C Lachize

G Verhille
email: gautier.verhille@irphe.univ-mrs.fr

P Le Gal

Large scale dynamics in a turbulent compressible rotor/stator cavity flow at high Reynolds number

Keywords: Rotor-stator flows, Large scale dynamics, Compressible turbulence

Large scale dynamics in a turbulent compressible rotor/stator cavity flow at high Reynolds number

C Lachize, G Verhille, P Le Gal

Introduction

For closed cylindrical geometries, laminar flows entrained by rotating disks are commonly assumed to be axisymmetric due to the spatial configuration and boundary condition symmetries. This feature was confirmed by early experimental observations of Escudier (1984) but is obviously particularly restricted to low Reynolds numbers flows before bifurcations and turbulence arise. In particular, one knows that these confined flows can naturally break their axial symmetry leading to stationary or oscillatory behavior. The multiplicity of flow states has motivated many studies, both numerical (Gelfgat et al. 2001, Lopez et al. 2001) and experimental (Stevens et al. 1999, Sørensen et al. 2006) where three dimensional and unsteady regimes were exhibited. However, we may think that increasing the Reynolds number will result in a fully developed turbulent flow where axisymmetry can be restored 'on average' that is without any persistent large scale coherent structures. From a fundamental point of view but also from an industrial point of view, it is of great interest to know if turbulence can sustain these large scale coherent motions and under which circumstances. For instance in turbomachinery, the presence of these large scale coherent structures could drastically modify thermal and momentum transfer predictions, as well as pressure and load distributions. In consequence, it is of capital interest to understand the complex and subtle dynamics that might occur in these systems at low frequency and small wavenumber even at high Reynolds numbers. The rotor-stator cavity flow has then become a popular prototype laboratory flow where physical mechanisms can be deeply analyzed.

Rotor-stator flows possess three relevant governing parameters that define the different hydrodynamics regimes: the height-to-radius aspect ratio (γ = H/R), the rotational Reynolds number Re and the Mach number M a (both based on the radius and the angular velocity of the disk). Using these parameters, the literature neglects generally the influence of compressibility and reports classically two different configurations: those with high aspect ratios (γ > 1) and those corresponding to thin cavities (γ < 1). In these two cases, if the Reynolds number is not too low (see for instance Schouveiler et al. (1998)), the structure of the basic flow (often referred as the Batchelor flow) consists in one boundary layer attached on each disk: a centripetal Bödewadt layer on the stator and an Ekman layer on the rotor creating a meridional recirculation because of Ekman pumping. Theses layers are separated by a core rotating nearly as a solid body at a rate equal to half the disk rotation rate. This core is surrounded by a cylindrical boundary layer attached to the sidewall of the cylindrical container. Note that if the description of the Batchelor flow ignores the finite geometry of the system and the presence of the cylindrical sidewall, it is usually admitted and experimentally observed that rotor-stator flows with stationary sidewall keep this arrangement. However reverse or separated boundary layers can in fact be observed in more complex geometries such as those with inward throughflow (Poncet et al. 2005) or contra-rotating end-walls or rotating sidewalls (Lopez 1998). Although we cannot achieve a detailed description of the velocity fields in our set-up, we will keep this classical description as it has also been observed in previous rotor/stator experiments using similar aspect ratios, see for instance Sørensen et al. (2006).

State of the art

Thin cylindrical rotor/stator cavities

For very thin cavities (γ ≈ 0.1), Gelfgat (2015) has observed that the flow becomes unstable for Reynolds numbers Re ∼ O(10 4 ) and with large azimuthal wave numbers m. These spiral patterns with around 20 arms and their different transitions have been the subject of many experimental studies in the 90's (see for instance Schouveiler et al. (1998), Schouveiler et al. (2001) and Gauthier et al. (2002), or the review by Launder et al. (2010)). They find their origin in the crossflow instability of the Bödewadt layer on the stator and were recently simulated by Lopez et al. (2009). The report of a small number of azimuthal structures is however scarce. It was described in the experimental visualizations of Czarny et al. (2002) who reported the occurrence of three dimensional unsteady large scale vortices for γ = 0.126 and 0.195 and Re ranged from 3.7 10 4 to 2.24 10 5 . For both lowest Re and lowest γ, no coherent structure was detectable whereas increasing Re to 1.12 10 5 activates the development of a 2-lobe pattern which rotates at approximately half the rate of the rotating disk. When Re and γ were increased, the flow was prone to produce organized large scale tripolar vortices or pentagonal structures. Finally, the estimation of their velocity enables to locate these structures in the core. These dynamics have been reproduced by [START_REF] Poncet | Three-dimensionnal unsteady large-scale vortical structures embedded in turbulent rotor-stator flow[END_REF] with both experimental visualizations and numerical simulations where the Reynolds number ranges up to Re = 2.15 10 6 . They have noticed that the generation of vortical structures is highly sensitive to the time history of the flow and depends on the experimental procedure (except for mode with m = 2 and 3 which are indifferently observed). Moreover, the selected azimuthal wave number decreases when the rotation rate increases and the presence of an inner central hub (annulus cavity) prevents the formation of such low azimuthal wavenumber structures.

Tall cylindrical rotor/stator cavities

In tall geometries (γ > 1), Ekman pumping is responsible for streamline deformations and induces stagnation points along the axis of rotation, driving the generation of steady axisymmetric recirculation bubbles. Escudier's experimental observations allow to identify and characterize the flow topology over a wide range of (Re,γ) respectively between [1000 ; 4000] (i.e. for laminar flows) and [1 ; 3.5]. He mapped out a transition-diagram, accounting for the existence of one or multiple steady bubbles as well as unsteady hydrodynamic structures. He associated these recirculations to vortex breakdown that occurs at a critical Reynolds number equal to approximately 2600. With the same goals, Lopez (1990) then Gelfgat et al. (1996) have treated this problem with axisymmetric numerical formulations keeping the same flow parameters than Escudier using respectively direct numerical simulations and numerical linear stability analysis. They have concluded that vortex breakdown does not result directly from instabilities but originates from continuous variations of meridional flow when the Reynolds number is increased. In the early 2000's, Gelfgat et al. (2001) have provided a numerical linear marginal stability of rotor-stator cavity flows for the same range of Re. For γ between 1.63 and 2.76, an axisymmetric mode is found to be the dominant unstable mode, bringing an explanation for the axisymmetric vortex breakdown, whereas out of this range, non-axisymmetric modes with azimuthal wavenumbers m = 1, 2, 3 and 4 can arise. The authors have particularly noticed that mode m = 2 is dominant for γ < 1.63 and m = 3 or m = 4 are prominent for γ > 2.76. These results have been reinforced by Marques & Lopez (2001) using three dimensional direct numerical simulations. In particular, these authors have observed that disturbances are more significant at the singular junction between the stator and sidewall boundary layers which may indicate that the instability is linked to wall effects. This analysis is corroborated by the calculations of [START_REF] Barbosa | Etude numérique des écoulements tridimensionnels dans des cuves cylindriques rotorstator[END_REF], who has performed direct numerical simulations for γ = 1 and 1.5 and Re in the range [2400 -7100] (laminar flows). In what concern non-linear regimes, [START_REF] Barbosa | Etude numérique des écoulements tridimensionnels dans des cuves cylindriques rotorstator[END_REF] has demonstrated that the linearly dominant modes m = 2 and m = 3 can feed multiples stable modes m = 2n and m = 3n. Besides, these two linearly unstable modes coexist and compete: the most unstable one will damp the other one because their kinetic energies are spatially localized at the same place (near the corner between the stator and the sidewall, as described by Marques & Lopez (2001)). At the same time, computational resources allowed to study the flow destabilization mechanisms. One of the most relevant contributions has been provided by Sotiropoulos & Ventikos (2001) with direct numerical simulations for γ = 1.75 and 2, and Re = 1850 (steady regime) and 7000 (well within the unsteady regime). It appears that disturbances organize themselves in azimuthal modes, involving an asymmetric separation of the sidewall boundary layer in the stator vicinity. The characterization of the cylindrical wall boundary layer has led them to establish that this unsteadiness is generated by a centrifugal-like instability. In the case of a rotating cylindrical wall, these sidewall instabilities have been described some years before in the experiments of Hart & Kittelman (1996). These results were furthermore detailed by the numerical simulations of Lopez & Marques (2010) where backward tilted diagonal rolls destabilize the sidewall boundary layer and sustain inertial waves in the rotating interior flow leading to complex spatiotemporal dynamics. In the same spirit i.e. when the cylindrical fluid cavity experiences a global rotation with a differentially rotating lid, low azimuthal wave number instabilities are known to destabilize inner shear layers. Impressive visualizations associated to numerical simulations have been published by Lopez et al. (2002). Three-dimensional non axisymmetric states and their associated complex non linear dynamics were further described in great details in Blackburn & Lopez (2002) and Lopez (2006) for respectively γ = 2.5 and 1.72. These numerical simulations show in particular that the coexistence of multi axisymmetric and non axisymmetric modes complicates a lot the prediction of the flow (at least for the considered moderate Reynolds numbers). Indeed, several time scales originate from the competing modal structures and lead to modulated rotating waves whose dynamics depends on initial conditions.

