COMBUSTION ENGINEERING
Dr. B.S.Samaga Former Prof. of Mech. Engineering
[email protected]
COMBUSTION AND THERMOCHEMISTRY Definitions: Mole of a gas: It is the quantity of any gas whose mass is numerically equal to its molecular weight. Thus, 2 gm of hydrogen, 32 gm of oxygen, 44 gm of carbon dioxide etc are each one gram mole. When the molecular weight is expressed in kg, it is called kg mole or kmole. At NTP ( 273K and 1.01325 bar) one gm mole of each gas will occupy a volume of 22.4 litres (one kg mole will occupy 22400 litres)
Stoichiometry: It is the study of combustion reactions converting reactants into products. Mass conservation principle: Total mass of each element is conserved during a chemical reaction. Also total mass of reactants will be equal to total mass of products. However, total number of moles of reactants need not be the same as the total number of moles of products. This means, there can be molecular (volumetric) contraction or expansion due to the reaction. Stoichiometric or theoretical air is the minimum amount of air required for the complete combustion of the fuel. Fuel air equivalence ratio ‘Φ’ is the ratio of actual fuel-air ratio supplied for combustion to the stoichiometric fuelair ratio. Thus Φ > 1 is rich and Φ < 1 is lean mixture.
Enthalpy of Reaction and Enthalpy of Combustion: Enthalpy of reaction is the difference between the enthalpy of the products and the enthalpy of reactants when a complete chemical reaction occurs at a specified pressure and temperature. If complete combustion occurs, this quantity is called Enthalpy of combustion. Since the reactants and products are at the same reference temperature, the enthalpy of reaction or combustion are negative, as the products contain no chemical energy. They are tabulated on mole basis and the value depends on the state of the fuel (liquid or gas) and the state of H2O formed (water or steam). Liquid fuel and steam in the product give lower values due to the latent heat absorbed by the fuel for its vaporization and the latent heat held by the steam in the product.
Internal Energy of combustion: It is the difference between the internal energy of products and reactants when measured at the same reference state. Enthalpy of Formation: It is the enthalpy change associated with the formation of a chemical compound from its elements, all at the standard reference state. Enthalpy of all elements at the standard reference state is assigned the value of zero. Calorific (Heating) value: It is the enthalpy of combustion on mass basis (per kg) with the sign changed, and is defined as the energy liberated when unit mass of the fuel undergoes complete combustion. We have higher and lower values, depending on whether the steam in the product is condensed or left out. Standard Reference State chosen are 1 atm and 25°C.
First Law applied to Reactive systems: Q + HR = W + HP When there is no work involved, Q = HP – HR, which is the enthalpy of combustion. Adiabatic Flame Temperature: It is the maximum temperature that the combustion products can attain with stoichiometric fuel-air mixture when there is no heat loss from the system to the surroundings during the combustion process. This temperature is found out by trial and error by equating the enthalpy of reactants at the standard state to the sensible enthalpy of hot products at this temperature. HP at T(adia) = HR at 298K
Second Law analysis of reactive systems (Ref: Engg.Thermodynamics by E. Rathakrishnan)
The irreversibility associated with a chemical reaction is, I = ToSgen (kJ) where To is the temp of the surroundings and Sgen is the entropy generated. For a steady flow combustion process, in the absence of kinetic and potential energy changes, the max work available will be Wrev = ∑ Nr( hfo + h- ho –Tos )rea - ∑Np( hfo + h- ho –Tos )pro where N is no of moles of each constituent, hfo is the enthalpy of formation, (h – ho) is the increase in sensible enthalpy from the standard ref temp to the actual reaction temp, all on mole basis, To is the surrounding temp and s is the entropy /mole of the constituent. For a combustion system involving heat transfer QR with a reservoir at temp TR, Wrev = ∑ Nr( hfo + h- ho –Tos )rea - ∑Np( hfo + h- ho –Tos )pro – QR(1- To/ TR)
Gibbs function: Gibbs Function G = H - Ts For the situation when both the reactants and products are at the temperature of the surroundings To, we have go = (h-Tos) , where go is the Gibbs function of unit mole of substance at To . For this case the maximum work, Wrev = ∑ Nr( gfo + g - go)rea - ∑Np( gfo + g - go)pro where, gfo is the Gibbs function of formation, which is zero for all stable elements at standard reference state (1 atm and 298K )like enthalpy of formation.
Second Law Efficiency of a Reactive System: For a fuel at To, po, the max available energy (chem.exergy) is the max reversible work that can be obtained by reaction with oxygen from the environment. But due to irreversibilities like heat loss and friction the actual work will be less. The second law efficiency EffyII = Actual work done / Max theoretical work = Wact / ( mfuel x Chem.Exergy) While implementing methods to improve the second law efficiency, additional cost must be weighed against reduction in exergy losses.
CHEMICAL EQUILIBRIUM The equilibrium criterion for reacting systems is based on the second law of thermodynamics. From the second law, dSsys ≥ δQ / T And for an adiabatic system dSsys ≥ 0 A chemical reaction in an adiabatic chamber proceeds in the direction of increasing entropy and when the entropy reaches a maximum the reaction stops and equilibrium is achieved. From the first and second laws we have, δQ = dU + pdV and dS ≥ δQ / T Or, dU + pdV – TdS ≤ 0…(1) At const T and p, Gibbs function is G = H – TS Therefore, (dG)T,p = dH – TdS – SdT = (dU+pdV+Vdp) – TdS – SdT = dU + pdV – TdS since T and p are constant. From eqn (1) we get (dG)T,p ≤ 0 Hence equilibrium criterion is S will be max or G will be min.
Criterion for chemical equilibrium at a given p and T dS=0 dS>0 dS<0 Pressure=p
This part is impossible since it violates II law
G
Temperature =T
dG<0
dG>0
dG=0 100% reactants
Chemical equilibrium composition
100% products
Reaction coordinate
The effect of pressure and temp change on the chemical equilibrium will be to drive the reaction in the direction to oppose the change.
EQUILIBRIUM CONSTANT Consider a mixture of 4 components A,B,C and D which exist in equilibrium at a specified p and T with NA, NB,NC and ND as their respective number of moles. Now consider the reaction to occur to an infinitesimal extent (at constant p and T) with differential amounts of reactants A and B converted into products. dNAA + dNBB → dNCC + dNDD For chemical equilibrium, (dG)T,p = ∑(gidNi)T,p = 0 where, i indicates each constituent. Or, gAdNA + gBdNB + gCdNC + gDdND = 0 ….(1) where g is the chemical potential or molar Gibbs function for each component at T and p, dNs are differential changes in the number of moles of the components. These changes in moles are proportional to the stoichiometric coefts from the stoichiometric chemical equation: νAA + νBB νCC + νDD …..(2) where „ν‟s are the stoichiometric coefficients.
Therefore, dNA = - ενA, dNB = - ενB, dNC = ενC and dND = ενD where, ε is the proportionality constant which represents the extent of reaction, the –ve sign indicating the consumption of reactants. Substituting in Eqn (1), we obtain, νC gC + νD gD - νA gA - νB gB = 0 This is the criterion for chemical equilibrium valid for any chemical reaction regardless of the phases involved. It can be extended for any number of reactants and products. The Equilibrium Constant KP for Reaction shown in Eqn (2) is defined as, KP = [(pC)νC (pD)νD ] / [ (pA)νA (pB)νB ] …..(3) where p is the partial pressure of individual component in the mixture (atm) and ν is the stoichiometric coefficient of the respective components. At a given temperature, it can be shown that change in Gibbs function with respect to pressure has a logarithmic relation as ∆G (T) = - RuT. ln [(pC)νC (pD)νD ] / [ (pA)νA (pB)νB ] Hence, KP = e - ∆G (T) /(RuT) ………….(4)
Partial pressure of the component, p = (Ni / N total) x P, Where, N total = total number of moles present in the chamber and P is the total pressure. Substituting in Eqn (3) we can write, KP = [(NC)νC (ND)νD ] / [ (NA)νA (NB)νB ] . [P/Ntotal ] (νC+ νD - νA – νB)
……(5)
Simultaneous Reactions: When more than one reaction is involved in the system the condition dG(T,p) = 0 must exist for every reaction for chemical equilibrium. Determination of equilibrium composition of a reacting mixture requires that there should be as many equations as unknowns. The mass balance for each element involved provides one equation and the rest of the equations must come from KP relations written for each reaction.
VARIATION OF KP WITH TEMPERATURE From Eqn (4), we have ln KP = - ∆G (T) /(RuT) But ∆G = ∆H - T ∆S Therefore we can write, d(ln KP)/dT = ∆H(T) /(RuT2) – d (∆H(T)) /(RuTdT) + d(∆S(T))/ RudT, where, Ru= Universal gas constant. At constant pressure the Tds relation: Tds = dh – vdp becomes Tds = dh. Therefore, Td (∆S) = d(∆H ). Thus, the above relation becomes, d(ln KP)/dT = ∆H(T) / (RuT2) = hR(T) / (RuT2) …… (6) Where, hR(T) is the enthalpy of reaction at temperature T. This is known as van’t Hoff relation from which we can calculate the heat of reaction for any given temp (range) from the KP value. For small temp intervals hR can be taken as constant and van‟t Hoff‟s eqn gives on integration, ln(KP2/KP1) ≈ (hR/Ru).(1/T1 – 1/T2) It can be seen that for exothermic reactions, since hR is -ve KP decreases with increase in temperature.
Laminar Flame Propagation
One dimensional adiabatic combustion wave
Structure of adiabatic combustion wave front
At point of inflection
The Temp-Distance (T-x) and Conc-Diastance(C-x) Diagram
Temp-Distance(T-x) and Conc-Distance(C-x) diagram across the laminar flame front
Mallard and Le Chatelier‟s approach Simplifying Assumptions: 1. No reaction occurs below ignition temperature Ti. 2. Gas from To (at x= - ∞) to Ti gets heated only by conduction. 3. Reaction takes place from xi to xf without any heat loss. 4. Cp and k are constant in the range of temp from To to Tf
For an energy balance, Sensible heat gain in the preheat zone = Heat conducted from the reaction zone Cp(ρo.SF)(Ti – To) = -k.dT/dx |x=xi per unit area. Assuming roughly a straight line temp variation, Tf -dT/dx ≈ (Tf - Ti)/(xf - xi) T
Therefore, SF =
k . (Tf – Ti) Cp.ρo(xf – xi) . (Ti – To)
Ti
To xo
Preheat
Reaction
zone
zone
xi
xf
Thermal Model: Semenov’s Equation
ρu
= Density of unburned gas (g/cc)
kb
= Mean Thermal conductivity of burned gases (cal/s.cm.K)
Tb and Tu = Burned and Unburned gas Temp (K) Eact = Activation energy (cal/gmol) k/( C
p.ρ.D)
= Thermal diffusivity, assumed to be ≈ 1
Concept of Diffusion Mechanism Tf Temp or Conc
Ti unburned gas
To
preheat
reaction
burned
zone
zone
gas
Distance x
The reasoning for a diffusional mechanism begins with the assumption that potential chain carriers such as H, O and OH radicals are present in the flame front in thermo-dynamic equilibrium concentration at the maxmimum temperature. These active species, particularly hydrogen diffuse so rapidly into the unburned gas region that their concentration there is found to be far more than corresponding to the calculated equilibrium conc. at the unburned gas temp. These chain carriers can activate chemical reaction in the unburned gas without much aid of temperature.
