AME 436, Prof. P. Ronney

Final Exam Study Guide

May 7, 2008

Format of the exam

The final exam will be open book. You may use any reference materials you want, but no laptop computers or other devices capable of running the aircycles4whatever.xls spreadsheets. The format will be the same as the midterm but will be 2 hours long. The exam will have graphical, numerical and short-answer questions.

· Short summary of the most important facts

· Hydrocarbon fuels are the most convenient, high-density way of storing energy; compression, combustion, expansion is the most convenient (high power/weight) way of converting this stored energy into useful work

· The simplest estimate of adiabatic flame temperature is T_ad = T_∞ + fQ_R/C_P (constant pressure), but at high temperatures, C_P increases and dissociation of CO₂ and H₂O causes T_ad to fall below this estimate, even if no heat losses are present

· Practically all chemical reactions of interest in this course have high activation energy, meaning that their rates increase rapidly with increasing temperature. This includes the chemical reactions causing heat release (thus affecting burning velocity of premixed flames), knock and most emissions. If you want to determine how a change in engine operating conditions affects performance, the first thing to check is how temperature is affected

· Flames come in two flavors – premixed and nonpremixed

o Premixed (e.g. Bunsen burner)

§ Fuel and air are completely mixed before combustion is initiated (e.g. via a spark)

§ Most important characteristic is the burning velocity S_L ~ (aW)^1/2

§ If the mixture is lean, T_ad and thus S_L will be low (bad) but NO emissions will be low (good)

§ If the mixture is too lean, the flame will extinguish completely (very bad)

o Nonpremixed (e.g. Bic lighter)

§ Fuel and air are un-mixed until combustion occurs

§ There are always stoichiometric surfaces (thus stoichiometric-like flame temperatures) somewhere between the regions of pure fuel and pure air

§ As a result, there are always high reaction rates even when the mixture is lean overall (good) but also high NO and soot formation rates (bad)

§ In most cases the burning rate is limited by mixing rates, not chemical reaction rates

· Engines are air processors – the air takes up most of the spacel, so if you can process more air, you can get more power

· Thermodynamically, the best way to burn is at the minimum volume or maximum pressure (which is really another way of saying, maximum temperature) because this gives you the most efficient Carnot cycle strips

· Reciprocating engines

o Premixed-charge

§ Performance (power, efficiency) is limited by compression ratio, which in turn is limited because of knock

§ Knock is an explosive, homogeneous reaction of the gas ahead of the flame front (“end gas”) before the flame gets to it

§ Knock depends on the temperature of the reactants (T_∞) (whereas flame propagation depends on product temperature T_ad)

§ Throttling (thus throttling loss) required to adjust power, since you can’t go very lean without misfire or flame extinction

o Non-premixed-charge

§ Burning takes longer since you have to mix and burn, whereas in premixed-charge engines the fuel and air are already mixed before combustion is initiated

§ As a result, the engine can’t rotate as fast, thus power is lower for same displacement / engine size

§ Not limited by compression ratio since only air is compressed, but you can’t burn near-stoichiometric without major soot, CO, UHC emissions

§ Since non-premixed, can burn very lean overall without throttling

§ Higher compression ratio + no throttling losses means higher efficiency

· Steady-flow (gas turbine) engines

o Since steady flow, can process more air for engine of given size/weight

o Compressor aerodynamics are challenging (to make air go from low P to high P without running back to low P)

o Power is limited by maximum allowable temperature of turbine

o At low Mach numbers, exit velocity is very high, so propulsive efficiency is low – solution is turbofan (much higher air flow, much lower exit velocity)

· Hypersonic propulsion

o Can’t decelerate incoming air to M = 0 because P and T will be too high

o Easy to get large pressure ratios (thus good thermal efficiency) even without mechanical compressor

o Large flight velocity, thus propulsive efficiency is good

o But - difficult to avoid large stagnation pressure losses

· Pollutant formation

o Emissions are a non-equilibrium phenemon – if everything went to equilibrium there would be no emissions!

o NOx – rich and cool better (no excess O₂), low temperatures

o CO, UHC – lean and hot better (excess O₂ to oxidize CO to CO₂ and UHC to CO₂ and H₂O)

o Soot

§ Premixed - only in rich mixtures, more soot at lower temperatures because soot formation must compete with oxidation

§ Nonpremixed – forms on rich side of flame, no competition between formation and oxidation there, so more at higher temperatures

