Geometry and flow influences on jet mixing in a cylindrical duct

To examine the mjxing characteristics of jets in an axisymmetric can geometry, temperature measurements were obtained downstream of a row of cold jets injected into a heated cross stream. Parametric, nonreacting experiments were conducted to determine the influence of geometry and flow variations on mixing patterns in a cylindrical configuration. Re.~ults show that jct-to-mainstream momentum-flux ratio and orifice geometry significantly impact the mixing characteristics of jets in a can geometry. For a lixed number of orifices, the coupling between momentum-flux ratio and injector geometry determines I) the degree of jet penetration at the injection plane and 2) the extent of circumferential mixing downstream of the injection plane. The results also show that, at a fixed momentum-flux ratio, jet penetration decreases with I) an increase in slanted slot aspect ratio and 2) an increase in the angle of the slots with respect to the mrunstream direction.


Introduction
M IXING of jets in a confined crossflow has a variety of practical applications and has motivated a number of studies over the past decades.In a gas turbine combustor, e.g., mixing of relatively cold air jets is important in the dilution zone where the products of combustion are mixed with air to reduce the temperatures to levels acceptable for the turbine blade materia l.Mixing of jets in a crossflow is also import ant in applications such as discharge of effluents in water, and in transition from hover to cruise of V/STOL aircraft.
To meet the air quali ty standards affecting gas turbines, low emissions combustors are being developed.' One of the Presented as Pape r 92-0773 at the AIAA 30lh Aerospace Sciences Meeting and Exhibit.Reno, NV, Jan. 6-9, 1992; received March 18, 1993; revision received Ju ne 2, 1994; accepted for publication July 14, 1994.Copyright© 1992 by the American Institute of Aeronautics and Astronau1ics, Inc.No copyright is asserted in 1he United States under Title 17, U.S. Code.The U.S. Governmenl bas a roya lty-free license to exercise all rights under the copyrigh1 claimed here in for Govern menta l purposes.All  promising low NOx combustor concepts is the rich-burn/quickmix/lean-burn (RQL) combustor. 2The RQL developmental effort poses new challenges in jet mixing in a confined crossflow.1.~More specifically, the range of jet-to-mainstream mass flow ratios encountered in the quick-mix region of a RQL combustor differ significantly from those of a conventional combustor dilution zone.J--' Most of the previous research of jets in a crossflow has been performed in rectangular geometries.Examples of these studies are provided in Table 1 and are summarized elsewhere.6The influence of orifice geometry and spacing, jet-to-mainstream momentum-flux ratio J, and density ratio have been documented for singleand double-sided injection (e.g., Ref. 6).These studies have identified J and orifice spacing as the most significant parameters influencing the mixing pattern.

Experiment
A series of parametric experiments were conducted in this study to determine the influence ofJ and orifice configuration on mixing of jets in a can geometry.The parametric experiments investigated a range of J values, including 25, 52, and 80.A jet-to-mainstream mass ratio of 2.2 was maintained at each tested J value.An area discharge coefficient of 0.80 was assumed in designing the orifices.
The modules were 6.5 in.(165 mm) long, with the center of the o rifice row placed at one radius from the edge.The orifice area for each module at the design J value was kept constant.As a result, the dimensions of a given orifice varied as a function of J.A representative module is shown in Fig.   and slot aspect ratio as well.For reference, tlie axial location of the trailing edge and blockage are presented in Table 2.The former is expressed as the ratio of the axial projection of the orifice lo the radius of the mixing module, and the latter is defined as the ratio of the circumferential projection of the orifice to the spacing between orifice centers.Mixing was examined by measuring the local mean temperature throughout the module.The mainstream flow entering the module was heated to the highest temperature (212°F) compatible with the upper temperature limits of Plexiglas.Jets were introduced at room temperature.The operating conditions are presented in Table 3. Reference velocity.defined as the velocity at the inlet to the mixing section and calculated based on the mainstream temperature and pressure , was 34.5 fps (10.5 mis).The actual discharge coefficient.and momentum-flux ratio for each case was determined by measuring the jet pressure drop.
A 12-in.-long, 0.125-in.type K thermocouple was used to measure the temperatures.Temperature was measured at 50 points in a quarter sector of the modules, for five planes downstream of the orifices.Figures 2a and 2b show the measurement points and the axial planes.A 90-deg sector was • . -

