## Abstract

Turbulent mixing in the near region of a round jet with three slot lobes is examined via mean velocity and turbulent statistics and structures at a Reynolds number of 15,000. The design utilizes separate flow motivations upstream of each geometric feature, deviating from conventional nozzles or orifice plates. Immediate outlet velocity profiles are heavily influenced by opposing pressure gradients between the neighboring round and slot streams. Spanwise mean velocity profiles reveal the majority of the convective exchange between a given slot and the round center occurs in the immediate near field, but has lasting effects on the axial centerline profiles downstream. This is also reflected by the velocity half-widths, exhibiting asymmetry across the entirety of available measurements. Centerline turbulence intensities exhibit strong and short-lived isotropy. The increasingly anisotropic intensities found downstream are lower than similar geometries from the literature, implying that mixing development is inhibited. Reynolds stresses at the round-slot interface are significantly smaller than the round-stagnant exchange, but achieve a symmetric condition at $x/D ≅$ 4. Two-point spatial correlations of the fluctuating streamwise velocity exhibit stronger dependence toward the axial centerline at the round-slot interface in comparison to the nominal round radius. In contrast, spanwise velocity fluctuations exhibit nearly identical, localized behaviors on each side of the jet. Corresponding differences in streamwise integral length scale peak in the range 1.0 ≤ $x/D$ ≤ 1.5, and so too do the turbulent structures in this area, as a result of the collated jet geometry.

## 1 Introduction

Turbulent jets and higher order statistics describing the underlying flow physics have been a topic of significant importance for many experimentalists from both an isothermal [14] and nonisothermal perspective [59]. It would be difficult to overstate the value that these and many other experimental studies on jets have provided in terms of fundamental insight into turbulence as well as important data to help guide modeling efforts. However, conditions in realistic scenarios are far removed from the ideal conditions of a free turbulent jet, which has prompted numerous studies considering the effects of nozzle geometry [8] or initial conditions [9], and their impact on far-field metrics or the rate at which a self-similar behavior is reached. For these and other applications, there is a need to conduct additional experiments to consider increasingly more complex types of jets in order to better bridge the gap between purely fundamental and application-driven conditions. Such a scenario exists in the nuclear industry, where designs of next generation reactors require higher fidelity predictive capabilities for reactor safety simulations, and the desired depth of a physics-based knowledge warrants more than only the foundation of fundamental turbulent jets. This application is the motivating drive behind the current experimental study.

The prismatic high temperature gas reactor is one of multiple nuclear reactor concepts under consideration for the U.S. Department of Energy's Next Generation Nuclear Plant project [10,11]. The design employs helium as the coolant medium with temperatures up to 1100 K [12]. Within the core, coolant flows downward in hundreds of circular channels through a series of graphite hexagonal blocks. These channels are combined to form dozens of jets issuing into the lower plenum. Gaps between the graphite blocks and the flow traveling through them complicate predictability of mass flow rate distributions [13]. A potential consequence of these flow physics is the production of unwanted thermal stresses. Further experimental and computational efforts are needed in order to more fully address this impact. A primary contribution of this work is to experimentally consider turbulent mixing with a higher degree of complexity above and beyond previous works [14]. A secondary contribution is to provide validation data for computational fluid dynamics efforts and help further assess the usefulness and claims of existing computational studies on this topic [13,15,16].

In order to make these contributions, the experiments here focus on a circular jet with rectangular-shaped extensions and complex upstream mixing conditions leading to the unique nozzle depicted in Figs. 1(c) and 2(c). Although this would be considered a nonstandard nozzle, it is useful to cast this flow scenario against the backdrop of jet related efforts over the past number of decades focused on turbulent mixing enhancements available with modified jet nozzles. An excellent review of this topic still pertinent today is from Gutmark and Grinstein [17]. For incompressible flow at moderate jet Reynolds numbers, the more recent studies by Mi and Nathan [18] and Aleyasin et al. [19,20] are worth noting. Among the various nozzles considered, these and other authors [2124] investigated the impact of lobes at evenly spaced locations around the jet circumference. Although one typically only sees an even number of lobes (2, 4, etc.) in those and related studies, it is useful to compare their impact to that of the three rectangular slots in this study. While the actual nozzle geometry of this work is not represented in these or other previous studies, the ultimate application is one of turbulent mixing (as in the case in Refs. [1820]), and therefore, the flow physics of interest there are of interest here as well.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

For experimental data in this study, constant temperature anemometry (CTA) and constant current anemometry (CCA) techniques provide velocity and temperature measurements, respectively, at the nozzle. Time-resolved particle image velocimetry (TR-PIV) measurements provide the instantaneous velocity fields produced by the collated jet and are used to derive ensemble-averaged first- and second-order statistics, as well as the turbulent structures.

## 2 Experimental Methodology

### 2.1 Experimental Setup.

The complex features of the nominal round and secondary bypass (rectangular slot) channels are reduced to a laboratory-grade geometry, representing a unit cell of the repetitive full scale flow physics expected in target application. It is important to note that the multiple jets in the full scale application are in close proximity and that each jet would be influenced by its neighbors. However, in order for future efforts to confidently quantify those interactions, this study provides the much needed baseline characteristics. An illustration of the fluid domain is provided in Fig. 1, where the round and slot channels are separate inlets at the top surface (see Fig. 1(b)). The distinct channels mix together to form a collated flow consisting of a single round outlet superimposed with the geometry of the slots (see Fig. 1(c)).

The laboratory-grade design is provided in Fig. 2, and consists of four inlet lines: three for the round channels and one for the slot channels. Similar to the conceptual illustration in Fig. 1, these four inlets are independent at the top of the device (see Fig. 2(b)) and are coerced to form the desired collated geometry at the outlet (see Fig. 2(c)). Referencing Fig. 2(c), the collated jet has a nominal round diameter of $D$ = 50.0 mm and an equivalent diameter ($De=2area/π$) of 59.16 mm. The origin is located at the center of the collated jet nozzle. Impractical for conventional machining methods, the entirety of the design is three-dimensional printed using Polyjet FullCure 810 VeroClear (Stratasys, Rehovot, Israel). Outer walls and proper gasketing (not pictured) complete the leak tight design. This work investigates the free jet formation from the nozzle of the coerced flow passage. As such, only key features of the design are presented here. A full disclosure of the upstream flow conditioning and device channel dimensions are presented in the Appendix.

