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IlllDt DMfl78'1

l'«D9Ii4 87-3550

Mixing in Variabie Density,

isothermai Turbuient Fiow and

impiications for Chemicaiiy

Reacting Turbuient Fiows

William M. Pitts Takashi Kashiwagi

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

May 1987

-3S50

iftl

Supported in part by:

U.S. Air Force

Office of Scientific Research

NBSIR 87-3550

MIXING IN VARIABLE DENSITY,

ISOTHERMAL TURBULENT FLOWS

AND IMPLICATIONS FOR CHEMICALLY

REACTING TURBULENT FLOWS

William M. Pitts Takashi Kashiwagi

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

May 1987

Supported in part by:

U.S. Air Force

Office of Scientific Research

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
TABLE OF CONTENTS

Page

List of Tables iii

List of Figures iv

Abstract 1

1. Introduction . 1

2. Project Objectives 2

3. Research Accomplishments 3

3.1 Diagnostic Development 3 3.1.1 Concentration Measurement Using

Rayleigh Light Scattering 4

3.1.2 Simultaneous Concentration and Velocity

Measurement 5 3.1.3 Development of a Digital Line Camera

for Concentration Measurement . 9

3.2 Characterization of Mixing and Velocity

Behavior in Axisymmetric Jets 14

3.2.1 Mixing in a Turbulent, Axisymmetric

Jet of Methane 14

3.2.2 Simultaneous Measurements of Concentration

and Velocity in a Propane Jet 15

3.2.3 Density and Reynolds Number Effects on Mixing in Axisymmetric Jets 16

4. Importance of Isothermal Studies to an Improved

Understanding of Turbulent Reacting Flows 21

4.1 Similarity of Mixing in Isothermal and Reacting

Flows 22

4.2 Lift-Off and Blow-Out of Turbulent Jet Diffusion

Flames 23

4.3 Application of Isothermal Findings to Turbulent

Mixing in Combustion Regions of Turbulent Jet Flames 28

4.4 Reynolds Number Effects in Diffusion Flames 31

5 . Summary 32

6. References 34

7. Tables 39

8. Figures 40
LIST OF TABLES

Table 1. Experimental parameters

Page

39

iii
LIST OF FIGURES

Figure 1.

Figure 2

Figure 3

Figure 4

Figure 5

Page

The experimental configuration for real-time Rayleigh

light scattering "point" measurements of concentration in

binary gas mixtures is shown schematically. The flow

system consists of a 6.35 mm diameter pipe with a sharpened edge enclosed within a 100 X 100 cm^ square

cylinder 43

The quality of the data which can be acquired utilizing

the Rayleigh light scattering technique for concentration

is demonstrated. Radial profiles of concentration (in

both mole and mass fraction terms) are plotted for a turbulent CH^ jet flowing into a slow coflow of air. The

downstream distance is z/r^ = 35 and the Reynolds number

is 3950 44

Partial time -resolved data records recorded during a simultaneous Rayleigh light scattering and hot-film

anemometry experiment are reproduced for a propane jet

(Re = 3960) flowing into a slow coflow of air. The

observation volume is located on the jet centerline at

z/r^ “ 31.5. The light scattering signals have been

calibrated and are plotted in terms of mole fraction of

propane. The raw data for the anemometer output is

plotted along with the velocity calculated utilizing the

calibrations of film response to changes in velocity and

gas composition 45

The correlation is shown for the heat transfer from a hot-wire as a function of flow velocity for nine

different gases. Experimental measurements are nondimensionalized by the use of the Nusselt number and

Reynolds number. Corrections have been included for heat

losses to the prongs of the hot-wire and thermal slip and

accommodation effects at the surface of the probe. (Kb),^

and (K^)x coefficients which are necessary to

compensate for variations in molecular properties from

gas to gas 46

The camera which has been developed for recording realtime Rayleigh light scattering intensity along a line is

shown. The top portion indicates the major components

and their configuration. The actual appearance of the

camera is shown below 47

iv
Page

Figure

Figure

Figure

Figure

Figure

Figure

6. The overall experimental configuration for real-time

measurements of concentration along a line in turbulent

flows is represented. Rayleigh light scattering is

induced along a line in the flow field by the Ar'*' ion

laser. Light scattering at 90° is recorded by the

digital line camera system consisting of the line camera

shown in figure 5, suitable interfaces, and a data

acquisition minicomputer 48

7. An example of time -resolved line measurements of propane

mole fraction across a turbulent jet of propane (Re =

3960) flowing into a coflow of air is reproduced.

Propane mole fraction is represented by a seven level

gray scale. The downstream position is 5 diameters and

the line read out rate is 830 Hz 49

8. Time-averaged radial profiles of propane mole fraction

are shown for five downstream positions in the

development region of a propane (Re = 3960) jet flowing

into a slow coflow of air. The growth of the boundary

layers on either side of the potential core with

increasing z and decrease of centerline concentration at

the end of the potential core can be clearly observed.

It is interesting to note that the data displayed

represents 164,000 individual concentration measurements

which were recorded during 1.54 s of actual acquisition

time 50

9. The apparatus for recording time -resolved shadowgraphs is

represented schematically. The light pulse generated by

the chopper has a temporal profile which is triangular in

shape and has a total duration of 310 fis 51

10. Three time -resolved shadowgraphs are shown for a SFg jet

(Re = 3950) flowing into a slow coflow of air. Three

different downstream positions recorded at different

times are represented. Note particularly the formation

of a fountain by the SFg at a downstream position of ~

37.5 r^ 52

11. Shadowgraphs are reproduced for jets of SFg (Re = 7890

and 11,860) entering slow coflows of air. For each jet

four views of the flow recorded at different times and

positions in the jet are superimposed. Note that the

fine scale turbulence becomes more pronounced with

increasing Re, but that the overall spreading rate of

the jet does not appear to be affected 53

V
Page

Figure 12 . Five sets of superimposed shadowgraphs are shown for

jets of one gas flowing into a second gas. With the

exception of the SFg flow, the Reynolds numbers are roughly the same. The effects of variations in the

global density ratio appear as changes in the

development region of the flow and modifications in the

eddy structure at downstream positions where the flows

are close to fully- developed

Figure 13. Superimposed shadowgraphs are reproduced for propane

jets at three Re entering into slow coflows of air. The

development of finer turbulent scales with increasing Re can be clearly seen. It is also evident that increasing

the Re results in a shortening of the distance required

for the development of vortical structures near the

nozzle. The overall spreading behavior of the jets is

independent of Re supporting the supposition that

entrainment is determined by large scale turbulent

structures

Figure 14. Values of (Y^, = is the centerline concentration

at z/r„ and Y„ is the mass fraction of iet fluid at the

jet exit) are plotted as a function of z/r^ for six

different jet/coflow gas combinations. The solid lines

are linear least squares fits of the results. Note the

decreasing slopes and upstream movement of the virtual

origins (z where “^0) which occur as the

jet/coflow density ratio is increased

Figure 15. Predicted values of inverse centerline mass fraction

(denoted as 1/C^ ) based on the analysis of Thring and

Newby [35] are plotted as functions of z/r^ for the six

jet/coflow gas pairs which have been experimentally

investigated. Comparison of figures 14 and 15 shows

that there is good agreement between prediction and

experiment

Figure 16. Values of centerline unmlxedness are plotted as a function of z/r^ for the six jet/coflow gas pairs

listed. Values of Yj[[/Yj^ for each jet approach a common

asymptote of « 0.23, but the flow distance required

increases dramatically as the jet/coflow density ratio

increases

Figure 17. The centerline unmlxedness values shown in figure 16 are replotted as a function of z/r^ . The collapse of the

data onto a single curve suggests that r^ is the proper

scaling parameter for correlating the growth of

unmlxedness in these variable density flows

54

55

56

57

58

59

vi
Page

Figure 18. Centerline unmixedness values for three different Re

jets of propane entering slow coflows of air are plotted

as functions of z/r^ . Flows at higher Re require longer

flow distances in order to achieve the asymptotic value

of unmixedness even though the value of the asymptote

does not change

Figure 19 . The concentration contour corresponding to that for

which the laminar flame speed of an ethylene/air mixture

is a maximum (Yj^ = 0.073) is plotted as functions of

z/r^j and r/r^^ . The virtual origin for the plot is

assumed to be at z = 0. Two representations are shown.

On the right the radial and axial axes have the same

scaling, while on the left the radial scale is expanded

by a factor of 3

Figure 20. Experimental values [47] of lift-off height (h) are plotted against jet exit velocity for turbulent jet

flames of methane, ethylene, and propane. These

measured values are compared with values (solid lines)

predicted using eq (5) and the known velocity and mixing

behaviors of the jets. The agreement is excellent. . .

Figure 21. Experimental [53] (s)rmbols) and calculated values

(lines) of blow out velocity are plotted as a function

of jet radius for axisymmetric turbulent jet flames of

five organic fuels. Calculated values are derived by

using eqs (6) and (7)

.

The agreement of the predicted

values with experiment is very good

Figure 22. Approximate radial density profiles for three

nondimens ional downstream distances are shown for

turbulent jet diffusion flames of hydrogen and a typical

organic fuel (methane) . These curves are based on measurements reported by several different authors

[63,67]

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ABSTRACT

This report summarizes the research findings of a project which has been

jointly funded by the Air Force Office of Scientific Research and the National

Bureau of Standards, The goal of the research was to improve the fundamental

understanding of chemically reacting turbulent flow. The approach which was

taken was to investigate mixing in variable density flows in order to better

understand the role of local density fluctuations (which result from chemical

heat release) on the turbulent mixing behavior. The development of new

experimental diagnostics having excellent spatial and temporal resolution is

described. These techniques have been utilized to investigate a wide range of

mixing properties in variable density flows. These results are siommarized

along with a discussion of their importance to an improved understanding of

chemically reacting flow.

