Experiments in Fluids

, Volume 53, Issue 2, pp 545–560

PIV analysis of merging flow in a simplified model of a rotary kiln

Authors

    • Division of Fluid and Experimental MechanicsLuleå University of Technology
  • B. Reine Granström
    • Division of Fluid and Experimental MechanicsLuleå University of Technology
  • T. Staffan Lundström
    • Division of Fluid and Experimental MechanicsLuleå University of Technology
  • B. Daniel Marjavaara
    • LKAB
Research Article

DOI: 10.1007/s00348-012-1309-1

Cite this article as:
Larsson, I.A.S., Granström, B.R., Lundström, T.S. et al. Exp Fluids (2012) 53: 545. doi:10.1007/s00348-012-1309-1

Abstract

Rotary kilns are used in a variety of industrial applications. The focus in this work is on characterizing the non-reacting, isothermal flow field in a rotary kiln used for iron ore pelletization. A downscaled, simplified model of the kiln is experimentally investigated using particle image velocimetry. Five different momentum flux ratios of the two inlet ducts to the kiln are investigated in order to evaluate its effect on the flow field in general and the recirculation zone in particular. Time-averaged and phase-averaged analyses are reported, and it is found that the flow field resembles that of two parallel merging jets, with the same characteristic flow zones. The back plate separating the inlet ducts acts as a bluff body to the flow and creates a region of reversed flow behind it. Due to the semicircular cross-section of the jets, the wake is elongated along the walls. Conclusions are that the flow field shows a dependence on momentum flux ratio of the jets; as the momentum flux ratio approaches unity, there is an increasing presence of von Kármán-type coherent structures with a Strouhal number of between 0.16 and 0.18. These large-scale structures enhance the mixing of the jets and also affect the size of the recirculation zone. It is also shown that the inclination of the upper inlet duct leads to a decrease in length of the recirculation zone in certain cases.

1 Introduction

Rotary kilns are used to heat materials to high temperatures in various industrial processes. The iron ore pelletizing kiln of interest in this work is distinguished from other mineral-processing kilns as to its geometry and operating conditions, motivating a systematic study of factors influencing the combustion behavior. In particular, there is a relatively large mass flow of air driven through the kiln.

Combustion in mineral-processing kilns can be considered rather unconventional, as it is usually not possible to completely regulate all of the combustion air. Kiln burners are characterized by long diffusion flames with only a small portion of the combustion air channeled through the mechanical confines of the burner while the remaining combustion air is induced through the kiln hood; these air streams are termed primary and secondary air, respectively. Generally, the combustion is largely controlled by turbulent diffusion mixing between the secondary air streams and the confined burner jet.

The early work of Thring and Newby (1953) laid ground for a theory of axisymmetric enclosed turbulent jets. Starting from Reynolds equations for an enclosed jet, a similarity parameter was derived by Curtet (1958) to describe the jet mixing and Becker et al. (1963) further developed his work. Hill (1965) used theory on free jets to predict the velocity field of confined jets. By using isothermal water and air models of a rotary cement kiln, Moles et al. (1973) studied the effect of the ratio of primary to secondary flow velocity on the external recirculation. They evaluated the similarity parameters of Thring and Newby (1953), Curtet (1958) and Becker et al. (1963), in favor of the two latter. The work of Moles et al. (1973) indicated that the secondary airflow pattern is affected by the kiln hood design and the cooler operation, and they concluded that a correctly scaled model of the particular system is needed for accurate results.

Modifications of the kiln hood or cooler are expensive compared to burner modifications, and therefore, the most common approach is to use primary measures to improve the mixing and combustion. Hence, the focus in the literature is mainly on kiln burner characterization, for example the CEMFLAME programmes conducted by the IFRF (van de Kamp and Daimon 1996). To the authors’ knowledge, apart from Granström et al. (2009) and Larsson et al. (2013), there is no attempt in the literature to study the aerodynamic aspects of rotary kilns of the same type as the one of interest here, justifying a systematical study of the influence of secondary airflow patterns. The secondary air ducts differentiate the design of this iron ore pelletizing kiln from typical lime or cement kilns, in which the secondary air usually enters through a single kiln hood or radial cooler inlets. Hence, new knowledge is required to decide whether the secondary airflow can have a significant effect on the jet flow and mixing.

Magnetite pelletizing plants usually require a larger amount of secondary air compared to other mineral-processing industries, since a sufficient amount of oxygen is needed in the flue gases for the oxidation of the pellets in the last stages of the grate (Burström et al. 2010). One implication of this is that it is more difficult to adjust the process, so that a recirculatory jet is formed that stabilizes the flame. Instead, the recirculation of hot gases relies on the recirculation zone formed behind the back plate between the secondary air ducts. Due to the design of the secondary air ducts, the flow in the kiln resembles the confined bluff body flow over a rectangular cylinder as well as the merging of two parallel jets under confinement. This flow field can be divided into three regions, starting from the dividing wall, as the converging, merging, and combined region according to Lai and Nasr (1999) who studied the merging flow of two unconfined parallel jets. Anderson et al. (2003) and Bunderson and Smith (2005) investigated the near-field region between plane parallel jets at high Reynolds numbers and both authors observed a periodic flapping of the jets. Wang and Tan (2007) carried out an experimental study on the interaction between two parallel jets at Re = 104; one of them free and the other one being a wall jet. They noted that while the outer shear layers of unbounded jets are freely developing, for confined jets, these will instead be wall boundary layers.

