Academic literature on the topic 'Finite rate stiff relaxation'
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Journal articles on the topic "Finite rate stiff relaxation"
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Vena, P. "A Computational Model of Viscoelastic Composite Materials for Ligament or Tendon Prostheses." Advanced Composites Letters 9, no. 3 (May 2000): 096369350000900. http://dx.doi.org/10.1177/096369350000900302.
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A constitutive model and a finite element formulation for viscoelastic anisotropic materials subject to finite strains is expounded in this paper. The composite material is conceived as a matrix reinforced with stiff fibres. The constitutive relations are obtained by defining a strain energy function and a relaxation function for each constituent. By means of this approach, the viscoelastic properties of the material constituents can be taken into account and therefore different time dependent behaviour can be assigned to the matrix and to the reinforcing fibres. The response provided by this kind of constitutive formulation allows for the description of mechanical behaviour for either natural anisotropic tissues (such as tendons and ligaments) and for the composite materials which are currently adopted for tissue reconstruction. The main features of those mechanical properties observed in an ideal uniaxial test are: a non linear stress-strain response and a time dependent response which is observed in relaxation of stresses for a prescribed constant stretch and in a moderate strain rate dependence of the measured response.
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WANG, Y., Y. L. HE, T. S. ZHAO, G. H. TANG, and W. Q. TAO. "IMPLICIT-EXPLICIT FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOWS." International Journal of Modern Physics C 18, no. 12 (December 2007): 1961–83. http://dx.doi.org/10.1142/s0129183107011868.
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We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Lewy numbers. As a result, with our implicit-explicit finite-difference scheme the computational convergence rate can be significantly improved compared with previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of the Riemann problem, Taylor vortex flow, Couette flow, and oscillatory compressible flows with shock waves show that our implicit-explicit finite-difference lattice Boltzmann method is accurate and efficient. In addition, it is demonstrated that with the proposed scheme non-uniform meshes can also be implemented with ease.
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Boscarino, S., G. Russo, and M. Semplice. "High order finite volume schemes for balance laws with stiff relaxation." Computers & Fluids 169 (June 2018): 155–68. http://dx.doi.org/10.1016/j.compfluid.2017.10.009.
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Abreu, Eduardo, Abel Bustos, and Wanderson Lambert. "A unsplitting finite volume method for models with stiff relaxation source terms." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 1 (March 2016): 5–20. http://dx.doi.org/10.1007/s00574-016-0118-1.
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Boscheri, Walter, and Raphaël Loubère. "High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms." Communications in Computational Physics 21, no. 1 (December 5, 2016): 271–312. http://dx.doi.org/10.4208/cicp.oa-2015-0024.
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AbstractIn this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms. This scheme is constructed with a single stencil polynomial reconstruction operator, a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources, a nodal solver with relaxation to determine the mesh motion, a path-conservative integration technique for the treatment of non-conservative products and ana posterioristabilization procedure derived from the so-called Multidimensional Optimal Order Detection (MOOD) paradigm. In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff. The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study. Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D. The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.
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Nshimiyimana, J. D., F. Plumier, C. Ndagije, J. Gyselinck, and C. Geuzain. "High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers." Advanced Electromagnetics 9, no. 1 (March 20, 2020): 49–58. http://dx.doi.org/10.7716/aem.v9i1.1245.
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Coupled problems result in very stiff problems whose char- acteristic parameters differ with several orders in magni- tude. For such complex problems, solving them monolithi- cally becomes prohibitive. Since nowadays there are op- timized solvers for particular problems, solving uncoupled problems becomes easy since each can be solved indepen- dently with its dedicated optimized tools. Therefore the co-simulation of the sub-problems solvers is encouraged. The design of the transmission coupling conditions between solvers plays a fundamental role. The current paper ap- plies the waveform relaxation methods for co-simulation of the finite element and circuit solvers by also investigating the contribution of higher order integration methods. The method is illustrated on a coupled finite element inductor and a boost converter and focuses on the comparison of the transmission coupling conditions based on the waveform iteration numbers between the two sub-solvers. We demon- strate that for lightly coupled systems the dynamic iterations between the sub-solvers depends much on the inter- nal integrators in individual sub-solvers whereas for tightly coupled systems it depends also to the kind of transmission coupling conditions.