As part of the current free jet configuration, the collated jet issues into the top surface of a rectangular test section as illustrated in Fig. 3, with dimensions of 21.4$D$, 14.8$D,$ and 15.0$D$ in the streamwise ($x$), spanwise ($y$), and lateral ($z$) directions, respectively. The test section provides a sufficiently large domain to ensure a free jet configuration, i.e., the jet is unperturbed by the surrounding ambient fluid medium in the measurement regions, and has the additional advantage of confining the seeder particles, discussed further in Sec. 2.3. The test section is composed of 9.525 mm polycarbonate walls, well suited for optical viewing access. The round outlet is centrally located on the bottom of the test section and has a diameter of 50.80 mm. The outlet returns the flow to the control system, completing the closed-loop system. As depicted in Fig. 3(b), this system consists of three independently controlled lines that supply air to the pipelines feeding the unit cell device. Performance details for the flow control system are provided in Ref. [25]. In reference to Fig. 2(b), the $y+z0$ and $y0z0$ inlets incorporate two of these lines. A manifold splits the remaining third line to accommodate the $y−z+$ and $y−z−$ inlets.

Fig. 4
Fig. 4
Close modal

Considerable preliminary effort was undertaken to ensure that an isovelocity condition is achieved between all four inlets depicted in Fig. 2(a). The individual and manifold configured pipelines were calibrated on separate occasions by directly mounting each to the rectangular test section, without the presence of the opaque collated jet assembly. Velocity data were then collected via planar PIV providing first- and second-order flow statistics of the two component velocity fields. Taking advantage of the axisymmetric profiles, the average velocity, mass flow rate, and kinetic energy ($k=∑i=1234Ui−Ui2$) were determined with respect to settings on the flow control system. The velocity profiles found were nearly parabolic, and scaled well across a wide range of flow rates when normalized by their respective bulk velocities. All bulk parameters are calculated according to the spatially integrated mean of their respective profiles at the nozzle exit ($x$ = 0), i.e., $Ub(y)=∫U(y)dy/∫dy$. It is recognized that the stagnant pressure within the enclosure changes when including the collated jet assembly in the flow paths. However, these quantities can still be used with confidence based on conclusions reached from the scaling analysis of the calibration data. The outcome of these preliminary calibrations constitute the momentum parameters in Table 1.

Table 1

Experimental test parameters

Uncertainty
MetricUnitsNominal valueTotal $ui$Systematic $bi$Random $si$
Geometry
Tube diametermm22.2250.4570.4570
Tube lengthmm609.61.01.00
Jet diameter, $D$mm502.0 × 10−72.0 × 10−70
Momentum
Pipe bulk inletm s−1, (m2 s−2)
velocity estimates
(T.K.E. estimates)8.71, (0.36)
$Uy0z0$, $(ky0z0$)8.70, (0.31)
$Uy+z0$, ($ky+z0$),8.52, (0.23)
$Uy−z+$, ($ky−z+$),8.99, (0.40)
$Uy−z−$, ($ky−z−$)
Jet bulk velocity, $Ub$m s−14.79
Energy
Jet bulk temperature, $Tb$K302.83
Ambient temperature, $Tamb$K295.410.860.850.14
Fluid properties
Density, $ρ$ [26]kg m−31.1710.0040.004
Dynamic viscosity, $μ$ [26]kg m−1 s−11.86 × 10−51.4892 × 10−71.4892 × 10−7
Thermal conductivity, $k$ [27,28]W m−1 k−10.02662.66 × 10−32.66 × 10−3
Specific heat, $cp$ [29]J kg−1 K−11005.17
Pressure gage, $Δp$Pa−5.1060.7830.4820.617
Ambient pressure, $pamb$kPa101.7945.3875.3850.166
Relative humidity, $ϕamb$%37.9653.8312.6932.725
Nondimensional properties
Reynolds number, $Re$, nominal $D$ (equivalent $D)$15,000, (18,000)
Prandtl number, $Pr$0.703
Uncertainty
MetricUnitsNominal valueTotal $ui$Systematic $bi$Random $si$
Geometry
Tube diametermm22.2250.4570.4570
Tube lengthmm609.61.01.00
Jet diameter, $D$mm502.0 × 10−72.0 × 10−70
Momentum
Pipe bulk inletm s−1, (m2 s−2)
velocity estimates
(T.K.E. estimates)8.71, (0.36)
$Uy0z0$, $(ky0z0$)8.70, (0.31)
$Uy+z0$, ($ky+z0$),8.52, (0.23)
$Uy−z+$, ($ky−z+$),8.99, (0.40)
$Uy−z−$, ($ky−z−$)
Jet bulk velocity, $Ub$m s−14.79
Energy
Jet bulk temperature, $Tb$K302.83
Ambient temperature, $Tamb$K295.410.860.850.14
Fluid properties
Density, $ρ$ [26]kg m−31.1710.0040.004
Dynamic viscosity, $μ$ [26]kg m−1 s−11.86 × 10−51.4892 × 10−71.4892 × 10−7
Thermal conductivity, $k$ [27,28]W m−1 k−10.02662.66 × 10−32.66 × 10−3
Specific heat, $cp$ [29]J kg−1 K−11005.17
Pressure gage, $Δp$Pa−5.1060.7830.4820.617
Ambient pressure, $pamb$kPa101.7945.3875.3850.166
Relative humidity, $ϕamb$%37.9653.8312.6932.725
Nondimensional properties
Reynolds number, $Re$, nominal $D$ (equivalent $D)$15,000, (18,000)
Prandtl number, $Pr$0.703

Table 1 also incorporates several reference measurements, collected in tandem with either the nozzle outlet or downstream experimental test measurements themselves. The jet bulk temperature is provided by CCA measurements discussed in Sec. 2.2. Test section gauge pressure is collected alongside these measurements and are provided by an Omega PX409-2.5CGUSBH compound gauge pressure transducer (Omega Engineering, Norwalk, CT) sampled at 1 kHz for 5 s. Ambient temperature is measured using a type T thermocouple with crushed ice bath reference point and a National Instruments 9213 acquisition unit. Ambient pressure and relative humidity are collected using an Apogee SB-100 barometric pressure sensor (Apogee Instruments, Logan, UT) and Omega model HX93BDV1 relative humidity transmitter, respectively. Both of these devices employed a National Instruments NI9205 voltage acquisition unit. All ambient readings are sampled at 100 Hz for 5 s during the six repeatable experimental trials discussed in Sec. 2.3. These reference quantities allow calculation of additional fluid and nondimensional properties, also depicted in Table 1. Extensive uncertainty quantification is provided for each sensor type or from referenced correlations which constitute the systematic uncertainty contributors. Repeatable trials make up the random contributions of uncertainty according to the students t-distribution with 95% confidence. The systematic and random components of uncertainty are then combined in a root mean sum of the square to form the total uncertainty in the quantity of interest. This table was designed with future computational validation efforts in mind and incorporates the appropriate standards put forth by Oberkampf and Smith [30] and ASME [31].

