ME 475/675 Introduction to

CombustionLecture 40

Announcements• Final: • Friday, December 12, 2014, 2:45-4:45 PM

• HW17 Ch. 10 () • Due Monday, 12/8/2013

• Term Project (3% of grade), Due December 8 or 9? • Instructions:

• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/TermProjectAssignment.pdf

• Times to meet with Rachel Green about projects, HREL 305 • Wednesday 12/3 12 – 5 pm• Thursday 12/4 1 – 4pm• Saturday 12/6 10 am – 3 pm• Sunday 12/7 10 am – 3 pm• Monday 12/8 12 – 5 pm

• Schedule other times by emailing rmgreen@unr.edu

Ch. 10 Droplet Evaporation and Burning• Liquid Fuels High Pressure Atomizer Droplets Evaporation Non-pre-

mixed flame• Spray Combustion Applications (more complex than droplet burning)

• https://www.youtube.com/watch?v=a6Z_SpU1MQs&feature=channel&list=UL

• Applications: Spray Combustion (not droplet burning)• Oil home heaters (http://www.oilheatamerica.com/index.mv?screen=burners)

Applications: Diesel Engines• Diesel Fuels: Less volatile

(prone to evaporate) than spark-ignition fuels but more easily auto-ignited (at high pressures and temperatures)• Engines• Indirect injection• Direct injection

• Droplets evaporate and premix with aire, burn then auto-ignite the rest of the mixture• Blows into main chamber

and completes combustion

Glow Plug

Injector

Pre-mix chamber

Gas Turbine Engines (aircraft and stationary)

• Annular Combustor is a relatively small component

Annular Multistage Combustor

• Fuel is atomize• Premixed and staged to avoid NOx formation• Walls are protected from high temperatures by film cooling

Liquid Rocket Engines (fuel and oxidizer are liquid)

• Pressure-fed by high pressure gas• Pump-fed by turbo-

pumps• Mixed by colliding jets

to form unstable sheets and break up

Simple Droplet Evaporation Model (no combustion yet)

• In Chapter 3 we assumed liquid temperature is same as and known• Now assume , so evaporation is controlled by Heat Transfer• Find:• (droplet life)

�̇�

�̇�𝐹=�̇�h𝑓𝑔

𝑇 𝑑=𝑇 𝐵𝑜𝑖𝑙

• Assumption1. Quiescent infinite medium2. Quasi-steady behavior3. Single compound liquid fuel4. (constant and uniform), 5. Binary diffusion with ( )

• Shvab-Zeldovich energy equation6. Constant average properties

• Must be chosen carefully

�̇�

Conservation Laws (isolated droplet)

• Mass: (radial speed decrease as r increases)• Energy: Page 245, eqn. 7.65, spherical coordinates

Rad. Advection Rad. Diffusion/conduction Heat of Combustion • multiply by • ; Let

�̇�=�̇�𝐹=𝜌 𝐴𝑠𝑣𝑟=𝜌 (4 𝜋𝑟2 )𝑣𝑟=�̇�h 𝑓𝑔 r

𝑣𝑟

𝑟 𝑠

Solution• ; where

• 2nd order differential equation for T(r), 2 boundary conditions; ;

• ; (1st order separable)

• ;

• (General Solution) • Find constants: apply

• ; Eqn. *; subtract * from gen solution

Apply Other Boundary Condition to find constants• Apply

• (“shorthand” )

• ;

• Plug into Eqn. *:

Particular Solution • Plug constants into general solution:

•

•

• ; ;

• Eqn. 10.7 page 378

Non-Dimensionalization

• ; • Let , Ratio of advection to conduction

(Dimensionless Mass Flow Rate)

T W R1( )

1 expWR1

1 exp W( )

200 400 600 800 1 1030

0.5

11.1

0

T 1 R1( )

T 10 R1( )

T 100 R1( )

T 1000 R1( )

10001 R1

W = 1000Large Flow

W = 100

W = 10

𝑟 /𝑟 𝑠

𝑇∞−𝑇𝑇 ∞−𝑇 𝐵𝑜𝑖𝑙

Find Evaporation Flow Rate,

• ;

• • ; ; • ;

Fuel Evaporation Rate

• Spalding or Transfer Number: • Driving force for Mass Transfer• In Chapter 2,

Droplet Lifetime

• (D squared law)• Evaporation Constant:

• Droplet lifetime

• Property Evaluations:

Example 10.1

• Consider a 500-mm-diameter liquid n-hexane (the C6H14) droplet evaporating in hot, stagnant nitrogen at 1 atm. The N2 temperature is 850 K. Determine the lifetime of the n-hexane droplet, assuming the droplet temperature is at its boiling point.

• Solution Outline