Modeling Multicomponent Fuel Droplet Vaporization with Finite Liquid Diffusivity Using Coupled Algebraic-Dqmom with Delumping

Multicomponent fuel droplet vaporization models for use in combustion CFD codes often prioritize computational efficiency over model complexity. This leads to oversimplifying assumptions such as single component droplets or infinite liquid diffusivity. The previously developed Direct Quadrature Method of Moments (DQMoM) with delumping model demonstrated a computationally efficient and accurate approach to solve for every discrete species in a well-mixed vaporizing multicomponent droplet. To expand the method to less restrictive cases, a new solution technique is presented called the Coupled Algebraic-Direct Quadrature Method of Moments (CA-DQMoM). In contrast to previous moment methods for droplet vaporization, CA-DQMoM solves for the evolution of two liquid distributions by coupling a monovariate, homogeneous DQMoM approach with additional algebraic moment equations, allowing for a more complex droplet vaporization model with finite rates of liquid diffusion to be solved with computational efficiency. To further decrease computational expense, an approximation that employs the same nodes for both distributions can be used in certain cases. Finally, a delumping technique is adapted to the finite diffusivity model to reconstruct discrete species information at minimal computational cost. The model is proven to be accurate relative to a full discrete component model for both a kerosene droplet comprised of 36 species and a multicomponent droplet of 200 species while maintaining the computational efficiency of continuous thermodynamics models. The combined accuracy and computational efficiency demonstrated by the CA-DQMoM with delumping model for a multicomponent fuel droplet with finite liquid diffusivity makes it ideal for incorporation into CFD models for complex combustion process

Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method

The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. (2004). The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox (2005) to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver

An Efficient Coal Pyrolysis Model for Detailed Tar Species Vaporization

An accurate and computationally efficient model for the vaporization of many tar species during coal particle pyrolysis has been developed. Like previous models, the molecular fragments generated by thermal decomposition are partitioned into liquid metaplast, which remains in the particle, and vapor, which escapes as tar, using a vapor-liquid equilibrium(VLE) sub-model. Multicomponent VLE is formulated as a rate-based process, which results in an ordinary differential equation (ODE) for every species. To reduce the computational expense of solving many ODEs, the model treats tar and metaplast species as a continuous distribution of molecular weight. To improve upon the accuracy of previous continuous thermodynamic approaches for pyrolysis, the direct quadrature method of moments (DQMoM) is proposed to solve for the evolving distributions without assuming any functional form. An inexpensive delumping procedure is also utilized to recover the time-dependent mole fractions and fluxes for every discrete species. The model is well-suited for coal-to-chemicals processes, and any application which requires information on a range of tar species. Using a modified CPD model as the basis for implementation of the VLE submodel, agreement between the full discrete model and DQMoM with delumping is excellent, with substantial computational savings

Computational Methods for Modeling Multicomponent Droplet Vaporization

Computational fluid dynamics (CFD) models for combustion of multicomponent hydrocarbon fuels must often prioritize computational efficiency over model complexity, leading to oversimplifying assumptions in the sub-models for droplet vaporization and chemical kinetics. Therefore, a computationally efficient hybrid droplet vaporization-chemical surrogate approach has been developed which emulates both the physical and chemical properties of a multicomponent fuel. For the droplet vaporization/physical portion of the hybrid, a new solution method is presented called the Coupled Algebraic-Direct Quadrature Method of Moments (CA-DQMoM) with delumping which accurately solves for the evolution of every discrete species in a vaporizing multicomponent fuel droplet with the computational efficiency of a continuous thermodynamics model. To link the vaporization model to the chemical surrogate portion of the hybrid, a Functional Group Matching (FGM) method is developed which creates an instantaneous surrogate composition to match the distribution of chemical functional groups in the vaporization flux of the full fuel. The result is a hybrid method which can accurately and efficiently predict time-dependent, distillation-resolved combustion properties of the vaporizing fuel and can be used to investigate the effects of preferential vaporization on combustion behavior