Experimental Facility
The test faci lity that is located at the UCI Combustion Laboratory and is shown schematically in Fig. 3   air that was filtered a nd regulated before branching into two isolated main and jet circuits.The jet circuit incorporated four independently metered flow legs.The main circuit consisted of a coarse and a fine leg that provided a total of 150 standard cubic feet per second (SCFM) for the mainstream flow .Each leg was regulated independently to eliminate the effects of pressure fluctuations.All circuits were metered by sonic ven turies.The mainstream air was heated to 212°F by a 20-kW air preheater (Watlow, PIN 86036-2).The outlet temperature was controlled by a Watlow heater controller (series 800).The mainstream air.after being metered and heated, passed through fl exible tubing into a 2-in.insulated carbon steel pipe immediately upstream of the mixing module.A combination honeycomb/screen in the pipe provided uniform flow to the mixing module.The flexible tubing upstream of the pipe allowed manual traversing of the experiment in the X, Y, and Z directions.A Mitutoya model PM-331 digital t raverse readout was used to read the coordinates.
The 3-in.mixing module used in the parametric phase was positioned inside a concentric Pyrex® manifold (see Fig. 3).The jet manifold incorporated four openings o n top and four on the bottom, each 90 deg apart.Four discrete jets were supplied to the manifold through the bottom openings.Two of the openings on the top were used to measure the manifold temperature and pressure, and the other two were blocked.Each jct circuit was metered individually and installed to provide symmetric flow conditions at the inlet to the manifold.Honeycomb was installed in the jet plenum upstream of the orifices to provide uniform flow through the mixing module.

Analysis
To compare the mixing characteristics of different modules, the temperature measurements were normalized by defining the mixture fraction fat each point in the plane: (1) A value off = 1.0 con-esponds to the mainstream temperature.whereas f = 0 indicates the presence of the pure jet flow.Complete mixing occurs when f approaches the equilibrium value that is nearly equal to the ratio of the upstream flow to the total flow.Note thatf = J -8, where 8 appears in previous studies. 6 To quantify the mixing effectiveness of each module configuration , an area-weighted standard deviation parameter ("mixture uniformity") was defined at each z/R plane: where A = ~a; , f; is the mixture fraction calculated for each node, andfc .. uH is the equilibrium mixture fraction , defined as (3) Complete mixing is achieved when the mixture uniformity parameter across a given plane reaches zero.