Both Djeridi et al. (2003) and Perrin et al. (2006) studied the flow past a confined circular cylinder with high blockage ratio (D/H = 0.208) at Re = 1.4 × 105 using laser doppler velocimetry (LDV) and particle image velocimetry (PIV), and three-component PIV, respectively. Both report a Strouhal number of 0.21 for the vortex structure in the cylinder wake. With visualization, Popiel and Turner (1991) studied the flow behind a large rectangular plate in a rectangular channel, observing a flag-like motion of the flow downstream the wake for Re >8,000. Similarly, Wang and Tan (2008) used PIV to visualize the flow around circular and square cylinders placed close to a wall, observing periodic vortex shedding for both configurations. Among other things, these studies tell us that regardless of parallel jets being formed by flow past a confined bluff body or emerging from openings, their interaction can have a significant influence on the flow field, in the near field as well as farther downstream.

Larsson et al. (2013) studied a similar setup as described in the current paper, where numerical simulations were validated with PIV experiments. Since the simulations were performed in steady state, the validation work mainly focused on the time-averaged results. In the current paper, the experimental investigation is considerably extended as compared to Larsson et al. (2013) to improve the resolution of the flow field in space and time and to better explore uncertainties. In addition, an inclination of the upper inlet duct is introduced to better model the real kiln geometry.

2 Method

A relatively simple downscaled model of the kiln with the main features was built in PMMA (transparent plastic) to enable experiments with PIV. The kiln is modeled as a fixed horizontal cylinder of constant cross-section (D = 100 mm) without the pellet bed, while the actual kiln is rotating and inclined with respect to the ground and has a minor diameter expansion. A schematic figure of the experimental setup, including a detailed drawing of the geometry of the test section can be seen in Fig. 1. The back plate is centered with respect to y/D = 0 and its height is D/3; the burner is excluded since only the non-reacting field is of interest in the present investigation.
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Fig. 1

Schematic picture of the experimental setup with geometry

The cross-sections of the kiln inlet ducts are approximated as being close to semicircular, and hence the hydraulic diameter DH is defined as DH = 4Aduct/P, where Aduct is the cross-sectional area of the semicircular duct and P is the wetted perimeter of the cross-section.

The top inlet duct has a 15° inclined section with a length of 2.4DH that ends in the kiln, while the bottom inlet duct is parallel to the kiln. The present model is a development from the one studied in Larsson et al. (2013), in which both ducts were parallel.

In the following sections, normalization is carried out for reported distances, velocities, and Reynolds stresses using the inner diameter of the kiln, D, the bulk velocity Ub of the kiln and its square Ub2, respectively. To achieve a fully developed flow profile before entering the kiln, the length of the inlet ducts in the model is 4.0 m, or 95DH. Doherty et al. (2007) carried out hot wire velocity profile measurements in a pipe at Re = 1 × 105 and 2 × 105, concluding that fully developed velocity and higher order statistics were obtained at 50DH and 80DH, respectively. Dean and Bradshaw (1976) obtained fully developed flow in a rectangular duct after 93.6DH for Re = 1 × 105 based on the height of the duct. Using pitot tubes to measure streamwise velocity in turbulent flow in a duct of rectangular cross-section, Monty (2005) concluded that the mean velocity field was fully developed after 70.5DH. An experimental study of turbulent flow in a semicircular duct with a length of 78DH was carried out by Berbish et al. (2010) at Reynolds numbers in the range 8,242–57,794. Since the study was focused on heat transfer and pressure drop, the authors did not investigate the development of the velocity field, but indicated that the flow was fully thermally developed. Generally, studies of semicircular ducts in the literature have mainly been focused on laminar flow in heat transfer applications; see for example Lei and Trupp (1990) or Etemad (1995). To the authors’ knowledge, results reporting fully developed velocity profiles have not been presented for turbulent flow through semicircular ducts. All results in Larsson et al. (2011) indicate however that the flow is fully developed for the setup used in this study.

