MAE 5380: Advanced Propulsion

MAE 5380: Advanced Propulsion Part 1: Introduction and Chemical Equilibrium Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

COMBUSTION FUNDAMENTALS • Thermodynamics • Energy Balance • Flame Temperature • Chemistry • Stoichiometry • Equilibrium • Kinetics • Emissions and Pollutants Combustion Technology • Fluid Mechanics • Flame Propagation • Laminar / Turbulent • Diffusion • Atomization • Combustor Aerodynamics • Rapid oxidation generating heat • Slow oxidation accompanied by relatively little heat and no light • Combustion transforms energy stored in chemical bonds to heat that can be utilized in a variety of ways

Key Combustion Concepts • Thermochemistry and Thermodynamics • Chemical Kinetics • Explosive and General Oxidative Characteristics of Fuels • Premixed Flames • Diffusion Flames • Ignition • Detonation • Emissions and Pollutants

1. THERMOCHEMISTRY • Combustion stoichiometry and thermodynamics • Balance of chemical equations • Lean, stoichiometric, and rich fuel-to-air mixtures • 1st Law of Thermodynamics and enthalpy of combustion • How hot is a flame? (usually 2,000-2,500 K) • Known Stoichiometry + 1st Law → Adiabatic Flame Temperature • Chemical equilibrium: 2nd Law of Thermodynamics • Important in fuel-rich combustion • Stable species at ambient conditions begin to dissociate when T > 1,250 K • Dissociation lowers flame temperature • Solution technique: Minimize Gibbs Free Energy, G=H-TS • Known P and T + Equilibrium Relations → Stoichiometry • Adiabatic combustion equilibrium • Equilibrium + 1st Law → Adiabatic Flame Temperature and Stoichiometry

2. CHEMICAL KINETICS • Equilibrium chemistry assumes that T & P are constant for a sufficiently long time for system to reach steady-state • While equilibrium chemistry lends insight into factors that control pollutant formation, greater understanding requires study of rates at which competing reactions proceed • Example: • If f↓ then T ↓ and [NO] ↓ • BUT for f ↓, hydrocarbon oxidation is slow • For finite combustor length emissions of CO and unburned hydrocarbons can ↑ • Understanding developed from basic kinetic theory → Arrhenius form • Endothermic and Exothermic reactions (forward and backward) • Simplified kinetics vs. detailed mechanisms

Explosion: very fast reacting systems (rapid heat release or pressure rise) In order for flames to propagate (deflagrations or detonations), reaction kinetics must be fast, i.e., mixture must be explosive Example At P=1 atm, NO EXPLOSION If P is lowered to a few % of 1 atm: EXPLOSION If P is raised to 2 atm: EXPLOSION What are explosive limits? Note that explosive limits are not flammability limits Explosion limits are P & T boundaries for a specific fuel-oxidizer mixture ratio that separate regions of slow and fast reaction Flammability limits are specify lean and rich fuel-oxidizer mixture ratio beyond which no flame will propagate 3. EXPLOSIVE AND GENERAL OXIDATIVE CHARACTERISTICS OF FUELS H2+O2, y=1 T=500 ºC P=1 atm

HINDENBURG: MAY 6, 1937

4. COMBUSTION MODES AND FLAME TYPES • Combustion can occur in flame mode • Premixed flames • Diffusion (non-premixed) flames • Combustion can occur in non-flame mode • What is a flame? • A flame is a self-sustaining propagation of a localized combustion zone at subsonic velocities • Flame must be localized: flame occupies only a small portion of combustible mixture at any one time (in contrast to a reaction which occurs uniformly throughout a vessel) • A discrete combustion wave that travels subsonically is called a deflagration • Combustion waves may be also travel at supersonic velocities, which are called detonations • Fundamental propagation mechanisms are different in deflagrations and detonations

4. LAMINAR PREMIXED FLAMES • Fuel and oxidizer mixed at molecular level prior to occurrence of any significant chemical reaction Flame color gives indication of temperature Not quite red: T~500-550 ºC Dark red: T~650-750 ºC Bright red: T~850-950 ºC Yellowish red: T~1050-1150 ºC Not quite white: T~1250-1350 ºC White: T > 1450 ºC