### 2.2 Anemometry Measurements.

Anemometry measurements provide velocity and temperature profiles at the nozzle outlet ($x$ = 1 mm), and utilize a hot (CTA circuit) and cold (CCA circuit) wire, respectively. The sensors are Dantec 55P16 single wire probes each consisting of a 5 μm tungsten wire sensor that is 1.25 mm in length. The CCA signal conditioning unit is an A.A. Labs AN-1002 (A.A. Labs Ltd., Kennett Square, PA) including a 15 mA input current, $×$1 decade range, 4.18 $Ω$ probe resistance compensation, and −9.0 V DC offset. The CTA circuit consists of a Dantec Dynamics MiniCTA 54T30 signal conditioner (Dantec Dynamics, Skovlunde, Denmark) with a wire temperature of 523.15 K and an overheat ratio (ratio of wire hot resistance to wire ambient resistance) of 1.83. A National Instruments NI 9215 acquisition unit records the signals from both circuits.

It is well known that CTA velocity measurements are strongly influenced by temperature differences between the ambient fluid during calibration and during testing; thus, the CCA temperature measurements' purpose is twofold. The CCA measurements provide an assessment of the temperature uniformity at the nozzle outlet, but also serve as a colocated ensemble-averaged reference fluid temperature for CTA voltage correction. The cold wire is calibrated against a platinum resistance thermometer in an automated Isotech Calisto Temperature Calibrator to produce a linear curve fit. CTA calibrations are performed at room conditions with an ambient temperature of 295.15 K. Frictional heating from the skid system produces steady-state fluid temperatures that are in excess of the ambient temperature condition (see Table 1). Several calibration methods were investigated to determine a suitable relation between CTA voltage and velocity. Bruun [17] broadly categorizes CTA calibrations in three groups: corrected voltages methods, nondimensionalized methods, and the direct calibration method. The direct calibration method provides the most accurate (and demanding) result, but in the absence of active heat control (a constant flow rate heat exchanger is utilized downstream of the test section), is deemed impractical for this work. Thus, three corrected voltage methods and one nondimensional voltage method were investigated. The corrected voltage methods include the fourth order polynomial relation of George et al. [18], power law relation of Bearman [19], and the heat transfer compensated method of Bruun [17]. It should be noted that the proposed relations of the first two methods employ the voltage correction of Kavence [20]. The nondimensionalization method is that of Hultmark and Smits [21] with the recommended fluid property correlations of Smits and Zagarola [22]. From comparison with the available PIV data, it was found that the power law method of Bearman [19] showed the most agreeable velocity profiles. The CTA and CCA probes have undergone six and twelve repeatable trials, respectively. Systematic uncertainty for both probes considered the calibrator accuracy, calibration curve fits, and data acquisition unit (National Instruments, Austin, TX) accuracy and resolution. The random component of uncertainty was determined according to the standard uncertainty in the mean for the one available trial for each of the three radial traces. The random component is thus much smaller than the systematic in this instance. The total uncertainty in the CTA and CCA measurements are found to be $±0.$39 m/s and $±$0.11 K, respectively.

The adjacent cold and hot wire probe stems are mounted axially with the streamwise flow ($x$-direction) and have a center-to-center distance of 4 mm. The probe wires are aligned with the radial length of each slot, consisting of three separate outlet measurements along the $y$ (0 deg), $y+z+$ (120 deg), and $y+z−$ (240 deg) locations. The probes are mounted on a Velmex Bi-Slide 3-axis linear stage setup (Velmex, Bloomfield, NY) inside of the test section with a straight-line accuracy of $±$0.076 mm over the entire travel distance of each stage and a repeatability of $±$0.005 mm. The probes are traversed carefully along a given slot's centerline length. These traces constitute the entirety of the outlet, starting just past the radial edge of the round portion of the jet and ending just past the outer edge of the respective slot. The probes are triggered simultaneously with a sampling rate of 10 kHz for 5 s at a given measurement point with 5 additional seconds of settling time between probe movements to dampen any vibrations. Before any outlet measurement is collected, the flow control system first reaches a steady-state condition, requiring a 140 min settling time between control input and data acquisition. Section 2.3 follows this same procedure.

### 2.3 Particle Image Velocimetry.

TR-PIV measurements capture the instantaneous velocity fields of the collated jet. The TR-PIV setup, originally displayed in Fig. 3(b), consists of two high-speed cameras positioned in front of the test section with a laser sheet illuminating the $xy$ plane at $z=$ 0. The cameras are Phantom Miro M120's (Wayne, NJ) with a 12 bit dynamic range and maximum resolution of 1920 × 1200 pixels. Each camera is outfitted with a Nikon AF NIKKOR 50 m f/1.8D lens (Nikon, Melville, NY) and a LaVision, Inc., 527 nm lens filter with 10 nm bandpass and 70% transmission efficiency. The laser sheet is generated by a Photonics Industries DM30-527-DH laser (Photonics Industries, Ronkonkoma, NY) with a maximum power of 60 mJ/pulse at 527 nm and a laser sheet thickness of approximately 1.0 mm. The flow is seeded just upstream of the mixing assembly with Dioctyl Sebacate (Sigma Aldrich, St. Louis, MO) using a TSI Six Jet Atomizer Model 9306 (TSI Incorporated, Shoreview, MN) with two of the seeder jets utilized. The two cameras are mounted on a linear stage that traverses in the $x$-direction, providing four separate viewing positions, from the collated jet outlet ($x/D=$ 0) and ending in excess of 8$D$ downstream. Measurements are taken at 1 kHz for 2.562 s with a viewing window of 1024 × 760 pixels for each position. Six repeatable trials are conducted across all four positions. This configuration provides a reasonable tradeoff between sampling rate, capture time, and measured spatial area for the desired flow measurements.

