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Phase-averaged velocity in a fluidic precessing jet nozzle and in its near external field
Experimental Thermal and Fluid Science 27 (2003) 515–524 www.elsevier.com/locate/etfs
Phase-averaged velocity in a fluidic precessing jet nozzle and in its near external field C.Y. Wong a
a,*
, P.V. Lanspeary a, G.J. Nathan a, R.M. Kelso a, T. OÕDoherty
b
Department of Mechanical Engineering, Engineering Building South, Adelaide University, Adelaide, SA 5005 Australia b School of Engineering, Division of Mechanical Engineering, University of Wales, Cardiff, Wales, CF24 OYF, UK Received 31 March 2002; accepted 30 June 2002
Abstract Phase averaged laser-Doppler measurements of the axial velocity components made within and in the near exit field of a precessing-jet nozzle have verified a number of flow features reported in the research literature. The nozzle is a short cylindrical tube with an axisymmetric inlet at one end, and with a centrebody and a small exit lip at the other end. The diameter ratio of the abrupt expansion at the inlet is 1:5. The measurements of the internal flow field reveal a radially deflected internal jet which reattaches asymmetrically and precesses around the wall of the chamber. The phase-averaged flow inside the chamber can be divided into regions of forward flow and regions of reverse flow. The distribution of these regions inside the chamber implies the presence of large-scale recirculation. Representative reverse mean flow speeds of recirculation are about 30% of the forward flow speed. Measurements inside the chamber suggest that the effect of reversed flow on the velocity decay of the inlet-jet flow is similar to that of an ambient counter flow. Measurements in the external jet suggest that the initial entrainment rate of the external precessing jet is between six and seven times that of an equivalent free turbulent jet. The phase-averaged deflection angle of the present emerging jet is 50° but this decreases to about 30° within 0.4 chamber diameters of the exit plane. Ó 2003 Elsevier Science Inc. All rights reserved. Keywords: Fluidic precessing jet; Laser-Doppler anemometry; Phase-averaged flow; Sudden expansion; Entrainment
1. Introduction The fluidic precessing jet (FPJ) nozzle (Fig. 1) consists of a cylindrical chamber with a small axisymmetric inlet at one end and an exit lip at the other. The inlet flow separates at the abrupt inlet expansion and reattaches asymmetrically to the wall of the chamber [1,2]. Asymmetry of the flow within the chamber causes the reattaching flow to precess around the inside wall of the chamber and so produces a precessing exit flow. The lip and large transverse pressure gradients near the outlet together steer the exit flow through a large angle, towards the axis and across the face of the nozzle outlet. In the cement and lime industries, burners based on the FPJ nozzle have demonstrated a significant reduction in NOx emissions and improvement in product *
Corresponding author. Tel.: +61-8-83036385; fax: +61-883034367. E-mail address: [email protected] (C.Y. Wong).
quality [3,4]. These benefits are a result of differences between the combustion in the flow field of traditional axial-jet burners and the combustion produced by the FPJ [5]––which in turn depends on the differences in the turbulent-jet flow-field. Since the invention of the FPJ nozzle by Luxton and Nathan [6] and its first application as an industrial burner, a significant research effort has been directed at optimising the geometry of the FPJ nozzle and at understanding the FPJ flow. Early research sought to characterise the internal and external flows using various flow visualisation techniques [1,2] and to determine frequency spectra using pressure transducers [2] and uncalibrated hot-wire anemometers [7]. Combustion trials by Newbold et al. [8] have more recently shown that thermal NOx emissions from unconfined external FPJ flows are lower than those from swirl, bluff-body and turbulent jet burners. Measurements of concentration scalar [9] and flow-field velocity [10] with a mechanical analogue of the FPJ confirm the existence of
0894-1777/03/$ - see front matter Ó 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0894-1777(02)00265-0
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Nomenclature Roman d dL D Deq k l0:5 L Nb Np Nr Q Qforward Qi Qreverse R r
symbols orifice diameter at the inlet plane (m) local duct diameter (m) internal diameter of FPJ nozzle (m) equivalent diameter based on jet perimeter (m) constant for Eq. (2) (dimensionless) perimeter of the shear layer (m) internal length of FPJ nozzle (m) average number of LDA bursts per measurement position average number of precession cycles per measurement position number of radial positions volume flow rate through a measurement plane (m3 /s) volume flow rate of forward flow (m3 /s) volume flow rate at the inlet plane (m3 /s) volume flow rate of reverse flow (m3 /s) internal radius of FPJ nozzle (m) radial distance from the axis of the FPJ nozzle (m)
very large-scale and long-lived turbulent features in external precessing-jet flows. Interest in precession instability is broader than in the FPJ flow alone. Direct numerical simulations of flows through large sudden expansions and precessing jet flows are limited to low Reynolds number (Red < 1000) [11,12]. More recently, Guo [13] has used a time dependent k–e model to study the asymmetrically reattached flow downstream from an inlet orifice, and to study the mechanism of precession in a long axisymmetric chamber. GuoÕs expansion ratio (D=d ¼ 5) and Reynolds number (Red ¼ 105 ) are approximately the same as in the present experimental study, but he commented on the need for more experimental data.
Red U Uc Uforward Ui Ujet;cl Ureverse Ux;max x x0 Dx
Reynolds number of flow through orifice, Red ¼ Ui d=m (dimensionless) velocity at each probe location (m/s) counter-flow velocity (m/s) average forward flow speed (m/s) time-averaged velocity at the inlet plane (m/s) maximum averaged velocity in a cross section (m/s) average reverse flow speed (m/s) maximum averaged velocity at distance x from the inlet plane (m/s) axial distance from the inlet plane (m) axial distance from the exit plane (m) radial step size (m)
Greek symbols j streamwise wall curvature of smooth contraction (m1 ) m kinematic viscosity of air, 14:7 106 (m2 /s)
Dellenback et al. [14] have measured the mean and fluctuating velocity fields downstream from a sudden expansion, but their expansion ratio was D=d ¼ 2 and precession was induced by a weak swirl in the inlet flow. For the FPJ, the expansion ratio is 5 or more and there is no swirl at the inlet. In experimental investigations, access to the flow inside an FPJ nozzle is somewhat restricted and variations in the direction of the velocity vector are expected [2]. Laser-based techniques which resolve direction are therefore the only ones capable of producing reliable data. This paper presents the first measurements of flow velocity within a precessing jet chamber without inlet swirl. The velocity data were obtained by laser-Doppler anemometry (LDA) and the signal from a pressure transducer was used as a reference for phase averaging. The technique is similar to that used by Fick [15] for measurements in the precessing vortex core of a swirl burner.
2. Experimental apparatus 2.1. The FPJ nozzle
Fig. 1. Quasi-2D representation of the internal FPJ flow field inferred from flow visualisation [1,2].
The dimensions and geometry of the FPJ nozzle used for the measurements of the precessing flow field are shown in Fig. 2. The most important geometric parameters determining the behaviour of the flow are the inlet expansion ratio (D=d ¼ 5:07), the length-to-dia-
C.Y. Wong et al. / Experimental Thermal and Fluid Science 27 (2003) 515–524
Fig. 2. Dimensions and features of the FPJ nozzle used for LDA measurements. Dimensions are in mm.
meter ratio of the chamber (L=D ¼ 2:7) and the location, size and shape of the centrebody. Nathan [1] observed that, in the absence of an obstruction just inside the exit plane, FPJ precession is intermittent, and that an obstruction such as the centrebody shown in Fig. 2 improves the regularity and reliability of precession. The centrebody is supported by three radial struts, each with a diameter of 4.0 mm. Care was taken to avoid placing the LDA probe volume in the wake of the struts. The exit lip has an upstream-facing chamber of 45°. 2.2. Flow conditioning As shown in Fig. 3, the air flow to the FPJ nozzle was supplied from an industrial air compressor via a pressure regulator, a 2000 l/min rotameter, a seeding ejector and a flow conditioner. The seeding ejector was supplied with sub-micron glycol particles from a ‘‘Rosco 4500’’ fog generator. These glycol particles have a typical mean diameter of 0.8 lm and a density ratio relative to air of 800. Estimates based on StokesÕ equation indicate that, at a frequency of 7.35 kHz, the ratio of particle speed to fluid speed is about 0.99. The glycol particles were therefore small enough to track the large-scale fluctuations in the flow field.
