Abderrahim Larabi

Michael Pereira

• Florent

Ravelet • Tarik

Hamid Oualli

Mahmoud Mekadem

Laiche Menfoukh

Farid Bakir
email: farid.bakir@ensam.eu

A Larabi •

T Azzam •

H Oualli •

M Pereira •

F Ravelet •

Numerical Investigation of Parietal Pressure Distribution on NACA-0012 Wing Controlled by Micro-cylindrical Rod Arranged in Tandem

Keywords: Laminar separated flow, Passive control, Bodies wake interaction, NACA0012 airfoil, Drag reduction, Lift enhancement

The primary aim of this study is to investigate the influence of an upstream cylindrical rod on the laminar separated boundary layer that develops on a symmetrical profile wing operating at a Reynolds number of Re c = 4.45 × 10 5 . To get further insight onto the aerodynamic performances of this wing at low Reynolds number, numerical simulations with a transitional turbulence model are performed with the ANSYS-Fluent software. The passive flow control technique is applied by setting up a cylindrical rod of diameter d upstream of a NACA-0012 airfoil of chord lenght c. The dimensionless rod diameter with respect to the chord length is d/c = 2/150. Simulations are carried out over a wide range of angles of attack for both the baseline case and the controlled case by the passive proposed technique. The effects of the wing incidence on the parietal pressure distributions on the suction surface of the wing are examined. The results show that the Laminar Separation Bubble that is formed on the upper surface is moving upstream toward the leading edge as the incidence is increased. Moreover, qualitative analysis of the transition zone revealed that presence of the wing in the rod wake exerted considerable effect on the pressure coefficient. Particularly, this passive turbulence generator contributes to eliminate the boundary layer separation

Introduction

The laminar separation bubble is one of the major issues met in several industrial applications, in particular those operating at low Reynolds numbers such as UAV (Unmanned Air Vehicle), Micro Air Vehicle, Race Cars and even Wind Turbines. The boundary layer transition mechanism from laminar to turbulent state of such winged devices is deeply influenced by the aerodynamic characteristics of the wing in terms of boundary layer thickness, transition and separation locations, and wake thickness. In particular, the dynamic behavior underlying behind these low Reynolds flows showed occurrence of slowly recirculating fluid characterized by a stationary rotating swirl known as a Laminar Separation Bubble (LSB) identified to be responsible for several negative effects on the overall aerodynamics performances, such as lift decreasing, drag increasing, aircraft stability reducing, vibration, and even disturbing noise. This separation bubble is basically developed when the laminar boundary layer cannot overcome the local flow deceleration just coming after its acceleration. Hence, when it bypasses the leading edge of the wing the boundary layer peels off from the wall surface under the influence of an adverse pressure gradient. However, at higher Reynolds numbers this laminar boundary layer grows drastically to a turbulent state due to the presence of large inertial forces, and is therefore better able to overcome this adverse pressure gradient. After that, the development of Kelvin-Helmholtz instabilities in this separated shear layer initiates turbulence which yields three-dimensional flow motions. This turbulent mixing is a complex process resulting in the separated streamline reattachement, through interactions between turbulent motions and the wing that incites the reattachment of the separated shear layer to the airfoil surface, leaving an enclosed region of dead recirculating air. Therefore, understanding the physics involved in this phenomenon and the possibility to control the resulting bubble are determinant for efficient engineering design.

Yang et al. [START_REF] Yang | Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature[END_REF] used numerical simulations based on RANS-LES turbulence model to compare the timeaveraged and instantaneous flow-field near the airfoil surface close to the separation region. Their main results show that typical Kelvin-Helmholtz instabilities in the shear layer are twisting into vortices that force the separated flow to stick towards the wall surface leading to a bubble shape in the time averaged outcome. Moreover, the experimental results presented by Hain et al. [START_REF] Hain | Dynamics of laminar separation bubbles at low-Reynolds-number airfoils[END_REF] with PIV measurements at a low Reynolds number flow around a SD7003 airfoil point out the existence of a shear layer rolling up into a vortex sheet in the separated boundary layer originating from the presence of Kelvin-Helmholtz instabilities just after triggering of the boundary layer transition. Zhang et al. [START_REF] Zhang | Hot-Film Measurements of Boundary Layer Transition, Separartion and Reattachment on a Low-Pressure Turbine Airfoil[END_REF] conducted a hot wire investigation on the suction side of a wing at low Reynolds number which showed that a transient boundary layer can reattach to form a bubble and then evolves into fully turbulent state. A review on laminar separation bubbles is presented by Tani [START_REF] Tani | Low-speed flows involving bubble separations[END_REF] where the effects of the Reynolds number on the laminar separation bubble occurrence are discussed. The bubble is observed to appear for a Reynolds number ranging in between [6 × 10 4 -6 × 10 6 ]. Russell [START_REF] Russell | Length and bursting of separation bubbles: A physical interpretation of pressure distribution[END_REF] introduced a theoretical model characterizing the laminar separation bubble in which he advocated a way of depicting the different critical points describing the LSB throughout the on-surface pressure measurements. The analysis clearly shows that pressure distribution on the suction side remains fairly constant when the laminar boundary layer separates, after that the boundary layer reattaches to the surface when shear layer transition is triggered as revealed by drastically pressure increase. Hu et al. [START_REF] Hu | An experimental study of the laminar flow separation on a low-Reynolds-number airfoil[END_REF] conducted time averaged and instantaneous PIV experiments to provide information about the transient behavior of the laminar separated flow on low speed NASA GA (W-1) airfoil at a Reynolds number of 7 × 10 4 . It is found that the bubble appears only when the incidence is in the range [8 • -11.8 • ]. Above this range at around 12 • the pressure gradient becomes so significant that it induces sudden bubble brust, causing the complete stalling of the airfoil. The authors reported also that LSB moves upstream towards the leading edge as the incidence increases in such a way its overall length remains unchanged. The laminar portion of this bubble, however, slightly extends in size, and the turbulent portion shrinks with the increasing angle of attack.

