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Velocity characteristics of a swirling recirculating flow
Velocity Characteristics of a Swirling Recirculating Flow M. V. Heitor A. L. N. Moreira Instituto Superior T@cnico, Department of Mechanical Engineering, Technical University of Lisbon, Lisbon, Portugal
liThe isothermal recirculating flow downstream of a model swirl burner is studied making use of a laser-Doppler velocimeter. The arrangement was designed to incorporate the injection of liquid fuel into a gas flame characterized by a large recirculation zone attached to the burner head and to allow a detailed analysis of turbulent transport processes in a strongly swirled recirculating flow. The results show that turbulent mixing in the present flow is not dominated by large-scale motions or precession. The production of turbulent kinetic energy depends upon mechanisms of shear-generated turbulence but is influenced by streamline curvature in the zone of mean shear. Inspection of the terms in the conservation equations for the turbulent stresses allows quantification of the extent to which the interaction of normal stresses and normal strains influence the flow and suggests the likely magnitude of turbulent diffusion and dissipation.
Keywords: swirling flow, turbulent transport, model burner INTRODUCTION Swirling recirculating flows are typical of a variety of power and propulsion devices (see, eg, Refs. 1-4), in which the separated recirculating flow established downstream of swirling vanes is used to allow the stabilization of high-intensity turbulent flames. The combustion process in these flames is partly dependent on the mixing of the fuel and air streams, which in turn is determined by the state of the flow turbulence [5-7]. In addition, analysis has shown that the details of the aerodynamics of the near burner zone are crucial to the description of the mechanisms of flame stabilization and fuel burnout [8], and further results are necessary to guide the development of optimized burner geometries and of tools to predict their effects. In particular, the analysis of isothermal models of the combusting flows allows much to be learned about the turbulent processes typical of recirculating flames in experimentally simpler flows and is considered in this paper. Although velocity measurements in swirling recirculating flows have been extensively reported [8-11], measurements have been mostly concerned with turbulence intensities, and only a few examples of other turbulence properties are available. In particular, third-order correlations of velocity fluctuations can provide information on the effects of curvature and proximity of a stagnation zone on the turbulence structure and are necessary to obtain a full second-order closure of the differential equations for turbulent transport of momentum and energy [12, 13]. However, most of the published works reporting higher order velocity measurements are concerned with the effects of curvature in simple mixing layers [14-18]. In addition, experiments in which the measurements are used to obtain magnitude estimates of other quantities of direct relevance to turbulence modeling, such as budgets and correlation coefficients of Reynolds stresses, are necessary but are
very demanding in the experimental technique [19]. Results of this kind were obtained with hot-wire anemometry [20-22], and more recently LDA measurements were used to derive such information [23-25]. In both cases, published works are concerned with somewhat simple flows, such as mixing layers, axisymmetric jets, and baffle-stabilized flames, and despite the wide practical importance of strongly swirled recirculating flows, they have not been fully addressed; see, for example, Ref. 26. This paper analyzes the turbulent characteristics of the isothermal flow in a typical swirling burner arrangement, which may incorporate the injection of liquid fuel into a gas flame. The experiments include laser-Doppler measurements of mean velocity together with those of double and triple velocity correlations in the three spatial directions. The results are used to obtain estimates of the convection and production terms in the transport equations of the Reynolds stresses and provide a basis for improving our understanding of relevant transport processes in industrial burners and for guiding turbulence modeling. The paper is presented in five sections including this Introduction. The following section describes the burner arrangement and the experimental method and gives details of the flow analyzed. The third section presents the mean and turbulent flowfields in the vicinity of the burner head, and the fourth discusses the results and analyzes the turbulent transport processes typical of the present flow. The final section summarizes the main findings and conclusions of the work. FLOW CONFIGURATION AND EXPERIMENTAL METHOD The burner arrangement and the experimental techniques used throughout this work are described in this section to-
Address correspondence to Professor Manuel V. Heitor, Instituto Superior T~cnico, Department of Mechanical Engineering, Technical University of Lisbon, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal.
Experimental Thermal and Fluid Science 1992; 5:369-380 © 1992 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/92/$5.00
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M . V . Heitor and A. L. N. Moreira
gether with their likely accuracy. The arguments associated with the assessments of accuracy provided are based on previous experiments and are presented in condensed form. Details can be found in Ref. 27. The flow configuration is based on those under " d u a l " burning of liquid and gaseous fuels in practical furnaces and is presented in Fig. 1. It comprises a commercial fuel atomizer with an external diameter of d = 23 mm, assembled in a low-velocity cofiow of propane gas (54 mm O.D.), which is externally surrounded by a high-velocity coflow of air (84 mm O.D.). A diverging quarl typical of those found in the burners of industrial furnaces was located at the burner exit and could be removed to permit the measurement of boundary conditions. Swirl is imparted to both streams by means of fixed blades at 45* [9] with resulting swirl numbers, estimated from the geometry of the blades as in Ref. 27 (see Nomenclature), equal to S O = 0.77 and S i = 0.85 for the outer and inner streams, respectively. The outer airflow rate was measured with a calibrated standard orifice meter, and integrated Pitot tube measurements have shown that the measured flow rates are accurate within 2 %. The inner flow rate was measured by a rotameter with an absolute error smaller than 0.1 L/s, which corresponds to an accuracy of 1.8% for the flow conditions studied here.
Dq
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Fuel =
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~ Liquid Fuel (Optional) Figure 1. Schematic diagram of the model burner.
The measurements presented here were obtained for nonreacting conditions in the absence of liquid fuel, with the propane gas replaced by air with a momentum flux similar to that of a flame with an air-to-fuel volumetric ratio equal to 27.6 and a heat load of about 350 kW. The resulting flow conditions correspond to bulk velocities, defined as the ratio between the flow rate and the cross-sectional area, equal to U o = 30 m / s (Re o = 49,500) in the outer airstream and U / = 2 ms ( R e / = 4000) in the inner stream, respectively. The origin of the axial axis, x, is taken at the center of the exit plane of the model burner, and the tangential velocity is taken positive in the anticlockwise direction, facing the burner. The burner is located vertically directed upward, and the symmetry of the flow was verified by measuring several complete radial profiles of mean and fluctuating velocity values. Velocity measurements were obtained with a dual-beam laser-Doppler anemometer based on an argon ion laser light source at 514.5 nm (1 W nominal) with sensitivity to the flow direction provided by light-frequency shifting from acoustooptic modulation (double Bragg cells) with a resulting shift of the Doppler signal in the range 0 - 1 0 MHz. The half-angle between the beams was 4.92", and the calculated dimensions of the measuring volume at the e - 2 intensity were 1.528 and 0.132 mm. The transfer function in the absence of frequency shift was 0.33 MHz/(m • s-1). Forward-scattered light was collected and focused into the pinhole aperture (0.300 mm) of a photomultiplier tube with a magnification of 0.74. The bandpassed filtered Doppler signals were processed by a commercial frequency counter (TSI 1980B) interfaced with a 16-bit microcomputer. The ~omplete laser-Doppler velocimeter (LDV) system was fixed, and the burner was mounted on a three-dimensional traversing unit, allowing the control volume to be positioned within +_0.25 mm. The distributions of the Reynolds shear stresses u ' u ' and u ' w ' and corresponding triple velocity correlations were obtained by traversing the control volume along two normal diameters with the laser beams in the horizontal and vertical planes and at +_45 °, as described in Ref. 28. The accuracy of the laser-Doppler measurements may be influenced by transit broadening [29] and nonturbulent Doppler broadening errors [30], which affect mainly the variance of the velocity fluctuations and were estimated to be 2 smaller than 5 × 10- 5 Uo2 and 1 × 10- 3 Uo, respectively. The number of individual velocity values used to form the averages was always above 15,000, which results in statistical (random) errors smaller than 1% and 4%, respectively, for the mean and variance values for a 95% confidence interval [31]. Systematic errors due to sampling bias were minimized by using data rates of valid Doppler signals higher than the fundamental velocity fluctuation rate [32]. To avoid bias errors due to unequal particle densities in the inner and outer airflows [33], the two streams and the ambient air in the vicinity of the burner head were seeded separately with powdered aluminum oxide (0.6-1 #m nominal diameter before agglomeration) dispersed in specially built cyclone generators [34]. "Fringe (angle)" bias was minimized by using large values of frequency shifting as suggested in Ref. 35, and for the present case the acceptance angle estimated as in Ref. 36 was 360 ° for a fringe-to-particle velocity ratio larger than 1, which could be achieved with frequency shifts up to 10 MHz.
