Droplet Evaporation and Combustion

Abstract

Liquid fuels are widely used in various combustion systems for their ease of transport and storage. Due to their high energy content, liquid fuels are the most common fuels in transportation applications. Before combustion can take place, liquid fuel must be vaporized and mixed with the oxidizer. To achieve fast vaporization, liquid fuel is injected into the oxidizer (normally air) at high speeds. Soon after injection, the liquid fuel breaks up into droplets, forming a spray. Droplets then collide and coalesce, producing droplets of different sizes. Due to the high density of liquid fuel, the momentum of the liquid spray has a profound impact on local flow fields, creating turbulence and gas entrainment. In piston engines, the complexities of droplet combustion are further complicated by the occurrence of successive multiple transient events including gasification, ignition, flame propagation, and, ultimately, burn-out. As such, droplets can be considered the building block for providing fuel vapor in combustion systems. Understanding of single-droplet evaporation and combustion processes therefore provides important guidance in design of practical burners. Topics covered in this chapter include (1) droplet evaporation in both quiescent and convective environments, (2) droplet combustion, (3) initial droplet heating, and (4) characterization of droplet distributions.

Exercises

• 8.1 Consider a droplet of methanol with an initial diameter of 80 μm. It is injected into a chamber with an ambient temperature of 750 K and ambient pressure of 1 atm. Calculate the lifetime of the droplet. An additive is reported to reduce the boiling temperature of methanol by 40 K without affecting the heat of vaporization. Unfortunately, the additive also causes the initial droplet size to increase to 95 μm. Calculate the new droplet lifetime. Describe briefly how droplet lifetime would be affected if the ambient pressure were increased to 10 atm.

• 8.2 A turbojet flies at 250 m/s. Liquid n-heptane (C₇H₁₆) is injected in the direction of the air flow into the front of the 2.5 m long combustor where it completely combusts. Neglecting droplet breakup and drag effects, estimate the maximum allowable initial size of n-heptane droplets. Use the following information:

  • (a) Air temperature and pressure inside the combustion chamber is 1,000 K and 1 atm

  • (b) Droplets are injected into the combustor with a velocity 20 m/s faster than the air

  • (c) The combustion chemistry process takes 1 ms after droplets are completely vaporized.

  • (d) Properties of liquid n-heptane: density = 684 kg/m³, boiling temperature = 283 K, heat of vaporization = 317 kJ/kg.

• 8.3 In a combustion chamber, fine droplets of octane with diameter 500 μm are injected into an atmosphere of air at 500°C and 1 atm. It is observed that some droplets are evaporating and others are burning. It is also observed that some of the droplets are moving with the same velocity as the air and others have significant velocities relative to the air.

  • (a) Calculate the lifetime of the evaporating droplets that are moving at the same velocity as the air (quiescent environment).

  • (b) Calculate the life time of the evaporating droplets that are moving with a velocity of 10 m/s relative to the air.

  • (c) Calculate the lifetime of the burning droplets that are moving at the same velocity as the air (quiescent environment).

  NOTE: Assume that the thermal layer thickness and the flame stand-off distance are both equal to half the droplet diameter.

• 8.4 Using the data below, determine the evaporation time (droplet life time) for an n-butanol droplet of 100 μm diameter in hot air under the following conditions:

  • (a) T _air  = 900 K, zero slip velocity (U _d  = 0) between droplet and air, P = 101.3 kPa

  • ,(b) Repeat (a) but with U _d  = 1 m/s

  • ,(c) T _air  = 900 K, U _d  = 0, P = 3,210 kPa, (same as (a) except at high pressure)

  • (d) Repeat (c) with a flame around the droplet with flame temperature of 2,200 K.

  Note: Use the air property data for estimate of conductivity at T _ave  = (T _air  + T _droplet )/2 and T _ave  = (T _flame  + T _droplet )/2.

• 8.5 Estimate the evaporation lifetime of a diesel droplet (500 μm) surrounded by quiescent air at 500°C. Assume that the thickness of the thermal layer surrounding the droplet is half the droplet diameter. Compare with the combustion lifetime if the flame standoff distance is also half the droplet diameter with flame temperature of 2,305 K. If you cannot find all the needed diesel properties then use properties of n-heptane.

• 8.6 The droplet size data in a spray have been experimentally determined and are shown in Table 8.3. Determine the cumulative volume distribution for

  Table 8.3 Exercise 8.6

  d = 60 μm, i.e., CVF (d _j  = 60 μm).