combustion of liquid fuels

7/30/2019 Combustion of Liquid Fuels

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INTRODUCTION

FUELS Are substances, which when heated, undergo a chemical reaction with an oxidizer

(typically oxygen in air) to liberate heat.

Liquid Fuels- Are derived primarily from crude oil.

- Can also be derived from oil shale, tar sands, coal, and biomass.

Crude OilA mixture of naturally occurring hydrocarbons with small amounts of sulfur,

nitrogen, oxygen, trace metals, and minerals. Crude oil is generally found

trapped in certain rock formations that were originally part of the ocean floor.

Organic matter on the ocean bottom was encased with in rock layers atelevated pressure and temperature, and over millions of years gradually

formed crude oil.

COMBUSTION OF LIQUID FUELS

9. Spray Formation and Droplet Behavior

Oil-fired furnaces and boilers, diesel engines, and gas turbines utilize liquidfuel sprays to

break up the liquid fuel in order to increase the fuel surface area and thus increase thevaporization and combustion rate.

9.1. Spray Formation

Types of Spray Nozzles:1. Pressure nozzleused predominantly in diesels2. Air or Stream Atomization nozzleused in burners and furnaces3. Swirl-type nozzleused where less forward penetration is required

Spray Breakup

The precise mechanism of spray breakup varies with the injection pressure and type of

atomizer. The resulting droplet size distribution for steady-flow injectors have been wellformulated empirically and as yet no validated theory for predicting droplet size has been

formulated for practical atomizers. In qualitative terms, the breakup mechanism may be

characterized by a set of six steps:

1. Stretching of fuel into sheets or streams2. Appearance of ripples and protuberances3. Formation of ligaments or holes in the sheets4. Collapse of ligaments or holes in the sheets5. Further breakup due to vibration of droplets6. Agglomeration or shedding from large drops

For simple orifices the behavior of the jet may be characterized by three dimensionlessgroups:


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Jet Reynolds number: Jet Weber number:

Ohnesorge number:

where: = Jet Reynolds number = density of liquid

= velocity of liquid

= absolute viscosity of liquid = Jet Weber number = density of gas = velocity of gas = diameter of undisturbed jet = surface tension of liquid (in contact with surrounding gas)Criteria for spray formation are given by a plot of log Oh versus log Rej, which is divided

into three zones as shown in Fig. 9.1. Zone I is named for Rayleigh, who did a wave instability

analysis of jets showing that breakups are due to the effects of surface tension forces on the jet.

The theory predicts that maximum stability (the breakup point) takes place where the jet

disturbance wavelength is about 4.6dj. In zone II helicoidal waves are observed prior tobreakup. Breakup reflects the beginnings of the influence of the ambient air; this is also called

wind-induced region. In zone III the jet is disrupted into droplets very close to the orifice. Here,

breakup is due to the effects of ambient air combined with effects of flow turbulence.

For swirl-type nozzle (Fig. 9.2):1. Conical sheets breakup first by formation of holes.2. Then the lace pattern breaks up into droplets.3. Droplets formed near the nozzle exit may undergo further breakup due to

aerodynamic forces.

4. Large droplets deform into a bag shape and then burst.5. Smaller droplets may vibrate and then separate into smaller parts.For noncritical conditions, the onset of droplet shattering due to aerodynamic forces is

related to the droplet Weber number:


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where: = relative velocity of the ambient gasd= droplet diameter

For Weber numbers greater than 12, one expects breakup.


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Example of droplet formation in some diesel engine conditions:

The various forces that can cause breakup of a droplet by a vibrational mechanism are

illustrated in Taylors analogy breakup model (TAB model). The small change in the droplet

radius, which we will callx, is calculated by:

where a is the initial droplet radius. Ifx exceeds a the droplet is assumed to break apart. For

many cases the damping and restoring forces due to viscosity and surface tension, respectively,can be small relative to the aerodynamic force. Then, taking , the criteria for breakup(x = a) gives:

and the minimum time delay for aerodynamic breakup is:

if it is assumed that and a are constant. In practice changes rapidly due to drag forces and adecreases as the droplet vaporizes.

