Scholarly article on topic 'An experimental investigation of the swirling flow in a tall-form counter current spray dryer'

An experimental investigation of the swirling flow in a tall-form counter current spray dryer Academic research paper on "Chemical engineering"

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{"Spray drying" / "Vortex flow" / "Swirl decay" / Friction / "Downstream effects" / PVC}

Abstract of research paper on Chemical engineering, author of scientific article — Victor Francia, Luis Martin, Andrew E. Bayly, Mark J.H. Simmons

Abstract This work studies the air flow in a large swirl counter-current dryer using sonic anemometry. Air velocity and turbulence fields are reported at isothermal conditions and in the absence of particles. In a tall-form unit the structure of the flow is largely influenced by the design of the exit. A contraction originates a central jet and suppresses the formation of recirculation zones despite the vortex acquires a high swirl intensity Ω (i.e. 1< Ω <2). Access to a full scale tower has permitted to: (a) identify asymmetries owed to the design of inlet and exhaust ducts, (b) present the first detailed turbulence data in production units, characterized by a highly anisotropic field and the axial decay of the turbulence kinetic energy, (c) study the flow stability, identifying the precession of the vortex core and oscillations at a constant Strouhal number and (d) study the impact that a rough wall has in the strength of the swirl. This work presents the first clear evidence of significant friction in spray dryers. The swirl intensity Ω decays exponentially in the dryer at a rate between 0.08 and 0.09, much higher than expected in pipe flow and independent of Re in the range 105–2.2⋅105. Production dryers have a large characteristic wall roughness due the presence of deposits, which explains the stronger friction and the discrepancies found in the past between data at full scale or clean laboratory or pilot scale units. It is essential to address this phenomenon in current numerical models, which are validated on laboratory or pilot scale facilities and ignore the role of deposits, thus causing an overprediction of the tangential velocity above 30–40%.

Academic research paper on topic "An experimental investigation of the swirling flow in a tall-form counter current spray dryer"

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Experimental Thermal and tei1* Fluid Science

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ELSEVIER

Contents lists available at ScienceDirect

Experimental Thermal and Fluid Science

journal homepage: www.elsevier.com/locate/etfs

An experimental investigation of the swirling flow in a tall-form counter current spray dryer

Victor Franciaa,b'*, Luis Martinb, Andrew E. Bayly5'1, Mark J.H. Simmons3

a School of Chemical Engineering, University of Birmingham, Birmingham, UK b Procter & Gamble R&D, Newcastle Innovation Centre, Newcastle upon Tyne, UK

ARTICLE INFO ABSTRACT

This work studies the air flow in a large swirl counter-current dryer using sonic anemometry. Air velocity and turbulence fields are reported at isothermal conditions and in the absence of particles. In a tall-form unit the structure of the flow is largely influenced by the design of the exit. A contraction originates a central jet and suppresses the formation of recirculation zones despite the vortex acquires a high swirl intensity X (i.e. 1 < X < 2). Access to a full scale tower has permitted to: (a) identify asymmetries owed to the design of inlet and exhaust ducts, (b) present the first detailed turbulence data in production units, characterized by a highly anisotropic field and the axial decay of the turbulence kinetic energy, (c) study the flow stability, identifying the precession of the vortex core and oscillations at a constant Strouhal number and (d) study the impact that a rough wall has in the strength of the swirl. This work presents the first clear evidence of significant friction in spray dryers. The swirl intensity X decays exponentially in the dryer at a rate between 0.08 and 0.09, much higher than expected in pipe flow and independent of Re in the range 105-2.2 • 105. Production dryers have a large characteristic wall roughness due the presence of deposits, which explains the stronger friction and the discrepancies found in the past between data at full scale or clean laboratory or pilot scale units. It is essential to address this phenomenon in current numerical models, which are validated on laboratory or pilot scale facilities and ignore the role of deposits, thus causing an overprediction of the tangential velocity above 30-40%. © 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://

creativecommons.org/licenses/by/4.0/).

CrossMark

Article history:

Received 1 December 2014

Received in revised form 14 February 2015

Accepted 2 March 2015

Available online 7 March 2015

Keywords: Spray drying Vortex flow Swirl decay Friction

Downstream effects PVC

1. Introduction

Among the main advantages of spray drying processes is the generation of low density granules with an open structure [1]. Product properties, particularly the morphology of the final granules, depend on the temperature history and the agglomeration undergone in the dryer, for which understanding the air fluid dynamics is a fundamental. Counter-current swirl dryers are used for the manufacture of thermally stable powders, such as detergents, and in occasions they apply strong swirling flows to enhance the heat and mass transfer and optimize the contact between the phases [2]. The structure of a strong turbulent swirling flow under confinement has been studied in detail for free developing or non-recirculating systems (i.e. also referred to as once through swirling flows, such as open pipes, tubes or concentric cylinders) and in

* Corresponding author at: School of Chemical Engineering, University of Birmingham, Birmingham, UK.

E-mail address: v.francia.chemeng@gmail.com (V. Francia).

1 Present address: School Chemical and Process Engineering, University of Leeds,

Leeds, UK.

systems where the confinement restricts the vortex development (i.e. combustors or cyclones). The study of large scale units such as a swirl drying tower is far more limited. In a long confinement the swirling motion decays due the development of the boundary layer and the action of the wall shear stress (frictional losses). This phenomenon is described in the research over open pipes (e.g. Kitoh [3]; Steenbergen and Voskamp [4]) and extended by Chang and Dhir [5,6] to a higher swirl intensity with the use of tangen-tially injected flows. By contrast, in a spray drying tower the swirl causes most of the solids to concentrate near the wall, and generates thick multi-layered deposits [7,8], which increase roughness and are expected to disrupt significantly the boundary layer and the structure of the turbulence [9,10].

