## Uintah and Related C-SAFE Publications

2005

S.G. Bardenhagen, A.D. Brydon, J.E. Guilkey.
**“Insight into the Physics of Foam Densification via Numerical Solution,”** In *Journal of Mechanics and Physics of Solids*, Vol. 53, No. 3, pp. 597--617. March, 2005.

DOI: 10.1016/j.jmps.2004.09.003

Foamed materials are increasingly finding application in engineering systems on account of their unique properties. The basic mechanics which gives rise to these properties is well established, they are the result of collapsing the foam microstructure. Despite a basic understanding, the relationship between the details of foam microstructure and foam bulk response is generally unknown. With continued advances in computational power, many researchers have turned to numerical simulation to gain insight into the relationship between foam microstructure and bulk properties. However, numerical simulation of foam microscale deformation is a very challenging computational task and, to date, simulations over the full range of bulk deformations in which these materials operate have not been reported. Here a particle technique is demonstrated to be well-suited for this computational challenge, permitting simulation of the compression of foam microstructures to full densification. Computations on idealized foam microstructures are in agreement with engineering guidelines and various experimental results. Dependencies on degree of microstructure regularity and material properties are demonstrated. A surprising amount of porosity is found in fully-densified foams. The presence of residual porosity can strongly influence dynamic material response and hence needs to be accounted for in bulk (average) constitutive models of these materials.

O. Borodin, D. Bedrov, G.D. Smith, J.A. Nairn, S. Bardenhagen.
**“Multiscale Modeling of Viscoelastic Properties of Polymer Nanocomposites,”** In *Journal of Polymer Science*, Vol. 43, No. 8, pp. 1005--1013. April, 2005.

DOI: 10.1002/polb.20390

A methodology for simple multiscale modeling of mechanical properties of polymer nanocomposites has been developed. This methodology consists of three steps: (1) obtaining from molecular dynamics simulations the viscoelastic properties of the bulklike polymer and approximating the position-dependent shear modulus of the interfacial polymer on the basis of the polymer-bead mean-square displacements as a function of the distance from the nanoparticle surface, (2) using bulk- and interfacial-polymer properties obtained from molecular dynamics simulations and performing stress–relaxation simulations of the nanocomposites with material-point-method simulations to extract the nanocomposite viscoelastic properties, and (3) performing direct validation of the average composite viscoelastic properties obtained from material-point-method simulations with those obtained from the molecular dynamics simulations of the nanocomposites.

J.A. Cooke, M. Bellucci, M.D. Smooke, A. Gomez, A. Violi, T. Faravelli, E. Ranzi.
**“Computational and Experimental Study of JP-8, a Surrogate, and its Components in Counterflow Diffusion Flames,”** In *Proceedings of the Combustion Institute*, Vol. 30, No. 1, pp. 439--446. January, 2005.

DOI: 10.1016/j.proci.2004.08.046

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component *n-*dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.

H. Davande, O. Borodin, G.D. Smith, T.D. Sewell.
**“Quantum Chemistry-Based Force Field for Simulations of Energetic Dinitro Compounds,”** In *Journal of Energetic Materials*, Vol. 23, No. 4, pp. 205--237. 2005.

DOI: 10.1080/07370650591006885

A quantum chemistry–based force field for molecular dynamics simulations of energetic dinitro compounds has been developed, based on intermolecular binding energies, molecular geometries, molecular electrostatic potentials, and conformational energies obtained from quantum chemistry calculations on model compounds. Nonbonded parameters were determined by fitting experimental densities and heats of vaporizations of model compounds. Torsional parameters were parameterized to reproduce accurately the relative conformational energy minima and barriers in 2,2-dinitropropane, di-methoxy di-methyl ether, 2,2-dinitro-3-methoxypropane, and bis(2,2-dinitropropyl)formal. Molecular dynamics simulations using the developed force field accurately reproduce thermodynamic and transport properties of 1,1-dinitroethane, 2,2-dinitropropane, and a eutectic mixture of bis(2,2-dinitropropyl)formal and bis(2,2-dinitropropyl)acetal.

D.E. DeMarle, C.P. Gribble, S. Boulos, S.G. Parker.
**“Memory Sharing for Interactive Ray Tracing on Clusters,”** In *Parallel Computing*, Vol. 31, No. 2, pp. 221--242. 2005.

E.G. Eddings, S. Yan, W. Ciro, A.F. Sarofim.
**“Formulation of a Surrogate for the Simulation of Jet Fuel Pool Fires,”** In *Combustion Science and Technology*, Vol. 177, No. 4, pp. 715--739. 2005.