A Hybrid Droplet Vaporization-Chemical Surrogate Approach for Emulating Vaporization, Physical Properties, and Chemical Combustion Behavior of Multicomponent Fuels

The complex nature of multicomponent aviation fuels presents a daunting task for accurately simulating combustion behavior without incurring impractical computational costs. To reduce computation time, chemical fuel surrogates comprised of only a few species are used to emulate the combustion of complex pre-vaporized fuels. These surrogates are often unable to match the vaporization behavior and physical properties of the real fuel and fail to capture the effect of preferential vaporization on combustion behavior. Therefore, a computationally efficient, hybrid droplet vaporization-chemical surrogate approach has been developed which emulates both the physical and chemical properties of a multicomponent kerosene fuel. The droplet vaporization/physical portion of the hybrid uses the Coupled Algebraic–Direct Quadrature Method of Moments with delumping to accurately solve for the evolution of every discrete species in a vaporizing fuel droplet with the computational efficiency of a continuous thermodynamic model. The chemical surrogate portion of the hybrid is linked to the vaporization model using a functional group matching method, which creates an instantaneous surrogate composition to match the distribution of chemical functional groups (CH2, (CH2)n, CH3 and Benzyl-type) in the vaporization flux of the full fuel. The result is a hybrid method which can accurately and efficiently predict time-dependent, distillation-resolved combustion property targets of the vaporizing fuel and can be used to investigate the effects of preferential vaporization on combustion behavior

Modeling Pyrolysis of Large Coal Particles with Many Species

Coal currently supplies 40% of the world’s electricity needs, and is one of the most important energy sources. As the initial stage of coal combustion, pyrolysis is a thermal decomposition process which converts coal into light gases and tars, which are subsequently consumed in combustion reactions, as well as solid char. Recently there has been interest in using slow pyrolysis as a stand-alone process for the production of chemicals and fuels from large (mm-scale) coal particles. Simulations can be used to efficiently study the impact of pyrolysis conditions on gas, tar and char yields, as well as gas and tar species compositions, which are an important output for a coal-to-chemicals process. In order to simulate pyrolysis of large coal particles, the Chemical Percolation Devolatilization (CPD) model, which predicts the mass fractions of char, tar and light gas, has been modified and improved. A transient multicomponent vaporization sub-model has been developed to predict the partitioning of heavy species into gaseous tar and liquid metaplast. The Direct Quadrature Method of Moments (DQMoM) is introduced as a computationally efficient method to solve for the evolution of the distribution of tar species as a function of molar mass, and the full discrete tar species distribution can be reconstructed by a novel delumping procedure. Finally, a heat transfer model that can predict temperature gradients within the particles has been incorporated using the finite volume method to discretize the energy equation, with the improved CPD model implemented at every position within the particle. The results show the necessity of resolving large particles spatially, due to the impact of the local temperature evolution on tar and gas mass fractions and the production of certain species. Higher pyrolysis temperatures result in increased yields of gas and especially large tar species, while decreasing pressures also increase the production of heavier tar species. The agreement between the full discrete species model, which solves differential equations for every tar species, and DQMoM with delumping, which solves many fewer equations, is excellent, while yielding a large improvement in computational efficiency

Doctor of Philosophy

dissertationThe Direct Quadrature Method of Moments (DQMOM) was implemented in the Large Eddy Simulation (LES) tool ARCHES to model coal particles. LES coupled with DQMOM was first applied to nonreacting particle-laden turbulent jets. Simulation results were compared to experimental data and accurately modeled a wide range of particle behaviors, such as particle jet waviness, spreading, break up, particle clustering and segregation, in different configurations. Simulations also accurately predicted the mean axial velocity along the centerline for both the gas phase and the solid phase, thus demonstrating the validity of the approach to model particles in turbulent flows. LES was then applied to the prediction of pulverized coal flame ignition. The stability of an oxy-coal flame as a function of changing primary gas composition (CO2 and O2) was first investigated. Flame stability was measured using optical measurements of the flame standoff distance in a 40 kW pilot facility. Large Eddy Simulations (LES) of the facility provided valuable insight into the experimentally observed data and the importance of factors such as heterogeneous reactions, radiation or wall temperature. The effects of three parameters on the flame stand-off distance were studied and simulation predictions were compared to experimental data using the data collaboration method. An additional validation study of the ARCHES LES tool was then performed on an air-fired pulverized coal jet flame ignited by a preheated gas flow. The simulation results were compared qualitatively and quantitatively to experimental observations for different inlet stoichiometric ratios. LES simulations were able to capture the various combustion regimes observed during flame ignition and to accurately model the flame stand-off distance sensitivity to the stoichiometric ratio. Gas temperature and coal burnout predictions were also examined and showed good agreement with experimental data