The chosen fluid for the physical model is water, allowing the smaller scale of the model kiln. The flow through each duct is controlled by manual valves and monitored with magnetic flow meters (Krohne Optiflux DN50) to an accuracy of reading of 0.1 %. The temperature of the water in the setup is controlled to 23 ± 0.4 °C using a cooling system in the tank. The turbulence intensity in the end of the inlet ducts, just upstream the kiln entrance, is approximately 6 %. To quantify the distribution of mass flow between the ducts, the momentum flux is defined as
$$ J_{\text {tot}} = \iint\limits_{A_{\text {duct}}} \! \rho U_{\text {duct}}^2 \hbox{d}y\hbox{d}z, $$
(1)
where Aduct is the cross-sectional area of the semicircular ducts, ρ is the fluid density, and Uduct is the axial velocity. The total and axial momentum flux ratios are approximated as
$$ \frac{ J_{1,{\text {tot}}}}{ J_{2,{\text {tot}}}} \approx \left( \frac{\dot{m}_{1}}{\dot{m}_{2}} \right)^2, $$
(2a)
$$ \frac{J_{1,x}}{J_{2,x}} \approx \left( \frac{\dot{m}_{1} \cdot \hbox{cos} \alpha}{\dot{m}_{2}} \right)^2, $$
(2b)
where α is the inclination angle of the upper duct and \(\dot{m}_{1}\) and \(\dot{m}_{2}\) are the mass flows through the upper and lower duct, respectively. Equations 2a, 2b introduce errors that possibly differ between the two ducts for the cases of non-matched momentum flux, but for the purpose of this work, this is not considered important. To facilitate the comparison between different cases, the ratios Rtot and Rx are defined as
$$ R_{\text {tot}}=\frac{\hbox{max}\left(J_{\text {tot},1}, J_{\text {tot},2}\right)}{\hbox{min}\left(J_{\text {tot},1}, J_{\text {tot},2}\right)}, $$
(3a)
$$ R_{x}=\frac{\hbox{max}\left(J_{x,1}, J_{x,2}\right)}{\hbox{min}\left(J_{x,1}, J_{x,2}\right)}, $$
(3b)
hence Rtot ≥1 and Rx ≥1 and decreasing ratio correspond to approaching matched momentum flux. Hereafter, in the text, momentum flux ratio refers to the total momentum flux ratio Rtot.

The Reynolds number in the real full-size kiln is approximately 3.2 × 105, based on its diameter. In the experiments, Reynolds numbers of 8 × 104 and 1 × 105 are used, which correspond to a total mass flow of 6.43 and 7.9 kg/s, respectively. Five cases of different momentum flux ratios are evaluated in order to detect how the ratio affects the flow field in general and the recirculation zone in particular. The lower Reynolds number is used for the largest momentum flux ratios due to the limitations of the pump used in the experiments. This is not an issue since, within this range of Reynolds numbers, the flow is Re independent with regard to the features studied; see Larsson et al. (2013).

The PIV system used is a commercially available system from LaVision GmbH. It consists of a Litron Nano L PIV laser, that is, a double-pulsed Nd:YAG with a maximum repetition rate of 100 Hz, and a LaVision FlowMaster Imager Pro CCD-camera with a spatial resolution of 1,280 × 1,024 pixels per frame. The laser is mounted on a traverse, so that the laser sheet and camera can be repositioned up to 500 mm in the x-, y-, and z-directions. The tracer particles used are hollow glass spheres with a mean diameter of 9–13 μm from LaVision GmbH.

PIV measurements are taken with a frequency of 80 Hz during 7.5 s, corresponding to a total of 600 image pairs for each recorded set. Due to reflections in the model walls, the raw images were cropped at some distance from the walls to isolate useful data for the PIV processing. The time interval between the laser pulses was individually adjusted for each momentum flux ratio, resulting in a typical mean displacement over the whole velocity field of about 3 pixels.

Measurements are taken at five positions in the streamwise direction; the position farthest upstream covers the section of the ducts where they connect to the kiln. To consider laser sheet attenuation in the image periphery, subsequent positions are set to give a 36 mm overlap of the images. At each streamwise position, measurements are taken in three xy-planes at z/D = ±0.25, and z/D = 0. For one momentum flux ratio at a time, the order in which the 15 positions are measured is randomized. In addition to the measurements in the vertical plane, measurements were taken in the xz-plane through the kiln centerline to complement the description of the flow field.

The raw PIV data were processed by applying a min/max filter for particle intensity normalization, followed by using a multi-pass scheme with decreasing window size and window off-set to calculate the particle displacements (LaVision GmbH 2007). The interrogation window size was 64 × 64 pixels (first pass) decreasing to 32 × 32 pixels (second pass) with adaptive window shift, both with an overlap of 50 %. The cross-correlation was performed using the standard cyclic FFT algorithm, followed by vector post-processing by applying a median filter to reject spurious vectors and to interpolate from surrounding interrogation windows (LaVision GmbH 2007). Finally, the vector statistics were extracted.

The overall measurement accuracy in PIV is a combination of a variety of aspects extending from the recording process all the way to the methods of evaluation (Raffel et al. 2007). A cornerstone in all experimental design is to randomize the experimental procedure. By proper randomization, the effects of extraneous factors that may be present have less impact on the result (Montgomery 2005). The measurement uncertainties consist of those due to biased errors and precision errors (or measurement errors) (Coleman and Steele 1999). The seeding particles should be small enough to follow the fluid flow well and should also scatter the laser light effectively. Based on the typical frequency of the periodic flow that is observed in the present study, the particle Stokes number is 2.5 × 10−5, indicating that they should respond fully to the large-scale fluid oscillations. Also, the very small ratio of solid-phase volume to liquid-phase volume suggests a negligible influence of the particles on the flow.