Recirculation patterns and the stability in vortices are often studied in terms of the Reynolds number Re and the ratio between the angular and axial momentum, characterized by a swirl number or intensity, X. When the swirl develops in an open cylinder, at a sufficiently high intensity the adverse pressure gradient generated by the centrifugal force causes the reversion of the flow. This originates a central recirculation zone, denoted CRZ, in the region upstream. As the swirl decays along the cylinder, the centrifugal

http://dx.doi.org/10.1016/j.expthermflusci.2015.03.004 0894-1777/© 2015 The Authors. Published by Elsevier Inc.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Nomenclature

Mi H P R

f r u x z

swirl decay rate in Eq. (12)

cross sectional area in the cylinder, m2

combined area of all inlet nozzles, m2

swirl decay constant in Eq. (12)

diameter of the cylinder, m

axial angular momentum flux, kg m_1 s~2

axial momentum flux, kg s~2

mass rate through the cylinder, kg s_1

combined mass rate through the inlets, kg s_1

distance from air inlets to vortex finder, m

static pressure, kg m_1 s~2

radius of the cylinder, m

radius of the cross-section at the inlets, m

Reynolds number Re = DUavlv

swirl number in Eq. (6)

time averaged air velocity, m s_1

bulk or superficial velocity, Uav = Mc/pAC, m s~

velocity at the inlets, Ui = Mi/pAi, m s_1

Strouhal number, St = f ■ D/Uav

diameter of the vortex finder, m

oscillation frequency, Hz

coordinate in the radial direction, m

velocity fluctuation, m s_1

distance from the centreline, m

axial position, m

Greek letters

X swirl intensity

a anemometer misalignment over a2 in Fig. 2, rad

b anemometer misalignment over a3 in Fig. 2, rad

e roughness height, m

n axial alignment of the air inlet nozzles, rad

C anemometer misalignment over a1 in Fig. 2, rad

k swirl decay rate in Eq. (10).

k specific turbulent kinetic energy, m2 s2

p density, kg m~3

s shear stress, kg m_1 s~2

t kinematic viscosity/Eddy viscosity, m2 s_1

U radial alignment of the air inlet nozzles, rad

Subscripts, superscripts

r, z, 0 along radial, vertical and tangential direction

- , + best estimate, under and over estimation ref a reference height, or length, in Eqs. (10) and (12). w at the wall

Abbreviations

CRZ central recirculation region PVC precession of the vortex core VBD vortex breakdown

force decreases and a stagnation point forms, after which the flow reverses back in what is referred to as a vortex breakdown, VBD, that often carries some associated oscillations. The instabilities are complicated by the interaction with the design in cases where the confinement is more restrictive, such as in a combustor or a drying tower. In these units, an increase in X or Re interacts in a more complex manner with the exit boundaries, which is referred to as downstream effects. Escudier et al. [11], Escudier and Keller [12] or Derksen [13] provide a detailed study of the effect that an exit contraction can have in stabilizing the flow upstream. The origin of periodic oscillations associated to the VBD, such as the precession of the vortex core, PVC, has been discussed extensively in the case of combustors [14] and cyclonic flows [15,16]. While these are beneficial in combustion, for they increase mixing and stabilize the flame, they are considered detrimental to the collection efficiency in cyclones. In co-current dryers, the studies of turbulence of among others, Usui et al. [17], Langrish et al. [18] and Kieviet et al. [19] report similar aerodynamic instabilities, followed by the work of Southwell and Langrish [20] and Langrish et al. [21], but no data in this regard is available for counter-current swirl units.

It is also very important to provide turbulence data in swirl dryers because large numerical simulations often lack any means to evaluate how the closure models actually perform. In counter-current swirl units an accurate turbulence prediction is particularly important to (a) determine the elutriation of fines, which concerns with the description of a high angular velocity core [22] and requires the application of a Reynolds-Stress Transport Model, RSTM [23,24], (b) describe the flow near the wall, in particular, assess how semi-empirical functions for rough walls could apply to strong swirling flows [24], (c) obtain an adequate replication of anisotropy and particle dispersion, and (d) the description of the aerodynamic instabilities observed experimentally, which increase the level of mixing and affect the inner jet.

In spite of the complexities above, experimental data on the air flow patterns in counter-current tall form dryers are rare and very

restricted in nature. The studies in pilot scale facilities included flow visualization and RTD analysis reported by Place et al. [25], Paris et al. [26] and Sharma [22] or Keey and Pham [27] in co-current units. Only in the last decade a higher level of detail has been obtained by taking advantage of laser-based flow diagnostic techniques in laboratory [28] or pilot plant units [29]. Data at production scales is much more restricted, from vane [30] to thermal anemometers [31], and a similar level of detail is not yet available. Detailed studies are of small scope and limited to particle image velocimetry, PIV, analysis near the wall [7].

This paper addresses the lack of data at a full scale providing the flow characterization on an industrial spray drying tower at isothermal conditions and in the absence of particles. Time average velocity and the turbulence field are reported at the cylindrical chamber of the unit. The common features to similar swirling flows in pipes, combustors or cyclones are discussed, including (a) the effects linked to the design of an exit contraction, Section 4.1.1, and Re, Section 4.1.2, (b) the asymmetry, Section 4.1.3, (c) the effect of wall roughness and the decay of the swirl intensity, Section 4.1.4, (d) the description of turbulence, Sections 4.2.14.2.3 and (e) periodic structures, Section 4.2.4.

2. Unit and instrumentation

An industrial scale counter-current swirl spray drying tower has been used for the conduction of the measurements, property of Procter & Gamble Co. The main design features are depicted in Fig. 1a, including the nomenclature and location of measurements. The air delivery system consists of inlet and exhaust fans, set manually to deliver a constant flow rate to the tower and a target exit pressure. Table 1 summarizes the design and the operating conditions. The air enters the unit near the bottom of the cylindrical body through a series of symmetrical nozzles, and exits through a top conduit, known as tubular guard or vortex finder. The alignment of the inlet ports, shown in Fig. 1b, imparts the flow with

Fig. 1. (a) General outline of the sections of a counter-current spray drying tower, the air delivery system and the swirl generation mechanism. (b) Detail of the alignment of the air inlet nozzles/ports.

Table 1

Tower design parameters, and operating conditions. Uav = MC/pAC and Reynolds number Re = p ■ D ■ Uav/f.

