Turbulent CombustionTurbulent Combustion

OutlineOutline

Types of FlamesTypes of Flames

Basic Concept of Turbulence Basic Concept of Turbulence

Turbulent FlameTurbulent Flame

Flame StabilityFlame Stability

Types of FlamesTypes of Flames

Two basic categoriesTwo basic categories– Pre-mixedPre-mixed– Non-premixed Non-premixed

(Diffusion)(Diffusion)

Both characterized as Both characterized as Laminar or TurbulentLaminar or Turbulent

PremixedPremixed

Results from gaseous Results from gaseous reactants that are mixed reactants that are mixed prior to combustionprior to combustion

Flame propagates at Flame propagates at velocities slightly less velocities slightly less than a few m/sthan a few m/s

Reacts quite rapidlyReacts quite rapidlyExample: Spark Ignition Engine

Non-premixed (Diffusion)Non-premixed (Diffusion)

Gaseous reactants Gaseous reactants are introduced are introduced separately and mix separately and mix during combustionduring combustion

Energy release rate Energy release rate limited by mixing limited by mixing processprocess

Reaction zone Reaction zone between oxidizer and between oxidizer and fuel zonefuel zone

                                                                                                                 

             

Example: Diesel Engine

LaminarLaminar

PremixedPremixed– Ex. Bunsen BurnerEx. Bunsen Burner– Flame moves at fairly low velocityFlame moves at fairly low velocity– Mechanically create laminar Mechanically create laminar

conditionsconditions

DiffusionDiffusion– Ex. Candle FlameEx. Candle Flame– Fuel: Wax, Oxidizer: AirFuel: Wax, Oxidizer: Air– Reaction zone between wax Reaction zone between wax

vapors and airvapors and air

TurbulentTurbulent

PremixedPremixed– Heat release occurs much fasterHeat release occurs much faster– Increased flame propagationIncreased flame propagation– No definite theories to predict No definite theories to predict

behavior behavior

DiffusionDiffusion– Can obtain high rates of Can obtain high rates of

combustion energy release per combustion energy release per unit volumeunit volume

– Ex. Diesel EngineEx. Diesel Engine– Modeling is very complex, no Modeling is very complex, no

well established approachwell established approach

Turbulence : Basic ConceptsTurbulence : Basic Concepts

Turbulent flowTurbulent flow results when instabilities in a flow are results when instabilities in a flow are not sufficiently damped by viscous action and the fluid not sufficiently damped by viscous action and the fluid velocity at each point in the flow exhibits random velocity at each point in the flow exhibits random

fluctuations.fluctuations. The random unsteadiness associated with various flow The random unsteadiness associated with various flow properties is the hallmark of a turbulent flow and is properties is the hallmark of a turbulent flow and is illustrated for the axial velocity component in the next illustrated for the axial velocity component in the next figure.figure.One particularly useful way to characterize a turbulent One particularly useful way to characterize a turbulent flow field is to define flow field is to define meanmean andand fluctuating quantitiesfluctuating quantities. . Mean properties are defined by taking a time-average of Mean properties are defined by taking a time-average of the flow property over a sufficiently large time interval the flow property over a sufficiently large time interval

∆ ∆t = t2 – t1.t = t2 – t1.

The fluctuation, p'(t), is the difference between the The fluctuation, p'(t), is the difference between the instantaneous value of the property, p(t), and the mean instantaneous value of the property, p(t), and the mean value, pvalue, pavgavg , or , or

p(t)= pp(t)= pavgavg+ p'(t)+ p'(t)

Or, in general, we can write:Or, in general, we can write:

Y(t)= YY(t)= Yavgavg + Y + Yii'(t)'(t)

This manner of expressing variables as a mean and a This manner of expressing variables as a mean and a fluctuating component is referred to as the fluctuating component is referred to as the Reynolds Reynolds decompositiondecomposition..

At this point, the key question arises :At this point, the key question arises :

““What is the physical nature of a What is the physical nature of a turbulent flow”?turbulent flow”?

The following figure gives a The following figure gives a partial answer to this partial answer to this question. In this figure, we question. In this figure, we see fluid blobs and filaments see fluid blobs and filaments of fluid intertwining. A of fluid intertwining. A common notion in fluid common notion in fluid mechanics is the idea of a mechanics is the idea of a fluid eddyfluid eddy

An An eddyeddy is considered to be is considered to be a macroscopic fluid element a macroscopic fluid element in which the microscopic in which the microscopic elements composing the elements composing the eddy behave in some ways eddy behave in some ways as a unit. as a unit.