Fig. 3. General arrangement of apparatus.
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Fig. 4. Details of the flow conditioner. Dimensions in mm.
The flow conditioner shown in Fig. 4 provides a swirl-free, low-turbulence and uniform flow at the FPJ inlet plane. It consists of a diffuser, a honeycomb section, a series of five screens and a contraction with a smooth profile. To avoid boundary-layer separation, the design of the diffuser follows the recommendations of Mehta [16]. The included angle of the diffuser is 9.1° and the area ratio is 2. The honeycomb has hexagonal cells with an equivalent length-to-diameter ratio of 11.0. The screens, which are constructed of 28 SWG (standard wire gauge) wire mesh woven at 16 meshes/in., help to reduce the intensity of large scale turbulence and the non-uniformity of the mean flow. Streamwise curvature, j, of the wall is an important contributor to boundarylayer separation in contractions, and so, for local duct diameter dL , the contraction profile is designed with the same maximum value of jjj=dL in the concave region as in the convex region. The contraction, which has an area ratio of 10:1, reduces the turbulence level and further improves the uniformity of the flow. The mean and r.m.s velocity distributions shown in Fig. 5a were obtained from measurements at 0:56d from the inlet plane and at a Reynolds number of Red ¼ 43; 000. For these measurements, the chamber was removed. They show that the boundary layer is thin and the remainder of the flow is uniform. Also, a ‘‘half profile’’ was obtained at Red ¼ 82; 500, x=d ¼ 1, with the chamber removed and is shown in Fig. 5b. In the potential core of the jet flow, the non-uniformity of the
Fig. 5. Mean and r.m.s. velocity distributions of the inlet flow (a) Red ¼ 43; 000, x=d ¼ 0:56 and (b) Red ¼ 82; 500, x=d ¼ 1. Data are non-dimensionalised using the average velocity in the jet core. For these measurements the chamber was removed.
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time-averaged axial velocity is 0.2% of the bulk flow velocity, and the r.m.s. turbulence intensity is approximately 1.8%. The near-inlet velocity distributions also indicate a boundary-layer thickness at the inlet plane of less than 0:12d. 2.3. Laser Doppler anemometry Measurements of the axial velocity component were obtained with a Dantec LDA system in backscatter mode and a Coherent Innova 70 5-W continuous wave Argon-ion laser. To remove directional ambiguity, one beam was frequency shifted by 40 MHz. The experiments were performed at the Division of Mechanical Engineering, University of Wales, Cardiff, UK. The LDA optical head had a focal length of 310 mm and a beam separation of 64 mm, giving a green-beam (514.5 nm) probe volume with a waist diameter of 0.17 mm and a length of 1.65 mm. It was mounted on a Dantec 57G15 three-axis traverse which had a position accuracy of about 0.05 mm in all three directions.
Fig. 6. Typical low-pass filtered pressure signal and oscilloscope trigger pulse.
six-pole Butterworth filter, and it was passed to an oscilloscope which generated a TTL trigger pulse from each falling edge (Fig. 6). The TTL pulse was stored by the LDA signal processor (Dantec 57N20 enhanced Burst Spectrum Analyser) as a false velocity reading and was used as a reference marker for phase averaging.
3. Experimental procedure 2.4. Phase averaging technique Phase averaging of a precessing-jet flow requires a reference probe which can identify the start time and end time of each 360° precession cycle. For these experiments, the reference signal was provided by a pressure transducer. The time interval defining a precession cycle is divided into 36 segments. Each segment corresponds to a 10° range of phase angles and for each segment there is an ensemble sum. The velocity data in each segment is added into the appropriate ensemble sum so that dividing each ensembled sum by the number of samples gives the phase-averaged velocity field. As there is only one reference probe, the phase angle must be calculated by assuming that the phase speed (i.e. precession frequency) and the precession direction does not change during a precession cycle. In practice, the effect of phase-speed variations is to reduce the measured amplitude of peaks and troughs in the phase-averaged mean flow speed and to increase the measured r.m.s. velocity fluctuations, especially in regions of mean shear flow. The reference probe for phase averaging was a 3-mm diameter tube with an open end bevelled at 45°. The probe was located midway between the centrebody and the lip of the nozzle. It was inserted with its bevelled end facing upstream and protruding 10 mm into the flow. A pressure transducer with a sensitivity of 2 mV/Pa and a frequency-response time of 1 ms was connected to the probe with a 300 mm length of PVC tube. This response time is more than adequate to track the precession, which has a typical frequency of 7.5 Hz. The result is a reference signal which fluctuates as the reattached precessing jet sweeps past the probe. The signal from the pressure transducer was low-pass filtered at 10 Hz by a
All the phase averaging measurements were obtained at an inlet Reynolds number of 84,500 and a bulk inlet velocity, Ui ¼ 78:7 m/s. Measurements were obtained along a radius at each of eight distances from the FPJ inlet plane (Fig. 7). Five of these eight radii were inside the nozzle and three were in the external flow field. For the internal measurements, data were recorded at 20 positions along each radius with a radial step size of 2 mm. For the external measurements, both the number of sampling positions and the radial step sizes were larger. These and other details, such as the average number of velocity samples and the average number of precession cycles at each measurement position are given in Table 1. Data from the first internal plane at x=d ¼ 1:52 was used to determine the bulk inlet velocity, Ui . The LDA data were processed with ‘‘Burstware––Version 3.21’’ and a collection of small BASIC programs.
Fig. 7. LDA measurement locations; - - - - - measurement ‘‘plane’’. Dimensions in mm.
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Table 1 Conditions at which the measurements were performed Plane
x=d
x0 =d
x (mm)
Dx (mm)
Nr
Nb
Np
Internal
– a b c d
1.52 3.67 5.32 7.03 8.93
– – – – –
24.0 58.0 84.0 111.2 140.8
2 2 2 2 2
20 20 20 20 20
22,648 23,698 14,181 10,636 3,814
615 1,159 2,146 3,081 3,577
External
A B C
14.60 15.86 17.13
0.67 1.93 3.20
230.5 250.5 270.5
2 3 4
41 35 36
11,346 16,877 15,141
363 263 401
x ¼ axial distance from inlet plane. Dx ¼ radial step size. Nr ¼ number of radial positions. Nb ¼ average number of LDA bursts per measurement position. Np ¼ average no. of precession cycles per measurement position.
4. Phase-averaged mean velocity field within the FPJ chamber Phase-averaged measurements of the internal flow are presented in Fig. 8. The contours of phase-averaged
mean velocity shown in Fig. 8 are consistent with the results of flow visualisation studies [2] which have identified an asymmetric reattaching jet in the FPJ chamber. They also agree closely with the result of Guo [13] at x=d ¼ 8:11, which is between the
Fig. 8. Contours of the phase-averaged axial velocity component inside the nozzle. The segments marked ‘‘A–A’’ show the phase angles over which velocity presented in Fig. 10 is averaged. Data are non-dimensionalised with the maximum mean velocity in the measurement plane, Ux;max . Red ¼ 84; 500.