Design parameters Operation Re • 10-5 Uav/Uav,Re1

H/D 10.58 Re1 1.06 ±0.03 0.98-1.02

d/D 0.29 Re2 1.49 ±0.02 1.39-1.44

Qi 5.1-5.4 Re3 2.22 ± 0.02 2.09-2.17

angular momentum, generating the swirl and the formation of a vortex in the conical section, which then rises into the cylinder

Fig. 2. Anemometer ensemble. The deviations between the door and the inner wall and the rotation of the head lead to a series of misalignments between the anemometer measurement axes, a1a2a3 and the polar reference frame, rzh.

above. The alignment, u and n to the radial and axial axes respectively determines the initial intensity of the swirl, Qi defined later as the non-dimensional flux of angular momentum normalized by the axial momentum based upon the superficial velocity Uav. In isothermal conditions, it reads

R ■ G,

MiUiohRi/nR2 M2 Ac Ri . ,

•-, p2 P ' sinUcos n

•z,av MCUav R/nR2

MC Ai R

Xi is an exclusive function of the geometry and constitutes a characteristic design parameter, in the same manner that the geometric swirl number is a characteristic of cyclones [32]. It results from 1 - the inlets alignment, 2 - the ratio between the mass rates through the inlets Mi and the cylinder MC (owed to entrainment of air from the bottom end) and 3 - the contraction ratios specific to the tower design, between the radius at the cylinder RC and that at the inlet Ri ring, and the combined area of all inlets, Ai and that of the cylinder, AC.

In the operation of counter-current towers the deposits grow considerably and distribute heterogeneously. This work however maintains homogeneous roughness with a twofold purpose: (a) replicate the best scenario in industry given by recently "cleaned" walls, and (b) ensure an easier numerical reproduction. Further experimental work [33] investigates the role of the deposits at the wall, comparing this reference to the flow field established under deposits of different thickness and coverage. In this case, reproducible conditions were obtained by cleaning the inner surface with an automatic ring designed to ensure the layer of deposits is thinner than 0.006D. A perfectly homogeneous layer cannot be obtained, but rather a coarse definition is given whereby the roughness height e ranges between 0 and 0.006D.

A Horizontal Symmetry Sonic Solent Anemometer HS-50 (Gill Instruments Ltd.) [34] served to acquire velocity measurements, depicted in Fig. 2. Three independent pairs of ultrasonic transducers alternate to emit and receive an acoustic pulse >4 ■ 104Hz [35]. Analysis of the propagation velocity allows one to derive the velocity of the medium along three independent directions in a finite sampling volume and with a temporal resolution of 50 Hz. Measurements were gathered during 60 s (~3000 samples). The data may be considered a spatial average across the pulse path in a steady non-uniform field operating at very low Mach numbers [36]. The potential effect of averaging and the shift of the sonic pulse are minimized because the paths are almost vertical and axial gradients are very small, with the exception of the central region where the errors are higher, similarly to sensors of a finite size [3].

A door was engineered adhoc to assemble around the anemometer frame, as shown in Fig. 2. This allows the centre of the sonic path to be placed at any desired location in the tower by sliding the frame

inwards, along a2, so that in all cases, the axis a1 is kept aligned with the tower axial coordinate z, which is required to minimize all the sources of error and the gradients in the sonic paths. Wind tunnel calibrations valid <45 ms 1 establish the accuracy as <1% RMS in velocity magnitude and 1° in direction. However, the technique is reapplied here to confined spaces and one must address the question of how the local disturbance can affect the measurement or distortion the flow field. The uncertainty depends on the orientation the instrument versus the air flow direction, known as attack angle, and the turbulence [37]. Errors vary from one to another location because the HS-50 keeps a constant orientation but the flow varies. The maximum range of uncertainty was quantified in the range of attack angles and turbulence levels characteristic of this application, by orientating the HS-50 in all possible angles at various sections of a long confined vortex [38,39]. The method is less accurate than the use of anemometers in atmospheric studies, or the use of lasers, hot-wires [3] or thermal anemometers [40] but it is more flexible and cost effective, which permits conducting experiments in industrial units (volumes > 100 - 1000 m3) where data is more limited [31]. In regions of the vortex that comply with the limit attack angles, errors are <1-4% in the velocity magnitude, <3° in direction and <7-31% in turbulent kinetic energy, k. In others, such as the central region, the flow attacks the HS-50 from the bottom and a stronger disruption results in a large deficit bias in the velocity. Fig. 2 defines the frames of reference for the anemometer and the tower cylinder, and the various alignments used to determine the measurement position and the instrument orientation. Measurements were carried out in all the accesses shown in Fig. 1a to gather, 240 individual locations in the cylinder, at 8 vertical levels, 2 tangential coordinates and 15 radial positions for each Re. The velocity and turbulence profiles obtained are in agreement with the measurement of thevolume rate inthedryer, past laser based methods [7] and recent improved models studying friction [24].

3. Analysis

3.1. Fluid dynamics parameters

At each location and Re, the time averaged velocity magnitude U and direction are obtained from a measurement at a sampling frequency of 50 Hz during 60 s. The Reynolds decomposition serves to compute the time series of instantaneous velocity fluctuations ur, uh, uz from which the stress tensor is obtained as normal uiui and Reynolds stresses uiuj and the turbulent kinetic energy computed as k = 1/2(urur + uhuh + uzuz). Averaged profiles of the axial and tangential velocity components, Uz and Uh are available at a higher accuracy. Under the assumption of an axi-symmetrical system the azimuthal average of Uz and Uh permits one to estimate the average radial velocity profile Ur, that satisfies the continuity equation below, where compressibility effects may be neglected.

Velocity gradients are computed with the spatial grid generated and eddy viscosities are estimated with Eqs. (3)-(5) [3] assuming an axi-symmetrical system and away from the exit where dUr/dz can be neglected.

Vr.z =--=r-

Vr.e = ~

vzfi = --=

dUr/dr r ■ Ui) / @r

dUe/dz

In addition to turbulence, the variability of velocity is also affected by the presence of periodical flow structures in the vortex. Their characteristic time scales are identified by applying a fast Fourier transform, FFT, to the velocity signal.

3.2. Swirl intensity

A circulation parameter, denoted swirl number or intensity, is often used to provide a general description of swirling flows. It defines at a cross section the ratio between the angular momentum flux, Gh, to the axial momentum flux, Gz, given below (i.e. [41]):

Strict integral definitions for Gh and Gz derive from the conservation of momentum and angular momentum and require knowledge of static pressure and the turbulent terms [42]. Often they are too convoluted for many practical applications, which has generalized the use of simplified swirl numbers where momentum fluxes are estimated only on the basis of the convec-tive flow, either excluding turbulence and/or static pressures, or estimating the latter through the tangential velocity profiles. In the unit investigated here the exit duct constitutes a 90% contraction of the flow area, which causes the acceleration of the flow and substantial changes in the pressure field. For that reason, an estimate of Gz neither accounting for the pressure term nor including accurate velocity measurements in the core region is not likely to be axially preserved, at least at the upper part of the cylinder, which would complicate the interpretation of S. The main focus of this work is not concerned with aerodynamic instabilities highly dependent on S, but rather examines the preservation of the swirl, which is especially relevant for the dynamics of the solid phase. On this basis, this work will follow the more usual practice in the study of decaying swirling flows in open cylinders by normalizing Gh in (6) by a constant mean axial momentum flux Gzav [43]. The resulting swirl intensity, X, is then defined as the non-dimensional flux of angular momentum normalized by the axial momentum flux Gzav based on the superficial air velocity Uav. This has been simplified to the expression below given by Kitoh [3].