1. INTRODUCTION

This report summarizes the major findings of a four-year study on

chemically reacting turbulent flow. This project was jointly funded by the

Air Force Office of Scientific Research (contract numbers ISSA-83-00012 , ISSA84-00005, ISSA-85-00012 , and lSSA-86-00008) and the National Bureau of

Standards. The period covered is October 1, 1982 to September 30, 1986.

In the following sections the overall objectives of the research project

are discussed, significant research accomplishments are listed and briefly

described, and the significance of the findings to the understanding of

chemically reacting turbulent flow is discussed.

1
2 . PROJECT OBJECTIVES

The primary objective of this research program was the improvement of the

fundamental understanding of chemically reacting turbulent flow. The most

complicated aspect of this problem is the complex coupling of fluid mechanics

and heat release which occurs for most flows in this class. Despite intense

efforts for several decades, this complicated process has remained poorly

characterized. This is unfortunate since chemically reacting turbulent flows

are of paramount importance in a wide range of combustion devices and other

chemical reactors which have military and industrial significance. An

improved understanding of the interactions of fluid d3mamics and heat release

is not only necessary to improve device efficiencies and contribute to the

conservation of dwindling fuel and feed stocks, but also to allow new types of

designs which can limit the release of undesirable pollutants.

In order to meet the above objective an approach was chosen in which the

effects of global density variations on turbulent mixing of axisymmetric jets

were investigated. This path was chosen since it was felt that one of the

major sources of coupling between heat release and fluid motion in a turbulent

flow is through the density variations introduced by chemical heat release.

In order to characterize these effects, it is first necessary to understand

the effects of global density differences.

The study of mixing in variable density, turbulent flows (or any

turbulent flow for that matter) is complicated by the wide range of spatial

and temporal scales which are of importance. These scales vary from the full

dimensions of the flow field down to the smallest scales where turbulent

dissipation occurs. It is clear that in order to obtain an improved

characterization of these processes diagnostics having high spatial and

2
temporal resolution are required. Since suitable diagnostics were not

available, an Important secondary goal for the project became the development

of new experimental techniques for the study of concentration and velocity

fluctuations In variable density flows. The Importance of large scale

turbulent structures In these flows fields necessitated the development of

multi-point diagnostics capable of high temporal and spatial resolution. A

digital line camera was designed and a prototype constructed. Preliminary

experiments utilizing the camera have been encouraging and development is

continuing.

3. RESEARCH ACCOHFLISHMENTS

In the subsection which follows, the development of new diagnostics are

described. The findings of an extensive study of mixing in variable density

turbulent flows are then summarized. Work in this laboratory, as well as

elsewhere, has demonstrated the importance of these findings to an improved

understanding of chemically reacting turbulent flow. This point is discussed

in the last subsection.

3 . 1 DIAGNOSTIC DEVELOPMENT

Throughout the course of this project there was an emphasis on the

acquisition of real-time data having high spatial resolution and accuracy.

Very few suitable experimental techniques were available and a great deal of

effort was directed toward the development of unique capabilities for the

measurement of concentration and velocity in variable density flow fields.

Significant progress has been made on the development of the necessary

diagnostic tools.

3
3.1.1 Concentration Measurement Using Rayleigh Light Scattering

The development of Rayleigh light scattering as a real-time diagnostic of

concentration fluctuations within small spatial volumes of turbulent binary

gas mixtures was completed during the very early stages of the project period.

Building on earlier work [1,2] it was demonstrated [3,4] that Rayleigh light

scattering can be utilized to measure a wide range of properties in these flow

fields

.

The Intensity of light scattered by a gas is proportional to the Rayleigh

scattering cross section. This scattering cross section is in turn related to

the index of refraction of the gas. Since the refractive indices of

individual gases vary, scattering intensity varies from gas to gas. For

mixtures, the scattering cross sections for the different gases are additive.

A measurement of scattering intensity from a binary gas mixture, following

calibration in the pure components, allows the concentrations of the two gases

in the observation volume to be determined.

Figure 1 shows the experimental apparatus which was developed for

Rayleigh light scattering measurements. In order to test this system, realtime concentration data were recorded in the turbulent flow field formed by an

axisymmetric jet of methane (Re = 4130) flowing into a slow coflow of air. It

was demonstrated [3,4] that this system is capable of recording real-time

measurements of methane concentration at data rates as high as 10 kHz for

observation volumes as small as 0.0003 mm^ . The accuracy of individual

measurements was estimated to be » 1.9% at the highest data rate.

From the resulting real-time data records such flow properties as the

time -averaged concentration, root mean square (RMS) in the concentration

fluctuations, and the concentration skewness and kurtosis were calculated.

4
Figure 2 shows the behavior of the time -averaged methane concentration in the

radial direction for a downstream distance of 30 r^^ . By using fast Fourier

transform analysis it was also possible to calculate the frequency spectrum

and correlation functions for the concentration fluctuations.

The availability of real-time data allowed a determination of whether or

not jet fluid was present in the imaged volume during the observation time.

In this manner, the intermittency function (based on the presence or absence

of jet fluid) could be determined and then utilized to provide conditionallysampled measurements for the properties described above.

Even though the results [3,4] of this work were of a preliminary nature,

they represented the most extensive and complete set of data for a variable

density flow available in the literature at the time of their publication.

Where comparisons were possible, results [3,4] were found to be in excellent

agreement with measurements reported in the literature.

3.1.2 Simultaneous Concentration and Velocity Measurement

The development of the Rayleigh light scattering technique provided a

powerful means for monitoring concentration behavior in a turbulent flow field

of two gases. However, in order to more fully characterize turbulent behavior

in variable density flows, measurements for velocity are also required. Of

particular importance is the capability for simultaneous measurements of

concentration and velocity which allows such parameters as the cross

correlation coefficient (Rye) velocity and concentration to be calculated.

Such correlations are very important since they often appear in models which

attempt to provide closure for the Navier- Stokes equations and in treatments

which utilize Favre averaging [5]. Such measurements have been very difficult

5
to make in the past and very few comparisons between theoretical estimates and

experimental findings are available.

Either of two techniques, hot-wire anemometry (HWA) and laser Doppler

velocimetry (LDV) , are usually employed for real-time velocity measurement.

LDV requires seeding of the flow with particles. This results in a strong Mie

scattering which completely obscures the Rayleigh light scattering signal

necessary for concentration measurement. Even though experiments have

demonstrated that simultaneous measurements of concentration and velocity are

possible in lightly seeded flows [6]

,

it has not been possible to make realtime measurements. For this reason, HWA was chosen as the velocity

diagnostic.

HWA in variable density flows is complicated by the variations in

molecular thermal conductivity which occur as the composition of the gases

around the probe changes. As a result, the response of the HWA is not only

sensitive to velocity changes, but also to concentration variations. This

sensitivity has been used as the basis for probes designed to measure

concentration in binary gas mixtures [7]. By combining two probes having

different heat transfer properties it has also been possible to make

simultaneous measurements of concentration and velocity [8,9]. However, these

measurements require extensive calibrations and data manipulation and have not

come into widespread or routine use.

By combining the HWA and Rayleigh light scattering techniques it is

possible to mitigate some of the limitations of HWA for velocity measurements

in variable density flow fields consisting of two gases. The Rayleigh light

scattering technique provides real-time concentration measurements which can

be utilized to correct the response of the HWA for variations in gas

6
composition once the velocity probe has been calibrated in a series of

mixtures. The necessary calibrations are considerably simpler than those

required when two hot-wires are employed. Limitations of such an approach

include the need for an obtrusive probe and the necessity of physically

separating the observation volume for the Rayleigh light scattering and the

position of the hot-wire (to avoid scattering).

Experimental work [10] has shown that the limitations mentioned above are

not serious and that the combination of Rayleigh light scattering and HWA can

be utilized for accurate, real-time measurement of concentration and velocity

in variable density flows. Figure 3 shows an example of the real-time

behavior of concentration and velocity for a turbulent jet of propane flowing

into a coflow of air. Such data records were utilized to calculate timeaverages , rms values, and cross-correlation values for the velocity and

concentration fluctuations of propane and methane jets. In all cases the

experimental measurements were in excellent agreement [10] with the limited

data available in the literature.

The measurements reported in [10] are for a single hot-wire (or hot- film)

aligned so that the probe is sensitive to velocity in the axial direction of

the jet flows. It is possible to also utilize an "X-probe" consisting of two

wires oriented at 45° in order to measure both the axial and radial components

of velocity. During the past year the response of such a probe to variable

density flows as well as the effects of flow direction have been extensively

investigated. In the near future this X-probe will be combined with the

Rayleigh light scattering system in order to form an experimental system which

can make real-time measurements of concentration and two components of

velocity in variable density flow fields. This system will be capable of

7
characterizing variable density turbulent flow fields to a degree which has

heretofore been impossible.

As part of the calibration work necessary to employ these HWA probes,

various correlations available in the literature for the heat loss from a

cylinder were considered. It was discovered that none of these correlations

were successful in correlating an extensive series of calibrations performed

in ten different gases [11,12]. The most widely quoted correlation for

different gases utilized a correction based on the Prandtl number (Pr) to

correct for variations in molecular properties [13-15] . This correlation was

found to be unsatisfactory for the gases investigated during this study.

Extensive analysis [11,12] of the data showed that it is necessary to consider

the temperature dependence of the molecular properties in order to obtain

accurate correlations. Figure 4 is a plot of the heat transfer behavior (in

terms of the nondimens ional Nusselt number) as a function of flow velocity (in

terms of the nondimens ional Reynolds number based on the probe diameter) . The

correlation of the results for the nine gases shown is excellent.

Other heat transfer characteristics such as thermal slip and surface

accommodation were also investigated during the course of this study [11,12].