Since the concentration of active particles in the unburned gas region is dependent on their equilibrium concentration at the flame temperature and their diffusion rate, it is concluded that the flame velocity should be related to these two factors, rather than the heat transfer from burned to unburned gases.
Work of Tanford and Pease 1. 2. 3.
4. 5.
Simplifying assumptions: Chain branching (leading to explosion) does not take place. Rate controlling step in the chemical reaction is the reaction of an active species like H with the fuel molecule. Rate of formation of comb.products per unit area of the flame surface is the sum total of products formed from each active species with their specific reaction rate constants. The speed with which the unburned gas is converted into comb. products per unit area of the flame surface is the flame velocity. The combustion zone temp and diffusion coefts for each species are assumed constant at their mean values in the reaction front.
Diffusion Model: Tanford and Pease Equation Sf =
at,m . X f,o . ∑ Ki.X i,F . D i,m ﴾ ------------- i ------------------ ﴿½ θm2 . Xp Bi
Where, • at,m = Total mean concentration (moles/cc) • Xf,o = Mole fraction of fuel in unburned gas; θm = 0.7 TF/To • XP = Mole fraction of potential combustion products in the unburned gas • Xi,F = Calculated mole fraction of ith active species at equilibrium flame temp, TF • Di,m = Diffusion Coeft for ith species into the unburned gas at the mean combustion zone temp (cm2/sec) • Bi = Dimensionless factor which allows for radical recombination (i.e., loss of active species due to reaction) • Ki = Specific rate constant for the reaction of ith species
Comparison of Thermal and Diffusion Models ----------------------------------------------------------------------------------------------------------------
Hydrocarbon in air
Burning Velocity (cm/s) --------------------------------------------------------Measured Diffusion Thermal (Tanford and Pease)
(Semenov)
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Methane Propane Hexane 2,2,3 Trimethyl butane Propene 1-Hexene Propyne Cyclohexane Benzene
33.8 39.0 38.5 35.8 43.8 42.1 69.9 38.7 40.7
33.9 37.7 37.3 36.6 45.3 41.7 61.3 37.4 40.4
40.2 39.0 37.2 37.0 48.9 42.0 64.9 38.3 44.5
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Evaluation of Thermal and Diffusion Models Equations based on thermal mechanism show a relation between flame velocity and thermal conductivity, whereas those based on diffusion mechanism relate flame velocity with diffusion coefficients and equilibrium concentrations of active particles. A critical evaluation of the two theories is therefore difficult for the following reasons: 1. Equations of heat conduction are mathematically similar to those of diffusion, and hence burning velocity relations based on the two concepts are similar. 2. Equilibrium concentrations of active species as well as heat conduction, both depend strongly on flame temperature. 3. Both the equations are based on broad simplifying assumptions and their validity varies for different combustion systems. 4. Chemical kinetic factors used in the equations have not been independently determined.
5. Thermal and transport properties of mixtures at high temperatures and diffusion coefficients for atoms and free radicals used in the equations are questionable. 6. The precision of burning velocity measurements is usually 2 to 5 %, while the accuracy is probably much less. Both the mechanisms have evidences as well as exceptions. Two experimental observations which clearly appear to favour diffusion mechanism are (i) increase in flame speed by the addition of hydrogen or water to non-hydrogen containing fuels (ii) changes in flame velocity caused by interchanging Helium and Argon as inert diluents. It is in fact probable that both heat conduction and diffusion contribute to propagation of any flame. Modified comprehensive equations including both these factors are therefore required which can give a satisfactory solution.
Factors affecting laminar flame velocity 1. Mixture temperature: C2H4 + air
200
SF(max) (cm/s)
160
C3H8 + air
120
CH4 + air
80 40
160
320
480
640
T0 (K) For Paraffins Empirical relation: For T0 = 200 to 615 K SF (at T0) / SF(at 298K) = ( 25 + 0.00085 T02 )/100
X 103
1(a) Effect of mixture temp.on burning velocity
2. Fuel-Air Equivalence Ratio:
100 1 atm, SF/SF(max) %
25°C
C2H4, C3H6, C5H12 with air
50
0.5
1.0 Φ
1.5
Empirical eqn for the above fuels applicable in the lean region: SF / S F(max) = 2.6 log10Φ + 0.94
2(a)Effect of mix.strength on flame velocity
by vol
2(b) Fuel-air equivalent ratio and mix temp:
Temp increasing SF
lean 1.0 Φ
rich
Max velocity shifts towards Φ = 1 as temperature increases.
3. Mixture pressure: SF1 / SF2 = (p1 / p2)n
0.2 0.1 For different hydrocarbons
n 0.0 -0.1 Cooler flames Hot flames
-0.2 -0.3 10
100 SF (cm/s)
1000
Pressure effect is not much pronounced. For very hot flames it slightly increases and for cooler flames it slightly decreases as pressure increases. For oxy- acetylene flame it is nearly constant, i.e., n = 0. For CH4 + air, n = -0.24 to – 0.49 ; for C3H8 + air, n = - 0.3
4. Electric field and Acoustical disturbances: No much effect of AC or DC field was seen. Flame speed slightly increased in the high voltage range owing to intense ionization and flame front break up. In the audible range of acoustical disturbances ( upto 20000 cps ) no much effect was observed. Beyond this flame speed may increase due turbulence until the flame breaks up into islands and the flame speed cannot be measured.
V
5. Mixture dilution:
200 O2 O2+N2
O2 conc increasing
SF 100 (cm/s)
0 lean 1.0 Φ
rich
Max velocity shifts towards Φ = 1 as O2 conc increases.
5(a) Effect of Nitrogen Dilution on the Flame Velocity
6. Hydrocarbon structure: Short straight chain length, minimum chain branching, unsaturation and small cyclo-alkane ring size increase flame speed. Oxygen containing Compounds have higher flame speed. But alcohols have flame speeds similar to alkanes. In general, Alkenes > Aldehydes and Ketones > Alkanes
7.Additives: a) For a fuel blend, empirically SF(blend) = SF(a).X(a) + SF(b).X(b) Where, x is the mole fraction of the component. But actually it is found to be slightly higher than that given by the simple mixing rule. b) Moisture has slight inhibiting effect on hydrocarbons, bur increases the flame speed of CO. c) Anti-knock agents such as TEL, Ethyl nitrate etc did not show any significant effect on flame speed of iso-octane or gasolene.
Additives contd… d) Inert diluents reduce flame speed in the following order: He, Ar, N2 and CO2, Helium having the maximum reducing effect. This is due to variations in the transport properties of the inert gases, such as specific heat, thermal conductivity and diffusion coefts.
8. Wall surface: Most wall surfaces of glass vessels and Bunsen tubes have a retarding effect due to quenching and chain carrier adsorption, being less with larger diameters. However, certain types of refractory surfaces are found to have an accelerating effect on flame velocity, due to its white hot surface inside the furnace or due to some catalytic action.
9. Turbulence: Turbulence, by far, has the greatest effect on flame propagation. Though the laminar speed does not change, the burning rate rapidly increases due to turbulent wrinkling of the flame surface and increase in the heat and mass transfer across the flame front.
TURBULENT FLAME PROPAGATION Concept of turbulence: Turbulent motion is a randomly fluctuating motion of small masses of fluid superimposed over a mean flow. u
U0
Mathematically, U = U0 + u, V = V0 + v and W = W0 + w , where, U0 , V0 and W0 are the time mean average values of flow velocities in the x,y and z directions and u, v and w are the instantaneous deviations from the mean velocity in the x, y and z directions. By definition, ∑u , ∑v and ∑w are all = 0. But we can define u‟, v‟ and w‟ as √u2, √v2 and √w2 which are components of turbulence intensity in the 3 directions. Turbulence intensity can also be defined as u‟/U0, v‟/V0 and w‟/ W0.
Mechanism of burning velocity enhancement due to turbulence Burning rate increases with turbulence due to any or several of the following reasons: 1. Increased burning area due to wrinkling of the flame front, with the burning velocity remaining constant at the laminar value normal to the flame front. 2. Increased rate of heat and mass transport due to eddy movements across the flame front. 3. Increased rate of mixing of burned and unburned gases due to eddy diffusion at the flame surface.
Uo – u’
Uou’+ u’ Uo +
Damkohler’s turbulent combustion wave model
Damkohler’s theory of turbulent flame propagation Large scale turbulence distorts the instantaneous velocity profile from the mean value with eddies (groups of molecules) randomly moving in and out across the flame front. The flame front profile will be similarly distorted forming +ve and –ve cones, thus giving the appearance of a wrinkled surface. This greatly enlarges the surface area available for combustion per unit gas flow area and the flame front can remain stationary only if the average gas velocity is increased to a value ST, which is the turbulent flame velocity. It should be noted that for any element of the distorted wave, the rate of propagation normal to the wave is assumed to be still laminar. Hence increase in flame area is an indication of increase in the flame velocity. In analogy to burner flames where the flame cone surface area is proportional to the gas velocity, Damkohler assumes that cone surface area in the turbulent flame front will be proportional to the fluctuating velocity u‟. Hence ST α u‟.
Now, by definition, in turbulent diffusion eddy diffusivity ε α u‟.l, where „l‟ is the scale of turbulence. Thus for a given scale of turbulence, we can write ST α ε. But from the turbulence theory, ε α Re.ν where „ν‟ is the kinematic viscosity, which depends only on the nature of the gas. Thus for a given gas and for a given scale of turbulence, ST α Re. However, to account for the effect of small scale turbulence which is inherent in the system, Damkohler modified equation as -
ST = aRe + B
Where, „a‟ is a constant and B is to account for small scale (micro) turbulence to be determined experimentally. Small scale turbulence: Scale of turbulence is smaller than flame thickness and does not produce any wrinkling of flame surface. But, the transfer processes in the combustion wave increase. He suggested the eqn: ST = SL.√ Re. High discrepancy between calculated and measured values were attributed to presence of eddy sizes.
Broken up flame islands in highly turbulent flow
Shelkin’s model for small scale (micro) turbulence Shelkin expanded Damkohler‟s thermal concept of turbulent flame propagation and proposed the following model for micro turbulence (i.e., eddy size „L‟ less than the flame thickness): ST / SL = √ (1+ ε/α) , Where, ST = Turbulent burning velocity SL = Laminar burning velocity α = Thermal diffusivity = KL/(CP.ρ0) ε = Eddy diffusivity = KT/(CP.ρ0) KL = Molecular heat transfer coeft KT = Turbulent heat transfer coeft
Shelkin’s model for large scale (macro) turbulence (l > flame thickness) Like Damkohler, Shelkin agrees that turbulence wrinkles the flame front surface and increases the burning area. He imagines that the flame surface consists of “dancing” cones formed by burning eddies which move up and down the flame surface. The cone base area is proportional to l2 where „l‟ is the cone dia, i.e., the eddy size. The height of this cone = u‟.t where, u‟ = average turbulent fluctuating velocity and „t‟ = the time during which an element of combustion wave is associated with this eddy moving in the direction normal to the wave and finally reducing it to zero size at the tip of the cone. Hence, „t‟ = l/SL = time for the consumption of the eddy of size l and height of the cone „h‟ = u‟. l/SL .