X = 2pq

UzUg 2 , ——t r2 • dr

o pPU2ttvR3

Other popular definitions, perhaps of a more difficult physical interpretation include the work of Chang and Dhir [5], who studied the decay in open tubes with tangential inlets but with no contraction. They defined intensity in terms of a "tangential momentum'' term. In a swirl dryer, the use of X is preferred in the benefit of a straight forward interpretation as the axial decay of Gh. In a confinement with smooth walls, the decay owes to the action of the tangential wall shear stress sw h in the velocity field, which is given below from the Reynolds averaged equation of the angular momentum in cylindrical coordinates, for an incompressible, stationary and axi-symmetric vortex [4].

Swh = I r2 @ I UhUz + UhUz - t| dr

Eq. (8) illustrates that the change in the angular momentum flux contained in the convective flow UhUz between two sections owes to the moments exerted on the fluid by three shear stresses: that at the wall, and those coming from the turbulent and viscous terms. A very common assumption in pipes consists of considering the wall as the main contributor, and neglect the stresses originated by uhu and the axial development od(Uz)/dz. In this way one may describe the rate of change of X as the non-dimensional

tangential wall shear stress, combining (7) and (8) to the expression given in (9) for where velocities have been normalized by Uav and the axial distance z by the cylinder diameter, D.

2sW;h dX

2 pUav - d(z/D) ()

X - Xref • e-1^) (10)

The axial variation of X shown in (10) provides the background to the experimental evidence of an exponential decay in open pipes. However, Eq. (10) is only a realistic approximation at small values of X where swh and X are proportional [3] or Steenbergen and Voskamp [4]). According to the measurements of Kitoh [3], strictly speaking this occurs only for X < 0.04 in an open pipe. At a higher X range the relation between sw,h and X requires either experimental measurement or the estimation from numerical studies (e.g. [44]). The work of Kitoh's (1991) provides data up to X = 0.9 and defines the ranges where the piecewise linear relation given in (11) can be assumed to render a slightly more complex decay function in (12), similar to that of Senoo and Nagata [45] where Xr and zr define an initial reference point.

- A • X + B (11)

2 pU'av ( )

X - (lXf + A) • e2 A ^) - A (12)

The study of swirl decay focuses in open pipes where X seldom exceeds 1 [4]. Swirl spray dryers operate at far higher values, better represented by the studies of Chang and Dhir [5,6]. They worked at a comparable X range to the dryer investigated in this work, and with a similar swirl generation mechanism, in order to promote turbulence and enhance the heat and mass transfer in open tubes. Although carried out at lower Re and in the absence of deposits their results are still useful to compare to the cylindrical chamber of a tall-form dryer. They propose a non-linear dependency to (z/D)0 7 and a decay rate strongly correlated to the ratio of the inlet tangential and axial rates, which in a sense remains a measure of geometry and the initial value of X, defined here by Xi. This correlation was later modified by Erdal [46] or Gomez et al. [47] to include the effect of Re and the number of tangential injectors.

The decay rate, 1 or A, is known to be a function of X in open pipes and it is expected to decrease for higher Re in a similar manner that the friction factor in fully developed pipe flow. Steenbergen and Voskamp [4] summarize the data over smooth and rough walls and attribute a considerable scatter to the swirl generation mechanisms and the X range. Few data are available for the swirl decay in a more restrictive design. In the cylindrical section of combustors, cyclones or dryers, the confinement has a dominant role and the response of the pressure field to an increase in X or Re is conditioned by the design of the exit duct. A purely geometric swirl number, similar to Xi, is usually defined in these cases according to the design of the inlets, body and outlets [32]. Finally, the wall roughness merits further comment because deposits occur on the walls of any dryer. Wall friction in cyclones has an important effect in the pressure drop and collection efficiency [48] and makes important to develop appropriate numerical models (e.g. [49,50]). In a counter-current swirl dryer the presence of deposits originates a high roughness. This work focuses in studying "cleaned" walls where the roughness height e varies between 0 and 0.006D, which is well above the experiments of Senoo and Nagata [45] who report values between 0.0018 and 0.0025 and most of the work reviewed in Steenbergen and Voskamp [4], who nonetheless shows some data with values as high as 0.015.

4. Results and discussion

This part of the paper discusses the influence of the exit contraction in the flow, Section 4.1.1, the self similarity and asymmetries in Sections 4.1.2 And 4.1.3, and the decay of the swirl in Section 4.1.4. The turbulence field is given in Section 4.2, presenting the development of the turbulent kinetic energy, k, and normal, uU, and Reynolds stresses, uUj, along with the estimates of eddy viscosities, v¡¿, and periodic flow structures.

4.1. Time averaged velocity field

4.1.1. Flow structure and downstream effects

Figs. 3-6 present the time averaged velocity profile, U, and its decomposition in vertical, tangential and radial direction, Uz, Uh and Ur, normalized by the superficial air velocity Uav, and for all Re given in Table 1. It includes the radial profiles at different heights in the cylinder, denoted with z, from figures (a) to (h). The error bars represent the maximum error limits, whilst measurements denoted by crosses represent data with a larger deficit error in the velocity.

