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 Oil A 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 at elevated 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 liquid fuel sprays to break up the liquid fuel in order to increase the fuel surface area and thus increase the vaporization and combustion rate. 9.1. Spray Formation Types of Spray Nozzles: 1. Pressure nozzle used predominantly in diesels 2. Air or Stream Atomization nozzle used in burners and furnaces 3. Swirl-type nozzle used 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 well formulated 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 streams 2. Appearance of ripples and protuberances 3. Formation of ligaments or holes in the sheets 4. Collapse of ligaments or holes in the sheets 5. Further breakup due to vibration of droplets 6. Agglomeration or shedding from large drops For simple orifices the behavior of the jet may be characterized by three dimensionless groups:
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 Re j, 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 to breakup. 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:
where:
= relative velocity of the ambient gas d = droplet diameter For Weber numbers greater than 12, one expects breakup.
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 call x, is calculated by:
where a is the initial droplet radius. If x 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 a decreases 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 the injection pressure rises very rapidly, the droplet breakup will be more rapid and effective that if
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 distribution of 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 given instant. (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 the spatial 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. One may calculate the average diameter, the size which gives the average surface area, or the size which gives the average volume. The average volume is given by
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 be relatively inexpensive and free of maintenance problems. For transportation engines, good atomization and dispersion are required over a wide range 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 unburned hydrocarbons 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 or L/do, where L is the orifice length.
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 diameter average particle size) for this atomizer is about 45m.
Aircraft gas turbines require a wide range of fuel flow rates. The higher flow rates require pressures of about 400 atm to be sure that satisfactory operation would take place at the lowest flow 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% excess air). The SMD of such atomizers increases with increasing liquid viscosity and surface tension and with decreasing air-to-liquid ratio.
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 common pipe (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 inwardly opening. Type of Nozzles: 1. Mutihole Nozzle
Fig. 9.11a shows a sac volume below the needle, which causes dribble at the end of injection. Elimination of this volume as shown in Fig. 9.11b reduces exhaust 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 of direct 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 incylinder engine sprays tend to influence the air motion significantly. Given a spray droplet size and 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 be approximated 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 is unaffected 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.
Fig. 9.15 illustrates the spray pattern and some important parameters. As the jet interacts with 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 density a and jet density 0 from a nozzle orifice diameter, d0, and the ratio of the entrained mass flow rate to nozzle flow rate is
For many practical problems the jet does not flow into stationary air, but rather into a flowing 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 behave similarly to dense gas jets, and thus dense gas jet theory have often been used as a crude method of 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 in addition 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 preceding droplets 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 farther downstream. Droplets formed later pass droplets formed earlier.
The unsteady air motion induced by the exchange of momentum with the droplets sweep 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 hot air 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 tip penetration 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 distance L 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 drop
A correction factor for the effect of a cross-flow velocity is given by the following equation; the penetration with cross flow, Lf, is:
where:
= rotational speed of air or swirl = velocity of liquid at the orifice
In 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 distance Lf was found to be 54 mm. Thus the swirl decreases the penetration distance of 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 d is
The first term is due to the buoyant force and can often be neglected, the second term is due to pressure 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 for the 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 history of 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 to approach thermodynamic critical state. 4. For the practical case of high ambient temperature the properties in the boundary are functions of temperature and composition, and at high pressures they are nonideal. If the Biot number
where:
= convection coefficient d = 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 drag at the surface, which pushes the liquid to the back end of the droplet. The liquid circulate back and through the droplet causing a double vortex (Fig. 9.19).
In the extreme case of very fast vaporization and small internal mixing effects, the heat conduction 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 drop minus 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
= convection coefficient = surface area of liquid = ambient gas temperature = temperature of liquid For a sphere:
and
Differentiating
gives the mass transfer equation
The second term in is the effect of thermal expansion as the droplet heats up. The convective heat transfer coefficient , for low vaporization rates, is obtained from a Nusselt number correlation. For high vaporization rates (corrected value) is used in place of . The difference in vapor pressure between the surface and the ambient is then the 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.