4. LAMINAR PREMIXED FLAMES

PREMIXED FLAMES • Fuel and oxidizer mixed at molecular level prior to occurrence of any significant chemical reaction

APPLICATION: ENGINE KNOCK • In internal combustion engines, compressed gasoline-air mixtures have a tendency to ignite prematurely rather than burning smoothly • This creates engine knock, a characteristic rattling or pinging sound in one or more cylinders. • Octane number of gasoline is a measure of its resistance to knock (or its ability to wait for a spark to initiate a flame). • Octane number is determined by comparing the characteristics of a gasoline to isooctane (2,2,4-trimethylpentane) and heptane. • Isooctane is assigned an octane number of 100. It is a highly branched compound that burns smoothly, with little knock. • Heptane is given an octane rating of zero. It is an unbranched compound and knocks badly. Flame Mode Non-Flame Mode (autoignition)

5. DIFFUSION FLAMES • Reactants are initially separated, and reaction occurs only at interface between fuel and oxidizer (mixing and reaction taking place) • Diffusion applies strictly to molecular diffusion of chemical species • In turbulent diffusion flames, turbulent convection mixes fuel and air macroscopically, then molecular mixing completes process so that chemical reactions can take place Orange Blue Full range of f throughout reaction zone

DIFFUSION FLAME: EARTH vs. SPACE

4+5: LOOK AGAIN AT BUNSEN BURNER • What determines shape of flame? (ANS: velocity profile and heat loss to tube wall) • Under what conditions will flame remain stationary? (ANS: flame speed must equal speed of normal component of unburned gas at each location) • Most practical devices (Diesel-engine combustion) has premixed and diffusion burning Secondary diffusion flame Results when CO and H products from rich inner flame encounter ambient air Fuel-rich pre-mixed inner flame

PROPULSION SYSTEMS X-37B Orbital Test Vehicle Gas Turbine Engine for Propulsion Gas Turbine Engine for Power Generation

5: DIFFUSION FLAMES

7. DETONATION • Pure Explosion vs. Detonation (not same) • Explosion requires rapid energy release • An explosion does not necessarily require passage of a combustion wave through exploding medium • Both deflagrations and detonations require rapid energy release and presence of a waveform • To have either a deflagration or a detonation, an explosive gas mixture must exist • Recall: • Deflagration: a subsonic wave sustained by a chemical reaction • Detonation: a supersonic wave sustained by a chemical reaction

7. PULSE DETONATION ENGINES

PULSE DETONATION WAVE ENGINES • Liquid methane or liquid hydrogen is ejected onto fuselage • Fuel mist is ignited, possibly by surface heating • The PDWE works by creating a liquid hydrogen detonation inside a specially designed chamber when aircraft is traveling beyond speed of sound • When traveling at such speeds, a thrust wall is created in front of the aircraft • When detonation takes place, airplane's thrust wall is pushed forward • This process is continually repeated to propel aircraft "...use a shock wave created in a detonation - an explosion that propagates supersonically- to compress a fuel-oxidizer mixture prior to combustion, similar to supersonic inlets that make use of external and internal shock wave for pressurization."

8. EMISSIONS AND POLLUTANTS • Major pollutants produced by combustion are: • Unburned and partially burned hydrocarbons, CnHm • Nitrogen oxides (NOx, NO and NO2) • Carbon monoxide (CO) • Sulfur oxides (SOx, SO2 and SO3) • Subjected to legislated controls (smog, acid rain, global warming, ozone depletion, health hazards, etc.)

EXAMPLES OF EMISSIONS Organic Compounds and Unburned hydrocarbons CO emissions Note that Clean Air Act of 1970 can be clearly seen in figures

8. EMISSIONS AND POLLUTANTS • Aircraft deposit combustion products at high altitudes, into upper troposphere and lower stratosphere (25,000 to 50,000 feet) • Combustion products deposited there have long residence times, enhancing impact • NOx suspected to contribute to toxic ozone production • Goal: NOx emission level to no-ozone-impact levels during cruise

DOES COMBUSTION SCALE? • What are limiting effects on combustion system size? • Can you burn at any scale? • Do any non-dimensional numbers exist to predict combustion scaling?