In particular, it was shown that the heat transfer from a cylinder to helium

is strongly influenced by surface accommodation. Using theories previously

developed for treating this process [16] it was possible to correct the

measurements for this effect and obtain an accurate correlation of the heat

transfer behavior of helium with the results for other gases. The helium data

included in figure 4 have been analyzed in this manner. The measurements also

yielded an vastly improved understanding of the dependence of the heat

8
transfer process on Re and transitions in flow behavior which occur as the Re

is varied.

The manuscripts which resulted from this work [10,11,12] are not only

significant for their importance to researchers who wish to utilize HWA in

different gases, but are also important for the much wider field of heat

transfer. The results considerably modify current concepts concerning the

role of molecular properties in heat transfer behavior.

Extensive measurements [17] have also been made for mixtures of gases.

For these mixtures the procedure described above does not provide accurate

correlations for the heat transfer measurements. Systematic variations are

observed with the mole fractions of the components which have tentatively been

ascribed to the effects of thermal diffusion on the heat transfer behavior.

If thermal diffusion is indeed the source of the variations, it is required

that its effects on heat transfer be roughly ten times larger than reported in

the literature. Dr. Howard Baum is currently developing a theory [17] for

this process which is designed to allow a test of this hypothesis.

3.1.3 Development of a Digital Line Camera for Concentration Measurement

The flow diagnostic techniques described above are designed to allow

accurate point measurements of velocity and concentration. Measurements

utilizing these techniques as well as findings in other laboratories have

suggested the importance of large scale structures for mixing in turbulent

flows such as axisymmetric jets. The availability of real-time point

measurements allows some characterization of these structures through the

determination of intermittency functions and conditional sampling. However,

such measurements provide very limited information about individual structures

9
and their role in the entrainment of surrounding gases. Clearly, simultaneous

measurements at many different points in space would provide much more

information concerning the structure and role of these large scale structures

in the turbulent mixing process

.

Recently there has been a great deal of research activity (e.g., [18-23])

on the development of optical diagnostics which are capable of nonobtrusive

,

multi-point measurements in flow fields. Such imaging experiments have been

reported along lines [18], in planes [19-21], and in three dimensions [23]. A

wide range of optical processes such as Rayleigh [19,23], Raman [20], Mie

scattering [19] and fluorescence [18,21,22] have been employed. Even though

there are exceptions, most of these experiments are characterized by the need

for image intensification (due to the relative insensitivity of the solidstate detectors which are usually employed) and the use of high-powered lasers

which provide sufficient signal levels to allow the optical measurements, but

which limit the experiments to low repetition rates.

Due to the ability of imaging experiments to provide a more complete

characterization of large scale structures in turbulent flows, it was clear

that a system utilizing Rayleigh light scattering for quantitative mass

fraction measurement would be very useful. A short proposal was prepared and

the necessary funding for the development of a digital line camera system was

provided internally by the National Bureau of Standards. Note that a similar

unintensified system has been utilized for concentration measurements in a

water jet [22]

.

A set of design goals were developed for the camera. The most important

of these are listed here:

1. A spatial resolution of 400 fxm along the line.

10
2 . Line readout rates greater than a kHz

.

3. Concentration measurements having an absolute accuracy of a few percent.

4. Utilization of an existing CW Ar ion laser and data

acquisition system.

5. Use of commercially-available components.

The first three of these goals were chosen to be consistent with the

capabilities of our experimental system for single point measurements of

concentration. The last two were required to minimize the cost of the system

and simplify its design and construction. These criteria were found to be in

competition with one another and it was necessary to make compromises in the

design of the camera.

An analysis [24] of the intensity of scattered light from the Ar'*' ion

laser beam and the sensitivity of commercially available solid-state line

detectors indicated that image intensification would be required in order for

the line camera to operate at the required data rates. This requirement

turned out to be the most difficult technical challenge of the camera design.

There are two major types of image intensifiers available commercially.

These are known as generation I (gen I) and generation II (gen II)

.

Gen I

tubes consist of a photocathode, accelerating and focusing electronics for

electrons emitted by the photocathode, and a phosphor screen. The optical

gain of the device results from the fact that a single accelerated electron

striking the phosphor screen results in the production of many photons.

Gen II tubes are similar to gen I tubes with the exception that a

microchannel plate (MCP) is inserted between the photocathode and the phosphor

screen. The MCP is an active device which can produce electron gains of

11
10^-10^. Since the channels which form the MCP are aligned, any electron

"image" present on the input face is maintained at the other end of the MCP.

Electrons emitted by the photocathode of a gen II image intensifier are

focused (either by proximity or electrically) onto the MCP and the resulting

amplified electron image from the MCP is focused onto a photocathode. Since

the MCP provides a very high gain, a single gen II image intensifier has a

much higher light gain than a single gen I tube. It is necessary to cascade

two or three gen I tubes in order to obtain intensification comparable to a

single gen II tube.

In most flow imaging experiments reported thus far gen II tubes have been

utilized. However we discovered [24] that for real-time imaging there is a

serious problem due to the maximum light output which can be generated by this

type of image intensifier. This limitation results from the limited output

current of the individual channels of the MCP. Calculations indicated that

the maximum brightness which can be generated by a gen II tube is comparable

to that available from the Rayleigh light scattering experiment and is not

sufficient for real-time detection using commercial, solid-state line

detectors. Since only moderate light gains were necessary, a gen I tube was

chosen as the image intensifier. These tubes can operate at much higher

current levels than the second generation devices and can therefore produce

more intense light outputs.

Measurements at data rates greater than a kHz also require consideration

of the response time of the phosphor screen used in the intensifier. The P-20

phosphor employed for standard tubes has a long-lived tail in its temporal

decay and for this reason is unsuitable for this application. A P-47 phosphor

screen was chosen instead. This screen has a submicrosecond lifetime, but it

12
is less efficient than P-20 and the overall gain of a single stage is

significantly reduced. The final selection for the image Intensifier

consisted of two stages of gen I tubes equipped with P-47 phosphor screens.

The detector chosen for the camera was a Reticon RL128S* line detector

which consists of 128 pixels on 25 /zm centers. A 4:1 reduction fiber optic

taper was utilized to couple the detector and the image intensifier. The

camera was completed by the addition of a f/1.9 1:1 focusing lens for imaging

the scattered light onto the image intensifier. With this arrangement each

pixel corresponds to a 100 /zm length of the image so that the entire line

image covers 12.8 mm. Figure 5 shows a schematic for the prototype camera.

The line detector is equipped with electronics which generate voltages

that are proportional to the light detected during the Integration period on

an individual pixel. The voltages for the 128 pixels appear sequentially on

the output. These voltages are digitized and stored in the memory of a

minicomputer. Since the maximum data rate for the acquisition system used is

333 kHz, the maximum line read-out rate is limited to 2.2 kHz. Figure 6 shows

the overall system for line measurements of concentration including the

digital line camera, the flow system, and the Ar'*’ ion laser.

In order to test the system, line measurements of propane mole fraction

for a propane jet flowing into a slow coflow of air have been recorded.

Figure 7 shows an example of the concentration behavior across the radial

profile of the jet at a downstream distance of 5 jet diameters and a line

read-out rate of 837 Hz. The total data acquisition time was ~ 300 ms. Even

* Certain commercial equipment, instruments, or materials are identified in

this paper in order to adequately specify the experimental procedure. Such

identification does not imply recommendation or endorsement by the National

Bureau of Standards nor does it imply the instruments or equipment are necessarily the best available for the purpose.

13
though the time resolution is not sufficient to fully resolve small details,

the importance of large scale structures is clear. The results of such

measurements can be time -averaged to yield the contour of the radial profile.

Figure 8 shows the results for five downstream positions. The growth and

spread of the turbulent boundary layers is evident.

While the performance of the initial camera prototype has been very

encouraging, it has not been possible to reach the full time resolution

potential of the camera due to limitations in the gain of the image

intensifier. A new, three-stage tube has been ordered and will be installed

shortly. This gen I image intensifier will provide a higher gain due to the

additional stage of amplification. It is also equipped with P-46 phosphor

screens which have the same short lifetime properties of P-47, but which have

outputs at longer wavelengths (green) . Green light is more efficiently

transmitted by the fiber optic taper and detected more efficiently by the line

scanner. This modification should therefore increase the sensitivity of the

tube significantly.

3.2 CHARACTERIZATION OF MIXING AND VELOCITY BEHAVIOR IN AXISYMMETRIC JETS

3.2.1 Mixing in a Turbulent, Axisymmetric Jet of Methane

As part of the development of Rayleigh light scattering as a diagnostic

for concentration, extensive measurements of such flow properties as timeaveraged concentration, unmixedness, skewness, kurtosis, concentration

fluctuation spectra, and correlation functions were made [3,4]. The existence

of time -resolved data records also allowed the intermittency functions for the

flow field to be determined and from these it was possible to generate

conditionally- averaged measurements of these flow properties.

14
Data were recorded at various positions along the jet centerline and

across the radial profile of the jet for one downstream position (z/r^ = 35).

In all cases where literature sources were available for comparison there was

excellent agreement. The availability of real-time data allowed the existence

of large-scale ramp-like structures in the intermittent region of the flow

field to be identified. Such structures are believed [25,26] to be the

primary mechanism by which jet entrainment occurs and for this reason their

characterization is crucial.

Even though the findings of the study [3,4] were of a preliminary nature,

they were chosen for comparison purposes with conserved scalar measurements in

a hydrogen jet flame [27,28]. These authors felt the measurements were the

most complete and accurate available at the time. A remarkable similarity was

found between mixing in the isothermal and combusting flows. The significance

of this finding is discussed below.

3.2.2 Simultaneous Measurements of Concentration and Velocity

in a Propane Jet

As a test of the combined hot-probe anemometry and Rayleigh light

scattering diagnostic, real-time concentration and velocity data were recorded

in jet flows of propane entering a slow coflow of air [10]

.