The centrifugal inertia shifts the point of maximum velocity, UMax in Fig. 3 and maximum tangential velocity, UhMax in Fig. 5 toward the wall, r ~ 0.70R, at the bottom end of the dryer. As the vortex rises, it converges inwards and UMax moves to the centre, increasing from UMax — 33Uav to 7Uav at the top. Chang and Dhir [5] describe the flow in an open tube at a comparable X, and show that the axial flow reverses down at the centre of the vortex due to the adverse pressure gradient caused by the swirl. The reversal however does not occur in a swirl dryer, where a jet forms at the centre in Fig. 4. The suppression of the recirculation is related to the influence of the top boundary, particularly well known in com-bustors or swirl injectors [12,51]. With no swirl, a contraction causes the acceleration of the flow in its vicinity and a global increase in pressure upstream. In the presence of swirl, these effects are complicated and the entire flow field is affected. The rise in pressure is transmitted down the chamber as a shock wave, which distortions the recirculation and produces a transition to a jet-like velocity profile [11]. A swirl dryer operates a constant flow rate and exit static pressure (see Fig. 1). Therefore, an increase in pressure in the chamber gives rise to higher pressure gradients and the velocities rise. The radial gradients overcome the centrifugal force and the air flow inwards forming a central jet (see Fig. 4) from which the air exits the unit. Escudier and Keller [12] describe how the velocity rise depends on the vortex swirl number because the radial pressure gradient caused by the centrifugal force opposes the inward flow. The higher X is, the larger are the radial gradients required to cause the flow inwards, or in other words, the further down the cylinder the influence of the contraction has to be transmitted. Fig. 4 shows that in this case, the contraction is sufficient to develop a jet across the entire cylinder, which confirms the reports of Sharma [22] or Bayly et al. [28] in tall-form dryers at isothermal conditions and associated simulations (e.g. [23,24]), but in turn contrasts experimental data [29] under actual operation conditions, where the sprays seem to hinder the formation of the jet.

Clearly, a rise or a reduction in X would modify the effect of the contraction in the flow structure. Different flow regimes have been correlated to the X range that prevails in the chamber [33], but in the case treated here of "cleaned" walls, Uz remains positive and shows two maxima: a central jet associated to the diameter of the vortex finder and one nearby the wall, related to the centrifugal inertia. As the flow approaches the top the velocity of the jet increases from 1.1 to 1.4Uav for z 6 5.7D to values > 5—6Uav close

Fig. 3. Velocity magnitude along the cylinder, U(x = —r for 6 < p and x = r for 6 < p).

to the top. In parallel, the axial flow reduces in the outer region. The value of UzMax near the wall drops from 1.5 to 1.8Uav to values < 1Uav at z = 10.3D, where the minimum is lost and the profiles become very similar to the data of Escudier et al. [11] and Derksen [13].

In regards to the swirl, comparison to ideal patterns defined by U6 = C ■ rn aids in the analysis of complex systems [42]. A forced vortex (i.e. solid body rotation) is defined by n = 1 while a free-like structure (i.e. potential vortex) shows an inverse relation between U6 and r defined by n = —1, descriptive of irrotational flows such tornados or whirlpools. Comparison to the Burgers solution or Rankine ideal patterns serves to study vortices of the so called ''concentrated'' type, which are comprised of an inner forced vortex

and an outer free-like structure. Actual experimental profiles include a transition region nearby the location of U6Max, where the gradient diminishes and blends both structures. According to these definitions, the flow may be divided into four regions: 1 -an inner forced vortex, 2 - an annular or transition region, 3 - an outer free-like vortex, and 4 - the boundary layer. Fig. 5 shows how the vortex develops a large transition region at the bottom of the tower, between r ~ 0.10 and 0.80R. As the flow rises the location of U6Max moves inwards from r ~ 0.70R to 0.20R and the transition region narrows substantially, particularly between the levels z = 3.4D and 5.7D. Above this point, the outer region shows a linear decrease of U6 with r, between z = 6.9D and 8.1D, which then develops into an inverse relation at z = 10.3D. At this point the transition region is restricted to between r ~ 0.15R and 0.20R and the profile follows closely a Rankine pattern. In every level the forced vortex is contained within the jet, and shows a constant radius r ~ 0.15R. The transfer of the angular momentum inwards makes U6Max to increase axially, and shifts its location to the centre where a forced vortex core of high U6 appears in z > 5.7D. In parallel, U6 decreases in the outer region from ~ 3.0Uav at z = 2.2D, r = 0.70R to values < 2.0Uav and 1.5Uav moving from z = 6.9D to 10.3D. The shapes of the profiles agree well with experimental and numerical studies in smaller scales and confirm the observations of Sharma [22]. However, the data show a much larger axial decrease in U6. Comparison against the data in a scaled down clean tower [28] shows a deficit from 27% to 37% in U6 at r = 0.70R and levels z = 0.30H and 0.90H respectively. This error range confirms past observations in full scale dryers. Hassal [7] reported Particle Image Velocimetry, PIV, data near the wall in a full scale and similar operation conditions. The comparison to Bayly et al. [28] showed very similar differences in U6, from 30% to 40% lower values for the same heights, and r = 0.91R. The discrepancies between data in full scale or laboratory dryers owe to a different wall roughness and the effect of friction, discussed in Section 4.1.4.

Radial velocities are given in Fig. 6. Despite a higher uncertainty, certain levels show significantly higher values than expected from continuity in Eq. (2) (see Fig. 6c or e) what suggests the presence of a consistent transversal flow, often neglected in numerical models, and an asymmetrical flow structure discussed in Section 4.1.3.

4.1.2. Self similarity

Comparison across the range of Re is included in Figs. 3-6. All the velocities collapse into a characteristic profile when they are normalized by Uav, in agreement with the self-similar nature of swirling flows at a sufficiently large Re number (e.g. [52]). An increase in rate and thus Uav and Re simply causes an increase in U at any point in the vortex structure, but no changes to its direction. In this way, no differences should be expected in the friction factor (see Section 4.1.4) nor in the effects caused by the contraction. The exception is the behavior of three dimensional asymmetries described below, and the deviations observed for U6 at the lowest range at Re1 in Fig. 5d and e.

4.1.3. Asymmetry

The asymmetries in Figs. 3-6 are likely related to the design of the exit and the swirl generation mechanism. The use of tangential inlets is known to develop asymmetric structures (i.e. [53]), which can be avoided by placing a sufficient number of inlets in a symmetrical arrangement. In counter-current dryers, the generation of the vortex is more complex because it does not respond directly to the tangential injection but also to the design of the bottom end of the unit, see Fig. 1a. Huntington [2] lists the usual design in large swirl towers and Sharma [22] or Harvie et al. [23] describe the

Fig. 4. Axial velocity Uz associated to the vortex in Fig. 3.

Fig. 5. Tangential velocity Uh associated to the vortex in Fig. 3.

sensitivity of the vortex shape to the orientation of the inlets. They discuss the difficulties to obtain stable patterns, for which attaining a good balance between the pressures at all inlet ports is fundamental.