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Busto, Saray, Michael Dumbser, and Laura Río-Martín. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows." Mathematics 9, no. 22 (November 21, 2021): 2972. http://dx.doi.org/10.3390/math9222972.
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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.
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Saxena, Nishank, and Gary Mavko. "Effects of fluid-shear resistance and squirt flow on velocity dispersion in rocks." GEOPHYSICS 80, no. 2 (March 1, 2015): D99—D110. http://dx.doi.org/10.1190/geo2014-0304.1.
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Laboratory measurements of rocks saturated with high-viscosity fluids (such as heavy-oil, bitumen, magma, kerogen, etc.) often exhibit considerable seismic velocity dispersion, which is usually underestimated by the Biot theory. Over the years, grain-scale dispersion mechanisms such as squirt (local-flow) and shear relaxation (nonzero shear stress in the pore fluid) have been more successful in explaining the measured dispersion. We developed a new method to quantify the combined high-frequency effects of squirt and shear dispersion on the effective moduli of rocks saturated with viscous fluids. Viscous fluid at high frequencies was idealized as an elastic solid of finite shear modulus, hydraulically locked in stiff and soft pores. This method entailed performing solid substitution in stiff pores of a dry rock frame, which itself was unrelaxed due to solid-filled soft pores. The unrelaxed frame stiffness solutions required information on the pressure dependency of the rock stiffness and porosity. This method did not have any adjustable parameters, and all required inputs can be directly measured. With various laboratory and numerical examples, we noted that accounting for combined effects of squirt and shear relaxation was necessary to explain laboratory-measured velocities of rocks saturated with fluids of high viscosity. Predictions of the new method were in good agreement with the laboratory data.
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Mendonça da Silveira, Francisco Eugenio. "TEARING MODES GROWTH RATE AMPLIFICATION DUE TO FINITE CURRENT RELAXATION." Acta Polytechnica 57, no. 1 (February 28, 2017): 32–37. http://dx.doi.org/10.14311/ap.2017.57.0032.
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In this work, we explore the influence of perturbative wavelengths, shorter than those usually considered, on the growth rate γ of the tearing modes. Thus, we adopt an extended form of Ohm’s law, which includes a finite relaxation time for the current density, due to inertial effects of charged species. In the long wavelength limit, we observe the standard γ of the tearing modes. However, in the short wavelength limit, we show that γ does not depend on the fluid resistivity any longer. Actually, we find out that γ now scales with the electron number density n<sub>e</sub> as γ ~ n<sub>e</sub><sup>−3/2</sup>. Therefore, through a suitable combination of both limiting results, we show that the standard γ can be substantially amplificated, even by moderate shortenings of perturbative wavelengths. Further developments of our theory may contribute to the explanation of the fast magnetic reconnection of field lines, as observed in astrophysical plasmas.
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Condat, C. A. "Solution to the Glarum model with a finite relaxation rate." Zeitschrift f�r Physik B Condensed Matter 77, no. 2 (June 1989): 313–20. http://dx.doi.org/10.1007/bf01313675.
Full textDissertations / Theses on the topic "Finite rate stiff relaxation"
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Chiocchetti, Simone. "High order numerical methods for a unified theory of fluid and solid mechanics." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346999.
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This dissertation is a contribution to the development of a unified model of
continuum mechanics, describing both fluids and elastic solids as a general
continua, with a simple material parameter choice being the distinction
between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic
media. Additional physical effects such as surface tension, rate-dependent
material failure and fatigue can be, and have been, included in the same
formalism.
The model extends a hyperelastic formulation of solid mechanics in
Eulerian coordinates to fluid flows by means of stiff algebraic relaxation
source terms. The governing equations are then solved by means of high
order ADER Discontinuous Galerkin and Finite Volume schemes on fixed
Cartesian meshes and on moving unstructured polygonal meshes with
adaptive connectivity, the latter constructed and moved by means of a in-
house Fortran library for the generation of high quality Delaunay and Voronoi
meshes.