Preliminary

measurements which were recorded are significant due to the limited number of

such measurements which have been reported in the literature for variable

density flows. For instance, time-averaged measurements of centerline

velocity showed that the data could be fit in the form

Uo/5o - K„(z-z„)/r, (1)

15
where is the effective radius defined as (Po/p®

^ ^

.

A least squares fit

of the results gave = 0.082 which is close to the value of 0.081

recommended by both List [29] and Chen and Rodi [30]

.

Values of the

correlation coefficients for velocity and concentration were also calculated

as a function of downstream position. Literature comparisons were very scare,

but measurements by Antonia et al. [31], Chevray and Tutu [32], and Catalano

et al. [33] showed that values of measured in this study were consistent

with previous measurements. The findings suggest that R^^. grows to an

as3onptotic value of » 0.39 on the jet centerline in this variable density

flow.

3.2.3 Density and Reynolds Nximber Effects on Mixing

in Axisymmetric Jets

An extensive study [34] of the effects of density and Reynolds number

variations on mixing in turbulent axisymmetric jets was performed.

Qualitative information concerning the flows was obtained using time-resolved

shadowgraphs while Rayleigh light scattering was utilized to investigate

quantitatively the centerline mixing behavior. Table 1 lists the gas pairs

investigated in this study, the ratio of jet to coflow densities. Re based on

the jet diameter, and whether or not shadowgraph and Rayleigh data were taken.

Figure 9 shows the experimental arrangement used to record shadowgraphs

of the variable density jet flows. The diameter of the shadowgraphs is 76 mm

and the light pulse has a measured FWHM of 165 /xs with a total duration of 310

/xs. It must be remembered that shadowgraphs provide an integrated view of the

flow field and that the signal is proportional to the second derivative of the

index of refraction variations which occur along the path of the light beam.

16
I

For these reasons, extreme caution must be utilized in drawing conclusions

from such photographs. However, with this in mind, it is possible to

characterize some of the effects of density and Reynolds number variations on

jet mixing behavior from the series of shadowgraphs which have been recorded.

Figure 10 provides a dramatic example of the effects of density

differences on the mixing behavior of a turbulent jet. Shadowgraph are shown

for a jet flow of sulfur hexafluoride into air with Re = 3950. The initial

jet density is 5.1 times higher than that of the surrounding air. As is

clearly shown by the shadowgraph covering the downstream region from z/r^^ = 25

to 45 , the Initial momentum of the jet is not high enough to overcome the

negative buoyancy (the jet is orientated vertically) of the flow and the jet

forms a fountain with jet fluid falling back through the surrounding coflow.

Interestingly, as can be seen in figure 11, this effect disappears for Re of

7890 and 11860.

Shadowgraphs for flows covering jet to coflow density ratios of 0.14 to

5.1 are shown in figure 12. The following conclusions have been drawn

concerning the effects of density and Re differences on mixing in these flows

from these and other shadowgraphs

.

1. The initial density ratio effects the shape of the vortices at

downstream positions in the flow field. Increasing density ratios

result in lengthening of vortices in the axial direction.

2. Changes in the density ratio effect the initial development of

turbulence in the jets. For smaller values of p^/Pa> the flow

distance required for initial growth of vortices is shorter.

Figure 13 shows shadowgraphs recorded for jet flows of propane into air

at three different Re. From these photographs as well as those shown in

figure 11, the general effects of changes in Re can be summarized as

1. As the Re is increased the turbulent structures in the flow field

extend to smaller scales.

17
2. Increasing the Re has very little effect on the angle of spread for

a given gas pair.

3. Turbulent structures develop at shorter flow distances as the Re is

increased.

Even though the shadowgraphs provided qualitative information concerning

mixing in variable density turbulent flows, very little quantitative

information could be obtained. Rayleigh light scattering was utilized to

perform quantitative measurements of fluid concentration behavior along the

centerlines of the jets.

Time -averaged concentration measurements provide an excellent example of

how significantly density differences can modify mixing. Figure 14 shows

experimental values of inverse time -averaged mass fraction (1/Yj^) plotted as a

function of nondimensionalized downstream position for different jets having a

wide range of density ratio. The data fall on straight lines having slopes

which decrease with increasing density ratio and virtual origins (value of z

where l/Y^jj extrapolates to zero) which move upstream as the density ratio

increases

.

In the early 1950 's Thring and Newby [35] suggested that the centerline

mixing behavior of axisymmetric turbulent jets could be correlated using an

expression which can be written as

l/\ - K,z/r. + (p,/p„-l)K' (2)

where r^ is the effective radius defined earlier and and K' are constants

which are determined by radial integrations of velocity and concentration

across the flow field. This equation can be derived utilizing conservation

equations and assuming self -similarity . It is strictly valid only for

downstream positions where ~ Po •

18
The predicted behavior of plots of 1/Y„ versus z/r^ using eq (2) are

shown in figure 15 for K^. = 0.114 and K' =0.5. Comparison with the

experimental results in figure 14 shows that there is excellent agreement.

The dependence of the slopes of the plots on p^/pa, has been documented in the

literature previously (e.g., [36,37]), but to our knowledge, this is the first

time that the predicted dependence of 7.^ on the this parameter has been

confirmed

.

Similar data were recorded for axisymmetric jets in which the Reynolds

number was varied. These measurements showed that the principal effect of

increasing the Re was to shift the virtual origin, z^ , downstream. Slopes of

plots of 1/Yjjj versus z/r^^ were independent of Re. This suggests that the

centerline mixing behavior in these flow fields is due primarily to large

scale turbulent structures which should be independent of Re (i.e., inviscid

flow)

.

The availability of time -resolved measurements allowed the behavior of

centerline unmixedness (defined as the RMS of the concentration fluctuations,

, divided by Y^^^ ) to be determined as a function of Po/p„ and Re. Figure 16

is a plot of YJ^/Yjjj versus z/r^^ for six variable density flows. It is clear

that in each case unmixedness values are approaching a common asymptote of ~

0.23, but that the flow distance required to attain this value is strongly

dependent on p^/p^ with higher ratio flows requiring longer flow distances.

There are very few measurements or theoretical predictions of unmixedness in

variable density flows reported in the literature. This study was the first

to provide data for a wide range of p^/PcaIn order to gain some understanding of the role of density ratio on the

flow distance required to attain the unmixedness asymptote, the experimental

19
values of were replotted as a function of z/r^ as shown In figure 17.

It is clear that plotting the data in this manner results in a collapse of the

growth curves for unmixedness and that r^ serves as a scaling parameter for

the growth. This conclusion is surprising in that the unmixedness development

is occurring in a flow region where the condition is not met and the

development which leads to the definition of r^ is not strictly valid. At the

same time it does suggest that r^ is a true scaling parameter which not only

results in a collapse of time -averaged data, but also scales the development

of turbulent structure in the flow field.

Similar measurements in CgHg/air (see fig. 18) and SFg/air flows have

shown that the asymptotic value of unmixedness is independent of Re, but that

the flow distance required to attain the asymptote increases as the Re is

increased. The longer flow distances required for turbulence growth in the

higher Re flows results in the downstream shifts of the virtual origins

observed for plots of l/Y^j as functions of z/r^^ . The observed Re dependence

of the flow distance required to attain fully- developed flow was surprising

since fully- developed turbulent behavior is generally associated with high Re.

The independence of the asymptotic value of Y^/Y^j on Re once again highlights

the importance of large scale structures in turbulent mixing behavior.

It was hypothesized [34] that the longer flow distances required for

fully- developed flow at higher Re is connected with development of smaller

scale vortices in the flow fields at higher Re. If a "pseudo -equilibrium”

exists between the different vortical scales, a longer flow distance would be

required for the entire turbulent structure to come into equilibrium at the

higher Re. More sophisticated experiments will be necessary to test this

hypothesis. Whether or not this h3rpothesis is correct, a more complete

20
characterization of the growth of centerline unmixedness in these flows is

required so that parameters which control the growth of turbulence in flow

fields can be identified.

The time records were also used to calculate skewness (third moment) and

kurtosis values (fourth moment) for concentration fluctuations. Distinct

effects of density ratio were observed on the centerline behavior of these

parameters, but in the absence of theoretical guidance it was not possible to

relate these variations to physical modifications of the mixing behavior.

The manuscript which was written to describe these results [34] contains

extensive comparison with previous literature findings. Generally,

quantitative agreement is excellent. Possible sources of disagreement, such

as the effects of buoyancy and the use of a coflow, were also analyzed and

were generally found to be minor perturbations. It was concluded that the

results are indicative of mixing behavior in free axisymmetric jets. The use

of a wide range of density ratios and Re resulted in the identification of

dependencies in the mixing behavior which had not been reported previously.

4. IMPORTANCE OF ISOTHERMAL STUDIES TO AN IMPROVED

UNDERSTANDING OF TURBULENT REACTING FLOWS

The significance of findings from the isothermal flow studies for

improving the understanding of the more complicated case of chemically

reacting flows was considered where appropriate. These analyses resulted in a

more clearly defined perception of the role of density variations (both global

and local) in chemically reacting turbulent flows. Consideration of mixing

behavior in the isothermal mixing regions of lifted and blown out turbulent

jet diffusion flames resulted in new correlation procedures for describing

these stabilization characteristics and suggested new physical models to

21
understand the behaviors. The role of local Re variations on mixing in

chemically reacting turbulent flows has been assessed. These points are

discussed in this section.

4.1 Similarity of Mixing in Isothermal and Reacting Flows

Numerical data from the original Rayleigh light scattering study of

methane [3,4] were provided to investigators at General Electric Corporate

Research and Development Center for comparison with extensive experimental

measurements recorded for a turbulent hydrogen jet flames. Drake et al.