The high-speed images are processed using lavisiondavis 8.4.0 software. Preprocessing includes an image subtraction filter using the ensemble-averaged intensity across all images to reduce background noise. Vector processing utilizes the sliding sum-of-correlation algorithm with a time filter length of +/6 images (Gaussian weighting) to ensure seeding particle displacements are in the neighborhood of 4–6 pixels for each image pair. As a result, 2550 velocity fields are computed. Velocity vectors are computed using the stereo cross-correlation with an initial 64 $×$ 64 pixel window, square 1:1 weighting, and 75% overlap for two passes. This is followed by a 32 × 32 pixel window, with an adaptive PIV grid, and 75% overlap for four passes. The adaptive PIV grid changes the interrogation window and size automatically to optimize local seeding density and flow gradients, achieving increased accuracy in results at the expense of additional computational time. As a result of the stereoscopic configuration, image correction is also implied and the high accuracy mode for the final pass is also enabled. Postprocessing removes any erroneous vectors and includes an allowable vector range of $U$ = $Ub,i±Ub,i$ and $V=0±$0.5$Ub,i$ where here, $Ub,i$ is the “initial” estimate of the bulk outlet velocity determined by the processed vector fields. Ensemble-averaged statistics and all other quantities of interest are determined from the postprocessed vector fields.

A consortium of experts in the field [32,33] compared four promising TR-PIV uncertainty methods against a simple jet experiment. The experiment employed two separate TR-PIV systems (LaVision Inc., Ypsilanti, MI), a test system (in question) and a high dynamic range system (significantly higher accuracy) in tandem with anemometry measurements to assess the uncertainty of the test system. The authors concluded that the correlation statistics method of Wieneke [34] provides the optimal uncertainty treatment for ensemble-averaged quantities. As such, the correlation statistics method is utilized to assess the systematic uncertainty of the ensemble-averaged velocities. Standard convention for the systematic uncertainty of propagated statistics, such as the root-mean-square (RMS) and Reynolds stresses, is still the subject of ongoing debate [35,36] and is thus omitted from the current results. The random uncertainties for each TR-PIV metric are calculated as discussed in Sec. 2.1, where here each vector position is essentially a probe assessed via the student's t-distribution with 95% confidence and six repeatable data sets available. Total uncertainties in the ensemble-averaged velocity components are calculated according to the root sum of the squares of the systematic and random contributors, while propagated uncertainties for the RMS velocities and Reynolds stresses are explicitly based on the random uncertainty in the measurements only.

## 3 Results

### 3.1 Boundary Conditions.

Measurement locations at the jet exit are depicted in Fig. 4(a) with corresponding ensemble-averaged velocity and temperature profiles presented in Figs. 4(b) and 4(c), respectively, for each of the radial slot lengths. Note that each curve is provided in the range −1.32 < $r/D$ < 0.5, where $r$ is the distance from the origin along the individual trace with a negative direction toward the slot. Therefore, $r/D=0$is the origin and a common point for all three traces, and $r/D$ = 0.5 represents the edge of the round jet domain opposite that of a particular slot. The length of each slot is 41.24 mm, which explains the leftmost bound in Figs. 4(b) and 4(c) since $y/D=$ −1.32.

Fig. 5
Fig. 5
Close modal

For a symmetric velocity condition, one would expect the velocity profiles in Fig. 4(b) to be identical. Although qualitatively this seems to be consistent with those expectations, there is also a clear offset between the three curves. While it is not surprising to see some amount of asymmetric flow distribution, the offset in this case is mostly credited to the uncertainty of the hotwire measurements which is calculated as $±$0.39 m/s. Further evidence that the measurement error explains the observed offset is realized when analyzing the points at $r/D=0$ for each curve. Since the hotwire probe would be in an identical location for these three points regardless of $θ$, the difference is best attributed to the measurement error. By comparison, there is less than a 1 K difference in temperature at that same point for the coldwire measurements (see $r/D=0$ in Fig. 4(c) for each curve), which is likewise within the uncertainty of that probe.

From Fig. 4(b), it is clear that the average velocity in the slot region is lower compared to that in the round jet region. This is not surprising given the fact that the flow would naturally gravitate to the path of least resistance in the center. But to provide more meaning to the velocity disparity that is observed, we first recognize that two limits exist to assess the measured distributions against expectations that fall out of the analysis from those two limits. First, under the assumption of very long channels where fully developed internal flow can be realized, the mass is expected to roughly distribute according to the area of each region. For the flow geometry at the $x$ = 0 plane (see Fig. 4(a)), the three slots represent 28.6% of the total flow area while the circular jet in the center accounts for 71.4%. The ratio of these two values would approximate the ratio of the average velocities in those same regions which yields 71.4/28.6 = 2.50, meaning the average velocity in the center region would be two and a half times higher than that in the slot channels. The other bounding case would be to assume zero mixing between the group of three round channels and that of the rectangular slot. Obviously a portion of the slot channels is swallowed up by the bulk flow in the center well before reaching the $x$ = 0 plane, but if all other avenues of mixing were somehow eliminated, then the center region would be comprised of flow from 3.37 of the 4 inlets. Given the fact that all four inlets supply approximately equal mass flow, then the ratio of average velocity in the center circular region to that in the slot region is expected to be 3.37/(4.00 − 3.37) = 5.35, which is more than twice as large as that found from fully mixed assumptions. After approximating mass flow in the slot versus the center jet region using average velocities shown in Fig. 4(b), a ratio of 2.82 is found. Clearly, the flow physics are more accurately depicted with a fully developed assumption (i.e., 2.82 is much closer to 2.50 than 5.35). This is an important preliminary finding in that it suggests the complex mixing within the assembly could be reasonably approximated by taking $x$ = 0 to be the condition of a fully developed profile.

Fig. 6
Fig. 6
Close modal

A similar conclusion can be reached when analyzing profiles of additional traces in the slot but orthogonal to those from Fig. 4, which are found to be near parabolic for locations between $r/D$ = −0.5 and $r/D$ = −1.0. The effective Reynolds number of the slot is roughly 1.6 × 103, which is inside a laminar flow regime, validating the expectation of a parabolic profile. For reference, the Reynolds number of the jet region is approximately 1.4 × 104. With that information, it may also be helpful to consider the mixing under investigation as that from a laminar (slot) and turbulent (jet) flow. If the collated jet is considered, then the hydraulic diameter is found to be 27.18 mm resulting in a Reynolds number of approximately 7.1 × 103, not as clearly turbulent as the independent jet, but well outside of the laminar regime. Alternatively, if the collated nozzle Reynolds number is quantified according to typical nozzle studies, i.e., using the equivalent diameter, then the result is $Re$ = 1.5 × 104, notably within the range of experiments considered in Refs. [1820]. It is also important to note that interaction between these two regions does indeed exist. When considering the trends in Fig. 4(b) near the outermost edge of the slot geometry, the velocity is seen to increase slightly for all three profiles (e.g., compare points at $r/D$ = −1.2 and $r/D$ = −0.9). Frictional losses are expected to be greater for the slot flow, and therefore at the interface between these two regions, the flow leaving the slot would then be expected to entrain additional flow from the slot to follow suit. But this pull and entrainment become weaker the further into the slot one is considering the flow. Based on the experimental data, this then reaches a condition where the slot flow is even repelled to the idea of being entrained radially inward, a reasonable explanation of the increase in velocity observed in that region.