Results and Discussion
This section presents the mixing characteristics for the baseline geometry (module 1), and the 8:1 and 4:1 slanted slots configurations (module 2 and module 5) as a function of momentum-flux ratio.Jn addition, the effects of slot aspect ratio and o rientation on mixing pattern are discussed.From an overall-mixing standpoint, an optimum mixer is defined as one that produces a uniformly mixed flowfield, without a persistent unmixed core or unmixed circumferential regions by the z/R = 1.0 plane.In the contour plots presented, the center of the jets are located at 22.5 and 67.5 deg, relative to the measurement plane.For slanted slots, the jets angle counterclockwise as one moves upstream.  0.40 -0.50 -0.30 -0.40 -0.20 -0.30 -0.10 -0.20 below 0.10 -0.40 -0.50 -0.30 -0.40 -0.20 -0.30 -0.10 -0.20 below 0.10 f ig. 5 Mixture fract ion, J80MO DI, baseline eight-hole, J = 84.2.
At the jet in1ection locations for J = 25 (J25MOD1) , f decreases monotonically in the radial direction , with the highest concentration of mainstream fluid on the duct centerline (R = 0.0), and lowest at the walls (R = 1.5).The monotonic variation off indicates that no backflow exists for this configuration.The radial variation off at z/R = 0.0 for J = 80 (J80MOD1), on the other hand, is nonmonotonic.For the J = 80 module at the injection location, f is relatively low at R = 0.0, increases as R is increased, and approaches zero at the jet inlet.This non monotonic variation off indicates backnow and overpenetration of jets for these configurations.
Overpenetration of jets is evident at the downstream axial locations for J = 80 (/80MOD1) by the high f near the wall.
At z/R 1.0.the J = 80 module (J80MOD1 ) shows low f values at the center, and an unmixed region along the wall.
whereas J "" 25 (J25MOD l) shows a more uniformly mixed Oowfield.The degradation in mixing for J = 80 (J 80MOD1), occurs because the increased jet penetration to the module center directs a larger portion of the jet flow to the core, thus decreasing the circumferential mixing along t he walls.In an axis-sym metric can geometry, where the majority of the mass is concentrated along the walls, good circumfe rential mixing is important in obtaining a well-mixed flowfield.Therefore, according to the definition presented earlier, the round holes at J = 25 (J25MOD1) display closer to optimum mixing than the J "' 80 case at zl R = 1.0.Following che methodology of Eq. ( 6) fou nd in Ho lde ma n / ' the optimum mo mentum-flux ratio for this eight-orifice case would be just over 20. Figure 6 compares the mixture unifo rmity parameter for all of the baseline modules tested as a function of mome ntum flux ratio.This plot confirms the qualitative observation that the increase in the mo me ntum-flux ratio improves mixing at the initial planes, but degrades the overall mixing downstream of the injection plane.The first axial location (z/R = 0.0) examined for the J = 25 module shows a large region at f > 0.9, indicating very small or no jet penetration to the center.For this configu-ra1ion.the relatively unmixed core persists with increasing z/R , and is present at the last axial location of z/R = 1.0.
This configuration represents an underpenetrated case.
The first indication of jet penetration to the center for the three 8: J aspect ratio modules tested is observed at the z/R = 0.0 plane of the J = 80 (J80MOD2) module.The mixcure fraction value ar the core of this plane ranges between 0.8-0.9 indicating that a portion of jet fluid is mixed with the mainstream .At the z/R = 1.0 plane, the main portion of the flow is close to the equilibrium value , while a slightly larger f is seen at the center.The presence of the slightly warmer core shows that this conriguration is still slightly unde rpenetrated.Mixing characteristics of this module a re similar to those at J =-25 (J25MOD1). -0.40 -0.50 -0.30 -0.40 -0.20 -0.30 -0.10 -0.20 below 0.10  and J80MOD5).The first axial location for the J = 25 module (at z!R = 0.0) shows a relatively large central region with mixture fraction values in the range of 0.8-0.9.This f value is less than unity, indicating slight jet penetration and mixing at the center of the module.Compared to the round hole jets (J25MOD1).the region of near unity val ues off is larger.The jet penetration for the round hole jets is stronger at this J value, therefore, the high mixture fraction region is smaller.As described previously, the 8:1 aspect ratio module at J = 25 (J25MOD?.) represents a case of underpenetration with central/ values above 0.9.At downstream locations.the J = 25 module (J25MOD5) produces a re la ti vely well-mixed flowfield with no indication ofunmixed walls.At z!R = 1.0, however, a slightly unmixed core is observed.
As J is increased, the penetration to the center is enhanced and the mixture fraction values at tbe core of the module at initial axial locations decrease.At J = 80 (J80MOD5) , a relatively low f value region is seen at the first axial location.
At downstream locations, a cool center and relatively unmixed regions a long the walls a re produced.At this momentum-flux ratio as well as at J = 52 (J52MOD5), the jets overpenetrate, a condition that is not desirable from an overall mixing standpoint.
Figure 12 compares the mixture uniformity parameter for the three 4: l aspect ra tio geometries.T he trend is very similar to that described for the baseline modules.At initial planes, t he higher the momentum-flux ratio, the better t he mixture uniformity.At downstream locations.the J value with the most initial overpenetration (80). is the poorer mixer due to degradation of circumferential mixing (J80MOD5).The slot aspect ratio affects 1) the amount of jet mass injected per unit length and 2) the axial extent over which the mass is injected.
For a given momentum-flux ratio and number of orifices, the smaller aspect ratio slots penetrate further into the cross stream.The larger aspect ratio slots on the other hand, produce a stronger swirl component that enhances the circumferential mixing.Figure 13 compares the mixture u niformity parameter for the 8:1 and 4:1 aspect ralio slots.At the lower and intermediate J values. the 4:1 aspect ratio geometry is a better mixer at all ax ial locations.At the highest J value tested, however, the 8: 1 aspect ratio behaves as the better mixing geometry beyond z!R = 0.5.This is because of the overpenetration of jets at J == 80 (J80MOD5) , which improves mixing at the initial pla nes.but produces unmixed regions a long the walls at downstream axial locations.As the slot angle is changed, the J value at which one mixer demonstrates more desirable mixing characteristics than the other can change also.
The slot angle affects 1) the axial length over which jet ma ss is injected and 2) the " blockage" that the jets present to the above 0.90 -0.80 -0.90 CJ 0.70 -0.80 D 0.60 -0.70 D 0.50 -0.60 -0.40 -0.50 -0.30 -0.40 -0.20 -0.30 -0.10 -0.20 below 0. 10 Examining the flowfield at the first axial location for these mod ules shows that by increasing the slot angle, the jet pen-  T he jet penetration at the initial axial location, although differen t for each module , results in similar val ues of the mixture un iformity parameter as shown in Fig. 18.The 0-deg slots (J52MOD3) produce the most jet penetration and display the worst mixture uniformity parameter a l z/R = 1.0.above 0.90 -0.80 -0.90 CJ 0.70 -0.80 D 0.60 -0.70 CJ 0.50 -0.60 -0.40 -0.50 -0.30 -0.40 -0.20 -0.30 -0.10 -0.20 below 0.10 The optimumlnixer based on these four cases appears to exist at an angle between 45 and 67.5 deg.These results suggest that slot angle does not have a big impact on mixtu re uniformity.However, this observation cannot be extended to cases where the aspect ratio, number of orifices, and momentum-flux ratio are allowed to vary along with slot angle.Conclusions 1) Jet-to-mainstream momentum-flux ratio J , and orifice geometry significantly impact the mixing characteristics of jets in a cylindrical geometry.
2) For a fixed number of orifices, the coupling between J and orifice geometry determi•nes the extent of penetration and circumferential mixing in a can configuration.
3) From an overall-mixing standpoint, moderate penetration to the center is desi rable.Underpenetration forms a relatively unmixed core that persists at downstream locations.Overp' enetration degrades circumferential mixing and forms unmixed regions along the walls.
4) For the momentum-flux ratio values considered, increasing the aspect ratio of slanted slots reduces jet penetration to the center and enhances mixing along the walls.5) For eight 4:1 aspect ratio slot orifices at] = 52, increasing the angle of the slots with respect to the mainstream reduces jet penetration while not markedly affecting the mixture uniformity one duct radius from the orifice leading edge.
6) The near optimum mixing modules identified in this study were based on a fixed number of orifices and limited variations in orifice angle and aspect ratio.Further investigation is needed to identify optimum mixing conditions when the number of orifices, orifice aspect ratio , and angle are varied over a larger parameter space."Fearn , R ., and Weston.R .P., " Vorticity Associated with a Jet in a Cross Flow," A / AA Journal.Vol. 12 , No . 12, 1974No . 12, , pp. 1666No . 12, , 1667. .

