2008

Q. Meng, J. Luitjens, M. Berzins.
**“A Comparison of Load Balancing Algorithms for AMR in Uintah,”** SCI Technical Report, No. UUSCI-2008-006, *University of Utah*, 2008.

R.P. Pawlowski, J.P. Simonis, H.F. Walker, J.N. Shadid.
**“Inexact Newton Dogleg Methods,”** In *SIAM Journal on Numerical Analysis*, Vol. 46, No. 4, pp. 2112--2132. 2008.

DOI: 10.1137/050632166

The dogleg method is a classical trust-region technique for globalizing Newton's method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton–Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton–GMRES dogleg method applied to benchmark CFD problems.

J.A. Schmidt.
**“Uintah Application Development,”** SCI Technical Report, No. UUSCI-2008-005, *University of Utah*, 2008.

M. Steffen, S. Curtis, R.M. Kirby, J.K. Ryan.
**“Investigation of Smoothness-Increasing Accuracy-Conserving Filters for Improving Streamline Integration Through Discontinuous Fields,”** In *IEEE Transactions on Visualization and Computer Graphics*, Vol. 14, No. 3, pp. 680--692. 2008.

M. Steffen, R.M. Kirby, M. Berzins.
**“Analysis and Reduction of Quadrature Errors in the Material Point Method (MPM),”** In *International Journal for Numerical Methods in Engineering*, Vol. 76, No. 6, pp. 922--948. 2008.

DOI: 10.1002/nme.2360

M. Steffen, P.C. Wallstedt, J.E. Guilkey, R.M. Kirby, M. Berzins.
**“Examination and Analysis of Implementation Choices within the Material Point Method (MPM),”** In *Computer Modeling in Engineering & Sciences*, Vol. 31, No. 2, pp. 107--127. 2008.

L.T. Tran, J. Kim, M. Berzins.
**“An Introduction to the Material Point Method using a Case Study from Gas Dynamics,”** In *Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics 2008. AIP Conference Proceedings*, Vol. 1048, Edited by T.E. Simos and G. Psihoyios and Ch. Tsitouras, pp. 26--29. 2008.

ISBN: 978-0-7354-0576-9

P.C. Wallstedt, J.E. Guilkey.
**“An Evaluation of Explicit Time Integration Schemes for use with the Generalized Interpolation Material Point Method,”** In *Journal of Computational Physics*, Vol. 227, No. 22, pp. 9628--9642. November, 2008.

DOI: 10.1016/j.jcp.2008.07.019

The stability and accuracy of the generalized interpolation material point (GIMP) Method is measured directly through carefully-formulated manufactured solutions over wide ranges of CFL numbers and mesh sizes. The manufactured solutions are described in detail. The accuracy and stability of several time integration schemes are compared via numerical experiments. The effect of various treatments of particle “size” are also considered. The hypothesis that GIMP is most accurate when particles remain contiguous and non-overlapping is confirmed by comparing manufactured solutions with and without this property.

**Keywords:** Material point method, Manufactured solutions, Time integration, MPM, GIMP, MMS, PIC

H.R. Zhang, E.G. Eddings, A.F. Sarofim.
**“A Journey From n-Heptane to Liquid Transportation Fuels. 1. The Role of the Allylic Radicals and Its Related Species in Aromatic Precursor Chemistry,”** In *Energy and Fuels*, No. 22, pp. 945--953. 2008.

The Utah normal heptane mechanism compiled from submechanisms in the literature was extended into a detailed normal decane combustion mechanism, which is a subset of the Utah surrogate mechanisms. Few species have greater impact on the concentrations of other species than the allyl radical CH_{2}CH=CH_{2} . Reactions involving the allyl radical and its isomers determine the concentration levels of all olefins, most higher unsaturated species, and benzene. To correctly predict the concentration of benzene, the reaction rates involving allyl-radical-related species need to be accurate and the concentration profiles of these species need to be satisfactory. Kinetic rates found in the literature are compared in the current work for various reference reactions that involve the allylic radicals. The improvements in numerical predictions of unsaturated species are achieved after a rigorous study in finding reliable reaction rates and kinetic correlations between various species. Some of these rates are adopted as the generic rates that have been used in the Utah surrogate mechanisms in previous studies. The modified mechanism is able to predict the concentration profiles of unsaturated species in *n*-decane and *n*-heptane flames with good numerical accuracy. The concentrations of these species are closely related to those of various allylic radicals, and reliable kinetics of allylic reactions are critical in predicting the concentrations of benzene and higher aromatics.