Reactants are initially separated, and reaction occurs only at interface between fuel and oxidizer (mixing and reaction taking place) PW4000 Fan Engine Cutaway Characteristics Fan tip diameter: 94 inches; Length: 132.7 inches Take-off thrust: 52,000 - 62,000 pounds; Bypass ratio: 4.8 to 5.0 Overall pressure ratio: 27.5 - 32.3; Fan pressure ratio: 1.65 - 1.80; Planes powered: Boeing 747-400, MD-11, Airbus A300-610, etc. DETAILED EXAMPLE: DIFFUSION FLAMES

MAJOR COMBUSTOR COMPONENTS Turbine Compressor

MAJOR COMBUSTOR COMPONENTS • Key Questions: • Why is combustor configured this way? • What sets overall length, volume and geometry of device? Fuel Combustion Products Turbine Air Compressor

COMBUSTOR EXAMPLE (F101)Henderson and Blazowski Fuel Turbine NGV Compressor

VORBIX COMBUSTOR (P&W) • Example of vortex enhanced combustion • Why is turbulence helpful?

COMBUSTOR REQUIREMENTS • Complete combustion (hb→ 1) • Low pressure loss (pb → 1) • Reliable and stable ignition • Wide stability limits • Flame stays lit over wide range of p, u, F/A ratio) • Freedom from combustion instabilities • Tailored temperature distribution into turbine with no hot spots • Low emissions • Smoke (soot), unburnt hydrocarbons, NOx, SOx, CO • Effective cooling of surfaces • Low stressed structures, durability • Small size and weight • Design for minimum cost and maintenance • Future – multiple fuel capability (?)

CHEMISTRY REVIEW • General hydrocarbon, CnHm (Jet fuel H/C~2) • Complete oxidation, hydrocarbon goes to CO2 and water • For air-breathing applications, hydrocarbon is burned in air • Air modeled as 20.9 % O2 and 79.1 % N2 (neglect trace species) • Complete combustion for hydrocarbons means all C → CO2 and all H → H2O Stoichiometric Mass fuel/air ratio Stoichiometric Molar fuel/air ratio • Stoichiometric = exactly correct ratio for complete combustion

COMMENTS ON CHALLENGES • Based on material limits of turbine (Tt4), combustors must operate below stoichiometric values • For most relevant hydrocarbon fuels, ys~ 0.06 (based on mass) • Comparison of actual fuel-to-air and stoichiometric ratio is called equivalence ratio • Equivalence ratio = f = y/ystoich • For most modern aircraft f ~ 0.3 • Summary • If f = 1: Stoichiometric • If f > 1: Fuel Rich • If f < 1: Fuel Lean

WHY IS THIS RELEVANT? • Most mixtures will NOT burn so far away from stoichiometric • Often called Flammability Limit • Highly pressure dependent • Increased pressure, increased flammability limit • Requirements for combustion, roughly f > 0.8 • Gas turbine can NOT operate at (or even near) stoichiometric levels • Temperatures (adiabatic flame temperatures) associated with stoichiometric combustion are way too hot for turbine • Fixed Tt4 implies roughly f < 0.5 • What do we do? • Burn (keep combustion going) near f=1 with some of ingested air • Then mix very hot gases with remaining air to lower temperature for turbine

SOLUTION: BURNING REGIONS Turbine Air Primary Zone f~0.3 f ~ 1.0 T>2000 K Compressor

COMBUSTOR ZONES: MORE DETAILS • Primary Zone • Anchors Flame • Provides sufficient time, mixing, temperature for “complete” oxidation of fuel • Equivalence ratio near f=1 • Intermediate (Secondary Zone) • Low altitude operation (higher pressures in combustor) • Recover dissociation losses (primarily CO → CO2) and Soot Oxidation • Complete burning of anything left over from primary due to poor mixing • High altitude operation (lower pressures in combustor) • Low pressure implies slower rate of reaction in primary zone • Serves basically as an extension of primary zone (increased tres) • L/D ~ 0.7 • Dilution Zone (critical to durability of turbine) • Mix in air to lower temperature to acceptable value for turbine • Tailor temperature profile (low at root and tip, high in middle) • Uses about 20-40% of total ingested core mass flow • L/D ~ 1.5-1.8