DOI: 10.1080/00102200590917248

The simulation of pool fires involving complex hydrocarbon fuels requires the development of a simplified surrogate with a limited number of compounds having known oxidation mechanisms. A series of six-component surrogates was developed for the simulation of JP-8 pool fires, and experiments were carried out with a 30-cm-diameter pool fire to allow comparison of the surrogate fuel behavior to that of the jet fuel. The surrogate was shown to simulate the burning rate, radiant heat flux, and sooting tendency of jet fuel under steady-state pool fire conditions. This study also illustrated the transient nature of batch pool fire experiments and highlighted the difficulties associated with formulating an appropriate surrogate to mimic jet fuel behavior over the lifetime of a batch pool fire. These difficulties were shown to arise from fuel compositional changes, with preferential destruction of lighter components and accumulation of heavier components during the course of the fire.

P. Fife, J. Klewicki, P.A. McMurtry, T. Wei.
**“Multiscaling in the Presence of Indeterminacy: Wall-Induced Turbulence,”** In *Multiscale Modeling and Simulation*, Vol. 4, No. 3, pp. 936--959. 2005.

DOI: 10.1137/040611173

This paper provides a multiscale analytical study of steady incompressible turbulent flow through a channel of either Couette or pressure-driven Poiseuille type. Mathematically, the paper’s two most novel features are that (1) the analysis begins with an underdetermined singular perturbation problem, namely the Reynolds averaged mean momentum balance equation, and (2) it leads to the existence of an infinite number of length scales. (These two features are probably linked, but the linkage will not be pursued.) The paper develops a credible assumption of a mathematical nature which, when added to the initial underdetermined problem, results in a knowledge of almost the complete layer (scaling) structure of the mean velocity and Reynolds stress profiles. This structure in turn provides a lot of other important information about those profiles. The possibility of almost-logarithmic sections of the mean velocity profile is given special attention. The sense in which the length scales are asymptotically proportional to the distance from the wall is determined. Most traditional theoretical analyses of these wall-bounded flows are based ultimately on either the classical overlap hypothesis, mixing length concepts, or similarity arguments. The present paper avoids those approaches and their attendant assumptions. Empirical data are also not used, except that the Reynolds stress takes on positive values. Instead, reasonable criteria are proposed for recognizing scaling layers in the flow, and they are then used to determine the scaling structure and much more information.

S. Izvekov, A. Violi, G.A. Voth.
**“Systematic Coarse-Graining of Nanoparticle Interactions in Molecular Dynamics Simulation,”** In *Journal of Physical Chemistry, B*, Vol. 109, No. 36, pp. 17019--17024. August, 2005.

DOI: 10.1021/jp0530496

A recently developed multiscale coarse-graining procedure [Izvekov, S.; Voth, G. A. *J. Phys. Chem. B***2005**, *109*, 2469] is extended to derive coarse-grained models for nanoparticles. The methodology is applied to C_{60} and to carbonaceous nanoparticles produced in combustion environments. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom MD simulations. The CG models are shown to reproduce accurately the structural properties of the nanoparticle systems studied, while allowing for MD simulations of much larger self-assembled nanoparticle systems.

R. McDermott, A. Kerstein, R. Schmidt, P.J. Smith.
**“The Ensemble Mean Limit of the One-Dimensional Turbulence Model and Application to Residual Stress Closure in Finite-Volume Large-Eddy Simulation,”** In *Journal of Turbulence*, Vol. 6, 2005.

DOI: 10.1080/14685240500293894

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy events act upon a velocity field linearized by the local resolved scale strain. EMC can account for viscous effects, addressing the laminar flow finite eddy viscosity problem without implementation of the dynamic procedure [2]. The algebraic form of the model lends itself to analysis [3] and we are able to derive a theoretical value for the eddy rate constant. This value is a bound on the rate constant for full ODT subgrid closure and yields good results in LES of decaying isotropic turbulence with EMC.

J.A. Nairn.
**“Simulation of Crack Growth in Ductile Materials,”** In *Engineering Fracture Mechanics*, Vol. 72, No. 6, pp. 961--979. April, 2005.

