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Presents a new method for the numerical simulation of diffusion with phase‐change. The method is able to handle hysteresis and finite‐rate kinetics in the phase‐change reaction. Such phenomena are frequent in solid‐solid phase transitions. The model problem discussed concerns hydrogen migration and hydride precipitation in zirconium and its alloys, a problem of interest to the nuclear industry. With respect to previous ones, our method is the first to incorporate an implicit treatment of diffusion, thus avoiding mesh‐dependent stability limits in the time step. The CPU time can in this way be reduced by a factor of 10–20 in applications. Addresses, through numerical studies, convergence with respect to mesh refinement and reduction of the time step. Also reports on an application of the method to the simulation of laboratory experiments. Shows that the method is a powerful tool to deal with general phase‐change problems, extendable to other physical systems.

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

A two‐dimensional mathematical model of flame spread and solid burning is presented. For the gas phase, it consists of variable density, fully elliptic Navier‐Stokes momentum, energy and chemical species mass equations. Combustion processes are treated according to a one‐step, finite‐rate, reaction. The solid phase model describes a porous cellulosic fuel for a range of thicknesses from the thermally thin to the thermally thick limit. Conductive and convective heat transfer takes place as the solid degrades, by two first order Arrhenius reactions, to volatiles and chars. Variations of solid phase densities account for fuel burn‐out. Effects of gas phase and surface radiation are also included. A steady formulation of gas phase equations with respect to the unsteady solid phase mathematical model is proposed, gas phase characteristic times being much shorter than those of the solid phase. The non‐constant density Navier‐Stokes equations are formulated in terms of vorticity and stream function, avoiding the pressure‐velocity coupling and, at the same time, the adoption of a sample‐fixed coordinate system allows unsteady flame spread processes to be simulated. The solution is computed numerically by means of an iterative, operator‐splitting method based on implicit finite‐difference approximations. Numerical simulations of the dynamics of flame spread over cellulosic solids are presented and extinction limits as a consequence of reduced rates of fuel generation are determined.

A two dimensional time‐dependent Navier Stokes formulation that encompasses aspects from both the LES formalism and the conventional k‐ε approaches was employed to calculate a range of reacting bluff‐body flows exhibiting high or low level large scale structure activity. Extensive regions of local flame extinction found in these bluff‐body flame configurations were treated with a partial equilibrium/two‐scalar exponential PDF combustion submodel combined with a local extinction criterion based on a comparison of the turbulent Damkohler number against the ratio of the scalar scale to the reaction zone thickness. A dual‐mode description, burning/ non‐burning, of combustion provided the local gas state. Comparisons between calculations and measurements indicated the ability of the method to capture all the experimentally observed variations in the momentum and reactive scalar mixing fields over a range of operating conditions from the lean to the rich blow‐out limit.

The aim of this paper is to find the optimal values of the reaction rates coefficients for the combustion of a methane/air mixture for a given reduced reaction mechanism which has a high appropriateness with full reaction mechanism.

A multi‐objective genetic algorithm (GA) was used to determine new reaction rate parameters (A's, β's, and E_a's in the non‐Arrhenius expressions). The employed multi‐objective structure of the GA allows for the incorporation of perfectly stirred reactor (PSR), laminar premixed flames, opposed flow diffusion flames, and homogeneous charge compression ignition (HCCI) engine data in the inversion process, thus enabling a greater confidence in the predictive capabilities of the reaction mechanisms obtained.

The results of this study demonstrate that the GA inversion process promises the ability to assess combustion behaviour for methane, where the reaction rate coefficients are not known. Moreover it is shown that GA can consider a confident method to be applied, straightforwardly, to the combustion chambers, in which complex reactions are occurred.

In this paper, GA is used in more complicated combustion models with fewer assumptions. Another consequence of this study is less CPU time in converging to final solutions.

Reports numerical simulations of an unconfined methane‐air turbulent diffusion flame expanding from a porous burner. Turbulent combustion is simulated using the eddy dissipation concept (EDC) which supposes that the reaction rate is controlled by the turbulent structures which enhance the mixing of fuel and oxidant. Two statistical k‐ε turbulence models have been tested: a standard high Reynolds number (HRN) and a more recent model based on the renormalization group theory (RNG). Radiation heat transfer and soot formation have been taken into account using P1‐approximation and transport submodels which reproduce the main phenomena encountered during soot production (nucleation, coagulation, surface growth). The set of coupled transport equations is solved numerically using a high order finite‐volume method, the velocity‐pressure coupling is treated by a projection technique. The numerical results confirm that 20‐25 percent of the combustion heat released is radiated away from the flame. Unsteady and unsymmetrical flame behaviour is observed for small Froude numbers which results from the development of Rayleigh‐Taylor like instabilities outside the flame surface. For higher Froude numbers the steady‐state and symmetrical nature of the solution is recovered.

This paper aims to assess the sensitivity of numerical simulation results of turbulent reactive flow to the formulation of inlet boundary conditions. The analysis concerns the profiles of the mean velocity the turbulence kinetic energy k and its dissipation rate ϵ. It is intended to provide guidance to the determination of inlet conditions when only global flow data are available. This situation can be met both in simple laboratory experiments and in industrial full-scale applications, when measurements are either incomplete or infeasible, resulting in lack of detailed inlet data.