Most of data shown are not fully axi-symmetric. Differences are particularly visible in Fig. 4, for the values of UzMax close to the wall and UzMin. At the bottom level, UzMax varies from 1.8Uav to 1.5Uav between both sides of the cylinder, while UzMin ranges between 0.1 Uav to 0.3Uav for Re!. As the flow rises, the asymmetry in the outer region stabilizes, but it persists within the transition to the jet. The correlation with Re is of interest: whilst one side remains self-similar, the opposite varies significantly. The location where Uz varies appears to spiral upwards in the cylinder from z = 2.2D

to 6.9D (see the tangential position of the accesses in Fig. 1a and its correlation to Fig. 4). Such a pattern points to a coherent asymmetric flow structure, a consequence perhaps of a difference mass rate at some of the inlet ports. As Re increases UzMin drops in all these locations, which could be explained by a better equilibration of the flow in the distributor when the pressure drop decreases at higher Re. At the top of the unit, asymmetries occur in both Uz and Ur, indicating a strong transversal flow (i.e. from one side to another in the cylinder). At z = 9.2D, lower Re results in an improved symmetry, which is attributed to the design of the vortex finder. The exit duct includes a series of inner channels that break the swirling motion and often become partially block, forming preferential paths.

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

RADIAL VELOCITY

(d) Re,

h*H Re2

t»l Re3

z = 5.7 D, 0.54 H

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

Ur / Ua

Re, h*H Re2

tól Re3

z = 10.3 D, 0.98 H

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

(c) Re,

1» Rej

KH Re3

' z — 4.5 D, 0.43 H

-1.0 -0.5 0.0 0.5 1.0

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -1

(g) Re,

if- KH Re3

JJ**«*^

z = 9.2 D, 0.87 H

.0 -0.5 0.0 0.5

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

(b) Rei h«H Re2

HH Re3

z = 3.4 D, 0.32 H

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

(f) Reí

h*H Re2 heh Re3

--""¿iiiii.:.....

z - 8.1 D, 0.76 H

-1.0 -0.5 0.0 0.5

-1.0 -0.5 0.0 0.5 1.0

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0

(a) Re, 2.5

w Re2 2.0

KH Re3 1.5 1.0

kÜWÜW 0.5 0.0 -0.5

z = 2.2 D, 0.21 H -2.5 -3.0

0.0 x/R

z = 6.9 D, 0.65 H

Re, w Re2

KH Re3

1.0 -1.0

0.0 x/R

Fig. 6. Radial velocity Ur associated to Fig. 3. Lines show the estimation based on (2).

4.1.4. The decay of the swirl

Fig. 7 presents the decay of the swirl intensity X along the cylinder. Fig. 7a shows that for such high X values the decay does not follow Eq. (10), which suggests the wall shear stress swh is not proportional to X. The evolution is better approximated by the piecewise linear relation assumed in Eq. (12). It should be noted that the method does permit measurement of velocities close to the wall. Figs. 4 and 5 show the range extrapolated, and used in Eq. (7) for the calculation of X. Three values are given according to the way in which Uz and Uh are reconstructed. The best estimate, Xo, is obtained by a linear extrapolation from the last measurement to an intermediate point after which the velocity follows the logarithmic law of the wall. The thickness of this region is set according to the condition of the volume rate complying with

the integration of Uz. In order to give perspective on the absolute maximum errors, the following estimates are also computed according to, (a) a linear decrease of the velocity from the last measurement to zero at the wall, which causes under prediction of X and the air flow rate, denoted X- (b) a constant value, causing over prediction of both, denoted X+. The data provided by Bayly et al. [28] or Hassal [7] indicate velocities do not start decaying sharply close to the wall up to r > 0.98R for at least Uh. As a result, X_ yields far greater errors in the integration of the mass rate. Errors in the mass rate used to compute Xo are kept <0.1% in all cases.

The decay rates from the fit to Eqs. (10) and (12) are summarized in Table 2. The decay rate k in a smooth pipe rises with increasing X and decreasing Re [44,54]. A swirl dryer operates at much higher swirl intensity, which explains why the values of k between 0.08 and 0.09, are significantly above the usual in pipe flow, which range between 0.019 and 0.032 for 5 ■ 104< Re <3 ■ 105 [4] or between 0.02 and 0.06 for 104 < Re < 105 in the work of Najafi et al. [44]. The open tube studied by Chang and Dhir [5] provides a comparable case to a swirl dryer but at a lower Re = 1.2 ■ 104 and shows that k ranges between 0.06 and 0.11 for Xr = 1.6 - 3.9. However, in the dryer, the decay rates are found comparable despite working at much higher Re > 105. In fact k is found independent of Re in the range studied, see Fig. 7b.

Several considerations follow. Firstly, the stronger swirl decay is related to the roughness of the walls caused by a thin layer of particulate deposits. Interestingly, k is within the same order of magnitude of the friction factor expected for coarse roughness in a fully developed pipe flow, 0.08 or 0.02 for the Darcy and Fanning friction factors at e/D = 0.05 [55]. This withstands the assertion of Steenbergen and Voskamp [4] who discuss a general relation between k and the friction factor for smooth open pipes, and whose correlation does not hold here in a rough flow. Secondly, the lack of correlation between k and Re is also due to a high roughness. The traditional view of pressure drop in a rough pipe states that when the height of the roughness elements e stands above the extension of the viscous sub-layer, the friction starts to depend exclusively on e/D. For the range used here, e/D ~ 0.006, the friction factor in rough pipes becomes independent of Reynolds numbers precisely for Re > 105 [55]. Finally, the confinement is likely to reduce the sensitivity of k to Re, because the higher the centrifugal force is the stronger is the influence of the contraction in the velocity profiles. Thus the relation between swh and X (i.e. k) becomes a stronger function of X and less sensitive to Re and the development of a boundary layer [54].