In order to determine the velocity, the particle pattern displacement \((\Updelta s_{\text {pixel}})\) between two images must be computed. Together with the time \((\Updelta t)\) between the exposures, a two-dimensional velocity field can be calculated by
$$ V=\frac{\Updelta s}{\Updelta t}= \frac{\Updelta s_{\text {pixel}}}{S\cdot\Updelta t}, $$
(4)
where S is the scaling factor that relates the pixel dimensions to physical distance. The time between exposures and the thickness of the laser sheet needs to be optimized in order to give suitable particle displacements and to minimize the particle loss out of the laser sheet. Sources of errors that affect the measurement accuracy include refraction through the model walls, calibration, camera repositioning accuracy, and characteristics of the optical components. Finally, the cross-correlation and other computed functions used in the post-processing are further sources of error (Kirschner and Ruprecht 2007).

For the calibration of the scaling factor S, it is estimated that the kiln diameter can be read from the camera image to within ±2 pixels and that the tolerance of the model diameter is ±0.5 mm; both are considered as bias uncertainties. Taylor (1997) provides a rule for estimating the propagation of individual uncertainties from quantities that are divided, yielding a bias uncertainty in the scaling factor of 0.55 %.

The typical frequency of the vortex shedding in the present study is about 12 Hz while recordings are made at a frequency of 80 Hz, so between 6 and 7 samples are taken within each period of oscillation. Consequently, subsequent samples are not independent and statistical sampling theory does not apply for estimating uncertainties in the time-averaged velocity field (Grant et al. 1992). It does, however, apply for estimating uncertainties in the phase-averaged velocity field. Based on the dominant frequency obtained from a FFT analysis, eight phases of the shedding cycle are selected and the phase-averaged velocity field is calculated as the mean of all instantaneous velocity fields pertaining to that phase ±5°; this corresponds to 12–15 frames among the total 600. As the number of individual samples used for calculating the phase average is considered insufficient for providing a good uncertainty estimate using statistical sampling theory, uncertainties in both phase- and time-averages are estimated by performing sampling studies in a low velocity region (0.4 < x/D < 0.7, −0.1 < y/D < 0.15) and a high velocity region (0.2 < x/D < 0.4, −0.4 < y/D < −0.2). The convergence of the time-averaged velocity components is evaluated by calculating a set of averaged velocity fields using 2, 3, 4, …, 712 samples. For each succeeding pair of averaged fields, the maximum difference among all interrogation windows is calculated and this value is then used as a measure of the convergence. The analysis shows that 600 samples decrease the random uncertainties for both mean velocity components to below 0.003Ujet in the high velocity segment and below 0.02Urev for the low velocity segment. Based on this, 600 samples are used for the present study. Similarly, the uncertainty in the phase-averaged axial velocity is estimated to 0.01Ujet and 0.09Ujet in the high and low velocity regions, respectively. For the y-component of the phase-averaged velocity, the corresponding uncertainties are 0.07Ujet and 0.005Ujet.

Hence, the random uncertainties are likely to dominate over the bias uncertainty in the scaling factor, at least in the low velocity regions. The random error in an instantaneous measurement is possibly high due to small pixel displacement in some parts of the measurement field. As the Reynolds stresses associated with the global mean flow are directly affected by these random uncertainties, which are difficult to quantify, the second moments of velocity presented in this work are likely to be noticeably elevated compared to reality. As an alternative method to evaluate the random uncertainty, three replicate measurements for matched momentum flux were taken. Following Coleman and Steele (1999), a repeatability test was performed yielding a maximum precision error of 5 % for both mean velocity components.

3 Results and discussion

All cases studied share the same basic characteristics, which resemble that of merging parallel jets as described in the introduction. After the jets have emerged from the inlet ducts, they converge over a distance of the same order of magnitude as the kiln diameter—the converging region. The back plate separating the inlet ducts acts as a bluff body and creates a region of reversed flow behind it, characterized by a pair of vortices that each entrain fluid from its adjacent jet. These vortices resemble elliptical cylinders with semimajor and semiminor axes parallel with the x- and y-axis, respectively, as roughly illustrated in Fig. 2. At the downstream end of this wake, the inner shear layers of the jets merge and the mean axial velocity is zero, defining the merging point at axial position xmp, see Fig. 3. Downstream the merging point, in the merging region, there is momentum exchange between the jets that persists up to the combined point xcp, where the saddle shape of the mean axial velocity profile vanishes. After the combined point, the mean velocity profile develops as a single jet in the combined region.
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Fig. 2

Illustration of the flow in the recirculation zone; the region of dark blue indicates reversed flow

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Fig. 3

Mean flow features, shown here for the largest momentum flux ratio with dominant upper jet

Although the propagation of the jets and the shape of the vortex pair are very distinct in the mean field, their dynamics are more complex and the flow needs to be examined both for time-averaged and phase-averaged characteristics. In the following subsections, the influence of the momentum flux ratio of the two jets is determined and the measurements show a clear dependence of the ratio on both the mean and instantaneous flow field. As the momentum flux ratio approaches unity, there is an increasing presence of von Kármán-type coherent structures, originating in the inner shear layers of the jets, which are convected downstream.

