation in a quiescent medium with the effect of flow replaced by quadrupole sources. In jet noise theory, Lighthill was able to obtain significant and useful qualitative results from the acoustic analogy. The acoustic analogy has influenced the theoretical and experimental research on jet noise since the early 1950s. This paper, however, focuses on another area in which the acoustic analogy has had a significant impact, namely, the prediction of the noise of rotating machinery. The governing equation for this problem was derived by Ffowcs Williams and Hawkings in 1969. This equation is a wave equation for perturbation density with three source terms, which have become known as thickness, loading, and the quadrupole source terms, respectively. The Ffowcs Williams–Hawkings (FW–H) equation has been used for the successful prediction of the noise of helicopter rotors, propellers, and fans. Several reasons account for the success and popularity of the acoustic analogy. First, the problems of acoustics and aerodynamics are separated. Second, because the FW–H equation is linear, powerful analytical methods from linear operator theory can be used to obtain closed-form solutions. Third, advances in digital computers and computational fluid dynamics algorithms have resulted in high-resolution near-field aerodynamic calculations that are suitable for noise prediction. We present some of the mathematical results for noise prediction based on the FW–H equation, including examples for helicopter rotors. In particular, we discuss the prediction of blade-vortex interaction noise and high-speed impulsive noise of helicopter rotors. For high-speed propellers, we briefly discuss the derivation of a singularity-free solution of the FW–H equation for a supersonic panel on a blade.

On some recent adventures into improved finite element CFD methods for convective transport

The quest continues for computational fluid dynamics (CFD) algorithms that are accurate and efficient for convection-dominated applications including shocks, travelling fronts and wall-layers. The boundary-value ‘optimal’ Galerkin weak statement invariably requires manipulation, either in the test space or in an augmented form for the conservation law system, to handle the disruptive character introduced by the discretized first-order convection term. An incredible variety of methodologies have been derived and examined to address this issue, in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation. The UTK CFD research group continues its search on examining the breadth of approaches leading to development of a consistent, encompassing theoretical statement exhibiting quality performance. Included herein are adventures into generalized Taylor series (Lax-Wendroff) methods, characteristic Euler flux resolutions, sub-grid embedded high-degree Lagrange bases with static condensation, and assembled-stencil Fourier analysis optimization for finite element weak statement implementations. For appropriate model problems, including steady convection-diffusion and pure unsteady convection, and benchmark Navier-Stokes definitions, recent advances have lead to candidate accurate monotone methods with linear basis efficiency. This contribution highlights the theoretical developments, and presents quantitative documentation of achievable high quality solutions.