1. Turbulent Combustion
Jehad Yamin

2. Outline Types of Flames Basic Concept of Turbulence Turbulent Flame
Flame Stability

3. Types of Flames Two basic categories
Pre-mixed
Diffusion
Both characterized as Laminar or Turbulent

4. Premixed
Results from gaseous reactants that are mixed prior to combustion
Flame propagates at velocities slightly less than a few m/s
Reacts quite rapidly
Example: Spark Ignition Engine

5. Diffusion
Gaseous reactants are introduced separately and mix during combustion
Energy release rate limited by mixing process
Reaction zone between oxidizer and fuel zone
                                                                                                                              
Example: Diesel Engine

6. Laminar Premixed Diffusion Ex. Bunsen Burner
Flame moves at fairly low velocity
Mechanically create laminar conditions
Diffusion
Ex. Candle Flame
Fuel: Wax, Oxidizer: Air
Reaction zone between wax vapors and air

7. Turbulent Premixed Diffusion Heat release occurs much faster
Increased flame propagation
No definite theories to predict behavior
Diffusion
Can obtain high rates of combustion energy release per unit volume
Ex. Diesel Engine
Modeling is very complex, no well established approach

8. Turbulence : Basic Concepts
Turbulent flow results when instabilities in a flow are not sufficiently damped by viscous action and the fluid velocity at each point in the flow exhibits random fluctuations.
The random unsteadiness associated with various flow properties is the hallmark of a turbulent flow and is illustrated for the axial velocity component in the next figure.
One particularly useful way to characterize a turbulent flow field is to define mean and fluctuating quantities. Mean properties are defined by taking a time-average of the flow property over a sufficiently large time interval
∆t = t2 – t1.

10. The fluctuation, p'(t), is the difference between the instantaneous value of the property, p(t), and the mean value, pavg , or
p(t)= pavg+ p'(t)
Or, in general, we can write:
Y(t)= Yavg + Yi'(t)
This manner of expressing variables as a mean and a fluctuating component is referred to as the Reynolds decomposition.

11. “What is the physical nature of a turbulent flow”?
At this point, the key question arises :
“What is the physical nature of a turbulent flow”?

12. The following figure gives a partial answer to this question
The following figure gives a partial answer to this question. In this figure, we see fluid blobs and filaments of fluid intertwining. A common notion in fluid mechanics is the idea of a fluid eddy
An eddy is considered to be a macroscopic fluid element in which the microscopic elements composing the eddy behave in some ways as a unit.

13. For example, a vortex imbedded in a flow would be considered an eddy.
A turbulent flow comprises many eddies with a multitude of sizes and vorticities, a measure of angular velocities.
A number of smaller eddies may be imbedded in a larger eddy. A characteristic of a fully turbulent flow is the existence of a wide range of length scales, i.e., eddy sizes.
For a turbulent flow, the Reynolds number is a measure of the range of scales present; the greater the Reynolds number, the greater the range of sizes from the smallest eddy to the largest. It is this large range of length scales that makes calculating turbulent flows from first principles intractable. We wilt discuss length scales in more detail in the next section.

14. The rapid intertwining of fluid elements is a characteristic that distinguishes turbulent flow from laminar flow.
The turbulent motion of fluid elements allows momentum, species, and energy to be transported in the cross-stream direction much more rapidly than is possible by the molecular diffusion processes controlling transport in laminar flows.
Because of this, most practical combustion devices employ turbulent flows to enable rapid mixing and heat release in relatively small volumes.

15. LENGTH SCALES IN TURBULENT FLOWS
In the turbulence literature, many length scales have been defined; however, the following four scales are of general relevance to our discussion and, in general, are frequently cited. In decreasing order of size, these scales are as follows:
1. (L) Characteristic width of flow or macroscale
This is the largest length scale in the system and is the upper bound for the largest possible eddies. In a reciprocating internal combustion engine, L might be taken as the time varying clearance between the piston top and the head, or perhaps the cylinder bore.

16. 2. (l o) Integral scale or turbulence macroscale
The integral scale physically represents the mean size of the large eddies in a turbulent flow; those eddies with low frequency and large wavelength. The integral scale is always smaller than L, but is of the same order of magnitude.
3. (l) Taylor microscale
The Taylor microscale is an intermediate length scale between the integral scale (lo) and Kolmogorov Scale (lk), but is weighted more towards the smaller scales. This scale is related to the mean rate of strain.