The momentum flux ratios for the present case with one inclined duct and for the case studied in Larsson et al. (2013), with two parallel ducts, are calculated using Eqs. 3a and 3b and presented in Table 1. For the cases of non-matched momentum flux, the axial momentum flux ratios can be seen to approach unity by 6–8 % due to the inclination. This is valid provided that the jet follows the bend of the duct perfectly, so this difference is considered the maximum possible.
Table 1

Mass flows and momentum flux ratios

 

\(\dot{m}_{1}\) (kg/s)

\(\dot{m}_{2}\) (kg/s)

Rtot

Rx

Present study (inclined)

1.93

4.51

5.44

5.83

3.16

4.75

2.26

2.42

3.97

3.96

1.00

1.07

4.75

3.15

2.27

2.12

4.50

1.93

5.44

5.07

Larsson et al. (2013) (parallel)

1.18

2.77

5.47

5.47

3.15

4.75

2.28

2.28

3.95

3.95

1.00

1.00

4.73

3.14

2.27

2.27

2.77

1.18

5.47

5.47

In order to identify dominant features and large-scale structures in the flow, a proper orthogonal decomposition (POD) analysis was performed using a Matlab script based on the snapshot POD method described in Meyer et al. (2007). POD is a method capable of distinguishing coherent structures and statistically significant events from incoherent structures in turbulent flows. The POD decomposition results in modes that are sorted according to decreasing POD eigenvalue, showing the most energy-containing structures of the flow. These are mainly large-scale structures, not necessarily coherent, and the modes can be used to describe the most dominant behavior of the flow (Kostas et al. 2005; van Oudheusden et al. 2005). In the case of matched momentum flux, the first two POD modes clearly show vortex shedding originating in the inner shear layers and these vortical structures being convected downstream; see Fig. 4. This pair of modes contain nearly 60 % of the total fluctuating energy in the flow and represents the orthogonal components of the harmonics of the vortex-shedding process as described in Kostas et al. (2005). The vortex shedding remains the dominant motion for increased momentum flux ratio, but the fraction of the total energy decreases significantly to about 20 % for the maximum ratio, see Table 2. The energy spectrum emphasizes the significance of this large-scale motion and justifies the focus on the vortex-shedding process later on.
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Fig. 4

First two POD eigenmodes for matched momentum flux at z/D = 0

Table 2

Fraction of total fluctuating energy in first two POD modes

Rtot

5.44a

5.44b

2.27a

2.26b

1.00

Energy fraction (%)

21

26

33

32

58

aDominant upper jet

bDominant lower jet

3.1 Time-averaged flow characteristics

To start with, it is of interest to examine the extent of flow symmetry about the xy-plane at z/D = 0. Hence, mean axial velocity profiles along vertical lines at x/D = 0.6, z/D = ±0.25 are compared and it is found that the flow is symmetric within 4% with regard to the maximum axial velocity, in agreement with Larsson et al. (2013).

Hereafter, in the figures, the non-matched momentum flux cases are differentiated by denoting the case with upper dominant jet ud, and the case with lower dominant jet ld. By studying the development of the mean axial velocity profile at z/D = 0 throughout the measurement length, it can be concluded that the introduction of the vertical component of momentum flux in the upper jet, due to the inclination of the duct, appears not to affect the jet interplay significantly; see Fig. 5 for a comparison. The velocity profiles coincide quite well, indicating that the inclination, and hence the decrease in axial momentum flux ratio has a minor effect on the main features. The obvious deviations evident in some of the profiles can be attributed to bias uncertainties in the measurements on parallel ducts. In this context, it must be emphasized that the actual inclination of the upper jet near the inlet, as estimated from the PIV velocity field, is about 3°–4° from the kiln axis, which differs significantly from the actual 15° inclination of the duct.
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Fig. 5

Impact of the inclination of the upper duct on the mean axial velocity profile at z/D = 0, asterisk present study, open circle Larsson et al. (2013)

Another result is that there is no indication of recirculation along the top wall above the upper jet for the cases studied, given the uncertainty that the mask excludes a region about 0.03D below the top wall as measurements right on to the wall are not possible. Hence, if there is recirculating flow, it is confined in this thin region. However, there is an increased amount of vorticity in the near-wall region in the upper part compared to the lower part of the kiln, see Fig. 6. This might be the result of recirculation near the kiln inlet, convecting downstream.
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Fig. 6

Contours of mean vorticity magnitude for different momentum flux ratios at z/D = 0. Velocity streamlines are added to highlight the flow patterns

