Liquid fuel combustion can be greatly enhanced by disintegrating the liquid fuel into droplets, an effect achieved by various configurations. A number of experiments carried out in the seventies showed that combustion of droplet arrays and sprays do not form individual flames. Moreover, the rate of burning in spray combustion greatly deviates from that of the single combustion rate. Such observations naturally challenge its applicability to spray combustion. A number of mathematical models were developed to evaluate 'group combustion' and the related 'group evaporation' phenomena. This study investigates the similarity and difference of these models and their applicability to spray combustion. Future work that should be carried out in this area is indicated

Shen, Hayley H.

English

NASA Technical Reports Server

1990
N91-19010
NASA/ASEE SUMMER FACULTY FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA
A STUDY OF THE CURRENT GROUP EVAPORATION/COMBUSTION THEORIES
Prepared By:
Academic Rank:
University and
Department:
Hayley H. Shen
Associate Professor
Clarkson University
Department of Civil and
Environmental Engineering
NASA/MSFC:
Laboratory:
Division:
Branch:
MSFC Colleague:
Propulsion
Propulsion Systems
Performance Analysis
Dr. Charles F. Schafer
Contract No: NGT-01-002-099
The University of Alabama
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https://ntrs.nasa.gov/search.jsp?R=19910009697 2020-03-19T18:41:49+00:00Z