[27,28] found that radial profiles of the first four moments of concentration

fluctuations (time -average , RMS , skewness , and kurtosis) for the isothermal

and reacting flow (in terms of the conserved scalar concentration, f [38])

were very similar. Such agreement suggests that heat release and combustion

have very little effect on the probability distribution functions (PDF) of

scalar mixing in turbulent reacting flows. This conclusion is extremely

important because it implies that the results of isothermal mixing studies can

be applied directly to chemically reacting turbulent flows and thus provides

additional justification for the approach taken in our own study. Theorists

have long used isothermal mixing results as the basis for models of chemically

reacting turbulent flow [39],

Drake et al. [27,28] also utilized the isothermal results of our earlier

study along with their own findings to test a parametric expression developed

by Effelsberg and Peters [40] which divided the conserved scalar PDF into

nonturbulent , fully turbulent, and superlayer parts. These authors concluded

that the measurements were not consistent with this model since the results

required that more than 50% of the PDF be due to superlayer contributions . An

22
alternate interpretation was offered in which the "apparent” superlayer was

attributed to the presence of large scale "ramp- like" structures in the flow

field. Such structures have been observed in time records recorded in our

earlier work [3,4] and by other researchers (e.g,, [31,41,42]).

4.2 Lift-off and Blow-Out of Turbulent Jet Diffusion Flames

There are certain properties of combusting jets for which isothermal

findings are directly applicable. In particular, lift-off and blow out of

turbulent jet diffusion flames must depend on the concentration and velocity

behavior of the turbulent flow upstream of the region where combustion or blow

out occurs. The results of our isothermal studies as well as other findings

available in the literature have been utilized [54] to develop a procedure

which is capable of accurately predicting experimental lift-off heights as a

function of jet exit velocity and blow out velocities as a function of jet

diameter for turbulent jet diffusion flames of many different fuels.

Interestingly, only time-averaged properties have been considered and it has

not been necessary to consider the actual turbulent behavior of the flow.

This is significant since most theoretical treatments either assume flame

stability is due to an equilibrium of flow velocities and turbulent flame

speeds (which depend on small scale turbulent structure) [43-47] or to flame

extinction processes in small scale structures [48-51].

A radically different explanation for flame stability has been suggested

by Broadwell et al . [52]. These researchers have argued that flame stability

is determined by the reentrainment of hot combustion gases (expelled by the

passage of earlier large scale structures) by large scale structures in the

flow field. These gases are rapidly mixed with the jet gases and if the

23
turbulent mixing time, is longer than the chemical ignition time, t^. , of

the fuel/air mixture in the jet, the structure will be ignited and the

combustion stabilized. When the mixing time becomes shorter than the chemical

reaction time (r^. > combustion can no longer be sustained.

The impetus for our investigation of flame stability mechanism was the

extensive experimental investigations of lift-off [47] and blow out [53] of

turbulent jet flames by Kalghatgi. He found that his results for lift-off

heights as a function of velocity for different fuels were well correlated by

an expression which can be approximated as

h - 0„(U„/(S„)S.,)^„(p./p.)l =, (3)

where is a constant, is the maximum laminar flame speed for the

fuel and air, and the density term is an approximation for a more complicated

expression. The form of this equation was based on dimensional analysis. The

inclusion of in the expression reflects the important role small scale

turbulent structures are believed to play in this stability behavior.

Blow out velocities as a function of jet diameter were found to have a

similar dependence on density and [53] . This correlation can be written as

where is a constant and is the mass fraction of fuel in a stoichiometric

mixture with air.

Attempts to predict the exponent of 1.5 for the density ratios in eqs (3)

and (4) in terms of the known concentration and velocity fields of isothermal,

variable density turbulent jets were not successful. On the other hand,

correlations in which the term ^ were omitted from eqs (3) and (4)

24
were found to accurately correlate Kalghatgi's experimental findings. The

simplicity of these correlations suggested that the time-averaged properties

of the flow field might be employed to predict lift-off heights and blow out

velocities. Subsequent calculations [54] have shown this to be the case.

The first step in the procedure is to calculate the time -averaged mass

fraction contour in the flow field along which the laminar flame speed is a

maximum. Both theory [43-45] and measurements [44,45,55] in turbulent jet

flames have shown that the most probable location for the shortest distance

between the nozzle and the instantaneous flame position is along this contour.

Figure 19 shows the form of this contour for an ethylene jet. In order to

make these calculations, the centerline mixing behavior is taken from our

variable density study and the radial behavior is based on expressions given

in Chen and Rodi's book [30]. Shifts in virtual origin with density ratio and

Re have been ignored.

An empirical procedure was then utilized to derive an expression for the

local velocity (Uj^ ) along the contour which results in the proper dependencies

[47] of lift-off heights on jet diameter (nearly independent) and exit

velocity (linearly dependent). The resulting expression has the form

- Ci'z2(S„)J.,Y|/r. (5)

where is the mass fraction of fuel necessary for The

corresponding velocity at the jet exit is then calculated utilizing the known

axial and radial dependencies for velocity [30]. C^' is a constant parameter

which has the units of an inverse kinematic viscosity. In order to determine

C^' a single experimental measurement of h for ethylene from the turbulent jet

25
flame data of Kalghatgl [47] was utilized. A value of C^' - 0.0484 s/cm^

resulted.

This calculational procedure was utilized to calculate values of the

lift-off height as a function of exit velocity for different fuels. Figure 20

reproduces the results of the calculation [54] for fuel jets of methane,

ethylene, and propane and compares the predictions with the experimental

results of Kalghatgi [47]. The agreement is excellent.

The success of the calculational procedure in reproducing the

experimental findings for lift-off heights of turbulent jet diffusion flames

suggests that small scale vortices may not be important in flame stability

since only global mixing properties which are independent of Re have been

utilized. The role of small scale structures cannot be total discounted since

it is possible that their properties may be correlated with the variables

included in eq (5) in some manner. The fluctuation properties of the

concentration and velocity in the radial positions where these calculations

have been made are not well enough characterized to test this

.

The form of eq (5) is consistent with the model for turbulent combustion

suggested by Broadwell et al. [52] in which flame stability is determined by

the behavior of large scale turbulent structures. However, it should be noted

that the authors reported, but did not test, an expression for lift-off

heights which is not consistent with the experimental observations of

Kalghatgl [47]

.

If their model is correct, eq. (5) suggests that the chemical

reaction time is inversely proportional to and that the turbulent

mixing time is proportional to z^/r^

.

The latter proportionality suggests

that two lengths scales are necessary to characterize the mixing time; one

which increases as z/r^ and a second which scales as z. It has already been

26
shown that z/r^ is the proper nondimens ionalizing length scale for centerline

mixing. Previous studies [30,36] have concluded that the radial spreading

rate as a function of downstream distance is linearly dependent on z and

Independent of density ratio. It is therefore expected that will scale

with the product of z and z/r^

.

The appearance of the in eq (5) is at first perplexing. Calculations

have shown that it serves to make the calculated values of independent of

. This is consistent with the absence of this parameter in the correlation

shown in figure 20 and suggests that may be independent of radial position

in these flows

.

It was possible to extend this calculatlonal procedure to the prediction

of blow out velocities [54]. It is known [44,45,53] that blow out occurs in

these flames well before the contour represented in figure 19 reaches the jet

centerline. This suggests that flame extinction occurs when

U, > Uj, , (6)

where Uj^ is a well-defined velocity. In order to reproduce the experimental

finding of Kalghatgi [53] for (Uq)jj as functions of jet radius and fuel it is

necessary that

Ub - C^(St)L:.ro- O)

A value of = 1.5 s/cxc? was determined using one of Kalghtgi's experimental

measurements [53]. Figure 21 compares predicted blow out behaviors (solid

lines) with Kalghatgi 's experimental results for five fuels. The agreement is

outstanding

.

27
Broadwell et al. [52] showed that their hypothesis concerning the role of

large scale structures in the stability of turbulent jet diffusion flames led

to an expression which also accurately correlated Kalghatgi's [53] blow out

data. Equation (7) is very similar to their development with the exception

that it is based on the local flow velocity while Broadwell et al. [52] found

it necessary to assume that flame extinction occurred when the centerline mass

fraction fell to some constant percentage of the value for stoichiometric

burning. The similarity of the two expressions lends support to their flame

stability theory.

4.3 Application of Isothermal Findings to Turbulent Mixing in

Combusting Regions of Turbulent Jet Flames

The similarity of the isothermal measurements of turbulent structure

[3,4] and those made in a hydrogen/air diffusion flame [27,28] suggests that

the combustion process may not significantly alter turbulent mixing behavior.

If this is the case, it is expected that the principal effect of combustion on

turbulent mixing arises from the density variations induced by heat release.

In an earlier manuscript [54] the role of these density fluctuations on

mixing in turbulent jet flames has been discussed. Several particular cases

were identified for which these density variations might be expected to

approximate those in isothermal flows having global density variations. As

summarized here, experimental findings suggest this approach may have some

validity in certain downstream positions of combusting flow fields.

Figure 22 is a representation of radial density profiles in turbulent jet

flames of hydrogen and a typical hydrocarbon (methane) . One of the

interesting aspects of the hydrogen jet flame is that the heated products and

the cold fuel have very nearly the same densities. In the near field of the

28
jet, combustion occurs primarily in the outer regions of the flow so that the

density is constant over nearly the full radial range of the turbulent flow.

For this reason, the mixing behavior of the flow near the jet exit should be

very similar to that observed for a constant density, isothermal flow.

Experimental evidence supporting or contradicting this conclusion was not

available in the literature.

Similar arguments lead to a different conclusion for the near- field

mixing behavior in hydrocarbon turbulent jet diffusion flames. Since the

heated combustion products are much less dense than the cold fuel, in the near

field the flow consists of a dense inner turbulent jet flowing into

considerably less dense surroundings (see fig. 22). This view is supported by

shadowgraphs recorded by Wohl et al. [56] and by the recent schlieren study of

Savas and Gollahalli [57] which show a more dense turbulent fuel jet entering

an apparently laminar, less dense surroundings.