Spray breakup for single-hole with high-pressure injection such as used in diesel engines

is the least understood of the various breakup phenomena. It is logical to assume that if theinjection pressure rises very rapidly, the droplet breakup will be more rapid and effective that if


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the pressure rises slowly. During this period the spray may go from zone II to zone III of Fig. 9.1

as the exit velocity increases with time.

9.2. Size Distributions

Since the theory of droplet breakup has not been adequate to predict the size distributionof droplets in practical sprays, it has been necessary to measure the distribution experimentally

and then fit the resulting data with empirical functions.

Two Basic Distribution Measurements:

1. Spatial Distribution is obtained by counting droplets in a given volume at a giveninstant. (e.g. using a camera to photograph a given volume of the spray and then counting

the number of droplets)2. Temporal Distribution is obtained by counting all droplets passing through a given

surface.

Velocity distribution and number distribution are also needed in order to compare thespatial and the temporal data. Drop size and velocity distributions can be obtained by use of a

laser analyzer. Drop size distribution measurements are typically as a histogram such as Fig. 9.4,

where is the fraction of droplets counted in size interval .

Various average sizes have been defined to characterize the spray in a simple way. Onemay calculate the average diameter, the size which gives the average surface area, or the sizewhich gives the average volume. The average volume is given by


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The most probable size is the size with the greatest number of counts. The mean size base on

number is

The mean size base on surface area (the diameter which gives the average surface area) and that

based on volume (the diameter which gives the average volume) are, respectively,

A number of spray model use the Sauter mean diameter (SMD), which is

9.3. Fuel Injectors

General Criteria which Govern Injector Design:

For simple on-off operations in furnaces and other stationary burners, the injector must berelatively inexpensive andfree of maintenance problems.

For transportation engines, good atomization and dispersion are required over a widerange of fuel flows.

In the case of gas turbines the combustor gas exit temperature must be uniform so as not

to overheat portions of the turbine. In both diesels and turbines, excessive smoke and unburnedhydrocarbons can result from poor engine performance. The degree of atomization required

depends primarily upon the time available for the vaporization-mixing process. In a diesel engine

this time can be as short as a few milliseconds and thus very small droplets are required.

Penetration and dispersion are inversely related, that is, high penetration is achieved only by loss

of dispersion.

Steady-Flow Injectors

Types of Steady-Flow Injectors:

1. Plain Orifice- The spray cone angle lies between 5 and 15 and is affected more by fluid

viscosity and surface tension than by the orifice diameter do orL/do, where L

is the orifice length.


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2. Simplex or Swirl Atomizer- The fluid is caused to swirl by tangential slots or other similar means (refer to

Fig. 9.6.). The high velocity causes an air core vortex so that the fluid forms a

hollow cone as it emerges from the orifice. The spray angle may be quite large

up to 90. The cross-section average SMD (Sauter mean diameteraverage

particle size) for this atomizer is about 45m.

Aircraft gas turbines require a wide range of fuel flow rates. The higher flow rates requirepressures of about 400 atm to be sure that satisfactory operation would take place at the lowestflow rate. However, these high pressures are much too high for the large steady flows of a gas

turbine or a furnace. To solve the problem of fuel turndown in aircraft and industrial gas turbines

and in oil-fired furnaces, various forms of air-blast atomizers have been designed.

Two Types of Air-Blast Atomizers:

1. Prefilming Pintle (Fig. 9.8a)2. Prefilming Double Swirl (Fig. 9.8b)

Air-blast atomizers provide additional air, which creates good mixing and thus reduces

soot formation (at the expense of NOx formation; NOx production is highest with 2545% excessair). The SMD of such atomizers increases with increasing liquid viscosity and surface tensionand with decreasing air-to-liquid ratio.


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Intermittent Injectors

Basic Types of Injector Systems for Diesels:

1. Individual Pump System- Each cylinder is provided with an individual metering and compression pump.

2. Distributor System- Combined individual pumps with injectors; pumps and meters the fuel to the

set of injectors.3. Common-Rail System

- The pump does not meter, but only supplies a constant pressure to a commonpipe (rail), which carries the fuel to the injectors.