Following these numerical simulations, Sørensen et al. (2006) confirm experimentally for the first time the presence of non-axisymmetric modes with small azimuthal wave numbers between m = 0 and m = 5. They described accurately by Laser Doppler Anemometry the presence of frequency peaks in the velocity spectra and by Particle Image Velocimetry the spatial structures of the different modes. Because of the possibility to change the height of their laboratory apparatus, they were also able to detail the instability thresholds as a function of the aspect ratio γ and of the Reynolds number Re. These experimental results were completed later by a dual experiment/numerical simulation study of the axisymmetry breaking of the flow in rotating lid driven cavities of larger aspect ratio (3.3 < γ < 5.5) (Sørensen et al. 2009). Note finally the recent article by Lopez (2012) that confirms the existence of supercritical Hopf bifurcations of low azimuthal wave number modes in these tall geometries, arising from the modulated rotating waves that result from three-dimensional instability of time periodic axisymmetric flows as seen before at intermediate γ (Blackburn & Lopez 2002, Lopez 2006). Our present experimental study can be seen as the pursuit of these two last experimental works of Sørensen et al. (2006) and Sørensen et al. (2009) but where the Reynolds number is not restricted to the vicinity of the instability thresholds (around a few thousands) but can reach much higher values, when developed turbulence invades the whole flow.

Inertial waves and rotating turbulence

Considering sufficiently rapidly rotating flows, when viscous effects are negligible, external excitations can also sustain inertial travelling waves into the solid body rotation region if their angular frequencies, in the rotating frame, are less than twice the fluid rotation rate. Jacques et al. (2002) performed 2D-axisymmetric numerical simulations in a rotor/stator configuration with γ = 0.125 in the transitional and turbulent regimes. They especially detailed results for Re = 3 10 5 and Re = 10 6 and underlined the presence of inertial waves for fast enough rotation rates (Re > 10 5 ) which are characterized by large amplitudes and low frequencies within the solid body rotating core. In their opinion, such modes are excited by large scales structures coming out of the turbulent stator boundary layer and propagating up to the rotor through the solid body rotation region. Lopez & Marques (2014) have investigated numerically for Reynolds numbers up to Re = 10 6 and for γ = 2, the stability and robustness of inertial modes in rotating cylinders when these are subjected to sidewall axial oscillations with periodic time-forcing. Their studies show that the propagation angle and axial wavenumbers of these waves only depend on the external forcing frequencies and found that the vortices emanating from the corners are responsible for these waves generation.

However with an axisymmetric forcing mechanism, azimuthal waves m = 0 are quickly damped. Recently, Gutierrez-Castillo & Lopez (2015) have carried out three dimensional simulations involving the sidewall instability of a rapidly rotating cylinder split at midheight and an extensive characterization of axisymmetric different states is done for a wide range of γ and Rossby number. It appears that the basic state loses stability through diverse ways involving sidewall boundary layer breathing causing inertial waves to propagate in the core of the flow. When their cavity is axially extended (γ > 1), large amplitude subharmonics are discernible, leading to the complex superposition of many inertial waves propagating at different angles.

These inertial waves might play also an important role on the energy transfer in rotating turbulence. The strength of the rotation is quantified in this case by the Rossby number Ro = u/LΩ f where Ω f is the fluid rotation rate, u a typical velocity and L a characteristic length. For small Rossby number, the flow tends to be invariant along the direction of the axis of rotation. Thus, rotating turbulence is expected to share some common properties with 2D turbulence. Kraichnan (1967) predicts that two cascades coexist. The first one is an inverse cascade of energy towards the large scales with a velocity power spectrum ∝ k -5/3 (where k is the magnitude of the wavenumber). The second is a direct cascade of enstrophy towards the small scales and is associated with a velocity power spectrum ∝ k -3 . [START_REF] Baroud | [END_REF] observed for the first time the direct cascade of enstrophy in rotating turbulence. One can notice that this enstrophy cascade stops at the Zeeman scale z defined by u z / z Ω f = 1 (i.e. when the Coriolis force become smaller than the inertial term). Then for smaller scales, the flow isotropy is recovered. Since 2010, more and more studies are devoted to the inverse cascade of energy and the eventual role of inertial waves in this transfer. Lamriben et al. (2011) studied the decay of turbulence generated by the displacement of a grid in a rotating cubic tank. They observed the apparition of three peaks in the velocity spectrum associated to three inertial modes. This experiment shows the existence of inertial waves in rotating turbulence but does not give any answer on their role in the inverse cascade. To tackle this point, Yarom & Sharon (2014) studied the flow spatio-temporal organisation in a rotating turbulence generated by small jets. They claim that inertial waves might be responsible of the inverse cascade of energy. Their study is based on the observation on an inverse cascade and on several spatio-temporal spectra for different wavenumbers k showing that the energy is mainly focus on the dispersion relation of inertial waves. However the different spatio-temporal diagrams were calculated for scales smaller than the injection scale, therefore in the enstrophy cascade. Therefore, to our point of view, their data does not allow to be as affirmative as the authors and we think that the interaction between inertial waves and turbulence is still an open question.

At the view of this abundant literature it is thus legitimate to wonder if nonaxisymmetric, low azimuthal wavenumber modes can arise in a rotor-stator configuration, at high Reynolds numbers, thus in the presence of a fully developed turbulence. We address here this question by performing experiments in an original device using sulfur hexafluoride SF 6 as working fluid at diverse temperatures and pressures. In this way, a huge range of Reynolds numbers can be explored with, as we will see, some visible compressible effects. To measure the flow characteristics, we record the pressure fluctuations on the stator for Reynolds numbers as high as 2 10 7 . The article is organized as follows: first our experimental set-up will be described in section 3. Then the main characteristics of turbulence and the appearance of low frequency dynamics will be described and discussed in section 4 before final conclusions will be drought in section 5.