From a temperature perspective (Fig. 4(c)), it is also worth noting that nearly uniform profiles are seen, except for regions in each slot. This is most likely due to the fact that no insulation is applied to the outside surface of the mixing assembly. Thermal energy would be lost to the room since the temperature of the surroundings is approximately 295.15 K. The flow furthest from the center would be most prone to that effect, as is clearly the case. For dedicated nonisothermal flows, this heat loss to the surroundings should be quantified, or more ideally, reduced to negligible levels with thick insulation. For the investigations in this work, the desired isothermal conditions are adequately reflected by the temperature data measured.

### 3.2 Mean Velocities.

The ensemble-averaged streamwise velocities are presented in Fig. 5, and are normalized by the bulk outlet velocity, $Ub$, determined from the TR-PIV results. From the ensemble-averaged vector field, streamwise velocity traces are compared immediately at the jet outlet to determine the most suitable upstream profile, in this instance, at $x/D$ = 6.02 mm. A no-slip condition is applied to the coordinates that constitute the edges of the jet, and the profile is then spatially integrated to provide the bulk velocity, $Ub$ = 4.82 m/s. While we acknowledge this is not the overall mean velocity at the outlet, the trends discussed are independent of the velocity chosen for normalization (note that a similar conclusion was made in Ref. [18]). Ensemble-averaged velocity contours at each camera position are presented in Figs. 5(a)5(d). In position 1 (Fig. 5(a)), the round and slot regions of the collated jet are distinctly visible. The bulk of the slot flow appears to be quickly absorbed into the main jet flow within a few diameters downstream. This is consistent with mixing behavior expectations between a laminar and nonlaminar flow [37], namely, that the turbulent kinetic energy of the nonlaminar flow very quickly dominates the mixing region and removes traces of the laminar flow that existed upstream. This does not, however, erase the impact of the rectangular lobe. The impact of the slot from the nozzle is still felt much further downstream, as evident when comparing the shear layer development on either side of the center round jet. The $y+$ spreading agrees with expectations for a single jet (nonslot side), but appears to be reducing in thickness on the opposite side until $x/D$ = 4. The shear layer thickness then seems to be more or less constant until approximately $x/D$ = 6 when it finally begins to grow. The impact of this asymmetric shear layer growth enables the bulk jet flow near the slot side to maintain a higher velocity further downstream. This ultimately ends up bending the jet toward the slot region and is more evident the further downstream the flow field is analyzed.

Fig. 7
Fig. 7
Close modal

These features of the flow are perhaps more clear when analyzing the trends in Figs. 6(a) and 6(b), where line traces are provided for $U$ and $V$, respectively, for multiple downstream distances. For the $U$ profiles in Fig. 6(a), the $y+$ side shows behavior similar to that of a more standard jet, namely, the shear layer increases in thickness with downstream distance. The $V$ profile at $x/D$ = 1 (top curve of Fig. 6(b)) reveals negative velocities for $y/D ≳$0.6 due to the strong entrainment effect of the shear layer pulling the surrounding air into the jet. This negative $V$ region on the round jet side of the profile drifts away from the jet center and disappears by $x/D$ = 4. It is worth noting that the entire $V$ profile at $x/D$ = 8 starts to take the form expected for a standard jet with negative values of $V$ on one side and positive on the other. It is also worth noting the $V$ signatures on the slot side of the profile. At $x/D$ = 2, there is a significant portion with negative values, revealing that flow is being pushed away from the jet center over that region. These values coincide with the outer radius of the slot lobe ($y/D=$ −1.32) and its effective shear layer. This development quickly dissipates further downstream, in which the conventional slot flow is broken up by higher energy flow toward the center round jet. Turning attention back to the $U$ profiles in Fig. 6(a), it is evident that although a self-similar condition would likely be reached with further downstream progression, that scenario is not present by $x/D$ = 8. This is not surprising considering a self-similar region is not achieved at this location in other jet studies (e.g., for all the nozzles represented in Ref. [19], this occurred well beyond $x/D$ = 15). Results in Fig. 6(a) also help to quantify the drift of the peak velocity in the $y−$ direction. This shift at $x/D$ = 8 is found to be roughly 0.2 units. For reference, this results in an angle of approximately 1.4 deg from the $x$-axis. While there exists the possibility of slight misalignments in the assembly with respect to the rectangular enclosure, great care was taken to ensure this effect would be minimal using a digital level on the test section, as well as the PIV camera mounts, and a simple frame rotation of the data could not adequately address this feature. There also is the potential issue of flow mal-distribution in the three rectangular slots. In other words, if flow through one was significantly lower or higher than the others, an asymmetric result would be expected. This was not the case however, when accounting for hotwire measurement uncertainties. It is worth noting the drift in peak velocity was also observed by Aleyasin et al. [19], but only for a triangular shaped nozzle. Of the eight nozzle geometries they tested, seven were symmetric about two axes, while the triangular shaped nozzle had symmetry about only one axis, a feature shared with this work. Their domain included measurement locations much further downstream than this work, and revealed that the peak velocity eventually recentered beyond $x/D$= 10. While Mi and Nathan [18] also considered triangular nozzles, their analysis did not include reporting spanwise profile measurements. Therefore, discussing the drift against their data is not applicable.

Fig. 8
Fig. 8
Close modal

The drift of the peak velocity in the $y−$ direction can also be observed when analyzing the velocity half widths of the jet as they progress downstream. The half-widths are defined according to the radial location where the velocity field reaches half of its centerline value. Half-widths on each side of the jet are shown in Fig. 7 in comparison to the PIV results of Aleyasin et al. [20]. Regarding the slot half width ($y0.5Um−)$, the drastic attenuation of the slot flow is seen to occur within the range of 0 < $x/D$< 2.5 and then exhibits a spreading rate similar to that on the round jet side though at notably higher magnitudes. Interestingly, the round half width ($y0.5Um+)$ is smaller in value and spreading rate than the round jet from Aleyasin et al.'s study. This is most likely explained by the out of plane interaction with the two additional radial slots, located equidistantly 60 degfrom the $y+$ axis, that appear to inhibit growth of the $y0.5Um+$ spreading rate compared to the conventional round jet.