Several groups (e.g., [58] and [59]) have recorded concentration

measurements in the near fields of both isothermal and combusting jets of

hydrocarbon fuel gases. In general, the flame jets have longer potential

cores, develop turbulent behavior further downstream, and have centerline fuel

mass fractions which fall off less rapidly with downstream distance than in

the corresponding isothermal flows. Based on the isothermal findings

discussed above, these behaviors are exactly those expected for a dense jet

flowing into less dense surroundings.

As the combusting jet move further downstream the most likely position

for combustion moves closer to the centerline and the radial density profiles

are modified. In the case of the hydrogen flame the result is that the

central part of radial profile has a density which remains nearly constant.

29
but in the outer regions of the flow there is a rapid increase in density (see

fig. 22, z/r^ = 80). The condition necessary for the application of the

isothermal findings (namely, "p^ ~ p^) is not fulfilled and it is not expected

that the centerline decay will obey a relation having the form of eq (2)

.

Detailed measurements of conseirved scalar concentrations in turbulent jet

flames of hydrogen are available [60,61]. In general, the authors have not

analyzed their data in the form suggested by eq (2)

,

but it appears that the

centerline decay of conserved hydrogen concentration does not have a

hyperbolic fall off with increasing downstream distance.

In the case of hydrocarbon fuels Hans Kremer (as described by Ebrahimi

and Kleine [59] and Lenze and Gunther [62]) has developed an analysis

procedure similar to that described here to predict the fall off of the

centerline conserved scalar concentration. Ebrahimi and Kleine [59] have

shown that this analysis gives accurate predictions of f along the jet

centerline for 20 < z/r^ < 100 when p„^ was assumed to be that for heated

combustion gases (T^ = 1600 K, p^/Pa, = 4.9).

For larger downstream distances ^ was found to fall off more quickly than

predicted. The authors attributed this to a buoyancy effect (i.e., an

increase in jet momentum). However, it is possible that the analysis fails

due to changes in the radial density profiles which invalidate the conditions

for which eq (2) was derived. As figure 22 shows, the radial density profiles

for the hydrocarbon flame are greatly modified at large downstream distances

(e.g., z/r^ = 160). Such radial profiles cannot be considered as that of

either a heavy jet into light surroundings or for a constant density jet. In

order to predict the centerline behavior of f in this flow region it may be

necessary to have a better understanding of the effects of local density

30
variations on turbulent mixing. Further experimentation is required to

clarify the roles buoyancy- induced momentum and radial density profiles on

turbulent mixing.

For regions of turbulent jet flames where direct comparisons of

isothermal mixing results are valid, it should also be possible to predict

centerline values of unmixedness. Measurements of unmixedness in several

different jet flames are available [59-61,63]. These suggest that unmixedness

levels in turbulent jet diffusion flames are of the same order as measured in

isothermal flows, but there are systematic variations in most of the

measurements which make direct quantitative comparison impossible.

As the above discussion suggests. Isothermal measurements in variable

density flows can provide important insights into the mixing behaviors of

turbulent jet diffusion flames. Further work is required to determine for

which conditions direct comparisons are valid and when it will be necessary to

allow for local radial density variations due to the heat release of

combustion.

4.4 Reynolds Number Effects in Diffusion Flames

The investigation of Re effects on mixing in variable density flows has

important implications for mixing in turbulent jet diffusion flames [54]. It

is well known that local Reynolds numbers, Re^^ , for turbulent flames are much

lower than calculated based on the room temperature properties of the flow at

the nozzle. This is due to the large Increase in kinematic viscosity which

occurs when gases are heated.

The isothermal studies [34] have shown that the centerline mixing

behavior is independent of Re except for downstream shifts in virtual origins

31
and longer flow distances required to attain asymptotic values of unmixedness

which are found with increasing Re. This suggests that the mixing behavior of

these turbulent flow fields is determined by large scale structures and that

as long as the local Reynolds number is high enough to insure the development

of large scale vortices, mixing in combustion regions of the flow field will

be independent of Re^^ . This conclusion is supported by the observations of

Becker and Yamazaki [64] who noted that flame lengths of turbulent jet

diffusion flames were independent of Re^^ even when the turbulent structure was

"fairly primitive, having little more than an appropriate large-eddy

structure"

.

For isothermal flows it has been shown that centerline unmixedness

attains asymptotic behavior over shorter flow distances at lower Re. This

suggests that for the lower Re characteristic of combusting flows, the flow

field should be able to respond to density fluctuations resulting from heat

release over relatively short flow distances. This conclusion may be very

helpful in understanding and predicting the effects of local density

variations on mixing in complex chemically reacting flows.

5. SUMMARY

During the four years of this joint AFOSR/NBS research program

significant progress has been made toward the goal of improving the

understanding of chemically reacting turbulent flow. The results of

experiments in this laboratory as well as measurements elsewhere on turbulent

jet diffusion flames have justified the original choice to investigate flows

having global density differences. It is anticipated that the experimental

findings and the data base which were generated will be utilized by

32
researchers who are attempting to develop calculational procedures for

describing chemically reacting flows. The real-time nature of the studies and

the conclusion that vortical structures are modified by global density

differences will be of particular interest for workers who are attempting to

develop sophisticated calculational procedures to describe the time behavior

of turbulent flows (e.g., see [65] and [66]).

During the past four years the use of Rayleigh light scattering for

characterizing turbulent mixing behavior in isothermal, variable temperature,

and combusting flows has become more widespread and many laboratories are now

utilizing the technique. It is gratifying that the original careful

characterization of the technique in this laboratory has contributed to this

growth. It is anticipated that the development of new diagnostics for

simultaneous point measurement of concentration and velocity and for line

measurements of concentration will lead to further utilization of this unique

and powerful technique

.

33
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[2] Dyer, T.M. AIAA J . 17(8): 912-914; 1979 August.

[3] Pitts, William M. ; Kashiwagi, Takashi. The application of laser-induced

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Stand. (U.S.) NBSIR 83-2641; 1983 January. 114 p.

[4] Pitts, William M. ; Kashiwagi, Takashi. J. Fluid Mech. 141: 391-429;

1984 April.

[5] Hinze, J.O. Turbulence. 2nd ed. New York: McGraw-Hill; 1975. 800 p.

[6] Schefer, R.W. ; Dibble, R.W. AIAA J . 23(7): 1070-1078; 1985 July.

[7] Brown, G.L.; Rebollo, M.R. AIAA J . 10(5): 649-652; 1972 May.

[8] Way, J.; Libby, P.A. AIAA J . 34(8): 1567-1573; 1971 August.

[9] McQuaid, J.; Wright, W. Inti. J. Heat Mass Transfer. 17(2): 341-349;

1974 February.

[10] Pitts, William M. ; McGaffrey, Bernard J.; Kashiwagi, Takashi. "A New

Diagnostic for Simultaneous, Time-Resolved Measurements of Concentration

and Velocity in Simple Turbulent Flow Systems," Presented at the Fourth

Symposium on Turbulent Shear Flows, Karlsruhe, W. Germany; 1983 September

12-14.

[11] Pitts, William M. ; McCaffrey, Bernard J. Response behavior of hot-wires

and films to flows of different gases. Nat. Bur. Stand. (U.S.) NBSIR 85-

3203; 1985 July. 123 p.

[12] Pitts, William M. ; McCaffrey, Bernard J. J. Fluid Mech. 169: 465-512;

1986 August.

[13] Wu, P. ; Libby, P.A. Inti. J. Heat Mass Transfer. 14(8): 1071-1077; 1971

August

.

[14] McQuaid, J.; Wright, W. Inti. J. Heat Mass Transfer. 16(4): 819-828; 1973

April

.

[15] Simpson, R.L. ; Wyatt, W.G. ; J. Phys . E: Sci. Instrum. 6(10): 981-987;

1973 October.

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15(10): 1765-1786; 1972 October.

34
[17] Baum, Howard R. ; McCaffrey, Bernard J.; Pitts, William M. unpublished

work.

[18] Alden, M. ; Edner, H. ; Holmstedt, G. ; Svanberg, S.; Hogberg, T. Appl.

Optics. 21(7): 1236-1240; 1982 April 1.

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8(5): 244-246; 1983 May.

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M. ; Penney, C.M. Science. 224(4647): 382-384; 1984 April 27.

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November

.

[23] Yip, B. ; Long, M.B. Optics Lett. 11(2): 64-65; 1986 February.

[24] Pitts, William M. Development of a line camera for real-time measurements

of concentration in turbulent flow fields. Proceedings of the

International Congress on Applications of Lasers and Electro-Optics:

Flow and Particle Diagnostics; Vol. 58; The Laser Institute of America;

1986 November 10-13. 7-15.

[25] Gibson, C.H.; Friehe, C.A.

;

McConnell, S.O. Phys. Fluids. 20(10, pt. 2):

S156-S167; 1977 October.

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scalar PDFS in a H2 turbulent jet diffusion flame. Presented at the Fifth

Symposium on Turbulent Shear Flows; Ithaca, New York; 1985 August 7-9.

[28] Drake, M.C.; Pitz, R.W.

;

Shyy, W. J. Fluid Mech. 171: 27-51; 1986

October.

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and Plumes, W. Rodi, ed. New York: Pergamon Press; 1982. 1-68.

[30] Chen, C.J.; Rodi, W . Vertical turbulent buoyant jets--a review of

experimental data. New York: Pergamon Press; 1980. 88 p.

[31] Antonia, R.A.

;

Prabhu, A.; Stephenson, S.E. J. Fluid Mech. 72(3): 455-

480; 1975 December 9.

[32] Chevray, R. ; Tutu, N.K. J. Fluid Mech. 88(1): 133-160; 1978 Septemer 13.

