Optimization of orifice geometry for crossflow mixing in a cylindrical duct

Mixing of gaseous jets in a cross(cid:143) ow has signi(cid:142)cant applications in combustion science and engineering, one example of which is the mixing zone of a rich-burn/quick-mix/lean-burn gas turbine combustor. A major design question is the jet ori(cid:142) ce shape and jet ori(cid:142) ce number that optimizes the mixing performance. To delineate the optimal ori(cid:142)ce features for a given axial distance and momentum-(cid:143)ux ratio, a statistical design of experiments test matrix was established around three variables: the number of ori(cid:142)ces, the ori(cid:142)ce aspect ratio, and the ori(cid:142) ce angle (in circumferential plane). A jet-to-mainstream momentum-(cid:143)ux ratio of 40 and a mass-(cid:143)ow ratio of 2.5 were selected as representative of a practical design. To yield an interpolating equation that predicts the mixing performanceofori(cid:142) ce geometrycombinationswithintherangeofthe test matrixparameters, a regression analysis was conducted on the data. The results reveal that 1) mixture uniformity is a nonlinear function of the number of ori(cid:142) ces, the ori(cid:142)ce aspect ratio, and the ori(cid:142) ce angle and that 2) optimum mixing occurs when the mean jet trajectories are in therangeof 0.30 < ‡ / R <0.5 (where ‡ = R ¡ r )at x / R = 1. At the optimumnumberof ori(cid:142) ces, the difference between shallow-angledslots with large aspect ratios and round holes is minimal and either geometry produces optimalmixingperformance.

(2) f = mean mixture fraction h = ori ce axial length J = momentum-ux ratio ( jet/mainstream), (q j V 2 j / q 1 U 2 1 ) MR = mass-ow ratio n = number of ori ces R = mixer radius r = radial coordinate (r = 0 at center) T = gas temperature U S = area weighted normalized variance, for example, see Eq. (3) x = axial distance a = ori ce angle with respect to mainstream ow in x ¡ h plane, 0 = long axis aligned with mainstream ow temperaturepattern factor,low emissions, and ef uent gas composition are strongly affected by the quality of the air jet-combustor gas mixing that is achieved. One scheme for advanced, low-pollutant emission combustors is the rich-burn/quick-mix/lean-burn (RQL) method. Because a signi cant amount of the combustion air is injected via jets through the sidewall, optimization of the mixer must consider wall ori ce distribution, ori ce size, ori ce shape, orice spacing jet penetrationcharacteristics,and local enthalpy levels due to the jet mixing characteristics. In conventional combustors, most of the important combustion mechanisms (e.g., strength and size of the recirculation zone, volumetric heat release patterns, liquid fuel evaporation and consumption characteristics) are linked to the primary jet mixing processes. Clearly, advances in gas turbine combustor technology are dependent on, and cannot occur without, improved understanding of jet mixing into con ned cross ows.
The need to understand and optimize jet mixing into cross ows is not limited to gas turbine combustor applications.Similar mixing problems exist in the design of fuel and air premixers, the discharge of ef uent into water, vertical/short takeoff and landing (V/STOL) aircraft in ground proximity and many other applicationswhere two continuously owing streams are mixed together.
The present study addressesthe characteristicsthat govern the optimal cross ow mixing in cylindrical ducts. The goals of the present study are to 1) characterize the relationship between the jet ori ce shape and number as it relates to mixture uniformity at an axial distance of one duct radius downstream of the ori ce leading edge and 2) identify the optimal mixing con gurationfor a given momentumux ratio.