Examining the cases with largest momentum flux ratio shows that the flow field characteristics for a dominant upper jet are similar to those for a dominant lower jet, with the rate of entrainment basically controlled by the curving of the weaker jet. In both cases, the dominant jet resembles a wall jet with a wall boundary layer that is developing downstream, while the weaker jet experiences more curvature and has a larger pertaining vortex, see the streamlines of Fig. 6a, b. In the mean field, the recirculating vortex of the weaker jet stays somewhat upstream the other one. An inclination of the weaker or the dominant jet appears to have the same increasing effect on the entrainment, which is confirmed by the distances to the merging points, see Table 3.
Table 3

Extension of the recirculation zone (xmp/D)

Rtot

5.44a

5.44b

2.27a

2.26b

1.00

Present study (inclined)

0.85

0.83

0.8

0.91

0.61

Larsson et al. (2013) (parallel)

0.93

n/a

0.93

0.92

0.6

aDominant upper jet

bDominant lower jet

The flow is also similar when decreasing the momentum flux ratio, though the entrainment of the weaker jet is not as strong and the dominant jet is curved somewhat more toward the weaker jet and away from the wall; see the streamlines in Fig. 6c, d. Compared to the case of dominant upper jet, the vortices appear more symmetric and the distance to the merging point is larger when the lower jet is dominant, see Table 3. Notice that the effect of the inclination does not follow the same trend as for the maximum momentum flux ratio. As the flow becomes more characterized by a mutual entrainment of the jets as the momentum flux ratio is decreased, it appears that the entrainment is only promoted by an inclination of the dominant jet as this has the higher momentum flux. No noticeable effect on the recirculation length can be detected from the inclination of the weaker jet, see Table 3.

The mean flow field of the matched momentum flux case shows a vortex pair that is symmetric about the xz-plane and a strong curvature of the jets, see Fig. 6e. The shortest recirculation zone among all cases is measured, as found for parallel ducts, and no noticeable change in recirculation zone length can be seen due to the inclination. This suggests that the entrainment for matched momentum flux is largely controlled by the large-scale periodical flow, rather than a predominant entrainment of one of the jets into the other.

For x > xmp, there is no reversed flow and the saddle shape of the mean axial velocity profile continues to decrease until it eventually vanishes at xcp, see Fig. 5. For all ratios except the matched momentum flux case, the jet flow is in the combined region at x/D = 3.04, with the cases of largest momentum flux ratio having the farthest upstream combined point. Despite having the smallest measured value of xmp, the flow in the case of matched momentum flux has not reached the combined point at x/D = 3.04. The mean velocity profile appears nearly developed, though the saddle shape can still be recognized and hence the combined point has not been reached. This feature will be discussed in the subsequent section on phase-averaged flow.

The mean flow field in the horizontal xz-plane at y/D = 0 can be seen in Fig. 7. Two regions can be distinguished: the recirculation zone to the left and the merging region to the right, separated by a region of converging streamlines. A direct comparison of the different cases is obstructed due to the merging points not lying in this xz-plane except for the matched momentum flux case, see Fig. 6. Inspecting the flow field at y/D ≈ 0 in Fig. 6a, c suggests that the planes in Fig. 7a, b cut through the wake closer to the lower vortex rather than in the middle between the two. However, the extension of the recirculation zone over the width of the kiln is clearly visible from the converging streamlines.
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Fig. 7

Time-averaged velocity contours with streamlines in the horizontal xz-plane at y/D = 0

The observation that the recirculation zone is considerably shorter for matched momentum flux compared to the other cases is also supported by these figures. The recirculation zone in the case with the largest momentum flux ratio appears to be more symmetric about the xy-plane at z/D = 0 than the other two. An explanation could be that there is some unknown three-dimensional motion in the wake, and that more samples are needed to average this out for the other cases. The effect of the semicircular cross-section of the jets emerging from the inlet ducts is reflected in the velocity field with clearly lower velocities along the sidewalls. This suggests that the wake is extended further downstream along the walls compared to the central part.

3.2 Phase-averaged flow characteristics

As seen from the time-averaged images, the recirculation zones in all cases are characterized by two vortices forming as the jet flow is separated at the edge of the back plate. In all cases, the phase-averaged flow shows that the motion of the vortices is coherent and that they convect downstream the wake. However, the vortex dynamics show a dependence on the momentum flux ratio of the two jets. This is in line with the findings of Bunderson and Smith (2005), though they did not specifically focus on the dynamics in the wake, as is attempted in this work.