DOI: 10.1016/j.engfracmech.2004.08.006

During crack growth of real materials, the total energy released can be partitioned into elastic and dissipative terms. By analyzing material models with mechanisms for dissipating energy and tracking all energy terms during crack growth, it is proposed that computer simulations of fracture can model crack growth by a total energy balance condition. One approach for developing fracture simulations is illustrated by analysis of elastic–plastic fracture. General equations were derived to predict crack growth and crack stability in terms of global energy release rate and irreversible energy effects. To distinguish plastic fracture from non-linear elastic fracture, it was necessary to imply an extra irreversible energy term. A key component of fracture simulations is to model this extra work. A model used here was to assume that the extra irreversible energy is proportional to the plastic work in a plastic-flow analysis. This idea was used to develop a virtual material based on Dugdale yield zones at the crack tips. A Dugdale virtual material was subjected to computer fracture experiments that showed it has many fracture properties in common with real ductile materials. A Dugdale material can serve as a model material for new simulations with the goal of studying the role of structure in the fracture properties of composites. One sample calculation showed that the toughness of a Dugdale material in an adhesive joint mimics the effect of joint thickness on the toughness of real adhesives. It is expected, however, that better virtual materials will be required before fracture simulations will be a viable approach to studying composite fracture. The approach of this paper is extensible to more advanced plasticity models and therefore to the development of better virtual materials.

A. Violi, G.A. Voth.
**“A Multi-scale Computational Approach for Nanoparticle Growth in Combustion Environments,”** In *High Performance Computing and Communications: Lecture Notes in Computer Science (LNCS)*, Vol. 3726, pp. 938--947. 2005.

In this paper a new and powerful computer simulation capability for the characterization of carbonaceous nanoparticle assemblies across multiple, connected scales, starting from the molecular scale is presented. The goal is to provide a computational infrastructure that can reveal through multi-scale computer simulation how chemistry can influence the structure and function of carbonaceous assemblies at significantly larger length and time scales. Atomistic simulation methodologies, such as Molecular Dynamics and Kinetic Monte Carlo, are used to describe the particle growth and the different spatial and temporal scales are connected in a multi-scale fashion so that key information is passed upward in scale. The modeling of the multiple scales are allowed to be dynamically coupled within a single computer simulation using the latest generation MPI protocol within a grid-based computing scheme.

T. Wei, P. Fife, J. Klewicki, P.A. McMurtry.
**“Properties of the Mean Momentum Balance in Turbulent Boundary Layer, Pipe, and Channel Flow,”** In *Journal of Fluid Mechanics*, Vol. 522, pp. 303--327. January, 2005.

DOI: 10.1017/S0022112004001958

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available high-quality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

T. Wei, P. Fife, J. Klewicki, P.A. McMurtry.
**“Scaling Heat Transfer in Fully Developed Turbulent Channel Flow,”** In *International Journal of Heat and Mass Transfer*, In *International Journal of Heat and Mass Transfer*, Vol. 48, No. 25-26, pp. 5284--5296. December, 2005.

DOI: 10.1016/j.ijheatmasstransfer.2005.07.035

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.

T. Wei, R. Schmidt, P.A. McMurtry.
**“Comment on the Clauser Chart Method for Determining the Friction Velocity,”** In *Experiments in Fluids*, Vol. 38, No. 5, pp. 695--699. May, 2005.

DOI: 10.1007/s00348-005-0934-3

A known difficulty with using the Clauser chart method to determine the friction velocity in wall bounded flows is that it assumes, a priori, a logarithmic law for the mean velocity profile. Using both experimental and DNS data in the literature, this note explicitly shows how friction velocities obtained using the Clauser chart method can potentially mask subtle Reynolds-number-dependent behavior.

S. Yan, E.G. Eddings, A.B. Palotas, R.J. Pugmire, A.F. Sarofim.
**“Prediction of Sooting Tendency for Hydrocarbon Liquids in Diffusion Flames,”** In *Energy and Fuels*, Vol. 19, No. 6, pp. 2408--2415. 2005.

DOI: 10.1021/ef050107d

A theoretical method for predicting the smoke point of pure hydrocarbon liquids is presented. The method is based on a structural group contributions approach and does not require any experimental procedures or information of fuel properties, other than the molecular structure of the fuel molecules. The proposed correlation is presented in the form of a multivariable regression. The average deviation is only 1.3 TSI (threshold soot index) units for ∼70 compounds from low-sooting paraffins to highly sooting aromatics, and the average relative error is 9.08%. The results of three different sets of structural groups derived from the Quann and Joback group contribution methods are tested and compared. For a mixture with a defined composition, the estimation of smoke point is also discussed. The method is of potential value for the formulation of surrogate fuels of hydrocarbon mixtures, where matching the fuel's sooting tendency is important.