Further, the thesis introduces a new family of exponential-type and semi-
analytical time-integration methods for the stiff source terms governing
friction and pressure relaxation in Baer-Nunziato compressible multiphase
flows, as well as for relaxation in the unified model of continuum mechanics,
associated with viscosity and plasticity, and heat conduction effects.
Theoretical consideration about the model are also given, from the
solution of weak hyperbolicity issues affecting some special cases of the
governing equations, to the computation of accurate eigenvalue estimates, to
the discussion of the geometrical structure of the equations and involution
constraints of curl type, then enforced both via a GLM curl cleaning method,
and by means of special involution-preserving discrete differential operators,
implemented in a semi-implicit framework.
Concerning applications to real-world problems, this thesis includes
simulation ranging from low-Mach viscous two-phase flow, to shockwaves in
compressible viscous flow on unstructured moving grids, to diffuse interface
crack formation in solids.
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Bilyeu, David Lawrence. "Numerical Simulation of Chemical Reactions Inside a Shock-Tube by the Space-Time Conservation Element and Solution Element Method." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1213363652.
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Nguyen, Trung Dung. "Experimental and numerical investigation of strain-rate dependent mechanical properties of single living cells." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/82791/1/Trung%20Dung_Nguyen_Thesis.pdf.
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The objective of this project is to investigate the strain-rate dependent mechanical behaviour of single living cells using both experimental and numerical techniques. The results revealed that living cells behave as porohyperlastic materials and that both solid and fluid phases within the cells play important roles in their mechanical responses. The research reported in this thesis provides a better understanding of the mechanisms underlying the cellular responses to external mechanical loadings and of the process of mechanical signal transduction in living cells. It would help us to enhance knowledge of and insight into the role of mechanical forces in supporting tissue regeneration or degeneration.
Book chapters on the topic "Finite rate stiff relaxation"
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Chiocchetti, Simone, and Christoph Müller. "A Solver for Stiff Finite-Rate Relaxation in Baer–Nunziato Two-Phase Flow Models." In Fluid Mechanics and Its Applications, 31–44. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-33338-6_3.
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Vidyasagar, M. "Introduction to Large Deviation Theory." In Hidden Markov Processes. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691133157.003.0005.
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This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct an empirical distribution. It then considers the notion of a lower semi-continuous function and that of a lower semi-continuous relaxation before discussing the large deviation property for i.i.d. samples. In particular, it describes Sanov's theorem for a finite alphabet and proceeds by analyzing large deviation property for Markov chains, taking into account stationary distributions, entropy and relative entropy rates, the rate function for doubleton frequencies, and the rate function for singleton frequencies.
Conference papers on the topic "Finite rate stiff relaxation"
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Tang, Qing, Martin Denison, Mike Maguire, Mike Bockelie, and Jyh-Yuan Chen. "Improvements on a Newton-Krylov Based Solver for CFD Models Using Finite Rate NOx Chemistry." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-3118.
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In this paper, we describe our progress on improving the performance of a newly developed Computational Fluid Dynamics (CFD) modeling tool, which uses reduced chemical kinetics mechanisms to model the finite rate chemistry effects and solves the resulting system of stiff partial differential equations with a matrix-free Newton-Krylov method. A multi-grid based preconditioner and a Newton iteration scheme have been implemented in the Newton-Krylov solver and the reduced mechanism module, respectively, to replace the original Picard based preconditioner and the point iteration scheme for steady state species evaluation. Preliminary tests of the improved modeling tool have been conducted using simple hotbox and a full-scale, coal fired electric utility boiler, and shown very promising results in terms of the accuracy, robustness, and efficiency of the new tool.
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Cook, David J., Heinz Pitsch, and Norbert Peters. "Numerical Simulation of Combustion Instabilities in a Lean Premixed Combustor With Finite Rate Chemistry." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38558.
