Droplet and spray combustion modelling

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Gaetano Continillo

Dipartimento di Ingegneria Università del Sannio

Benevento, Italy

Politechnika Krakowska – Monday 5 June 2017

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Droplet and spray combustion is fundamental to many practical applications. Physics and chemistry involved are among the most complex for multiphase reacting systems, and this is reflected in the complexity of modelling

approaches introduced and employed since the early Fifties of last century.

The lecture will introduce the essential aspects of the phenomenon, then illustrate models of intermediate

complexity, show some application to ideal configurations, discuss relevant results by comparing them to

experimental evidence, and indicate areas of current and future development.

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Combustion processes call for improvement in terms of:

• Thermal efficiency

• Pollution control

• Development of combustion technologies for renewable fuel sources

• Thermal efficiency contributes to save energy

• Pollution control is necessary for global and local environmental protection

• Renewable fuels are necessary in view of fossil fuel shortage and to avoid greenhouse effect due to increase of CO₂ concentration in the atmosphere.

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A definition of Combustion

Rapid oxidation generating heat, or both light and heat; also, slow oxidation accompanied by relatively

little heat and no light.

This definition emphasizes the intrinsic importance of chemical reactions to combustion.

It also emphasizes why combustion is so important:

combustion transforms energy stored in chemical bonds to heat that can be utilized in a variety of ways.

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Combustion modes and flame types

Combustion can occur in flame and non-flame mode.

The difference between flame and non-flame mode can be explained for example with the knocking phenomena in spark ignition internal combustion engines.

A flame is a thin zone of intense chemical reaction.

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As the flame moves across the combustion space, temperature and pressure rise in the unburned gas.

Unburned fuel-air mixture Burnt fuel-air mixture

Propagating flame Spark

location

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Under certain conditions, rapid oxidation reactions occur at many locations

Autoigniting fuel-air mixture

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There are premixed flames and non-premixed (diffusion) flames

In a premixed flame fuel and oxidizer are mixed at the molecular level prior to the occurence of any significant reaction. Spark ignition engines are a good example.

In a diffusion flame, the reactants are initially separated, and reaction occurs only at the interface between the fuel and the oxidizer. An example af a diffusion flame is a

simple candle.

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Oxidizer diffusing from outside

Flame sheet

Liquid fuel climbing for capillarity

Solid fuel

Vapor fuel diffusing from inside

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Important topics in the study of combustion are:

• Thermochemistry

• Chemical kinetics

• Molecular transport of mass and heat

• Fluid mechanics

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Thermochemistry provides the link between chemical composition of the system, temperature and pressure.

Chemical bonds break and form during chemical reactions.

Chemical potential energy is destroyed (exothermic

reactions) and accumulated (endothermic reactions), to the benefit or expense of kinetic energy of the molecules. The kinetic energy of the molecules in the system is related to temperature.

Under proper circumstances, all systems reach equilibrium.

Equilibrium is achieved via the available path according to physical constraints (for example contant volume, constant pressure). Equilibrium is met when a conveniently defined state function (e.g. Gibbs free energy) reaches its minimum.

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Chemical reactions proceed towards equilibrium with a finite rate. This rate depends on composition and

temperature according to laws studied and assessed in chemical kinetic studies.

Thus, thermochemistry sets the target and chemical kinetics dictates the rate.

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Example: first–order gas–phase bi–molecular reactions.

Chemical transformation events in a gaseous system occur in large amount if:

• Both reactant molecules are present in large number (the more there are, the more probably they hit each other)

• Kinetic energy of molecules (temperature) is high (each hit is more probable to break/form chemical bonds)

r kc c A B

 

₀ ^exp



_A ^/



k  k T  k E RT

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Fuels are often transported and stored in condensed phase (solid or liquid). This ensures high energy density (in terms of storage), easier handling, especially for liquids, and higher safety.

Combustion technology therefore involves heterogeneous processes, like grinding (for solids), atomization (for

liquids), phase changes (liquefaction, evaporation), multiphase mixing.

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Real systems are non-uniform in space. This produces gradients in species concentrations and temperature.

Flames are present when strong gradients exist. Gradients are the driving forces for molecular transport of mass and heat.

Molecular transport phenomena govern both premixed and diffusion flames.

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Most combustion processes take place in fluids in motion. Thus, when composition and temperature

gradients are present in a flow field, convection can be an important, if not dominant, mechanism of transport.

Moreover, most combustion processes are designed to take place in a turbulent flow. Turbulent flows are the most complex phenomena in fluid mechanics.

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Finally, observe that all of the above phenomena are physically coupled to each other. Temperature

increases due to exothermic chemical reactions, thus density must decrease according to the constitutive

equation (for example the ideal gas law). Density decrease implies expansion in the fluid flow. This creates motion that influences the spatial distribution of species and

temperature, and so on. Moreover, molecular transport coefficients, including viscosity, all depend on temperature.

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Simulation of many gas–phase combustion processes is nowadays feasible by means of computer codes solving initial and boundary value problems on Navier–Stokes equations written for reactive systems.

Multi–phase combustion can also be described by

coupling gas–phase and condensed–phase equations, via boundary conditions when a separation interface is

present, or via source terms for dispersed condensed–

phase.

However, most systems are just too complex to be fully described in their detail. Therefore one has to resort to some modelling.

