Multi-dimensional Fluid Dynamics Research Articles

On the existence of energy‐variational solutions in the context of multidimensional incompressible fluid dynamics

We define the concept of energy‐variational solutions for the Navier–Stokes and Euler equations and prove their existence in any space dimension. It is shown that the concept of energy‐variational solutions enjoys several desirable properties. Energy‐variational solutions are not only known to exist and coincide with local strong solutions, but the operator, mapping the data to the set of energy‐variational solutions, is additionally continuous and all restrictions and all concatenations of energy‐variational solutions are energy‐variational solutions again. Finally, different selection criteria for these solutions are discussed.

A CFD-sectional algorithm for population balance equation coupled with multi-dimensional flow dynamics

A novel CFD-sectional algorithm is developed to address the challenges in the existing sectional simulations coupled with multi-dimensional fluid dynamics, including solution of complex sectional coefficients, serious computational burden for lots of coupled partial differential equations, and nonlinear source terms. The sectional coefficients are specified by a numerical quadrature with adaptive integration limits, which proves to be computationally efficient and accurate. The inter-equation coupling is treated by hybrid-segregated procedures and the source term is linearized by the operator splitting method. The CFD-sectional algorithm is validated against a self-preserving solution of particles undergoing Brownian coagulation. The acoustic agglomeration in a standing wave is simulated as a representative case. It has been demonstrated that the predictions regarding the particle size distribution and agglomeration process agree well with the experimental data, which verifies the capability of the developed CFD-sectional algorithm in simulating the spatially inhomogeneous population balance equation coupled with multi-dimensional flows.

Experimental database of two-phase natural circulation with local measurements

A new database of two-phase natural circulation with a vertical annulus heated and riser section is developed by the Multiphase Thermo-fluid Dynamics Laboratory (MTDL) at the University of Illinois at Urbana-Champaign, focusing on such two-phase phenomena as boiling, condensing, and flashing under natural circulation in a vertical section. In addition to flow parameters, local two-phase measurements such as void fraction, interfacial area concentration, gas velocity, and Sauter mean diameter are measured at various axial locations on the annular test section. Furthermore, the area-averaged and void-weighted measurements are calculated to provide an overview on the evolution of two-phase parameters along the test section. The dataset is valuable for the validation of one-dimensional system codes as well as multi-dimensional fluid dynamics codes. Several representative cases are presented in this work to discuss the effect of flow parameters on the formation and evolution of the natural circulation in the flow loop.

Effects of reformed exhaust gas recirculation on the HC and CO emissions of a spark-ignition engine fueled with LNG

Reformed exhaust gas recirculation (REGR), which can generate onboard hydrogen-rich gas (i.e., the reformate including H2, CO, unreformed hydrocarbon, etc.) via catalytic reforming of fuel and engine exhaust gas, is an attractive way to improve the performance and emissions characteristics of the engine fueled with liquefied natural gas (i.e., NG engine). However, the leakage during the valve overlap period and incomplete burning of the added reformate may lead to extra HC and CO emissions from the engine with REGR. In the present study, a multi-dimensional computation fluid dynamics model coupled with a detailed chemical kinetic mechanism was developed to investigate the effects of the ratio of reformate addition (Rref) and exhaust valve closed (EVC) timing on the total emissions characteristics as well as the sources of HC and CO emissions from the engine. The emissions from the combustion and the leaking were included to calculate the total emissions. Moreover, the unburned CO from the added reformate was distinguished from the total CO emissions by adding marked-species. Results show that the unburned CH4 in the cylinder is the main component of the total CH4 emissions. Due to the increase of the concentrations of OH, O and H radicals during the combustion process, the oxidization of CH4 is promoted with the increase of Rref at high load, and therefore the total CH4 emissions decrease. However, the total CO emissions increase with the increase of Rref, and it is demonstrated that the unburned CO from the added reformate increases and turns to be the main sources of the total CO emissions. At Rref of 10%, the total CH4 and CO emissions firstly remain nearly constant and then increase dramatically with the delay of EVC timing. Therefore, low concentration of CO in the reformate and short valve duration are recommended to achieve low HC and CO emissions for the NG engine with REGR.