Optimal Moment Sets for Multivariate Direct Quadrature Method of Moments

The direct quadrature method of moments (DQMOM) can be employed to close population balance equations (PBEs) governing a wide class of multivariate number density functions (NDFs). Such equations occur over a vast range of scientific applications, including aerosol science, kinetic theory, multiphase flows, turbulence modeling, and control theory, to name just a few. As the name implies, DQMOM uses quadrature weights and abscissas to approximate the moments of the NDF, and the number of quadrature nodes determines the accuracy of the closure. For nondegenerate univariate cases (i.e., a sufficiently smooth NDF), the N weights and N abscissas are uniquely determined by the first 2N non-negative integer moments of the NDF. Moreover, an efficient product-difference algorithm exists to compute the weights and abscissas from the moments. In contrast, for a d-dimensional NDF, a total of (1 + d)N multivariate moments are required to determine the weights and abscissas, and poor choices for the moment set can lead to nonunique abscissas and even negative weights. In this work, it is demonstrated that optimal moment sets exist for multivariate DQMOM when N ) nd quadrature nodes are employed to represent a d-dimensional NDF with n ) 1-3 and d ) 1-3. Moreover, this choice is independent of the source terms in the PBE governing the time evolution of the NDF. A multivariate Fokker-Planck equation is used to illustrate the numerical properties of the method for d ) 3 with n ) 2 and 3

Efficient search for inputs causing high floating-point errors

pre-printTools for floating-point error estimation are fundamental to program understanding and optimization. In this paper, we focus on tools for determining the input settings to a floating point routine that maximizes its result error. Such tools can help support activities such as precision allocation, performance optimization, and auto-tuning. We benchmark current abstraction-based precision analysis methods, and show that they often do not work at scale, or generate highly pessimistic error estimates, often caused by non-linear operators or complex input constraints that define the set of legal inputs. We show that while concrete-testing-based error estimation methods based on maintaining shadow values at higher precision can search out higher error-inducing inputs, suitable heuristic search guidance is key to finding higher errors. We develop a heuristic search algorithm called Binary Guided Random Testing (BGRT). In 45 of the 48 total benchmarks, including many real-world routines, BGRT returns higher guaranteed errors. We also evaluate BGRT against two other heuristic search methods called ILS and PSO, obtaining better results

A Quadrature-based Moment Closure for the Williams Spray Equation

Sprays and other dispersed-phase systems can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). In principle, the kinetic description is valid from the dilute (non-collisional) to the dense limit. However, its numerical solution in multi-dimensional systems is intractable due to the large number of independent variables. As an alternative, Lagrangian methods discretize the density function into parcels that are simulated using Monte-Carlo methods. While quite accurate, as in any statistical approach, Lagrangian methods require a relatively large number of parcels to control statistical noise, and thus are computationally expensive. A less costly alternative is to solve Eulerian transport equations for selected moments of the kinetic equation. However, it is well known that in the dilute limit, Eulerian methods have great difficulty describing correctly the moments as predicted by a Lagrangian method. A two-point quadrature-based Eulerian moment closure is developed and tested here for the Williams spray equation. It is shown that the method can successfully handle highly non-equilibrium flows (e.g., impinging particle jets, jet crossing, and particle rebound off walls) that heretofore could not be treated with the Eulerian approach