A literature review on flow control shows the existence of several techniques to manoeuvre a boundary layer, either in purpose of flow separation postponement so that the flow remains attached to the airfoil surface, or to achieve lift enhancement, drag decreasing and noise damping. The flow control techniques are categorized into two major classes: active and passive techniques. Gad el Hak [START_REF] Gad-El-Hak | Flow control: passive, active, and reactive flow management[END_REF] added a reactive class to the above and showed up more specific ways of control depending upon the sought main goal. A good flow control technique with such a control device needs to be simple to implement, cheap and keeping the overall geometry unchanged. For these reasons, the so-called passive control techniques are the most widely used for simplicity, affordness and do not require any external energy supplying.

Several numerical and experimental studies on passive control of laminar separated flows have been carried out around different airfoils. Zhang et al. [START_REF] Zhang | Aerodynamic Loading on a Cylinder behind an Airfoil[END_REF] experimentally investigated aerodynamic performances of a cylinder placed downstream a NACA-4412 airfoil at low Reynolds numbers ranging between [1.47 × 10 4 -1.4 × 10 5 ]. They pointed out an abrupt decrease in both lift and drag forces as the side distance is increased. Zhou et al. [START_REF] Zhou | A Numerical Study of a Circular Cylinder in the Wake of an Airfoil[END_REF] examined numerically the wake body interaction between a cylinder placed in the near wake of NACA-4412 airfoil for a Reynolds number of 200 based on the cylindrical body diameter. The main outcomes indicate a significant impact on the aerodynamic loadings, vortex patterns and shedding frequencies acting on the cylinder with an upstream streamlined body. An exhaustive review on the effects of wakes interaction and shedding frequencies between the added bluff body and the cambered airfoil arranged in tandem was given by Bajalan et al. [START_REF] Bajalan | Experimental Study of Frequency Behavior for a Circular Cylinder behind an Airfoil[END_REF]. The findings highlighted the global physical involved phenomena when the airfoil wake interact with the cylinder body. This mutual interference led to a significant change in Strouhal number values of both obstacles and the vortex patterns depending upon the spacing between them. Shan et al. [START_REF] Shan | Numerical study of passive and active flow separation control over a NACA[END_REF] focused their numerical investigation on both passive and active vortex generators used to control the flow separation over NACA-0012 airfoil at 6 • incidence angle. The results showed a reduction of the separation zone over a sig-nificant extent up to 80% when the passive vortex generator is added. On the other hand, the active vortex generator made the separation zone almost to vanish in the time averaged flow results. However, this control technique did not impart drag reduction neither lift enhancement. Igarashi et al. [START_REF] Igarashi | Enhancement of heat transfer and reduction of drag of a square prism in an air stream[END_REF][START_REF] Igarashi | Drag reduction of a square prism by flow control using a small rod[END_REF][START_REF] Igarashi | Enhancement of heat transfer and reduction of drag of a square prism arranged diamond-shape in an air stream[END_REF] suggested a control method of the separated shear layer from bluff bodies by placing a cylindrical rod in tandem arrangement in the upstream crossflow. The idea consisted in forcing the free shear layer to reattach on the body surface. This technique was applied to a cylinder, flat plate, square prism, diamond arranged square prism in order to investigate the flow response to this control method. The outcome recorded a pressure drag reduction of 63%, 30%, 75% and 34% respectively to each bluff body compared to the baseline bodies. Hafien et al. [START_REF] Hafien | Passive Separation Control on a Symmetric Airfoil via Elastic-Layer[END_REF] carried out numerical simulations to consider the effect of self adapting flexible flaps on flow separation over NACA-0012 airfoil at moderate Reynolds number. The results showed a large modification of flow structure when elastic flap deforms under fluid-structure interaction forcing the wake to reduce in size and to lower intensity for shedding vortices. This resulted in a maximum lift enhancement of 69.49% for variable length flaps. Fan et al. [START_REF] Fan | Numerical analysis of broadband noise reduction with wavy leading edge[END_REF] investigate by LES the effect of turbulence generated by a rod of 10 mm in diameter in front of a wavy leading edge wing on its broadband noise for Reynolds number of 3.97 × 10 5 . Results showed the fluctuations of lift and drag coefficients are damped out by 65.4% and 71.4% respectively causing a substantial reduction in the mean noise of 9.5 dB. Supreeth et al. [START_REF] Supreeth | Experimental and Numerical Investigation of the Influence of Leading Edge Tubercles on S823 Airfoil Behavior[END_REF] highlighted the effectiveness of vortex generators in the shape of tubercles on the overall wing performances of a S823 airfoil. They postulated the main part of tubercles in smoothening and mitigating the stall effects to higher incidences which widen the scope of engineering operations for this modified wing. Moreover, the technique offered an additional increase of 19.38% in the overall aerodynamic efficiency. Sefiddashti et al. [START_REF] Sefiddashti | Experimental study of effects of circular-cross-section riblets on the aerodynamic performance of Risø airfoil at transient flow regime[END_REF] conducted experimental investigation to assess the aerodynamic performances of Riso airfoil based wing controlled by a micro-riblets placed on its suction surface at wide range of angles of attack. They showed a significant drag reduction of 29.7% and 54% for Reynolds numbers of 2.02 × 10 5 and 1.4 × 10 5 respectively, which occurred at 7 • incidence. Durhasan [START_REF] Durhasan | Passive Flow Control over an Airfoil by Control Rod at Low Reynolds Number[END_REF] studied experimentally the laminar separation bubble flow mechanism at pres-stall regime for SD7062 airfoil controlled by small rod of different diameters at Reynolds number of 3 × 10 4 placed on the suction side at various chordwise locations. The PIV results revealed significant reduction in the size of LSB for proper rod diameter and location, along with decrease in height of the boundary layer by 22% which is coherent with the correlated reduction of 34% in the eddies' turbulent energy in the flow.