[33] Catalano, G.D.; Morton, J.B.; Humphris, R.R. AIAA J . 14(9): 1157-1158;

1976 September.

35
[34] Pitts, William M. Effects of global density and Reynolds number

variations on mixing in turbulent, axisymmetric jets. Nat. Bur. Stand.

(U.S.) NBSIR 86-3340; 1986. 172 p.

[35] Thring, M.W. ; Newby, M.P. Combustion length of enclosed turbulent jet

flames. Fourth symposium (inti) on combustion. Pittsburgh, PA: The

Standing Committee on Combustion; 1953. 789-796.

[36] Sunavala, P.D. ; Hulse, C. ; Thring, M.W. Com. Flame. 1(2): 179-193; 1972

June

.

[37] Wilson, R.A.M. ; Danckwerts , P.V. Chem. Eng. Science. 19: 885-895; 1964.

[38] Bilger, R.W. Prog. Energy Com. Science. 1(2/3): 87-109; 1976.

[39] Williams, F.A. Combustion Theory, 2nd ed. Reading, MA: Benjamin/Cummings;

1985. 680 p.

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[41] Gibson, C.H.; Chen, C.C.; Lin, S.C. AIAA J . 6(4): 642-649; 1968 April.

[42] Screenivasan, K. R. ; Tavoularis, S. J. Fluid Mech. 101(4): 783-795; 1980

December 29.

[43] Vanquickenborne , L. ; van Tiggelen, A. Com. Flame. 10(1): 59-69; 1966

March.

[44] Hall, L. ; Horch, K. ; Gunther, R. Brennstoff-Wdrme -Kraft . 32(1): 26-31;

1980 January.

[45] Gunther, R. ; Horch, K. ; Lenze, B. The stabilization mechanism of free jet

diffusion flames. First specialist meeting (inti) of the combustion

institute. Pittsburgh, PA: The Combustion Institute; 1981. 117-122.

[46] Eickoff, H. ; Lenze, B.;, and Leuckel, W. Experimental investigation on

the stabilization of jet diffusion flames. Twentieth sjrmposium (inti) on combustion. Pittsburg, PA: The Combustion Institute; 1984. 311-318.

[47] Kalghatgi, G.T. Com. Science. Tech. 41(1+2): 17-29; 1984.

[48] Byggst/yl, S.; Magnussen, B.F. A model for flame extinction in turbulent

flow. Turbulent Shear Flows 4, eds . Bradbury, L.J.S. et al . , SpringerVerlag, Berlin; 1985. 381-395.

[49] Janicka, J.; Peters, N. Prediction of turbulent jet diffusion flame liftoff using a PDF transport equation. Nineteenth symposium (inti) on combustion. Pittsburg, PA: The Combustion Institute; 1982. 367-374.

[50] Peters, N. ; Williams, F.A. AIAA J . 21(3): 423-429; 1983 March.

36
[51] Peters, N. Partially premixed diffusion flamelets in non-premixed

turbulent combustion. Twentieth symposium (inti) on combustion.

Pittsburgh, PA: The Combustion Institute; 1984. 353-360.

[52] Broadwell, J.E.; Dahm, W.J.A.; Mungal, M.G. Blowout of turbulent

diffusion flames. Twentieth symposium (inti) on combustion. Pittsburgh,

PA: The Combustion Institute; 1984. 303-310.

[53] Kalghatgi, G.T. Com. Science Tech. 26(5 and 6): 233-239; 1981.

[54] Pitts, William M. The effects of global density and Reynolds number

variations on mixing in turbulent, axisymmetric jets --implications for

turbulent jet diffusion flames. Proceedings of the 2nd ASME/JSME Joint

Thermal Engineering Conference, Book #102198, Volume 1; Honolulu, HI 1987

March 23-27.

[55] Sobiesiak, A.; Brzustowski, T.A.

,

On the structure of the stabilization

region of lifted turbulent diffusion flames. Presented at the 1986 Spring

Meeting of the Western States Section of the Combustion Institute, Banff,

Canada; 1986 April 27-30.

[56] Wohl , K. ; Gazley, C.; Kapp, N. Diffusion Flames. Third symposium on combustion, flame, and explosion phenomena. Baltimore, MD: Williams and

Wilkins; 1949. 288-300.

[57] Savas, 0.; Gollahalll, S.R. AIAA J . 24(7): 1137-1140; 1986 July.

[58] Chigier, N.A.; Strokin, V. Com. Science Tech. 9(3 and 4): 111-118; 1974.

[59] Ebrahimi, I.; Kleine, R. The nozzle fluid concentration fluctuation field

in round turbulent free jets and jet diffusion flames. Sixteenth

s3nnposium (inti) on combustion. Pittsburgh, PA; The Combustion Institute;

1977. 1711-1723.

[60] Kennedy, I.M.; Kent, J.H. Measurements of a conserved scalar in turbulent

jet diffusion flames. Seventeenth symposium (inti) on combustion.

Pittsburgh, PA: The Combustion Institute; 1979. 279-287.

[61] Drake, M.C.; Bilger, R.W.

;

and Starner, S.H. Raman measurements and

conserved scalar modeling in turbulent diffusion flames. Nineteenth

symposium (inti) on combustion. Pittsburgh, PA; The Combustion Institute;

1982. 459-467.

[62] Lenze, B. and Gunther, R. Brennstoff -WArme-Kraft . 27(10); 387-394; 1975

October

.

[63] Gunther, R. Prog. Energy Com. Science. 9(1/2): 105-154; 1983.

[64] Becker, H.A. and Yamazaki, S. Com. Flame. 33(2): 123-149; 1978.

[65] Grinstein, F.F.; Oran, E.S.; Boris, J.P. AIAA J . 25(1): 92-98; 1987

J anuary

.

37
[66] Ghoniem, A.F. and Sethian, J.A. AIAA J. 25(1): 168-171: 1987 January.

[67] Lockwood, F.C. and Moneib, H.A. Com. Flame. 47(3): 291-314; 1982

September

.

38
TABLE 1

Experimental Parameters

Jet/Coflow Po/P<o Re Experiments (R =» Rayleigh,

He/air 0.14 3950 R,S

CH^ /air 0.55 3950 R.S

CaHg/CO^ 1.02 3960 R,S

CaHg/air 1.55 3960 R,S

CaHg/air 1.55 7890 R,S

CgHg/air 1.55 11860 R,S

CF^ /air 3.01 3960 R

CF^ /air 3.01 7920 R

SFg/air 5.11 3950 R,S

SFg/air 5.11 7890 R,S

SFg/air 5.11 11860 R,S

SFg/He 37.0 3960 R,S

S “= Shadowgraph)

39
FIGURE CAPTIONS

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

The experimental configuration for real-time Rayleigh light

scattering "point" measurements of concentration in binary gas

mixtures is shown schematically. The flow system consists of a 6.35 mm diameter pipe with a sharpened edge enclosed within a 100 X

100 cm^ square cylinder.

The quality of the data which can be acquired utilizing the

Rayleigh light scattering technique for concentration is

demonstrated. Radial profiles of concentration (in both mole and mass fraction terms) are plotted for a turbulent CH^ jet flowing

into a slow coflow of air. The downstream distance is z/r^ = 35

and the Reynolds number is 3950.

Partial time -resolved data records recorded during a simultaneous

Rayleigh light scattering and hot- film anemometry experiment are reproduced for a propane jet (Re = 3960) flowing into a slow coflow

of air. The observation voliome is located on the jet centerline at

z/r^ = 31.5. The light scattering signals have been calibrated and

are plotted in terms of mole fraction of propane. The raw data for

the anemometer output is plotted along with the velocity calculated

utilizing the calibrations of film response to changes in velocity

and gas composition.

The correlation is shown for the heat transfer from a hot-wire as a function of flow velocity for nine different gases. Experimental

measurements are nondlmensionalized by the use of the Nusselt

number and Reynolds number. Corrections have been included for

heat losses to the prongs of the hot-wire and thermal slip and

accommodation effects rt the surface of the probe. (Kg)^^ and (K^)^ are coefficients which are necessary to compensate for variations

in molecular properties from gas to gas.

The camera which has been developed for recording real-time

Rayleigh light scattering intensity along a line is shown. The top

portion indicates the major components and their configuration.

The actual appearance of the camera is shown below.

The overall experimental configuration for real-time measurements

of concentration along a line in turbulent flows is represented.

Rayleigh light scattering is induced along a line in the flow field

by the Ar'*' ion laser. Light scattering at 90° is recorded by the

digital line camera system consisting of the line camera shown in

figure 5, suitable interfaces, and a data acquisition minicomputer.

An example of time - resolved line measurements of propane mole

fraction across a turbulent jet of propane (Re = 3960) flowing into

a coflow of air is reproduced. Propane mole fraction is

represented by a seven level gray scale. The downstream position

is 5 diameters and the line read out rate is 830 Hz.

40
Figure 8. Time -averaged radial profiles of propane mole fraction are shovm

for five downstream positions in the development region of a propane (Re = 3960) jet flowing into a slow coflow of air. The

growth of the boundary layers on either side of the potential core with increasing z and decrease of centerline concentration at the

end of the potential core can be clearly observed. It is

interesting to note that the data displayed represents 164,000

individual concentration measurements which were recorded during

1.54 s of actual acquisition time.

Figure 9

.

The apparatus for recording time -resolved shadowgraphs is

represented schematically. The light pulse generated by the

chopper has a temporal profile which is triangular in shape and has

a total duration of 310 /is

.

Figure 10

.

Three time -resolved shadowgraphs are shown for a SFg jet (Re =

3950) flowing into a slow coflow of air. Three different

downstream positions recorded at different times are represented.

Note particularly the formation of a fountain by the SFg at a downstream position of == 37.5 r^ .

Figure 11

.