Velocity Characteristics of Swirling Flow
371
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Systematic errors incurred in the measurement of Reynolds shear stress can arise from lack of accuracy in the orientation angle of the normal to the anemometer fringe pattern, as shown in Ref. 28, and can be particularly large in the vicinity of the zones characterized by zero shear stress. For the present experimental conditions, the largest errors are expected to be smaller than - 2 %. RESULTS Detailed measurements of mean and turbulent velocity characteristics were obtained at six different horizontal planes downstream of the burner head. Sample results are presented in Figs. 2 - 5 , as either radial profiles or isocontours. The choice depends on the intention of the figure, and no attempt was made to provide all data with the same uniformity of precision. Figures 2 and 3, respectively, show mean streamlines and radial profiles of mean velocity and indicate the most salient features of the time-averaged flow in the vicinity of the burner head. The values of the stream function were calculated by integrating the radial profiles of mean axial velocity as described, for example, in Ref. 10. The results exhibit features typical of strongly swirling jets with a region of recirculation attached to the burner head and extending up to about x / D o = 3.7. The maximum negative reverse velocity is - 0 . 7 5 U o and occurs at x / D o = 1.0, where the recirculation zone exhibits its maximum width. This velocity is important because it quantifies the strength of the recirculation zone and also because it influences the magnitude of the recirculating mass flow rate. The reverse flow zone is surrounded by a region of large and positive axial velocity values with maxima moving outwards and decaying far downstream, and with the loci of maxima radial gradients of mean axial velocity approximately coincident with the zero velocity line up to x / D o = 1.5. The radial component of mean velocity, V, is positive up to x / D o = 1.5 and has two maxima with an inflection point in the shear layer around the recirculation zone. Downstream of x / D o = 1.5, the values of V show a trend similar to that observed in the recirculating swirl flow of Ref. 10, with negative values inside the recirculation zone and positive values for larger radii. The profile of the mean
tangential velocity component, W, at the exit of the quarl ( x / D o = 0.6) exhibits a linear distribution typical of solid body rotation within the recirculation zone (ie, for r i D o < 0.5), whereas in the outer flow region W reaches a maximum at the edge of the flow and then decreases rapidly. Inside the recirculation zone the fluid rotates with an angular velocity that increases initially up to x / D o = 1.0 and then decreases gradually with the downstream distance. The transition from the exit profile to a Rankine type of vortex profile, as defined in Ref. 1, takes place at x / D o = 1.0, with the maximum swirl velocities occurring at the edge of the recirculation zone up to x / D o = 1.5. These maxima move radially outwards and decay rapidly. The distributions of the Reynolds normal stresses must be related to those of mean shear and are represented in Fig. 4 in the form of isocontours. In general, the results reveal that upstream of x / D o = 1.0 the levels of velocity fluctuations are small inside the recirculation zone and large in the highly strained annular shear layer, where turbulence is strongly anisotropic with u ,2max=_ 2.2v, Zmax= 2.2w ,2max" Downstream of x / D o = 1.5 the three normal stresses decrease as the distance to the burner increases, with v '2 and w "2 slightly larger than u' 2 in the vicinity of the rear stagnation point. As a result, the distribution of turbulent kinetic energy (Fig. 4d) show maximum values along the edge of the backflow region in contrast to the observations of Refs. 14 and 24 downstream of axisymmetric and plane baffles, where the stagnation region is characterized by the highest values of turbulent kinetic energy. The correlation coefficients for the shear stresses
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have been calculated from the results to assess the extent to which the turbulence in the present flow is affected by "unusual" mechanisms and are plotted in Fig. 5. The
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nondimensional distribution of the shear stress u' v' indicates maximum values coincident with those of u '2, with the radial profiles exhibiting two peaks. The inner, negative peaks occur near the edge of the recirculation zone where the mean shear rate OU/Or is characterized by the maximum positive values, and the outer, positive peaks are located in the outer shear_layer and coincide with the maximum negative values of aU/Or. The sign of the shear stress is related to the sign of the shear strain OU/Or in accordance with a turbulent viscosity hypothesis [37], except for a narrow zone in the upstream part of the shear layer adjacent to the reverse-flow zone, where the shear strain is close to zero. This agrees with the results of Ref. 24 in the shear layer adjacent to a baffle-induced flow and in the initial mixing region of the curved two-dimensional j e t of Ref. 18 and may be related to the large shear strain OF~Or associated with the sudden expansion at the exit of the quarl. Whereas in the outer shear layer, where OU/Or < 0, the peak values of Ruv are of the order of 0.5, in the inner shear layer, where cgU/ar > 0, the absolute values of Ru~ increase from 0.3 at the exit plane of the quarl (ie, at x / D o = 0.6) up to values considerably
higher, about 0.7 at x / D o = 1.0, and decrease to a constant value equal to - 0 . 4 far downstream. Similar trends have been observed in other recirculating flows [20-24] and were attributed in Ref. 15 to the effects of streamline curvature. In addition, the values of the shear stresses normalized by the turbulent kinetic energy, which are not shown here due to lack of space, exhibit values smaller than 0.3 in the inner shear layer in agreement with the observations in Refs. 15-17, and values larger than 0.3 in the outer shear layer. The results therefore reveal departures from the values expected in " n o r m a l " shear layers [38, 39] and suggest that the shear stress in the present flow is primarily induced by streamline curvature in the inner and outer shear layers and that large-scale motions are likely to have minor importance in the balance of turbulent kinetic energy. The values of R.w are similar to those of R.v at x / D o = 0.6 and are considerably attenuated with the exception of the region around x / D o = 1.5, where the mean shear strain OW/ar reaches maximum negative values. It should be pointed out that, with the exception of this region, peak values of R.w would be expected to be smaller than those of
Velocity Characteristics of Swirling Flow 373 4.0
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DISCUSSION The foregoing presented the measurements of mean and turbulent velocities obtained in the vicinity of the model burner considered throughout this paper. This section discusses the results, analyzes their practical significance, and considers their implications for the calculation of swirling flows using turbulence models. The flowfield under analysis includes zones of recirculation, acceleration, and near-uniform velocity that are qualitatively similar to those reported for other separated flows with a free stagnation point, such as the swirling flow of Ref. 10 or the baffle-induced flow of Ref. 24. The aspects of the flow that are of particular interest here are the size and strength of the swirl-induced recirculation zone, the recirculating massfloff rate, and the levels of turbulence that are generated. These were conveniently identified in the previous sections, and the axial distribution to those related to the time-averaged flowfield is summarized in Fig. 6. The loci of the separation streamline, ~b = 0, reveals the large curvature undergone by the flow streamlines, which is associated with pressure gradients that are directed normally to the streamlines and depend on the degree of curvature. As a result, a pressure minimum exists at the zone where the reverse velocity reaches a maximum value. Far downstream the flow recovers to the ambient pressure and the acceleration of the fluid is dominated by the magnitude of this pressure gradient. The implications of the results for the design of practical burners should be analyzed in terms of the extent and strength of the recirculating flow and the spreading rate of the outer flow, which determine the length of the flame in practical burners and influence their efficiency. The extent to which the flame propagates and anchors at the burner head depends upon the ratio of the local flow velocity to the burning velocity, which in turn varies with the local stoichiometry [3]. This is a function of the mixing that has taken place between fuel and oxidant and depends upon the magnitude of the swirl level. The present results provide detailed information about these aerodynamic characteristics and should be used to evaluate the performance of calculation methods of the flow in practical burners in order to allow extrapolation of the experimentally acquired information to more realistic flow conditions. Inspection of the time-resolved velocity characteristics measured along the three spatial coordinates reveals that the recirculation zone up to its maximum width is a zone of intense generation of turbulence. The existence of zones characterized by large turbulence anisotropy in the present flow has important implications, because calculation methods
374
M . V . Heitor and A. L. N. Moreira
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(a) Ruu =
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based on scalar effective viscosities do not adequately represent the behavior of the normal stresses. The deviation from isotropy beyond the central zone is very clear and, following the analysis of Ref. 46, suggests that turbulence is mainly transported in the axial direction by means of large-scale eddies. On the other hand, the comparatively low magnitude of the normal stresses and their relative isotropy near the centerline suggest that the flow there is dominated by dissipating small-scale eddies. Therefore, the results suggest that the calculation of swirling flows, such as those in industrial burners, should involve a turbulence model at the level of transport equations for the Reynolds stresses, rather than at the level of a turbulent viscosity closure. This can be further analyzed by examination of some of the terms in the conservation equations for the Reynolds stresses, as explained below.