Nozzles for Intermittent Injectors

Diesel fuel injectors are typically of the hole type in which the needle is inwardlyopening.

Type of Nozzles:

1. Mutihole Nozzle


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- Fig. 9.11a shows a sac volume below the needle, which causes dribble at theend of injection. Elimination of this volume as shown in Fig. 9.11b reducesexhaust smoke greatly.

2. Single-Hole Nozzle- Fig. 9.12 shows standard and throttling pintle nozzles, which are typical of

single-hole nozzles. Such single-hole nozzles are used in some designs ofdirect injection stratified-charge engines. The throttling pintle tends to prevent

weak injection at start of injection and such faster to prevent dribble at the end

of injection.

9.4. Spray Dynamics

The fuel sprays used in direct-injection reciprocating engines are unsteady; all of the in-

cylinder engine sprays tend to influence the air motion significantly. Given a spray droplet sizeand velocity distribution near the spray nozzle, relationships for droplet motion, vaporization,

and agglomeration may be modeled. For some sprays such as the air atomization sprays and the

very-high-pressure (1400 atm) diesel sprays, the spray momentum is large and the droplet size is

very small. For such sprays, the droplets may vaporize quickly and the spray may beapproximated as a gas jet.

As a simple example, consider a gas jet in a stagnant surrounding gas. As gas leaves the

nozzle, a boundary layer grows along the outer portion of the jet stream. The inner portion that isunaffected by the boundary layer gradually diminishes until the boundary layer has filled the

entire jet region. After a transition region, the profile becomes fully developed. The unaffected

core region is about 4 to 5 diameters long, and the transition region is about 10 diameters long.

Fig. 9.13 shows the various regions.


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Fig. 9.15 illustrates the spray pattern and some important parameters. As the jet interactswith the surrounding air, it exchanges momentum and entrains the air. Fig. 9.16 shows the

patterns of streamlines for a circular, turbulent jet. The air flows perpendicular to the axis and

then turns sharply as it enters the jet region. For an air densityaand jet density0 from a nozzle

orifice diameter, d0, and the ratio of the entrained mass flow rate

to nozzle flow rate

is


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For many practical problems the jet does not flow into stationary air, but rather into aflowing air stream. For example, the flow may be perpendicular to the jet. For such cross flows,

the jet bends until its axis is parallel to the stream direction. In the cross-flow region, the flow

around the jet causes vortices to form behind the jet. The jet cross section is no longer circular,but becomes kidney-shaped. The behavior of burning gas jets in cross flow has been studied

experimentally at atmospheric pressure; however, less is known about the behavior of such jets

at high pressures and temperatures. Liquid sprays in high-temperature air are found to behavesimilarly to dense gas jets, and thus dense gas jet theory have often been used as a crude methodof modeling liquid sprays.

For thin sprays such as used in gas turbines, the droplet vaporization time is important

and can be worked out using single-droplet trajectory and vaporization equations. Note that inaddition to momentum exchange, the droplets exchange heat, primarily by taking energy from

the air, to provide the latent heat of vaporization needed to vaporize the liquid.

Diesel Spray Dynamics

As breakup takes place for the first liquid out of the nozzle, the droplets encounter the

undisturbed flow field. For the moment, let us consider stagnant surroundings. The first droplets quickly give up their momentum to the air and quickly slow down

(momentum exchange).

The next droplets formed at the nozzle now see air set in motion by the precedingdroplets and thus do not slow down as quickly. In this way it is possible to build up

the entrained air flow and allow to the following droplets to penetrate fartherdownstream.

Droplets formed later pass droplets formed earlier.


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The unsteady air motion induced by the exchange of momentum with the dropletssweep fresh air into the spray and transports vapor towards the end of the spray.

Of course, sprays in real combustors often encounter cross flows. For high-pressure

liquid sprays, the spray is not deflected very much by the cross flow; however, small droplets can

be swept sideways out of the spray. These droplets may vaporize rapidly in the surrounding hotair and thus form a vapor cloud downstream of the spray axis.

