Combustion models for CFD

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Combustion models for CFD refers to combustion models for computational fluid dynamics. Combustion is defined as a chemical reaction in which a hydrocarbon fuel reacts with an oxidant to form products, accompanied with the release of energy in the form of heat. Being the integral part of various engineering applications like: internal combustion engines, aircraft engines, rocket engines, furnaces, and power station combustors, combustion manifests itself as a wide domain during the design, analysis and performance characteristics stages of the above-mentioned applications. [1] With the added complexity of chemical kinetics and achieving reacting flow mixture environment, proper modeling physics has to be incorporated during computational fluid dynamic (CFD) simulations of combustion. Hence the following discussion presents a general outline of the various adequate models incorporated with the Computational fluid dynamic code to model the process of combustion. [2]

Contents

Overview

Computational fluid dynamics modeling of combustion calls upon the proper selection and implementation of a model suitable to faithfully represent the complex physical and chemical phenomenon associated with any combustion process. The model should be competent enough to deliver information related to the species concentration, their volumetric generation or destruction rate and changes in the parameters of the system like enthalpy, temperature and mixture density. The model should be capable of solving the general transport equations for fluid flow and heat transfer as well as the additional equations of combustion chemistry and chemical kinetics incorporated into that as per the simulating environment desired [1]

Critical considerations in combustion phenomenon

The major consideration during any general combustion process includes the mixing time scale and the reacting time scale elapsed for the process. The flame type and the type of mixing of flow streams of the constituents also have to be taken into account. Apart from that as far as the kinetic complexity of the reaction is concerned, the reaction proceeds in multiple steps and what appears as a simple one line reaction actually completes after a series of reactions. [1] [2] Also the transport equations for mass fractions of all the species as well as the enthalpy generated during the reaction have to be solved. Hence even the simplest combustion reaction involves very tedious and rigorous calculation if all the intermediate steps of the combustion process, all transport equations and all flow equations have to be satisfied simultaneously. All these factors will have a significant effect on the computational speed and time of the simulation. But with proper simplifying assumptions Computational fluid dynamic modeling of combustion reaction can be done without substantial compromise on the accuracy and convergence of the solution. [2] The basic models used for the same are covered in the following paragraphs.

Simple chemical reacting system model

This model takes into consideration only the final concentration of species and takes into account only the global nature of combustion process where the reaction proceeds infinitely fast as a single step process without much stress on the detailed kinetics involved. [1]

The reactants are assumed to react in stoichiometric proportions. The model also deduces a linear relationship between the mass fractions of fuel, oxidant and the non dimensional variable mixture fraction. [2] The model also takes into account an additional assumption that the mass diffusion coefficients of all species are equal. [3] Owing to this additional assumption the model only solves one extra partial differential equation for mixture fraction and after solving the transport equation for the mixture fraction the corresponding mass fractions for fuel and oxidant are calculated.

This model can very well be applied to a combustion environment where laminar diffusion effects are dominant and the combustion proceeds via non premixed fuel and oxidant streams diffusing into each other giving rise to a laminar flame. [1]

Eddy break–up model

Simulation of can combustor using eddy dissipation model. Combustor-Temp-Plane.png
Simulation of can combustor using eddy dissipation model.

This model is used when turbulent mixing of the constituents has to be taken into consideration. The k/Ɛ turbulent time scale is used to calculate the reaction rate. A comparison between the turbulent dissipation rates of the fuel, oxidant and products is done and the minimum amongst all is taken as the rate of the reaction. The transport equations for the mass fractions of the constituents are solved using this rate of reaction. [1] Apart from this a mean enthalpy equation is also solved and temperature, density and viscosity are calculated accordingly. The model can also be implemented when finite rate kinetically controlled reaction is to be simulated. In such situation while deciding the rate of the reaction the Arrhenius kinetic rate expression is also taken into account and the rate of reaction is taken as minimum amongst the turbulent dissipation rates of all the constituents and the Arrhenius kinetic rate expression. [2] Since turbulent mixing governs the characteristics of this model, there exists a limit to the quality of the combustion simulation depending upon the type of the turbulent model implemented to represent the flow. The model can also be modified to account for mixing of fine structures during the turbulent reaction. This modification of the model results in the eddy dissipation model which consider the mass fraction of fine structures in its calculations. [1]