Material covered

• Engineering scrutiny

• Review of thermodynamics

• Classifications of IC engines; advantages and disadvantages of each type

• Alternatives to IC engines

• Introduction to combustion

• Fuel types

• Chemical thermodynamics

• Stoichiometry, lean & rich mixtures, mass & mole fractions

• 1^st Law of Thermodynamics for chemically reacting systems

• Heating value

• Adiabatic flame temperature

• Degrees of reaction freedom

• Conservation of atoms

• 2^nd Law of Thermodynamics for chemically reacting systems; chemical equilibrium, equilibrium constants

• Isentropic expansion with frozen and equilibrium products

• Elementary combustion theory

• Chemical reaction rates

• Homogeneous reaction

• Premixed flames (deflagration)

• Effects of turbulence

• Non-premixed flames

• Unsteady flow engines

• Design parameters

• rc, Vd, N

• Performance parameters

• Indicated and Brake work, torque, power, MEP

• Efficiency - thermal, mechanical, volumetric

• Emissions

• Air-cycle (also called “ideal gas cycle”) analysis

• KNOW T-S AND P-V DIAGRAMS BACKWARDS AND FORWARDS!

• Otto and Diesel cycles and variations (e.g. complete expansion)

• Cycle comparisons

• Fuel-air cycles

• Modifications to ideal cycles

• Irreversible compression/expansion

• Heat transfer

• Slow burn

• Exhaust residual

• Friction

• Combustion in unsteady flow engines

• Knock

• What is it and why is it bad?

• Effect of fuel type and fuel structure

• Effect of operating conditions

• Flammability/misfire limits

• Incomplete combustion / flame quenching

• Steady-flow engines

• Thrust calculation
• Propulsive, thermal and overall efficiencies
• Brequet range equation

• Compressible flow

• Frictionless, adiabatic, variable area
• Frictionless, diabatic, constant area, pressure or temperature
• Frictional, adiabatic, constant area
• Frictionless, adiabatic, constant area (shock solutions)
• Stagnation conditions

• Airbreathing propulsion systems

• Gas turbines

• Ideal Brayton-cycle turbojet analysis (lots of algebra!)
• t_l limit
• Performance maps - T/ma & TSFC vs. t_l, M, p_c
• Afterburner
• T-s diagrams
• Turbofan

• Effect of bypass ratio and fan pressure ratio
• Optimization

• Non-ideal cycles

• Component efficiencies
• Effects on cycle performance

• Ramjets

• Hypersonic propulsion systems

• Advantages over rocket propulsion - carry only fuel, use wing lift
• Challenges - high stagnation temperature and pressure
• Burning at finite Mach no.
• T-s diagrams

• Pollutant formation and control

• NOx

• Zeldovich mechanism - high Ea

• "Prompt" mechanism

• Effect of operating conditions

• CO - due to incomplete combustion, bad mixing

• UHC - similar to CO but with effects of crevices, deposits, etc.

• Particulates

• Soot - mostly applicable to nonpremixed engines – forms on rich side of flame at high temperatures

• Treatment of pollution

• CO, UHC - lean and hot

• NOx - rich and cool

• Modern systems - f = 1, EGR, catalyst

Last year’s final exam (average score was 62/100)

Open book exam. Use any printed reference materials you want, but no laptop computers, PDAs, etc. capable of running excel spreadsheets are allowed. (Of course, calculators are allowed.) 120 minutes allowed. Write your answers on the exam sheet; if you mess up or need more space, use the back sides of the pages.

Problem #1 (the dreaded T-s diagrams) (20 points total; 5 points each part)

In an ideal t_ll-limited afterburning turbojet without fan, how would the T-s diagrams be affected if

a) The compressor is irreversible, but all other components are still ideal

b) A new turbine with a higher maximum allowable inlet temperature is used, thus t_l increases (but the afterburner temperature limit t_l,_AB does not change.)

c) There are pressure losses in both the main burner and the afterburner (all other components are still ideal)

d) A new fuel with a larger heating value per unit mass is used

In all cases, the compressor pressure ratio is the same for the baseline and modified cycle. When useful, add statements like “this DT = that DT,” “this area = that area,” etc. Please make your modifications clear; cycles that look like random scribbles and have no explanations don’t get much credit!

a)
	The compressor is irreversible, but all other components are still ideal.

b)
	A new turbine with a higher maximum allowable inlet temperature is used, thus tl increases (but the afterburner temperature limit tl,AB does not change.)
c)
	There are pressure losses in both the main burner and the afterburner (all other components are still ideal.)
d)
	A new fuel with a larger heating value per unit mass is used.