The measurements of the mean and turbulent velocity characteristics reported in the previous section have allowed estimation of the convection and production terms in the transport equations for turbulent kinetic energy and for Reynolds shear stresses, which are discussed here to improve the analysis of the mechanisms involved in the generation of turbulence in the present flow. The estimates are approximate because of the error in evaluating the spatial gradients, but the values are sufficiently accurate for the purpose of establishing the relative importance of the separate terms in the conservation equations. Figure 7 shows radial profiles of the production and convection terms in the conservation equation for turbulent kinetic energy normalized by U3/Do, with convection plotted so that a negative value represents a gain. The results show distributions in the outer shear layer (where OU/ar < O)
Velocity Characteristics of Swirling Flow 250
200 E E
150
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~
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~=0
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X (mm)
0.8 1.0 Figure 6. Axial distribution of time-averaged aerody__namiccharacteristics of the flowfield: reverse-flow boundary, U = 0; eddy boundary, ~k = 0; locus of maximum axial velocities, U = Ureax ; jet boundary, U = 0.10Umax; recirculating mass flow rate,
mr/m0. qualitatively similar to those observed in other mixing layers [20, 47]; production is mainly due to the interaction between shear stress and shear strain and is balanced by turbulent diffusion and dissipation. In the core of the annular jet, turbulence production by normal and shear stresses is negligible; convection is the largest term and represents a gain, which is balanced by turbulent diffusion and dissipation. For smaller radii, and in the region of the separation streamline and upstream of stagnation (ie, x / D o < 2.0), the distribution of the various terms resembles that in the mixing layer of Ref. 48 and upstream of the reattachment zone in the backstep flows of Refs. 20 and 22. Convection is small, production is mainly by shear stress, and turbulent diffusion and dissipation are important and represent a loss. Around x / D o = 2.1, the deflection of the separation streamline (see Fig. 2) occurs in a zone where turbulence production by the interaction of normal stresses with normal strains is large, with maximum values in the vicinity of r i D o = 0.4. This observation is in accordance with the decrease in the ratio between u '2 and v '2 measured in this region of the shear layer and agrees with the results of Ref. 24 in a baffle-stabilized wake flow. In agreement with the analyses presented before, it should be noted that for these flows in which there is production of turbulent kinetic energy through normal stresses, calculations using a scalar effective-viscosity turbulence model will be inaccurate. This is because such models do not adequately represent normal stresses and although the gradients of normal stresses are not large terms in the transport of mean momentum (see Ref. 27 for details), the importance of the various production terms in generating turbulent kinetic energy implies that it is necessary to calculate the individual
375
normal stresses adequately if the correct turbulent kinetic energy is to be obtained. As noted in Ref. 49 for the turbulence in stagnation zones downstream of bluff-body flows, this distribution is crucial to correct representation of the effective viscosity, and the latter quantity is of importance in the mean momentum equations. The terms in the transport equation of shear stress u' u' (Fig. 8) show that production is dominated over the whole length of the measurements by the interaction of normal stresses with shear strains, that is, o'2(OV/Or), as in the swirling jet of Ref. 46 and in the recirculating flow of Ref. 24. Around the core of the annular jet, where u' v'= O, this term reverses its sign, but in either the inner or outer parts of the flow it is likely to be balanced by pressure-redistribution terms. Diffusion of turbulent energy and shear stress may be associated with the gradients of third-order correlations of velocity fluctuations, which are strongly affected by both longitudinal curvature and proximity of a stagnation zone, and has been attributed to large-scale motions [46, 50, 51]. Figure 9 shows radial profiles across the recirculation bubble of the triple products u'2v ', 0'3, and u'o '2, which represent the turbulent radial fluxes of u '2, 0 '2, and u' v', respectively. The results show that the triple velocity correlations are one order of magnitude smaller than the corresponding Reynolds stresses and have distributions qualitatively similar to those in other recirculating flows, such as the backstep flows of Refs. 2 0 - 2 2 or the bluff body flow of Ref. 24. The distributions of Fig. 9 also show that turbulent transport of both normal and shear stresses is mainly in the gradient sense. The triple products are close to zero at the loci of zero radial gradients of the corresponding second-order correlations, and their positive values are associated with turbulent transport of the Reynolds stresses from the high-production-rate zones to the outer flow. It should also be noted that the values of u'2o ' and 0 '3 along the edge of the recirculation zone are negative and are associated with the transport of turbulent kinetic energy from the highly turbulent shear layer to the backflow region of weak turbulent fluctuations, as in the other recirculating flows [51, 52]. However, minimum values of 0'3 diffuse toward the centerline faster than those of u'2o ', suggesting that the radial transport of_f_o'2 toward the stagnation point is faster than that of u '2. This observation is similar to the effect of streamline curvature observed in Ref. 17 and is consistent with measured values of i)'2/u '2 larger than unity. This is restricted to the vicinity of the centerline and in the outer shear layer, where OU/Or < 0 and the distributions of the triple velocity correlations are in agreement with those observed in the entrainment region of axisymmetric free jets [53] and plane mixing layers [48]. CONCLUSIONS Laser-Doppler measurements have provided detailed information about the turbulenee characteristics of the isothermal recirculating flow established downstream of a model swift burner, which was designed to allow the injection of liquid fuel into a gas flame. Measurements were obtained for a Reynolds number of the main airflow of 49,500 and a swirl
376
M . V . Heitor and A. L. N. Moreira 100.0
I
'
'
IO0.0
'
x/Do
=
.
.
.
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.
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Figure 7, Radial profiles of the production and convection terms in the conservation equation for turbulent kinetic energ 3 (Re = 49,500). (O) Production by normal stresses; ( A ) production by shear stresses; ( V ) convection• Solid curves indicat( imbalance.
number of 0.77. The flow is characterized by the presence of a large recirculation zone that is curved along its length and imposes mean velocity effects on the turbulent field. The
Inspection of the terms in the conservation equations fo~ the turbulent stresses show that the interaction between normal stresses and normal strains influences the turbulent flow,
normal stresses show substantial departures from isotropy, and their ratios are strongly d e p e n d e n t on the local m e a n strain rate. In the upstream part of the annular swirling jet,
particularly in the upstream part of the annular swirling jet and in the vicinity of the rear stagnation point, where turbulent diffusion and dissipation are likely to be important in the balance o f turbulent kinetic energy.
the ratio u'2/o '2 is larger than unity and the flow is dominated by large values o f the shear strain rate aU/Or, whereas in the vicinity o f the stagnation region, values of u'2/v '2 smaller than unity are associated with large values o f the normal strain rate OU / a x.
The experiments were performed at the Centro de Termodin~mica Aplicada e Mechnica dos Fluidos da Universidade T6cnica de Lisboa, CTAMFUTL-INIC. Financial support has been provided by the Com-
Velocity Characteristics o f Swirling Flow 100.0
377
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-50.0
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~ .... 1.5
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. . . .
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. . . .
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r/Do
F i g u r e 8. Radial profiles o f the p r o d u c t i o n a n d c o n v e c t i o n t e r m s in the c o n s e r v a t i o n equation for the Reynolds shear stress u ' v' (Re = 49,500). Symbols as for Fig. 7. mission of the European Communities under the contract Science-SC10459.
Lq m0 m r
r Re R.o
NOMENCLATURE D d k L,
diameter, m diameter of liquid atomizer, m t u r b u l e n t k i n e t i c energy + w'2)/21, mZ/s z recirculation length, m
quarl length, m total air mass flow rate, kg/s recirculating mass flow rate, kg/s radial coordinate, m Reynolds number, dimensionless correlation coefficient for the Reynolds shear stress U' V'
[=
(u 'z +
v 'z
R uw
S
[ =
U t II'/(U
t 2
. Vt
2)
I/2],
dimensionless
correlation coefficient for the Reynolds shear stress u' w ' [ = u' w ' / ( u 'z • w'2)1/2], dimensionless swirl number, defined as S = ( 2 / 3 ) { [ 1 ( D i / 1 ) o ) 3 ] / [ 1 - ( D i / 1 ) o ) 2 ] } t g a , dimensionless
378
M . V . Heitor and A. L. N. Moreira :30
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~.-.,---~
15
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1.00
0.0
. . . .
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'
~o
" ~ " " " ' -10.0 1.0 1.5
r/Do
a)
b)
Figure 9. Radial profiles of third-order velocity correlations for Re = 49,500 at two different axial locations, X / D o = 0.6 and 1.5. Filled symbols, second-order moments; open symbols, third-order moments.
U,V,W t l r , 0 p, W ~
X, r, 0 CL ;'T
¢
m e a n velocity c o m p o n e n t s in the x, r, and 0 directions, m s fluctuating velocity c o m p o n e n t s in the x, r , and 0 directions, m s coordinate system
Greek Symbols vane angle, deg eddy viscosity, m2s - l stream function
Subscripts inner flow
o q max
outer flow quarl m a x i m u m value along a radius
REFERENCES 1. Gupta, A, K., Lilley, D. G., and Syred, N., Swirl Flows, Abacus Press, 1984. 2. Lefebvre, A. H., Gas Turbine Combustion, McGraw-Hill, New York, 1983. 3. Lawn, C. J., Principles of Combustion Engineeringfor Boilers, Academic, 1987.