Experimental setup

The flow is generated within a cylindrical enclosure consisting of a stationary shroud, two smooth rotor and stator with diameters of respectively 2R = 68 mm and 70 mm. The outer wall is fixed to the stator as illustrated on figure 1 (left) and the rotor is driven by a brush-less electric motor which could reach an angular velocity of 10,500 rotations per minute (rpm) (i.e. a maximal rotation frequency f 0,max = 175 Hz). The interdisc spacing is H = 40 mm, corresponding to a heigth-to-radius aspect ratio γ = 1.18. The rotor/stator cavity with the motor is integrated into a pressurized 140 mm inner diameter cylindrical vessel (with a maximum pressure of 120 bar). The temperature control of the cavity is ensured by a thermostatically-controlled bath that regulates the entire vessel temperature through an internal circulation in the cylindrical wall of the pressurized vessel. To fill the rotor-stator cavity, gaseous SF 6 is transferred from a storage bottle and then condensed in the vessel in a 5 • C environment. Then the pressure is gently increased to the desired working conditions by raising the temperature of the outer vessel wall. By changing the quantity of SF 6 in the vessel, different thermodynamics conditions can be chosen. The goal of this study is to describe the large scales azimuthal structures that appear on a well developed turbulence background by varying the rotational Reynolds number Re = 2πρµ -1 f 0 R 2 . Measurements are performed at a rotation frequency f 0 from 17 Hz to 170 Hz, a density ρ from 6.17 kg.m -3 in the vapor phase to 830 kg.m -3 in the supercritical phase. Note however that most of the present experimental results have been obtained in the vapor phase. The SF 6 dynamic viscosity µ and the speed of sound c was determined from the temperature and the pressure measurements using the relation given in Quiñones-Cisneros et al. ( 2012) and the equation of state derived by Guder & Wagner (2009). The evolution of the dynamical viscosity and the speed of sound at 46 • C is presented on figure 1 center and right panel, respectively. The speed of sound of SF 6 lies between 70 and 135 m/s for the different thermodynamical conditions we have explored. Variations of these quantities allow variations of the Mach number M a = 2πRf 0 /c between 0.03 and 0.5 and of the Reynolds number between 5 10 4 and 2 10 7 . We performed 361 runs corresponding to 17 different densities whose values can be read in the legend of figure 7.

In terms of instrumentation, three static pressure sensors are mounted flush to the stator surface and located at three different radii 10 mm, 15 mm and 20 mm from the rotation axis to determine the absolute pressure when the fluid is at rest and to characterize the distribution of the mean pressure field in the presence of a flow. Moreover, two dynamic pressure sensors are fixed on the stator at a radius of 15 mm and separated with an angle of π/2 in the azimuthal direction. These sensors have a response frequency range that extends between 0.5 Hz and 10 5 Hz. Finally, a temperature probe is placed onto the cylindrical shroud, which allows us, a posteriori and associated with the absolute pressure measurements, to determine the working isochores and the corresponding thermodynamical conditions. Experimentally, these conditions are reached by varying the fluid density (from higher to lower densities) by evacuating SF 6 under pressure out of the vessel. An initial measure at zero rotation rate is performed at the beginning of each experimental run in order to determine precisely the physical properties of the fluid and in particular its dynamic viscosity µ and the speed of sound c.

Results and discussions

Description of the spectra: cascades and mode appearance

The power spectral densities of temporal pressure fluctuations are calculated and presented for three different Reynolds numbers in the three figures 2, 3 and 4 for one of the two dynamic pressure sensors. Frequencies have been normalized by the rotating frequency f 0 as the energy is expected to be injected from the rotating disk to the fluid through the turbulent Ekman boundary layer. As can be observed, the spectra are The inverse and the direct cascades are visible with a series of peaks superimposed on the continuous spectrum for frequencies in the range 1/4 < f /f 0 < 3/2. The red line marks the cut-off frequency of the pressure sensor high pass filter. The inverse and the direct cascades are still visible, the peaks have merged and only three or four peaks are visible for frequencies f /f 0 ≈ 1, 3/4, 1/2 and 1/4. A very low frequency band appears at f /f 0 ≈ 10 -2 . The cut-off frequency of the pressure sensor high pass filter is no more visible on this plot.

divided in several frequency zones that we will describe in the following starting from the highest frequencies. For all Reynolds numbers that we have explored and for frequencies higher than f 0 , a turbulent inertial cascade is observed. This part of the spectra starts at the rotor frequency f 0 and is observable up to 3f 0 . Unfortunately, because of the presence of the thick stainless steel wall of the pressurized vessel, we were not able to avoid the important electronic noise that pollutes the signals at higher frequencies. As can be observed on figures 2 and 3, the slope of this part of the spectra is very far from the -7/3 power law usually observed in classical 3D turbulence but close to -5. As described earlier, in rotating turbulence a direct enstrophy cascade is expected with a velocity spectrum proportional to k -3 as predicted by Kraichnan. This relation leads to a pressure spectrum proportional to k -5 . Therefore, using the Taylor hypothesis which assumes that small eddies are advected by the mean flow, one get a temporal spectrum for the pressure proportional to f -5 . Our observations are in accordance with the Kraichnan prediction for the direct cascade of enstrophy.

In addition to this cascade and starting at a Reynolds number around ≈ 10 5 , a series of frequency peaks appears in the range 1/4 < f /f 0 < 3/2. As can be observed on figure 3, these peaks are numerous for Reynolds numbers between 10 5 and 10 6 . Note that these observations can be a priori compared to the observations of Sørensen et al. (2009) and Sørensen et al. (2006), however we stress that here the frequency peaks grow on a fully turbulent background. When increasing the Reynolds number above 10 6 , only four of these peaks are selected and remain visible at frequencies f /f 0 ≈ 1, 3/4, 1/2 Figure 5. A global view of the spectra that shows the appearance of the peaks and their selection for a Reynolds number above 10 6 . Each spectrum has been shifted vertically by 20 log Re to make the pattern visible. Reynolds number varies between 10 5 (bottom) and 2 10 7 (top). and 1/4. As we will see in the following section, this low frequency dynamics can be associated to large scale azimuthal structures. One can see on figure 4 that the two most energetic peaks are located at f 0 /2 and f 0 /4. Figure 5 gives a synthetic view of the variations of the spectra for the whole set of Reynolds numbers. On this figure, each spectrum has been shifted vertically to make the pattern visible. The appearance, then the spreading of these peaks between f 0 /4 and 3f 0 /2, and then the selection of the peaks for Re ∼ 10 6 where their amplitudes increase with the Reynolds number, are particularly visible. We will focus on the description of these structures and on their evolution with the Reynolds number in subsection 4.2. Then we will present an interpretation of the growth of these modes by using a low dimensional amplitude equation model.