Shelkin’s model contd…. Cone base area = π Cone ht h = (u‟. l/SL ) Slant surface area = π.(l/2).s = π.(l/2).√(h2 + l2/4) l2/4
Shelkin’s Model of turbulent burning cone
h
Shelkin’s theory: l ST/SL = Cone surface area/ Cone base area = √( 1 + 4 h2/l2) = √ [ 1 + (2u‟/SL)2 ] Allowing for the crudeness of the model, Shelkin prefers to replace 2 by a const „B‟ which may be taken as ≈ 1. Therefore, ST = SL.√ [ 1 + (B.u’/SL)2 ] Note: When u‟=0, ST=SL. When u‟ >>1, ST α u‟, independent of fuel, exactly as Damkohler said, but is not fully supported by measured data.
FACTORS AFFECTING TURBULENT BURNING VELOCITY 1.Effect of mix.strength on turbulent burning velocity
2. Effect of equivalence ratio on burning velocity
1.0
SL / SLmax And
ST / STmax
0.5
0 0.6
0.8
1.0
1.2
1.4
1.6
Φ/ Φmax
Effect is similar for both laminar and turbulent flames
3. Effect of Mix. Strength on Reynolds Number of pipe flow
Ethene-Air Mixture
100
Re = 33700
Re = 20000
ST
Re = 10000 Re = 3000 50 0
5 Fuel %
10
4. Effect of turbulence intensity on turbulent burning velocity
PREMIXED AND DIFFUSION FLAMES
Pre-mixed and Diffusion Flames Pre-mixed flames: Fuel and oxidant are mixed prior to arriving in the burning zone and hence chemical reactions leading to combustion will be faster or the burning zone will be shorter in length than diffusion flames. Examples: Domestic LPG gas stove, Bunsen burner with the air valve open, combustion in the S.I.Engine, explosion in mines etc. Structure of Pre-mixed Flame: 1750 C
Flame front
Oxygen
Flat flame burner; 0.755 x 2.19 cm 8.7% Natural gas in Air
1800 C 1850 C
Products
Fuel
Burner Centreline
Conc. Profiles
Intermediate products
Temp. Profiles
Diffusion Flames (Jet Flames): Fuel and oxidant arrive separately at the combustion zone and mixing takes place in the reaction zone itself by diffusion. Diffusion of oxygen into the fuel gas being a slow process, carbon formation takes place which glows to give a bright luminous flame. Diffusion rate depends on nature of gases, pressure, density etc. Height of the flame is decided by the gas flow rate and the oxygen diffusion rate and is given by the point at which air just diffuses to the axis of the flame. At higher flow rates soot formation takes place and the flame tip will not be clearly defined. The maximum soot free length of the flame is an indication of the soot forming tendency of the fuel. Examples: Candle flame, kerosene wick lamps, Bunsen burner with air valve closed, Combustion in the diesel engine, flames in furnaces etc.
Structure of Diffusion Flame: Diffusion flame structure is influenced by the following factors(1) Width of the reaction zone (2) Radiation heat losses (3) Carbon forming tendency of he fuel (4) Convective flow pattern (5) Momentum Transfer (6) Diffusion Coefficient and (7) Air-fuel ratio. C2H2-Air flame (Burner dia=24 mm)
N2 2800°C
C2H2
Complex HC molecules
O2 OH
C
Carbon Zone
Centre line of flame
Temp. profile
CH
Reaction Zone
Burner rim
Effect of air flow rate on flame boundary of jet flames When air flow is in excess (Over ventilated) More air will diffuse into the fuel and the flame boundary will close at the top at a Shorter distance.
Over ventilated Under ventilated
When air flow is in deficit (Under ventilated) Fuel gas diffuses more into the air and the flame will flare up to the outer wall.
In both cases, flame height is definable.
Air
Fuel
Distinction between pre-mixed and diffusion flames Pre-mixed flames Diffusion flames ----------------------------------------------------------------------------------------------1. For a pure pre-mixed flame Fuel - Air ratio is const at the molecular level, and will not be altered by addition of, say, Oxygen from outside. 2. Burning velocity can be defined and Measured. 3. Flame is bluish and less luminous, as carbon formation is less pronounced. 4. Pre - ignition reactions occur during premixing which causes some heat loss in the process. Hence flame temp will be slightly less than the theoretical max.
True Fuel – Air ratio cannot be defined since the mixing continues as the reaction is in progress. Since the reaction rate is controlled by diffusion rate, no burning velocity can be adequately defined. Flame is luminous due to carbon formation from deficit oxygen on the fuel side, which glows as bright yellow flame at high temp. Since the reaction begins and ends in the burning zone itself, the temperature in the burning zone is near the theoretically max possible value.
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BURNING VELOCITY MEASUREMENT
MEASUREMENT OF LAMINAR BURNING VELOCITY OF PREMIXED FLAMES 1.
Bunsen burner method: l=slant length
Ug = Gas velocity Ab = burner area
Su = Flame velocity Af = flame cone area
Inner cone (flame boundary)
burned Af
α
Ug
α
unburned
Parabolic velocity profile
Rate of gas flow through Ab = Rate of burning over Af Ab.Ug = Af.Su Therefore, Su= (Ab/Af).Ug But Ab = π Rb2 and Af = πRb.l Ab/Af = Rb/l = Sin α ,where α is half cone angle. Thus, Su = Ug Sin α
Ab Rb
Su
Limitations of the Bunsen burner method: 1. Ug is not uniform throughout the burner area, since the velocity profile is parabolic (Poiseuille flow). Soln: (a) Measure Ug at a distance of 0.707 Rb from the centre using a pitot tube which represents the average velocity. (b) Ug = Vg/Ab where, Vg is the measured volume flow rate of gas. (c) Divide the flame cone into small horizontal segments and sum up the individual surface areas of segments to get a more accurate value af for Af to be used in the eqn: Su = (Ab/Af). Ug Af=∑af 2. Actual wave shape will be different from right circular cone, particularly for weak mixtures. The cone becomes thin and pointed for higher gas velocities and becomes blunter at the tip for low gas velocities. Soln:
Select the mid region of the flame area, where the slant surface is straight.
r1 s
For cylindrical burners, r2
Su = 2Um(r2 – r1)[ 1 – (r22 – r12)/(2R2) ] / s R
Where, Um is the average gas velocity in the burner of radius R, r2 and r1 are the radii at the base and top of the frustrum, and „s‟ is the slant height of the frustrum. A further modification is to use rectangular ( flat ) burner tubes, in which the combustion wave assumes the shape of two inclined planes so that the concave curvature of the wave (which is a source of error) is eliminated.
3. The change of burning velocity at the base (due to quenching effect by the burner rim) and at the tip due to high temperature are not taken into account. 4. Outward deflection of gas flow lines at the burner exit increases the base radius of the flame cone. The burner method is more accurate when a nozzle is used instead of the cylindrical burner, since the nozzle yields more or less a uniform velocity profile and hence, the errors due to distorted flame geometry at the cone base are reduced. Particle Track Method: To visualize the flame cone profile more clearly, particle track can be Illuminated used which is developed by Lewis and von Elbe. The particles track is traced using a stroboscopic disc by intermittently illuminated MgO dust sent along with the fuel. Flat burner
2. Soap Bubble Method: This is a spherical propagation velocity measurement, applicable for mixtures having isotropic propagation. Gas filling tube
Gold wire ring support 10
Velocity, m/s
Spatial velocity
.
5 Burning velocity (Transformation vel) 30
Soap bubble
50
70
Flame front
d 90
D
Vol % of fuel in mixture Electrode
Soap bubble experiment: Soap bubble is inflated with the combustible mixture to a dia of about 10 cm around the centrally located ignition electrode. When the spark is created, a spherical flame moves and the bubble freely expands ensuring const pressure combustion. Expansion of the bubble and the flame front movement are photographed with high speed photography. If Ssp is the spatial velocity as measured from the photograph, the true burning velocity will be Su = Ssp / ε, where ε is the correction factor for the forward transportation of the flame front due to the expansion of gases behind the flame front. If d and D are the initial and final bubble diameters at time 0 and any selected time t, then ε = (D/d)3. Thus, Su = Ssp/(D/d)3 Limitations: 1) Moisture in soap bubble affects the flame speed. 2) Expt must be done immediately after filling the bubble to avoid diffusion of the gas through the soap film. 3) Method not suitable for corrosive gases like H2-Cl2 and H2-O3. 4) Bubble will not be truly spherical due to buoyancy effects; hence ε may not be accurate.
3. Flame tube method: Initial mark
Final mark
Porous plug (flame arrester)
L Spark Pyrex tube: 2 cm dia and 3 m long Mixing chamber
Fuel
Air
Tube dia should be >> quenching dia, and length > 1 m for better accuracy of time measurement. Too large a dia will cause gas vibration and turbulence, which will enhance flame velocity. E.g, for propane, for which dq is 0.3 cm, a tube dia of 3 cm is chosen. Time interval „t‟ for the flame travel between the two marks is counted by an electronic counter, which is triggered by sensors (photo cells or ionization probes) when the flame moves across them. Su = L/ t . Ignition is made from the open end to eliminate the effect of flame transportation by the expanding gases behind the flame.
The measured values from the flame tube method depends on the orientation of the tube. The flame velocity is the highest for vertical tubes with upward flame. This is due to the effect of buoyancy and heat convection in the upward direction. For downward flame the value is minimum and for horizontal movement it is in between the two. Hence while reporting the values, it is necessary to mention the orientation of the tube used in the experiment.
4. Constant volume bomb method: A spherical steel vessel is filled with the mixture and fired by a spark from the centre. The pressure is continuously recorded with respect to time using a pressure probe. The progress of the spherical flame is calculated using thermodynamically relating it to the rate of pressure increase, and the flame velocity is estimated duly accounting for the apparent effect of expanding gases on flame transportation. Su = (dri/dt).(ri/rb)2.(pi/p)1/ku), where, Su is the instantaneous flame velocity at time „t‟, ri is the initial flame radius at „t‟ (at pi ), dri/dt is obtained from a plot of calculated ri vs t, rb is the flame radius at t + dt (at p) and ku is the sp.heat ratio of unburned gas.
Comparison of different methods A simple nozzle burner method is the best and most practical (with a large flame, rim and tip effects are relatively small). Cylindrical burners do not exhibit a right circular flame cone. Flat burners are better as they have reduced rim effect. Particle track technique is superior, but the procedure is laborious without much improvement in accuracy. Soap bubble technique suffers from moisture effect and possible quenching at the electrode and give a reduced value. Spherical bomb method involves a pressure record. Thermodynamic calculations being sensitive to the accuracy of pressure values, it generally gives lower velocity values.
Measurement of premixed turbulent flame speed in cylindrical burners Burner tubes should be long enough to ensure fully developed turbulent pipe flow. Flame height decreases due to turbulence brush and the average flame cone boundary is considered for flame velocity calculation. Methods to calculate ST:
Laminar flame cone Turbulent brush
bf
Average Turbulent flame cone
1. ST= U Sin α, where U is the mean gas flow rp velocity, α is the half angle of average turbulent cone. 2. ST = (Ap/Af).U where Af is the flame surface area = (4/3)π.rp.bf, calculated by assuming the flame surface as a paraboloid of revolution (rather than a cone), where bf is the mean height of the flame and rp is the port radius and Ap is the port area.
LAMINAR JET (DIFFUSION) FLAMES Flame lengths for circular port and slot burners Roper’s Correlations: Roper‟s experimental results are applicable for jet flames emerging into either a quiescent oxidiser or a coflowing oxidiser stream, so long as the oxidiser is in excess ( i.e., flame is not under-ventilated ) Circular port: Lf = 1330.QF(T∞/TF) / ln(1 + 1/S) where Lf is the length of the jet flame (m), S is the molar stoichiometric oxidiser-fuel ratio, T∞ and TF are the oxidiser stream and fuel stream temperatures (K), QF is the flow rate of fuel gas (m3/s). Roper‟s theoretical equations include mean diffusion coefts as well as flame temperatures both of which can only be calculated with limited accuracy. Hence experimental formulae are preferred.