Background
Many studies of con ned jet mixing have been conducted on combustor components for advanced gas turbine engines. Recent NASA-supported studies are summarized in works by Holdeman et al. 1,2 for cylindrical and rectangular ducts, respectively. Previous studies, mostly with smaller ori ces in rectangular and annular ducts, are summarized by Holdeman. 3 A summary of previous jetin-cross ow studies (mostly con ned) is given by Margason. 4 These summaries contain substantial reference listings, including previous works of other researchers. Therefore, only those 929 references from which material is speci cally cited are included herein. In all of these summaries the importance of the momentumux ratio and the spacing between adjacent ori ces is delineated. Hatch et al. 5 studied the mixing characteristics of both circular and slanted slot ori ces in a cylindrical duct, where the number of ori ces for each mixer was held constantat eight.Mixing qualitywas quanti ed at an axial distance equal to one duct radius downstream of the leading edge of the ori ce using an area weighted standard deviation value for experimentally determined mixture fractions. The best mixer had the smallest value of area weighted standard deviation at the evaluation plane. Among other results, it was observed that the optimum mixing con guration varied in the number of ori ces at a xed momentum-ux ratio. Consequently, because the number of ori ces was not varied, an optimum mixer could not be identi ed.
In a study limited to round hole ori ces, Kroll et al. 6 determined experimentallythe optimum number of ori ces for momentum-ux ratios of J = 36 and 70. The optimum number of round hole orices for these momentum-ux ratios based on the same criteria as the Hatch et al. 5 study was found to be 10 and 15 round hole congurations, respectively. The results agreed well with the design equation reported by Holdeman et al. 1 and Holdeman 3 : where C = 2.5 as suggested in Ref. 3. Oechsle et al. 7 considered the optimization requirements of the different ori ce designs reported by Hatch et al. 5 Oechsle et al. 7 used several different parameters for optimization including an area weighted standard deviation, and concluded that the relatively shallow-angledslanted slot ori ces would provide optimum jet penetration and mixing characteristics.
Although the preceding studies have provided substantial insight on ori ce optimization,none of the studies followed an optimization approach that systematically varied ori ce design parameters at a xed momentum-ux ratio such that a mathematical response surface could be created. This is the goal of the currentstudy,namely, to identify the sensitivity of jet mixing performance to small changes in ori ce slot angle, A R, and number of ori ces. All ori ces are rectangles with semicircular ends where, for A R = 1, the ori ce is a round hole.

Experiment Facility
The experimental facility that was used for this research is the same basic test stand and ow panel that is described by Hatch et al. 5,8 and Kroll et al. 6,9 This facility provided 100 ± C (212 ± F) mainstream air at atmospheric pressure.Jet air was supplied at 23 ± C (74 ± F) to a manifold that supplied the ori ces in the mixer. A thermocouple probe was used to measure the local temperature where the jet uid mixed with the heated mainstream uid. Figure 1 depicts the arrangementof the test assembly and the thermocouple probe. The displacement of the three axes was monitored with a Mitutoya digital displacement indicator with a precision of 0.0025 cm (0.001 in.). The 0.32-cm ( 1 8 -in.) type K thermocouple used for thermal ow eld mapping was centered and aligned prior to each experiment.
The mainstream ow entered the bottom of the mixing module at a temperature of 100 ± C (212 ± F) and a bulk velocity of 9.4 m/s (31 ft/s). The jet air manifold was manufactured with four ports equally spaced around the manifold's circumference at both the top and bottom. Four individually metered airstreams supplied the lower four manifold ports with jet air at approximately23 ± C (74 ± F). After entering the bottom of the manifold, the jet air owed upward through a 1.27-cm-( 1 2 -in.-) thick honeycomb ring. The honeycomb aided in removing any swirl from the jet air prior to its passage through the mixer's ori ces. One of the manifold's top ports was used to monitor the air pressure, a thermocouple was located in a second port to measure the jet temperature, and the remaining two  ports were capped off. A dimensioned mixer is shown in Fig. 2 for reference.