For frequency lower than f 0 , in addition to the peaks, one can also observe a region with a slope close to -5/3. This low frequency part of the spectra is present in the entire range of Reynolds number and in particular for the lowest Reynolds numbers before the appearance of the peaks (see figure 2). Although we have no direct proof of it, this range of frequencies -around one tenth of the injection frequency -may correspond to an inverse cascade of energy. Indeed, if we transform the -5/3 exponent visible on our pressure fluctuation power spectra into the corresponding exponent for the velocity fluctuation power spectra, it becomes a -4/3 in complete agreement with the temporal spectra exhibited by Yarom & Sharon (2014) in a rotating turbulence experiment. According to them, this exponent might appear by the interaction between inertial waves and may correspond to an inverse cascade of energy. Here, we have no proof if there is or not a direct link between the observed peaks in the intermediate range of frequencies and the cascade of enstrophy or the cascade of energy. Finally, as can be observed on figure 4, at very small frequencies and although the presence of a cut-off frequency of our pressure sensors high-pass filters, we observe the appearance for the highest Reynolds number of a slow dynamics with periods as long as 100 times the disk rotation period. Note that this kind of slow dynamics has already been observed in rotating von Kármán flows (de la Torre & Burguete 2007).

Azimuthal mode dynamics

We will focus in this section on the dynamics of the hydrodynamics structures associated with the peaks observed between f 0 /4 and f 0 . To confirm the loss of axisymmetry and to understand the flow pattern, the cross power spectral densities (PSD) of the two synchronized dynamical pressure measurements have been calculated, displaying both PSDs and phase differences between both pressure sensors. By examination of the frequencies on figure 6 (left), we recognize the four peaks at the same particular values already observed on the pressure spectra. This is the proof that these structures occur indeed at large scales as they exhibit a strong coherence on the separation distance between the two pressure probes. They possess different azimuthal wave numbers m which are given by the phase difference ϕ between the two sensors. Indeed, as can be seen on figure 6 (right) for f /f 0 1/4 a phase angle of π/2 is observed, for f /f 0 1/2 it is equal to π, to 3π/2 for f /f 0 3/4 and to 2π for f 0 . Taking into account that the sensor locations make an angle of π/2 in the azimuthal direction, leads to the determination of the lowest azimuthal wavenumbers: m = 1, 2 and 3 that correspond respectively to frequencies f 1 /f 0 1/4, f 2 /f 0 1/2 and f 3 /f 0 3/4. We cannot of course distinguish between a wavenumber m and m p = m + 4p, where p is an integer, due to the position of the pressure sensors.

The determination of the azimuthal wavenumber m associated with its frequencies f m leads also to the calculation of the azimuthal phase velocity V ϕ,m = 2πRf m /m that shows that all of these structures rotate at the same phase velocity equal to V ϕ,m = +2πRf 0 /4 for all m. This velocity corresponds to the half of the solid body rotation rate of the rotating core that co-rotates at half the rotating disk rate as commonly admitted for rotor/stator flows. This suggests that the excitator of these modes is spatially located into the stator boundary layer and travels at the average velocity of the rotating core and the stationary disk.

For Reynolds numbers smaller than 10 6 , the numerous peaks cannot be associated to azimuthal structures due to our limited azimuthal resolution (only two probes separated by an angle of π/2) which only allows to detect large scale structures. When the Reynolds number is increased the flow organizes itself in a particular way such that a transition occurs with a selection of a few number of modes. This threshold around 10 6 is also visible on the evolution of the energy E m of the modes m as a function of the Reynolds number Re. At relatively low Re, one can see on figure 7 that the measurements are broadly distributed which indicates that the mode is not yet selected as we saw on figures 5 and 6. Then, for Re larger than 10 6 , figure 7 shows that the experimental measurement lye on master curves with a much weaker dispersion. This observation indicates that after the transition, the geometry of the modes and their interactions with each other are independent of the Reynolds number. We also observe that E 3 and E 4 are much smaller than E 1 and E 2 . When the Reynolds number is fixed, the different experimental runs at different fluid densities differ only by the Mach number. It is thus reasonable to wonder if the dispersion of the data points depends on this number. To test this idea, we select all the experiments within a narrow window of Reynolds numbers [Re ; Re + 10 6 ]. For each of these windows, the Mach number varies typically between 0.1 and 0.3. We then define two parameters χ Re = (Re -min(Re))/max(Re -min(Re)) and χ M a = (M a -min(M a))/max(M a -min(M a)) where the minimum and the maximum are determined for each window. These definitions allow us to compare on the same graph the influence of the compressibility on the amplitude of each mode. We have plotted on figure 8 the evolution of the amplitude of mode m = 1 as a function of these two parameters for different windows. One can see that, as expected, the evolution as a function of χ Re does not show any trend but only a cloud of data points reflecting that the Reynolds number is nearly constant in the selected window. Then χ Re can be seen as the experimental dispersion of the data points. On the contrary, the same data plotted as a function of the normalized Mach number χ M a clearly show that the amplitude of the mode increases quite linearly with the fluid compressibility showing that the small azimuthal wavenumber modes that we observe, are sensitive to the fluid compressibility.

χ R e / χ M a E 1 -E 0 1 R e ∈ [ 6 • 1 0 6 , 7 • 1 0 6 ] M a ∈ [ 0 . 1 , 0 . 3] M a R e

Mode selection and non-linear dynamics

As it has been shown in numerical studies, inertial waves in rotor/stator cavities may be excited by the turbulent fluctuations at the boundary layer. Moreover, one can expect that at high Reynolds numbers, when viscous dissipation becomes less important, the wavelengths of these waves can be tuned within the cavity geometry and a resonance may occur. A similar phenomenon was observed in purely rotating turbulence where the inertial mode selection was due to the geometry, cf. Lamriben et al. (2011). In their work, turbulence was generated by a grid which excites 3 inertial modes at resonant frequencies f 1 = 0.29f 0 , f 2 = 0.49f 0 and f 3 = 0.74f 0 . We observe that these frequencies are very close to our own observation. This suggests that the modes we have discovered might also be inertial modes, possibly modified by compressible effects. Further studies should be necessary to determine the exact origin of these modes.

But to go further in the characterization of the mode interactions and in the characterization of their mutual interactions, we have plotted on figure 9 the evolution of the energy E m of modes m = 2, 3 and 4 as a function of energy of the mode m = 1, 1 and 2, respectively. One can see that as expected for lowest values, no global tendency can be defined. As already speculated, this regime corresponds to relatively low Reynolds number experiments where the frequency peaks are numerous. On the contrary, when the amplitudes increase, i.e. when the Reynolds number is increased above 10 6 , the flow organizes itself to reach an asymptotic regime where the amplitude E 2 is nearly proportional to E 2/3 1 , E 3 to E 1 and E 4 to E 2 as can be checked on figure 9. To describe the behavior of the different modes, we first notice that for large Re, modes m = 3 and m = 4 are slaved to respectively modes m = 1 and m = 2. Their amplitudes are much smaller and their evolution with the Reynolds number Re follows the evolution of modes m = 1 and m = 2. Therefore, the system can be reduced to the two interacting master modes m = 1 and m = 2. In order to interpret the observed scalings, we propose the following amplitude equations:

   ∂ t A 1 = σA 1 -α 1 A 2 Ā1 ∂ t A 2 = α 2 A 2 1 -κA 2 -βA 2 |A 2 | 2 (1)
where the energy E m is equal to A m Ām where • stands for the complex conjugate. Here, we assume that energy is injected from the turbulence to the modes through the linear term σA 1 . Then, mode m = 1 saturates and feeds mode m = 2 through the resonant term α 1 A 2 Ā1 with α 1 > 0. The amplification of mode m = 2 is then modeled by the resonant term α 2 A 2 1 with α 2 > 0. Finally, we can assume that energy is dissipated through the two other contributions: κA 2 and βA 2 |A 2 | 2 . The first term represents the classic viscous dissipation. The second term is related to the non linear transfer of energy from the mode m = 2 to other modes. Note that when β = 0 the system of equations corresponds to the classical Landau model that describes the saturation of the fundamental by harmonics generation. At high Reynolds numbers, we expect that viscous dissipation is negligible compared to non linear interactions. Thus, at high Reynolds number, the stationary solution of the model given in equations (1) verifies |A 2 | ∝ |A 1 | 2/3 and |A 1 | ∝ σ 3/2 as observed experimentally. Note that this saturation mechanism with the unexpected 2/3 exponent that does not imply viscous dissipation, should be rather general any time the energy is dissipated through non linear selfinteractions. Moreover, on figure 7, we can see that at high Reynolds number Re, the amplitude of mode m = 1 is proportional to Re 3/2 . As energy is injected by the term σA 1 , σ should then be proportional to Re which is a reasonable and simple model for the forcing.

Conclusion

This paper has described an experimental study of a flow confined within a smooth rotor/stator cavity with a height-to-radius aspect ratio closed to unity and using SF 6 in particular thermodynamical conditions allowing large variations of its physical properties and consequently the obtention of high Reynolds and Mach numbers. For frequencies higher than the rotation frequency of the disk f 0 , an inertial cascade is observed with a slope on the spectra very close to -5. This -5 slope for the pressure fluctuation spectrum corresponds to the -3 exponent of the velocity fluctuation power spectra as predicted by Kraichnan (1967) for the 2D turbulence direct enstrophy cascade. For small frequencies, we have also detected on the pressure temporal spectra a -5/3 slope region which may correspond to an inverse cascade of energy. Starting at a Reynolds number around 10 5 and in addition to the cascades, a series of peaks appears at frequencies in the range 1/4 < f /f 0 < 3/2. They imply that non axisymmetric oscillating coherent structures come into play and lead to a complex flow topology. Whereas these peaks are numerous for Reynolds numbers in the range 10 5 < Re < 10 6 , when increasing the Reynolds number above 10 6 , only three of them are selected at frequencies f /f 0 ≈ 1/4, 1/2 and 3/4. The study of the phase difference between two pressure probes shows that these peaks correspond to modes with azimuthal wavenumbers m = 1, 2 and 3 respectively. The appearance of these modes at very high Reynolds numbers can then be interpreted as the response to a turbulent forcing coming from the stator boundary layer. Although we have no proof of it, we suspect these modes to be inertial modes, possibly modified by compressible effects as their amplitude depends on the Mach number. Finally their scaling behavior has been interpreted with a low dimensional amplitude equations. Therefore, our experiments on rotor-stator cavity flows at very high Reynolds number demonstrate that large scale structures are not destroyed by turbulence. On the contrary, we show that they are fed by turbulence and then can even grow and survive superimposed on inertial turbulent cascades.

Figure 1 .

 1 Figure 1. Left, drawing of the rotor/stator cavity with its motor, inside the thermalized pressure vessel. Center, evolution of the kinematic viscosity of the SF 6 at 46 • C as a function of the ambiant pressure P . The red line represents the kinematic viscosity of water for comparison. Right, evolution of the speed of sound of SF 6 at 46 • C as a function of the ambiant pressure. The cusp at the vicinity of the critical point is clearly visible.

Figure 2 .

 2 Figure 2. Example of power spectral densities for Re = 2 10 5 and ρ = 830 kg.m -3 . The inverse and the direct cascades are visible on each side of the injection frequency f 0 . The red line marks the cut-off frequency of the pressure sensor high pass filter.

Figure 3 .

 3 Figure3. Example of power spectral densities for Re = 10 6 and ρ = 830 kg.m -3 . The inverse and the direct cascades are visible with a series of peaks superimposed on the continuous spectrum for frequencies in the range 1/4 < f /f 0 < 3/2. The red line marks the cut-off frequency of the pressure sensor high pass filter.

Figure 4 .

 4 Figure 4. Example of power spectral densities for Re = 1.5 10 7 and ρ = 830 kg.m -3 .The inverse and the direct cascades are still visible, the peaks have merged and only three or four peaks are visible for frequencies f /f 0 ≈ 1, 3/4, 1/2 and 1/4. A very low frequency band appears at f /f 0 ≈ 10 -2 . The cut-off frequency of the pressure sensor high pass filter is no more visible on this plot.

Figure 6 .

 6 Figure6. Evolution of the amplitude (left) and the phase (right) of the co-spectrum for the three Reynolds numbers discussed in section 4. Whereas the phase difference seems chaotic for the two lowest Re, it is well defined and exhibits plateaus at the locations of the large peaks showing the existence of large scale structures.

Figure 7 .

 7 Figure 7. Evolution of the amplitude of the modes as a function of the Reynolds number Re: m =1 (top-left), m =2 (top-right), m= 3 (bottom-left), m= 4 (bottomright). The color is coding the fluid density from 830 kg.m -3 (supercritical state in black) to 16 kg.m -3 (vapor in light gray).

  [ 2 • 1 0 6 , 3 • 1 0 6 ] M a ∈ [ 0 . 0 7 , 0 . 3 ] [ 3 • 10 6 , 4 • 10 6 ] M a ∈ [ 0 . 09 , 0 . 3]

Figure 8 .

 8 Figure 8. Evolution of the amplitude of mode m = 1 as a function of the normalized number χ n . The solid blue dot represents the evolution for the normalized Mach number (χ M a ) and the empty green square represents the evolution for the normalized Reynolds number (χ Re ), cf. text for details.

Figure 9 .

 9 Figure9. From left to right, evolution of the energy E 2 of mode m = 2 as a function of the energy E 1 of mode m = 1 for all the experimental runs (the 2/3 power law is a guide for the eye), of E 3 as a function of E 1 and of E 4 as a function of E 2 .

Acknowledgments

This work has been carried out in the framework of the Labex MEC Project (No. ANR-10-LABX-0092) and of the A*MIDEX Project (No. ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir" French Government program managed by the French National Research Agency (ANR).