Laminar flamelet model

This model approximates the turbulent flame as a series of laminar flamelet regions concentrated just around the stoichiometric surfaces of the reacting mixture. [1] This model exploits the use of experimental data for determining relations between the variables considered like mass fraction, temperature etc. The nature and type of dependence of the variables is predicted through experimental data obtained during laminar diffusion flame experiment and laminar flamelet relationship is deduced based on the same. These relationships are then used to solve the transport equations for species mass fraction and mixture composition. [2] The model can very well be implemented for situations where concentration of minor species in the combustion is to be computed like quantifying the generation of pollutants. [1] A simple enhancement to the model results in the flamelet time scale model which takes finite rate kinetics effect into consideration. The flamelet time scale model produces steady laminar flamelet solution when reaction proceeds very fast and captures the finite rate effects when reaction chemistry is dominant. [4]

Presumed probability distribution function model

This model takes into account a statistical approach for calculating the variables like species mass fractions, temperature and density while the mixture composition is calculated at the grids. [2] Then these all variables are calculated as functions of the mixture fraction around a presumed probability distribution function. [1] [5] The model can produce satisfactory results for turbulent reactive flows where convection effects due to mean and fluctuating components of velocity are dominant. [6] The model can be extended for adiabatic as well as non adiabatic conditions.

Conditional moment closure

Conditional moment closure (CMC) is an advanced combustion model. The basic idea is to model the chemical source based on conditional averages. The model was first introduced for non-premixed flows and hence the conditioning is done in the mixture fraction. [7]

Other models

The following are some of the other relevant models used for computational fluid dynamic modeling of combustion.

The chemical equilibrium model considers the effect of intermediate reactions during turbulent combustion. [1] The concentration of species is calculated when the combustion reaction reaches equilibrium state. The species concentration is calculated as a function of mixture fraction by deploying certain equilibrium calculation programs available to serve the purpose. The conditional closure model solves the transport equations for the mean components of the flow properties without considering the fluctuating composition of the reaction mixture. [6]

Related Research Articles

<span class="mw-page-title-main">Combustion</span> Chemical reaction

Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While the activation energy must be overcome to initiate combustion, the heat from a flame may provide enough energy to make the reaction self-sustaining.

<span class="mw-page-title-main">Fluid dynamics</span> Aspects of fluid mechanics involving flow

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

<span class="mw-page-title-main">Computational fluid dynamics</span> Analysis and solving of problems that involve fluid flows

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.

<span class="mw-page-title-main">Chemical reactor</span>

A chemical reactor is an enclosed volume in which a chemical reaction takes place. In chemical engineering, it is generally understood to be a process vessel used to carry out a chemical reaction, which is one of the classic unit operations in chemical process analysis. The design of a chemical reactor deals with multiple aspects of chemical engineering. Chemical engineers design reactors to maximize net present value for the given reaction. Designers ensure that the reaction proceeds with the highest efficiency towards the desired output product, producing the highest yield of product while requiring the least amount of money to purchase and operate. Normal operating expenses include energy input, energy removal, raw material costs, labor, etc. Energy changes can come in the form of heating or cooling, pumping to increase pressure, frictional pressure loss or agitation.

Thermofluids is a branch of science and engineering encompassing four intersecting fields:

<span class="mw-page-title-main">Premixed flame</span>

A premixed flame is a flame formed under certain conditions during the combustion of a premixed charge of fuel and oxidiser. Since the fuel and oxidiser—the key chemical reactants of combustion—are available throughout a homogeneous stoichiometric premixed charge, the combustion process once initiated sustains itself by way of its own heat release. The majority of the chemical transformation in such a combustion process occurs primarily in a thin interfacial region which separates the unburned and the burned gases. The premixed flame interface propagates through the mixture until the entire charge is depleted. The propagation speed of a premixed flame is known as the flame speed which depends on the convection-diffusion-reaction balance within the flame, i.e. on its inner chemical structure. The premixed flame is characterised as laminar or turbulent depending on the velocity distribution in the unburned pre-mixture.

<span class="mw-page-title-main">Multiphase flow</span>

In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve some form of multiphase flow. It is also prevalent in many natural phenomena.

Turbulent diffusion is the transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions. It occurs when turbulent fluid systems reach critical conditions in response to shear flow, which results from a combination of steep concentration gradients, density gradients, and high velocities. It occurs much more rapidly than molecular diffusion and is therefore extremely important for problems concerning mixing and transport in systems dealing with combustion, contaminants, dissolved oxygen, and solutions in industry. In these fields, turbulent diffusion acts as an excellent process for quickly reducing the concentrations of a species in a fluid or environment, in cases where this is needed for rapid mixing during processing, or rapid pollutant or contaminant reduction for safety.