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x=d ¼ 7:03 and 8:93 measurement positions (‘‘c’’ and ‘‘d’’ in Fig. 7). The contours at x=d ¼ 1:52 are not shown in Fig. 8 because they are axisymmetric and almost the same as the contours at x=d ¼ 3:67. Radial deflection of the jet is clearly visible further downstream (at x=d ¼ 5:32 and 7:03) and, closer to the centrebody (x=d ¼ 8:93), the flow is fully attached to the wall of the chamber. Fig. 9 compares the non-dimensional centreline velocity of the FPJ inlet jet flow with that of an unconfined-jet [17], a plane offset jet of equivalent offset ratio [18] and a jet in a uniform counter flow [19]. The unconfined jet measurements of Crow and Champagne [17] were obtained at a Reynolds number of Red ¼ 83; 000.
Fig. 9. Maximum non-dimensional mean velocity, Ujet;cl =Ui , at each phase-averaged cross-section of the FPJ velocity field. Ui ¼ time-averaged velocity at inlet. Uc ¼ counter-flow velocity. Note the log–log axes and data from [17–19].
Fig. 10. Radial distributions of the phase-averaged axial velocity component for the internal FPJ flow compared with the time-averaged velocity in an unconfined jet [17]. The coordinate system for each axial position is progressively shifted by U =Ui ¼ þ0:5. The distributions of phase-averaged velocity are obtained by averaging over the phaseangle arcs ‘‘A–A’’ in Fig. 8. Red ¼ 84; 500 for the FPJ.
For a deflected jet, it is convenient to define the phaseaveraged ‘‘centreline’’ velocity, Ujet;cl , as the maximum velocity in the measurement plane rather than as the value measured at the axis of the chamber. For the unconfined-jet data, where there is no ambient co-flow (Uc ¼ 0), the length of the potential core region is about 6d. On these log–log axes, the decay rate slope of )1.07 in the region x=d > 9 indicates an almost linear spreading rate. On the other hand, the potential core of the flow from the FPJ inlet orifice has a length of approximately 3:5d and the decay rate slope of )1.5 indicates a non-linear spreading rate. The large decay rate in Fig. 9 implies that the spreading rate of the precessing inlet flow is larger than for a non-precessing unconfined jet [17]. This is confirmed in Fig. 10 which shows radial distributions of axial velocity for the unconfined jet and shows phaseaveraged axial velocity distributions for the FPJ. Asymmetry and reverse flow are also visible in Fig. 10. The reattachment length is about x=d ¼ 5:3, and at x=d ¼ 8:93 the inlet flow is clearly in contact with and confined by the wall. At least two other types of jet flow have similarities with the FPJ inlet flow. Nasr and Lai [18] have measured the velocity distribution in a plane offset jet, which is free on one side and confined by a wall on the other. In Nasr and LaiÕs experiments, the Reynolds number was Red ¼ 11; 000 and the offset ratio was R=d ¼ 2:125. The corresponding offset ratio for the FPJ is R=d ¼ 2:53. Nasr and Lai report a reattachment length (x=d ¼ 4:65) which is a little shorter than for the FPJ. In the region before reattachment (x=d < 5:32) the axial-velocity decay rate of the offset jet is also approximately the same as for the FPJ, but after reattachment the decay rate is much lower. Chan and Lam [19] have measured the effect of counter-flow on the centreline velocity of a turbulent jet, and they have produced an advective algebraic model which agrees well with their experimental data. Their model also provides an estimate of the effect of counter-flow on the length of the potential-core region. To estimate representative counter-flow speeds in the FPJ chamber, each internal cross-section in Fig. 8 is divided into regions of forward and reverse phaseaveraged flow by a contour of zero axial flow velocity. The phase-averaged axial velocity component is then averaged over the forward flow area and is also averaged over the reverse flow area to obtain the Ureverse =Uforward velocity ratios shown in Table 2. At a
Table 2 Estimates of the average reverse flow velocity component Ureverse as a fraction of average forward flow velocity component Uforward x=d Ureverse =Uforward
1.52 0.15
3.67 0.23
5.32 0.37
7.03 0.43
8.93 0.37
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counter-flow velocity ratio of Uc =Ui ¼ 0:324, which is similar in magnitude to an average value of 0.3 from Table 2, the Chan and Lam model produces a centreline-velocity decay very close to the phase-averaged decay in Fig. 9 (shown as dotted lines). The length of the potential-core region given by the model (3:2d) is also close to the value obtained from the phase-averaged FPJ data (3:5d).
5. Phase-averaged velocity field outside the FPJ chamber Phase averaging in the external-flow field (Fig. 11(A)) shows that the precessing jet flow is squeezed into a crescent shape as it passes between the centrebody and the wall of the FPJ chamber. Velocity contours for x0 =d ¼ 1:93 (Fig. 11(B)), where x0 is distance from the exit plane, clearly show the effect of the exit lip and the centrebody; the emerging jet flow is deflected towards the axis of the FPJ nozzle. For this case, the deflection angle is about 50°.
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Fig. 9 shows that the maximum axial component of the external jet velocity at x0 =d ¼ 1:93 is larger than at x0 =d ¼ 0:67, because the impact of the crescent-shaped jet flow converging near the axis steers the flow towards the axial direction. This process is also shown in the radial distributions of Fig. 12. As a result of the flow convergence, the deflection angle of the phase-averaged jet is reduced to about 30°. This reduction in deflection angle is apparent from inspection of Fig. 11(B) (x0 =d ¼ 1:93) and Fig. 11(C) (x0 =d ¼ 3:20). Fig. 13 provides a summary of the flow features identified in Sections 4 and 5.
6. Phase averaged r.m.s. velocity field within the FPJ chamber In Fig. 14 phase-averaged r.m.s. velocity distributions of the flow in the FPJ chamber are plotted as contours. The velocity fluctuations are non-dimensionalised using the maximum mean velocity in the measurement
Fig. 11. Contours of the phase-averaged axial velocity component in the external flow. The segments marked ‘‘A–A’’ show the phase angles over which velocities presented in Fig. 12 are averaged. Data are non-dimensionalised using the maximum mean velocity in each measurement plane, Ux;max . Red ¼ 84; 500.
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Fig. 13. Schematic diagram of flow features obtained from the phase averaged LDA axial velocity data through sections ‘‘A–A’’ from Figs. 8 and 11.
Fig. 12. Radial distributions of the phase-averaged axial velocity component for FPJ external flow. For each axial position the coordinate system is progressively shifted by U =Ui ¼ þ0:1. The distributions of phase-averaged velocity are obtained by averaging over the phaseangle arcs ‘‘A–A’’ in Fig. 11.
‘‘plane’’, Ux;max . A comparison of Figs. 8 and 14 shows that, in many locations, the r.m.s. velocity fluctuations are higher than the mean forward flow speeds. Instantaneous flow reversals are typical at such high levels of
Fig. 14. Contours of the r.m.s. fluctuation of phase-averaged axial velocity inside the nozzle. Data is non-dimensionalised using the maximum mean velocity, Ux;max in the respective measurement planes. Red ¼ 84; 500.