Two turbulence–chemistry interaction models were studied: eddy dissipation concept and partially stirred reactor. Three different velocity profiles and related turbulence statistics were applied to present feasible scenarios and their consequences. Simulations with the most appropriate inlet data were accompanied with profiles of turbulent quantities obtained with a proposed method. This method was contrasted to other approaches popular in the literature: the pre-inlet pipe and the separate cold flow simulations of a burner. The methodology was validated on two laboratory-scale jet flames: Delft Jet-in-Hot-Coflow and Sandia CHN B. The simulations were carried out with open source code OpenFOAM.

The proposed relations for turbulence kinetic energy and its dissipation rate at the inlet are found to provide results comparable to those obtained with the use of experimental data as inlet boundary conditions. Moreover, from a certain location downstream the jet, weakly dependent on the Reynolds number, the influence of inlet conditions on flow statistics was found to be negligible.

This work reveals the consequences of the use of rather crude assumptions made for inlet boundary conditions. Proposed formulas for the profiles for k and epsilon are attractive alternatives to other approaches aiming to determine the inlet boundary conditions for turbulent jet flows.

The purpose of this paper is to review the applications of the chemical reactor network (CRN) approach for modeling the combustion in gas turbine combustors and classify the CRN construction methods that have been frequently used by researchers.

This paper initiates with introducing the CRN approach as a practical tool for precisely predicting the species concentrations in the combustion process with lower computational costs. The structure of the CRN and its elements as the ideal reactors are reviewed in recent studies. Flow field modeling has been identified as the most important input for constructing the CRNs; thus, the flow field modeling methods have been extensively reviewed in previous studies. Network approach, component modeling approach and computational fluid dynamics (CFD), as the main flow field modeling methods, are investigated with a focus on the CRN applications. Then, the CRN construction approaches are reviewed and categorized based on extracting the flow field required data. Finally, the most used kinetics and CRN solvers are reviewed and reported in this paper.

It is concluded that the CRN approach can be a useful tool in the entire process of combustion chamber design. One-dimensional and quasi-dimensional methods of flow field modeling are used in the construction of the simple CRNs without detailed geometry data. This approach requires fewer requirements and is used in the initial combustor designing process. In recent years, using the CFD approach in the construction of CRNs has been increased. The flow field results of the CFD codes processed to create the homogeneous regions based on construction criteria. Over the past years, several practical algorithms have been proposed to automatically extract reactor networks from CFD results. These algorithms have been developed to identify homogeneous regions with a high resolution based on the splitting criteria.

This paper reviews the various flow modeling methods used in the construction of the CRNs, along with an overview of the studies carried out in this field. Also, the usual approaches for creating a CRN and the most significant achievements in this field are addressed in detail.

Safety improvement and pollutant reduction in many practical combustion systems and especially in aero-gas turbine engines require an adequate understanding of flame ignition and stabilization mechanisms. Improved software and hardware have opened up greater possibilities for translating basic knowledge and the results of experiments into better designs. The present study deals with the large eddy simulation (LES) of an ignition sequence in a conical shaped bluff-body stabilized burner involving a turbulent non-premixed flame. The purpose of this paper is to investigate the impact of spark location on ignition success. Particular attention is paid to the ease of handling of the numerical tool, the computational cost and the accuracy of the results.

The discrete particle ignition kernel (DPIK) model is used to capture the ignition kernel dynamics in its early stage of growth after the breakdown period. The ignition model is coupled with two combustion models based on the mixture fraction-progress variable formulation. An infinitely fast chemistry assumption is first done, and the turbulent fluctuations of the progress variable are captured with a bimodal probability density function (PDF) in the line of the Bray–Moss–Libby (BML) model. Thereafter, a finite rate chemistry assumption is considered through the flamelet-generated manifold (FGM) method. In these two assumptions, the classical beta-PDF is used to model the temporal fluctuations of the mixture fraction in the turbulent flow. To model subgrid scale stresses and residual scalars fluxes, the wall-adapting local eddy (WALE) and the eddy diffusivity models are, respectively, used under the low-Mach number assumption.

Numerical results of velocity and mixing fields, as well as the ignition sequences, are validated through a comparison with their experimental counterparts. It is found that by coupling the DPIK model with each of the two combustion models implemented in a LES-based solver, the ignition event is reasonably predicted with further improvements provided by the finite rate chemistry assumption. Finally, the spark locations most likely to lead to a complete ignition of the burner are found to be around the shear layer delimiting the central recirculation zone, owing to the presence of a mixture within flammability limits.

Some discrepancies are found in the radial profiles of the radial velocity and consequently in those of the mixture fraction, owing to a mismatch of the radial velocity at the inlet section of the computational domain. Also, unlike FGM methods, the BML model predicts the overall ignition earlier than suggested by the experiment; this may be related to the overestimation of the reaction rate, especially in the zones such as flame holder wakes which feature high strain rate due to fuel-air mixing.

This work is adding a contribution for ignition modeling, which is a crucial issue in various combustion systems and especially in aircraft engines. The exclusive use of a commercial computational fluid dynamics (CFD) code widely used by combustion system manufacturers allows a direct application of this simulation approach to other configurations while keeping computing costs at an affordable level.

This study provides a robust and simple way to address some ignition issues in various spark ignition-based engines, namely, the optimization of engines ignition with affordable computational costs. Based on the promising results obtained in the current work, it would be relevant to extend this simulation approach to spray combustion that is required for aircraft engines because of storage volume constraints. From this standpoint, the simulation approach formulated in the present work is useful to engineers interested in optimizing the engines ignition at the design stage.