From the measurements of the largest momentum flux ratio with dominant upper jet, it is shown that the roll up and subsequent shedding are predominantly occurring in the inner shear layer of the dominant jet, see Fig. 8. Over the shedding period, the weaker jet is more strongly curved toward the wake; hence, it seems that its pertaining vortex is more anchored in the wake and does not shed as easily. The same behavior can also be seen when the lower jet is dominant and these plots are therefore excluded.
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Fig. 8

Phase-averaged vorticity contours with velocity streamlines at z/D = 0 for Rtot = 5.44, ud. Each picture is a mean of 12–15 frames corresponding to the correct phase ±5°

For decreasing momentum flux ratio, the dynamic characteristics are similar, although the shear layer pertaining to the dominant jet becomes more discontinuous, as seen from the vorticity field in Fig. 9. Similar to the largest momentum flux ratio, the shedding predominantly occurs in the inner shear layer of the dominant jet. However, shedding of the vortex pertaining to the weaker jet is also evident, though it appears that only part of it is shed; hence, its downstream trace is less distinct compared to the counter-rotating vortex.
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Fig. 9

Phase-averaged vorticity contours with velocity streamlines at z/D = 0 for Rtot = 2.27, ud. Each picture is a mean of 12–15 frames corresponding to the correct phase ±5°

When the momentum fluxes are matched, von Kármán-type vortices are alternately shed from the upper and lower inner shear layers forming an anti-symmetric pattern, see Fig. 10. The result is a large-scale flapping motion of the jets that persists far downstream the wake with significantly less damping than for the other ratios. The inclination of the upper inlet duct changes the velocity profile and causes a disturbance of the flow before the kiln entrance. This may explain the unsymmetrical vorticity profile that can be seen for matched momentum flux with a less distinct region of high vorticity magnitude pertaining to the vortex shed from the upper shear layer. The characteristics of the shedding process are very similar at z/D = 0 and z/D = ±0.25. In the interval 0 < x/D < 1.25, the variation in the spanwise direction of the vorticity magnitude of the shed vortices is small. Neither is there any noticeable variation in the spanwise direction of the growth of the wall shear layer of the inclined jet within this interval. Further downstream, the variation in the spanwise direction of the vorticity magnitude of the shed vortices increases. At z/D = 0 in the interval 1.25 < x/D < 2.5, the shed vortices are clearly distinguishable from concentrated regions of high vorticity magnitude, while at z/D = ±0.25, the vortices are significantly more difficult to identify. This indicates more rapid damping of the vortical motion when moving away from z/D = 0 in the spanwise direction.
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Fig. 10

Phase-averaged vorticity contours with velocity streamlines at z/D = 0 for Rtot = 1. Each picture is a mean of 12–15 frames corresponding to the correct phase ±5°

Figure 11 shows a single-sided FFT amplitude spectrum of the fluctuations of the V-velocity component for all cases at a point inside the recirculation zone (x/D = 0.6, y/D = 0). Several positions were evaluated in the analysis, and similar trends were seen in all points. This point was chosen to represent the trends since it shows the difference in amplitude of the fluctuations between the ratios in a clear way.
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Fig. 11

Single-sided FFT amplitude spectrum of the fluctuations of the V-velocity component inside the recirculation zone (x/D = 0.6, y/D = 0). The cases are shifted for clarity

The Strouhal number of the shedding cycle is defined as St = fL/U, where f is the shedding frequency, L is the height of the back plate, and U is the maximum axial velocity of the dominant jet. The Strouhal numbers corresponding to the frequency peaks in Fig. 11 are 0.18, 0.16, and 0.17 for the momentum flux ratios 1, 2.27, and 5.44, respectively. The trend of increasing amplitude of the dominant frequency peak when approaching matched momentum flux is in agreement with the increased effect of the vortex shedding on the phase-averaged flow field seen in Figs. 8, 9 and 10.

Recall from Fig. 10 that for the matched momentum flux case, two vortices of similar scale were shed with equal frequency though shifted half a period. This implies that the frequency at which any vortex is shed is twice that of the identified dominant frequency seen in Fig. 11. For increasing momentum flux ratio, the size of the vortex shed from the shear layer of the weaker jet can be seen to gradually decrease, essentially diminishing for the largest ratio. This can further explain the significant difference in the jet propagation when the momentum fluxes are matched compared to other ratios.

Additional results can be obtained by analyzing the measurements further downstream in the kiln. The vortices converge toward a position in the y-direction off the centerline, close to the walls, leading to a coupling between the wall shear layer and the vortex originating from the shear layer of opposite vorticity. This interaction results in a portion of the wall shear layer being ejected by the influence of the shed vortices. This can clearly be seen further downstream for the case of matched momentum flux. For the case with maximum momentum flux ratio, recirculation is observed in the lower part of the kiln further downstream as a consequence of the entrainment of the weaker jet into the dominant one.

Some similarity to the results presented here can be seen in Wang and Tan (2008); as the velocity profile across their square cylinder became more symmetric, the recirculation length in the mean image was decreased as the inner shear layers began to penetrate each other and forming von Kármán-like vortices. For appreciably asymmetric flow past the cylinder, the vortex shedding was completely suppressed.

The periodic flow causes a strong entrainment, explaining the short distance to the merging point in the mean field for matched momentum flux. The opposite trend for the location of the combined point with change in momentum flux ratio, as mentioned for the time-averaged flow, can be explained by the time-resolved measurements. As the strong coherent structures in the case with matched momentum fluxes persist over a larger distance without significant damping, their effect on the mean flow field also extends farther downstream. This is believed to be the explanation of the saddle-shaped velocity profile persisting as far downstream as x/D = 3.04, despite that the strong jet interaction might suggest a more efficient momentum exchange and hence more rapid combining. Though the flapping motion is strong, it is still coherent and this evidently tracks far downstream.