1 .
(All modules are presented in Ref. 7.) While the leading edge of each orifice was fixed at the same axial location (z/R = 0.0), the axial extent of jet mass addition varied according to orifice size and, in the case of the slots, ~-1~----'--~ Heq ::illli: • -• Jet, B
ig. 3 Schematic of the test facility.DR 1.26

Module 1 -
Baselioe Geometry (Holes) Three baseline geometrics were tested as part of the parametric experiments.Figures 4 and 5 present the mixture fraction variations between planes z/R = 0.0 to z/R = LO for the momentum-flux ratio range endpoin~s: J = 25, and 80 (cases J25MOD1 and /80MOD1).The actual J is shown in the figure caption.A comparison of the mixture fraction distribution at the first axial location (z/R = 0.0) shows a decrease inf at the center, with increasing momentum-flux ratio.For J = 25 (J25MOD1), f is in the range of 0.8-0.9 at the core of the module, indicating the penetration of some jet fluid to the center.For J = 80 (/80MOD1), the mixture fraction values at the center are in the range 0.2-0.3.These f values are at or below the totally mixed value off Cfcqu;i = 0.31) indicating overpenetration lo the center.

Figure 9
compares the mixture uniformity parame te r for the 8: I. aspect ratio geome tries.At the first axial location.the J = 25 modul e (J25MOD2) produces degraded mixing due

Fig. 18
Fig. 18 Effect of slot angle on mixture uniformity.
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Table l (
Co11ti11ued) Summary of selected jet mixing studies Ta ble 2 Axial location of orifice trailing edge and orifice blockage Fig. 1 Mixing module dimensions.1.5 featured house