Shadowgraphs are reproduced for jets of SFg (Re = 7890 and 11,860)

entering slow coflows of air. For each jet four views of the flow

recorded at different times and positions in the jet are superimposed. Note that the fine scale turbulence becomes more pronounced with increasing Re, but that the overall spreading rate

of the jet does not appear to be affected.

Figure 12

.

Five sets of superimposed shadowgraphs are shown for jets of one

gas flowing into a second gas. With the exception of the SFg

flow, the Reynolds mombers are roughly the same. The effects of

variations in the global density ratio appear as changes in the

development region of the flow and modifications in the eddy

structure at downstream positions where the flows are close to

fully - developed

.

Figure 13

.

Superimposed shadowgraphs are reproduced for propane jets at three

Re entering into slow coflows of air. The development of finer

turbulent scales with increasing Re can be clearly seen. It is

also evident that increasing the Re results in a shortening of the

distance required for the development of vortical structures near

the nozzle. The overall spreading behavior of the jets is

independent of Re supporting the supposition that entrainment is

determined by large scale turbulent structures.

Figure 14. Values of Y„/Y„ (Y„ = Y„ is the centerline concentration at z/r„

and Yjj is the mass fraction of jet fluid at the jet exit) are plotted as a function of z/r^ for six different jet/coflow gas

combinations. The solid lines are linear least squares fits of

the results. Note the decreasing slopes and upstream movement of

the virtual origins (z where Y^/Y^, - 0) which occur as the

jet/coflow density ratio is increased.

41
Figure 15. Predicted values of inverse centerline mass fraction (denoted as

1/C|^ ) based on the analysis of Thring and Newby [35] are plotted

as functions of z/r^^ for the six jet/coflow gas pairs which have

been experimentally investigated. Comparison of figures 14 and 15

shows that there is good agreement between prediction and

experiment

.

Figure 16. Values of centerline unmixedness are plotted as a function of z/r^^

for the six jet/coflow gas pairs listed. Values of for each

jet approach a common asymptote of == 0.23, but the flow distance

required increases dramatically as the jet/coflow density ratio

increases

.

Figure 17

.

The centerline unmixedness values shown in figure 16 are replotted

as a function of z/r^

.

The collapse of the data onto a single curve suggests that r^ is the proper scaling parameter for

correlating the growth of unmixedness in these variable density

flows

.

Figure 18. Centerline unmixedness values for three different Re jets of

propane entering slow coflows of air are plotted as functions of

z/r^j . Flows at higher Re require longer flow distances in order

to achieve the as3npaptotic value of unmixedness even though the

value of the asymptote does not change.

Figure 19. The concentration contour corresponding to that for which the

laminar flame speed of an ethylene/air mixture is a maximum = 0.073) is plotted as functions of z/r^ and r/r^^ . The virtual

origin for the plot is assumed to be at z = 0. Two

representations are shown. On the right the radial and axial axes have the same scaling, while on the left the radial scale is

expanded by a factor of 5.

Figure 20. Experimental values [47] of lift-off height (h) are plotted

against jet exit velocity for turbulent jet flames of methane,

ethylene, and propane. These measured values are compared with

values (solid lines) predicted using eq. (5) and the known

velocity and mixing behaviors of the jets. The agreement is

excellent

.

Figure 21. Experimental [53] (symbols) and calculated values (lines) of blow

out velocity are plotted as a function of jet radius for

axis)nnmetric turbulent jet flames of five organic fuels.

Calculated values are derived by using eqs . (6) and (7). The

agreement of the predicted values with experiment is very good.

Figure 22. Approximate radial density profiles for three nondimens ional

downstream distances are shown for turbulent jet diffusion flames

of hydrogen and a typical organic fuel (methane) . These curves

are based on measurements reported by several different authors

[63,67] .

42
BEAM

EXPANDER

Figure 1. The experimental configuration for real-time Rayleigh light

scattering measurements of concentration.

43
44

Figure

2.

Radial

profiles

of

concentration

are

plotted

for

a

turbulent

CH^

jet

flowing

into

a

slow

coflow
0.5

PROPANE MOLE FRACTION

HOT-FILM OUTPUT

Z)

CALCULATED VELOCITY

Figure 3. Partial time-resolved data records recorded during a simultaneous

Rayleigh light scattering and hot- film anemometry experiment.

45
m

ind

Q)

Qi

csj

46

Figure

4.

The

correlation

is

shown

for

the

heat

transfer

from a

hot-wire

asa

function

of

velocity

for

nine

different

gases.
RET I

CON

LINE

SCANNER

47

Figure

5.

The

camera

for

recording

real-time

Rayleigh

light

scattering

intensity

along a

line

is

shown.
Enclosure

Q.

<i> D

Q.

E

o

o

c

48

Figure

6.

The

overall

experimental

configuration

for

real-time

measurements

of

concentration

along

a

line

in

turbulent

flows

.
0.0

00

49

Figure

7.

An

example

of

timeresolved

line

measurements

of

mole

fraction

across a

turbulent

let

of

C^H3i
UOjpOJJ 9|0^ dUDdOJJ

pe6DjeAD-8Ui{j,

50

Time

-averaged

radial

profiles

of

mole

fraction

are

shown

for

a

propane

jet

flowing

into

air.
51

Figure

9.

The

apparatus

for

recording

time

-

resolved

shadowgraphs

is

represented

schematically
50

. J I I \ L

-10 0 10

I'/f'c,

Figure 10. Three time - resolved shadowgraphs are shown for a SFg j

3950) flowing into a slow coflow of air.

et (Re =

52
Figure 11. Shadowgraphs are reproduced for jets of SFg entering slow coflows

of air.

a) SFg/air b) SFg/air

Re = 7890 Re = 1 1860

60i- n 1 1

1

\

^ r

-I 60

-10 0 10 -10 0

- 50

- 40

30

-20

-10

- 0

53
air

b)

CH4

/air

c)

CjHg/C02

d)

CjHg/air

e)

SFg/air

3950

Re=

3950

Re=

3960

Re=

3960

Re=

7890

54

Figure

12.

Superimposed

shadowgraphs

are

shown

for

jets

of

one

gas

flowing

into a

second

gas.
a)

CjHg/air

b)

CjHg/air

c)

CjHg/air

Re=

3960

Re=

7930

Re=

11880

55

Superimposed

shadowgraphs

for

propane

jet

at

three

Re

entering

slow

coflows

of

air.
56

Figure

14.

Values

of

Y^/Y^

are

plotted

as

a

function

of

z/r^

for

six

different

jet/coflow

gas

combinati
Figure 15. Predicted values of inverse centerline mass fraction based on the

analysis of Thring and Newby.

57
o

(£>

O

ID

O

Oro

O

CN

O

O

O O O O O

N

58

Figure

16.

Values

of

centerline

unmixedness

are

plotted

as

a

function

of

z/r^^

for

the

jet/coflow

pairs

listed.
o o o o o

'a/7

59

Figure

17.

The

centerline

unmixedness

values

shown

in

figure

16

are

replotted

as

a

function

of

z/r^
4-1O

“A/“A

w

15O

rH4-1 Oo&o1—I w

W)c

•I—I

5-i Q) 4-) C0)

<UC

COa.o

!-i a

4-1ow4J

Q)0) pci 4.) C

<UU

Q) 4-1 4-1 •H

T)0) (U5-1 • ,C o 4-)

!-l O

4-1w

<u

—I

cfl

CO

CO0) dt30) X

cuC

•r^ t—I 04 U H

0) CCJ 4-) d Vl

04 T-l u cci

CO1—I

04d

bO

»r^

60

plotted

as

functions

of

z/r^
Y 0.073 C2H4

Figure 19. The concentration contour for which the laminar flame speed of an ethylene/air mixture is a maximum.

61
25 -

Uo (m/s)

Figure 20. Experimental values of lift-off height (h) are plotted against jet

exit velocity.

62
350

Figure 21. Experimental [53] (symbols) and calculated values (lines) of blow

out velocity are plotted.

63
CVJ

t o CO CD

O O

(gUJ/6>|)d

o

CM O

o

64

Figure

22.

Approximate

radial

profiles

for

three

nondimens

ional

downstream

distances

are

shown

for

turbulent

jet

diffusion

flames

of

hydrogen

and

a

typical

organic

fuel

(methane).
NBS>114A (REV, 2»8C) U.s. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-87/3550

2. Performing Organ. Report No. 3. Publication Date

JUNE 1987

4. TITLE AND SUBTITLE

Mixing in Variable Density, Isothermal Turbulent Flow and Implications for

Chemically Reacting Turbulent Flows

5. AUTHOR(S)

William M. Pitts and Takashi Kashiwagi

6. PERFORMING ORGANIZATION (If joint or other than MBS, see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. ISSA-86-00008

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

Air Force Office of Scientific Research

Bolling AFB

Building 410

Washington, DC 20332

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report summarizes the research findings of a project which has been

jointly funded by the Air Force Office of Scientific Research and the National

Bureau of Standards. The goal of the research was to improve the fundamental

understanding of chemically reacting turbulent flow. The approach which was

taken was to investigate mixing in variable density flows in order to better

understand the role of local density fluctuations (which result from chemical

heat release) on the turbulent mixing behavior. The development of new

experimental diagnostics having excellent spatial and temporal resolution is

described. These techniques have been utilized to investigate a wide range of

mixing properties in variable density flows. These results are summarized

along with a discussion of their importance to an improved understanding of

chemically reacting flow.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) concentration fluctuations; concentration measurement; density effects; digital

line earner; flow visualization; hot wire anemometry; jet flames; Rayleigh

light scattering; Reynolds number; turbulent flames; velocity measurement

13. AVAILABILITY

Uni imited

I I For Official Distribution. Do Not Release to NTIS

f I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[2Q Order From National Technical Information Service (NTIS), Springfield, VA, 22161

14. NO. OF

PRINTED PAGES

73

15. Price

$13.95

USCOMM-DC 6043-P80
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