Measurements
A thermocouple probe was chosen to perform the point temperature measurements in accordance with the desire to use a simple and reliable measurement technique. The relatively large time constant of the thermocouplehad the effect of averagingthe temperature uctuationsin the fully turbulent ow eld. Four probe designs were investigatedto evaluate which design minimizes ow eld perturbations. Each probe design used a 30.5-cm- (12- The following criteria were established to evaluate alternative probe designs: 1) The calculated jet uid back ow should be minimized and approach zero at the ori ce leading edge.
2) At the plane of the ori ce trailing edge (x / h = 1),100% of the jet uid mass should be accounted for.
3) Deviation of the mean mixture fraction from the calculated equilibrium value at x / R = 1 should be minimized.
The initial probe design was a straight, axially aligned probe. Because this probe was aligned with the bulk uid ow direction, it would perturb the ow the least downstream of the ori ces. The experimentsbore this out. For the straight,axial-alignedprobe, oweld perturbations were not signi cant except in the ori ce region.
However, in the vicinity of the ori ces, the strong degree of crossow normal to the probe caused perturbations that resulted in the appearance of a high degree of jet uid back ow, that is, the propagation of jet uid in the upstream direction.
To minimize the perturbations in the ori ce region, three other thermocoupleprobe designs were analyzed. The rst was an axially aligned probe with a 90-deg bend near the thermocouple junction. In this arrangement, the 90-deg section of the probe pointed into the oncoming jet stream, thereby eliminating the strong cross ow that was problematic for the straight probe. Analysis of data collected with the 90-deg probe revealed that this arrangement was biased to the mainstream ow. Where the straight probe was unrealistically cold in the ori ce region (biased to the jets), the 90-deg probe was unrealistically hot (biased to the mainstream). In both cases, the cross-stream uid tended to bias the measurement.
The second was an axially aligned probe with a 45-deg bend. The 45-deg probe results fell almost exactly between the two extremes. Mass balance closure testing of the 45-deg probe data set revealed that 100% jet mass addition was accounted for at the ori ce trailing edge. The differences between a shielded and a nonshielded thermocouple probe were also investigated. No differences were observed. Consequently, an exposed-junction, 45-deg thermocouple probe was used to acquire the entire data set reported herein.
Each of the ori ce optimization experiments involved the measurement of at least six planes of data. Several planes were concentrated in the ori ce region where the strongest thermal gradients were located. A limited number of only eight planes of data were acquired due to tradeoff between having enough mixing detail while keeping the time associated with each experiment to a reasonable length. The planes included x / R = 0, h/ 2, h, and 1 where x / R is the nondimensional downstream distance relative to the leading edge of the ori ce, h/ R is the ori ce axial length, and R is the mixer radius. Whereas the data at all of the planes provide the perspective of jet penetration and mixing, the x / R = 1 plane was selected for the detailed analysis of mixture fraction. The selection of this plane 1) corresponds to prior studies, and 2) corresponds to a location in practical systems where, due to hardware constraints, mixing must be complete.
In each plane, the data were taken in a region consisting of a twoori ce sector. If the two-ori ce sector was less than (greater than) 90 deg, then the grid was spatiallycompressed(expanded) so that the relative density of the measurements was preserved. The gridding scheme followed in this study for a 90-deg, two-ori ce sector is shown in Fig. 3. The central portion of the grid is composed of a Cartesian type of scheme employing equal y and z increments. Additionally,data points are arranged in an equal increment fashion along the initial and nal sector radial lines, as well as around the circumference of the sector.

Global Ori ce Optimization
On the basis of the results reported by Hatch et al. 5 and Kroll et al., 6 a Box-Behnken test matrix was established for this study. The previous studies were used to identify parameter ranges that would encompassthe optimal mixing geometry at a momentum-ux ratio of 40 and at a xed jet-to-mainstream mass-ow ratio of 2.5. Table 1 shows the variable settings for each case considered. Three parameters were varied: number of ori ces (n = 6, 8, 10, 12, and 16), slot aspect ratio (AR = 1, 3, 5), and slot angle (a = 0, 30, 60). The rst 13 experimentstabulatedin Table 1 are shown in Fig. 4. The Box-Behnken test matrix allowed the tting of nonlinearregression equations to the data while minimizing the number of required experiments. As noted, Fig. 2 details the mixer design used. In this study all of the ori ces had circular ends. Consequently, a slot with an AR of 1 was corresponded to a round hole. The operating conditions are T main = 212 ± F, T iet = 74 ± F, P = 14.7 psia, V main = 31.0 ft/s, M main = 0.090 lbm/s, mass-ow ratio = 2.5, density ratio = 1.28, and momentum-ux ratio = 40 J.
On completion of the data acquisition for the initial 13 cases in Table 1, the unmixedness was calculated at each plane. The measurements at the x / R = 1 axial plane were repeated to provide an estimate of experimental error for each of the initial 13 cases. A regression analysis was performed on the results to arrive at a model that quanti es U S as a function of the number of ori ces, the orice A R and the ori ce angle. The results of this regression analysis highlighted the need to conduct a second Box-Behnken test matrix to better re ne the response surface.
Cases 14-26 in Table 1 detail the second test matrix. This test matrix was identical to the rst except that the number of ori ces was 6, 8, and 10. This matrix was tested when analysis revealed that cases 1-13 were biased to underpenetration.Cases 14-26 were added to balance the results. When the measurementscorresponding to cases 14-26 were completed, a cubic model was t to the data sets and used to further understand the relationship between design parameters.