Overall, the major part of the numerical studies are carried out only with fully turbulent classical RANS models (Spallart-Almaras, k -and k -ω SST). The primary purpose of this study is to allow further insights into the fundamental knowledge behind the laminar separated boundary layer on a symmetrical airfoil at low Reynolds number using a transition sensitive RANS turbulence model known as Transition SST (γ-Re θ,t ). In addition, a cylindrical rod is set upstream of the NACA0012 airfoil to control the separated flow around it. It is aimed to assess the feasibility of such a passive control technique and establish the optimum size and location of the rod to enhance aerodynamic performances of the considered wing.

Geometry

The profile which is studied and the geometrical arrangment of the passive control are sketched in Fig. 1. Preliminary experiments have been performed in a wind tunnel. The exeprimental profile consists of a symmetric NACA-0012 profile with a chord length c = 150 mm and a span equals to 3 × c = 450 mm. It has two lateral endplates. The cylinder of circular cross-section with diameter d = 2 mm is placed L = 3 × d = 6 mm upstream of the leading edge of the profile. This distance has been chosen for the following reason:

Under the flow conditions of the study, i.e. with a freestream velocity of 43.3 m.s -1 , the Reynolds number based on the micro-cylinder diameter is Re d = 5931. According to Norberg [START_REF] Norberg | LDV-measurements in the near wake of a circular cylinder[END_REF], the formation length of the Von-Karman vortex street behind this tiny cylinder at this Reynolds number is roughly equals to 2 × d. The purpose behind setting the distance L at three times the rod diameter is thus to be as close as possible to the vortex formation length.

Computational Domain

The three-dimensional computational domain used to carry out this numerical study is illustrated in Fig. 2. The coordinate system origin is placed at the leading edge of the wing. The overall domain dimensions are 42×c in lenght, 24×c m in height and 3×c in width. The inlet boundary condition of the main domain is 12 × c upstream of the airfoil. The domain extension has been chosen in order to maintain a low blockage level and to ensure as little influence of all the domain boundaries as possible; a sensitivity test has been performed to optimize calculations in terms of time, memory and cost. The final domain gives a discrepancy of less than 1% in terms of aerodynamic force with respect to the experiment.