Fig. 9
Fig. 9
Close modal

Figure 8 displays the axial centerline velocity profile provided by each of the four separate camera positions. Note the results are normalized in this case by the equivalent diameter ($De$ = 59.16 mm for our geometry) to be consistent with other studies. The centerline profiles of each position were carefully appended without overlapping, and as such, are still indicative of the true measurements from each frame. These appended intersections are still subject to some level of scrutiny in smoothly describing the flow. Falchi and Romano [38] have provided excellent insight into the limitations found for high speed PIV measurements in accurately depicting the axial profiles of turbulent jets. As described by the authors, the mean profile suffers from vertical discontinues in higher order statistics as a result of time resolved measurements not being effectively independent, i.e., high sampling rates in short time intervals. Thus, the axial velocity profile exhibits vertical bands that prevent a smooth profile as seen in slower sampling methods, i.e., conventional PIV or CTA. The uncertainty quantification of the velocity fields, as described in Sec. 2.3, is included here to aid in these limitations.

Fig. 10
Fig. 10
Close modal

In Fig. 8(a) the profile is nondimensionalized according to the centerline outlet velocity for comparison to the PIV experiments of Hu et al. [39]. Though comparison is limited to the immediate near field region only, the collated jet behavior agrees well with the round jet of Hu et al. and has a starkly different development than the six lobed jet. From $x/D$= 4 onward, the collated jet profile takes on a more linear relationship comparable to the well-reviewed classical round jet. Despite significant differences in the onset location of linear decrease, the slope of Hu et al.'s six lobe jet is markedly similar to the collated jet. Figure 8(b) nondimensionalizes the profile according to the bulk velocity, where this normalization is inverted in accordance with typical investigations of this type. The CTA results of Madjid et al. [8] are plotted here for comparison. Interestingly, the collated jet provides better agreement with the four and six lobe jets of Madjid et al. and is again also favorable with their round jet. Both Hu et al. and Madjid et al. incorporated smooth, six lobed nozzles with relative 60 deg separation. As is evident here, the collated design fits somewhere within the wealth of orifice and nozzle geometries available, while still providing unique mixing effects of its own.

### 3.3 Turbulence Intensities.

The centerline RMS velocities are shown in Figs. 9(a) and 9(b) for the streamwise and spanwise fluctuations, respectively. When nondimensionalized by a characteristic jet velocity, they are also referred to as the turbulence intensities of the velocity components. Comparisons to the literature draw from several different jet configurations, including both orifice plates [8] and nozzles [19] measured by CTA/CCA wire probes and PIV, respectively. From Fig. 9(a), the evolution of $uc′$ begins with an initially constant magnitude up until $x/De≈$ 3 before experiencing a significant rate of increase. Past this location, the collated jet's growth rate fits neatly between the round and daisy nozzle configurations of Aleyasin et al. [19]. It is also interesting to consider the lobed jet orifice plate results of Madjid et al. [8] in this discussion. For $x/De>$ 4, the growth rate of streamwise turbulence intensity is nominally equal between the daisy nozzle and the 4- and 6-lobed nozzles, even though the latter two were at much lower Reynolds numbers. Of course, the onset of the intensity increase varies between these studies, but it is worth noting that nozzle geometries from the same family share common characteristics. The rate of increase for the present three lobed jet is slightly higher compared to data from lobed or daisy nozzles. In fact, it is almost as high as the round jet data in the same figure, suggesting these fluctuations are not heavily influenced by the three slots.

Fig. 11
Fig. 11
Close modal

The spanwise RMS fluctuations are shown in Fig. 9(b), and unlike their streamwise counterparts, no longer fall between the round and daisy nozzle data. The $vc′$ component experiences a much more gradual growth rate compared to these other nozzles. This can be explained by analyzing what is termed a “pipe jet” [40]. There are two significant differences between a smooth contraction nozzle and that of a straight pipe. First, downstream of the nozzle, the spanwise fluctuations are noticeably smaller for the pipe jet, while the streamwise fluctuations are fairly consistent between both nozzles, and this is observed as far downstream as $x/De$ = 30 [41]. The second difference is that the turbulence intensity is higher at the nozzle for a pipe jet compared to a smooth contraction or even an orifice plate [6,7]. Therefore, it is not surprising that near the outlet, the current data exhibits higher fluctuations in both directions compared to the other nozzle data taken from the literature. In comparing both Figs. 9(a) and 9(b), the homogeneity factor, $uc′/vc′$ is nearly 1 directly at the outlet of the collated jet, implying strong isotropy. This behavior is short-lived as anisotropy becomes more characteristic downstream. Across the available profile, the homogeneity factor increases gradually up to $uc′/vc′≈$ 2.7 at $x/De=$ 6.

### 3.4 Reynolds Stresses.

Consistent with the $xy$ measurement plane coordinates, all three of the available Reynolds stress terms are presented in Fig. 10. It is well understood that the round jet has a minimum streamwise normal stress, $u′u′/Ub2$, along its axis and that this value increases, forming a distinct peak toward the outer radius as indicative of the mean shear [1,4]. From Fig. 10(a), these behaviors are evident at the $y/D=$ 0 and $y/D=$0.5 locations. Along the $y−$ direction however, there is a clear departure from the axisymmetric profile as a result of the intersection of the center round and outer slot. The normal stress promoted by this intersection develops immediately in the outlet region, and for $x/D≥$ 2, the largest peaks in $⟨⟨u′u′⟩/Ub2⟩$ occur at the round-slot interface, $y/D$ = −0.5, and at the confluence of the round to stagnant region, $y/D$ = 0.5. Interestingly, the actual magnitude of the peaks in these regions are approximately the same, despite one involving two forced convection streams and one involving a forced and stagnant fluid interface. However, the two-dimensional plane of view for this experiment is limited, and the effects of the additional two slot regions on the “stagnant interface” side of the round jet region cannot be easily determined. It is possible that the effect of those two slots, at angles of 120 deg to each other and ±60 deg about the $y$+ axis, combine to create a similar effect as that of the 0 deg slot in the current plane of view.