Square Port: Lf = 1045 QF(T∞/TF) / [ inverf { (1 + S) -0.5 }]2 inverse error function.
ω 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 E.g. :
where, inverf is the
Sample error function table erf ω ω erf ω ω erf ω 0.00000 0.36 0.38933 1.04 0.85865 0.04511 0.40 0.42839 1.12 0.88679 0.09008 0.48 0.50275 1.20 0.91031 0.13475 0.56 0.57162 1.40 0.95228 0.17901 0.64 0.63459 1.60 0.97635 0.22270 0.72 0.69143 1.80 0.98909 0.26570 0.80 0.74210 2.00 0.99532 0.30788 0.88 0.78669 2.40 0.99931 0.34913 0.96 0.82542 2.80 0.99992 inverf (0.2657) is value of ω for which erf is 0.2657, i.e., = 0.24
Slot burner – Momentum controlled ( Flame Froude No >>1): Lf = 8.6x104(T∞/TF)2. (bβ2QF)/(hIYf,stoic) where, b and h are the slot width and length, and function β = 1/ { 4 inverf [1/( 1 + S )] } and I is the ratio of actual initial flow momentum from the slot to that of uniform flow, = 1 for uniform flow and = 1.5 for fully developed flow with parabolic exit velocity profile and Yf,stoic is oxidiser/fuel ratio by mass in stoichiometric mixture (…to be checked) Slot burner – Buoyancy controlled ( Flame Froude No. << 1): Lf = 2000 [ (β4QF4T∞4) / (a h4TF4) ]⅓ , where, a is the mean buoyant acceleration = 0.6 g (Tf /T∞ - 1), g being the accln due to gravity and Tf is the flame temperature, assumed to be 1500K. In the above expression b is neglected relative to h, assuming h >> b. Slot burner – Transition Regime (Flame Froude No. ≈ 1): Roper proposes an expression to find an intermediate average value from the above two calculated flame lengths.
Mechanism of soot formation in jet flames Soot formation in jet (diffusion) flames is basically due to lack of oxidiser reaching the right zone at the right time. It is generally agreed that soot is formed over a temperature range of 1300 to 1600 K within the flame. The soot particles radiate light particularly in the infrared region of the spectrum and make it look bright readable light. Soot formation is believed to take place in four sequential steps: 1. Formation of polycyclic aromatic hydrocarbons as intermediates between the original fuel molecule and the primary soot particle. 2. Formation of small primary soot particles of critical size (3000 to 10000 atomic mass units) from growth by both chemical process and coagulation. 3. Further surface growth and agglomeration of these primary soot particles due to exposure to the pyrolizing fuel as they travel through the flame.
4. At some point further these soot particles will pass through an oxidizing region of the flame, namely, the flame tip where they get an opportunity to get oxidized. When all the soot is oxidized, it results in a non-sooting flame, while incomplete oxidation causes a sooting flame. The amount of soot formed depends on the type of fuel and the fuel flow rate. The minimum flow rate at which smoke is observed to escape from the flame tip is a measure of the „smoke point‟. The maximum flame height of a non-sooting flame is also taken as a measure of the smoking tendency of the fuel. Non-sooting fuels will have a higher non-smoking flame length and a higher flow rate at the smoke point. The sooting tendency of fuels from least to greatest is found to be in the order of alkanes, alkenes, alkynes and aromatics. Also in a given grouping, the sooting tendency generally increases with the number of carbon atoms.
FLAME STABILIZATION IN LAMINAR FLOW
THE TUBE BURNER Combustion in a tube burner involves fuel gas flow, combustion and quenching at the burner rim. Let Tu, Ti* and Tb* be the isotherms for the Reaction zone plane adiabatic combustion wave. Ti Tb The gas flow lines diverge at the open end due to heating and expanTb* sion effect while the solid rim acts as a heat sink to quench the flame by Tu Ti* absorbing heat and chain carriers. Dead space The quenching effect decreases as Burner the distance from the rim increases. rim Near the rim the actual Ti and Tb Gas flow lines surfaces diverge from Ti* and Tb*
due to rim quenching effect. Heat loss to the rim reduces the Tb surface temperature below Tb*. The Ti surface, which marks the starting point of chemical reactions will have to be higher than Ti* since some of the chain carriers (active species) are lost to the sink. As such the burned gas temperature Tb isotherm and the inflexion point temperature Ti isotherms will merge together in the vicinity of the rim. Hence due to this rim effect the burning velocity decreases below its standard value Su* (away from the rim) to zero near the sink at the merging point where the unburned gas flow into the reaction zone will also reduce to zero. This region of the vanishing burning velocity is considered as the „fringe‟ of the combustion wave. The region between the fringe and the rim is called the „dead space‟ which shows the closest possible approach of the reaction zone to the sink. For the flame to be stably anchored to the rim, the flame velocity should equal the flow velocity in opposing directions. This happens only at one point near the fringe and at all other points on the wave the gas velocity exceeds flame velocity making the wave surface inclined.
Stabilization of flame in a laminar jet Su* is the standard burning velocity of the mixture, away from the quenching effects of the burner rim. Consider the fringe of the wave near the burner rim ( ≈ 1 mm above the rim for a slow burning mixture like methane + air). For relatively large burner dimensions, the gas velocity profile can be assumed to be linear at the burner tube wall (Poiseuille flow). Consider 3 positions of the wave profile.
Su* Su* Su* Su*
3
Su* Su>Ug
Su*
Su=Ug
2 Open
1 atmos
Su
Ug Gas vel. profile
Solid rim
Position 1: Combustion wave is too close to the rim. Quenching effect is predominant. Gas velocity exceeds the burning velocity every where. The flame is driven back (upwards). Position 2: Equilibrium and stable position. The increased distance from the solid rim reduces quenching and the burning velocity increases. At some point it equals the gas velocity, and the flame gets anchored to the burner. At the outermost region of the fringe excessive dilution by diffusion of atmospheric air decreases the burning velocity and the flame profile will be driven back (curved). Position 3: Wave is too far from the rim. The burning velocity exceeds the gas velocity and the flame moves towards the equilibrium position 2. (Note: At all points away from the rim all along the wave profile, the gas velocity exceeds the burning velocity and therefore the wave profile is inclined to the gas flow vector at an angle governed by the relation Su* = Ug Sin α where α is half the cone apex angle.)
Flash back and blow off principle Case I: Flame inside the burner tube - Fig [ I ] Velocity gradient is assumed to be linear from the burner wall towards the centre such that Ug = g.y , where g = boundary velocity gradient dU/dy and y is the distance from stream boundary. Till certain distance from the wall, flame does not exist due to wall quenching effect. The flame velocity gradually increases till it reaches Su* away from the wall and remains steady at this value towards the centre. 1,2,3 are three boundary velocity gradients Critical gF condition Burner rim shown for the gas flow. For gradient 1, at flame flash back there is a region where the flow veloDead space Su* city is less than the burning velocity. Xpen,F Thus flash back occurs. For gradient 3, Su=Ug U g the flow velocity at all points exceeds Gas vel profile the burning velocity and the flame will
be lifted up towards the free stream. Gradient 2 is at a tangent to the Su curve and defines the upper limit of gas flow at which flash back just occurs. This gradient is called the critical boundary velocity gradient for flash back gF. Penetration distances Xpen,F and Xpen,B are arbitrary defined quantities used to illustrate the effect of wall quenching (in flash back) and secondary air dilution (in blow off) and is equal to the ratio of fundamental flame velocity to the critical velocity gradient. Xpen,F = Su*/ gF and Xpen,B = Su*/ gB. Critical gB condition The penetration distance represents at flame blow off Xpen,B the distance from the burner wall, at Su* Diffusing which the local gas stream velocity air Dead equals local burning velocity and is Su=Ug Ug space defined only for flash back and blow Gas vel profile off conditions. Dead space indicates wall quenching distance during flash back similar to that seen above the rim for a normal stable flame.
Case II: Flame in free jet - Fig [ II ] Consider a stable flame in free jet above the burner rim. Curves A, B and C show flame velocity variations on three different wave profiles at different distances above the rim. Each of these curves start at a distance = quench distance from the stream boundary which decreases as the distance of the wave above the burner rim increases. They end up with the standard Su* value beyond the quench free distance along the wave profile. Lines 1,2,3,4 and 5 represent 5 different increasing gas velocity profiles corresponding to 5 different boundary velocity gradients. When the gas flow is reduced, „g‟ decreases and the equilibrium flame position shifts closer to the solid rim. Position 2 represents critical boundary velocity gradient for flash back „gF‟, below which (e.g.,line 1) a flash back occurs, i.e., the flame will move into the burner tube.
When the gas flow is increased, the equilibrium position of the flame shifts upwards away from the burner rim. Flame position B represents stable position for the flame. However, with increasing lift, the mixture becomes progressively diluted due to inter-diffusion of air from the surrounding atmosphere and the burning velocity in the outermost region of the wave fringe decreases considerably. At the boundary velocity gradient given by line 4 the wave profile will be lifted to a critical position C beyond which the excessive dilution effect will more than offset the burning velocity improvement due to increased distance from the rim and the flame blows off. The boundary velocity gradient corresponding to this position is called the critical boundary velocity gradient for blow off „gB‟. For a velocity gradient > gB, such as line 5, the wave will be driven upwards and blown off.
Critical Boundary Velocity Gradients for Flash back and Blow off Fig I
Fig II 1
CRITICAL FLOWS FOR FLASH BACK IN TUBES
stoichiometric
On-set of flash back near critical flow
Critical flow for blow off in cylindrical tubes
to the right of dotted line
Stability regime between flash back and blow off
Stability diagrams for different tube diameters
Characteristic Stability Diagram for open Flames The characteristic stability diagram is a plot of gas velocity versus mixture strength indicating regions of stable flame, flash back, blow off, lifted flame and blow out (i.e., blow off from lifted flame position). Flash back curve ABC: This occurs at low gas velocities and relatively low mixture strengths. Maximum tendency for flash back occurs for a mixture slightly richer than stoichiometric, which would correspond to maximum flame velocity mixture. Beyond 8% butane (Φ ≈ 2.6) the rich mixture does not support a flame to flash back into the burner since no additional air is available inside the burner tube to diffuse into the mixture. But the flame sustains itself at the port as a stable flame due to oxygen diffusion from outside, which makes the mixture combustible. To the left of A the mixture is so lean that no flame can exist at any flow velocity.