Problem #2 (Gas turbine performance) (20 points total) The following 5 changes to a t_l-limited turbofan engine flying at subsonic conditions (M₁ < 1) are being considered:

1) Increase the fan air bypass ratio (a) by a factor of 2

2) Increase the flight Mach number (M₁) by a factor of 2

3) Increase the turbine inlet temperature limit (t_l) by a factor of 2 (yeah, right…)

4) Increase the compressor pressure ratio (π_c) by a factor of 2 (ditto…)

5) Increase the fuel heating value (Q_R) by a factor of 2

Briefly explain:

a) Which of these would increase thermal efficiency the most?

b) Which of these would decrease overall efficiency the most?

c) Which of these would increase specific thrust the most?

d) Which of these would decrease NO_x emissions the most?

Problem #3 (reciprocating engine performance) (15 points total, 5 points each part)

An engine designer claims to have developed a naturally-aspirated (not turbocharged or supercharged) gasoline-fueled 4-stroke engine with a 100 cubic inch displacement volume, compression ratio of 8, operating at 4,000 rpm that produces 300 brake horsepower.

Possibly useful information: C_P = 1400 J/kgK; g = 1.4; ambient air density 1.18 kg/m³; Q_R (gasoline) = 4.5 x 10⁷ J/kg; stoichiometric fuel mass fraction in air (f) (gasoline) = 0.0622; 1 in³ = 1.64 x 10^‑5 m³; 1 horsepower = 746 Watts.

a) Do you believe this claim? Why or why not? (Hint: your answer should be NO.) Support your answer with calculations.

b) Would increasing compression ratio from 8 to 24 (without changing displacement volume) make the claim of 300 horsepower reasonable? Assume that somehow knocking is not a problem even at this high compression ratio. Again, support your answer with calculations.

c) Would increasing the intake pressure to 3 atm (with compression ratio 8) using a turbocharger make the claim of 300 hp reasonable? Again, support your answer with calculations.

Problem #4 (compressible flow, hypersonic propulsion) (20 points total, 5 points each part)

Two hypersonic engine designs, A and B, are being considered for a high-speed transport aircraft operating at a flight Mach number of 5.

Engine A produces a flow at the exit with a stagnation pressure 80 times the ambient pressure and a stagnation temperature 12 times the ambient temperature.

Engine B produces a flow at the exit with a stagnation pressure 100 times the ambient pressure and a stagnation temperature 10 times the ambient temperature.

Because these two engines are made by rival companies with trade secrets, little is known about what happens inside the engines. It is not known for either engine it uses a compressor or not, whether combustion occurs at constant P, T, A or none of the above, if the diffuser is reversible or not, nor is t_l known. All that is known is that for both engines (1) the same fuel is used, (2) reversible adiabatic expansion occurs in the exhaust nozzle to ambient pressure, (3) during the expansion the gas has constant specific heats with g = 1.4, and (4) the fuel to air ratio (FAR) is much less than 1.

a) Which engine, A or B, has the higher exhaust velocity?

b) Which engine, A or B, has the higher mass flow per unit throat area?

c) Which engine, A or B, has the higher specific thrust?

d) Which engine, A or B, has the higher thrust specific fuel consumption?

Problem #5 (Combustion, miscellaneous) (25 points total, 3 points each part, 1 point free)

Ronney Oil & Gas Company claims to have developed a fuel, called PDR®, whose chemical formula is C₈H₁₈ (octane) and has all the same thermodynamic properties, transport properties, etc. as C₈H₁₈. The only difference between C₈H₁₈ and PDR® is that using PDR® leads to 10% lower activation energy (E) for all chemical reactions. If PDR® fuel were used instead of C₈H₁₈, how would each of the following be affected? In particular, state whether the property would increase, decrease or remain the same, and if there is a change, would it be by more than, less than, or equal to 10%. (Notice the operative words: LOWER ACTIVATION ENERGY.) No credit without explanation!

There are 9 parts here, but answer only 8; leave one part blank or cross out your answer to 1 part

a) Fuel heating value

b) Constant-volume adiabatic flame temperature

c) Burning velocity of a stoichiometric premixed octane-air flame

d) Burning time of a liquid octane fuel droplet

e) Indicated thermal efficiency of a premixed charge engine

f) BMEP of a nonpremixed-charge engine

g) The equivalence ratio at the lean misfire limit of a premixed-charge engine

h) Amount of unburned hydrocarbon emissions in a premixed-charge engine

i) Amount of soot emission from a rich premixed flame