Analysis
The mixture fraction value is a measure of the degree of local unmixedness at a given point. Temperature measurements were made as a means of tracking the local mixture fraction. This was possible because the experiments were nonreacting. In an incompressible ow such as this, temperature is a conserved scalar; that is, no sourcesor sinks.Conservedscalarscan track other conservedscalars (e.g., local elemental mass fractions) in a nonreacting system. 10 The jet mixture fraction takes the following form when based on temperature: In this form, a value of f = 0 correspondsto the presence of pure mainstream ow, whereas f = 1 indicates the presence of pure jet ow. Complete mixing occurs when f approaches the equilibrium value determined by the mass-ow ratio f equil = MR/ (1 + h R) and temperatures of the jet and mainstream.
To quantify the mixing effectivenessof each mixer con guration, a spatial unmixedness parameter U S (Ref. 11) was de ned at each measurement and interpolated data plane: where f i is the average planar mixture fraction,a i is the nodal area at which f is calculated,and A = a i . Note that at planesdownstream of the trailing edge of the ori ce,f equals the equilibrium mixture fraction (0.715). Complete mixing is achieved when the U S across a given plane reaches zero. This parameter is based on Ref. 12.

Results
In addition to con guration speci cs, Table 1 lists the ori ce axial length, the percentage of ori ce blockage, and the spatial unmixedness for the 26 con gurations considered.The dimensionless ori ce axial length is expressed as the ratio of the axial projection of the ori ce h to the radius of the mixing module R. The percent blockage is expressed as a ratio of the total circumferential projection of the ori ces to the circumferential spacing between adjacent ori ces.
The normalized ori ce axial length h / R is a measure of the axial rate of jet mass addition. To illustrate its importance to mixing, consider two extreme cases, h / R = 1 and h / R ¼ 0. For the case where h / R = 1, the jet uid addition process is continuing right up to the mixing analysis plane at x / R = 1. The jet uid that passes through the trailing portion of the ori ce does not have the opportunity to mix with the main uid. This results in warm and cool spots in the analysis plane and can cause a correspondingly high mixture fraction variance. At the other extreme is the case where h / R = 0. This corresponds to the jet uid being added instantaneously, thereby having the entire residence time between x / R = 0 and 1 to mix with the main uid. Note that in both the six-ori ce case with A R = 5 and an angle of 30 deg, and the eight aligned slot case with A R = 5, the trailing edge of the ori ce (ori ce axial length) extends beyond one duct radii downstream of the leading edge. Also, in several other cases, the ori ce trailing edge is at an axial distance nearly equal to one duct radius. The smallest h / R (0.353) studied experimentally was the round hole case.
The percentage of ori ce blockage increases for an increasing number of ori ces and an increasing slant angle when the other variables are constant. A high aspect ratio design at a 0-deg ori ce inclination angle (aligned with the mixer's centerline) will have a large h / R and a small percentage of ori ce blockage. The opposite is also true.
As the percentage of ori ce blockage approaches 100, the jet ow approaches the point of appearing to completely inhibit the ow of the mainstream uid near the module wall. This can have the advantage of cooling the walls at the expense of allowing an undiluted core of main uid to pass through the mixer section, that is, underpenetration. Similarly, with an ori ce angle of zero, that is, no ori ce-induced swirl component, and as the percentage of ori ce blockage approaches zero, the jet penetration will be greater and a large portion of the walls will be exposed to undiluted main uid while the jets impinge on one another at the module centerline, that is, overpenetration. Slotted ori ce designs at ori ce angles 0 and 90 deg act as swirl vanes to the approaching main ow. In the consideration of jet penetration, the swirl component imparted on the main ow must be considered.