H.R. Zhang, E.G. Eddings, A.F. Sarofim.
**“Pollutant Emissions from Gasoline Combustion: 1. Dependence on Fuel Structural Functionalities,”** In *Environmental Science and Technology*, Vol. 42, No. 15, pp. 5615--5621. June, 2008.

DOI: 10.1021/es702536e

To study the formation of air pollutants and soot precursors (e.g., acetylene, 1,3-butadiene, benzene, and higher aromatics) from aliphatic and aromatic fractions of gasoline fuels, the Utah Surrogate Mechanisms is extended to include submechanisms of gasoline surrogate compounds using a set of mechanism generation techniques. The mechanism yields very good predictions of species concentrations in premixed flames of *n*-heptane, isooctane, benzene, cyclohexane, olefins, oxygenates, and gasoline using a 23-component surrogate formulation. The 1,3-butadiene emission comes mainly from minor fuel fractions of olefins and cyclohexane. The benzene formation potential of gasoline components shows the following trends as functions of (i) chemical class: *n*-paraffins isoparaffns olefins nphthalnes alkylbenzees cycloparaffis toluene; (ii)carbon number: *n*-butane < *n*-pentane < *n*-hexane; and (iii) branching: *n*-hexane ne 2,4-trimethylpentane utane. In contrast, fuel structure is not the main factor in determining acetylene formation. Therefore, matching the benzene formation potential of the surrogate fuel to that produced by the real fuel should have priority when selecting candidate surrogate components for combustion simulations.

2007

B. Banerjee.
**“The Mechanical Threshold Stress Model for Various Tempers of AISI 4340 Steel,”** In *International Journal of Solids and Structures*, Vol. 44, No. 3-4, pp. 834--859. February, 2007.

DOI: 10.1016/j.ijsolstr.2006.05.022

Numerical simulations of high strain rate and high temperature deformation of pure metals and alloys require realistic plastic constitutive models. Empirical models include the widely used Johnson-Cook model and the semi-empirical Steinberg-Cochran-Guinan-Lund model. Physically based models such as the Zerilli-Armstrong model, the Mechanical Threshold Stress model, and the Preston-Tonks–Wallace model are also coming into wide use. In this paper, we determine the Mechanical Threshold Stress model parameters for various tempers of AISI 4340 steel using experimental data from the open literature. We also compare stress–strain curves and Taylor impact test profiles predicted by the Mechanical Threshold Stress model with those from the Johnson-Cook model for 4340 steel. Relevant temperature- and pressure-dependent shear modulus models, melting temperature models, a specific heat model, and an equation of state for 4340 steel are discussed and their parameters are presented.

C. Duncan, R. Scherer, J. Guilkey, T. Harman.
**“Simulations of Vocal Fold Movement and Aerodynamics Using the Uintah Computational Framework,”** In *Journal of the Acoustical Society of America*, Vol. 121, No. 5, pp. 3201-3202. 2007.

DOI: 10.1121/1.4782473

This study applies a tightly coupled fluid‐structure interaction algorithm to the modeling of phonation. The Uintah Computational Framework models vocal fold material using the Material Point Method (MPM), which permits arbitrarily large material displacements and multiple materials characterizing the vocal fold properties. The air is modeled using a compressible Navier‐Stokes solver, the Implicit Continuous‐fluid Eulerian (ICE) method developed at Los Alamos National Laboratory by B. A. Kashiwa. The MPM and ICE methods are coupled together to generate a unique simulation tool. Preliminary simulations are shown of 2‐D model vocal folds interacting with prescribed transglottal pressures between 100 Pa and 800 Pa illustrating the intrinsic coupling between the vocal folds and the air. Results are presented showing how the new simulation scheme characterizes the materials and how the aerodynamics that results displays the essential characteristics of glottal flow. The next steps of incorporating three‐dimensionality and acoustics will be discussed. The present simulations set the stage for a realistic computational glottis and for eventual modeling of the effects of vocal fold pathologies on the acoustical output. [Work supported at Bowling Green State University in part by the National Institutes of Health and at the University of Utah by the Department of Energy.]

J.E. Guilkey, T.B. Harman, B. Banerjee.
**“An Eulerian-Lagrangian Approach for Simulating Explosions of Energetic Devices,”** In *Computers and Structures*, Vol. 85, No. 11-14, pp. 660--674. June-July, 2007.