C.Y. Wong et al. / Experimental Thermal and Fluid Science 27 (2003) 515–524
velocity fluctuations. The largest fluctuations occur at x=d ¼ 8:93, where the jet is fully attached to the wall. 7. Entrainment The phase-averaged velocity data provide a convenient method of estimating the forward and reverse flow rates through a given cross-section. For each cross-section of Figs. 8 and 11, the positive phase-averaged velocity component is integrated over the area of the forward flow, and the negative velocity component is integrated over the area of the reverse flow. These forward (Qforward ) and reverse (Qreverse ) flow rates are nondimensionalised with the inlet flow rate (Qi ), and are plotted in Fig. 15 as upward-pointing and downwardpointing triangles respectively. Calculations of flow rate provide a useful consistency check for continuity and they may also reveal large-scale features in the flow. For continuity to be satisfied, the sum of non-dimensional forward and reverse flow rates at each cross-section within the nozzle must be unity; i.e. Qreverse Qforward þ ¼ 1; Qi Qi
ð1Þ
but the measurements in Fig. 15 do not show this. The primary source of experimental error is likely to be severe seeding loss in the reverse flow and in the reattachment region. This problem, which was discussed by Durst et al. [20], leads to an underestimate of the reverse flow and an overestimate of the forward flow velocities, but the results are sufficient to indicate that recirculation flow rate in the chamber (Fig. 13) is similar in magnitude to the inlet flow rate. The region where forward flow rates level off at x=d 6 coincides with the region of reattachment identified in Section 4 and by Nathan et al. [2]. A rapidly increasing forward flow rate in the region x < 6 is gen-
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erally consistent with the rapid rates of spread and decay shown in Figs. 9 and 10. The measured value of forward flow just beyond the exit plane (x=d ¼ 13:9) is only 8% greater than at the inlet plane (x=d ¼ 0). Given the rapid initial spreading of the external jet, the possibility of reverse flow through the exit plane and experimental error, this measurement of flow rate may be considered consistent with continuity. At the exit plane, ambient reverse flow is unseeded and therefore is not detected by LDA. The estimates of the forward flow rate (Qforward ) of the external jet can be used to compare the entrainment rate of the FPJ with the entrainment rate of a free turbulent jet. The non-dimensional entrainment rate of a self-similar turbulent jet is of the form, Q x
k ; Qi d
ð2Þ
where k depends on the initial conditions. Therefore, when comparing the entrainment rate of the external precessing jet with that of a self-similar, round turbulent jet [17], it is necessary to define an equivalent orifice diameter (Deq ) for the precessing jet. The entrainment rate usually scales with the perimeter of the jet shear layer, and so we can define an equivalent diameter in terms of the length, l0:5 of the ‘‘U =Ux;max ¼ 0:5’’ contour in Fig. 11(A): Deq ¼
l0:5 : p
ð3Þ
For this definition, the equivalent exit diameter of the external precessing jet is 0:67D, and in the region 0:67 < x0 =d < 3:20, the entrainment rate is about 6.8 times that of an equivalent free turbulent jet. With an appropriate adjustment for a different definition of equivalent exit diameter, this is consistent with the value of 5 obtained by Nathan and Luxton [21].
8. Conclusion
Fig. 15. Non-dimensional forward and reverse flow-rates; D, forward flow; r, reverse flow; Qi is the flow-rate at the inlet plane.
Phase-averaged LDA has revealed a number of features in the internal and external flow fields of an FPJ nozzle (Fig. 13). The dominant feature is an asymmetric deflection of the phase-averaged inlet flow and its reattachment to the wall of the chamber. This is consistent with observations reported in the research literature. Measurements of axial velocity inside the FPJ chamber show that the phase-averaged flow from the inlet spreads and decays much more rapidly than a free turbulent jet. The decay rate before reattachment is similar in magnitude to that of an offset jet but the reattachment length of the FPJ inlet flow is slightly longer. If a free turbulent jet is immersed in a uniform counter flow, there is a counter-flow velocity which
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produces nearly the same jet decay rate as in the FPJ chamber. The required counter-flow velocity is typical of the phase-averaged reverse flow in the FPJ chamber. This indicates that reverse flow in the FPJ chamber may accelerate the decay and spreading of the FPJ flow. Accurate entrainment calculations from the internal phase-averaged FPJ velocity field are not possible because there is severe loss of seeding in the reattachment region. However, the entrainment calculations do indicate that there is a recirculation with a flow rate similar in magnitude to the inlet flow rate. Phase-averaged measurements in the near external FPJ flow are more reliable and they indicate an initial entrainment rate about 6.8 times that of an equivalent round turbulent jet. The core of the external precessing jet has an initial deflection angle of about 50° but this decreases to about 30° within 0:4d of the exit plane. Acknowledgements CYW gratefully acknowledges the International Postgraduate Research Scholarship (IPRS) and the University of Adelaide Scholarship (UAS). He is also thankful to the Australian Research Council for its International Research Exchange (IREX) grant which allowed him to make the LDA measurements at the University of Wales, Cardiff (UWC). He most sincerely thanks the staff and postgraduate students of UWC for their help with the experiments. References [1] G.J. Nathan, The enhanced mixing burner, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1988. [2] G.J. Nathan, S.J. Hill, R.E. Luxton, An axisymmetric ‘‘fluidic’’ nozzle to generate jet precession, Journal of Fluid Mechanics 370 (1998) 347–380. [3] C.G. Manias, G.J. Nathan, Low NOx clinker production, World Cement 25 (5) (1994) 54–56. [4] C.G. Manias, A. Balendra, D. Retallack, New combustion technology for lime production, World Cement 27 (12) (1996) 34–39. [5] G.J.R. Newbold, G.J. Nathan, R.E. Luxton, Large-scale dynamics of an unconfined precessing jet flame, Combustion Science and Technology 126 (1997) 71–95.
[6] R.E. Luxton, G.J. Nathan, Mixing of fluids, Australian Patent Office, Patent Application no. 16235/88, International Patent Application no. PCT/AU88/00114, 1988. [7] J. Mi, G.J. Nathan, S.J. Hill, Frequency characteristics of a selfexcited precessing jet nozzle, in: E. Cui (Ed.), Proceedings of the Eighth Asian Congress of Fluid Mechanics, Asian Fluid Mechanics Committee, International Academic Publishers, Shenzhen, China, 1999, pp. 755–758. [8] G.J.R. Newbold, G.J. Nathan, D.S. Nobes, S.R. Turns, Measurement and prediction of NOx emissions from unconfined propane flames from turbulent-jet, bluff-body, swirl, and precessing jet burners, Proceedings of the Combustion Institute, vol. 28, 2000, pp. 481–487. [9] D.S. Nobes, The generation of large-scale structures by jet precession, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1997. [10] G.M. Schneider, Structures and turbulence characteristics in a precessing jet flow, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1996. [11] F. Battaglia, Numerical simulations of instabilities and asymmetric characteristics for suddenly expanded channel flows, Ph.D. thesis, Department of Mechanical Engineering, The Pennsylvania State University, The Graduate School, 1997. [12] S.S. Manohar, Three-dimensional numerical analysis of low Reynolds number precessing jets (computational fluid dynamics), Ph.D. thesis, Department of Mechanical Engineering, The Pennsylvania State University, The Graduate School, 1997. [13] B. Guo, CFD simulation of flow instability in axisymmetric sudden expansions, Ph.D. thesis, Department of Chemical Engineering, The University of Sydney, 2001. [14] P.A. Dellenback, D.E. Metzger, G.P. Neitzel, Measurements in turbulent swirling flow through an abrupt axisymmetric expansion, AIAA Journal 26 (6) (1988) 669–681. [15] W. Fick, Characterisation and effects of the precessing vortex core in swirl burners, Ph.D. thesis, Division of Mechanical Engineering and Energy Studies, School of Engineering, University of Wales, Cardiff, 1998. [16] R.D. Mehta, The design of wide angle diffusers, I.C. Aero Report 76-03, Imperial College of Science and Technology––Department of Aeronautics, June 1976. [17] S.C. Crow, F.H. Champagne, Orderly structure in jet turbulence, Journal of Fluid Mechanics 48 (1971) 547–591. [18] A. Nasr, J.C.S. Lai, Comparison of flow characteristics in the near field of two parallel jets and an offset plane jet, Physics of Fluids 9 (1997) 2919–2931. [19] C.H.C. Chan, K.M. Lam, Centreline velocity decay of a circular jet in a counterflowing stream, Physics of Fluids 10 (3) (1998) 637– 644. [20] F. Durst, A. Melling, J.H. Whitelaw, Principles and practice of laser-doppler anemometry, second ed., Academic Press, London, 1981. [21] G.J. Nathan, R.E. Luxton, The entrainment and combustion characteristics of an axisymmetric, self exciting, enhanced mixing burner, Proceedings of the 3rd ASME/JSME Thermal Engineering Joint Conference, Reno, Nevada, vol. 5, March 1991, pp. 145–152.