MD Cedric Pastoret

MD Beatrice Ly Sunnaram

MD, PhD Thierry Fest

MD Mikael Roussel
email: mikael.roussel@chu-rennes.fr

Integration of Immature Granulocytes Quantification With

Keywords: Immature Granulocytes, HematoFlow, DxH 800, EGC, Productivity, Slide Review Rates, WBC Differentials

published or not. The documents may come

Introduction

Immature granulocytes (IG) are the precursors of neutrophils and include promyelocytes, myelocytes and metamyelocytes. IG are normally found in the bone marrow. With the exception of newborns, they are rarely observed in the peripheral blood of normal, healthy individuals. Therefore, the presence of IG in a peripheral blood sample is considered abnormal and indicates increased myeloid cell production, which can be the result of infection (especially of bacterial origin), as a response to severe inflammation, hematological myeloid diseases such as myelodysplastic or myeloproliferative syndroms or, finally, as a result of metastatic bone marrow infiltration by tumors. Accordingly, enumerating IG can be helpful, not only for detecting the aforementioned diseases, but also in monitoring treatment and progression of these diseases. [START_REF] Nierhaus | Revisiting the white blood cell count: immature granulocytes count as a diagnostic marker to discriminate between SIRS and sepsis--a prospective, observational study[END_REF] To date, the reference method for their enumeration is still the microscopic slide review. [START_REF] Koepke | Reference Leukocyte (WBC) Differential Count (proportional) and Evaluation of Instrumental Methods: Approved Standard-Second Edition[END_REF] Unfortunately, manual counts show a large inter-observer variation and poor reproducibility, especially when IG are present in low numbers in the peripheral blood. [START_REF] Hotton | Performance and Abnormal Cell Flagging Comparisons of Three Automated Blood Cell Counters: Cell-Dyn Sapphire, DxH-800, and XN-2000[END_REF] The UniCel DxH 800 (Beckman Coulter, Brea, CA) is an automated analyzer capable of performing complete blood counts (CBC) and the leukocyte differential. [START_REF] Hedley | Initial performance evaluation of the UniCel® DxH 800 Coulter® cellular analysis system[END_REF] In addition, IG are classified using the expanded VCSn (Volume, Conductivity, Scatter with multiple angles) technologies on the DxH 800 and are called Early Granulocyte Cells (EGC%_DxH).

In our laboratory the differential workflow and slide review incorporates the DxH 800 connected to the HematoFlow (HF) (Beckman Coulter) immunodifferential flow cytometry process. [START_REF] Roussel | Refining the white blood cell differential: the first flow cytometry routine application[END_REF] HematoFlow is an innovative technique that uses a cocktail of six monoclonal antibodies for immunophenotyping and production of an accurate A c c e p t e d m a n u s c r i p t extended WBC differential including an IG count. [START_REF] Roussel | Refining the white blood cell differential: the first flow cytometry routine application[END_REF] The 2.0 version of the gating software has been recently released and is implemented in our routine lab. [START_REF] Cottard | Improvement of the leukocyte differential performed by flow cytometry using the advanced 2.0 version of the CytoDiff CXP software[END_REF] With this workflow, qualitative flags generated by the DxH 800 (i.e. Blast, Atypical lymphocyte and IG) trigger a HematoFlow immunodifferential with or without slides review. IG is the most frequent flag generated by Haematology Analyzers in our experience and this finding has been confirmed by other reports in the literature. [START_REF] Tan | Evaluation of the Beckman Coulter UniCel DxH 800, Beckman Coulter LH 780, and Abbott Diagnostics Cell-Dyn Sapphire Hematology Analyzers on Adult Specimens in a Tertiary Care Hospital[END_REF] Therefore accurate, automatic and rapid quantification of IG could improve productivity, avoid unnecessary analyses and improve the time of reporting for clinicians to take appropriate action.

The primary objective of our study therefore was to evaluate the performances of the new EGC%_DxH count and compare this with the reference method used routinely in our laboratory. The secondary objective was to determine the reduction in the number of HF and/or slide reviews by the integration of the EGC%_DxH parameter into the algorithm of our routine workflow.

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Material and Methods

Patient samples and study design

During a 10 day period (from January 28 th to February 8 th 2014), consecutive blood samples exhibiting an IG flag after CBC and leukocyte differential on DxH 800 were included in this study. CBC and leukocyte differential were performed on K2-EDTA anticoagulated blood samples from the clinical departments of University Hospital of Rennes, as recommended by manufacturer instructions. This non-interventional study did not require patient consent according to French law. In total 6,913 CBC samples were routinely processed during this evaluation period. As defined in our laboratory procedures, the IG flag does not allow automatic validation and generates a HF differential for verification. Briefly, after red blood cell lysis and immunostaining with CytoDiff Reagent on a FP1000 sample preparation system (Beckman Coulter), the HematoFlow leukocyte differential is performed as previously described with a FC500 flow cytometer (Beckman Coulter). [START_REF] Roussel | Refining the white blood cell differential: the first flow cytometry routine application[END_REF] The CytoDiff CXP software version 2.0 was employed for automatic gating of the population of interest. [START_REF] Cottard | Improvement of the leukocyte differential performed by flow cytometry using the advanced 2.0 version of the CytoDiff CXP software[END_REF] Accordingly to previous internal evaluation comparing Hematoflow and manual slide review, the threshold for IG obtained by Hematoflow (IG%_HF) is at 1.4% for a cut off at 1% on manual review (unpublished data). As such, in our routine procedure IG%_HF <1.4% is reported as zero on the CBC diff report. value of IG obtained by HematoFlow (IG%_HF) is considered as negative when the percentage is lower than 1.4% (unpublished data). As immature granulocytes are considered as pathological condition, in these cases, the IG% is reported as zero on the CBC-diff report.

The HF algorithm is able to detect the 5 regular populations (neutrophils, eosinophils, basophils, lymphocytes, monocytes) as well as 2 abnormal populations (immature granulocytes and blasts). After exclusion of B-cells (Side scatter (SS low /CD19 pos ), A c c e p t e d m a n u s c r i p t monocytes (CD36 pos /CRHT2 neg and CD2 neg ) and mature neutrophils (SS high /CD16 pos ), IG are defined as cells with high granularity on SS axis with lower expression of CD45 and CRTH2 than eosinophils on a biparametric dot-plot CD2-CRTH2/CD45. [START_REF] Roussel | Refining the white blood cell differential: the first flow cytometry routine application[END_REF][START_REF] Gac | Evaluation of CytoDiff™ on cord blood WBC differential[END_REF] The IG phenotype is confirmed by a lower expression of CD16 and CD45 than mature neutrophils on SS/CD16 and SS/CD45 plots respectively which is used in the process of the validation. In our workflow, when IG are higher than 15% without previous results in the seven preceding days or if leukocytes are missidentified by HematoFlow, a systematic manual slide review is required to confirm the amount of IG.

Statistical analysis

For consecutive samples presenting with the IG flag on DxH 800, we recorded the automatic flags, absolute leucocyte count, EGC%_DxH, IG%_HF and a 200 cells manual differential count (IG%_manual). Differences between these values were calculated. Demographic data (age and clinical departments) were also collected.

Discordant cases were defined either as a difference higher than 5% between the two techniques or by qualitative discrepancies (EGC%_DxH neg and IG%_HF pos ). For these cases, microscopic leucocyte differential were performed and each slide was retained for further review. Standard statistical methods including Spearman correlation, linear regression and Bland-Altman test were used for data analysis using GraphPad 5.0 (Prism Software).

Results

Samples

During the period from January 28 th to February 8 th 2014, 6,913 samples were tested in our laboratory for a CBC and leukocytes differential profile. For 470 out of these 6,913 samples (6.8%), an IG flag was generated thus not allowing automatic validation and triggering a HF differential. After exclusion of error flagged samples (Rflag) for ECG% parameter, 402 (85.5%) patients were available for analysis in this study. Both HF and slide review were performed for the training set on 143 samples whereas in the validation set of 259 patients, a HF panel with or without slide review was performed according to our routine workflow.

The median age of these patients was 60.5 years (Interquartile range 36.5-74.5 years). The source of the samples included 46.3% from General Medical Departments, 15.3% from Emergency and Intensive Care Departments, 9.5% from Surgical Departments, 6.2% from Pediatric Non Hematology-Oncology Departments and 22.3% from Hematology-Oncology departments (17.6% adult and 4.5% pediatric).