Characteristic stability diagram for butane-air open flames
(m/s)
20
(3.13 % by vol)
30
10
H
G
0
10
20 (Butane % by vol)
Blow off and lift curve ADE: The stream velocity, and hence the boundary velocity gradient is so high that the flame has to be blown off. However entrainment of ambient air at the stream boundary produces a more favourable combustible mixture extending to some depth into the stream and also decreases the average gas velocity due to momentum loss at the interaction zone. Hence at some height from the rim the gas velocity and the burning velocity become equal and the flame finds itself stable in this lifted position. The lifted position is possible only for very rich mixtures as it can be made combustible by diffusion of diluting air. To the left of D, where the mixture is relatively lean, it will be further leaned by air diffusion and the flame, therefore, simply blows off without a lifted position. The lift will be higher if the flow continues to remain laminar, and will decrease if the flow turns out to be turbulent (due to higher flame speed). Blow out curve DF: This corresponds to the gas velocity required to remove a lifted flame
down stream causing a blow out. This rises very steeply with mixture strength, and possibly no blow out may occur for highly rich mixtures or pure fuel gas when it will burn like a pure lifted diffusion flame. The dashed line DG is a continuation of the blow out limit. For mixture composition between D and G, the flame may be removed from the stream either by blow out or by blow off. However, the lifted flames are more vulnerable (for removal by blow out), than the seated flames (by blow off). Drop back curve GH : When the stream velocity is decreased for a lifted flame, it may drop back to the burner rim and there is a region between the lift and drop back limit in which the flame has a choice between these two positions of stability, one the lifted and the other seated. Intershifting between these positions is possible by introducing some disturbances in the flow stream. Below the drop back limit, the flame remains stably seated on the rim at all mixture strengths beyond the flash back regime.
Flame stabilization in high speed flow
Low velocity flow over a bluff body
Effect of bluff body on high speed flow
High speed flow over a rod with and without combustion
Flame anchored to the bluff body
Characteristics of bluff body flame holders
Some practical schemes of flame stabilization in high speed flow
Flow Pattern in a Jet Engine Combustor
Stability Characteristics of Gas Turbine Combustion Chambers Due to high velocity of air in the ignition zone, it is difficult to form homogeneous mixing with the injected fuel in such a short available time. Therefore, actual strength and limits measured in the expt will indicate higher air/fuel ratios since some of the air will flow past the ignition zone without mixing with the fuel. The nearly horizontal portions of the stability curve correspond to rich (A-B) and lean (D-E) limits of mixture strengths in the primary zone because, the air-fuel ratios are constant irrespective of flow velocity. Point C corresponds to a mixture strength in the primary zone giving the maximum flame velocity. At still lower velocities, the rich and lean limits deviate. Along the lean stability limit, the flame moves towards the spray cone and sticks to it where it finds the desired mixture strength. Irrespective of the A/F, a small flame remains stuck to the spray cone.
Stability Characteristics of Gas Turbine Flames
E D C A B Theoretical
Along the rich limit 1, the flame moves towards the secondary zone (the primary zone being over rich) and stabilizes at the interface between the vortex and the secondary zone where the desired strength is possible. (This cannot occur in the rich limit 2, since the flow velocity at the interface is high which will blow off the flame). At the rich limits the system is found to be susceptible to pulsating combustion and explosion blow out. This is because, at the rich limit flame is sensitive to the rate of air supply to the vortex and a temporary dynamic disturbance can cause a momentary decrease in heat liberation so that a strong feed back exists between the flame and the disturbance. The flame may then decrease to such an extent that substantial quantities of explosive mixture accumulate in the duct which will get ignited with violent effects by the residual flame. On the lean side the flame is relatively insensitive to air flow and such disturbances are not observed. With increase in temp, pr and atomization of fuel, the stability limits are enlarged. With decrease in pressure the rich and lean limits approach each other, and below a critical pressure the combustor fails to support a flame.
LIMITS OF INFLAMMABILITY
Limit of inflammability pertains to condition at which the mixture cannot be ignited, or if ignited, it is incapable of sustained burning. This is because, the flame at its flammability limit becomes fairly weak and vulnerable due to its low burning velocity, and the heat released becomes less than the heat dissipated by convection and radiation to the unburned gas which quenches the flame. 1. Tube diameter: Tube dia should be more than the quenching dia to eliminate direct flame quenching due to heat and active mass loss to the walls. Flammable range widens upto 5 cm dia due to reduced quenching effect of the wall.
Mix.Pressure (cm.Hg abs)
Factors affecting the flammability limits:
Φ=1 Lean limit
40 30
Rich limit
Tube dia 1.6 cm
Flammability region 2.2 2.8 4.7 6.6
20 10 1
2
3
4
5
6
C3H8 in air (% by Volume)
7
2.
Mixture Pressure: (i) Flammability range widens with increase of pressure. In most cases this variation is small. (ii) The pressure for any given rich or lean limit mixture decreases with increase in tube diameter. (iii) As the pressure decreases, the lean and rich limits progressively converge for all diameters. (iv) Flammable range at any given pressure is wider for larger tubes at least near the quenching diameter. 3. Mixture Temperature: Increased mixture temperature Mix Flammability improves the flammability limits temp Range at any given pressure. Natural gas % by Vol
Inert gas, % by vol
4. Ignition energy: Ignition energy must be sufficient so that no limitation is caused on flame development on account of it. A strong ignition source or a small naked flame will give true results. 5. Fuel type: Branched chain hydrocarbons have some what smaller inflammable range than the corresponding straight chain fuels. Benzene has still a smaller range. 6. Inert Diluents: N2 40 Effectiveness of inert gases on flame Exh.gas 30 extinction increases in the order of CO2 N2 , Exh.gas, CO2, CCl3F, CH3Br. 20 Flame cannot be sustained when % CCl3F 10 CH3Br of CCl3F (tri-chlorofluoromethane) in 0 2 4 6 8 10 the mixture exceeds 11%, while with Gasolene vapor, % by vol in air N2, flames can propagate upto 43%.
7. Velocity and Turbulence: Opinions differ in this respect. For CH4 + Air , limits are widened, where as for C3H8 + Air, limits are narrowed. Generally upto a certain level of turbulence limits may widen; beyond this limits are narrowed. 8. Orientation of Experimental Combustion tube: In vertical tubes, the limits are observed to be wider when the flame travels up compared with when the flame travels down. This is because the buoyancy effect (low density hot gases moving up) enhances heat transfer to the unburned gas which helps the upward flame movement. For horizontal tubes the limits ar found to be in between the above two values. Typical observations with some mixtures are given below: Upward Downwards Horizontal
CH4 + Air Lean Φ Rich Φ 0.54 1.7 0.60 1.5 0.54 1.6
C2H6 + Air Lean Φ Rich Φ 0.54 2.9 0.56 1.9 0.54 2.5
C6H6 + Air Lean Φ Rich Φ 0.53 2.9 0.54 2.1 0.53 2.6
Important factors to be considered for determining the true limits of inflammability : 1. Strong ignition source (or a small naked flame) should be used to ignite the mixture. 2. Pyrex glass may be chosen for the flame tube and its diameter should be far larger than quenching diameter (5 cm or more). 3. Large tube length should be used (1.3 m or more) to enable the flame to travel steadily and indefinitely. 4. Direction of flame movement in the flame tube should be specified (upward, downward or horizontal). 5. Ignition end of the tube should be open to equalize the pressure with the ambient atmosphere.
FLAME QUENCHING AND QUENCHING DISTANCE
Flame quenching Flames can be quenched in the following ways: 1. Excessive loss of heat and active mass to the surrounding surface 2. Flame stretch due to divergent flow 3. Diffusional stratification in fuel-air strength, particularly with limit mixtures 4. Excessive turbulence causing rapid heat dissipation to the surrounding gas. Definition of Quenching distance and Quenching diameter: The minimum distance between the walls of a slit or the minimum tube diameter, which can just permit a laminar flame to propagate through it, is called the quenching distance (dq) or quenching diameter(Dq). Application of quenching distance: (1) Davy lamp used in mines. (2) To estimate UBHC emission from combustion engines.
Measurement of Quenching Distance 1.
2.
3.
A strong spark is generated at the centre of a pair of parallel plates with adjustable distance between them, containing the test mixture. The minimum distance at which the flame just propagates from the source is the quenching distance. A rectangular burner with adjustable width is used and the flame is established above the burner. The gas flow is suddenly stopped. The flame will now strike back through the tube. The maximum width through which the flame does not strike back is measured as the quenching distance. Similarly experiments can be conducted on tube burners with variable mouth diameters. The minimum diameter through which the flame is just able to pass is measured as quenching diameter.
Factors affecting quenching distance 1.
2.
3.
Geometry of the measuring device (whether rectangular or circular). Geometrical factor B = dtube/dslit = 1.25 for CH4 + air = 1.45 for C3H8 + air Nature of surface ( whether glass, metal, etc): No significant effect was noticed, because conductivity of the gas layer is far less than that of solids. Type of fuel: Quenching distance decreased in the following order: Iso-octane > n-heptane > propane > benzene, when looked up from the lean side. This is attributed to the decreasing thermal conductivity of the fuel mixture in the above order. On the rich side some overlap was observed. Fuels having higher flame velocities like hydrogen, acetylene etc have lower quenching distance. So also fuel + O2 mixtures have lower quenching distance relative to fuel + air mixtures.
4.5
Iso-octane n-heptane propane benzene
3.0
Dq (mm) 1.5 H2 0.6
0.8
1.0
1.2
1.4
1.6
1.8
Φ
4.
Min. Ign. Energy: dq increases with increase in Emin requirement for the mixture. Emin α dq2 (Ref: Strehlow, p 234) This relation holds good for a good number of hydrocarbons.
10 HC1
HC2
Emin (mJ) 1.0 0.1 0
1.0
dq(cm)
2.0
5.
Mixture strength: Quenching distance increases as the limits of inflammability are approached. Minimum dq exists for the fastest burning mixture.
Stoichiometric strength
6.
Initial temperature: dq decreases with increase of temperature.
(C3H8 + Air)
5
27°C
4
127°C 210°C 285°C
Dq 3 (mm) 2 1 0.6
7.
0.8
1.0
Φ
1.2
1.4
1.6
Mixture pressure: dq decreases with increase of mixture pressure since quantity of mixture available is more in the slot at higher pressures. Expts have shown that dq α 1/p-0.9 holds good for several 6.3 cm.Hg 20 hydrocarbons. 15
16.4cm.Hg
Dq 10 (mm)
27.3cm.Hg 76 cm.Hg
5
Log-log plot
dq
0 0.8
1.0
1.2
1.4
Φ (C3H8 + Air
Temp = 24°C)
Mix. pressure
8.
Inert diluents: Experiment was conducted by choosing the proportion of diluents to give the same flame temp (2340°C) so that the sole effect of diluent properties on dq could be singled out. Quenching distance varies as He > A > N2 > CO2, chiefly due to thermal and transport property variations among these gases. 2.5 He
2.0
H2 + O2 Mixture Atmos. pressure and Temperature
Dq (mm)
1.5
A
1.0
N2
0.5
CO2
0.6
0.8
1.0
1.2
Φ
1.4
1.6
9.
Oxygen concentration: Quenching distance decreases as the oxygen concentration increases. This is due to better combustibility with higher oxygen concentration.
O2/(O2+N2) 0.21
10
0.35
0.5
0.67
=1.0
Dq 1.0 (mm)
0.1 0
20
40
60
CH4 % by volume (Pr = 1 atm)
10.
Turbulence: With increased turbulence heat loss to the wall increases, and hence, quenching possibilities increase. When the turbulence is very high, the unburned gas may act as a sink for heat and chain carriers thereby causing „homogeneous‟ quenching by excessive heat dissipation to the unburned gas itself.
Models for flame quenching Models based on thermal and diffusional mechanisms have been developed by various scientists. Predicted values are shown in the table. ________________________________________________________ Fuel/O2 ratio Observed dq (cm) Predicted dq (cm) (% stoichiometric) Thermal Diffusional -----------------------------------------------------------------------------------73.8 0.35 0.47 0.67 100
0.41
0.48
0.68
149 0.44 0.50 0.72 _________________________________________________________ Values predicted by thermal theory are more near to measured values.