Phase-averaged velocity in a fluidic precessing jet nozzle and in its near external field C.Y. Wong a
a,*
, P.V. Lanspeary a, G.J. Nathan a, R.M. Kelso a, T. OÕDoherty
b
Department of Mechanical Engineering, Engineering Building South, Adelaide University, Adelaide, SA 5005 Australia b School of Engineering, Division of Mechanical Engineering, University of Wales, Cardiff, Wales, CF24 OYF, UK Received 31 March 2002; accepted 30 June 2002
Abstract Phase averaged laser-Doppler measurements of the axial velocity components made within and in the near exit field of a precessing-jet nozzle have verified a number of flow features reported in the research literature. The nozzle is a short cylindrical tube with an axisymmetric inlet at one end, and with a centrebody and a small exit lip at the other end. The diameter ratio of the abrupt expansion at the inlet is 1:5. The measurements of the internal flow field reveal a radially deflected internal jet which reattaches asymmetrically and precesses around the wall of the chamber. The phase-averaged flow inside the chamber can be divided into regions of forward flow and regions of reverse flow. The distribution of these regions inside the chamber implies the presence of large-scale recirculation. Representative reverse mean flow speeds of recirculation are about 30% of the forward flow speed. Measurements inside the chamber suggest that the effect of reversed flow on the velocity decay of the inlet-jet flow is similar to that of an ambient counter flow. Measurements in the external jet suggest that the initial entrainment rate of the external precessing jet is between six and seven times that of an equivalent free turbulent jet. The phase-averaged deflection angle of the present emerging jet is 50° but this decreases to about 30° within 0.4 chamber diameters of the exit plane. Ó 2003 Elsevier Science Inc. All rights reserved. Keywords: Fluidic precessing jet; Laser-Doppler anemometry; Phase-averaged flow; Sudden expansion; Entrainment
1. Introduction The fluidic precessing jet (FPJ) nozzle (Fig. 1) consists of a cylindrical chamber with a small axisymmetric inlet at one end and an exit lip at the other. The inlet flow separates at the abrupt inlet expansion and reattaches asymmetrically to the wall of the chamber [1,2]. Asymmetry of the flow within the chamber causes the reattaching flow to precess around the inside wall of the chamber and so produces a precessing exit flow. The lip and large transverse pressure gradients near the outlet together steer the exit flow through a large angle, towards the axis and across the face of the nozzle outlet. In the cement and lime industries, burners based on the FPJ nozzle have demonstrated a significant reduction in NOx emissions and improvement in product *
Corresponding author. Tel.: +61-8-83036385; fax: +61-883034367. E-mail address: [email protected] (C.Y. Wong).
quality [3,4]. These benefits are a result of differences between the combustion in the flow field of traditional axial-jet burners and the combustion produced by the FPJ [5]––which in turn depends on the differences in the turbulent-jet flow-field. Since the invention of the FPJ nozzle by Luxton and Nathan [6] and its first application as an industrial burner, a significant research effort has been directed at optimising the geometry of the FPJ nozzle and at understanding the FPJ flow. Early research sought to characterise the internal and external flows using various flow visualisation techniques [1,2] and to determine frequency spectra using pressure transducers [2] and uncalibrated hot-wire anemometers [7]. Combustion trials by Newbold et al. [8] have more recently shown that thermal NOx emissions from unconfined external FPJ flows are lower than those from swirl, bluff-body and turbulent jet burners. Measurements of concentration scalar [9] and flow-field velocity [10] with a mechanical analogue of the FPJ confirm the existence of
0894-1777/03/$ - see front matter Ó 2003 Elsevier Science Inc. All rights reserved. doi:10.1016/S0894-1777(02)00265-0
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Nomenclature Roman d dL D Deq k l0:5 L Nb Np Nr Q Qforward Qi Qreverse R r
symbols orifice diameter at the inlet plane (m) local duct diameter (m) internal diameter of FPJ nozzle (m) equivalent diameter based on jet perimeter (m) constant for Eq. (2) (dimensionless) perimeter of the shear layer (m) internal length of FPJ nozzle (m) average number of LDA bursts per measurement position average number of precession cycles per measurement position number of radial positions volume flow rate through a measurement plane (m3 /s) volume flow rate of forward flow (m3 /s) volume flow rate at the inlet plane (m3 /s) volume flow rate of reverse flow (m3 /s) internal radius of FPJ nozzle (m) radial distance from the axis of the FPJ nozzle (m)
very large-scale and long-lived turbulent features in external precessing-jet flows. Interest in precession instability is broader than in the FPJ flow alone. Direct numerical simulations of flows through large sudden expansions and precessing jet flows are limited to low Reynolds number (Red < 1000) [11,12]. More recently, Guo [13] has used a time dependent k–e model to study the asymmetrically reattached flow downstream from an inlet orifice, and to study the mechanism of precession in a long axisymmetric chamber. GuoÕs expansion ratio (D=d ¼ 5) and Reynolds number (Red ¼ 105 ) are approximately the same as in the present experimental study, but he commented on the need for more experimental data.
Red U Uc Uforward Ui Ujet;cl Ureverse Ux;max x x0 Dx
Reynolds number of flow through orifice, Red ¼ Ui d=m (dimensionless) velocity at each probe location (m/s) counter-flow velocity (m/s) average forward flow speed (m/s) time-averaged velocity at the inlet plane (m/s) maximum averaged velocity in a cross section (m/s) average reverse flow speed (m/s) maximum averaged velocity at distance x from the inlet plane (m/s) axial distance from the inlet plane (m) axial distance from the exit plane (m) radial step size (m)
Greek symbols j streamwise wall curvature of smooth contraction (m1 ) m kinematic viscosity of air, 14:7 106 (m2 /s)
Dellenback et al. [14] have measured the mean and fluctuating velocity fields downstream from a sudden expansion, but their expansion ratio was D=d ¼ 2 and precession was induced by a weak swirl in the inlet flow. For the FPJ, the expansion ratio is 5 or more and there is no swirl at the inlet. In experimental investigations, access to the flow inside an FPJ nozzle is somewhat restricted and variations in the direction of the velocity vector are expected [2]. Laser-based techniques which resolve direction are therefore the only ones capable of producing reliable data. This paper presents the first measurements of flow velocity within a precessing jet chamber without inlet swirl. The velocity data were obtained by laser-Doppler anemometry (LDA) and the signal from a pressure transducer was used as a reference for phase averaging. The technique is similar to that used by Fick [15] for measurements in the precessing vortex core of a swirl burner.
2. Experimental apparatus 2.1. The FPJ nozzle
Fig. 1. Quasi-2D representation of the internal FPJ flow field inferred from flow visualisation [1,2].
The dimensions and geometry of the FPJ nozzle used for the measurements of the precessing flow field are shown in Fig. 2. The most important geometric parameters determining the behaviour of the flow are the inlet expansion ratio (D=d ¼ 5:07), the length-to-dia-
C.Y. Wong et al. / Experimental Thermal and Fluid Science 27 (2003) 515–524
Fig. 2. Dimensions and features of the FPJ nozzle used for LDA measurements. Dimensions are in mm.
meter ratio of the chamber (L=D ¼ 2:7) and the location, size and shape of the centrebody. Nathan [1] observed that, in the absence of an obstruction just inside the exit plane, FPJ precession is intermittent, and that an obstruction such as the centrebody shown in Fig. 2 improves the regularity and reliability of precession. The centrebody is supported by three radial struts, each with a diameter of 4.0 mm. Care was taken to avoid placing the LDA probe volume in the wake of the struts. The exit lip has an upstream-facing chamber of 45°. 2.2. Flow conditioning As shown in Fig. 3, the air flow to the FPJ nozzle was supplied from an industrial air compressor via a pressure regulator, a 2000 l/min rotameter, a seeding ejector and a flow conditioner. The seeding ejector was supplied with sub-micron glycol particles from a ‘‘Rosco 4500’’ fog generator. These glycol particles have a typical mean diameter of 0.8 lm and a density ratio relative to air of 800. Estimates based on StokesÕ equation indicate that, at a frequency of 7.35 kHz, the ratio of particle speed to fluid speed is about 0.99. The glycol particles were therefore small enough to track the large-scale fluctuations in the flow field.