17. 4. (lk) Kolmogorov microscale
The Kolmogorov microscale is the smallest length scale associated with a turbulent flow and, as such, is representative of the dimension at which the dissipation of turbulent kinetic energy to fluid internal energy occurs. Thus, the Kolmogorov scale is the scale at which molecular effects (kinematic viscosity) are significant.
The final point we wish to make concerning lk is possible physical interpretations. In Tennekes model of a turbulent flow, lk represents the thickness of the smallest vortex tubes or filaments that permeate a turbulent flow, while others suggest that lk represents the thickness of vortex sheets imbedded in the flow.

18. DEFINITION OF TURBULENT FLAME SPEED
Unlike a laminar flame, which has a propagation velocity that depends uniquely on the thermal and chemical properties of the mixture, a turbulent flame has a propagation velocity that depends on the character of the flow, as well as on the mixture properties.
For an observer traveling with the flame, we can define a turbulent flame speed, St as the velocity at which unburned mixture enters the flame zone in a direction normal to the flame.

19. In this definition, we assume that the flame surface is represented as some time-mean quantity, recognizing that the instantaneous position of the high-temperature reaction zone may be fluctuating wildly.
Since the direct measurement of unburned gas velocities at a point near a turbulent flame is exceedingly difficult, at best, flame velocities usually are determined from measurements of reactant flow rates. Thus, the turbulent flame speed can be expressed as :
St= m / (Aavg u)
The reason for using this time-smoothed flame area is shown below :

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

21. STRUCTURE OF TURBULENT PREMIXED FLAMES
Again, referring to the previous figure we can say that The instantaneous flame front is highly convoluted, with the largest, folds near the top of the flame (Fig. a). The positions of the reaction zones move rapidly in space, producing a time-averaged view that gives the appearance of a thick reaction zone (Fig. b).
This apparently thick reaction zone is frequently referred to as a turbulent flame brush.
The instantaneous view, however, clearly shows the actual reaction front to be relatively thin, as in a laminar premixed flame. These reaction fronts are sometimes referred to as laminar flamelets.

22. As mentioned above, spark-ignition engines operate with turbulent premixed flames. Recent developments in laser-based instrumentation have allowed researchers to explore, in much more detail than previously possible, the hostile environment of the internal combustion engine combustion chamber. This is shown in the next slide.
In these flame visualizations, we see that the division between the unburned and burned gases occurs over a very short distance and the flame front is distorted by both relatively large- and small-scale wrinkles.

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

24. Three Flame Regimes
The visualizations of turbulent, flames presented before suggest that the effect of turbulence is to wrinkle and distort an essentially laminar flame front.
Turbulent flames of this type are referred to as being in the wrinkled laminar-flame regime.

25. This is one pole in our classification of turbulent premixed flames
This is one pole in our classification of turbulent premixed flames. At the other pole is the distributed-reaction regime.
Falling between these two regimes is a region sometimes referred to as the flamelets-in-eddies regime.

26. Regime Criteria
Recall that the smallest scale, the Kolmogorov microscale, lk, represents the smallest eddies in the flow. These eddies rotate rapidly and have high vorticity, resulting in the dissipation of the fluid kinetic energy into internal energy, i.e., fluid friction results in a temperature rise of the fluid.
At the other extreme of the length-scale spectrum is the integral scale, lo which characterizes the largest eddy sizes. The basic structure of a turbulent flame is governed by the relationships of lk and lo to the laminar flame thickness, l.

27. The laminar flame thickness characterizes the thickness of a reaction zone controlled by molecular, not turbulent, transport of heat and mass. More explicitly, the three regimes are defined by :
Wrinkled laminar flames: l < lk
Flamelets in eddies: lo > l > lk
Distributed reactions: l > lo

28. When the flame thickness, is much thinner than the smallest scale of turbulence, the turbulent motion can only wrinkle or distort the thin laminar flame zone. The criterion for the existence of a wrinkled laminar flame is sometimes referred to as the Williams-Klimov criterion.
At the other extreme, if all scales of turbulent motion are smaller than the reaction zone thickness, then transport within the reaction zone is no longer governed solely by molecular processes, but is controlled, or at least influenced, by the turbulence. This criterion for the existence of a distributed-reaction zone is sometimes referred to as the Damkohler criterion.

29. Hence, in addition to the Reynolds Number (Re), we have another number that that characterizes the turbulent flame velocity called DamkÖhler number (Da).
The fundamental meaning of the DamkÖhler number, Da, used here is that it represents the ratio of a characteristic flow or mixing time to a characteristic chemical time.
It represents the ratio between the characteristic flow time to the characteristic chemical time.

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

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

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

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

34. Flame stabilization Low velocity bypass ports Refractory burner tiles
Bluff body Flame-holder (Recirculation)
Swirl or jet-induced recirculating flows
Rapid increase in flow area creating recirculating separated flow