I. INTRODUCTION
Liquid fuel combustion can be greatly enhanced by
disintegrating the liquid fuel into droplets, achieved by various
injector configurations. Although this fact has been known for more
than a century, a scientific understanding of liquid fuel spray
combustion started only but forty years ago. For most part of this
time, effort has been focused on single droplet combustion. A
number of experiments carried out in the seventies have shown that
combustion of droplet arrays and sprays do not form individual
flames. Moreover, the rate of burning in spray combustion greatly
deviates from that of the single droplet combustion rate. Such
observations naturally challenge its applicability to spray
combustion.
A number of mathematical models have been developed to
evaluate the "group combustion" and the related "group evaporation"
phenomena. This study investigates the similarity and difference
of these models, and their applicability to spray combustion.
Future work that should be carried out in this area is indicated.
II. Group Evaporation
Evaporation precedes and maintains combustion after ignition.
Understanding this process is a natural first step towards
understanding combustion. Two major approaches in modeling group
evaporation are represented by the works of Bellan and co-workers,
and Chiu and co-workers. The physical pictures that are
mathematically described in these two approaches are not the same.
Bellan's model is a field of uniformly distributed identical
droplets with unlimited extent. The initial conditions of the
droplets and the surrounding gas are given. Chiu's model is an
arbitrary cloud of uniform droplets, the conditions far away from
the cloud are known.
In either case, the total evaporation of the group, that being
a uniform cluster or an arbitrary cloud of droplets, is the
integral of the evaporation of each droplet enclosed. Therefore,
the question comes back to what is the evaporation rate of each
droplet, except that the "environment" in which each droplet
evaporates must now be influenced by the neighboring droplets. This
"environment" includes the detailed temperature, pressure, and
species concentration surrounding each droplets. Given an
environment, the evaporation rate of each droplet depends on its
surface temperature, which is influenced by the fluid dynamic and
thermodynamic processes inside the droplet.
Because the fluid/thermo-dynamic processes have been studied
for a single droplet in an infinite field of gas, Bellan's work
concentrates on incorporating realistic boundary conditions located
at the edge of a "bubble" surrounding each droplet. The bubbles
subdivide the whole space occupied by the mixture of droplets and
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the gas. Spatial variations of any variables inside each bubble and
the droplet are carefully studied. The possible variation of any
variable from one bubble to the other is not incorporated. This
work has later been extended to a moving spherical cluster, and to
finite kinetics of evaporation. Among many important results,
several major finding are:
i. D2-t law for droplet size reduction does not apply at a
surprisingly lean condition.
2. Evaporation time can be an order of magnitude higher than that
predicted from the single droplet case.
3. Saturation occurs at a much leaner condition than that predicted
from the single droplet theory.
4. The above effects are significant even for very dilute clusters,
provided that the gas phase is fuel rich.
Chiu's work, on the other hand, puts more emphasis on the
thermodynamic interaction between the inside and outside of the
cloud. Spatial gradient of all variables in the gas phase is
modeled. But the droplets are considered as point sources of vapor.
The fluid/thermo-dynamics within the droplets are ignored. The
evaporation rate of each droplet is considered to be influenced by
the "bubble" size, the near neighbors, and the far neighbors that
constitute the "ambient" conditions. The bubble size, the extend
and distribution of near neighbors are both functions of the
droplet volume concentration. An important concept defined by the
"group number" is used in the analysis. This number G (=evaporation
time/diffusion time) controls the deviation of the group
evaporation from single droplet evaporation. Important results are:
I. D2-t law does not apply. Which agrees qualitatively with
Bellan's result.
2. The spatial gradients of all variables from any given droplet
outward depend strongly on the group number. For a transient
process, this gradient is important even for very small group
numbers.
III. GROUP COMBUSTION
Mathematical studies of group combustion began withSuzuki and
Chiu. The physical picture is a spherical cloud surrounded by the
oxidizer gas with given condition far away from the cloud. This
picture is the same as that in Bellan's evaporation model, except
that the internal gradient of variables are modeled inside the
cloud. However, the droplet's own fluid/thermo-dynamics are again
neglected. All droplets are treated as fuel vapor sources only.
Important results include:
I. High group number condition dominates most practical operation
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V
conditions in a combustor.
2. As the group number increases, only a thin layer of droplets in
the cloud participates in burning. This fact may complicate the
picture of incomplete burning.
Labowsky and Rosner also studied the group combustion
phenomenon. They assumed a cubic lattice of point droplets.
Although the analysis is different, they obtained essentially the
identical group number as Chiu. The analysis of Labowsky and Rosner
however covers the entire range from incipient group combustion
(droplets at the center of a cloud start to share flame) to total
group combustion. An interesting result of their work is that a
small difference of group number can trigger the jump from
individual combustion to group combustion. This may be important
to the stability of combustion process.
IV. CONCLUSIONS
It is clear from the above modeling effort that group
evaporation/combustion impacts combustor performance. This
phenomenon can be rigorously analyzed. For group evaporation, each
of the two current approaches has its strong and weak points. They
are summarized below.
Bellan
strong points- Detailed fluid/thermo-dynamics of droplet/
environment interaction. Easy to incorporate aero-
dynamic, thermal and chemical effects rigorously.
Weak Points- No spatial gradient in the cluster of droplets.
Analysis is restricted to a single cluster. No
indication of how to extend it to a spray.
Chiu
Strong Points- Spatial gradient inside a cloud of droplets is
included. In the later work, spray evaporation is
modeled based on the earlier single cluster
concepts.
Weak Points- Droplet's own fluid/thermo-dynamics are ignored.
Extension to spray combustion from the group
evaporation is not clear.
Furthermore, neither of the two have experimental data
validation.
for
Based on their strong and weak points, it is clear that
Bellan's analysis is applicable to larger droplets (compared with
the local spray size), colder droplet temperature, hence the region
closer to the spray injector. Chiu's analysis, on the other hand,
applies to fine droplets, larger spray size, nearly boiling droplet
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temperature, hence the region further downstream from the injector.
At this point, a group combustion theory only exists for the
ideal case of a single cluster. There is no model for a true spray.
V. RECOMMENDATIONS
Recommended future analyses are summarized below.
I. Improve the existing models by combining the strong points of
both approaches.
2. Relax the assumptions made in current models, such as constant
mass and heat diffusion, negligible aerodynamic effects,
infinite evaporation kinetics, infinite reaction rate, single
step reaction, negligible radiation. Prioritizing the above
should precede the analysis if possible.
3. Begin spray combustion analysis based on the single cluster
idea. The group evaporation idea has been applied to spray
evaporation by Chiu. However, extension from single cluster
combustion to spray combustion has not been done. Combustion
adds not only heat, but also changes the distribution of
oxidizer and fuel concentrations in the spray. The picture
obtained from pure evaporation cannot be translated to spray
combustion easily.
4. Need more experimental work. First, mathematical modelers need
experimental observations to assist creating a correct physical
picture. Second, data obtained from experiments are necessary
for model verification. Carefully designed basic experiments
should go side by side with true spray combustion experiments,
because in a true spray, the simultaneous heat, mass, momentum
and chemical processes all interact together. The data obtained
represents the bulk effect. It is impossible to use it for
differentiating the degree of importance of each individual
mechanism. Prototype experiments should be done primarily for
observation. Only at the final stage, when modeling is
"completed", can prototype results be used for model
verification. Basic experiments designed for studying a few
number of mechanisms at a time will have to be done to assist
and verify the modeling at the building stage.
VI. ACKNOWLEDGEMENTS
Many thanks to C. Schafer, K. Gross, H. Trinh, D. Bai for the
many valuable discussions. Thanks to all others in the Performance
Analysis Branch for their assistance. Words cannot express the
amount of inspiration experienced from my colleagues here. Thanks
to M. Freeman and F. Six for all the many thoughtful arrangements.
It has been a wonderful program.
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A study of the current group evaporation/combustion theories

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