COMBUSTOR DESIGN • Combustion efficiency, hb = Actual Enthalpy Rise / Ideal Enthalpy Rise • h=heat of reaction (sometimes designated as QR) = 43,400 KJ/Kg • General Observations: • hb↓ as p ↓ and T ↓ (because of dependency of reaction rate) • hb↓ as Mach number ↑ (decrease in residence time) • hb↓ as fuel/air ratio ↓ • Assuming that fuel-to-air ratio is small:

COMBUSTOR LOCATION Commercial PW4000 Combustor Military F119-100 Afterburner • Why is AB so much longer than primary combustor? • Pressure is so low in AB that they need to be very long (and heavy) • Reaction rate ~ pn (n~2 for mixed gas collision rate)

EQUATION OF STATE • An equation of state provides a relationship among P, T and V (or r) of a substance • Ideal gas behavior (neglect intermolecular forces and volume of molecules themselves): • P=rRT • Pv=RT • PV=mRT • R=Runiversal/MW, Runiversal=8314 J/kmol K • Assumption is appropriate for nearly all systems we will consider in MAE 5310 since high temperatures associated with combustion generally result in sufficiently low densities for ideal gas behavior to be a reasonable approximation Aside: • Real gas laws try to predict true behavior of a gas better than ideal gas law by putting in terms to describe attractions and repulsions between molecules • These laws have been determined empirically or based on a conceptual model of molecular interactions or from statistical mechanics • Examples: van der Waals and Redlich-Kwong equations

Fixed Mass In Words:Heatadded to system in going from state 1 to state 2 (Q) minus workdone by system in going from state 1 to state 2 (W) equals change in total system energy (E) in going from state 1 to state 2 Control Volume In Words: Rate of heat transferred across control surface from the surroundings to control volume minus rate of all work done by control volume (including shaft work, but excluding flow work) equals rate of energy flowing out of control volume minus rate of energy flowing into control volume plus net rate of work associated with pressure forces where fluid crosses the control surface, called flow work Assumptions: CV is fixed relative to coordinate system Properties of fluid at each point within CV, or on the CS, do not vary with time Fluid properties are uniform over inlet and outlet flow areas Only one inlet and outlet stream – keep this form simple, but can be easily relaxed to allow for multiple inlet/outlet streams 1st LAW OF THERMODYNAMICS Units of Energy (J) Unit mass basis (J/kg) Units of Power (W) Unit mass basis Representing an instant in time

Example: Enthalpy often approximated as h(T)=CpT In combustion chemistry, enthalpy must take into account variable specific heats, h(T)=Cp(T)T If Cp(T) can be fit with quadratic, solution for flame temperature for certain classes of problems f < 1 and T < 1,250 K leads to closed form solutions For higher order fits or f > 1 and/or T > 1,250 K, iterative closure schemes are required for solution of flame temperature ADDED, BUT HIGHLY IMPORTANT, COMPLEXITY

Mole fraction of species i, ci Sum of all constituent mole fraction is unity Mass fraction of species i, Yi Sum of all constituent mass fractions is unity Converting mole fraction to mass fraction MW = molecular weight Converting mass fraction to mole fraction IDEAL-GAS MIXTURES: SOME USEFUL FORMULAS

HOW TO CALCULATE STOICHIOMETRIC FUEL/AIR RATIO • General hydrocarbon, CnHm • Complete oxidation, hydrocarbon goes to CO2 and water • For air-breathing applications, hydrocarbon is burned in air • Air modeled as 20.9 % O2 and 79.1 % N2 (neglect trace species) • Stoichiometric Molar fuel/air ratio • Stoichiometric Mass fuel/air ratio

ABSOLUTE (STANDARD) ENTHALPY, hi, AND ENTHALPY OF FORMATION, hºf,i • For chemically reacting systems concept of absolute enthalpy is very valuable • Define: • Absolute enthalpy = enthalpy that takes into account energy associated with chemical bonds (or lack of bonds) + enthalpy associated only with T • Absolute enthalpy, h = enthalpy of formation, hf + sensible enthalpy change, Dhs • In symbolic form: • In words first equation says: • Absolute enthalpy at T is equal to sum of enthalpy of formation at standard reference state and sensible enthalpy change in going from Tref to T • To define enthalpy, you need a reference state at which enthalpy is zero (this state is arbitrary as long as it is same for all species). • Most common is to take standard state as Tref=298.15 K and Pº=1 atm (Appendix A) • Convention is that enthalpies of formation for elements in their naturally occurring state at reference T and P are zero. • Example, at Tref=25 ºC and Pº=1 atm, oxygen exists as a diatomic molecule, so: • Note: Some text books use H for enthalpy per mol (Glassman), some books use h for enthalpy per mol, some use for enthalpy per mol. Use any symbol you like, just know what equations require.