Fig. 3. General arrangement of apparatus.
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Fig. 4. Details of the flow conditioner. Dimensions in mm.
The flow conditioner shown in Fig. 4 provides a swirl-free, low-turbulence and uniform flow at the FPJ inlet plane. It consists of a diffuser, a honeycomb section, a series of five screens and a contraction with a smooth profile. To avoid boundary-layer separation, the design of the diffuser follows the recommendations of Mehta [16]. The included angle of the diffuser is 9.1° and the area ratio is 2. The honeycomb has hexagonal cells with an equivalent length-to-diameter ratio of 11.0. The screens, which are constructed of 28 SWG (standard wire gauge) wire mesh woven at 16 meshes/in., help to reduce the intensity of large scale turbulence and the non-uniformity of the mean flow. Streamwise curvature, j, of the wall is an important contributor to boundarylayer separation in contractions, and so, for local duct diameter dL , the contraction profile is designed with the same maximum value of jjj=dL in the concave region as in the convex region. The contraction, which has an area ratio of 10:1, reduces the turbulence level and further improves the uniformity of the flow. The mean and r.m.s velocity distributions shown in Fig. 5a were obtained from measurements at 0:56d from the inlet plane and at a Reynolds number of Red ¼ 43; 000. For these measurements, the chamber was removed. They show that the boundary layer is thin and the remainder of the flow is uniform. Also, a ‘‘half profile’’ was obtained at Red ¼ 82; 500, x=d ¼ 1, with the chamber removed and is shown in Fig. 5b. In the potential core of the jet flow, the non-uniformity of the
Fig. 5. Mean and r.m.s. velocity distributions of the inlet flow (a) Red ¼ 43; 000, x=d ¼ 0:56 and (b) Red ¼ 82; 500, x=d ¼ 1. Data are non-dimensionalised using the average velocity in the jet core. For these measurements the chamber was removed.
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time-averaged axial velocity is 0.2% of the bulk flow velocity, and the r.m.s. turbulence intensity is approximately 1.8%. The near-inlet velocity distributions also indicate a boundary-layer thickness at the inlet plane of less than 0:12d. 2.3. Laser Doppler anemometry Measurements of the axial velocity component were obtained with a Dantec LDA system in backscatter mode and a Coherent Innova 70 5-W continuous wave Argon-ion laser. To remove directional ambiguity, one beam was frequency shifted by 40 MHz. The experiments were performed at the Division of Mechanical Engineering, University of Wales, Cardiff, UK. The LDA optical head had a focal length of 310 mm and a beam separation of 64 mm, giving a green-beam (514.5 nm) probe volume with a waist diameter of 0.17 mm and a length of 1.65 mm. It was mounted on a Dantec 57G15 three-axis traverse which had a position accuracy of about 0.05 mm in all three directions.
Fig. 6. Typical low-pass filtered pressure signal and oscilloscope trigger pulse.
six-pole Butterworth filter, and it was passed to an oscilloscope which generated a TTL trigger pulse from each falling edge (Fig. 6). The TTL pulse was stored by the LDA signal processor (Dantec 57N20 enhanced Burst Spectrum Analyser) as a false velocity reading and was used as a reference marker for phase averaging.
3. Experimental procedure 2.4. Phase averaging technique Phase averaging of a precessing-jet flow requires a reference probe which can identify the start time and end time of each 360° precession cycle. For these experiments, the reference signal was provided by a pressure transducer. The time interval defining a precession cycle is divided into 36 segments. Each segment corresponds to a 10° range of phase angles and for each segment there is an ensemble sum. The velocity data in each segment is added into the appropriate ensemble sum so that dividing each ensembled sum by the number of samples gives the phase-averaged velocity field. As there is only one reference probe, the phase angle must be calculated by assuming that the phase speed (i.e. precession frequency) and the precession direction does not change during a precession cycle. In practice, the effect of phase-speed variations is to reduce the measured amplitude of peaks and troughs in the phase-averaged mean flow speed and to increase the measured r.m.s. velocity fluctuations, especially in regions of mean shear flow. The reference probe for phase averaging was a 3-mm diameter tube with an open end bevelled at 45°. The probe was located midway between the centrebody and the lip of the nozzle. It was inserted with its bevelled end facing upstream and protruding 10 mm into the flow. A pressure transducer with a sensitivity of 2 mV/Pa and a frequency-response time of 1 ms was connected to the probe with a 300 mm length of PVC tube. This response time is more than adequate to track the precession, which has a typical frequency of 7.5 Hz. The result is a reference signal which fluctuates as the reattached precessing jet sweeps past the probe. The signal from the pressure transducer was low-pass filtered at 10 Hz by a
All the phase averaging measurements were obtained at an inlet Reynolds number of 84,500 and a bulk inlet velocity, Ui ¼ 78:7 m/s. Measurements were obtained along a radius at each of eight distances from the FPJ inlet plane (Fig. 7). Five of these eight radii were inside the nozzle and three were in the external flow field. For the internal measurements, data were recorded at 20 positions along each radius with a radial step size of 2 mm. For the external measurements, both the number of sampling positions and the radial step sizes were larger. These and other details, such as the average number of velocity samples and the average number of precession cycles at each measurement position are given in Table 1. Data from the first internal plane at x=d ¼ 1:52 was used to determine the bulk inlet velocity, Ui . The LDA data were processed with ‘‘Burstware––Version 3.21’’ and a collection of small BASIC programs.
Fig. 7. LDA measurement locations; - - - - - measurement ‘‘plane’’. Dimensions in mm.
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Table 1 Conditions at which the measurements were performed Plane
x=d
x0 =d
x (mm)
Dx (mm)
Nr
Nb
Np
Internal
– a b c d
1.52 3.67 5.32 7.03 8.93
– – – – –
24.0 58.0 84.0 111.2 140.8
2 2 2 2 2
20 20 20 20 20
22,648 23,698 14,181 10,636 3,814
615 1,159 2,146 3,081 3,577
External
A B C
14.60 15.86 17.13
0.67 1.93 3.20
230.5 250.5 270.5
2 3 4
41 35 36
11,346 16,877 15,141
363 263 401
x ¼ axial distance from inlet plane. Dx ¼ radial step size. Nr ¼ number of radial positions. Nb ¼ average number of LDA bursts per measurement position. Np ¼ average no. of precession cycles per measurement position.
4. Phase-averaged mean velocity field within the FPJ chamber Phase-averaged measurements of the internal flow are presented in Fig. 8. The contours of phase-averaged
mean velocity shown in Fig. 8 are consistent with the results of flow visualisation studies [2] which have identified an asymmetric reattaching jet in the FPJ chamber. They also agree closely with the result of Guo [13] at x=d ¼ 8:11, which is between the
Fig. 8. Contours of the phase-averaged axial velocity component inside the nozzle. The segments marked ‘‘A–A’’ show the phase angles over which velocity presented in Fig. 10 is averaged. Data are non-dimensionalised with the maximum mean velocity in the measurement plane, Ux;max . Red ¼ 84; 500.
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x=d ¼ 7:03 and 8:93 measurement positions (‘‘c’’ and ‘‘d’’ in Fig. 7). The contours at x=d ¼ 1:52 are not shown in Fig. 8 because they are axisymmetric and almost the same as the contours at x=d ¼ 3:67. Radial deflection of the jet is clearly visible further downstream (at x=d ¼ 5:32 and 7:03) and, closer to the centrebody (x=d ¼ 8:93), the flow is fully attached to the wall of the chamber. Fig. 9 compares the non-dimensional centreline velocity of the FPJ inlet jet flow with that of an unconfined-jet [17], a plane offset jet of equivalent offset ratio [18] and a jet in a uniform counter flow [19]. The unconfined jet measurements of Crow and Champagne [17] were obtained at a Reynolds number of Red ¼ 83; 000.