The data provide evidence that full scale dryers operate under a high level of friction. One must stress the importance of finding ways to characterize deposits and account for their effect in the fluid dynamics. The implications for numerical modeling should not be ignored. Large scale computational fluid dynamics, CFD, models using smooth wall assumptions over-predict Uh at the top of the tower by 30-40%. The use of wall functions in a swirling system remains a challenging task [56], and inclusion of these effects entail operating out of the limits of the standard functions for an unidirectional flow in rough walls (e.g. [9]). In these circumstances, it is unclear how boundary conditions may be treated if roughness elements in the order of mm or cm govern the friction. Perhaps more importantly, it is unclear which impact friction brings to the generation of turbulence and the structure of the boundary layer, both fundamental aspects in particle flow and wall deposition. The reason for friction having remained unnoticed lies in the challenge of obtaining full scale data [2,29]. Numerical works rarely benefit from data in production units but gain validation from laboratory or pilot-scale facilities that serve as valid guides for design purposes but cannot easily replicate the

Fig. 7. Axial decay of ß across the cylindrical chamber. ßo, ß+ and ß_ provide respectively the best estimate and over and under predictions of ß. (a) Fit to Eqs. (10) and (12). (b) Effect of Re.

Table 2

Swirl decay rates. Fit to a proportional or linear relation between Tw 8 and X in (10) and (12).

Case Xref A B k

Re, 1.96 -0.080 0.054 0.085

Re2 2.02 -0.086 0.061 0.089

Re3 1.93 -0.081 0.051 0.090

characteristics of production. Having ignored the friction has potentially caused fully coupled models to contain severe bias errors in the prediction of particle centrifugal inertia, known to be critical in swirl units where the interaction with the wall is fundamental [8].

4.2. Turbulence statistics and periodicity

4.2.1. Turbulent kinetic energy and intensity

The turbulent kinetic energy, k, is reported in Fig. 8 for all positions and Re. Figs. 9 and 10 present the decomposition in

normal stresses for the outer region. A large maximum in k is observed in every level at the centre of the tower, varying from 0.2 to 0.3U2v at the bottom to > 0.lWav at 9.2D and down to 0.3—0.5U2v at the top. The region of high variability agrees well with the extension of maximum in the axial velocity, and is likely to be the result of an unstable jet, commonly reported in cyclonic flows (e.g. [51,58,53]).

Vortices present aerodynamic instabilities when the strength of the swirl increases. For low Re, local recirculation starts for swirl numbers >0.6 in a straight exit type of device. The stagnation of the flow [15] leads to various types of VBD depending on the flow characteristics and the geometry of the system, which is subject of ample research in aeronautics or combustion [59]. For sufficiently large Re the instability manifests by formation of periodical structures. The breakdown then results in a coherent oscillation whereby the core of the vortex precesses around its symmetry axis, referred to as the PVC and widely reported in combustors [14], the exit duct of cyclones [15,16,48] and the inlet of co-current dryers [21]. The conditions for its occurrence, its characteristics and its transmission are highly dependent on Re, X, the confinement, and the condition of the flow between the CRZ, the VBD and the exit, i.e. subcritical of supercritical according to its ability to withstand or not inertial waves [12].

Put simply, the PVC responds to the instability of the core causing it to acquire a spiral shape around which axis fluctuates in a helical orbit. It becomes identifiable by its effect on velocity variability. The velocity variance at a fixed point in the region affected by PVC comprises of a turbulent term and a periodic signal owed to the fluctuation of the relative position between the observer and the core. This sort of phenomenon is responsible for the large central maximum observed in Fig. 8 associated with no turbulent energy but indicative of the unstable nature of the core, see Section 4.2.4.

Fig. 9a presents the radial and axial development of k. The outer region shows comparable values and profiles to the data in an open

Fig. 9. Axial variation of normal stresses at Re2 in Table 1. (a) k, (b) UzUz, (c) ueue, and (d) uu. Error bars indicate the variation across tangential locations. The maximum uncertainty ranges are -31%, +1% for k, -41%, +19% for uuz, -23%, +19% for uw, and -35%, +22% for uur [38,39].

tube [5]. The maximum outer value KMax moves inwards as the flow approaches the exit, and k decrease axially from between 0.06 and 0.09U2v to 0.02-0.03U2v, following a linear relation to the decay of X suggested by Chang and Dhir [5]. The normal stresses uzuz and urur show the same transition between the inner jet and outer regions, ranging between 0.02 and 0.01U2v at the bottom, to 0.02-0.03U2v close to the exit (see Fig. 9b and d). Both present an outer maximum that converges inwards with increasing height. The turbulent mixing in the azimuthal direction is given by uhu (Fig. 9c). In contrast to an open tube where all normal stresses are similar, uhu is 30-40% lower than uu and uzu and shows no outer maximum. Such behavior can be explained by the effect the contraction according to Large Eddy Simulations, LES. Derksen [13] described the disruption caused upstream by an exit contraction, and showed the evolution of the vortex structure in tubes moving from an open system to high contraction ratios. An open cylinder shows an inner stabilizing forced vortex and a highly turbulent outer free vortex. Moving into narrow contractions, the core is distorted and Taylor-Gortler vortices appear in the outer region, suppressing mixing in the azimuthal direction. Finally, Fig. 10 shows that k and normal stresses are reduced with increasing Re, particularly at the bottom of the unit where the differences are significant.

4.2.2. Reynolds stresses

Figs. 11 and 12 present the development of Reynolds stresses. ujuh is associated to the transfer of angular momentum downstream due to the turbulence, and thus is predominantly positive (see Fig. 11a). It shows a maximum at r = 0.58R that moves inwards when the angular momentum flux is transferred to the jet. ujuh decays axially, in agreement with the decay of X and the behavior observed in open tubes [5]. In contrast, two zones of negative values appear in this case: 1 - at the inner region also noticed in by Chang and Dhir [5], who in general report higher values and 2 -at the vicinity of the top exit, z = 10.3D, indicative of the recirculation originated at the dead regions above.

Fig. 11. Development of the Reynolds stresses at Re2 in Table 1). (a) uZuh, (b) uu, and (c) uruz. Error bars indicate the variation across tangential locations. Maximum uncertainty ranges are for uZuh, ±60%, for uu ± 100% and for uruz, ±200—400% [38,39].

Fig. 13. Anisotropy, and eddy viscosities for all levels at Re2 in Table 1. For nomenclature see Fig. 11. (a) oz6, (b) or,e, (c) or,z and (d) at = (uruz2 + uru/)/2K.

Fig. 12. Impact of Re in the development of Reynolds stresses. (a) uZuh, (b) uruh, and (c) uruz. Error bars indicate the variation across tangential locations. The maximum uncertainty ranges are given in Fig. 11.

uruh increases axially in Fig. 12b showing positive values and a similar transition at the jet between r = 0.25 and 0.30R, where it is predominantly positive. uruz takes large negative values in the outer region and shows a similar range and evolution to an open tube [5]. The values drop axially, and acquire a positive sense only close to the exit. A similar transition occurs at the inner region, where uuZ change direction between z = 6.9D and 10.3D. In contrast to the behavior of normal stresses, no changes can be

observed in the development of the Reynolds stresses as a function of Re in Fig. 12.