Mesh Generation

The adopted grid topology for the considered computational domain is generated using ANSYS-Meshing commercial software as illustrated in Fig. 2.In order to construct a high-quality structured mesh, the domain is divided into several blocks allowing finer mesh in regions of susceptible eddies formation and coarse grid in far field regions. This strategy is performed using interface boundary conditions between different blocks. Furthermore, to reduce the overall skewness and to ensure better cells orthogonality for the near wall grid elements as density is increased for the following mesh dependence analysis, an O-grid type topology is adopted and centerd around both the wing and the cylindrical rod. This approach gives a smooth mesh transition in the leeward zone of the rod to the leading edge of the wing and allows a high resolution of the boundary layer while keeping relatively a low cell counts compared to C-grid type topology used in former similar studies which showed a reduction of about 50% in mesh size. The structured quadrilateral elements are chosen for the whole computational domain since they provide a high flexibility to control the cell counts with low memory consumption, accurate flow resolution and good flow alignment with respect to the mesh cells thus the overall rate of solution convergence is increased. Refined quadrilateral meshes are applied to critical flow zones where most important phenomena affecting the flow structure around the wing are recorded. These zones are mainly the leeward side of the rod where the vortex shedding interacts with the leading edge of the wing ensuring thus minimization of the numerical viscosity effect responsible of artificial dissipation of the shedded vortices. In addition, a particular attention is paid to the mesh refinement at the airfoil suction side to capture accurately flow features (Laminar Separation Bubble) involved in vicinity of the wing airfoil including leading and trailing edges. In order to assess the significant impact of grid density on accuracy and convergence rate of the numerical solution, three different grid sizes are investigated for the mesh dependency analysis (Tab. 1). The coarse grid (MESH-1) contains 200 points on the suction side of the airfoil, the fine mesh (MESH-2) with 450 grid points and the refined grid (MESH-3) has 640 points. It is noticed throughout sensitivity assessment for lift coefficient force that a deviation of about 4.59% is recorded for the coarse (MESH-1) and fine (MESH-2) meshes. While for the refined mesh (MESH-3), this difference in c L drops to reach a value of roughly 0.56%. As a result, MESH-2 is retained and found to be suited to achieve accurately enough results for this numerical investigation. Another important grid independence was found to be in the exposure of turbulence models to y + values. Values of y + less than unity found to be necessary in order to capture transitional features of the flow on the suction side of the airfoil by accurately modelling the boundary layer. A target value of 0.7 based on the freestream inlet velocity is applied to the entire wing surface and the cylindrical rod during pre-processing simulation case. After that, y+ distribution along the extrados and intrados of the airfoil and around the cylinder circumference is checked in postprocessing phase for all simulations and showed to be less than unity. A total of 15 inflation layers were chosen with a stretching ratio of 18% at the wall surface giving a prism layer thickness large enough to fit development of the boundary layer along with the separation bubble that may occur. As a result of this parametric strategy, a reasonable quality and sufficiently fine structured mesh is with solution-mesh independency condition satisfied.