DOI: 10.1016/j.compstruc.2007.01.031

An approach for the simulation of explosions of "energetic devices" is described. In this context, an energetic device is a metal container filled with a high explosive (HE). Examples include bombs, mines, rocket motors or containers used in storage and transport of HE material. Explosions may occur due to detonation or deflagration of the HE material, with initiation resulting from either mechanical or thermal input. This approach is applicable to a wide range of fluid–structure interaction scenarios, the application to energetic devices is chosen because it demonstrates the full capability of this methodology.

Simulations of this type are characterized by a number of interesting and challenging behaviors. These include the transformation of the solid HE into highly pressurized gaseous products that initially occupy regions which formerly contained only solid material. This rapid pressurization of the container leads to large deformations at high strain rates and eventual case rupture. Once the container breaks apart, the highly pressurized product gas that escapes the failing container generates shock waves that propagate through the initially quiescent surrounding fluid.

The approach, which uses a finite-volume, multi-material compressible CFD formulation, within which solid materials are represented using a particle method known as the Material Point Method, is described, including certain of the sub-grid models required to close the governing equations. Results are first presented for "rate stick" and "cylinder test" scenarios, each of which involves detonating unconfined and confined HE material, respectively. Experimental data are available for these configurations and as such they serve as validation tests. Finally, results from an unvalidated "fast cookoff" simulation in which the HE is initiated by thermal input, which causes deflagration, are shown.

J. Luitjens, B. Worthen, M. Berzins, T.C. Henderson.
**“Scalable Parallel AMR for the Uintah Multiphysics Code,”** In *Petascale Computing Algorithms and Applications*, Edited by D. Bader, Chapman and Hall/CRC, 2007.

N.D. Marsh, I. Preciado, E.G. Eddings, A.F. Sarofim, A.B. Palotas, J.D. Robertson.
**“Evaluation of Organometallic Fuel Additives for Soot Suppression,”** In *Combustion Science and Technology*, Vol. 179, No. 5, pp. 987--1001. 2007.

DOI: 10.1080/00102200600862497

In this work, we investigate the utility of the smoke lamp for evaluating the soot-reducing potential of additives, by comparing it to a more complex liquid-fed laminar diffusion flame. The additives, ferrocene (bis(cyclopentadienyl) iron-Fe(C_{5}H_{5})_{2}), ruthenocene (bis(cyclopentadienyl)ruthenium-Ru(C_{5}H_{5})_{2}), iron naphthenate (a 12% iron salt of naphthenic acid, which is a mixture of fatty carboxylic acids, some of which may include a cyclopentane ring), and MMT (Methylcyclopentadienyl manganese tricarbonyl-CH_{3}C_{5}H_{4}Mn(CO)_{3}) are evaluated at various concentrations in the jet fuel JP-8. Although the smoke lamp is a simple, inexpensive, and widely-available test for evaluating the sooting potential of liquid fuels, it does not provide an effective measure of soot suppression by metal-containing additives. The drop-tube reactor more accurately captures the physical conditions and processes—droplet vaporization, ignition, and rich vs. lean operation—typically found in more complex systems. We find in the smoke lamp that ferrocene, and to a lesser degree ruthenocene, are effective soot suppressors when used in JP-8, and that their effectiveness increases with increasing concentration. In the smoke lamp, MMT and iron naphthenate have minimal effect. On the other hand, in the drop-tube reactor, all four additives are quite effective, especially at fuel lean conditions, where soot suppression reaches 90–95%. Under fuel-rich conditions, where in some cases the additives elevate the yield of soot aerosol slightly, we find a significant increase in the production of the soluble organic fraction of the aerosol, i.e., tar. In order to understand why the smoke lamp sometimes fails to indicate a soot suppressing potential (i.e., from MMT and iron naphthenate), soot samples were collected from a wick lamp burning ferrocene and iron naphthenate additives in JP-8. These samples, as well as several from the drop-tube reactor, were analyzed by X-Ray Fluorescence (XRF) in order to determine their metal content, and we find that the soot aerosol produced by the wick lamp using ferrocene-containing fuel had roughly 30 times the iron content of the soot aerosol produced by the wick lamp using iron-naphthenate-containing fuel. This difference in metal content is not found in samples produced in the drop-tube reactor. We conclude that the poor performance of iron naphthenate in the smoke lamp is likely the result poor vaporization of the additive from the wick, a consequence of its high molecular weight (average 465).