4.2.3. Eddy viscosity and anisotropy

Eddy viscosities are summarized in . vz,h shows a transi-

tion at 0.35R < r < 0.40R where @Uh/dz achieves its locus (see Fig. 13a), thus defining the regions where the axial change of Uh is dominated by wall friction (i.e. at a higher r) or by the transfer of angular momentum inwards caused by the influence of the exit (i.e. at a lower r). In the transition region vr,h shows a minimum and maintains positive values, but vrz decreases from large positive in the outer region to low values at the centre where it can turn negative (indicative of negative turbulence energy production).

Comparison of the of vz,h to vr,h and vrz, show a substantial difference, in the same order of magnitude than the reports of Kitoh [3] and Chang and Dhir [5]. The data confirm the ample evidence of the mixing length theory not being able to describe anisotropy in swirling flows. An anisotropy factor af has been estimated as the ratio of the shear stress to 2 k in the same manner as Kitoh [3]. aD varies significantly in the radial direction, and increases axially. In agreement with the observations in pipe flow at also tends to 0.15 in the outer region and diminishes substantially in the transition inwards, taking values between 0.01 and 0.04. However in this case, at rises again at the jet.

4.2.4. Precession of the vortex core

This work focuses in studying the structure of the flow at large scale. In this context, the use of sonic anemometry is beneficial despite it entails working with lower accuracy than laser-based techniques. Having said that analysis of the time scales contained in the velocity signal produce reasonable results and reveals periodicity at various time scales. High-amplitude oscillations and long history effects are a common feature of the inner vortex of cyclones or in co-current spray dryers. Fig. 14a presents an example of the same behavior in a counter-current unit by showing the velocity signal at several positions. At the top section of the vortex core,

Fig. 14. Periodical flow structures. Analysis at r1 = 0.14R, r2 = 0.35R, r3 = 0.57R. (a) Times series for Uh. (b) Periodogram of U for all heights at the inner region r1 (left), transition r2 (centre) and outer region r3 (right). Arbitrary y unit; scaling changes from 1 on r2 or r3 to 0.5 on r1.

an oscillation in the order of seconds is superimposed upon faster fluctuations owed to the turbulence. Fig. 14b analyses the different time scales with a FFT. The correlation of periodicity, position and Re is illustrated by superimposing the periodograms obtained for U at the inner and outer vortices, and the transition between both. Several periodic signals are visible, (a) a large time scale oscillation appears in the core, restricted to the top of the dryer, 9.2D < z < 10.3D, and (b) an oscillation at a higher frequency occurs in transition to the inner vortex, between r = 0.20R and 0.35R and extends upstream in the cylinder from z = 9.2D to levels < 5.1D, 3.4D or 2.2D according to the increase in Re.

Periodical structures such as the PVC are often characterized by the Strouhal number, St (St = f ■ D/Uav where f is the oscillation frequency). At large Re, the PVC in confined units maintains at constant St [14], which means that when increasing the bulk velocity in cyclones [15] or [16]) or tangential swirlers [52] the fluctuation occurs faster. Fig. 14b shows the same behavior in a swirl dryer. The oscillation frequency, f, in the transition region increases linearly with the Uav (from 0.8 to 1.1 and 1.6 Hz for Re1, Re2 and Re3) what means it occurs at a constant St«1.4-1.5. In this case no similar correlation with Re can be appreciated at top core, perhaps due to the low resolution. The presence of this sort of oscillations at a constant St suggests that swirl dryers present a similar preceding core to cyclones where the entire inner jet adopts a sort

of helical movement [48]. At some point before or within the exit, perhaps between levels 5.1D < z < 6.9D, the high centrifugal force in the forced vortex destabilizes the jet and originates the fluctuation.

5. Conclusions

The swirling air fluid dynamics in a full industrial scale tall-form spray dryer operating at isothermal conditions and in the absence of the solid phase has been described, identifying the following main features:

• A significant role of the confinement and the downstream effects in the vortex structure.

• Consistent field asymmetries.

• The development of a self-similar vortex structure, invariant within the Re operating range.

• Strong swirl decay owing to the confinement and presence of particulate deposits at the walls.

• The characteristic turbulence structure, including its anisotropy through the description of normal stresses, and rough estimates of Reynolds stresses and the eddy viscosity ranges

• Periodical structures that oscillate at constant St, likely related to the precession of the vortex core.

The phenomena described in this paper, such as the suppression of the recirculation owed to the vortex finder, the mixing owing to the PVC, or most importantly the role that friction at the walls has in the swirl decay, were observed in a relevant range of Re for a production swirl dryer, and thus will be relevant in isothermal and non-isothermal operation. Of course, one must expect the flow structure to be affected by the density gradients when the solids are present, in addition to the exchange of momentum with the spray which hinders the formation of the jet and the concentration near the wall, which is likely to cause a further attenuation of the swirl. However, fully coupled large scale models currently lack validation and the observations in this work indicate they need to be revised on a fluid dynamics level.

The importance of friction and how this affects the vortex structure needs to be addressed in computational fluid dynamic simulations. Consider that the omission of the swirl decay is responsible of an over prediction of Uh > 30—40% in isothermal models using smooth walls as a boundary conditions. Such an error gains relevance in the prediction of particle dispersion, drying and aggregation because in any tower, the particle dynamics is intimately related with the centrifugal inertia that the solids gain from the air. In essence, the swirl establishes the concentration of particles near the wall and the rates of deposition and erosion, crucial to the process [8]. In addition, description of turbulence and recirculation affect particle residence time and the elutriation of powder. Clearly one must first be able to understand and replicate numerically the air flow structure, stability and swirl decay observed at isothermal cases and in the absence of solids before one can rely in more complex tools. In this line, the study of semi-empirical wall functions for rough walls over pipes and how to apply a similar approach to strong swirling flows must become an area of focus.

Acknowledgments

VF was supported by an Engineering Doctorate Studentship sponsored by the Engineering and Physical Sciences Research Council (EPSRC) and Procter & Gamble in the Industrial Doctoral Centre in Formulation Engineering, School of Chemical Engineering, University of Birmingham.

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