Turbulence Model

The conventional turbulence models available for RANS formulation such as the one equation Spalart-Allmaras model and ther two equations k -and k -ω models, do not include laminar effects especially for low Reynolds number flows. Even though, DNS and LES methods solve turbulence with sufficient precision so that laminar and transition effects can be predicted, grid density and time resolution requirements are prohibitive and probably inappropriate to be used for industrial design purposes. This led to an attempt to include laminar transitional effects using damping func- The γ-Re θ,t turbulence model still solves the transport equations for both k and ω quantities as k -ω SST does, which are otherwise identical with an exception for production, P k and dissipation, D k terms in kinetic energy (Eq.( 1)) along with the blending function F 1 in specific dissipation rate (Eq.( 2)) that controls the use of ω near the walls and far away. The production term, P k is correlated with a turbulence intermittency, γ (Eq.( 3)) bounded between values of 0 and 1, indicating physically the state of the flow locally by accounting for the percentage of time corresponding to the presence of turbulent fluctuations in the boundary layer. Where a value of 0 indicates that the flow is locally laminar hence close to the leading edge of the airfoil and when γ saturates to a value of 1 the flow is fully turbulent. Notice that freestream flow contains turbulent kinetic energy and specific dissipation rate, thus γ should have a value of 1 at inlet boundary condition and freestream so that it will be represented by the fully k -ω SST model. Regarding the dissipation term, Dk it is limited by a min max limiter (Eq.( 4)) calibrated to ensure that its value does not drop below 10% of its fully turbulent value when γ = 0, because even when the boundary layer is laminar with no production of turbulent kinetic energy, if is there any turbulence the wall still dissipate it by damping these turbulent fluctuations of the flow. In other hand, numerical tweak is used to correct the blinding function, F 1 to prevent it to take a value of 0 in the laminar boundary layer near the wall where normally takes a value of 1 allowing the Transition SST model to take its k -ω form of k -ω SST turbulence formulation rather than k -which is ineffective in the near wall regions particularly when the values of y + are very small. Hence, the blending function is limited; to prevent it to switch accidentally to 0 in the laminar region; by a new term defined by an exponential decay of a Reynolds number like term (Eq.( 5)) governed by a square-root of turbulent kinetic energy which is very small in the laminar portion of the boundary layer making this new term to tend to 1. In order to compute the values of γ in the flow field an additional standard transport equation for intermittency is solved (Eq.( 6)). The production terms, P γ is used to control the length of the transition region of the boundary layer by producing turbulent fluctuations and pushing γ to saturates at a value of 1 in the full turbulent region. This term takes the form of Eq.( 7) characterized by two main terms F onset and F length , where the former is a switching function for the production of intermittency and the latter controls the rate of this production happens to be when Flength is large γ is produced quickly and saturates to 1 rapidly which shortens the length transition region. To assess the Fonset, the Transition SST model introduced another transported variable, Re θ,t calculated everywhere in the computational domain (Eq.( 8)). This variable connects the empirical correlations to the onset criterion of intermittency by calculating two local values Re θ,t and Re θ,c where transition occur and fluctuations begin to take place respectively. The source term, P θ,t of Eq. ( 8) is included to force Re θ,t to take its experimental value (proprietary of ANSYS-Fluent CFD code) specified at the inlet except near the wall where it is turned off allowing the freestream value of Re θ,t to convect and diffuse toward the wall by introduction a blending function F θ,t (Eq.( 9)). Once Re θ,t is computed F length and F onset are evaluated using algebraic relationships and when they are beyond certain threshold the source term, P γ is switched on, hence production of intermittency γ will start for each cell ( [START_REF] Langtry | Correlationbased transition modeling for unstructured parallelized computational fluid dynamics codes[END_REF][START_REF] Malan | Calibrating the-re transition model for commercial cfd[END_REF]).

∂ (ρk) ∂t + ∇ • (ρUk) = ∇ • µ + µ t σ k ∇k +P k -D k (1)
∂ (ρω) ∂t + ∇ • (ρUω) =∇ • µ + µ t σ k ∇ω + γ ν t P k -βρω 2 + 2 (1 -F 1 ) ρσ ω2 ω ∇k : ∇ω (2)
Where, ∇k : ∇ω = ∂k ∂x j ∂ω ∂x j

P k → P k γ 0 ≤ γ ≤ 1 (3) D k → D k min [max (γ, 0.1) , 1.0] (4)
F 1 , new = max (F 1 , F 3 ) (5)
Where, F 3 = e -(Rey/120) 3 and Re

y = ρy √ k µ ∂ (ργ) ∂t + ∇ • (ρUγ) = ∇ • µ + µ t σ γ ∇γ +P γ -D γ (6)
P γ,1 = F length C a1 ρ S (γ F onset ) 0.5 (1 -C e1 γ) (7)
∂ ρ Re θ,t ∂t + ∇ • ρU Re θ,t =∇ • µ + µ t σ θ,t ∇ Re θ,t +P θ,t (8)
P θ,t = 0.03 ρ t Re θ,t -Re θ,t (1 -F θ,t ) (9)

Boundary Conditions

In addition to the domain sensitivity analysis conducted to set right dimensions of upstream, downstream, top and bottom boundaries of the computational domain, an appropriate implementation of boundary conditions needs to be carefully considered. This is achieved by splitting the domain boundaries into three distinct regions, velocity inlet, pressure outlet downstream and symmetry side boundaries. A velocity inlet type was specified as Dirichlet boundary condition at inlet boundaries in such a way that freestream velocity is set to maintain a chord-based Reynolds number at 4.45 × 10 5 . The used method for freestream turbulence is by setting values of turbulent kinetic energy and specific dissipation rate at the inlet boundary condition, unless otherwise stated, as k = 2.53 m 2 .s -2 , ω = 151.55 s -1 and an intermittency factor of 0.85 as dependence of flow features on γ values at the inlet was observed. These quantities are calculated based on empirical correlations related to SST k-ω turbulence model. The downstream domain boundary was prescribed as pressureoutlet boundary condition and set to a value of zerogauge pressure as operating conditions of the working fluid are specified according to standard atmospheric pressure of 101.325 kPa and temperature of 288.15 K. In addition, an estimation of turbulent length scale of 10% the characteristic length is set at the pressureoutlet along with 5% backflow turbulence intensity. A stationary wall condition is adopted for both airfoil and rod surfaces with no-slip boundary condition, hence, no turbulence production from the wall itself to the freestream flow. The two side boundaries of the computational domain are assigned to symmetry boundary condition which enforces to null the normal component of all flow variables gradient by acting as zero shear slip wall. This condition seems to be satisfactory as the computational domain is large enough to maintain these far boundaries at constant static pressure (Fig. 2).