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Combustion instabilities in lean premixed gas turbine combustors remain a major limitation in decreasing NOx emissions. Computational Fluid Dynamics (CFD) has become an important design and analysis tool that is often used to predict thermoacoustic oscillations caused by these instabilities. Limitations to prediction accuracy are imposed by the choice of chemistry and combustion model. The focus of this study is to compare CFD calculations using Eddy Dissipation and Finite Rate Chemistry models to experimental data reported by Richards and Janus (1997) on the single-injector lean premixed DOE-NETL combustor. The computational domain consists of an annular swirl inlet, fuel injection, a can combustor, a plug for reduced flow area, and an exhaust plenum. The numerical calculations were done using a RANS solver. A 2D axisymmetric-swirl model with RANS turbulence model was employed. The Eddy Dissipation Model has become popular largely because of its robust performance. It is shown that this model does not predict combustion instabilities for the present case. On the other hand, the Finite Rate Chemistry Model is numerically stiff, but is capable of capturing the onset of combustion instabilities.
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Chen, Leitao, Hamid Sadat, and Laura Schaefer. "A Multi-Relaxation-Time Finite Volume Discrete Boltzmann Method for Viscous Flows." In ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/ajkfluids2019-5034.
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Abstract Conventional constitutive law-based fluid dynamic models solve the conservation equations of mass and momentum, while kinetic models, such as the well-known lattice Boltzmann method (LBM), solve the propagation and collision processes of the Boltzmann equation-governed particle distribution function (PDF). Such models can provide an a priori modeling platform on a more fundamental level while easily reconstructing macroscopic variables such as velocity and pressure from the PDF. While the LBM requires a rigid and uniform grid for spatial discretization, another similar unique kinetic model known as the finite volume discrete Boltzmann method (FVDBM) has the ability to solve the discrete Boltzmann equation (DBE) on unstructured grids. The FVDBM can easily and accurately capture curved and more complicated fluid flow boundaries (usually solid boundaries), which cannot be satisfactorily realized in the LBM framework. As a result, the FVDBM preserves the physical advantages of the LBM over the constitutive law-based model approach, but also incorporates a better boundary treatment. However, the FVDBM suffers larger diffusion errors compared to the LBM approach. Building on our previous work, the FVDBM is further developed by integrating the multi-relaxation-time (MRT) collision model into the existing framework. Compared to the existing FVDBM approach that uses the Bhatnagar–Gross–Krook (BGK) collision model, which is also known as the single-relaxation-time (SRT) model, the new model can significantly reduce diffusion error or numerical viscosity, which is essential in the simulation of viscous flows. After testing the new model, the MRT-FVDBM, and the old model, the BGK-FVDBM, on Taylor-Green vortex flow, which can quantify the diffusion error of the applied model, it is found that the MRT-FVDBM can reduce the diffusion error at a faster rate as the mesh resolution increases, which renders the MRT-FVDBM a higher-order model than the BGK-FVDBM. At the highest mesh resolution tested in this paper, the reduction of the diffusion error by the MRT-FVDBM can be up to 30%.
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Pellicotte, Jacob, Mario Cotto, and Calvin Stewart. "Assessment of Calibration Approaches for the Stress Relaxation Test." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90616.
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Abstract Advanced manufacturing technologies are enabling the next generation of superalloys for extreme temperatures, pressures, and longevity. There is a need for Accelerated Creep Test (ACT) methods to reduce the time needed to implement new creep resistant superalloys. Without the development of ACTs, the qualification of new superalloys using conventional creep tests can take 11+ years corresponding to the 100,000-hour service life of long-lived turbomachinery components. A refined stress relaxation test (SRT) is introduced to succeed real-time conventional creep tests (CCTs). The stress relaxation test generates extensive stress versus creep-strain-rate data within a single specimen. Since the specimen is held below the elastic limit and relatively little creep deformation has occurred, several SRTs at different temperatures can be performed using a single specimen. To obtain data, specimens are rapidly loaded in force-control to just below the elastic limit. The specimen is switched to displacement-control and held at a fixed displacement while stress relaxation occurs. This generates a stress versus time curve that must be converted into stress versus creep-strain-rate. The stress versus creep-strain-rate curves are utilized to calculate creep activation energy and produce a creep-strain-rate master curve. The objective of this study is to determine the best calibration approach for SRT: regression of stress, regression of creep strain, and the finite difference of creep strain. It is recommended that the differentiation be applied; however, finite difference applied to the raw data produces inconsistent calculations of the creep-strain-rate. In this study, a MATLAB algorithm is written to evaluate all three calibration options where, stress and creep deformation are regressed into natural logarithm functions. The resulting creep-strain-rate curves are compared to determine the most reliable and consistent method. Analyzing and evaluating the results the regression of stress and regression or creep strain calibration methods prove to provide accurate results. These methods will help replace CCTs by conducting less expensive ACTs, while increasing the overall efficiency of the development of new materials.