Empirical observations of thick sprays formed by pressure atomization have been carried

out for more than 50 years. The basic measurements have been spray cone angle and tippenetration distance. For a short time, tb, during the early development of the spray, the tip

moves linearly with time; after that the spray length is proportional to the square root of time.

For the initial linear portion (t tb), the penetration distanceL is given by:

where:

and

For t tb the penetration distance is proportional to the power of the pressure difference and to

the square root of the hole diameter:

where: = density of air = density of liquid = time duration of injection

= nozzle hole diameter

= pressure dropA correction factor for the effect of a cross-flow velocity is given by the following

equation; the penetration with cross flow,Lf, is:


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where: = rotational speed of air or swirl = velocity of liquid at the orificeIn a certain sample problem for diesel fuel injector, with the air swirl not considered, the

penetration distance L was calculated to be 63.9 mm. Now, considering the air swirl, the

penetration distanceLfwas found to be 54 mm. Thus the swirl decreases the penetration distanceof the spray, but it also improves fuel-air mixing within that smaller volume.

Single-Droplet Dynamics

For steady flow with Reynolds number less than 1, the Stokes drag equation applies. The total

force F of the fluid on the sphere of diameter dis

The first term is due to the buoyant force and can often be neglected, the second term is due topressure drag, and the third term is due to viscous drag. The total pressure drag and viscous drag, , may be expressed by the use of a drag coefficient :

where for Stoke flow. There are numerous empirical formulas used to compute forthe drag coefficient depending on the Reynolds number.

9.5. Vaporization of Single Droplets

The vaporization rate of the spray can, in principle, be calculated by following the historyof each droplet in the spray. Calculation of air motion and composition would, of course, also be

necessary in order to provide boundary conditions for the droplet calculations.

Factors Affecting Droplet Vaporization:

1. Effects of free and forced convection.2. For unsteady state, some of the energy reaching the surface goes into heating the droplet

liquid, and heat transfer within the liquid is important.

3. Effects of high pressure cause changes in the properties and may cause the droplet toapproach thermodynamic critical state.

4. For the practical case of high ambient temperature the properties in the boundary arefunctions of temperature and composition, and at high pressures they are nonideal.

If the Biot number


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where: = convection coefficientd= diameter of droplet= thermal conductivity

the temperature gradient in the sphere are negligible and the temperature is a function only of

time. For droplets in flowing air the situation is complicated by the effects of internal mixing,which tends to augment the rate if heat transfer (increasing ). The mixing is caused by the dragat the surface, which pushes the liquid to the back end of the droplet. The liquid circulate backand through the droplet causing a double vortex (Fig. 9.19).

In the extreme case of very fast vaporization and small internal mixing effects, the heatconduction to the liquid may only penetrate a very short distance, so the center core stays nearly

at a constant temperature (onion skin model).

Unsteady Vaporization

Consider an energy balance on a single droplet assuming a uniform liquid temperature which

changes with time. The time rate of energy storage in the drop equals the heat flux to the dropminus the enthalpy carried away by the vapor.

Expanding,

where: = mass of liquid = mass flow rate of vaporizing liquid = specific heat of liquid = specific enthalpy of liquid = specific enthalpy of vapor


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= convection coefficient = surface area of liquid = ambient gas temperature = temperature of liquidFor a sphere: and

Differentiating gives the mass transfer equation

The second term in is the effect of thermal expansion as the droplet heats up. Theconvective heat transfer coefficient , for low vaporization rates, is obtained from a Nusseltnumber correlation. For high vaporization rates (corrected value) is used in place of .

The difference in vapor pressure between the surface and the ambient is thenthe driving force for the mass transfer similar to

Steady-State Vaporization

For steady state droplet temperature and pure air surroundings, becomes

The mass transfer is:

where:

= vaporization constant

the vaporization time for a droplet with initial diameter d0 is: Reference:Borman, G. L., Ragland, K. W., Combustion Engineering, McGraw-Hill Companies, Inc., 1998.

combustion of liquid fuels

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