Minimum Ignition Energy
Minimum ignition energy „Emin‟ is the minimum energy to be imparted by a spark (in milli Joules) so as to cause a stable combustion wave capable of self propagation. The electric spark can be either a capacitive or inductive and is a very hot and fast discharging source (10-8 to 10-7 sec). Chances of ignition of the mixture depend on the following factors: (i) Ignition energy supplied (ii) Ignition limits (flammability limits) of the mixture, (iii) Flame quenching possibilities (iv) Ignition temperature of the mixture ( i.e., the lowest temperature at which heat loss from the gas is over-balanced by the heat generated by the chemical reaction) (v) Duration of contact of the source with the mixture. Emin can be measured by the arrangement shown in the diagram. Capacitance can be varied from 100 to 5000 μF in the capacitance bank.
Set up to determine minimum Ignition Energy for Mixtures
Desired electrode gap is set and the capacitors are slowly charged. Voltage V at which spark occurs is noted. If no flame occurs, capacitance is increased in steps, until the critical capacitance „C‟ at which ignition occurs is found. Emin = ½ C V2, where V is the voltage value at the threshold of ignition. Similarly, if inductive spark is used, Emin = ½ Li2, where, L is the inductance (Henry) and „i‟ is the current (Amp) in the circuit.
Factors affecting Min. Ign. Energy 1. Electrode Gap: Too small gaps require higher energy due to quenching effect and due to lack of mixture quantity in the path of discharge. For flanged electrodes this increase is very sharp below 2mm gap, which correspond to quenching distance „dq‟. For larger gaps Emin is fairly constant. When the gap is very large, spark becomes less intense since its energy is distributed over a longer spark length, which increases Emin. Too high a spark energy will increase turbulence and hence quenching effects which fails to generate a flame. --------------
Glass flanged tips
16
Glass flanged tips
Free electrode tips
12 Emin (mj) 8
100
10 Emin (mj)
Ignition region
1.0
4 0.1
0
1 2 3 Elecrode gap (mm)
4
2
2.5 Electrode gap (mm)
3
Effect of Pressure on Min. Ign. Energy at Different Electrode Gaps
2. Pressure: As the pressure decreases, the Min.ign energy requirement increases since quantity of mixture available in the gap to support the flame becomes less at reduced pressure. Similarly at any given pressure, once the electrode gap exceeds the quenching distance, the mini. Ign. energy remains fairly constant as the gap increases, but increases at very large gaps due to weaker spark intensity. 3. Effect of dilution (Oxygen concentration): Min. ign. energy increases with dilution by inert gases. This is due to reduction in oxygen concentration due to dilution. The effect is minimum with Argon. Next comes nitrogen and CO2. Maximum effect is seen with Helium. Though all these diluents are inert, the difference in their effect on min. ign. energy is due to the difference in their transport and thermal properties such as specific heat, thermal conductivity, diffusion coefficient etc.
Effect of dilution on Min.Ign Energy at different pressures
4. Inert gas dilution:
O2 / (O2 + Inert gas)=0.21
He
Emin (mJ) 0.045
CO2
0.04
N2
0.02
A
0.01
Lean
1.0
rich
Φ with H2 as fuel
The effect of inert gases in increasing the min. ign. energy, increases in the order of A,N2,CO2 and He, which is chiefly attributable to (i) high thermal conductivity of He (ii) larger specific heat of CO2 relative to N2. The other transport properties too have some small effects.
5. Mixture strength:
Pr = 1 atm
2.5 2.0 Emin 1.5 (mJ) 1.0 0.5
CH4
C7H16
C3H8
0 0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Φ
The minimum energy value is fairly the same for all the three hydrocarbons, apprx. 0.2 mJ., but the mixture strength at which it occurs goes on increasing as the number of Carbon atoms in the fuel increases. This is presumed to be due to the diffusion processes giving rise to non-isotropic flame propagation with heavier hydrocarbons.
Methods of Ignition 1. 2.
3.
4.
5.
Spark Ignition: Most commonly used as it is very quick. Ignition by hot wires: If electrically heated, E = i2Rt, where i is the current, R is the resistance and t is the time period required. This is a relatively slow process requiring more contact time. Ignition by large heated bodies: Due to high heat capacity a hot solid bar maintains a constant surface temperature. Ignition is more reliable due to large surface contact area. Ignition of high velocity streams by hot bodies: The process involves igniting and stabilizing the flame. Large spheres or cylinders internally electrically heated can ignite the flame and stabilize the flame in the wake of the flow stream. Ignition by pilot flames: Heat energy is continuously provided by a small pilot flame. Governing factors are:
(a) (b) (c) (d) (e)
(f) 6.
Temp. of pilot flame: Higher the temperature, quicker the ignition. Size of the flame: Larger flame height requires shorter period of contact for ignition. Duration of contact: Depends on flame size and mixture strength, being minimum for a mixture slightly richer than stoichiometric. Mixture strength: Slightly richer than stoichiometric strength will give quickest ignition. Pressure of the mixture: Higher pressure requires shorter period of contact. Diluents in the mixture: They reduce the ignitability. Ignition by hot air (or gas): Fuel gas is quickly mixed in hot air (in about 6 ms) and ignition occurs after the elapse of ignition lag. Influencing factors are (i) mixing process (ii) Physico-chemical nature of the fuel (iii) Temp and pressure of the hot air (iv) Fuel concentration (v) Thermal cracking of fuel.
7.
8.
Ignition by adiabatic compression: Fuel is injected in a finely atomized form into the hot compressed air. Auto ignition takes place after the elapse of delay period. Method is used in diesel engines. Influencing factors are (i) Cetane number of the fuel (ii) Temperature Pressure and Density of air (iii) Mixing process (iv) Fuel injection characteristics. Ignition by shock waves: A shock wave is generated within a tube containing an ignitable mixture, by rupturing a diaphragm across a pressure differential which travels with supersonic velocity. It creates a pressure and temperature jump when it gets reflected at the tube end. This temperature jump will ignite the mixture. The time interval between the point of reflection and point of ignition (as sensed by a photocell) gives the ignition delay. Some calculated theoretical results are given below:
Ratio of pressures 2 10 100 1000
Shock velocity (m/s) 452 978 3021 10122
Temp behind shock °C 62.8 432.2 3587.7 18813.7
Adiabatic compr Temp.°C (given for comparison) 57.2 242.2 676.6 1437.7
DROPLET COMBUSTION
Model of single droplet combustion
Liquid droplet
Vapour envelope
Tf
Tg, ρg Oxidiser gas (air)
do ρf
Ts
Burning time of the droplet increases with surface area and fuel density, but decreases with the surrounding gas (air) density, diffusion rate between vapour and air and the rate of mass transfer from the liquid droplet. Thus burning time tb(sec) = (do2.ρf) / [ 8 loge(1+B). γ ], where, do = initial dia. of the droplet (cm) or [m] ρf = fuel density, (g/cc) or [ kg/m3] γ(gamma) = D.ρg = Exchange coeft (g/cm.s) or [ kg/m.s] D = diffusion coeft. - vapour to air (cm2/s) or [ m2/s] ρg = gas density, (g/cc) or [ kg/ m3] B = Transfer number, which represents the rate of mass transfer from the droplet, which in turn increases with temp.difference (Tg-Tf), heating value of the fuel, oxygen concentration and decreases with increase in latent heat and boiling point of the fuel.
Transfer number: For liquid droplets : B = [ (H. mO2,g) / r + Cp (Tg – Ts) ] / Q where, H = heat of combustion of the fuel (calorific value) (cal/g) or [ kJ/kg ] mO2,g = mass concentration of oxygen in the gas = 1.0 if the oxidiser gas is only oxygen, = 0.232 if the gas is air r = mass ratio of oxygen to fuel in the chemical reaction equation Cp = Sp. heat of gases at const pressure (Cal/g°C) or [ kJ/kg.K] Tg = gas temp. (°C) Ts = droplet surface temp. (°C) which is always ≤ boiling point of fuel. Q = Heat required to vaporize unit mass of fuel = Latent heat of fuel if the droplet is at boiling point (Cal/g) or [ kJ/kg ] (Note: Set of SI units given in Sq. brackets will also give dimensional consistency)
For Solid fuels : Ts will reach Tg. B = mO2,g / r, where r = 16/12 for the reaction C + O = CO and r = 32/12 for the reaction C + O2 = CO2
Combustion of cluster of droplets In a cluster of droplets, as in diesel engine or gas turbine combustion, burned gases produced from the combustion of one droplet will affect the combustion of the neighboring droplet due to oxygen dilution by inert products of combustion. Hence modeling for cluster of droplets becomes more involved and single droplet model cannot be directly applied. Particularly when gas turbulence is present, only empirical models are possible which have to be validated with experimentally measured results.
COMBUSTION IN PRACTICAL SYSTEMS
COMBUSTION OF SOLID COAL
Traveling chain grate over feed stoker
Combustion in Over feed fuel bed
Primary air
Diagramatic cross section of over feed fuel bed
Overfeed Coal Combustion Scheme
Typical under feed stoker
Underfeed Coal Combustion Scheme
Cyclone Furnace for Pulverized Coal Combustion
The Cyclone Furnace
Oil Burner for Power Plants
Pressure Jet Oil Burner
Steam atomized Oil Burner
Atmospheric Gas Burner
Gas Turbine Combustors Principal requirements are: 1. Low weight and small frontal area 2. Low pressure loss 3. Stable and efficient combustion over the operating flight altitudes and speeds 4. Reliability, serviceability and reasonably long life 5. Thorough mixing of hot and cold fluids to give a final temperature sustainable by the blades without warping or mechanical damage A compromise will have to be sought in the design since some of the requirements are conflicting. E.g., large ducts and pipes reduce pressure drop but increase size, weight and frontal area. Addition of diluting air is a thermodynamic loss, but is needed to prevent mechanical damage to the blades. A/F ratio may vary from 50:1 to 150:1, while primary air (≈25% of total air), is properly controlled with load to avoid rich or lean blow out.
Straight through combustion system (Can or Tubular type design) Primary air
Ign torch
Secondary dilution air Fixed blades Moving blades
Fuel line
Nozzle
Shaft cL
Exh. Jet
Ign.zone Reaction zone Quenching & mixing zone
Compressor
Turbine
Return flow combustion system (Industrial type design) mixing zone
reaction Ign
zone
Secondary air
zone
Ign torch Fuel line Primary air
Fixed blades Moving blades Compressed air from compressor
Nozzle Exh. Jet Shaft cL
Turbine
Annular combustion system (used in Aircrafts) Fuel line
Fixed blades Moving blades
C.C. Nozzle Compressor inlet
Turbo-compressor shaft
C.C.
Ign
Reaction
Quenching and
zone
zone
mixing zone
Gas Turbine
Exh. Jet
Comparison of return flow and straight through combustors Return flow Straight through ------------------------------------------------------------------------------------------1.
---------
2. Permits automatic compensation of expn without any special joints. 3. Turbine stator and rotor blades are shielded from high temp flame radiation. 4. Involves two 180° bends in the path of the gas and hence higher pr loss. 5. ---------6. Larger frontal area. 7. ---------8. Easier assembly and dissembly. 9. Chances of uneven air distribution.