Faster solvers for large kinetic mechanisms using adaptive preconditioners

The adaptive preconditioners developed in this paper substantially reduce the computational cost of integrating large kinetic mechanisms using implicit ordinary differential equation (ODE) solvers. For a well-stirred reactor, the speedup of the new method is an order of magnitude faster than recent approaches based on direct, sparse linear system solvers. Moreover, the new method is up to three orders of magnitude faster than traditional implementations of the ODE solver where the Jacobian information is generated automatically via finite differences, and the factorization relies on standard, dense matrix operations. Unlike mechanism reduction strategies, the adaptive preconditioners do not alter the underlying system of differential equations. Consequently, the new method achieves its performance gains without any loss of accuracy to within the local error controlled by the ODE solver. Such speedup allows higher fidelity mechanism chemistry to be coupled with multi-dimensional fluid dynamics simulations.

Kinetic Simulation of Combustion Process in the Combustor of the Aero-Engine

The use of detailed chemical reaction mechanisms of aviation fuels is still very limited in analyzing the combustion process concerning complex multidimensional fluid dynamics issues. In this work, a reduced chemical kinetic mechanism containing 210 elemental reactions (including 92 reversible reactions and 26 irreversible reactions) and 50 species was introduced and studied in the kinetic simulation of the ignition and combustion of n-decane (n-C10H22) at various combustion regimes. Moreover, it was validated with the experimental results obtained from both premixed flame of a flat-flame burner and n-C10H22 shock-tube ignition. The results show that the calculated ignition delay time of fuel n-C10H22 in the shock-tube under typical conditions viz. a pressure of 12 or 50 bar and corresponding equivalence ratio at 1.0 or 2.0, as well as the calculated mole fractions of the main reactants and products of fuel n-C10H22 in the premixed combustion process, agree very well with the experimental data. The combustion processes in the single flame tube of a tube annular combustor were simulated through coupling this reduced reaction mechanism of surrogate fuel n-C10H22 and one step reaction mechanism of surrogate fuel C12H23 into the computational fluid dynamics (CFD) software, and this combustion process was also experimentally studied. It is found that the reduced reaction mechanism exhibits clear advantages in simulating the combustion processes and certain species formation in the single flame tube over the one step reaction mechanism. In particular, the temperature radial distribution at the outlet of the single flame tube computed by using reduced reaction mechanism of surrogate fuel n-C10H22 is found to be more reasonable and agreed better with the experimental data than that computed by one step reaction mechanism of surrogate fuel C12H23.

Effects of bathymetric lidar errors on flow properties predicted with a multi-dimensional hydraulic model

New remote sensing technologies and improved computer performance now allow numerical flow modeling over large stream domains. However, there has been limited testing of whether channel topography can be remotely mapped with accuracy necessary for such modeling. We assessed the ability of the Experimental Advanced Airborne Research Lidar, to support a multi-dimensional fluid dynamics model of a small mountain stream. Random point elevation errors were introduced into the lidar point cloud, and predictions of water surface elevation, velocity, bed shear stress, and bed mobility were compared to those made without the point errors. We also compared flow model predictions using the lidar bathymetry with those made using a total station channel field survey. Lidar errors caused < 1 cm changes in the modeled water surface elevations. Effects of the point errors on other flow characteristics varied with both the magnitude of error and the local spatial density of lidar data. Shear stress errors were greatest where flow was naturally shallow and fast, and lidar errors caused the greatest changes in flow cross-sectional area. The majority of the stress errors were less than ± 5 Pa. At near bankfull flow, the predicted mobility state of the median grain size changed over ≤ 1.3% of the model domain as a result of lidar elevation errors and ≤ 3% changed mobility in the comparison of lidar and ground-surveyed topography. In this riverscape, results suggest that an airborne bathymetric lidar can map channel topography with sufficient accuracy to support a numerical flow model.

A new reduced reaction mechanism of a surrogate fuel for kerosene

AbstractThe introduction of detailed chemical reaction mechanisms for aviation fuels into complex multidimensional fluid dynamics problems is not practical at the present time. Simplified reaction mechanisms that have been thoroughly evaluated must be developed to address specific issues arising in realistic combustor configurations. A reduced chemical kinetic mechanism features 210 elemental reactions (including 92 reversible reactions and 26 irreversible reactions) and 50 species for the ignition and combustion of n‐decane was compiled and validated for a wide range of combustion regimes. Validations were performed using experimental measurements on a premixed flame of Jet‐A1, O2 and N2, stabilised at 1 atm on a flat‐flame burner, as well as from n‐decane shock‐tube ignition experiments. Numerical calculations were performed using this reduced mechanism and the detailed mechanism respectively for n‐decane surrogate fuel. The calculated values of ignition delay times at pressures of 12, 50 bar and equivalence ratio is 1.0, 2.0, respectively and the main reactants and main products mole fractions agree well with experimental data. The present study shows that this reduced mechanism for the n‐decane surrogate can be employed to predict premixed combustion of kerosene. © 2012 Canadian Society for Chemical Engineering