Velocity Characteristics of Swirling Flow 4. Bahr, D. W., Aircraft Turbine Engine Combustors--Development Status/Challenges, in Combasting Flow Diagnostics, D. F. G. Dur~o, M. V. Heitor, J. M. Whitelaw and P. O. Witze, Eds., Kluwer, Boston, 1991. 5. Leuckel, W., and Fricker, N., The Characteristics of Swirl-Stabilized Natural Gas Flames. Part I: Different Flame Types and Their Relation to Flow and Mixing Patterns, J. Inst. Fuel, June, 103-112, 1976. 6. Rowe, R., and Kremer, H., Stability Limits of Natural Gas Diffusion Flames with Swirl, 18th Symp. (Int.) on Combustion, The Combustion Institute, 667-677, 1981. 7. Dixon, T. F., Truelove, J. S., and Wall, T. F., Aerodynamic Studies on Swirled Co-Axial Jets from Nozzles with Divergent Quads, J. Fluids Eng., 105, 197-202, 1983. 8. Hardalupas, Y., Taylor, A. K. M. P., and Whitelaw, J. H., Velocity and Size Characteristics of Liquid Fuelled Flames Stabilized by a Swirl Burner, Proc. Roy. Soc. London., A428, 129-155, 1990. 9. Mathur, M. L., and Maccallum, N. R. L., Swirling Air Jets Issuing from Vanes Swirls. Part l: Free Jets, J. Inst. Fuel, May, 214-225, 1967. 10. Sislian, J. P., and Cusworth, R. A., Measurements of Mean Velocity and Turbulent Intensities in Free Isothermal Swirling Jet, A I A A J., 24(2), 303-309, 1986. 11. Tangirala, V., Chen, R. K., and Driscoll, J. F., Effect of Heat Release and Swirl on the Recirculation Within Swirl-Stabilized Flames, Combust., Sci. Technol., 51, 75-95, 1987. 12. Launder, B. E., Second Moment Closure: Present... and Future?, Int. J. Heat Fluid Flow, 10, 282-299, 1989. 13. Jones, W. P., Turbulence Modelling: Current Practice and Future Trends, Proc. Intl. Symp. on Engineering Turbulence Modelling and Measurements, Dubrovnik, Yugoslavia, 24-28, Sept., 1990. 14. Castro, I. P., and Hague, A., The Structure of a Turbulent Shear Layer Bounding a Separation Region, J. Fluid Mech., 179, 439-468, 1987. 15. Smith, A. J., Young, S. T. B., and Bradshaw, P., The Effect of Short Regions of High Surface Curvature on Turbulent Boundary Layers, J. Fluid Mech., 94(2), 209-242, 1979. 16. Gibson, M. M., and Younis, B. A., Turbulence Measurements in a Developing Mixing Layer with Mild Destabilising Curvature, Exp. Fluids, 1, 23-30, 1983. 17. Gibson, M. M., Verriopoulos, C. A. and Vlachos, N. S., Turbulent Boundary Layer on a Mild Curved Convex Surface, Exp. Fluids, 2, 17-24, 1984. 18. Masuda, W., and Andoh, S., Effects of Curvature on the Initial Mixing Region of a Two-Dimensional Jet, A I A A J., 27(19), 52-56, 1989. 19. Dur~o, D. F. G., and Heitor, M. V., Modern Diagnostic Techniques for Combusting Flows: An Overview, in Combusting Flow Diagnostics, D. F. G. Dur~o, M. V. Heitor, J. M. Whitelaw and P. O. Witze, Eds., Kluwer, Boston, 1-46, 1992. 20. Chandrsuda, C., and Bradshaw, P., Turbulence Structure of a Reattaching Mixing Layer, J. Fluid Mech., 110, 171-194, 1981. 21. Driver, D. M., and Seegmiller, H. C., Features of a Reattaching Turbulent Shear Layer Subject to an Adverse Pressure Gradient, AIAA Paper 82-1029, 1982. 22. Pronchick, S. W., and Kline, S. J., An Experimental Ivnestigation of the Structure of a Turbulent Reattaching Flow Behind a Backward-Facing Step, Rep. MD-47, Thermoscience Division, Dept. Mech. Eng., Stanford University, Calif., 1983. 23. Starner, S. H., and Bilger, R. W., Some Budgets of Turbulent Stresses in Round Jets and Diffusion Flames, Combust. Sci. Technol., 53, 377-398, 1987. 24. Heitor, M. V., Taylor, A. M. K. P., and Whitelaw, J. H., The Interaction of Turbulence and Pressure Gradients in Baffle-Stabilized Premixed Flame, J. Fluid Mech., 101, 387-413, 1987.
379
25. Johansson, T. G., and Karlsson, R. I., The Energy Budget in the Near-Wall Region of a Turbulent Boundary Layer, in Applications o f LA to Fluid Mechanics, Vol. 5, R. J. Adrian, D. F. G. Dur[o, F. Durst, R. Raeda and J. M. Whitelaw Eds., Springer-Verlag, New York, 3-22, 1989. 26. Takagi, T., Recent Measurements and the Consequent Understanding of Flow, Mixing and Combustion in Turbulent Diffusion Flames, 23rd. ASME/AIChE Nat. Heat Transfer Conf., Denver Colorado, Aug. 4-7, ASME HTD-45,281-291, 1985. 27. Moreira, A. L. N., Experimental Analysis of Combusting Systems, Ph.D. Thesis, Technical University of Lisbon, 1991 (in Portuguese). 28. Melling, A., and Whitelaw, J. H., Turbulent Flow in a Rectangular Duct, J. Fluid Mech., 78, 283-315, 1976. 29. Zhang, Z., and Wu, J., On Principal Noise of Laser-Doppler Velocimeter, Exp. Fluids, 5, 193-196, 1987. 30. Kreid, D. K., Laser-Doppler Velocimeter Measurements in NonUniform Flow: Error Estimates, Appl. Opt., 13(8), 1872-1881, 1974. 31. Yanta, W. J., and Smith, R. A., Measurements of Turbulent Properties with Laser-Doppler Velocimeter, AIAA Paper 73-169, 1lth Aerospace Science Meeting, Washington, 1978. 32. Dimotakis, P. E., Single Scattering Particle Laser-Doppler Measurements of Turbulence, AGARD CP-193, Paper 10, 1978. 33. Dur[o, D. F. G., Heitor, M. V., and Moreira, A. L. N., Flow Measurements in a Model Burner. Part 1, J. Fluids Eng., 113, 668-674, 1991. 34. Glass, M., and Kennedy, I. M., An Improved Seeding Method for High Temperature Laser Doppler Velocimetry, Combust. Flame, 5, 193-196, 1977. 35. Durst, F., and Zar6, M., Laser Doppler Measurements in Two-Phase Flow~, in The Accuracy o f Flow Measurements by Laser Doppler Methods, Proceedings of the LDA Symposium, Copenhagen, 403-429, 1975. 36. Lau, J. C., Whiffen, M. C., Fisher, M. J., and Smith, D. M., A Note on Turbulence Measurements with a Laser Velocimeter, J. Fluid Mech., 102, 353-366, 1981. 37. Jones, W. P., and Whitelaw, J. H., Modelling and Measurements in Turbulent Combustion, 20th Symp (Intl.) on Combustion, The Combustion Institute, 233-249, 1985. 38. Bradshaw, P., Ferris, D. H., and Atwell, N. P., Calculation of Boundary-Layer Development Using the Turbulent Energy Equation, J. Fluid Mech., 28, 593-616, 1967. 39. Harsha, P. T., and Lee, S. C., Correlation Between Turbulent Kinetic Stress and Turbulent Kinetic Energy, A I A A J., 8, 1508-1510, 1970. 40. Fujii, S., Eguchi, K., and Gomi, M., Swirling Jets With and Without Combustion. A I A A J., 19, 1438-1442, 1981. 41. Janjua, S. I., McLaughlin, D. K., Jackson, T. W., and Lilley, D. G., Turbulence Measurements in a Confined Jet Using a Six-Orientation Hot-Wire Probe Technique, AIAA Paper 82-1262, 1982. 42. Smith, G. S., Giel, T. V., and Catalone, C. G., Measurements of Reactive Recirculating Jet Mixing in a Combustor, A I A A J., 21, 270-276, 1983. 43. Brum, R. D., and Samuelsen, G. S., Two-Component Laser Anemometry Measurements of Non-Reacting and Reacting Complex Flows in a Swirl-Stabilized Model Combustor, Exp. Fluids, 5, 95-102, 1987. 44. Beyler, C. L. B., and Gouldin, F. C., Flame Structure in a Swirl-Stabilized Combustor Inferred by Radiant Emission Measurements, 18th Symp. (Int.) on Combustion, The Combustion Institute, 1011-1019, 1981. 45. Gouldin, F. C., Depsky, J. S., and Lee, S. L., Velocity Field Characteristics of a Swirling Flow Combustor, A I A A J., 23(1), 95-102, 1985. 46. Ribeiro, M. M., and Whitelaw, J. H., Coaxial Jets With and Without Swirl, J. Fluid Mech., 96(4), 769-795, 1980.