For example, a For example, a vortexvortex imbedded in a flow would be imbedded in a flow would be considered an eddy. considered an eddy.

A turbulent flow comprises many eddies with a multitude A turbulent flow comprises many eddies with a multitude of sizes and vorticities, a measure of angular velocities. of sizes and vorticities, a measure of angular velocities.

A number of smaller eddies may be imbedded in a larger A number of smaller eddies may be imbedded in a larger eddy. A characteristic of a fully turbulent flow is the eddy. A characteristic of a fully turbulent flow is the existence of a wide range of length scales, i.e., eddy existence of a wide range of length scales, i.e., eddy sizes. sizes.

For a turbulent flow, the Reynolds number is a measure For a turbulent flow, the Reynolds number is a measure of the range of scales present; the greater the Reynolds of the range of scales present; the greater the Reynolds number, the greater the range of sizes from the smallest number, the greater the range of sizes from the smallest eddy to the largest. It is this large range of length scales eddy to the largest. It is this large range of length scales that makes calculating turbulent flows from first that makes calculating turbulent flows from first principles intractable. We wilt discuss length scales in principles intractable. We wilt discuss length scales in more detail in the next section.more detail in the next section.

The rapid intertwining of fluid elements is a The rapid intertwining of fluid elements is a characteristic that distinguishes turbulent flow characteristic that distinguishes turbulent flow from laminar flow. from laminar flow.

The turbulent motion of fluid elements allows The turbulent motion of fluid elements allows momentum, species, and energy to be momentum, species, and energy to be transported in the cross-stream direction much transported in the cross-stream direction much more rapidly than is possible by the molecular more rapidly than is possible by the molecular diffusion processes controlling transport in diffusion processes controlling transport in laminar flows. laminar flows.

Because of this, most practical combustion Because of this, most practical combustion devices employ turbulent flows to enable rapid devices employ turbulent flows to enable rapid mixing and heat release in relatively small mixing and heat release in relatively small volumes.volumes.

LENGTH SCALES IN TURBULENT FLOWSLENGTH SCALES IN TURBULENT FLOWS

In the turbulence literature, many length scales have In the turbulence literature, many length scales have been defined; however, the following four scales are of been defined; however, the following four scales are of general relevance to our discussion and, in general, general relevance to our discussion and, in general, are frequently cited. In decreasing order of size, these are frequently cited. In decreasing order of size, these scales are as follows:scales are as follows:

1. (L) Characteristic width of flow or macroscale1. (L) Characteristic width of flow or macroscale

This is the largest length scale in the system and is the This is the largest length scale in the system and is the upper bound for the largest possible eddies. In a upper bound for the largest possible eddies. In a reciprocating internal combustion engine, L might be reciprocating internal combustion engine, L might be taken as the time varying clearance between the piston taken as the time varying clearance between the piston

top and the head, or perhaps the cylinder bore.top and the head, or perhaps the cylinder bore.

2. 2. (l(l oo) Integral scale or turbulence macroscale) Integral scale or turbulence macroscale The integral scale physically represents the The integral scale physically represents the

mean size of the large eddies in a turbulent mean size of the large eddies in a turbulent flow; those eddies with low frequency and large flow; those eddies with low frequency and large wavelength. The integral scale is always wavelength. The integral scale is always smaller than L, but is of the same order of smaller than L, but is of the same order of magnitude. magnitude.

3. (l3. (l) ) Taylor microscale Taylor microscale

The Taylor microscale is an intermediate length The Taylor microscale is an intermediate length scale between the integral scale (scale between the integral scale ( llo) and o) and Kolmogorov Scale (Kolmogorov Scale (llk), but is weighted more k), but is weighted more towards the smaller scales. This scale is towards the smaller scales. This scale is related to the mean rate of strain.related to the mean rate of strain.