Development of a Multi-Dimensional Fluid Dynamics Code and Its Benchmarking for the Subcooled Boiling Flow

In a two-phase flow analysis, the interfacial area concentration (IAC) is a dominant factor governing the interfacial transfer of the momentum or energy. For a dynamic analysis with the implementation of IAC transport equation, a multi-dimensional computational fluid dynamics code was developed. The code is based on the two-fluid model and the simplified marker and cell algorithm by using the finite volume method, where the conventional approach for a single-phase flow has been modified in order to consider the term for a phase change. As benchmark problems of a single-phase flow and two-phase flow, a natural convection in a rectangular cavity and a subcooled boiling in an annulus channel were selected, respectively. In the calculation for the single-phase flow, the developed code predicted a reasonable behavior for a buoyancy-driven flow depending on the Rayleigh number. In the analysis of the subcooled boiling, the calculation results showed the robustness of code for the analysis of the boiling phenomena and void propagation, where they represented limitations of the one-dimensional IAC model. To conduct a multi-dimensional analysis for the two-phase flow, it is confirmed that the implementation of an IAC transport equation into the code is essential.

Low-Mass Extremely Metal-Poor Stellar Models: Yields, Uncertainties and the Galactic Halo Stars

AbstractWe have calculated a set of low-mass (0.85 M⊙ ≤ M ≤ 3.0 M⊙) zero metallicity and extremely metal-poor (−6.5 ≤ [Fe/H] ≤ −3.0) stellar models, including nucleosynthetic yields for 74 species. As far as we are aware these are the first detailed yields in the mass and metallicity range considered. Due to the difficulty in modelling such stars the yields naturally contain numerous uncertainties, and thus present interesting challenges for future stellar modelling. We briefly present some results in the context of the Galactic Halo star observations, and also discuss qualitatively some of the uncertainties in the modelling. We conclude by suggesting that much work is still necessary in this research area. For example, multidimensional fluid dynamics models are needed to simulate the violent proton ingestion events that occur during the core He flash and early TPAGB, observations and theory of mass loss at low metallicities are needed, the effects of reaction rate uncertainties need to be quantified, and low temperature opacities variable in carbon (and nitrogen) need to be included in the models.

Experimental and Analytical Examination of the Development of Inhomogeneities and Autoignition During Rapid Compression of Hydrogen-Oxygen-Argon Mixtures

The reliable prediction of the processes leading to autoignition during the rapid compression of an initially homogeneous mixture of fuel and air requires the coupled modeling of multidimensional fluid dynamics and heat transfer together with a sufficiently detailed description of the chemical kinetics of the oxidation reactions. To satisfy fully such requirements tends at present to be unmanageable. The paper describes an improvised approach that combines multidimensional fluid dynamics modeling (CFD KIVA-3) with derived variable effective global chemical kinetic data. These were generated through a fitting procedure of the corresponding results obtained while using a detailed chemical kinetic scheme; albeit with uniform properties, at constant volume and an initial state similar to that existing during the ignition delay. It is shown while using such an approach that spatially nonuniform properties develop rapidly within the initially homogeneous charge due to piston motion, heat transfer and any preignition energy release activity. This leads autoignition to take place first within the hottest region and a reaction front progresses at a finite rate to consume the rest of the mixture. The present contribution examines the compression ignition of hydrogen-oxygen mixtures in the presence of argon as a diluent. Validation of the predicted results is made using a range of corresponding experimental values obtained in a single-shot pneumatically driven rapid compression apparatus. It is to be shown that the simulation which indicates the build up of temperature gradients during the compression stroke, predicts earlier autoignition than that obtained with a single-zone simulation. Good agreement between predicted and experimental results is achieved, especially for lean and stoichiometric mixtures under high compression ratio conditions. The CFD-based simulation results are found to be closer to the corresponding experimental results than those obtained with an assumed reactive system of uniform properties and using detailed reaction kinetics.