Fig. 9. Maximum non-dimensional mean velocity, Ujet;cl =Ui , at each phase-averaged cross-section of the FPJ velocity field. Ui ¼ time-averaged velocity at inlet. Uc ¼ counter-flow velocity. Note the log–log axes and data from [17–19].
Fig. 10. Radial distributions of the phase-averaged axial velocity component for the internal FPJ flow compared with the time-averaged velocity in an unconfined jet [17]. The coordinate system for each axial position is progressively shifted by U =Ui ¼ þ0:5. The distributions of phase-averaged velocity are obtained by averaging over the phaseangle arcs ‘‘A–A’’ in Fig. 8. Red ¼ 84; 500 for the FPJ.
For a deflected jet, it is convenient to define the phaseaveraged ‘‘centreline’’ velocity, Ujet;cl , as the maximum velocity in the measurement plane rather than as the value measured at the axis of the chamber. For the unconfined-jet data, where there is no ambient co-flow (Uc ¼ 0), the length of the potential core region is about 6d. On these log–log axes, the decay rate slope of )1.07 in the region x=d > 9 indicates an almost linear spreading rate. On the other hand, the potential core of the flow from the FPJ inlet orifice has a length of approximately 3:5d and the decay rate slope of )1.5 indicates a non-linear spreading rate. The large decay rate in Fig. 9 implies that the spreading rate of the precessing inlet flow is larger than for a non-precessing unconfined jet [17]. This is confirmed in Fig. 10 which shows radial distributions of axial velocity for the unconfined jet and shows phaseaveraged axial velocity distributions for the FPJ. Asymmetry and reverse flow are also visible in Fig. 10. The reattachment length is about x=d ¼ 5:3, and at x=d ¼ 8:93 the inlet flow is clearly in contact with and confined by the wall. At least two other types of jet flow have similarities with the FPJ inlet flow. Nasr and Lai [18] have measured the velocity distribution in a plane offset jet, which is free on one side and confined by a wall on the other. In Nasr and LaiÕs experiments, the Reynolds number was Red ¼ 11; 000 and the offset ratio was R=d ¼ 2:125. The corresponding offset ratio for the FPJ is R=d ¼ 2:53. Nasr and Lai report a reattachment length (x=d ¼ 4:65) which is a little shorter than for the FPJ. In the region before reattachment (x=d < 5:32) the axial-velocity decay rate of the offset jet is also approximately the same as for the FPJ, but after reattachment the decay rate is much lower. Chan and Lam [19] have measured the effect of counter-flow on the centreline velocity of a turbulent jet, and they have produced an advective algebraic model which agrees well with their experimental data. Their model also provides an estimate of the effect of counter-flow on the length of the potential-core region. To estimate representative counter-flow speeds in the FPJ chamber, each internal cross-section in Fig. 8 is divided into regions of forward and reverse phaseaveraged flow by a contour of zero axial flow velocity. The phase-averaged axial velocity component is then averaged over the forward flow area and is also averaged over the reverse flow area to obtain the Ureverse =Uforward velocity ratios shown in Table 2. At a
Table 2 Estimates of the average reverse flow velocity component Ureverse as a fraction of average forward flow velocity component Uforward x=d Ureverse =Uforward
1.52 0.15
3.67 0.23
5.32 0.37
7.03 0.43
8.93 0.37
C.Y. Wong et al. / Experimental Thermal and Fluid Science 27 (2003) 515–524
counter-flow velocity ratio of Uc =Ui ¼ 0:324, which is similar in magnitude to an average value of 0.3 from Table 2, the Chan and Lam model produces a centreline-velocity decay very close to the phase-averaged decay in Fig. 9 (shown as dotted lines). The length of the potential-core region given by the model (3:2d) is also close to the value obtained from the phase-averaged FPJ data (3:5d).
5. Phase-averaged velocity field outside the FPJ chamber Phase averaging in the external-flow field (Fig. 11(A)) shows that the precessing jet flow is squeezed into a crescent shape as it passes between the centrebody and the wall of the FPJ chamber. Velocity contours for x0 =d ¼ 1:93 (Fig. 11(B)), where x0 is distance from the exit plane, clearly show the effect of the exit lip and the centrebody; the emerging jet flow is deflected towards the axis of the FPJ nozzle. For this case, the deflection angle is about 50°.
521
Fig. 9 shows that the maximum axial component of the external jet velocity at x0 =d ¼ 1:93 is larger than at x0 =d ¼ 0:67, because the impact of the crescent-shaped jet flow converging near the axis steers the flow towards the axial direction. This process is also shown in the radial distributions of Fig. 12. As a result of the flow convergence, the deflection angle of the phase-averaged jet is reduced to about 30°. This reduction in deflection angle is apparent from inspection of Fig. 11(B) (x0 =d ¼ 1:93) and Fig. 11(C) (x0 =d ¼ 3:20). Fig. 13 provides a summary of the flow features identified in Sections 4 and 5.
6. Phase averaged r.m.s. velocity field within the FPJ chamber In Fig. 14 phase-averaged r.m.s. velocity distributions of the flow in the FPJ chamber are plotted as contours. The velocity fluctuations are non-dimensionalised using the maximum mean velocity in the measurement
Fig. 11. Contours of the phase-averaged axial velocity component in the external flow. The segments marked ‘‘A–A’’ show the phase angles over which velocities presented in Fig. 12 are averaged. Data are non-dimensionalised using the maximum mean velocity in each measurement plane, Ux;max . Red ¼ 84; 500.
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Fig. 13. Schematic diagram of flow features obtained from the phase averaged LDA axial velocity data through sections ‘‘A–A’’ from Figs. 8 and 11.
Fig. 12. Radial distributions of the phase-averaged axial velocity component for FPJ external flow. For each axial position the coordinate system is progressively shifted by U =Ui ¼ þ0:1. The distributions of phase-averaged velocity are obtained by averaging over the phaseangle arcs ‘‘A–A’’ in Fig. 11.
‘‘plane’’, Ux;max . A comparison of Figs. 8 and 14 shows that, in many locations, the r.m.s. velocity fluctuations are higher than the mean forward flow speeds. Instantaneous flow reversals are typical at such high levels of
Fig. 14. Contours of the r.m.s. fluctuation of phase-averaged axial velocity inside the nozzle. Data is non-dimensionalised using the maximum mean velocity, Ux;max in the respective measurement planes. Red ¼ 84; 500.