Solver and Numerical Schemes

Ripley et al. [START_REF] Ripley | The unsteady structure of two-dimensional steady laminar separation[END_REF] have shown that the laminar separation bubble does not involve any vortex shedding via their time-dependent numerical investigation of the laminar separated flow subjected to an adverse pressure gradient. As a motivation, three dimensional, incompressible, steady state, pressure based and segregated double precision numerical solver is adopted to conduct present simulations. All Steady RANS CFD runs were undertaken using the industry standard commercial CFD package known as AN SY S c -Fluent, Release 18.1. The code solves the Reynolds Averaged Navier Stokes equations in a finite volume environment with Message Passing Interface library parallelization. The Transition SST (γ -Re θ,t ) four equations turbulence closure model is adopted to model the Reynolds stresses term. Pressure-Velocity field coupling is ensured using SIMPLE algorithm advantageous for problems requiring boundary layer high resolution. Spatial discretization of pressure term is treated by a standard interpolation scheme. Moreover, momentum diffusive terms, turbulent kinetic energy and specific dissipation rate equations are second-order central difference special discretization scheme and convection terms are treated using second-order upwind discretization scheme in space. Finally, the cell gradients of all variables are computed using weighted least square cellbased scheme. The initial flow field for all simulations is set according to predicted freestream inlet conditions. The different cases are computed for 50000 iterations where scaled residuals of all equations along with lift and drag coefficients of the wing are monitored to ensure adequate convergence. The overall computational time for every simulation to be converged was achieved in about 144 hours (wall clock) that led to reduction in the residuals of O(6).

Results and Discussions

Simulations of the flow around the wing at various angles of attack ranging between [0 • -24 • ] for a chordbased Reynolds number of 4.45×10 5 . are carried out for both baseline and controlled configurations in order to understand how wing surface pressure are altered when a passive control method is introduced to enhance the overall wing aerodynamic performances at pre-stall and stall regimes.

Validation

For reason of results confidence, it is imperative to compare the obtained results from CFD simulations of the baseline wing with Wind Tunnel experiments to validate the numerical model adopted herein. Tests are carried out in an open jet closed circuit wind tunnel having circular test section of 600mm in diameter. The wing model is NACA 0012 airfoil based with 150mm chord length and 450mm span giving a maximum blockage ratio of 6.4%. The forces acting on the wing under the stream are measured by an aerodynamic balance composed of three parralel parts. The measurements range of each one is respectively [-100N -+100N ] for two of them and [-50N -+50N ] for the last one. A mechanism for angle of attack variation is also incorporated with the balance allowing α to bet set between [-20

• -+40 • ].
The experiments for the baseline wing configuration used for CFD validation are obtained for a freestream velocity of 43.3 m.s -1 , that corresponds to a Reynolds number based on the chord length of 4.45 × 10 5 . The turbulence intensity for these flow conditions is 1%. Table 2 shows the error in the aerodynamic forces predicted by current numerical investigation when compared to CFD simulations of Huang et al. [START_REF] Huang | Numerical study of blowing and suction control mechanism on NACA0012 airfoil[END_REF] and the wind tunnel results. It is noteworthy that deviations remain less than 8.28% in all instances except at 14 • incidence where the wing stalls and making this region quite difficult to solve with turbulence modelling formulation of Navier-Stokes equations. Although simulations overpredict lift force coefficient the fact that the error is relatively consistent for each case, highlights that the overall trends shown by the numerical results are coherent with those occurring in the wind tunnel.

The distribution of the parietal dimensionless distance, y + on both wing surfaces and on the rod circumference have been computed. The average value is largely less than unity and is of the order of 10 -1 . The maximum values are obtained at the leading edge separation point and are close to 0.7. Thus, resolution of the boundary layer of the flow near both bodies is performed accurately enough throughout the grid used to conduct the different CFD simulations. Hence, spacing of the first cell from the wall is validated for this numerical study.