Fig. 12
Fig. 12
Close modal

The Reynolds normal stress, $v′v′/Ub2$, depicted in Fig. 10(c), is also expected to increase further downstream, past the collated jet outlet region. As expected, this component has a much smaller magnitude compared to $u′u′/Ub2$. A distinct peak develops immediately on the round-stagnant interface, $y/D=$ 0.5, but is not emulated at the round-slot intersection. This again represents a clear departure from the axisymmetric jet condition, requiring a radial normal stress independent of orientation (i.e., $v′v′=w′w′$ [1]). Similar to the streamwise normal stress however, approximate symmetry is obtained for $x/D≥$ 3.

The shear component of the Reynolds stress, $u′v′/Ub2$, presents the second moment as a result of both in plane velocity components. At $y/D$ = 0.5 the shear is maximum between the round-stagnant interface, consistent across all downstream profiles as seen in Fig. 10(b). The peak then moves slightly to the left with each downstream profile, which is possibly due to the influence of the two other slot jets not captured in the plane of view. Shear stress development in the $y−$ direction yields a more complicated evolution. The initial $x/D=$1 profile promotes a peak at the round-slot interface that is opposite in sign and roughly 2.5 times smaller than that at $y/D=$ 0.5. Consistent with the behavior at $y/D=$0.5, this maximum also moves leftward with increasing distance downstream. It is possible that the slot jet minimizes the Reynolds stress at this point in the outlet region and as the slot jet loses influences further downstream, the plot resembles a more classical round jet.

### 3.5 Two-Point Spatial Correlations and Integral Length Scales.

Turbulent mixing produced at the collated jet outlet is uncharacteristic of more familiar axisymmetric jets. The collated outlet geometry promotes different mechanisms driving the free shear flow in the $y−$ and $y+$ directions, as a result of the rectangular interface and round edge, respectively. It is clear that there are several important underlying structures that drive the shearing motion and entrainment at each outer radius. It is beneficial then to incorporate two point velocity correlations at these outer radii locations to infer information about the driving coherent structures and to obtain averaged length scales [41]. Two-point spatial cross-correlations of the fluctuating velocities are computed from the TR-PIV measurements in the near field (0 < $x/D$ < 2) region of the jet. The analysis prioritizes the outer radii, comparing $y/D$ = −0.5 and 0.5 at given discrete downstream locations. The two-point velocity cross-correlation, $Ruu$, is computed according to Eq. (1) for the fluctuating velocity component, $u$
$Ruu(xr,η,τ)=u(xr,t)×u(xr+η,t+τ)u2(xr,t)u2(xr+η,t)$
(1)
where $τ$ is the time interval, $xr$ represents the coordinates of the reference measurement point, and $η$ is the spatial separation between two measurement point coordinates. Correlation values closer to one indicate that there are strong similarities in flow structure between the two reference points. Conversely, low correlation implies that there is dissimilarity in flow structure between the points. By suppressing the time dependence, $τ$ = 0, the two-point correlation coefficients of velocity are only a function of the separation of two spatial points. The length scales of the correlated spatial region can then be computed from $Ruu0=Ruu(xr,η,0)$ via the spatial separation length to produce an estimate of the integral length scale, $Lxk$, according to the following equation:
$Lxk=∫0∞Ruu(xr,ηk,0)dη$
(2)

where the superscript $k$ indicates the direction of the separation length along which the integral is computed and here the subscript $x$ signifies the velocity component direction. From analysis of the spatial two point correlations, the integral length scale can also be estimated as the separation distance where $Ruu0=1/e≈$ 0.37 for experimental measurements [38,42]. The integral length scales provide some understanding of the length and shape of the underlying eddy structures and their energy content. By computing these scales at the outer radii, differences in the flow mixing effects promoted by the geometry and corresponding shear flows can be quantitatively assessed.

The two-point spatial cross-correlations, $Ruu0$ and $Rvv0$, are calculated for discrete downstream locations $x/D$ = 0.5, 1.0, 1.5, and 2.0 and spanwise locations $y/D$ = −0.5 and 0.5, and are presented in Fig. 11. It can be seen that the reference points are strongly correlated with the streamwise direction, i.e., $Ruu0$ and $Rvv0$ contours encompass larger correlation areas further downstream as a result of increased spreading and entrainment with the ambient fluid. From Fig. 11(a), the $y/D$ = −0.5 reference locations provide similar peak correlation shapes as their $y/D$ = 0.5 counterparts. Both locations exhibit slightly elongated trails in the streamwise flow direction as expected of a heavily unidirectional free jet flow. The most notable discrepancy between the $y/D$ = −0.5 and 0.5 reference locations is that the $y/D$ = −0.5 correlation shapes exhibit a larger dependency toward the axial centerline of the jet. Visually, this is the stretching of the correlation toward the axial centerline of the jet for all $y/D$ = −0.5 shapes compared to the more centric or symmetric shapes of the $y/D$ = 0.5 reference points. Nguyen et al. [42] have examined similar behaviors in a highly three-dimensional flow and concluded that this stretching is a result of shearing from the mean velocity field. It is evident then that the $y−$ shear layer is more heavily influenced by the interaction of the rectangular outlet region with the potential core of the jet and so too are the corresponding gradients in velocity found in this area as compared to the $y+$ side of the jet. From Fig. 11(b), it is immediately apparent that the $Rvv0$ correlation shapes on each side of the jet exhibit far more similarity than the $Ruu0$ shapes. Despite the complicated three-dimensional nature of the collated jet interactions, similarity in $Rvv0$ values at each downstream location imply that the velocity fluctuations exhibit strong, localized, and nearly identical behaviors on each side of the jet, even in the immediate outlet region at the $x/D$ = 0.5 location. Similarly to the observation of $Ruu0$, it appears that the $Rvv0$ correlation contours grow in size with downstream distance, though to a lesser extent. Figure 12 collapses the $y/D$ = −0.5 and 0.5 cross-correlations for both $Ruu0$ and $Rvv0$ in the near field region. As denoted, each cross-correlation is computed along is major axis direction, i.e., the $x$-direction for $Ruu0$ and the $y$-direction for $Rvv0$. Comparing each row of Figs. 12(a) and 12(b), the results indicate that a much stronger spatial dependence is indeed found in the $Ruu0$ profiles than in the $Rvv0$ ones. The $Rvv0$ profiles maintain more distinct elbows at the base of their correlation peaks signifying a smaller spatial dependence or more localized peaks. The $Ruu0$ shapes produce more of a linear decrease on either side with increasing downstream distance reflecting a larger spatial dependence and strong correlation with surrounding turbulent fluctuations.

Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal

The two intercepts of each profile with $1/e≈$0.37 are determined and then averaged to produce Table 2. Similar integral length scales have been confirmed from laser Doppler velocimetry measurements by Kerhervé and Fitzpatrick [43] on an equivalent 50 mm diameter round jet. An order of magnitude comparison shows that in the immediate outlet of the jet, the $Lxx$ length scales are roughly 4.5 times as large as their analogous $Lyy$ values. The comparison decreases in the $x+$direction however, toward a magnitude of ∼2.5 at $x/D$ = 2.0. This is a substantial decrease in a relatively short distance downstream, as a result of a large increase in $Lyy$ and more moderate increase in $Lxx$. From Table 2, relative differences in $Lxx$ are noticeably larger in the area 0.5 $≤x/D≤$1.5 than immediately downstream ($x/D$ = 2.0). This implies that the streamwise length of the structures in this region differ significantly, and so too must the transfer of kinetic energy on each side of the jet with respect to the streamwise turbulent velocity fluctuations. Relative differences across the radial $Lyy$ estimates, however, produce a more straightforward trend, decreasing with downstream distance. This confirms that as a function of $x+$, the spanwise length of the eddy structures from adjacent radial locations move toward identical shapes and corresponding effects on the turbulent spanwise velocity fluctuations.

Table 2

Integral length estimates from spatial two-point cross-correlations

$x/D$$Lxx$ (mm)$|Lxx−(Lxx)|max(Lxx,(Lxx))$$Lyy$ (mm)$|Lyy−(Lyy)|max(Lyy,(Lyy))$$Lxx\Lyy$
0.511.5, (12.7)9.7%3.2, (2.4)23.4%3.6, (5.2)
117.2, (15.1)12.6%3.4, (3.9)13.1%5.1, (3.9)
1.519.2, (17.1)11.1%5.1, (5.5)5.7%3.7, (3.1)
220.5, (20.4)0.4%7.8, (8.4)7.5%2.6, (2.4)
$x/D$$Lxx$ (mm)$|Lxx−(Lxx)|max(Lxx,(Lxx))$$Lyy$ (mm)$|Lyy−(Lyy)|max(Lyy,(Lyy))$$Lxx\Lyy$
0.511.5, (12.7)9.7%3.2, (2.4)23.4%3.6, (5.2)
117.2, (15.1)12.6%3.4, (3.9)13.1%5.1, (3.9)
1.519.2, (17.1)11.1%5.1, (5.5)5.7%3.7, (3.1)
220.5, (20.4)0.4%7.8, (8.4)7.5%2.6, (2.4)

Values without and with parenthesis account for the $y/D$ = −0.5 and $y/D$ = 0.5 locations, respectively.

## 4 Conclusions

Detailed analysis of experimental data has been conducted for a round jet with slot lobes. The nozzle geometry and upstream flow conditioning are unique compared to existing jet literature, but important conclusions have been reached through in depth analysis and comparison to existing results from orifice plate, smooth contractions, and pipe nozzles. In addition, data were compared to a range of nozzle geometries including round, lobed, and triangular. The behavior of the jet in this study is found to exhibit characteristics common to each of these nozzle types and geometries. As a result, the following key discoveries are made:

• The jet outlet behaves very similar to a pipe jet, especially in the circular portion in the center of the nozzle geometry, and the flow is characterized by a fully developed flow condition, including turbulence intensities at the centerline of the outlet and their developments downstream;

• the peak velocity is seen to drift away from the centerline with increasing downstream distance, caused by the difference in shear layer growth on either side of the jet;

• velocity signatures of the slot lobe portion of the nozzle are quickly absorbed into the center bulk flow, with first- and second-order statistics behaving in accordance with expectation of a standard round jet by $x/D$= 6, and suggesting the significant convective exchange occurs in the immediate near field; and

• two-point spatial correlations reveal that spanwise velocity fluctuations exhibit strong, localized, and nearly identical behaviors on each side of the jet, while streamwise fluctuations reveal correlation shapes with larger dependency toward the axial centerline of the jet as a result from the shearing of the mean velocity field.

An important consequence of this work is the realization that although the mixing scenario in the application of interest is extremely complex, the metrics of interest might reasonably be approximated by a combination (or superposition) of multiple well-studied jet conditions and geometries. This would enable computationally efficient modeling approaches to further investigate downstream mixing in an altered environment (e.g., including a crossflow). Additional experiments should be conducted aimed at nonuniform mass flow rate distribution upstream of the nozzle to evaluate the validity of these conclusions outside of the specific operating conditions considered here.

## Acknowledgment

The authors gratefully acknowledge support from the Nuclear Energy University Program (NEUP) through Project 15-8627 (ID: DE-NE0008414) titled, “Experimental Validation Data and Computational Models for Turbulent Mixing of Bypass and Coolant Jet Flows in Gas-Cooled Reactors.”

### Appendix

Each of the flow lines consists of two aluminum tubes connected by a custom coupling, inside of which is a honeycomb flow straightener with a wall thickness of 0.53 mm and flat to flat hex cell size of 2.17 mm. The total length of the honeycomb is 76.20 mm. The cumulative tube length for each of the four pipelines is 615.95 mm with inner diameter of 22.23 mm. The bypass slot flow is achieved from a custom adapter to transition the round pipe flow of the fourth supply line to three distinct yet joined rectangular slots. This adapter is shown in Fig. 13 and consists of a round-to-slot expansion region followed by a straight section of the rectangular slots. The expansion angle is roughly 8.8 deg with a length that represents approximately 15.4 supply line tube diameters, and the straight section has a length that represents 48 slot widths. This design allows the slot flow to be fully developed by the time it reaches the mixing blocks further downstream. Details and dimensions of these mixing blocks are shown in Fig. 14 for the round channels (see Figs. 14(a) and 14(b)) and the collated channels (see Figs. 14(c) and 14(d)). Note that each block is actually comprised of three identical sub-blocks and together form a triangular footprint. The cross-sectional views (Figs. 14(a) and 14(c)) represent a slice starting at a vertex and then bisecting the opposite side of the same triangular footprint. The round channel block is primarily used to direct the three round inlets toward the central location. Toward the bottom of this block, mixing is initiated, not only between those three inlets, but with the slot channels as well. The resulting flow geometry is a single circular region in the center with three narrow channels at relative 120 deg angles to one another. This flow cross section remains unchanged in the collated channel block (Figs. 14(c) and 14(d)).

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