380
M . V . Heitor and A. L. N. Moreira
47. Gutmark, E., and Wygnanski, I., The Planar Turbulent Jet, J. Fluid Mech., 73(3), 465-495, 1976. 48. Wood, D. H., and Bradshaw, P., A Turbulent Mixing Layer Constrained by a Solid Surface. Part 1: Measurements Before Reaching the Surface, J. Fluid Mech., 122, 57-89, 1981. 49. Taylor, A. M. K. P., and Whitelaw, J. H., Velocity Characteristics in the Turbulent Near Wakes of Confined Axisymmetric Bluff Bodies, J. Fluid Mech., 139, 391-416, 1984. 50. Castro, I. P., and Bradshaw, P., The Turbulence Structure of a Highly Curved Mixing Layer, J. Fluid Mech., 73, 265-304, 1976. 51. Simpson, R. L., Chew, Y. T., and Shivaprasad, B. G., The
Structure of a Separating Turbulent Boundary Layer. Part 1: Higher Order Turbulence Results, J. Fluid Mech., 113, 53-73, 1981. 52. Gould, R. D., Stevenson, W. H., and Thompson, D., A Parametric Study o f Statistical Velocity Bias, Proc. ICALEO 86, Laser Inst. America, 58, 89-96, 1986. 53. Tennekes, H., and Lumley, J. L., A First Course in Turbulence, MIT Press, Cambridge, Mass., 1972.
Received April 25, 1990; revised November 18, 1991
liThe isothermal recirculating flow downstream of a model swirl burner is studied making use of a laser-Doppler velocimeter. The arrangement was designed to incorporate the injection of liquid fuel into a gas flame characterized by a large recirculation zone attached to the burner head and to allow a detailed analysis of turbulent transport processes in a strongly swirled recirculating flow. The results show that turbulent mixing in the present flow is not dominated by large-scale motions or precession. The production of turbulent kinetic energy depends upon mechanisms of shear-generated turbulence but is influenced by streamline curvature in the zone of mean shear. Inspection of the terms in the conservation equations for the turbulent stresses allows quantification of the extent to which the interaction of normal stresses and normal strains influence the flow and suggests the likely magnitude of turbulent diffusion and dissipation.
Keywords: swirling flow, turbulent transport, model burner INTRODUCTION Swirling recirculating flows are typical of a variety of power and propulsion devices (see, eg, Refs. 1-4), in which the separated recirculating flow established downstream of swirling vanes is used to allow the stabilization of high-intensity turbulent flames. The combustion process in these flames is partly dependent on the mixing of the fuel and air streams, which in turn is determined by the state of the flow turbulence [5-7]. In addition, analysis has shown that the details of the aerodynamics of the near burner zone are crucial to the description of the mechanisms of flame stabilization and fuel burnout [8], and further results are necessary to guide the development of optimized burner geometries and of tools to predict their effects. In particular, the analysis of isothermal models of the combusting flows allows much to be learned about the turbulent processes typical of recirculating flames in experimentally simpler flows and is considered in this paper. Although velocity measurements in swirling recirculating flows have been extensively reported [8-11], measurements have been mostly concerned with turbulence intensities, and only a few examples of other turbulence properties are available. In particular, third-order correlations of velocity fluctuations can provide information on the effects of curvature and proximity of a stagnation zone on the turbulence structure and are necessary to obtain a full second-order closure of the differential equations for turbulent transport of momentum and energy [12, 13]. However, most of the published works reporting higher order velocity measurements are concerned with the effects of curvature in simple mixing layers [14-18]. In addition, experiments in which the measurements are used to obtain magnitude estimates of other quantities of direct relevance to turbulence modeling, such as budgets and correlation coefficients of Reynolds stresses, are necessary but are
very demanding in the experimental technique [19]. Results of this kind were obtained with hot-wire anemometry [20-22], and more recently LDA measurements were used to derive such information [23-25]. In both cases, published works are concerned with somewhat simple flows, such as mixing layers, axisymmetric jets, and baffle-stabilized flames, and despite the wide practical importance of strongly swirled recirculating flows, they have not been fully addressed; see, for example, Ref. 26. This paper analyzes the turbulent characteristics of the isothermal flow in a typical swirling burner arrangement, which may incorporate the injection of liquid fuel into a gas flame. The experiments include laser-Doppler measurements of mean velocity together with those of double and triple velocity correlations in the three spatial directions. The results are used to obtain estimates of the convection and production terms in the transport equations of the Reynolds stresses and provide a basis for improving our understanding of relevant transport processes in industrial burners and for guiding turbulence modeling. The paper is presented in five sections including this Introduction. The following section describes the burner arrangement and the experimental method and gives details of the flow analyzed. The third section presents the mean and turbulent flowfields in the vicinity of the burner head, and the fourth discusses the results and analyzes the turbulent transport processes typical of the present flow. The final section summarizes the main findings and conclusions of the work. FLOW CONFIGURATION AND EXPERIMENTAL METHOD The burner arrangement and the experimental techniques used throughout this work are described in this section to-
Address correspondence to Professor Manuel V. Heitor, Instituto Superior T~cnico, Department of Mechanical Engineering, Technical University of Lisbon, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal.
Experimental Thermal and Fluid Science 1992; 5:369-380 © 1992 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/92/$5.00
369
370
M . V . Heitor and A. L. N. Moreira
gether with their likely accuracy. The arguments associated with the assessments of accuracy provided are based on previous experiments and are presented in condensed form. Details can be found in Ref. 27. The flow configuration is based on those under " d u a l " burning of liquid and gaseous fuels in practical furnaces and is presented in Fig. 1. It comprises a commercial fuel atomizer with an external diameter of d = 23 mm, assembled in a low-velocity cofiow of propane gas (54 mm O.D.), which is externally surrounded by a high-velocity coflow of air (84 mm O.D.). A diverging quarl typical of those found in the burners of industrial furnaces was located at the burner exit and could be removed to permit the measurement of boundary conditions. Swirl is imparted to both streams by means of fixed blades at 45* [9] with resulting swirl numbers, estimated from the geometry of the blades as in Ref. 27 (see Nomenclature), equal to S O = 0.77 and S i = 0.85 for the outer and inner streams, respectively. The outer airflow rate was measured with a calibrated standard orifice meter, and integrated Pitot tube measurements have shown that the measured flow rates are accurate within 2 %. The inner flow rate was measured by a rotameter with an absolute error smaller than 0.1 L/s, which corresponds to an accuracy of 1.8% for the flow conditions studied here.
Dq
"t ://
ii
f,# -~Ld -I--~, ..,~}~
g o .-------.mm~
Air
Fuel =
I
Atomization
Air
--.Im,~
I
~ Liquid Fuel (Optional) Figure 1. Schematic diagram of the model burner.
The measurements presented here were obtained for nonreacting conditions in the absence of liquid fuel, with the propane gas replaced by air with a momentum flux similar to that of a flame with an air-to-fuel volumetric ratio equal to 27.6 and a heat load of about 350 kW. The resulting flow conditions correspond to bulk velocities, defined as the ratio between the flow rate and the cross-sectional area, equal to U o = 30 m / s (Re o = 49,500) in the outer airstream and U / = 2 ms ( R e / = 4000) in the inner stream, respectively. The origin of the axial axis, x, is taken at the center of the exit plane of the model burner, and the tangential velocity is taken positive in the anticlockwise direction, facing the burner. The burner is located vertically directed upward, and the symmetry of the flow was verified by measuring several complete radial profiles of mean and fluctuating velocity values. Velocity measurements were obtained with a dual-beam laser-Doppler anemometer based on an argon ion laser light source at 514.5 nm (1 W nominal) with sensitivity to the flow direction provided by light-frequency shifting from acoustooptic modulation (double Bragg cells) with a resulting shift of the Doppler signal in the range 0 - 1 0 MHz. The half-angle between the beams was 4.92", and the calculated dimensions of the measuring volume at the e - 2 intensity were 1.528 and 0.132 mm. The transfer function in the absence of frequency shift was 0.33 MHz/(m • s-1). Forward-scattered light was collected and focused into the pinhole aperture (0.300 mm) of a photomultiplier tube with a magnification of 0.74. The bandpassed filtered Doppler signals were processed by a commercial frequency counter (TSI 1980B) interfaced with a 16-bit microcomputer. The ~omplete laser-Doppler velocimeter (LDV) system was fixed, and the burner was mounted on a three-dimensional traversing unit, allowing the control volume to be positioned within +_0.25 mm. The distributions of the Reynolds shear stresses u ' u ' and u ' w ' and corresponding triple velocity correlations were obtained by traversing the control volume along two normal diameters with the laser beams in the horizontal and vertical planes and at +_45 °, as described in Ref. 28. The accuracy of the laser-Doppler measurements may be influenced by transit broadening [29] and nonturbulent Doppler broadening errors [30], which affect mainly the variance of the velocity fluctuations and were estimated to be 2 smaller than 5 × 10- 5 Uo2 and 1 × 10- 3 Uo, respectively. The number of individual velocity values used to form the averages was always above 15,000, which results in statistical (random) errors smaller than 1% and 4%, respectively, for the mean and variance values for a 95% confidence interval [31]. Systematic errors due to sampling bias were minimized by using data rates of valid Doppler signals higher than the fundamental velocity fluctuation rate [32]. To avoid bias errors due to unequal particle densities in the inner and outer airflows [33], the two streams and the ambient air in the vicinity of the burner head were seeded separately with powdered aluminum oxide (0.6-1 #m nominal diameter before agglomeration) dispersed in specially built cyclone generators [34]. "Fringe (angle)" bias was minimized by using large values of frequency shifting as suggested in Ref. 35, and for the present case the acceptance angle estimated as in Ref. 36 was 360 ° for a fringe-to-particle velocity ratio larger than 1, which could be achieved with frequency shifts up to 10 MHz.