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Fiolitakis, A., R. Lückerath, O. Lammel, G. Schmitz, H. Ax, M. Stöhr, C. Arndt, B. Noll, and D. Kluß. "Assessment of a Finite-Rate-Chemistry Model for ANSYS® CFX® Using Experimental Data of a Downsized Gas Turbine Combustor." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75638.
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In this work the implementation and validation of a finite-rate-chemistry (FRC) combustion model for ANSYS® CFX® 15.0 is presented. For the solution of the stiff system of species transport equations a splitting scheme is used where transport processes and chemical reactions are solved numerically in separate steps. In this splitting scheme the software Cantera is used for the integration of the chemistry sub-step. It is coupled via user-defined-functions (“USER-Fortran”) to ANSYS® CFX® 15.0. To provide validation data for this model under gas turbine relevant conditions, a down sized version of an industrial burner is investigated experimentally at different operating conditions and with different fuels. The burner is operated in a high-pressure combustion test rig with optical access at technically relevant pressures. Data for emissions of nitric oxide and carbon monoxide are obtained along with OH* chemiluminescence images of the flame. Additionally, investigations are made on the risk of flashback in this burner. The operating points are simulated using the FRC model developed in this work. It is demonstrated that this model approach can predict carbon monoxide and nitric oxide emissions very well, despite the simplistic treatment of turbulence-chemistry interaction. Moreover, it is shown that this model approach can also predict the onset of flashback: the change in flame shape, which is an indicator for flashback, can be well reproduced with this model.
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Hares, Edward, Mahmoud Mostafavi, Richard Bradford, and Chris Truman. "The Influence of Creep Strain Rate on Creep Damage Formation in Austenitic Stainless Steel." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84635.
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Motivated by the need to more accurately account for real, in-service, operating conditions, this paper aims to investigate whether creep strain accumulated at different strain rates is equally damaging. Previous research has suggested that creep strain is more damaging when accumulated more slowly in creep of notched bars. The research presented here seeks to address this question by considering the accumulation of creep strain during stress relaxation of notched bars. Repeat stress relaxation tests with varying dwell lengths were conducted so that the relative damaging effects of the early, rapid accumulation and later, slow accumulation of creep strains could be compared. Another aim was to determine how a lower test temperature affects this creep strain accumulation. In repeat relaxation tests the load is reestablished repeatedly after relaxation dwells of equal duration, until rupture of the specimen occurs. The material used was an ex-service powerplant stainless steel Type 316H. Notched bar specimens were used to introduce stress triaxiality at the notch tip to imitate the multiaxial loads plant components are subjected to during in-service operation. The stresses and strains in the specimens were then assessed using finite element analysis; a user subroutine was implemented so the onset and propagation of creep damage could be simulated throughout the specimens’ creep life. The research found that the material in question had a lower creep ductility at 515°C than at 550°C. The research also showed that creep strain accumulated rapidly at the start of a dwell is significantly less damaging than creep strain accumulated more slowly towards the end of the dwell.
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Pressburger, Yoram, Renato Perucchio, and David A. Field. "A Two-Level Multigrid Algorithm for Solving 3-D Quadratic Finite Element Models." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0098.
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Abstract A two-level multigrid algorithm for solving a quadratic finite element models containing tetrahedral meshes is presented. The basic idea is to generate two nested finite element models, first a linear model and then a quadratic one embedded hierarchically into the linear one. The exact solution to the linear model is computed and a two-level iterative procedure is used to solve for the quadratic model. In particular, the Successive Over Relaxation (SOR) method is used for the smoothing iteration on the quadratic model in each two-level cycle. A numerical study is carried out to determine how the relaxation factor and the number of SOR iteration in each two-level cycle influence the convergence rate of the complete algorithm. The stopping criterion for the iteration is based on the notion that the error in the iterative procedure will be of the same order as the error in the finite element approximation. Finally, the efficiency of the algorithm is evaluated by comparing the computational time with that of an exact solver based on Gauss elimination. Results indicate that the present algorithm produces substantial saving of CPU time.