Baseline Flow Analysis

Figure 3 shows the variation of the aerodynamic coefficients, c L and c D , at low Reynolds number and various angles of attack for the baseline NACA0012 wing simulations along with a schematic of the flow patterns observed for each representative state. It is noticed that, for incidence ranged between [2 • -13 • ] a monotonous linear increase in the lift coefficient relatively growing in a constant rate up to a maximum value depicted at α = 13 • . After reaching the peak, the value of c L drops drastically at α = 14 • showing turbulent stalling phenomenon of the boundary layer taking place as clearly illustrated by the schematic of the streakline patterns on the wing surface. The flow separation is led to move upstream causing the wing to stall. Above incidence of α = 20 • , the lift shows a tendency to be relatively constant. This is basically due to the main flow separation indicated by the presence of counter-rotating vortices on the suction side of the wing hence the post-stall is triggered. Regarding drag coefficient c D , it remains almost unchanged for small angles of attack [0

• -6 • ].
Thereafter, it increases slightly in the meantime as the angle of attack is further changed possibly because of premature separation of the laminar boundary layer, followed by a significant rise for α = 14 • indicating presence of turbulent stall of the boundary layer. By further increasing the angle of attack, the drag coefficient continues growing till a maximum value is attained at incidence 24 • .

The streamline close to the wing surface is presented in Fig. 4. to make a comparison between various angles of attack and the presence of flow separation on the upper surface of the airfoil. It is believed that the nonlinearity in the lift curve slope is linked to presence of laminar boundary layer separation occurring at this low Reynolds number flow (Re c = 4.45 × 10 5 ). For an angle of attack between 0 • to 8 • , a separation bubble appears on the airfoil suction side that travels from the trailing edge to the leading edge as the incidence is increased, leading effectively to a change in location Effect of the passive control technique on development of the LSB is analysed and the most relevant results are presented in Fig. 6. The figure depicts average pressure distribution contour on the upper surface of the wing at an incidence of α = 10 • . Comparing the two configurations side to side, baseline case and controlled case, it seems that the rod has significant influence on dimensions of the laminar separation bubble occurring on the suction side as a result of premature laminar boundary layer separation. Both regions, laminar and transitional, are influenced by presence of the rod wake. A significant reduction of approximately 50% in the laminar region is depicted by the three-dimensional average pressure distribution on the wing surface which yielding to a considerable enlargement of the transitional zone by approximately 30%. Thus, this vortex generator placed upstream the wing showed that LSB is extremely sensitive to the interaction between the rod wake and the airfoil leading to a bubble size reduction that is considered to be harmful for the wing overall aerodynamic performances. Therefore, a promising enhancement in aerodynamic characteristics will certainly contribute to improve efficiency of such wings operating at low Reynolds numbers.