To validate the repeatability of the IG count on the DxH 800, 3 random samples with low, intermediate and high count of IG (mean at 2.13, 5.26 and 20.86, respectively) were re-run 10 times. Coefficients of variation were calculated at 9.1%, 3.9% and 4.7% respectively. Then, we assessed the longitudinal reliability of ECG%_DxH by A c c e p t e d m a n u s c r i p t testing two samples with low or high level of IG% at the beginning and at the end of each series (every 8 hours in our institution). The coefficient of variation obtained with this method on two consecutive series, on the three DxH 800 with three different operators was of 7.63% and 5.70% for low (3% of IG) and high level (10% of IG) respectively (data not shown).

Threshold calculation on a training set

A first training set of 143 patients was evaluated in order to define the best threshold for EGC%_DxH compared to our reference methods: Flow cytometry (Hematoflow) and manual 200 cells differential count (Figure 1). The median EGC%_DxH was at 1.4% ranged from 0.0 to 17.3%. The median value of IG%_HF was at 2.1% (from 0.0 to 35.0%). ECG%_DxH and IG%_HF were correlated (r=0.873) (Figure 1A). No significant bias was evidenced by Bland-Altman analysis (Figure 1B). Forty-six samples (32.2%) were considered as negative and 97 (68.8%) positive with IG%_HF (threshold at 1.4%). ROC curve analysis showed a positive threshold of EGC%_DxH at 0.9% with a sensitivity of 91.8% and a specificity of 93.5% and an area under the ROC curve of 0.965 (Figure 1C). The concordance rate between the two methods was at 92.3%.

After slide review, IG%_manual showed a median value of 2.0% (from 0.0% to 35.0%) and exhibit a good correlation with ECG%_DxH with (r=0.899) (Figure 1D).

No significant bias was evidence with Bland-Altman analysis (Figure 1E). Forty-two samples (29.4%) were considered as negative and 101 (70.6%) exhibited an IG%_manual higher than 1.0%. The concordance rate was 91.8%. ROC curve analysis showed that the same threshold of 0.9% for ECG%_DxH exhibited a sensitivity of 90.1% and a specificity of 97.6% with an area under ROC curve of

The good correlation observed between ECG%_DxH and both IG%_HF and

IG%_manual enabled to evaluate this new parameter in our workflow with a threshold at 0.9%.

Comparison of IG% on the DxH 800 and with HF strategy

In the validation set of 259 patients, we compared the performance of DxH 800 and HF for IG% quantification with the thresholds previously defined (Figure 2). The mean EGC%_DxH was 1.8% (range from 0.0% to 77.9%) and a mean IG%_HF of 1.9% (range from 0.0% to 44.0%). The linear regression was comparable with the initial training set data (y=1.188x+1,086 with a Spearman correlation at r=0.775.

Considering the thresholds previously calculated, results from DxH and HematoFlow were concordant in 226 samples (87.3%) of cases with 123 DxH neg /HF neg and 103 DxH pos /HF pos (Figure 2A).

For 33 samples (12.7%) discrepant results was found. Six samples were considered false negative (DxH neg /HF pos ) and 27 false positive (DxH pos /HF neg ). Under these conditions, EGC%_DxH exhibited a sensitivity of 79,2%, a specificity of 95.3%, a negative predictive value of 94.5% and a positive predictive value of 82.0%. Not surprisingly the source of samples (clinical department site) influenced the rate of discrepant samples. The percentage of discrepant samples was much higher from the Hematology-Oncology departments (44.4%) compared to those from non-Hematology-Oncology departments (22.3%) and was statistically significant (p=0.02).

Major discrepancies defined as a difference higher than 5% between IG%_HF and EGC%_DxH were found in 16 samples. These are denoted and plotted in red in figure 2C and Eight samples presented with others cytopenias (thrombocytopenia or neutropenia).

Eleven of these samples emanated from the Hematology-Oncology departments.

The biggest difference was found in a case of myeloblastic leukemia with 76% of myeloblasts identified both by HF and slide review. These myeloblasts were assessed as EGC% by the DxH (Figure 3A).

We proposed a validation algorithm integrating the EGC%_DxH for patients presenting with "Imm Gran" flag (Figure 2C). Quantitative flags "Blasts" or "Atypical lymphocytes" require HF analysis whatever the differential count or EGC%_DxH.

Then, in the absence of EGC (EGC%_DxH≤ 0.9), the blood differential count can not be validated and requires HF or slide review in case of i) lymphocytosis, monocytosis or cytopenia (thrombocytopenia or neutropenia) if no concordant results in the previous 7 days ii) previous results without IG in the last 7 days iii) first hematology consultation. In all other cases without additional flags for WBC review the results for EGC%_DxH<0.9 can be validated and reported as 0.0% on CBC-diff report. In presence of EGC%_DxH>0.9, HF is still necessary in case of i) unknown cytopenia or lymphocytosis or monocytosis ii) major IG% discrepancies (delta >5%) in the last 7 days or absence of previous results iii) first hematology consultation. In other situations the EGC% results can be reported as part of WBC differential without performing IG count with HF analysis. Using this algorithm, 92 out of the 259 patients (36%) could be validated (37 EGC%_DxH neg and 55 EGC_DxH pos ) directly after DxH analysis (Figure 2B). This procedure efficiently selected samples requiring HF. Indeed, 9 out of the 33 discrepant samples were validated with EGC%_DxH values: 7 were DxH neg /HF pos whereas 2 were DxH pos /HF neg . Interestingly, seven corresponded to IG% amount lower than 2%. The last 2 samples EGC%_DxH neg A c c e p t e d m a n u s c r i p t were quantified at 4% and 26% with HF. For these samples, HF count was overestimated, due to eosinophils being incorrectly classified as IG (Figure 3B). Therefore our results showed real discrepancies only concerned in very low counts of IG% where the clinical impact is negligible. Moreover, EGC%_DxH validated results showed excellent correlation with results obtained with our actual workflow (HF and eventual slide review) with a spearman correlation coefficient of r=0.953 and a linear regression of y=1.339x+0,689 (Figure 2B).

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Discussion

The algorithm within the DxH 800 Hematology Analyzer System identifies, extracts and enumerates the immature granulocyte subpopulation (called early granulocyte cells) of white cells within the granulocyte population using mathematical transformation and/or combinations of the VCSn measurements which the granularity, the size and the opacity of each cell. "Immature Gran" (IG) flag is the most frequent DxH 800 flag that requires HematoFlow differential validation and possible eventual slide review in our actual routine workflow. The sensitivity of the IG flagging enables us to validate the leukocyte differential without IG for unflagged samples. [START_REF] Depoorter | Optimal flagging combinations for best performance of five blood cell analyzers[END_REF] For IG flagged samples the HematoFlow procedure and especially slide review is time consuming and might require an excellent level of expertise in morphology. Noteworthy, our routine workflow has been implemented with the CytoDiff CXP version 2.0. [START_REF] Cottard | Improvement of the leukocyte differential performed by flow cytometry using the advanced 2.0 version of the CytoDiff CXP software[END_REF] This new version benefit of improvements notably useful in defining IG that were frequently misidentified with the version 1.0; for instance IG were sometime miscounted as eosinophils or CD16 dim polynuclear neutrophils incorrectly counted as IG, leading to high variability in IG count. [START_REF] Cottard | Improvement of the leukocyte differential performed by flow cytometry using the advanced 2.0 version of the CytoDiff CXP software[END_REF] The version 1.0 was employed in recent papers and to our knowledge our work is the first one using the new version. [START_REF] Park | An extended leukocyte differential count (16 types of circulating leukocytes) using the CytoDiff flow cytometric system can provide information for the discrimination of sepsis severity and prediction of outcome in sepsis patients[END_REF] We showed that the EGC%_DxH correlated well with HF with a positive cut-off of 0.9% in an IG flagged population. In our ten day study of 6,913 samples we were able to demonstrate that incorporation of the EGC% from the DxH 800 into our routine slide review algorithm had a positive impact.