GRAPHICAL EXAMPLE • See Figure 2.6 and Appendix A.11 and A.12 • Physical interpretation of enthalpy of formation: net change in enthalpy associated with breaking the chemical bonds of the standard state elements and forming news bonds to create the compound of interest Graphical interpretation of absolutely enthalpy, heat of formation and sensible enthalpy

COMMENTS ON TABLE 1: POTENTIAL ENERGY CHART Consider two reactions: H2+½O2 → H2O • Heat of formation (gas): -241.83 kJ/mol • Reaction is exothermic ½O2 → O • Heat of formation (gas): 249.17 kJ/mol • Reaction is endothermic H2O → H2+½O2 • Reaction 1 going backwards • Reaction is endothermic More Exothermic More Endothermic

ENTHALPY OF COMBUSTION AND HEATING VALUES • The heat of combustion, also known as heating value or heat of reaction, is numerically equal to enthalpy of reaction, but with opposite sign • Heat of combustion (or heat of reaction) = - enthalpy of combustion (or = - enthalpy of reaction) • If heat of combustion (or heat of reaction) is positive → Exothermic • If heat of combustion (or heat of reaction) is negative → Endothermic • If enthalpy of combustion (or enthalpy of reaction) is positive → Endothermic • If enthalpy of combustion (or enthalpy of reaction) is negative → Exothermic • The upper or higher heating value, HHV, is the heat of combustion calculated assuming that all of water in products has condensed to liquid. • This scenario liberates most amount of energy, hence called ‘upper’ • The lower heat value, LHV, corresponds to case where none of water is assumed to condense

LATENT HEAT OF VAPORIZATION, hfg • In many combustion systems a liquid ↔ vapor phase change may occur • Example 1: A liquid fuel droplet must first vaporize before it can burn • Example 2: If cooled sufficiently, water vapor can condense from combustion products • Latent Heat of Vaporization (also called enthalpy of valorization), hfg: Heat required in a constant P process to completely vaporize a unit mass of liquid at a given T • hfg(T,P) ≡ hvapor(T,P)-hliquid(T,P) • T and P correspond to saturation conditions • Latent heat of vaporization is frequently used with Clausius-Clapeyron equation to estimate Psat variation with T • Assumptions: • Specific volume of liquid phase is negligible compared to vapor • Vapor behaves as an ideal gas • If hfg is constant integrate to find Psat,2 if Tsat,1 Tsat,2, and Psat,1 are known • We will do this for droplet evaporation and combustion, e.x. D2 law T, v diagram for heat process of water at P=1 atm

SELECTED PROPERTIES OF HYDROCARBON FUELS

ADIABATIC FLAME TEMPERATURE • For an adiabatic combustion process, with no change in KE or PE, temperature of products is called Adiabatic Flame Temperature • Maximum temperature that can be achieved for given concentrations of reactants • Incomplete combustion or heat transfer from reactants act to lower temperature • Adiabatic flame temperature is generally a good estimate of actual temperature achieved in a flame, since chemical time scales are often shorter than those associated with transfer of heat and work • Most common is constant-pressure adiabatic flame temperature • Conceptually simple, but in practice difficult to evaluate because requires detailed knowledge of product composition, which is function of temperature

1st LAW FOR COMBUSTION PROBLEMS (GLASSMAN) • Most general form (rarely used, but know what each term means) • Note on sign of Q is negative. This is consistent with the 1st Law, but you must recall that Qp the is heat evolved, or the heat given off by the system, or the heat of combustion or heat of reaction. Sensible enthalpy change from T=298 to some reference Term is zero if reference T=298 Enthalpy of formation of products at T=298 K Sensible enthalpy change (kJ/mol) relative to some reference T Sensible enthalpy change relative to some reference T Term is zero if reactants enter at some reference T Sensible enthalpy change from T=298 to some reference Term is zero if reference T=298 Enthalpy of formation of reactants at T=298 K

MAE 5380: Advanced Propulsion