S. Yan, Y.J. Jiang, N.D. Marsh, E.G. Eddings, A.F. Sarofim, R.J. Pugmire.
**“Study of the Evolution of Soot from Various Fuels,”** In *Energy and Fuels*, Vol. 19, No. 5, pp. 1804--1811. 2005.

DOI: 10.1021/ef049742u

JP-8, a surrogate fuel, and several model compounds were used to produce soot aerosols in a drop-tube furnace with optical access. The soluble organic fractions (SOF) of soot aerosols were studied with GC, GC−MS, and ^{13}C NMR. The residue of each aerosol sample was studied with Raman spectroscopy, ESR, and a recently developed technique used to determine the conductivity and extent of turbostratic structure formation in soot. The SOF values from different fuel sources exhibit variations in yield, and carbon aromaticity values, and the latter parameter correlates with the extent of turbostratic structure formation in the aerosol residues. Raman data of the soot residues indicate the presence of highly disordered graphitic structures, but the graphite factor measurements reveal differences among these disordered structures that are not apparent in the Raman data.

2004

C. Ayyagari, D. Bedrov, G.D. Smith.
**“A Molecular Dynamics Simulation Study of The Influence of Free Surfaces on the Morphology of Self-Associating Polymers,”** In *Polymer*, Vol. 45, No. 13, pp. 4549--4558. June, 2004.

DOI: 10.1016/j.polymer.2004.04.044

Molecular dynamics simulations of thin films and bulk melts of model self-associating polymers have been performed in order to gain understanding of the influence of free surfaces on the morphology of these polymers. The self-associating polymers were represented by a simple bead-necklace model with attractive groups (stickers) at the chain ends (*end-functionalized* polymer) and in the chain interior (*interior-functionalized* polymer). The functionalized groups were found to form clusters in the melt whose size is representative of that found experimentally in many ionomer melts. While the size distribution and shape of the clusters in the thin films were found to be relatively unperturbed compared to their corresponding bulk melts, the morphology of the self-associating melts was found to be significantly perturbed by the free surfaces. Specifically, a strong depletion of stickers near the interface and the emergence of clearly defined layers of stickers parallel to the surface was observed. Increased bridging of clusters by the functionalized polymers was also observed near the free surface. We conclude that these effects can be associated with a high free energy for stickers in the low-density interfacial regime: stickers prefer to be in the higher-density interior of the film where relatively unperturbed sticker clusters can form.

**Keywords:** Molecular dynamics, Ionomers, Telechelic polymers

B. Banerjee.
**“MPM Validation: Sphere-Cylinder Impact: Low Resolution Simulations,”** C-SAFE Internal Report, No. C-SAFE-CD-IR-04-002, *Department of Mechanical Engineering, University of Utah*, August, 2004.

This report compares the simulated and experimental axial velocity and axial strain histories observed during a low resolution study of the impact of an aluminum sphere on an aluminum plate supported by a hollow aluminum cylinder. In a previous report, an optimal set of input parameters was identified that minimizes ringing and reduces energy increase over the time of the simulations. These input parameters were used in the simulations discussed in this report. We observe that though the initial time of arrival of the stress wave at various locations matches the experimentally observed data, the time evolution of velocities and strains can be considerably different from the experimental data.

B. Banerjee.
**“MPM Validation: Sphere-Cylinder Impact: Medium Resolution Simulations,”** C-SAFE Internal Report, No. C-SAFE-CD-IR-04-003, *Department of Mechanical Engineering, University of Utah*, August, 2004.

In a previous report we compared the experimental and the computed axial velocity and axial strain from a low spatial resolution study of the impact of an aluminum sphere on an aluminum plate supported by a hollow aluminum cylinder. We report results from a higher resolution study of the same problem using input parameters that conserve both momentum and energy quite accurately. The simulations show a slower wave speed than the experiments which suggests that the elastic moduli and density of the material used in the experiments may be different from those used in the simulations. The simulated free surface velocity also differs from the experimental data. Further study is required to determine the cause of these differences.

B. Banerjee.
**“MPM Validation: Sphere-Cylinder Impact Tests : Energy Balance,”** C-SAFE Internal Report, No. C-SAFE-CD-IR-04-001, *Department of Mechanical Engineering, University of Utah*, 2004.

This report discusses the energy balance results observed during the simulation of the impact of an aluminum sphere on an aluminum plate supported by a hollow aluminum cylinder. Due to the high impact velocity, there is considerable ringing of the cylinder which causes the sum of the mechanical energies to increase. An optimal set of input parameters is identified that minimizes ringing and reduces energy increase over the time of the simulation.

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