Mixture Fraction Contours at x/R = 1
The mixture fraction contour plots at an axial distance equal to one duct radius downstream of the ori ce leading edge are shown in Fig. 5 for the 16-ori ce case. Each case in Fig. 5 represents a twoori ce measurement sector that has been ori ce averaged. Similar gures for the 12-, 10-, 8-, and 6-ori ce cases are shown in Figs. 6-9, respectively. In these mixture fraction contour plots, each contour image is labeled with a numerical designator of the form: number/ aspect ratio/angle. For example, 16/3/30 signi es the 16-ori ce module at a A R of 3 and an ori ce slant angle a of 30 deg from the mainstream ow direction. In the contour plots, a mixture fraction value of 0 corresponds to pure main ow material, a value of 1 corresponds to pure jet ow material. Because an A R of one corresponds to a round hole, the performance of an A R = 1 mixer is independent of orientation angle. In the gures that follow, for convenience, the A R = 1 cases are associated with an angle corresponding to what the Box-Behnken test matrix would call for if the  All 4 of the 16 ori ce cases shown in Fig. 5 demonstrate underpenetrating jets. This is evident by the high mixture fraction values adjacent to the wall (blue) and low values on the mixer centerline (yellow). (If the jet penetrationwere balanced, a broad band of mixture fraction values containingthe equilibriumvalue of 0.715 would be present with a band of slightly lower or higher mixture fraction values near the mixer centerline and wall.) For the 16-ori ce case, the best value of unmixedness (closest to zero) is the 16/3/0 case, which is a slot aligned with the main ow. This is due to its having no induced swirl motion as do cases 16/3/60 and 16/5/30, and its having much less blockage than the 16/1/30 case.
As was seen with 16 ori ces, the 12-ori ce cases are largely underpenetrating(see Fig. 6). However, the mixing is, in some cases, much improved over the 16-ori ce cases. The 12/5/0 case is the most balanced case and has the lowest spatial unmixedness for the 12-ori ce cases. This, as was true for 16/3/0, results from a low blockage and no induced swirl because it is aligned with the main ow. The good mixing performance at one duct radius downstream is especially interesting given that the ori ce axial length extends close to the evaluation plane.
Of all of the cases considered, the 10-ori ce modules displayed the best mixing performance. In Fig. 7, only the 10/3/60 case displays signi cant underpenetration.This underpenetrationis highly correlated with the swirl induced by the steep ori ce angle. The sensitivity of mixing performance to blockage appears to be less important as the number of ori ces approaches the optimum number. In the better-mixed cases, only two color ranges are represented that are close to the equilibrium mixture fraction value (0.715). As was discussed by Kroll et al., 6 it can be seen that the optimum mean jet penetration depth falls between the half-area radius and the half radius as determinedby the radial location where the lowest mixture fraction is measured in the evaluation plane.
The eight-ori ce cases were the overlap condition between the two Box-Behnken test matrices discussed earlier. Therefore, more data planes are present than would be expected for either matrix alone. The seven cases are shown in Fig. 8. (Recall that the A R = 1 case is a round hole and is angle independent.) In the eight-ori ce cases, jet underpenetration, balanced, and overpenetration are evident. The steep ori ce angles still exhibit underpenetration likely due to the strong induced swirl. The no swirl cases, 8/5/0 and 8/3/0, show a tendency toward overpenetration. For eight ori ces, however, the greater blockage of the 8/1/angle-independent case improves the mixing. The 8/5/30, 8/3/30, and 8/1/angle-independent cases all showed excellent mixing performance that is equivalent to the ten-ori ce, good-mixing cases especially when considering the degree of case-to-case repeatability.
With six ori ces (Fig. 9), only the steep-angledslanted slot ori ce case 6/3/60 shows balancedjet penetration.The spatialunmixedness for this case is close to the best values measured in the 8-and 10ori ce cases. All of the other six-ori ce cases are overpenetrating and consequently display degraded mixing performance. In some cases the ori ce heights extend up to (6/3/0) and beyond (6/5/30) the evaluation plane.
Four repeat measurements were made for the eight round hole ori ce case. The repeatcases were representativeof the repeatability seen in all of the experiments. In general, the measured repeatability in the unmixednesswas on the order of 0.008. The cases that had the steepest gradients in the measured mixture fraction generally had the worst repeatability.