Velocity Characteristics of Swirling Flow
371
B
Systematic errors incurred in the measurement of Reynolds shear stress can arise from lack of accuracy in the orientation angle of the normal to the anemometer fringe pattern, as shown in Ref. 28, and can be particularly large in the vicinity of the zones characterized by zero shear stress. For the present experimental conditions, the largest errors are expected to be smaller than - 2 %. RESULTS Detailed measurements of mean and turbulent velocity characteristics were obtained at six different horizontal planes downstream of the burner head. Sample results are presented in Figs. 2 - 5 , as either radial profiles or isocontours. The choice depends on the intention of the figure, and no attempt was made to provide all data with the same uniformity of precision. Figures 2 and 3, respectively, show mean streamlines and radial profiles of mean velocity and indicate the most salient features of the time-averaged flow in the vicinity of the burner head. The values of the stream function were calculated by integrating the radial profiles of mean axial velocity as described, for example, in Ref. 10. The results exhibit features typical of strongly swirling jets with a region of recirculation attached to the burner head and extending up to about x / D o = 3.7. The maximum negative reverse velocity is - 0 . 7 5 U o and occurs at x / D o = 1.0, where the recirculation zone exhibits its maximum width. This velocity is important because it quantifies the strength of the recirculation zone and also because it influences the magnitude of the recirculating mass flow rate. The reverse flow zone is surrounded by a region of large and positive axial velocity values with maxima moving outwards and decaying far downstream, and with the loci of maxima radial gradients of mean axial velocity approximately coincident with the zero velocity line up to x / D o = 1.5. The radial component of mean velocity, V, is positive up to x / D o = 1.5 and has two maxima with an inflection point in the shear layer around the recirculation zone. Downstream of x / D o = 1.5, the values of V show a trend similar to that observed in the recirculating swirl flow of Ref. 10, with negative values inside the recirculation zone and positive values for larger radii. The profile of the mean
tangential velocity component, W, at the exit of the quarl ( x / D o = 0.6) exhibits a linear distribution typical of solid body rotation within the recirculation zone (ie, for r i D o < 0.5), whereas in the outer flow region W reaches a maximum at the edge of the flow and then decreases rapidly. Inside the recirculation zone the fluid rotates with an angular velocity that increases initially up to x / D o = 1.0 and then decreases gradually with the downstream distance. The transition from the exit profile to a Rankine type of vortex profile, as defined in Ref. 1, takes place at x / D o = 1.0, with the maximum swirl velocities occurring at the edge of the recirculation zone up to x / D o = 1.5. These maxima move radially outwards and decay rapidly. The distributions of the Reynolds normal stresses must be related to those of mean shear and are represented in Fig. 4 in the form of isocontours. In general, the results reveal that upstream of x / D o = 1.0 the levels of velocity fluctuations are small inside the recirculation zone and large in the highly strained annular shear layer, where turbulence is strongly anisotropic with u ,2max=_ 2.2v, Zmax= 2.2w ,2max" Downstream of x / D o = 1.5 the three normal stresses decrease as the distance to the burner increases, with v '2 and w "2 slightly larger than u' 2 in the vicinity of the rear stagnation point. As a result, the distribution of turbulent kinetic energy (Fig. 4d) show maximum values along the edge of the backflow region in contrast to the observations of Refs. 14 and 24 downstream of axisymmetric and plane baffles, where the stagnation region is characterized by the highest values of turbulent kinetic energy. The correlation coefficients for the shear stresses
R.o = u'v/(u "~ . ~'2) ~/2 and Ruw = u'w
/(
U '2
"
W'2) 1/2
have been calculated from the results to assess the extent to which the turbulence in the present flow is affected by "unusual" mechanisms and are plotted in Fig. 5. The
2.5 2.0 1.5
i1 .o
:).5
o.o
Figure 2. Measured streamline distribution for Re = 49,500.
r/Do
372
M . V . Heitor and A. L. N. Moreira
0.20 [ 0.15|
1.00 f 0.75 |
0.10| o.o5~
0.50 0.25 |
000 • ~
,=.a~eee~.=_=
__
0.40 | 0.30 |
-.~
j
1.oo [ 0.75 |
0.00 ~
0.50 |
~ _
o.15t o.lo~ 0.05 [
---,,,~_
............
..-7
-0.25 .......... , ............. 1 . 5 ~ 1.0 0.5 ~ 0.0 \ -0.5
,~ _,,-
0.50
"X.
"~.
- o.oo,;,,~-
0.25
-0.10 ..........................
0.00
-0.05|
0
-0.5 -1.0 I ' ' ' "
....... ' .............
~ -°.°i--0.1 . . . . . . . . . . . . . . . . . . ._. . . . I> 0 . 3 0.2 0,1 -0.0 -0.1 -0.2
,,
0.75 [ 0.50 I
2.0
/%
1.0 0.5 0'0 . . ~ . . . ~.
0.00
1.00 0.75
_-
,111,
0
.
5
0
~
0.25
X/Do
0.00 0 .
7
5
=
1,5
~
1.00
X/Do = 1.0
~
0.75 0.50 0.25
0.50 0.25
o.oor
-0.25 ; . . . . . . . . . . . . . . . . . . . . . . . . . o.o 0.5 1.o 1.5 2.0 2.5 r/Do
a)
X/Do = 2.1 v
0.75
0.00
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.5
0.25
0,25
-0.5
r/Do
~
0.50
0 . 2 5 ~
2 . 0 ~ 1.5 1.0 0.5 0.0 -0.5q -1.0 0.0 0.5 1.0 1.5 2.0
X/Do = 2.7
0.75 i 0.50
0.2 0.1. _
1.0 0.5 0.0
X/Do = 3.3
. . . . . . . . . . . . . . . . . " ....
0.75 r
0.20 [
0.25 ~ . ~
- - 1 , 0
0.20 ~ _ . , ~ , - ~ _ o.lo L"
1 -0.05 . . . . . . . . . . . . . . . . . . . . . . . . . - 0.00 ~ t r ; . - ~
_o'.25.t~... .....................
0.00
0.50 f
b)
X/Do
=
0.6
0.00
0.0 0.5 1.0 1.5 2.0 2.5 r/Do
c)
Figure 3. Radial profiles of mean velocity components for Re = 49,500. (a) Axial velocity, U/Uo; (b) radial velocity, V/Uo; (c) tangential velocity, W~ Uo.
nondimensional distribution of the shear stress u' v' indicates maximum values coincident with those of u '2, with the radial profiles exhibiting two peaks. The inner, negative peaks occur near the edge of the recirculation zone where the mean shear rate OU/Or is characterized by the maximum positive values, and the outer, positive peaks are located in the outer shear_layer and coincide with the maximum negative values of aU/Or. The sign of the shear stress is related to the sign of the shear strain OU/Or in accordance with a turbulent viscosity hypothesis [37], except for a narrow zone in the upstream part of the shear layer adjacent to the reverse-flow zone, where the shear strain is close to zero. This agrees with the results of Ref. 24 in the shear layer adjacent to a baffle-induced flow and in the initial mixing region of the curved two-dimensional j e t of Ref. 18 and may be related to the large shear strain OF~Or associated with the sudden expansion at the exit of the quarl. Whereas in the outer shear layer, where OU/Or < 0, the peak values of Ruv are of the order of 0.5, in the inner shear layer, where cgU/ar > 0, the absolute values of Ru~ increase from 0.3 at the exit plane of the quarl (ie, at x / D o = 0.6) up to values considerably
higher, about 0.7 at x / D o = 1.0, and decrease to a constant value equal to - 0 . 4 far downstream. Similar trends have been observed in other recirculating flows [20-24] and were attributed in Ref. 15 to the effects of streamline curvature. In addition, the values of the shear stresses normalized by the turbulent kinetic energy, which are not shown here due to lack of space, exhibit values smaller than 0.3 in the inner shear layer in agreement with the observations in Refs. 15-17, and values larger than 0.3 in the outer shear layer. The results therefore reveal departures from the values expected in " n o r m a l " shear layers [38, 39] and suggest that the shear stress in the present flow is primarily induced by streamline curvature in the inner and outer shear layers and that large-scale motions are likely to have minor importance in the balance of turbulent kinetic energy. The values of R.w are similar to those of R.v at x / D o = 0.6 and are considerably attenuated with the exception of the region around x / D o = 1.5, where the mean shear strain OW/ar reaches maximum negative values. It should be pointed out that, with the exception of this region, peak values of R.w would be expected to be smaller than those of
Velocity Characteristics of Swirling Flow 373 4.0
a}
'
"
" I- ~ - '
"
'
I
. . . .