The strong flapping motion leads to improved mixing between the jets. The maximum streamwise velocity can be used as a mixing measure, since it will be smaller for jets that are better mixed than for those that are poorly mixed (Bunderson and Smith 2005). In Fig. 5, it is clearly seen that the lowest maximum streamwise velocity can be found in the matched momentum flux case. Jets that are well mixed also have a smaller mean velocity gradient and, therefore, smaller Reynolds stresses, since the Reynolds stress is generally proportional to the gradient in the mean velocity profile (Bunderson and Smith 2005). Figure 12 shows contour plots of Reynolds shear stress τxy for the different cases at the farthest downstream measuring position. The magnitude of the Reynolds shear stress is found to decrease at a rate that increases with reduced momentum flux ratio. This indicates enhanced mixing of the jets for decreasing momentum flux ratio, particularly when approaching unity.
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Fig. 12

Contour plots of Reynolds shear stress τxy at z/D = 0

4 Conclusions

The non-reacting, isothermal flow field in a downscaled, simplified model of a rotary kiln was experimentally investigated with PIV. Five different momentum flux ratios were evaluated in order to detect how the distribution affected the flow field in general and the recirculation zone in particular.

It is found that the flow field resembles that of two parallel merging jets, with the same characteristic flow zones. The back plate separating the inlet ducts acts as a bluff body to the flow and creates a region of reversed flow behind it, characterized by a pair of vortices that each entrain fluid from the adjacent jet. Due to the semicircular cross-section of the jets, the wake is elongated along the walls compared to the central part. Although the propagation of the jets and the shape of the vortex pair are very distinct in the mean field, their dynamics are more complex and hence the flow was examined both for time-averaged and phase-averaged characteristics.

The time-averaged results show that the flow field is symmetric about the xy-plane at z/D = 0 and that the introduction of a vertical component of momentum flux in the upper jet, due to the inclination of the duct, shortens the length of the recirculation zone for some of the non-unity momentum flux ratios, although the actual inclination of the upper jet near the inlet, estimated from the PIV velocity field to about 3°–4° from the kiln axis, differs from the duct’s inclination of 15°. It is likely that two mechanisms contribute to the shortening of the wake: an increased jet entrainment or an increased jet penetration. No recirculation zone can be seen along the top wall above the upper jet; this is probably since the velocity field cannot be measured right on to the wall. Nevertheless, an increased amount of vorticity can be seen in the upper part of the kiln and this might be the result of the inclination of the upper jet.

The characteristics of the cases with momentum flux ratios above unity are very similar; the dominant jet resembles a wall jet with a wall boundary layer that is developing downstream, while the weaker jet has more curvature and a larger pertaining vortex. In the mean field, the recirculating vortex of the weaker jet stays somewhat upstream the other one. The mean flow field of the matched momentum flux case shows a strong curvature of the jets and a vortex pair that is symmetric about the xz-plane at y/D = 0; this case has the shortest recirculation zone but also the farthest downstream combined point. This is attributed to the strong oscillations of the flow field occurring for matched jet momentum fluxes, causing the jets to merge over a shorter distance but also affecting the mean flow field further downstream as the coherent structures are not easily damped.

The extent of the recirculation zone differs significantly depending on jet momentum flux ratio, motivating an analysis of the phase-averaged flow characteristics to gain more insight into the jet interaction. As the momentum flux ratio approaches unity, there is an increasing presence of von Kármán-type coherent structures, with dominant Strouhal numbers in the range 0.16–0.18. The phase-averaged measurements of the cases with the largest ratio suggest that the roll up and subsequent shedding are predominately occurring in the inner shear layer of the dominant jet. Over the period of oscillation, the weaker jet is more strongly curved toward the wake; hence, it seems that its pertaining vortex is more anchored in the wake and does not shed as easily. The same behavior is seen when decreasing the momentum flux ratio, although the amplitude of the shedding vortex as it convects downstream is larger in this case. For the matched momentum flux case, von Kármán-type vortices are alternatingly shed at the same frequency from the upper and lower inner shear layers forming an anti-symmetric pattern. The result is a large-scale flapping motion of the jets that persists far downstream the wake with significantly less damping than the other momentum flux ratios.

It is shown that the mixing of the jets emerging from the semicircular ducts is enhanced by the oscillations arising for matched jet momentum flux. The size of the recirculation zone is also affected by this parameter in combination with the inclination of the jet emerging from the upper inlet duct, which decreases the extent of the recirculation zone for some ratios. A suitable and important future work is therefore to investigate how the entrainment of the secondary air into the primary fuel jet is affected by these large-scale coherent structures as well as the inclination of the incoming jets.

Acknowledgments

This work was carried out within the framework of the Faste Laboratory, a VINNOVA Excellence Centre. The authors also acknowledge discussions with LKAB, who also partly financed the work via the Faste Laboratory.

Copyright information

© Springer-Verlag 2012