4. (lk) 4. (lk) Kolmogorov microscale Kolmogorov microscale

The Kolmogorov microscale is the smallest length scale The Kolmogorov microscale is the smallest length scale associated with a turbulent flow and, as such, is associated with a turbulent flow and, as such, is representative of the dimension at which the dissipation representative of the dimension at which the dissipation of turbulent kinetic energy to fluid internal energy occurs. of turbulent kinetic energy to fluid internal energy occurs. Thus, the Kolmogorov scale is the scale at which Thus, the Kolmogorov scale is the scale at which

molecular effects (kinematic viscosity) are significant.molecular effects (kinematic viscosity) are significant. The final point we wish to make concerning The final point we wish to make concerning lklk is possible is possible physical interpretations. In physical interpretations. In TennekesTennekes model of a model of a turbulent flow, turbulent flow, lklk represents the thickness of the smallest represents the thickness of the smallest vortex tubes or filaments that permeate a turbulent flow, vortex tubes or filaments that permeate a turbulent flow, while others suggest that while others suggest that lklk represents the thickness of represents the thickness of vortex sheets imbedded in the flow. vortex sheets imbedded in the flow.

DEFINITION OF TURBULENT FLAME DEFINITION OF TURBULENT FLAME SPEEDSPEED

Unlike a laminar flame, which has a propagation velocity Unlike a laminar flame, which has a propagation velocity that depends uniquely on the thermal and chemical that depends uniquely on the thermal and chemical properties of the mixture, a turbulent flame has a properties of the mixture, a turbulent flame has a propagation velocity that depends on the character of the propagation velocity that depends on the character of the flow, as well as on the mixture properties.flow, as well as on the mixture properties.

For an observer traveling with the flame, we can define a For an observer traveling with the flame, we can define a turbulent flame speedturbulent flame speed, S, Stt as the velocity at which as the velocity at which

unburned mixture enters the flame zone in a direction unburned mixture enters the flame zone in a direction

normal to the flame.normal to the flame.

In this definition, we assume that the flame surface is In this definition, we assume that the flame surface is represented as some time-mean quantity, recognizing represented as some time-mean quantity, recognizing that the instantaneous position of the high-temperature that the instantaneous position of the high-temperature reaction zone may be fluctuating wildly. reaction zone may be fluctuating wildly.

Since the direct measurement of unburned gas velocities Since the direct measurement of unburned gas velocities at a point near a turbulent flame is exceedingly difficult, at a point near a turbulent flame is exceedingly difficult, at best, flame velocities usually are determined from at best, flame velocities usually are determined from measurements of reactant flow rates. Thus, the turbulent measurements of reactant flow rates. Thus, the turbulent flame speed can be expressed as :flame speed can be expressed as :

St= m / (Aavg St= m / (Aavg uu))The reason for using this time-smoothed flame area is The reason for using this time-smoothed flame area is

shown below :shown below :

Experimental Experimental determinations of determinations of turbulent flame speeds turbulent flame speeds are complicated by are complicated by determining a suitable determining a suitable flame area. A, for thick, flame area. A, for thick, and frequently curved, and frequently curved, flames. The ambiguity flames. The ambiguity associated with associated with determining this flame determining this flame area can result in area can result in considerable uncertainty considerable uncertainty in the measurement of in the measurement of turbulent burning velocity. turbulent burning velocity.

STRUCTURE OF TURBULENT PREMIXED STRUCTURE OF TURBULENT PREMIXED FLAMESFLAMES

Again, referring to the previous figure we can say that Again, referring to the previous figure we can say that The instantaneous flame front is highly convoluted, with The instantaneous flame front is highly convoluted, with the largest, folds near the top of the flame (Fig. a). The the largest, folds near the top of the flame (Fig. a). The positions of the reaction zones move rapidly in space, positions of the reaction zones move rapidly in space, producing a time-averaged view that gives the producing a time-averaged view that gives the appearance of a thick reaction zone (Fig. b).appearance of a thick reaction zone (Fig. b).

This apparently thick reaction zone is frequently referred This apparently thick reaction zone is frequently referred to as a to as a turbulent flame brushturbulent flame brush. .

The instantaneous view, however, clearly shows the The instantaneous view, however, clearly shows the actual reaction front to be relatively thin, as in a laminar actual reaction front to be relatively thin, as in a laminar premixed flame. These reaction fronts are sometimes premixed flame. These reaction fronts are sometimes referred to as laminar referred to as laminar flameletsflamelets..