C.Y. Wong et al. / Experimental Thermal and Fluid Science 27 (2003) 515–524
velocity fluctuations. The largest fluctuations occur at x=d ¼ 8:93, where the jet is fully attached to the wall. 7. Entrainment The phase-averaged velocity data provide a convenient method of estimating the forward and reverse flow rates through a given cross-section. For each cross-section of Figs. 8 and 11, the positive phase-averaged velocity component is integrated over the area of the forward flow, and the negative velocity component is integrated over the area of the reverse flow. These forward (Qforward ) and reverse (Qreverse ) flow rates are nondimensionalised with the inlet flow rate (Qi ), and are plotted in Fig. 15 as upward-pointing and downwardpointing triangles respectively. Calculations of flow rate provide a useful consistency check for continuity and they may also reveal large-scale features in the flow. For continuity to be satisfied, the sum of non-dimensional forward and reverse flow rates at each cross-section within the nozzle must be unity; i.e. Qreverse Qforward þ ¼ 1; Qi Qi
ð1Þ
but the measurements in Fig. 15 do not show this. The primary source of experimental error is likely to be severe seeding loss in the reverse flow and in the reattachment region. This problem, which was discussed by Durst et al. [20], leads to an underestimate of the reverse flow and an overestimate of the forward flow velocities, but the results are sufficient to indicate that recirculation flow rate in the chamber (Fig. 13) is similar in magnitude to the inlet flow rate. The region where forward flow rates level off at x=d 6 coincides with the region of reattachment identified in Section 4 and by Nathan et al. [2]. A rapidly increasing forward flow rate in the region x < 6 is gen-
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erally consistent with the rapid rates of spread and decay shown in Figs. 9 and 10. The measured value of forward flow just beyond the exit plane (x=d ¼ 13:9) is only 8% greater than at the inlet plane (x=d ¼ 0). Given the rapid initial spreading of the external jet, the possibility of reverse flow through the exit plane and experimental error, this measurement of flow rate may be considered consistent with continuity. At the exit plane, ambient reverse flow is unseeded and therefore is not detected by LDA. The estimates of the forward flow rate (Qforward ) of the external jet can be used to compare the entrainment rate of the FPJ with the entrainment rate of a free turbulent jet. The non-dimensional entrainment rate of a self-similar turbulent jet is of the form, Q x
k ; Qi d
ð2Þ
where k depends on the initial conditions. Therefore, when comparing the entrainment rate of the external precessing jet with that of a self-similar, round turbulent jet [17], it is necessary to define an equivalent orifice diameter (Deq ) for the precessing jet. The entrainment rate usually scales with the perimeter of the jet shear layer, and so we can define an equivalent diameter in terms of the length, l0:5 of the ‘‘U =Ux;max ¼ 0:5’’ contour in Fig. 11(A): Deq ¼
l0:5 : p
ð3Þ
For this definition, the equivalent exit diameter of the external precessing jet is 0:67D, and in the region 0:67 < x0 =d < 3:20, the entrainment rate is about 6.8 times that of an equivalent free turbulent jet. With an appropriate adjustment for a different definition of equivalent exit diameter, this is consistent with the value of 5 obtained by Nathan and Luxton [21].
8. Conclusion
Fig. 15. Non-dimensional forward and reverse flow-rates; D, forward flow; r, reverse flow; Qi is the flow-rate at the inlet plane.
Phase-averaged LDA has revealed a number of features in the internal and external flow fields of an FPJ nozzle (Fig. 13). The dominant feature is an asymmetric deflection of the phase-averaged inlet flow and its reattachment to the wall of the chamber. This is consistent with observations reported in the research literature. Measurements of axial velocity inside the FPJ chamber show that the phase-averaged flow from the inlet spreads and decays much more rapidly than a free turbulent jet. The decay rate before reattachment is similar in magnitude to that of an offset jet but the reattachment length of the FPJ inlet flow is slightly longer. If a free turbulent jet is immersed in a uniform counter flow, there is a counter-flow velocity which
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produces nearly the same jet decay rate as in the FPJ chamber. The required counter-flow velocity is typical of the phase-averaged reverse flow in the FPJ chamber. This indicates that reverse flow in the FPJ chamber may accelerate the decay and spreading of the FPJ flow. Accurate entrainment calculations from the internal phase-averaged FPJ velocity field are not possible because there is severe loss of seeding in the reattachment region. However, the entrainment calculations do indicate that there is a recirculation with a flow rate similar in magnitude to the inlet flow rate. Phase-averaged measurements in the near external FPJ flow are more reliable and they indicate an initial entrainment rate about 6.8 times that of an equivalent round turbulent jet. The core of the external precessing jet has an initial deflection angle of about 50° but this decreases to about 30° within 0:4d of the exit plane. Acknowledgements CYW gratefully acknowledges the International Postgraduate Research Scholarship (IPRS) and the University of Adelaide Scholarship (UAS). He is also thankful to the Australian Research Council for its International Research Exchange (IREX) grant which allowed him to make the LDA measurements at the University of Wales, Cardiff (UWC). He most sincerely thanks the staff and postgraduate students of UWC for their help with the experiments. References [1] G.J. Nathan, The enhanced mixing burner, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1988. [2] G.J. Nathan, S.J. Hill, R.E. Luxton, An axisymmetric ‘‘fluidic’’ nozzle to generate jet precession, Journal of Fluid Mechanics 370 (1998) 347–380. [3] C.G. Manias, G.J. Nathan, Low NOx clinker production, World Cement 25 (5) (1994) 54–56. [4] C.G. Manias, A. Balendra, D. Retallack, New combustion technology for lime production, World Cement 27 (12) (1996) 34–39. [5] G.J.R. Newbold, G.J. Nathan, R.E. Luxton, Large-scale dynamics of an unconfined precessing jet flame, Combustion Science and Technology 126 (1997) 71–95.
[6] R.E. Luxton, G.J. Nathan, Mixing of fluids, Australian Patent Office, Patent Application no. 16235/88, International Patent Application no. PCT/AU88/00114, 1988. [7] J. Mi, G.J. Nathan, S.J. Hill, Frequency characteristics of a selfexcited precessing jet nozzle, in: E. Cui (Ed.), Proceedings of the Eighth Asian Congress of Fluid Mechanics, Asian Fluid Mechanics Committee, International Academic Publishers, Shenzhen, China, 1999, pp. 755–758. [8] G.J.R. Newbold, G.J. Nathan, D.S. Nobes, S.R. Turns, Measurement and prediction of NOx emissions from unconfined propane flames from turbulent-jet, bluff-body, swirl, and precessing jet burners, Proceedings of the Combustion Institute, vol. 28, 2000, pp. 481–487. [9] D.S. Nobes, The generation of large-scale structures by jet precession, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1997. [10] G.M. Schneider, Structures and turbulence characteristics in a precessing jet flow, Ph.D. thesis, Department of Mechanical Engineering, University of Adelaide, Australia, 1996. [11] F. Battaglia, Numerical simulations of instabilities and asymmetric characteristics for suddenly expanded channel flows, Ph.D. thesis, Department of Mechanical Engineering, The Pennsylvania State University, The Graduate School, 1997. [12] S.S. Manohar, Three-dimensional numerical analysis of low Reynolds number precessing jets (computational fluid dynamics), Ph.D. thesis, Department of Mechanical Engineering, The Pennsylvania State University, The Graduate School, 1997. [13] B. Guo, CFD simulation of flow instability in axisymmetric sudden expansions, Ph.D. thesis, Department of Chemical Engineering, The University of Sydney, 2001. [14] P.A. Dellenback, D.E. Metzger, G.P. Neitzel, Measurements in turbulent swirling flow through an abrupt axisymmetric expansion, AIAA Journal 26 (6) (1988) 669–681. [15] W. Fick, Characterisation and effects of the precessing vortex core in swirl burners, Ph.D. thesis, Division of Mechanical Engineering and Energy Studies, School of Engineering, University of Wales, Cardiff, 1998. [16] R.D. Mehta, The design of wide angle diffusers, I.C. Aero Report 76-03, Imperial College of Science and Technology––Department of Aeronautics, June 1976. [17] S.C. Crow, F.H. Champagne, Orderly structure in jet turbulence, Journal of Fluid Mechanics 48 (1971) 547–591. [18] A. Nasr, J.C.S. Lai, Comparison of flow characteristics in the near field of two parallel jets and an offset plane jet, Physics of Fluids 9 (1997) 2919–2931. [19] C.H.C. Chan, K.M. Lam, Centreline velocity decay of a circular jet in a counterflowing stream, Physics of Fluids 10 (3) (1998) 637– 644. [20] F. Durst, A. Melling, J.H. Whitelaw, Principles and practice of laser-doppler anemometry, second ed., Academic Press, London, 1981. [21] G.J. Nathan, R.E. Luxton, The entrainment and combustion characteristics of an axisymmetric, self exciting, enhanced mixing burner, Proceedings of the 3rd ASME/JSME Thermal Engineering Joint Conference, Reno, Nevada, vol. 5, March 1991, pp. 145–152.