I ~ ' ~ - I - ~ - V
"r
'
'
'
1
Ru, once u '2 is the only stress that contributes to the production of u'w' through the interaction with a W / a r . Maximum values of Ruw in other swirl recirculating flows [40-43] are in the range 0.2-0.4 and follow this expectation. An important feature of the present flow is the absence of large-scale high-energy oscillations, which distinguishes it from those swirling flows containing energetic precessing vortex cores or other low-frequency, high-energy oscillations, as reported in Refs. 44 and 45. The probability density functions of the three velocity components follow near-Gaussian distributions, with values of the skewness and flatness factors in the ranges - 0 . 9 to 0.9 and 2.8 to 4.8, respectively.
. . . .
3.5
u'Z/Uo x 102
3.0 2.5 o
2.0 1.5 1.0 0.5 0.0
b)
4.0
. . . .
I
. . . .
I
. . . .
I
. . . .
I
. . . .
I
. . . .
I
. . . .
,
3.5
v'Z/Uo x
3.0
I0a 0.5
2.5 2.0
0
1.5 1.0 0.5 I
0.0
t
I
I
,i
. . .
4.0
c)
3.5
a)'Z/Uo x 102
3.0 2.5
0.5
2.0
O
E3 1.5
.~...~---- . . . . .
~
1.0 0.5 0.0
4.0
d)
''
'|
. . . .
1
. . . .
I
' ' ' '
I
. . . .
I
. . . .
I
. . . .
3.5 k / U o x 10 ~
3.0
0.5
2.5 0
r~
2.0 1.5 1,0 0.5 O.O 0.5
1.0
1.5
2.0
2.5
3,0
3.5
4.0
x/Do Figure 4. Isocontours of Reynold_.~snormal stresses for Re = 49,500. (a) A__xialnormal stress, u ' E / u 2 x 102; (b) radial normal stress, o'2/Uo2 x 1 0 2 ; (C) tangential normal stress, w'2/Uo2 × 102; (d) turbulent kinetic energy, k / U 2 x l02.
DISCUSSION The foregoing presented the measurements of mean and turbulent velocities obtained in the vicinity of the model burner considered throughout this paper. This section discusses the results, analyzes their practical significance, and considers their implications for the calculation of swirling flows using turbulence models. The flowfield under analysis includes zones of recirculation, acceleration, and near-uniform velocity that are qualitatively similar to those reported for other separated flows with a free stagnation point, such as the swirling flow of Ref. 10 or the baffle-induced flow of Ref. 24. The aspects of the flow that are of particular interest here are the size and strength of the swirl-induced recirculation zone, the recirculating massfloff rate, and the levels of turbulence that are generated. These were conveniently identified in the previous sections, and the axial distribution to those related to the time-averaged flowfield is summarized in Fig. 6. The loci of the separation streamline, ~b = 0, reveals the large curvature undergone by the flow streamlines, which is associated with pressure gradients that are directed normally to the streamlines and depend on the degree of curvature. As a result, a pressure minimum exists at the zone where the reverse velocity reaches a maximum value. Far downstream the flow recovers to the ambient pressure and the acceleration of the fluid is dominated by the magnitude of this pressure gradient. The implications of the results for the design of practical burners should be analyzed in terms of the extent and strength of the recirculating flow and the spreading rate of the outer flow, which determine the length of the flame in practical burners and influence their efficiency. The extent to which the flame propagates and anchors at the burner head depends upon the ratio of the local flow velocity to the burning velocity, which in turn varies with the local stoichiometry [3]. This is a function of the mixing that has taken place between fuel and oxidant and depends upon the magnitude of the swirl level. The present results provide detailed information about these aerodynamic characteristics and should be used to evaluate the performance of calculation methods of the flow in practical burners in order to allow extrapolation of the experimentally acquired information to more realistic flow conditions. Inspection of the time-resolved velocity characteristics measured along the three spatial coordinates reveals that the recirculation zone up to its maximum width is a zone of intense generation of turbulence. The existence of zones characterized by large turbulence anisotropy in the present flow has important implications, because calculation methods
374
M . V . Heitor and A. L. N. Moreira
0.5 O• 0
0.5 O .I 0
-~
-0.5
"°i
"il
0.5
-1'0 .......................... °
.
.
.
.
.
.
.
.
.
~
.
.
.
.
.
_
1.o
5.5
X/Do =
2.7
.
1.0
> 1!::~
.................
Iz: 1.0 0 . 5 ~
~ - : " : ~ . i n,-" 1.0 0.5 I
0.0
0.0~..
-0.5 -1.0 1 . 0
-0.5 -1.0 1.0
0.5 0.0
0.5
.......
X/Do = 1.5 .....................
L
0.0~
-
j
-0.5
-o.5[ -I .0 . . . . . . . . . . . . . . . . . . . . . . . . .
'°I •
°I
05
010
-0.5~.... 0.5
.................. 1.0
1.5
2.0
2.,5
X/Do = 2.1
-,,r~
-I .0
10 0.0
X/Do =
0.5
-~ - -
""
....
0.5 0.0 -0.5~ 10 0.0 0.5
X/Do = 1.0
--
X/Do = 0.6 1.0
............... 1.5
r/Do
r/Do
a)
b)
2.0
2.5
Figure 5. Radial profiles of the correlation coefficients for Reynolds shear stresses for Re = 49,500.
(a) Ruu =
LI'U'/
(u '2" v'2)1/2; (b) R,w = u'w'/(u '2. w'2) 1/~.
based on scalar effective viscosities do not adequately represent the behavior of the normal stresses. The deviation from isotropy beyond the central zone is very clear and, following the analysis of Ref. 46, suggests that turbulence is mainly transported in the axial direction by means of large-scale eddies. On the other hand, the comparatively low magnitude of the normal stresses and their relative isotropy near the centerline suggest that the flow there is dominated by dissipating small-scale eddies. Therefore, the results suggest that the calculation of swirling flows, such as those in industrial burners, should involve a turbulence model at the level of transport equations for the Reynolds stresses, rather than at the level of a turbulent viscosity closure. This can be further analyzed by examination of some of the terms in the conservation equations for the Reynolds stresses, as explained below.
The measurements of the mean and turbulent velocity characteristics reported in the previous section have allowed estimation of the convection and production terms in the transport equations for turbulent kinetic energy and for Reynolds shear stresses, which are discussed here to improve the analysis of the mechanisms involved in the generation of turbulence in the present flow. The estimates are approximate because of the error in evaluating the spatial gradients, but the values are sufficiently accurate for the purpose of establishing the relative importance of the separate terms in the conservation equations. Figure 7 shows radial profiles of the production and convection terms in the conservation equation for turbulent kinetic energy normalized by U3/Do, with convection plotted so that a negative value represents a gain. The results show distributions in the outer shear layer (where OU/ar < O)
Velocity Characteristics of Swirling Flow 250
200 E E
150
0.1
50
o2 ~
.4
~
0.6
O ~ U max )
~=0
-~ ~
X (mm)
0.8 1.0 Figure 6. Axial distribution of time-averaged aerody__namiccharacteristics of the flowfield: reverse-flow boundary, U = 0; eddy boundary, ~k = 0; locus of maximum axial velocities, U = Ureax ; jet boundary, U = 0.10Umax; recirculating mass flow rate,
mr/m0. qualitatively similar to those observed in other mixing layers [20, 47]; production is mainly due to the interaction between shear stress and shear strain and is balanced by turbulent diffusion and dissipation. In the core of the annular jet, turbulence production by normal and shear stresses is negligible; convection is the largest term and represents a gain, which is balanced by turbulent diffusion and dissipation. For smaller radii, and in the region of the separation streamline and upstream of stagnation (ie, x / D o < 2.0), the distribution of the various terms resembles that in the mixing layer of Ref. 48 and upstream of the reattachment zone in the backstep flows of Refs. 20 and 22. Convection is small, production is mainly by shear stress, and turbulent diffusion and dissipation are important and represent a loss. Around x / D o = 2.1, the deflection of the separation streamline (see Fig. 2) occurs in a zone where turbulence production by the interaction of normal stresses with normal strains is large, with maximum values in the vicinity of r i D o = 0.4. This observation is in accordance with the decrease in the ratio between u '2 and v '2 measured in this region of the shear layer and agrees with the results of Ref. 24 in a baffle-stabilized wake flow. In agreement with the analyses presented before, it should be noted that for these flows in which there is production of turbulent kinetic energy through normal stresses, calculations using a scalar effective-viscosity turbulence model will be inaccurate. This is because such models do not adequately represent normal stresses and although the gradients of normal stresses are not large terms in the transport of mean momentum (see Ref. 27 for details), the importance of the various production terms in generating turbulent kinetic energy implies that it is necessary to calculate the individual
375
normal stresses adequately if the correct turbulent kinetic energy is to be obtained. As noted in Ref. 49 for the turbulence in stagnation zones downstream of bluff-body flows, this distribution is crucial to correct representation of the effective viscosity, and the latter quantity is of importance in the mean momentum equations. The terms in the transport equation of shear stress u' u' (Fig. 8) show that production is dominated over the whole length of the measurements by the interaction of normal stresses with shear strains, that is, o'2(OV/Or), as in the swirling jet of Ref. 46 and in the recirculating flow of Ref. 24. Around the core of the annular jet, where u' v'= O, this term reverses its sign, but in either the inner or outer parts of the flow it is likely to be balanced by pressure-redistribution terms. Diffusion of turbulent energy and shear stress may be associated with the gradients of third-order correlations of velocity fluctuations, which are strongly affected by both longitudinal curvature and proximity of a stagnation zone, and has been attributed to large-scale motions [46, 50, 51]. Figure 9 shows radial profiles across the recirculation bubble of the triple products u'2v ', 0'3, and u'o '2, which represent the turbulent radial fluxes of u '2, 0 '2, and u' v', respectively. The results show that the triple velocity correlations are one order of magnitude smaller than the corresponding Reynolds stresses and have distributions qualitatively similar to those in other recirculating flows, such as the backstep flows of Refs. 2 0 - 2 2 or the bluff body flow of Ref. 24. The distributions of Fig. 9 also show that turbulent transport of both normal and shear stresses is mainly in the gradient sense. The triple products are close to zero at the loci of zero radial gradients of the corresponding second-order correlations, and their positive values are associated with turbulent transport of the Reynolds stresses from the high-production-rate zones to the outer flow. It should also be noted that the values of u'2o ' and 0 '3 along the edge of the recirculation zone are negative and are associated with the transport of turbulent kinetic energy from the highly turbulent shear layer to the backflow region of weak turbulent fluctuations, as in the other recirculating flows [51, 52]. However, minimum values of 0'3 diffuse toward the centerline faster than those of u'2o ', suggesting that the radial transport of_f_o'2 toward the stagnation point is faster than that of u '2. This observation is similar to the effect of streamline curvature observed in Ref. 17 and is consistent with measured values of i)'2/u '2 larger than unity. This is restricted to the vicinity of the centerline and in the outer shear layer, where OU/Or < 0 and the distributions of the triple velocity correlations are in agreement with those observed in the entrainment region of axisymmetric free jets [53] and plane mixing layers [48]. CONCLUSIONS Laser-Doppler measurements have provided detailed information about the turbulenee characteristics of the isothermal recirculating flow established downstream of a model swift burner, which was designed to allow the injection of liquid fuel into a gas flame. Measurements were obtained for a Reynolds number of the main airflow of 49,500 and a swirl
376
M . V . Heitor and A. L. N. Moreira 100.0
I
'
'
IO0.0
'
x/Do
=
.