Requires a longer shaft involving a third bearing and a flexible coupling. Requires expansion joints to allow differential expansion. High blade temperature may exist due to direct flame radiation requiring special cooling. Involves no bends and hence less pressure loss. Allows a greater cross sectional area for combustion within a given overall dia. --------Simpler to manufacture. --------Provides more even air distribution.
----------------------------------------------------------------------------------------------------
In both return flow and straight through systems, several combustion chambers are symmetrically disposed around the turbine inlet. The length to dia ratio of C.C.s may vary from 2.25 to 5 and the heat release rates may vary from 50 to 130 x106 kJ/m3Hr. Annular combustion chamber is more compact than multi-cell burner arrangement with a smaller overall dia (frontal area). Both single or multiple ignition points can be used to initiate combustion. Uniform mixing and cooling is more difficult to accomplish and also it is difficult to vary primary and secondary air as precisely as is possible with other unitary designs. Chances of serious warpage of the combustion chamber exists due to the above. Flame stability can be achieved by creating a recirculation zone in the flow path after the primary air entrance by any of the techniques discussed earlier. To increase the jet thrust, an after burner is placed in the exit stream of the gases where extra fuel is burned using the excess air present.
Combustion in rocket motors Rockets work in space where there is no air available to supply the required oxidant. Hence rockets have to carry fuels and oxidants on board. These are burned in a simple combustion chamber at an enormous rate to produce the required jet thrust through the exhaust nozzle at supersonic flow velocities. Despite the simplicity in its principle, the development of a reliable rocket jet-propulsion system encounters several perplexing problems. The system should be light in weight, the rocket motor (rocket engine) must be capable of sustained operation in contact with gases at above 20 bar pressure and 2800°C. Hence major problems encountered are choice of material, techniques of construction, method of propellant admission, ignition for smooth start up, thrust control, cooling methods, control of combustion instabilities and design of reliable electronic remote control systems.
Bi-propellant Rocket Motor system
Fuel
Comb. Chamber Thrust
Oxidiser
Nozzle
Pc , Tc Throat
Exh. Jet
The propellants employed may be a solid, two liquids (fuel + oxidiser) or mono-propellants (materials containing adequate supply of oxygen in their chemical composition. Solid Propellant rocket motor system: Direction of burning
Steel wall
Thrust
Solid Propellant stick
Exh.Jet
Flexible liner to ensure uniform burning
No cooling required since it is supposed to burn off after its period of operation (45 to 80 sec). Used for projectiles, missiles, assisted take off of air crafts etc. Propellants used are mono-propellants like, nitroglycerin(C3H5(ONO2)3), picric acid, TNT (tri-nitro toluene), nitromethane etc.
Bi-propellant liquid rocket propulsion Oxidiser tank
Fuel tank
Pressure feed (using mech. pumps or high pressure inert gas storage)
Propellant control Remotely operated propellant control valve
Injection Rocket motor
Combustion
Exhaust from nozzle
Liquid propellant systems can be operated for longer durations depending on the quantity of propellant storage. Thrust control is possible by remote control of propellant flow. Propellant injection comprises several pairs of fuel and oxidant streams impinging on each other as follows: Arrangement of jets
i) Like on like Oxidant jets Fuel jets
ii) Shower head
iii) Impinging triplets
Arrangement of Injector (Like-on-unlike is not much favoured due to possibility of aerodynamic disturbance causing combustion instability)
Fuel oxidiser combinations for bi-propellant systems Liquid Oxygen with.. Liquid hydrogen, Gasolene, Ethanol, Methanol, Hydrazine (N2H4), Liquid Ammonia (NH3), UDMH (Unsymmetrical Di-Methyl Hydrazine: (CH3)2N:NH2 Nitric Acid(HNO3) with .. Aniline (C6H5NH2), Furfuryl alcohol (C4H3OCH2OH), Monoethylaniline (C2H5C6H4NH2) Hydrogen Peroxide(H2O2) with .. Ethanol, Methanol, Hydrazine, Ethylene Diamine (C2H4N2H4)
Ignition and Starting Methods for Rocket Motors Ignition should be quick, since otherwise, large accumulation of unburned propellants may cause chamber pressures far in excess of design pressures when the combustion starts. If one of the propellants is cryogenic liquid, it is usually chosen as the leader since it prevents accumulation due to rapid evaporation. Ignition methods: 1. Pyrotechnic device such as a large fire work, which is fired electrically via a small priming charge providing a shower of incandescent particles for a few seconds. 2. A spark discharge or a glow plug, either of which is effective only at low flows and thus may require a pre-combustion chamber. 3. For hypergolic propellants (self igniting when come in contact) no external source of ignition is necessary. 4. Initial addition of a spurt of hypergolic material via one of the main propellant flows.
Rocket motor cooling Cooling methods: 1. Suitable choice of material and thickness of the wall so as to absorb the heat during the period of operation (used only in solid propellant motors of short duration) 2. One of the propellants is circulated around the walls, called the regenerative system. 3. High temperature resistant refractory material lining is used. This is generally combined with method 2. 4. Film cooling can be effectively applied. A complete film of fuel is formed over the inside wall of the chamber which by its evaporation keeps the surface cool. In one German design, 7% of total fuel was used for this purpose. About 5% of heat liberated by combustion is dissipated through the chamber and the nozzle walls, which is about 120 to 200 kJ/sec.
Combustion Instability in rocket motors Low frequency (50 – 250 cps) ‘Chugging’: This form of combustion instability appears to be connected with the finite time which elapses between the injection of liquid propellants and starting of combustion, i.e., the combustion delay. This is due to the time required for the atomization, heating, ignition and burning and is of the order of a few milliseconds. Because of this delay, the adjustments in burning rate will cause a mass variation and hence pressure fluctuation within the combustion chamber, which in turn, causes changes in propellant inflow that lags behind it and so oscillations may be set up. The consequences of chugging is not usually disastrous and can be controlled by throttling the propellant flow through a higher pressure difference, thereby making it more insensitive to chamber pressure variations.
High frequency (1000 to 2000 cps) ‘Screaming’: The mechanism of screaming is not well understood. It is generally agreed to be an acoustic disturbance of such a high frequency that the propellant inflow is virtually unaffected. These oscillations are generally tangential and correspond to a pressure wave moving to and fro across a diameter or round and round the circumference of the chamber. One plausible theory is that the circumferential (and to some extent radial) gas velocities associated with the resonance disturb the propellant droplets, thereby affecting the mixing and combustion rates. This suggests that critical injection arrangements such as impinging triplets which are easily disturbed by cross currents should be avoided. Chambers of large size are more prone to screaming, probably due to reduced damping effect of friction at the walls. The results of screaming are generally devastating, resulting in rapid failure of thrust chamber on account of high rates of mixing, heat release and heat transfer to the chamber walls.
PRACTICAL APPLICATIONS OF COMBUSTION STUDY
SOME PRACTICAL APPLICATIONS OF COMBUSTION STUDIES Premixed Flames: Domestic stoves, S. I. engines, Mine explosions Diffusion Flames: Candle light, Reading lamps, Diesel engine Flame Propagation Models: S.I. engines and Industrial burners Turbulent flame Models: S.I. engines, Gas Turbine Combustion Flammability Limits: Identification of fire hazards at coal mines, petrol car garages, LPG kitchens with possible fuel leakages Flame Quenching: Davy lamp, Prevention of fire spreading Min.Ign.Energy: Design of Ign. system for SI engines and Gas lighters Ignition Methods: I.C.Engines, Gas turbines, Rocket motors, Domestic Gas Stoves, Industrial Furnaces Flame Stability: Bunsen burner, Gas welding torch, Domestic burners Flame Stability in High Speed Flow: Gas turbines, Rocket Motors Droplet Combustion: Diesel engines, Gas turbines, Pulverized coal Combustion systems Basic Reaction Kinetics: Research on chemistry of reaction rates
Elements of Organic Chemistry Organic chemistry is the chemistry of compounds containing Carbon. Hydrocarbons are compounds containing Carbon and Hydrogen and in addition may also contain elements like N, O, S, P etc. Carbon can combine with other atoms in a serial way, giving rise to side chain, branched chain and ring structures. Aliphatic compounds are those which contain only C & H with open chain structure. Aromatic compounds are those which have a ring structure. Compounds of homologous series are those whose composition can be represented by a general formula.
Homologous Series: Alkanes (paraffins) : CnH2n+2 CH4, C2H6,.. C8H18, … C16H34 ……All carbon valences satisfied, hence the name-saturated hydrocarbons. e.g., methane, ethane, propane, butane, pentane, hexane, heptane, octane, nonane, decane, … cetane (hexa decane), etc Alkenes (Olefines) : CnH2n C2H4, C3H6, …C8H16…(Double bond) e.g., ethene(ethylene), propene, butene, …. etc. Alkines: CnH2n-2 C2H2, C3H4, C4H6…C8H14 …… (Triple bond) e.g., Ethyne (acetylene), propyne, butyne … etc. Aromatic series: CnH2n-6 C6H6, C7H8, C8H10 … (ring structure) e.g., benzene, toluene, xylene … etc. C
H H H H-C-C-C-H H H H propane
-C-C=C propene
-C C-Cpropyne
C
C
C
C
C
C
C
C
C
C
C
benzene
toluene
C
Hydrocarbon derivatives: 1. H atom or group of atoms is replaced by another atom: e.g., CH3I, C2H5Cl … where CH3 , C2H5 are called Alkyl radicals „R‟. 2. H atom is replaced by a hydroxyl group to give an alcohol. e.g., CH3OH, C2H5OH etc. Compd General formula Functional group Alcohol
R - OH
Hydroxyl group
Aldehydes
R - C=O
Aldehyde group
H Ketones
R - C- R‟
Carbonyl group
O Esters
R - C-O-R’
Ester group
O Acid
R - C=O
Carboxyl group
OH Peroxide
R - O-O-R’
Peroxide group
Isomers: These are compounds having the same chemical formula, but different chemical structure and hence different properties. Normal Octane: C8H18 Iso-Octane :
C8H18
……………. -C-C-C-C-C-C-C- -C-
- C-C-C-C-C-C-C-C-
Similarly, Isomers of HC derivatives: Ethyl alcohol:
C 2 H 6O
Dimethyl ether: C2H6O
……………… -C-O-C-
-C-C-O-
Some Commonly known Hydrocarbon Derivatives Alcohols: CH3OH(Methanol), C2H5OH(Ethanol), C4H9OH(Butyl alcohol), C6H5OH(Phenol)(carbolic acid) Acids: HCOOH(formic acid), CH3COOH(Acetic acid) Aldehydes: HCHO(formaldehyde), CH3CHO(acetaldehyde), C6H5CHO (benzaldehyde) Esters: HCOOCH3(methyl formate) Ethers: (C2H5)2O(Diethyl ether), (C6H5)O(C3H5)(propyl phenyl ether) Ketones: (CH3)2CO(acetone)(dimethyl ketone), (C2H5)CO(C4H9)(ethyl butyl ketone) Peroxides: HOOH = H2O2(hydrogen peroxide), R-O-O-R‟ (organic peroxides) Amines: R-NH2 Nitro alkyl compounds: R-NO2
BASIC REACTION KINETICS
Chemical Kinetics Chemical kinetics is that branch of physical chemistry which deals with the factor of reaction velocity in chemical processes. It seeks to define the rate of reaction in terms of several possible variables such as temperature, pressure, composition, state of agregation, external energy sources and presence or absence of catalysts. Rate of reaction: It is measured by the rate of decrease of concentration of reactants or by the rate of increase of concentration of products. Rate = - dC/ dt , (mole/litre.sec) where C is the concentration of the reactant under consideration at time „t‟. C = n/V (mole/litre) where „n‟ is the number of moles of the reactant present in volume V. Note: One Mole of a gas = Quantity of the gas whose wt numerically = molecular weight. Volume occupied by 1 mole of any gas = 22.4 litres per gm.mole (or 22400 litres/ kmol) at NTP (273K & 1 atm.pr).