The Sugden Award is an annual award for contributions to combustion research. The prize is awarded by the British Section of The Combustion Institute for the published paper with at least one British Section member as author, which makes the most significant contribution to combustion research. The prize is named after Sir Morris Sugden.

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and as a continuum. In the MP-PIC approach, the particle properties are mapped from the Lagrangian coordinates to an Eulerian grid through the use of interpolation functions. After evaluation of the continuum derivative terms, the particle properties are mapped back to the individual particles. This method has proven to be stable in dense particle flows, computationally efficient, and physically accurate. This has allowed the MP-PIC method to be used as particle-flow solver for the simulation of industrial-scale chemical processes involving particle-fluid flows.

<span class="mw-page-title-main">KIVA (software)</span>

KIVA is a family of Fortran-based Computational Fluid Dynamics software developed by Los Alamos National Laboratory (LANL). The software predicts complex fuel and air flows as well as ignition, combustion, and pollutant-formation processes in engines. The KIVA models have been used to understand combustion chemistry processes, such as auto-ignition of fuels, and to optimize diesel engines for high efficiency and low emissions. General Motors has used KIVA in the development of direct-injection, stratified charge gasoline engines as well as the fast burn, homogeneous-charge gasoline engine. Cummins reduced development time and cost by 10%–15% using KIVA to develop its high-efficiency 2007 ISB 6.7-L diesel engine that was able to meet 2010 emission standards in 2007. At the same time, the company realized a more robust design and improved fuel economy while meeting all environmental and customer constraints.

Geochemical modeling or theoretical geochemistry is the practice of using chemical thermodynamics, chemical kinetics, or both, to analyze the chemical reactions that affect geologic systems, commonly with the aid of a computer. It is used in high-temperature geochemistry to simulate reactions occurring deep in the Earth's interior, in magma, for instance, or to model low-temperature reactions in aqueous solutions near the Earth's surface, the subject of this article.

Reactive transport modeling in porous media refers to the creation of computer models integrating chemical reaction with transport of fluids through the Earth's crust. Such models predict the distribution in space and time of the chemical reactions that occur along a flowpath. Reactive transport modeling in general can refer to many other processes, including reactive flow of chemicals through tanks, reactors, or membranes; particles and species in the atmosphere; gases exiting a smokestack; and migrating magma.

The eddy break-up model (EBU) is used in combustion engineering. Combustion modeling has a wide range of applications. In most of the combustion systems, fuel and oxygen are separately supplied in the combustion chamber. Due to this, chemical reaction and combustion occur simultaneously in the combustion chamber. However, the rate of the chemical reaction is faster than the rate of mixing fuel and oxygen. Therefore, that rate of combustion is controlled by rate of mixing. Such cases, where formation of pre-mixture is difficult, are called diffusion combustion or diffusion flames.

The simple chemical reacting system (SCRS) is one of the combustion models for computational fluid dynamics. This model helps us to determine the process of combustion which is a vital phenomenon used in many engineering applications like aircraft engines, internal combustion engines, rocket engines, industrial furnaces, and power station combustors. The simple chemical reacting system (SCRS) refers the global nature of the combustion process considering only the final species concentrations. The detailed kinetics of the process is generally neglected and it postulates that combustion does proceed via a global one-step without intermediates. Infinitely fast chemical reaction is assumed with oxidants reacting in stoichiometric proportions to form products. SCRS considers the reaction to be irreversible i.e. rate of reverse reaction is presumed to be very low.

Chemical reaction models transform physical knowledge into a mathematical formulation that can be utilized in computational simulation of practical problems in chemical engineering. Computer simulation provides the flexibility to study chemical processes under a wide range of conditions. Modeling of a chemical reaction involves solving conservation equations describing convection, diffusion, and reaction source for each component species.

The laminar flamelet model is one of the methods of modelling turbulent combustions apart from SCRS, eddy flamelet model and others. Combustion is a very important thermochemical process with significant material and aerodynamic implications and thus CFD modeling of combustion has become indispensable. The laminar flamelet model is basically for non pre-mixed fuel.

In combustion, the Karlovitz number is defined as the ratio of chemical time scale to Kolmogorov time scale , named after Béla Karlovitz. The number reads as

Paul Andrews Libby was a professor of mechanical and aerospace engineering at the University of California, San Diego, a specialist in the field of combustion and aerospace engineering.

References

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