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Gao, Wen, Tom Harrup, Yuxia Hu, and David White. "Effect of a Strong Middle Layer on Spudcan Penetration." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23925.
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The rapid penetration of one or more of the foundations of a mobile jack-up rig into the seabed is an ongoing major problem in the offshore industry, with the potential to cause major damage to the structure and endangering any personnel on board. A recent example is the jack-up drilling rig Perro Negro 6 incident happened near the mouth of the Congo river in July 2013 with one of the rig’s crew of 103 reported missing and six others injured. This uncontrollable displacement is due to a form of failure known as punch through failure and commonly occurs on stratified seabed profiles. It has been reported that unexpected punch-through accidents have resulted in both rig damage and lost drilling time at a rate of 1 incident per annum with consequential costs estimated at between US$1 and US$10 million [1]. This paper presents the bearing capacity profiles and associated soil flow mechanisms of a common spudcan foundation penetrating into a three layer soft-stiff-soft clay soil through the use of large deformation finite element (LDFE) analysis. The Remeshing and Interpolation with Small Strain (RITSS) [2, 3] technique was implemented in the software package AFENA [4] to conduct the LDFE analysis. Both soil layer thickness and soil layer strength ratios were varied to study their effect on the spudcan penetration responses. The LDFE results of spudcan penetration into the soft-stiff-soft clay soils were calibrated by existing centrifuge test data. A parametric study was then conducted to study the bearing capacity responses and soil flow mechanisms during spudcan large penetrations by varying the soil layer strength ratio and relative layer thickness to the diameter of spudcan. It was found that there were three types of bearing responses during continuous penetration of spudcan: (a) when the top soft layer is relatively thin, the spudcan bearing response was similar to that of two layer soils with stiff over soft clays; (b) when the top soil layer thickness is medium, a peak resistance is observed when spudcan penetrates into the middle stiff layer followed by reduction; (c) when the soil layer is thick, the peak resistance occurs when spudcan gets into the bottom soft soil layer. The critical thickness of top soil layer is a function of soil strength ratio and middle stiff soil layer thickness. The bearing response types were also corresponding to the soil cavity formations during spudcan initial penetration.
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Agrawal, Govind P. "Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.maa3.
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The dynamic response of semiconductor lasers is generally studied by solving the single-mode rate equations which assume an instantaneous relaxation of carriers within the conduction and the valence bands. Even though the intraband relaxation time is typically ~0.1 ps, it can affect laser dynamics significantly. To the first order, the effects of a finite intraband relaxation time are included in the rate equations by assuming that the modal gain g decreases linearly with the intracavity mode intensity I, i.e., g = g0 (1–εI). This functional form of the nonlinear gain becomes questionable at high intensities. A nonperturbative solution of the densitymatrix equations shows that the modal gain saturates with the intensity as g = g0(I + I/Is)−1/2, where Is is the intraband saturation intensity. At the same time, the modal refractive index also becomes intensity dependent. We include the intensity dependence of both the gain and the refractive index in the single-mode rate equations and study how their inclusion affects the dynamic response of semiconductor lasers by considering the laser parameters such as the modulation bandwidth and the damping time of relaxation oscillations.
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Wang, Xin, H. Jerry Qi, and Mark E. Rentschler. "Analysis of Wheel-Tissue Interaction for In Vivo Robotic Mobility." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37570.
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Providing mobility of miniature, in vivo surgical robots under a variety of changing in vivo conditions is necessary to help expand the application of minimally invasive surgery. Analytical and finite element analysis results of wheeled mobility on tissue inside abdominal cavity are presented here, as a preliminary step towards further improved mobility performance. Results indicate that the mobility of a wheeled robot on tissue is influenced by factors including wheel torque application rate and material relaxation time. While using a viscoelastic standard linear solid material tissue model, the steady state translation speed of the wheel decreases with the increase of material relaxation time given a constant torque application time. Interestingly, at a relaxation time threshold value, the wheel’s steady-state speed no longer decreases, but abruptly undergoes continuous acceleration. Results also indicate that for very small and very large relaxation times the viscoelastic material can be approximated as an elastic material.