As mentioned above, spark-ignition engines operate with As mentioned above, spark-ignition engines operate with turbulent premixed flames. Recent developments in turbulent premixed flames. Recent developments in laser-based instrumentation have allowed researchers to laser-based instrumentation have allowed researchers to explore, in much more detail than previously possible, explore, in much more detail than previously possible, the hostile environment of the internal combustion the hostile environment of the internal combustion engine combustion chamber. This is shown in the next engine combustion chamber. This is shown in the next slide.slide.

In these flame visualizations, we see that the division In these flame visualizations, we see that the division between the unburned and burned gases occurs over a between the unburned and burned gases occurs over a very short distance and the flame front is distorted by very short distance and the flame front is distorted by both relatively large- and small-scale both relatively large- and small-scale wrinkleswrinkles. .

This figure shows a time This figure shows a time sequence of two-sequence of two-dimensional flame dimensional flame visualizations in a spark-visualizations in a spark-ignition engine from a ignition engine from a study.study.The flame begins to The flame begins to propagate outward from propagate outward from the spark plug, as shown the spark plug, as shown in the first frame, and in the first frame, and moves across the moves across the chamber until nearly all chamber until nearly all the gas is burned. the gas is burned.

Three Flame RegimesThree Flame Regimes

The visualizations of The visualizations of turbulent, flames turbulent, flames presented before suggest presented before suggest that the effect of that the effect of turbulence is to wrinkle turbulence is to wrinkle and distort an essentially and distort an essentially laminar flame front.laminar flame front.

Turbulent flames of this Turbulent flames of this type are referred to as type are referred to as being in the being in the wrinkled wrinkled laminar-flame regimelaminar-flame regime. .

This is one pole in our This is one pole in our classification of turbulent classification of turbulent premixed flames. At the premixed flames. At the other pole is the other pole is the distributed-reaction distributed-reaction regimeregime. .

Falling between these Falling between these two regimes is a region two regimes is a region sometimes referred to as sometimes referred to as the the flamelets-in-eddies flamelets-in-eddies regimeregime..

Regime CriteriaRegime Criteria

Recall that the smallest scale, the Kolmogorov Recall that the smallest scale, the Kolmogorov microscale, microscale, lklk, represents the smallest eddies in the flow. , represents the smallest eddies in the flow. These eddies rotate rapidly and have high vorticity, These eddies rotate rapidly and have high vorticity, resulting in the dissipation of the fluid kinetic energy into resulting in the dissipation of the fluid kinetic energy into internal energy, i.e., fluid friction results in a temperature internal energy, i.e., fluid friction results in a temperature rise of the fluid. rise of the fluid.

At the other extreme of the length-scale spectrum is the At the other extreme of the length-scale spectrum is the integral scale, integral scale, lolo which characterizes the largest eddy which characterizes the largest eddy sizes. The basic structure of a turbulent flame is sizes. The basic structure of a turbulent flame is governed by the relationships of governed by the relationships of lklk and and lolo to the laminar to the laminar flame thickness, flame thickness, l. l.

The laminar flame thickness characterizes The laminar flame thickness characterizes the thickness of a reaction zone controlled the thickness of a reaction zone controlled by molecular, not turbulent, transport of by molecular, not turbulent, transport of heat and mass. More explicitly, the three heat and mass. More explicitly, the three regimes are defined by :regimes are defined by :

Wrinkled laminar flames: Wrinkled laminar flames: ll < < llkk

Flamelets in eddies: Flamelets in eddies: lloo > > ll > > llkk

Distributed reactions: Distributed reactions: ll > > lloo

When the flame thickness, is much thinner than the When the flame thickness, is much thinner than the smallest scale of turbulence, the turbulent motion can smallest scale of turbulence, the turbulent motion can only wrinkle or distort the thin laminar flame zone. The only wrinkle or distort the thin laminar flame zone. The criterion for the existence of a wrinkled laminar flame is criterion for the existence of a wrinkled laminar flame is sometimes referred to as the sometimes referred to as the Williams-Klimov Williams-Klimov criterioncriterion. .

