Solved Problems in Combustion Engineering

MME 1221 Combustion Engineering

Combustion of Liquid Fuels Solved Problems

Prepared by: Richard Jess L. Chan

Submitted to: Dr. Edwin Carcasona

9.1. Consider the following very simple distribution: ¼ of the droplets have a diameter of 10  μm ½ of the droplets have a diameter of 20  μm ¼ of the droplets have a diameter of 30  μm

                                                                                                                                              

Show that Solution:

9.3. For the prefilming air-blast nozzle shown in Figure 9.8, use the following data (given in the book) and assume the correlation of Eq. 9.18 hold. Compute the SMD for liquids A and B. the diameter of the pintle is 1 cm. If the air velocity is doubled, but keeping constant, what is the effect on the SMD for each fuel?



Solution: Solve for the density of air:

                                           For fuel A at 100 m/s:

                                                                                                                                                                              

For fuel A at 200 m/s:

For fuel B at 100 m/s:

For fuel B at 200 m/s:

9.6. Consider a droplet of 100  μm diameter moving in 1000 K air at 50 atm pressure. a) What droplet relative velocity will give an Re d  of 10? At this velocity, how far would the droplet move in 10 CA° at 2000 rpm engine speed? b) Determine the drag force F  x with and without a cross flow of velocity equal to the initial velocity.

             

Solution: a) From Appendix B:

b)

                                                                                                                   

11.1. For the gas turbine cited in Table 11.1, determine the following: a) The simple cycle and combined cycle thermal efficiency b) The fuel feed rate per nozzle (gal/h) assuming no. 2 fuel oil c) The combustor inlet temperature assuming no heat loss d) Overall excess air e) Velocity at combustor outlet f) Water injection rate to meet the specified turbine in let temperature Solution: a)

            

For simple cycle:

For combined cycle:

b)

                                                                                                           

Total mass flow:

Mass flow per nozzle:

Fuel feed rate:

c) For standard condition:

d)

Ideal condition:

12.1. Using the data of Table 12.2, calculate the average piston speed for each engine. Plot average piston speed versus displacement. Solution:

                 

Column 1:

Column 2:

                                            

Column 3:

Column 4:

Column 5:

Column 6:

12.2. Consider a piston with an on-axis cylinder bowl of diameter 60 mm and depth 30 mm. The bore and stroke are each 120 mm. Calculate the volume at bottom dead center (BDC) and the compression ratio. Assume the squish area clearance between piston and head is 1 mm. Solution: Assuming a cylindrical bowl

                                                            

12.5. Calculate the discharge velocity and mass flow rate for a 0.2- mm injector hole with a Δ p of  8000 psi. Use a flow coefficient of 0.7 and properties of dodecane. Solution: From Table A.1: S.G. of dodecane = 0.749

                                            

Discharge velocity:

                         Mass flow rate:

12.6. Using the data of problem 12.2 and 12.5, calculate the injection duration for a four-hole nozzle, F  = 0.8 and volumetric efficiency of 95%, naturally aspirated with an inlet air density of  3 1.17 kg/m . Use dodecane fuel properties and use  f s = 0.067. Find the duration of the spray in milliseconds and crankdegrees for an engine speed of 2000 rpm. To do this, first find the trapped air mass. Solution: From Prob. 12.2:

                                                                                 

For each nozzle:

From Prob. 12.5:

13.1. What are the breakup time and breakup distance for 0.1-mm water drop subject to a Mach number = 2.5 shock wave propagating through air initially at standard conditions? Solution: For standard conditions: Breakup time = 0.5 ms

          

13.5. What is the thickness of a liquid layer of decane which will yield a stiochiometric mixture with (a) standard oxygen and (b) standard air in a 1-cm-dia tube? Solution: a) From Figure 13.8: equivalence ratio = 0.005

                

b) From Figure 13.8: equivalence ratio = 0.001