EGC%_DxH showed a very good overall correlation with our reference methods, HF and/or slide review (r=0.953). Linear regression and correlation obtained for EGC is comparable with the other classical leukocyte subpopulations which are present usually in smaller numbers -particularly monocytes and eosinophils which present A c c e p t e d m a n u s c r i p t with similar range of values in the peripheral blood. [START_REF] Roussel | Refining the white blood cell differential: the first flow cytometry routine application[END_REF][START_REF] Tan | Evaluation of the Beckman Coulter UniCel DxH 800, Beckman Coulter LH 780, and Abbott Diagnostics Cell-Dyn Sapphire Hematology Analyzers on Adult Specimens in a Tertiary Care Hospital[END_REF][START_REF] Gac | Evaluation of CytoDiff™ on cord blood WBC differential[END_REF] The EGC%_DxH correlation as per our study showed similar performance to the quantification of immature granulocytes as seen with those generated by the Sysmex XE analyser platform. [START_REF] Maenhout | Immature granulocyte count in peripheral blood by the Sysmex haematology XN series compared to microscopic differentiation[END_REF] Based on our study incorporation of the EGC% into our routine algorithm results in a reduction of 92/259 (36%) of samples that requires either HematoFlow differential and/or microscopical slide review.

In those samples where the EGC% was discrepant with HF we found some samples where eosinophils were misidentified as IG. This mis-classification can be identified by the operator, either by the difference in eosinophils count between DxH 800 and HematoFlow, or by the observation of the SS/CD45 and SS/CD16 plots (eosinophils are CD45high whereas IG are CD45low) (Figure 3B). Another possible reasons for IG mis-classification include exceptions when mature neutrophils can lose CD16 in pathologic conditions like severe sepsis [START_REF] Tansho-Nagakawa | Analysis of membrane antigens on neutrophils from patients with sepsis[END_REF] and paroxysmal nocturne hemoglobinuria [START_REF] Tsagarakis | A simple flow cytometric assay for routine paroxysmal nocturnal hemoglobinuria testing based on immature reticulocytes and A c c e p t e d m a n u s c r i p t[END_REF] leading to false IG identification. These conditions can be easily suspected on HF histograms. Indeed, IG presents a gradual gain of CD16 during their maturation. Therefore, they exhibit a continuum of CD16 expression and as such a specific pattern on SS/CD16 histogram. In case of hematologic malignancy (PNH) or myelodysplastic syndromes, the pathologic cells exhibit a low but homogenous CD16 expression leading to a distinct cluster on SS/CD16 histogram (Figure 3C).

Otherwise, myeloblastic blasts can be identified as immature granulocytes by DxH but accurate flagging avoid automatic validation. HF histogram reviewing enable to suspect blasts with their lower CD45 expression and SS intensity, leading to a systematic slide review for each new diagnosis. Indeed, HF never substitutes a manually performed differential count for the initial diagnosis of hematologic malignancies. In all these malignant conditions where there is a potential risk of

  An initial training set enabled to compare ECG%_DXH with the two reference methods IG%_HF and IG% manual and define an EGC%_DxH threshold with receiver operating characteristic (ROC) curve using the MedCalc statistics program (MedCalc Software, Mariakerke, Belgium). A validation set was used to evaluate the A c c e p t e d m a n u s c r i p t integration of EGC%_DxH in our routine HematoFlow workflow. A second sample set evaluated a validation reflex algorithm to integrate ECG%_DxH parameter in our laboratory workflow.

  s c r i p t samples showed seven had a "Blast" flag requiring HF independently of IG% status.

A

  c c e p t e d m a n u s c r i p t autovalidation of an incorrect EGC%, the incorporation in our algorithm of other criteria (flags, unknown cytopenia and samples from hematology departments) results in these samples being accurately identified and processed for HF and/or slide review (see Figure2C). As reported by et Allou et al, the workflow can also be improved by an automated flagging strategy on HematoFlow reviewing that enables an automatic validation of HF leukocyte differential 14 .Therefore in conclusion DHX800 accurately quantifies the presence of immature granulocytes through the new EGC%_DxH parameter and can be safely integrated into the WBC differential workflow and the HematoFlow process. Thus we propose an improved validation algorithm, which integrates the EGC%_DxH from the DxH 800 Haematology Analyzer with our current HematoFlow strategy to further streamline and improve our slide review process. The EGC%_DxH parameter is automatically generated by the DxH 800 so therefore is available at no additional cost. It allows us to further reduce our slide review rate in IG flagged samples by 36% and also allows for improved turn-around time for reporting to clinicians in the various departments we service. Only minor discrepancies in low IG% may be missed however as our study showed these have little if any clinical relevance.

A

  c c e p t e d m a n u s c r i p t granulocytes. Cytometry B Clin Cytom 2012;82:259-263. 14. Allou K, Vial J-P, Bene MC, et al. The routine leukocyte differential flow cytometry HematoFlow™ method: A new flagging system for automatic validation. Cytometry B Clin Cytom 2015 (in press).

Figure 1 :

 1 Figures legends

Figure 2 :

 2 Figure 2: Integration of EGC%_DxH in HematoFlow strategy A-Comparison of ECG%_DxH and IG%_HF in validation set (N=259): linear regression y=1.188x+1,086 with a Spearman r=0.775. Logarithmic representation of results after thresholds application. B-Logarithmic representation of the 92 validated EGC%_DxH following the algorithm of validation detailed on figure C. C-Reflex algorithm for ECG%_DxH validation. N represents the number of samples in the subgroup. *Discordant results are defined by IG% delta above 5% or qualitative discrepancies with previous results in the last 7 days.

Figure 3 :

 3 Figure 3: Example of major discrepancies A-Representative HematoFlow (HF) dotplots identifying blasts Xm (red dots) defined as CD45 low /SSC low /CD16 neg cells. EGC%_DxH was quantified at 77.9% and slide review confirmed the presence of 76% of myeloblasts (right picture) without immature granulocytes (IG). B-HF dotplots identified 5% of IG whereas ECG%_DxH was <0.9%. Slide review exhibited 4% of eosinophils and no IGs. Note the high CD45 expression, CRTH2 positivity and CD16 negativity of purple dots suggesting a false identification of IGs. C-CD16 neg neutrophils identified as IG by HematoFlow in the context of a confirmed paroxysmal nocturne hemoglobinuria. Note the absence of continuum in CD16 expression in purple cells. Slide review did not evidenced IG but only neutrophils, according to ECG%_DxH.

  A c c e p t e d m a n u s c r i p t

  in Table 1 (Range from 5.6 to 77.9%). Further analysis of these 16