Linear Regression Analysis
To further generalize the results, a linear regression was performed on 63 valuesof area weightedvariancegeneratedfrom the 26 cases noted using the Rummage II (see Ref. 13) statistical analysis software. An interpolatingequation was created as a function of the three experimental parameters (n = number of ori ces, AR = ori ce aspect ratio, and a = ori ce slant angle). Insigni cant terms were eliminated from the model using conventional statistical methods. The regression model took into account that at an A R of 1, the result had to be angle independent. The regression data were scaled to remove any unnecessary ill conditioning due to the data ranges considered. The resulting equation is where The regressionequationhad a correlationcoef cient of 0.926 and an estimated standard deviation of 0.011. Although potential outliers were identi ed in the data set, no data were removed when tting the regression equation. Not removing the outliers resulted in 6 of the 63 data points accounting for 46.6% of the regression sum of squares error. Figure 10 shows the predicted values of U S as number of ori ces, ori ce AR, and ori ce angle are changed. Many of the observations made in the preceding gures (Figs. 5-9) can be more easily seen. First, only in the six-ori ce case is the steep-angled slot at a high A R an advantage. As the number of ori ces increases, the performance of the steep-angled slot at a high A R becomes more and more degraded. At a high number of ori ces, a zero-angled slot with a high aspect is the best. Second, the highly nonlinearrelationshipbetween the three controlled variables is evident. It was this highly nonlinear relationship that required introducing third-order cross terms into the correlation equation. Third, it appears that the optimum number of ori ces falls between eight and ten when the unmixedness is the optimizing parameter. Fourth, it is also evident that in the nearoptimum con guration,the ori ce A R is of lesser importanceas long as the ori ce angle is shallow. However, as emphasized in Refs. 1-3, a single parameter, such as U S , can help identify an optimum mixer, but must be examined in the context of the distributions.
The independence of ori ce A R when using shallow-angled orices at the optimum number of ori ces is better understoodby considering a contour plot for the nine-ori ce case shown in Fig. 11. In Fig. 11, two optimums are present. One optimum is at an A R of 1 and the second optimum is at an A R of 5 and an ori ce angle of 20. Given the uncertainty in the measurements (discussed earlier), one would expect equally good mixing performance at many combinations of shallow-angled slanted slots and A Rs. The existence of two optimums is also predicted in the 8-and 10-ori ce cases. When the ori ce number increases beyond 10, only one optimum is predicted at high A Rs and shallow angles. In an effort to verify the existence of two optimums, two additionalcases were considered:9/1/angle-independentand 9/5/22. The contour plots for these cases are shown in Fig. 12. The 9/1/angleindependent case demonstrated an experimentally derived spatial unmixedness of 0.013, which is close to the predicted value. The 9/5/22 case displayed greater jet penetration to the centerline than expected. This resulted in an experimentally derived unmixed-ness of 0.021, which is higher than the predicted value of 0.013. Because  the repeatability of the measurement of U S (as discussed earlier) is on the order of 0.008, the 9/5/22 result is within the uncertainty band. However, this experimental result for the 9/5/22 case is somewhat anomalous because the 10/5/30 and the 8/5/30 cases (see Figs. 7 and 8) both display balanced jet penetration. It is, however, possible that the nonlinearsensitivityof the interpolatingequation is not suf cient. Consider, for example, that the 8/5/0 case does display jet overpenetration.

Conclusions
This study focused on the relationship between number of orices, ori ce A R, and ori ce angle at a xed momentum-ux ratio (40) in a plenum fed cylindricalcan mixer. The mixture fraction eld at one duct radius downstream of the leading edge of the ori ces was measured experimentallyusing thermocouplesin a nonreacting ow eld. The mixture fraction elds as well as the spatial unmixedness values were used to assess mixing performance. A general interpolating equation was found using least-squares regression that was used to further elucidate the trends. The optimization experiments resulted in the following conclusions: 1) Mixture uniformity is a nonlinear function of the number of ori ces, the ori ce long-to-short A R, and the ori ce angle.
3) Optimum mixing occurs when the asymptotic mean jet trajectories at x / R = 1.0 are in the range of 0.30 < f / R < 0.5 (where f = R ¡ r ). 4) An optimum number of ori ces exists for a given momentumux ratio that minimizes the unmixednessvalue.Althoughan overall minimum for a given momentum-ux ratio can be established, a local minimum for a given number of ori ces occurs as well. Thus, the appropriate con guration may depend on given values of both the momentum-ux ratio and the number of ori ces. 5) When the optimum number of ori ces is exceeded,underpenetration is expected, and steep-angled slanted slots lead to extremely poor mixing performance, punctuated by degraded penetration. In this case, aligned slots that minimize the blockage without inducing swirl provide the best mixing performance.
6) At the optimum number of ori ces, the difference between shallow-angled slots with large A Rs and round holes is minimal and either approach yields good mixing performance. At the optimum number of ori ces, two local optimums can exist where one corresponds to a round hole and the second to a shallow-angled slanted slot. 7) When the number of ori ces is below the optimum number, overpenetration is expected with an advantage to having steepangled slanted slots at a high A R. In this case, the slot-induced swirl minimizes the degree of overpenetration. 8) Understanding how the number of slots, ori ce A R, and ori ce angle relate to one another provides a means to further address design issues as load changes in devices that rely on jet mixing as an inherent part of their operation.