Molecularity of a reaction: It is based on the number of molecules participating in a chemical reaction. 1. Uni-molecular reaction (mostly decomposition reactions): A → Products e.g., Br2 → Br + Br 2. Bi-molecular reaction ( most common reaction): A + B → Products e.g., H2 + Br2 → 2HBr 3. Tri-molecular reaction (very rare since ternary collisions are very difficult to occur): A + B + C → Products e.g., 2NO + O2 → 2NO2 Note: In some cases when two atoms collide with each other the sum of the energy of reactions and the K.E. of collision will be more than the dissociation energy of the formed diatomic molecule, and hence in effect no reaction occurs. Such a reaction may be effected by using a third body which mainly functions as an energy absorbent and keeps the product alive. The third body can be any other molecule of inert gas or solid metal surface. In the case of two poly-atomic molecules colliding with each other, a third body may not be necessary for the reaction, since this energy of reaction is distributed among the various number of degrees of freedom (translational, rotational, vibrational..) and is no longer concentrated in any one bond.
Law of mass action: The rate of chemical reaction is proportional to the active masses (i.e., concentration) of the participants. Thus, for the reaction A →B, Rate „r‟ = - dCA/ dt is α CA = k. CA Where, k = rate constant or specific reaction rate. For the reaction 2H2 + O2 → 2H2O Rate „r‟ = k. CH2. CH2. CO2 = k. CH22. CO2 Similarly, for the reaction aA + bB + … → Products, Rate „r‟ = k. CAa . CBb . …. Order of the reaction: Order indicates the manner in which the rate of reaction varies with the concentration of the reacting substance. Thus, the above reaction is said to be of the ath order w.r.t. A, bth order w.r.t. B and so on. The overall order of the above reaction is a + b +…
In complex reactions involving a number of steps, the rate can be a complex function of concentrations involving terms in the denominator also. The order of reaction is strictly an experimental quantity and merely provides information about the way in which the rate depends on concentration. In complex reactions molecularity may not be equal to the order of the reaction. They are the same only for elementary reactions. Rate Constant ‘k’ : Consider the reaction aA + bB + . . . → Products Reaction rate = k. CAa . CBb . …. Or, k = Rate / CAa . CBb . …. (mole/litre.sec) / (mole/litre)n mole(1-n).litre(n-1).sec-1 Where n = a + b + . . . = overall order. Thus for 1st order reaction k will be in sec-1 For 2nd order reaction k will be in litre.mole-1.sec-1
Representation of 1st order reaction
conc
A → Products Rate of reaction = -dCA/dt where CA is the conc. of A at time t. Therefore, -dCA/dt = k CA Integrating, logCA - ∫dCA/CA = k ∫dt or, - lnCA = k t + const Or, log CA = -kt / 2.303 + Const t If CA = a = initial conc. at t = 0, we get Const = log a. Substituting, we get log CA = log (a-x) = -kt / 2.303 + log a Or, k = (2.303/ t). log [a/(a-x)], where „x‟ is the no. of moles reacted at time „t‟. Half life of a reaction is the time required to reduce the concentration a to half its initial value. Therefore by putting x=a/2, we get Half life of 1st order reaction t½ = 0.693/k (sec) a/2 t1/2
time
Representation of 2nd order reaction A + B → Products Rate of reaction = -dCA/dt = -dCB/dt = kCA.CB , from the law of mass action. Let „a‟ be the initial conc of A, „b‟ initial conc of B at t = 0. Then at time t, CA = a – x and CB = b – x, where x is the no. of moles of A or B reacted at time t. - d(a-x)/dt = dx/dt = k(a-x).(b-x) CA hyperbolic Case(i): Equal initial concentrations: a = b t dx/dt = k(a-x)2 Integrating, ∫ dx/(a-x)2 = k ∫ dt from which, 1/(a-x) = kt + C At t = 0, x = 0. Hence C = 1/a Therefore, 1/(a-x) = kt + 1/a 1/CA Hence, k = x / [t.a(a-x)] ( litre.mol -1.sec -1 ) Putting, x = a/2, we get Half life = t½ = 1 /(k.a) t
2nd order reaction with unequal initial concentrations: k = {2.303 / [t.(a-b)] }. log [b(a-x)/ a(b-x)]
3rd order reaction with equal initial conc. of all three reactants: A + B + C → Products We obtain, 1/CA2 = 2kt + 1/a2 from which k = (2ax – x2) / [2 t a2(a – x)2]
1/CA2
Slope=2k
t
Half life of nth order reaction with equal initial conc. of all reactants: t½ = (2n-1 -1) / [(n-1)k.an-1 ]
Arrhenius Rate Equation Rate constant is independent of the concentration of reactants. All other factors that affect the reaction rate, in general, also affect the rate constant. The temperature dependence of „k‟ was studied by Arrhenius (in 1889) who proposed the relationship Reaction Rate = Z.P.e–Ea/RT , where Z is the number of collisions/sec, P is the Steric factor, Ea is the activation energy (cal / gm.mole or kJ / kg.mole), R is the Universal gas constant (8.314 kJ/ kmol.K), T is the temperature in K. But, Rate = k.N1.N2 where N1 and N2 are concentrations of the two reactants in the bi-molecular reaction (from law of mass action). Therefore, „k‟ = [(Z.P) / (N1.N2)].e–Ea/RT For hydrocarbons, Ea ≈ 40,000 cal/gm.mole = 1,67,440 kJ/ kmole.
Meaning of Steric factor: Collision geometry unfavorable:
H
No Reaction
I
Collision geometry favorable:
H H I
Reaction occurs: 2HI → H2 + I2
I
The physical concept of rate equation is that successful collisions between two reaction partners result if the two colliding molecules possess in a specific degree of freedom an energy equal to or more than the activation energy Ea, and if the geometry of collision (line of approach of the colliding molecules) is favorable for their interaction. The latter condition is expressed as Steric factor, whose value is undefined by theory, except that it should be < 1. The Arrhenius factor e–Ea/RT represents the fraction of collisions involving molecules possessing an energy more than the activation energy. When the temp. is increased the velocity and hence the K.E.of the molecule increases and therefore the rate constant increases.
Experimental determination of Activation Energy Determine the rate constant values for a reaction at two different temperatures. From these values Ea for this temperature range can be worked out. k = A. e–Ea/RT ln k = -Ea/RT + ln A Log k Or, log k = (-Ea/RT)/2.303 + log A 1/T For the given temp range of T1 to T2, log k1 = (-Ea/RT1)/2.303 + log A and log k2 = (-Ea/RT2)/2.303 + log A we can show that log(k1/k2) = (Ea / 2.303R) . [(T1-T2)/T1T2] from which Ea can be worked out for the temp range T1 to T2
Concept of Activated Complex
Energy
The classical collision theory has been supplanted by a more sophisticated rate theory based on the concept of activated collision complexes and their statistics. The collision theory equations remain valid for reactions of atoms and simple molecules. However for large molecules this theory becomes grossly inadequate as the Steric factor becomes unrealistically high or low. Activated complex B (Transition state) Activated Complex Theory: Ea ΔHa This theory considers an intermediate A Reactant ΔH configuration of atoms with the highest Product C energy level on the “reaction path way”. The concept has enabled to develop Reaction coordinate more satisfactory equations to evaluate A→B: energy required for activation reaction rates in complex reactions. B→C: energy released when activated complex breaks down into products Reactants→ Activ.complex→Products ΔH is the Heating value
HI + HI
→
H - H
(slow)
I - I
→ (fast)
H2 + I2
Study of fast reactions All chemical reactions are studied at constant temperature to eliminate the variable temperature effect on the reaction rates.
Slow reactions: Static method: Reactants are introduced into a bulb (reaction vessel) maintained at the desired temperature. Composition of samples are determined at intervals either directly by chemical analysis or indirectly by pressure measurements (for reactions involving change in total number of moles). Dynamic method: Sample tubes are attached at the entrance and exit of the reaction vessel to measure the concentration changes. The residence time in the reaction vessel is calculated by knowing the flow rate and the vessel volume. Experiment is repeated for various flow rates. Chemical analysis of sampled gas can be done using (i) Mass spectroscopy (ii) Chromatography or (iii) Spectrophotometers.
Fast Reactions: The static and dynamic methods described earlier can be used only for slow reactions with half life of the order of at least a few minutes. For faster reactions continuous recording of variables (concentration, pressure, radiation etc) is required using oscillographs, spectrophoto -meters etc with sophisticated electronic instrumentation. Stopped flow technique: In this method, the flow into the reaction vessel is suddenly stopped and spectrophotometric measurements of concentration are recorded continuously. Study of fast reactions require techniques of instantaneous starting of the reactions for counting the time to follow the reaction velocity. Following techniques have been developed for various reactions: Relaxation method (1960s) : The reaction is first allowed to go to equilibrium. It is then instantly disturbed by „pressure jump‟ or „temp. jump‟ technique using large currents. The approach to equilibrium (relaxation time) is then followed by high speed techniques.
Shock tube technique: (1960s) A supersonic shock wave is generated by breaking a diaphragm through a shock pressure ratio. As the wave traverses an element of gas it instantly raises it to high temperature and reaction occurs in and behind the shock front. The course of reaction is followed by fast techniques. Flash Photolysis: (1956) A light flash of very high intensity and very short duration (1μs) is produced in the neighbourhood of the reaction vessel. Under suitable conditions this will produce atoms, free radicals and excited species in the system which will initiate further reactions and can be followed by spectroscopic means. This method is also known as „kinetic spectroscopy‟ and is used for the study of Cl2 + H2 reaction. Reactions in molecular beams: It is a recently developed technique in which mono-energetic molecular beams are produced. By allowing two molecular beams impinge on each other it has been possible to study the kinetics of bi-molecular reactions such as K + HBr → KBr + H.
Summary of Fast Reaction Study Techniques Method 1. 2. 3.
4. 5.
Conventional Flow Relaxation method: Pr. Jump Temp. Jump Field Pulse Shock Tubes Kinetic Spectroscopy
Range of half life (sec) 102 - 108 (3.2 yr) 10-3 - 102
10-6 10-7 10-10 10-9 10-15 -
1 1 10-4 10-3 10-10
REFERENCES 1. 2. 3. 4.
5. 6. 7.
Kenneth Wark Jr., Thermodynamics, 5th Ed.,Mc Graw Hill, 1989. P.K.Nag, Engineering Thermodynamics, 3rd Ed.,TMH., 2005. S.P.Sharma and Chander Mohan, Fuels and Combustion, TMH., 1984. Stephen R.Turns, An Introduction to Combustion (Concepts and Applications), 2nd Ed., Mc Graw Hill, 2000. H.N.Gupta, Fundamentals of Internal Combustion Engines, Prentice Hall, EEE Edition, 2006. M.J.Zucrow, Principles of Jet Propulsion and Rocket Systems, John Wiley. B.Lewis and G.von Elbe, Combustion, Flames and Explosion of Gases, Academic Press Inc., NY, 1961.
CHAIN REACTION AND COOL FLAMES