An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds

A new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems. The method uses a finite difference mesh with vertices that may be moved with the fluid (Lagrangian), be held fixed (Eulerian), or be moved in any other prescribed manner, as in the Arbitrary Lagrangian–Eulerian (ALE) technique. In addition, it employs an implicit formulation similar to that of the Implicit Continuous-fluid Eulerian (ICE) technique, making it applicable to flows at all speeds.This paper describes the basic methodology, presents finite difference approximations, and discusses such matters as stability, accuracy, and zoning. In addition, illustrations are included from a number of representative calculations.

A singular perturbation model of fluid dynamics in the vestibular semicircular canal and ampulla

A matched asymptotic analysis is presented that describes the mechanical response of the vestibular semicircular canals to rotation of the head and includes the fluid–structure interaction which takes place within the enlarged ampullary region of the duct. New theoretical results detail the velocity field in a fluid boundary layer surrounding the cupula. The governing equations were linearized for small perturbations in fluid displacement from the prescribed motion of the head and reduced asymptotically by exploiting the slender geometry of the duct. The results include the pressure drop around the three-dimensional endolymphatic duct and through the transitional boundary layers within the ampulla. Results implicitly include the deflected shape of the cupular partition and provide an expression for the dynamic boundary condition acting on the two surfaces of the cupula. In this sense, the analysis reduces the three-dimensional fluid dynamics of the endolymph to a relatively simple boundary condition acting on the surfaces of the cupula. For illustrative purposes we present specific results modelling the cupula as a simple viscoelastic membrane. New results show that the multi-dimensional fluid dynamics within the enlarged ampulla has a significant influence on the pointwise deflection of the cupula near the crista. The spatially averaged displacement of the cupula is shown to agree with previous macromechanical descriptions of endolymph flow and pressure that ignore the fluid–structure interaction at the cupula. As an example, the model is applied to the geometry of the horizontal semicircular canal of the toadfish, Opsanus tau, and results for the deflection of the cupula are compared to individual semicircular canal afferent responses previously reported by Boyle &amp; Highstein (1990). The cupular-shear-angle gain, defined by the angular slope of the cupula at the crista divided by the angular velocity of the head, is relatively constant at frequencies from 0.01 Hz up to 1 Hz. Over this same range, the phase of the cupular shear angle aligns with the angular velocity of the head. Near 10 Hz, the shear-angle gain increases slightly and the phase shows a lead of as much a 30°. Results are sensitive to the cupular stiffness and viscosity. Comparing results to the afferent responses represented within the VIIIth nerve provides additional theoretical evidence that the macromechanical displacement of the cupula accounts for the behaviour of only a subset of afferent fibres.

The turn function and vorticity method for numerical fluid dynamics

A numerical method is presented that solves in a consistent fashion, conservation equations for both vorticity and linear momentum in multidimensional fluid-dynamics calculations. The equations are given in both two- and three-dimensional Cartesian geometry, and it is shown how the method can be easily implemented in a two-dimensional Eulerian fluid-dynamics code. The results of example calculations, which were performed with and without the new method, show the large errors that can arise when the vorticity equation is not solved in compressible flow calculations.

Tensor viscosity method for convection in numerical fluid dynamics

A new method, called the tensor viscosity method, is described for differencing the convective terms in multidimensional numerical fluid dynamics. The method is the proper generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping. It is a single-step method that is distinguished by simplicity and ease of implementation, even in the case of an arbitrary non-rectangular mesh. It should therefore be useful in finite-element as well as finite-difference formulations.

An arbitrary Lagrangian-Eulerian computing method for all flow speeds

A new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems. The method uses a finite difference mesh with vertices that may be moved with the fluid (Lagrangian), be held fixed (Eulerian), or be moved in any other prescribed manner, as in the Arbitrary-Lagrangian-Eulerian (ALE) technique. In addition, it employs an implicit formulation similar to that of the Implicit Continuous-Fluid Eulerian (ICE) technique, making it applicable to flows at all speeds. This paper describes the basic methodology, presents finite difference approximations, and discusses such matters as stability, accuracy, and zoning. In addition, illustrations are included from a number of representative calculations.

Generalized aerodynamic forces on an oscillating cylindrical shell -Subsonic and supersonic flow.

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