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There are distributed–parameter models, in which state variabes are function of position and time, and lumped–

parameter models, in which variables may be only function of time or of a time-like variable.

Lumped parameter models, in contrast with distributed parameter models, are built by making assumptions on spatial uniformity of the state variables.

Models

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Droplet vaporization and combustion

Even in the simplest ideal configuration, droplet vaporization is not simple.

Take a spherical droplet, made of a simple liquid (for example, n-heptane) and imagine it surrounded by a

omogeneous gas mixture (for example, air), in absence of gravity, and imagine that droplet and surrounding gas are at room temperature. Imagine there is spherical symmetry.

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The concentration of vapour fuel in the gas-phase at the droplet surface will correspond to a partial pressure equal to the n-heptane vapour pressure at room temperature.

This will obviously create a concentration gradient in the gas-phase, that will create a mass flux by diffusion. As a consequence, evaporation must happen, to maintain the equilibrium vapour pressure, as the fuel vapour diffuses towards infinity.

r Y_f

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The source for fuel vapour is the droplet. Obviously, the mass of the droplet will decrease progressively, and also its volume.

There is also a need for energy to evaporate the liquid fuel, in the amount represented by the latent heat of

vaporization per unit mass. This energy must come from the sensible heat in the surroundings of the droplet

surface, both in the liquid and in the gas layer.

r Y_f, T

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The scenario we have depicted represents a quasi-

isothermal condition. When the gas-phase temperature is high, a limit condition is met.

The droplet surface temperature reaches a maximum, corresponding to the boiling point.

r Y_f, T

T_b

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The story becomes more complex, even for vaporization only, when one considers:

- Multicomponent fuel droplets - Droplets in motion

- Motion inside the droplet

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Droplet vaporization and combustion - Multicomponent fuel

droplets

This is the common case, as fuels are blends of different hydrocarbons. Each component has a different boiling point.

Depending on the time of

evolution of the phenomenon, the process can go from batch

distillation (slow heatup,

perfectly mixed liquid) to flash evaporation (fast heatup, vapor fuel retains the composition of the original blend and leaves the droplet in layers like an onion

shell). flash evaporation batch distillation

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Droplet vaporization and combustion - Droplets in motion

Especially in regions where liquid fuel jets enter the

combustion chamber, slip motion between droplets and gas is significant, and the two phases influence each other’s motion. Heat, mass and

momentum transfer must be computed via proper transport coefficients, as a function of the Reynolds number and of other physical parameters.

Obviously, convective

transport is enhanced with respect to the stagnant case.

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- Motion inside the droplet In most industrial codes,

physical parameters inside the droplet are lumped, i.e. a

scalar value for temperature and drop composition, and the droplets are treated as solid spheres. However, there is evidence that internal droplet motion occurs, and that this influences the distribution of quantities inside the droplet and droplet-gas interactions.

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Droplet combustion: the simplest concept

The ideal combustion process occurs with a droplet acting as a fuel vapour source and an envelope flame surrounding the droplet.

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Droplet vaporization

r Y_f, T

T_b

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The droplet surface temperature attains a limiting maximum T_b, corresponding to the boiling point. The gas-phase

temperature attains a maximum T_f, at the flame location. Fuel and oxidizer mass fractions reach a zero value, both at the flame location.

Droplet combustion

r Y_f, Y_o, T

T_b

r_f T_f

T_f T_f

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Multiple droplets combustion

Depending on droplet spacing and other parameters, multiple droplets may form individual envelope flames or join in clusters, surrounded by enveloping flame surfaces. [Figure from Wu & Sirignano, 2011]

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Spray combustion

SPRAY MODELLING

Fuel sprays are usually treated as a dispersed liquid phase, which moves in and interacts with the surrounding continuous gas phase. In this approach, a fuel spray is represented by an ensemble of discrete droplet groups or

"parcels", each parcel containing a number of droplets with the same size, velocity and temperature. The droplet parcels are tracked in a Lagrangian

fashion as they move through the gas phase, exchanging mass, momentum and energy.

The effect of the droplet parcels on the continuous phase due to drag, heat and mass transfer is implemented via source terms in the gas phase conservation equations. Sub-models are provided for:

droplet drag

droplet heat and mass transfer primary and secondary breakup droplet coalescence and collisions droplet-turbulence interactions spray-wall interactions

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Spray combustion in ideal configurations

We now will see two ideal configurations:

- A 1D, spherically-symmetric unsteady spray combustion, with ignition at the sphere center and uniform initial spray distribution.

- A 2D (made 1D by similarity solution) steady counterflow spray combustion

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These works were made during a long research visit at University of California, Irvine, 1986 – 1988

To place these study in the stream of spray combustion simulation development, note that:

• The first public release of KIVA was made in 1985 through the National Energy Software Center (NESC) at Argonne National Laboratory

• The computers we used were like this:

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• The computers we used were like this:

Motorola 68000 CPU, 8 MB RAM (MEGA Bytes please note), <1 MIPS

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But at that time I had a good postdoc.

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1D, spherically-symmetric unsteady spray combustion, with ignition at the sphere center and uniform initial spray distribution.

Closed Vessel.

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Closed Vessel.

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Closed vessel

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Closed vessel

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Open geometry

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2D (made 1D by similarity solution) steady counterflow spray combustion

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