At the other extreme, if all scales of turbulent motion are At the other extreme, if all scales of turbulent motion are smaller than the reaction zone thickness, then transport smaller than the reaction zone thickness, then transport within the reaction zone is no longer governed solely by within the reaction zone is no longer governed solely by molecular processes, but is controlled, or at least molecular processes, but is controlled, or at least influenced, by the turbulence. This criterion for the influenced, by the turbulence. This criterion for the existence of a distributed-reaction zone is sometimes existence of a distributed-reaction zone is sometimes referred to as the Damkohler criterion.referred to as the Damkohler criterion.

Hence, in addition to the Reynolds Number (Re), we Hence, in addition to the Reynolds Number (Re), we have another number that that characterizes the have another number that that characterizes the turbulent flame velocity called Damkturbulent flame velocity called DamkÖhler number (Da).Öhler number (Da).

The fundamental meaning of the DamkThe fundamental meaning of the DamkÖÖhler number, hler number, Da, used here is that it represents the ratio of a Da, used here is that it represents the ratio of a characteristic flow or mixing time to a characteristic characteristic flow or mixing time to a characteristic

chemical timechemical time..It represents the ratio between the characteristic flow It represents the ratio between the characteristic flow time to the characteristic chemical time.time to the characteristic chemical time.

When chemical reaction When chemical reaction rates are fast in rates are fast in comparison with fluid comparison with fluid mixing rates, then Da > 1, mixing rates, then Da > 1, and a and a fast-chemistry fast-chemistry regimeregime is defined. is defined. Conversely, when Conversely, when reaction rates are slow in reaction rates are slow in comparison with mixing comparison with mixing rates, then Da < 1.rates, then Da < 1.This is shown in the This is shown in the figure to the right.figure to the right.

Definition of the three flame regionsDefinition of the three flame regions

1) WRINKLED LAMINAR-FLAME REGIME1) WRINKLED LAMINAR-FLAME REGIMEIn this regime, chemical reactions occur in thin In this regime, chemical reactions occur in thin sheets. sheets. Referring again to the previous figure, we see Referring again to the previous figure, we see that reaction sheets occur only for Damkohler that reaction sheets occur only for Damkohler numbers greater than unity, depending on the numbers greater than unity, depending on the turbulence Reynolds numbers, clearly indicating turbulence Reynolds numbers, clearly indicating that the reaction-sheet regime is characterized that the reaction-sheet regime is characterized by fast chemistry (in comparison with fluid by fast chemistry (in comparison with fluid mechanical mixing). mechanical mixing).

2) DISTRIBUTED-REACTION REGIME2) DISTRIBUTED-REACTION REGIMEOne way to enter this regime is to require One way to enter this regime is to require small integral length scales, (lo / lk) < 1, and small integral length scales, (lo / lk) < 1, and small Damkohler numbers (Da < 1). This is small Damkohler numbers (Da < 1). This is difficult to achieve in a practical device, difficult to achieve in a practical device, since these requirements imply that, since these requirements imply that, simultaneously, lo, must be small and vrms simultaneously, lo, must be small and vrms must be large, i.e., small flow passages and must be large, i.e., small flow passages and very high velocities. very high velocities. Pressure losses in such devices surely Pressure losses in such devices surely would be huge and, hence, render them would be huge and, hence, render them impractical. Also, it is not clear that a flame impractical. Also, it is not clear that a flame can be sustained under such conditions. can be sustained under such conditions.

3) FLAMELETS-IN-EDDIES REGIME3) FLAMELETS-IN-EDDIES REGIME

This regime lies in the wedge-shaped This regime lies in the wedge-shaped region between the wrinkled laminar flame region between the wrinkled laminar flame and distributed-reaction regimes as shown and distributed-reaction regimes as shown in the previous figure. This region is in the previous figure. This region is typified by moderate Damkohler numbers typified by moderate Damkohler numbers and high turbulence intensities. This and high turbulence intensities. This region is of particular interest in that it is region is of particular interest in that it is likely that some practical combustion likely that some practical combustion devices operate in this regime. devices operate in this regime.

Flame stabilizationFlame stabilization

Low velocity bypass portsLow velocity bypass ports

Refractory burner tilesRefractory burner tiles

Bluff body Flame-holder (Recirculation)Bluff body Flame-holder (Recirculation)

Swirl or jet-induced recirculating flowsSwirl or jet-induced recirculating flows

Rapid increase in flow area creating Rapid increase in flow area creating recirculating separated flowrecirculating separated flow