J. Van Rij, T. Harman, T. Ameel.
**“The effect of creep flow on two-dimensional isoflux microchannels,”** In *International Journal of Thermal Sciences*, Vol. 46, No. 11, pp. 1095--1103. November, 2007.

DOI: 10.1016/j.ijthermalsci.2007.04.007

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.

**Keywords:** Microchannel, Slip, Creep, Viscous dissipation, Nusselt number, Poiseuille number

A. Santamaria, E.G. Eddings, F. Mondragon.
**“Effect of Ethanol on the Chemical Structure of the Soot Extractable Material of an Ethylene Inverse Diffusion Flame,”** In *Combustion and Flame*, Vol. 151, No. 1-2, pp. 235--244. October, 2007.

DOI: 10.1016/j.combustflame.2007.06.004

The effect of fuel-side ethanol addition on the chemical structure of the soot extractable material generated in an ethylene inverse diffusion flame was evaluated by means of average structural parameters. The results indicate that the ethanol effect on the aromatic components was more pronounced, with an increase of about 40% in the average number of aromatic fused rings (R a) as compared to the results of a neat flame. This observation also helps explain the low percentage of chloroform-extractable material in the soot samples obtained from the flame with ethanol addition. In contrast, the aliphatic component of the extractable material did not demonstrate significant changes with ethanol addition.

A. Santamaria, F. Mondragon, W. Quinones, E.G. Eddings, A.F. Sarofim.
**“Average Structural Analysis of the Extractable Material of Young Soot Gathered in an Ethylene Inverse Diffusion Flame,”** In *FUEL*, Vol. 86, No. 12-13, pp. 1908--1917. August, 2007.

DOI: 10.1016/j.fuel.2006.12.002

Conventional analytical methods such as ^{1}H NMR, vapor pressure osmometry (VPO) and elemental analysis were used to characterize the soot precursor material represented by the chloroform extractable fractions of the young soot gathered at different heights of an ethylene inverse diffusion flame in terms of average structural parameters. The results indicate that the soot soluble fraction obtained at a 6 mm height has a relatively large molecular weight and has long aliphatic chains which later disappear with an increase in height above the burner base, especially in the region where the temperature is high (1200 K). This behavior is also accompanied by an increase in the aromaticity (*f _{a}*) of the samples.

P.C. Wallstedt, J.E. Guilkey.
**“Improved Velocity Projection for the Material Point Method,”** Subtitled **“Computer Modeling in Engineering and Sciences,”** Vol. 19, No. 3, pp. 223--232. 2007.

DOI: 10.3970/cmes.2007.019.223

The standard velocity projection scheme for the Material Point Method (MPM) and a typical form of the GIMP Method are examined. It is demonstrated that the fidelity of information transfer from a particle representation to the computational grid is strongly dependent on particle density and location. In addition, use of non-uniform grids and even non-uniform particle sizes are shown to introduce error. An enhancement to the projection operation is developed which makes use of already available velocity gradient information. This enhancement facilitates exact projection of linear functions and reduces the dependence of projection accuracy on particle location and density for non-linear functions. The efficacy of this formulation for reducing error is demonstrated in solid mechanics simulations in one and two dimensions.

H.R. Zhang, E.G. Eddings, A.F. Sarofim.
**“Combustion Reactions of Paraffin Components in Liquid Transportation Fuels Using Generic Rates,”** In *Combustion Science and Technology*, Vol. 179, No. 1-2, pp. 61--89. 2007.

DOI: 10.1080/00102200600805975

The approach of mechanism generation is the accepted one of assigning generic rates to reactions in the same class. The procedure has been successfully applied to higher paraffins that include detailed sub-models of n-hexane, cyclohexane, n-heptane, n-decane, n-dodecane, and n-hexadecane and semi-detailed sub-models of iso-octane and methyl cyclohexane, in addition to reactions of aromatic formation and oxidation. Comparison between predictions and experimental data were found to be satisfactory for n-heptane, iso-octane, n-decane and gasoline premixed flames. The mechanism was also able to reproduce the measured concentrations for a n-hexadecane experiment in a jet stirred reactor. The numerical accuracy in predicting the flame structures of soot precursors, including acetylene and benzene, is one of the major foci of this study. The predicted maximum concentrations of acetylene and benzene are within 20% for most flames in this study.