.
.
.
I
0.6
.
.
x/Do
50.0
.
.
=
1.0
50.0
0.01
0.O
-50.0
-50.0
-100.0
'
.
.
.
.
'
0.0
40.0
-100.0
0.5
. . . .
,
.0
....
, x/Do
0.0
~
10.0 =
.
1.55
20.0
5.0
0.0
0.0
-20.0
1.0
0.5
.
.
.
I
.
.
.
.
I
.
.
.
.5
.
I
.
.
.
.
4
-5.0
-40.0
. . . . . . . . 0.0
5.0
•
•
I
. . . .
,
. . . .
,
. . . .
t
1.0
0.5 . . . .
,
1.5
. . . .
x/Do
,
=
. . . .
-10.0
.
0.0
0.0
-2.5
-1.0
.
.
.
,
0,5
. . . .
J . . . .
1.0
i
1.5
. . . .
.
I
,
,
,
,
0.5
I
,
,
,
1.0
,
I
.
.
.
.
1.5
2.0
2.74
1.0
0.0
.
2.0
2.5
--5.0
.
0.0
i
2.0
. . . .
--2.0
2.5
r/Do
. . . .
0.0
'
0.5
. . . .
'
1.0
.
•
,
,
I
1.5
. . . .
I
2.0
. . . .
I
2.,5
r/Do
Figure 7, Radial profiles of the production and convection terms in the conservation equation for turbulent kinetic energ 3 (Re = 49,500). (O) Production by normal stresses; ( A ) production by shear stresses; ( V ) convection• Solid curves indicat( imbalance.
number of 0.77. The flow is characterized by the presence of a large recirculation zone that is curved along its length and imposes mean velocity effects on the turbulent field. The
Inspection of the terms in the conservation equations fo~ the turbulent stresses show that the interaction between normal stresses and normal strains influences the turbulent flow,
normal stresses show substantial departures from isotropy, and their ratios are strongly d e p e n d e n t on the local m e a n strain rate. In the upstream part of the annular swirling jet,
particularly in the upstream part of the annular swirling jet and in the vicinity of the rear stagnation point, where turbulent diffusion and dissipation are likely to be important in the balance o f turbulent kinetic energy.
the ratio u'2/o '2 is larger than unity and the flow is dominated by large values o f the shear strain rate aU/Or, whereas in the vicinity o f the stagnation region, values of u'2/v '2 smaller than unity are associated with large values o f the normal strain rate OU / a x.
The experiments were performed at the Centro de Termodin~mica Aplicada e Mechnica dos Fluidos da Universidade T6cnica de Lisboa, CTAMFUTL-INIC. Financial support has been provided by the Com-
Velocity Characteristics o f Swirling Flow 100.0
377
100.0 x/Do
=
0.6
x/Do = 1.0
50.0
50.0
. A A A A A A A A "
0.0 t
0.0 ~
-50.0
-50.0
i
-100.0
i
0.0
i
I
0,5
.0
40.0
-100.0 0.5
0.0
10.0
. . . .
i
1.0
. . . .
i
. . . .
x/Do = 1.55
1.5 I
. . . .
x/Do = 2.14
20.0
5.0
0.0
0.0
-20.0
-5.0
1
--40.0 0.
0.5
.
.
.
.
1.0
5.0
'
'
i
. . . .
,5 t
.
-
-10.0
I
2.0
'
l
l
l
i
l
l
l
. . . .
t
, l l
t
0.5
0.0
1.0
. . . .
i
.
I
I
I
,
I
1.5
,
i
. . . .
2.0 i
-
-
•
x/Do = 3.33
x/Do =2.74
1.0 0 o
00
0.0
t
-2.5
-5.0
.... 0.0
~ .... 0.5
~ .... 1,0
~ .... 1.5
' .... 2.0
- - 2 . 0
2.5
. . . .
0.0
'
'
'
0.5
'
I
. . . .
I
1.0
x.5
. . . .
I
. . . .
2.0
2.5
r/D0
r/Do
F i g u r e 8. Radial profiles o f the p r o d u c t i o n a n d c o n v e c t i o n t e r m s in the c o n s e r v a t i o n equation for the Reynolds shear stress u ' v' (Re = 49,500). Symbols as for Fig. 7. mission of the European Communities under the contract Science-SC10459.
Lq m0 m r
r Re R.o
NOMENCLATURE D d k L,
diameter, m diameter of liquid atomizer, m t u r b u l e n t k i n e t i c energy + w'2)/21, mZ/s z recirculation length, m
quarl length, m total air mass flow rate, kg/s recirculating mass flow rate, kg/s radial coordinate, m Reynolds number, dimensionless correlation coefficient for the Reynolds shear stress U' V'
[=
(u 'z +
v 'z
R uw
S
[ =
U t II'/(U
t 2
. Vt
2)
I/2],
dimensionless
correlation coefficient for the Reynolds shear stress u' w ' [ = u' w ' / ( u 'z • w'2)1/2], dimensionless swirl number, defined as S = ( 2 / 3 ) { [ 1 ( D i / 1 ) o ) 3 ] / [ 1 - ( D i / 1 ) o ) 2 ] } t g a , dimensionless
378
M . V . Heitor and A. L. N. Moreira :30
.r__,. ~
_~_r_.~
~~
_r__ ~ ~
. _ .,--1.- _~ -
~.-.,---~
15
30
30
2O
20
10
ID~
%
-
10
" 10
%
%
10
o
%
x
x O
0
x o
....
%
5
q
o :D
-10 -20
-20 -30
-30 0.00
0.25
0.50
0.75
.00
• L ~.
i ....
i . . . .
0.5
0.0
1.0
1.5
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.
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.
.
.
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.
.
.
.
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. . . .
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5.0 2.5
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o
o
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--5 ~
vw 1-2.5 -5.0
--10 --15 0.00
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i ....
I . . . . 0.5
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-~--r--'v--T~---r-""
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0.0
. . . .
r/Do
' " ' 0.5
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a)
b)
Figure 9. Radial profiles of third-order velocity correlations for Re = 49,500 at two different axial locations, X / D o = 0.6 and 1.5. Filled symbols, second-order moments; open symbols, third-order moments.
U,V,W t l r , 0 p, W ~
X, r, 0 CL ;'T
¢
m e a n velocity c o m p o n e n t s in the x, r, and 0 directions, m s fluctuating velocity c o m p o n e n t s in the x, r , and 0 directions, m s coordinate system
Greek Symbols vane angle, deg eddy viscosity, m2s - l stream function
Subscripts inner flow
o q max
outer flow quarl m a x i m u m value along a radius
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Received April 25, 1990; revised November 18, 1991