Effect of Passive Control on Parietal Pressure Distribution

Figure 7 demonstrates both friction lines and average pressure distribution on the wing upper surface. When incidence is null (α = 0 • ), friction lines on the wall surface are uniform and flows in the same direction as that of the main incoming flow, starting from the leading edge towards the trailing edge. As the angle of attack is increased (α < 11 • ), friction lines begin to loose their uniformity and smoothness behavior. An instability is triggered on both ends of the trailing edge, indicating presence of a partial separation of the boundary layer, developing progressively from the trailing edge towards the leading edge. Furthermore, the average pressure gradually increases in the chordwise direction starting from the leading edge. It begins with a zone of depression at the leading-edge level indicated by a uniform and homogeneous coloured zone and keeps growing to a high-pressure region at the trailing edge. For the baseline configuration at α = 11 • , the depression zone is narrow on both ends of the leading edge, because the instability generated between endplates and airfoil boundary layers mutually interact. This is much clearer through the friction lines distribution showing a pair of counter-rotating vortices swirling on the wing suction side. Consequently, partial turbulent stall of the main wing is triggered close to these regions. In case of controlled wing configuration, it shows, however, important changes noticeable on the mean pressure field as well as on the friction lines (Fig. 7). Mainly, the depression region near the leading edge is getting uniformized in the spanwise direction starting from mid-dle towards endplates. Another important outcome is revealed by new friction line patterns resulting from the control and consisting in the fact that the pair of vortices near endplates shrink in size making the incident flow more dominate on the wing surface. As a result, a reduction of about 56% on the overall drag force is reported for the controlled case. As the angle of attack is increased the instability amplifies more and more to form two large counter-rotating vortices covering a large part of the wing upper surface. A backflow is generated as a consequence of these two vortices. This reveals that energy of the incoming flow is more dominant than that of the backflow. As a result of this dominance the incident flow imposed its presence mainly in the midspan zone, hence, the boundary layer is not completely separated from the wing surface except in the region where the vortices are present. For α = 12 • , direction of friction lines on the midspan zone shows that the backflow becomes dominant and imposes its presence with respect to the incoming flow. The two counter-rotating vortices still exist, but larger in dimensions and intensities when compared to those observed for incidence α = 11 • . Therefore, secondary instabilities appear as a consequence of this interaction between the two flows of opposite sense and the significant energy of this backflow, Fig. 8.In this case, the boundary layer is completely separated from the wall. This irregularity behind appearance of this instability disturbs the uniform distribution of the average pressure in both ends of the wing close to the leading edge. However, when flow control is applied, the average pressure distribution becomes uniform and homogeneous and the disturbed zones near the endplates vanish. In addition, this depression portion grows in size compared to previous angles. Moreover, presence of the rod has a significant impact on the flow developing on the wing suction side. From the Fig. 8 it is easily noticeable that secondary instabilities reported before completely disappear and the incoming flow gained energy from the feeding vortex generator to become dominant over a large portion of the wing because it overpassed the early backflow seen without control. As a consequence, the tow counterrotating vortices died out and straitened in size resulting a reduction in the drag force by 73% including the rod contribution. For incidence greater than 12 • , the uniform distribution of the mean pressure over the entire upper surface is completely disturbed for the baseline configuration, Fig. 9. Consequently, the flow within the boundary layer is completely unstable. The intensity of these instabilities increases with the angle of attack causing the so-called turbulent stall to launch. As α increases, these instabilities are intensified and the boundary layer separation is generalized to the entire wing surface. For α = 13 • the flow seems to behave in the same way as for 12 • incidence without control. This is clearly shown by friction lines pattern, where the dominance of the backflow resulting from instabilities generated inside the boundary layer is well represented leading to secondary irregularities as a result of the interaction between the incident and back flows. In this case, the boundary layer is completely detached from the surface and this incident angle corresponds to the turbulent and massive stall angles of the flow. In the other hand, as the control technique is applied, the mean pressure distribution on the suction side of the wing exhibits a different behavior in comparison to the baseline case. As stated earlier, the mean pressure distribution is random due to partial separation of the boundary layer near endplates caused by the primary and secondary vortices that gain intensity to cover an important portion of the wing surface as illustrated in friction lines patterns showing dominance of the backflow over the incoming one. Thereby, presence of the vortex generator brought the depression zone near the leading edge from its randomness attitude to its uniform and homogenous shape similar to what was observed at lower angles of attack when control is absent. It is worthwhile noting from pressure contours that flow characteristics are delayed by 2 • from the baseline configuration with flow control applied. In other words, the stall is postponed when the wing is operating in the rod wake. In fact, looking at the new pattern of friction lines after low control is set, what have been seen in average pressure distribution is emphasized throughout the assessment of the flow before and after the control. As a matter of fact, the wake produced by the rod evolves into shedded eddies interacting with the boundary layer developing on the wing upper surface in a way that they feed energy to the flow close to the wall from free-stream. Premature separated boundary layer is reinforced to overcome pressure gradients that is subjected to and stick again to the wall surface. Consequently, this phenomenon of energizing the upcoming flow is established by defeating the dominance of the backflow spotted in the baseline case, so that the flow recovered its chordwise direction mostly in the midspan portion of the wing. Although the pair of vortices remain near the endplates a part of consequence of threedimensionalities attitude of the flow outcomes of interferences between the two boundary layers developing on either endplates and wing body, the secondary instabilities are completely vanished for the controlled case. To sum up this qualitative analysis that provides main differences on the flow structures before and after control, it is important to link these essential findings to their impact on aerodynamic loads specifically lift and drag forces. It is found that actual aerodynamic coefficients are highly sensitive to flow control in an extent of a lift enhancement of 17% to gather with a maximum drag reduction of 49% which is promising in a perspective of fineness improvement.

Figure 10 depicts mean surface pressure distribution on the suction side generated by the wing operating in the low Reynolds number condition and at 15 • incidence angle. For the non-controlled case the surface pressures appear very instable, as expected, whilst at such high angle of attack a presence of an intense turbulent agitation of the flow within the boundary layer is naturally understandable as turbulent stall of the boundary layer has taken place. This is shown on the friction lines illustration (bottom right-hand column), which reveal in the low-pressure regions near endplates formation of a pair of counter rotating vortices due to circulation of flow from higher to lower pressure regions. Also, when looking at the evolution way of these lines going from the trailing edge towards the leading edge over the entire wing surface is an evidence on the backflow dominance over the incoming stream. Similarly, to what have been described in the previous angle of attack, the boundary layer is fully separated from the wing upper surface giving rise to a wing stalled state. In other hand, a micro rod is used for prospective wing performances enhancement. Some relevant findings are presented in the left-hand column of the Fig. 10. The instabilities in the average pressure distribution seem to be damped down to an extent where uniformity and homogenous appearance is recovered close to the leading edge. An analogy of this pressure contour with the baseline case, turns up this flow pattern resulting from the control device is already seen at earlier angle of attack, 11 • . This inferred that this passive control delays heavy stall by few degrees. There appear to be larger area of low pressure in the mid-span region of the wing as the main flow gain control over the backflow and sticks to the wing again through involvement of rod eddies that convey energy from free-stream to boundary layer. Whereas, close to the endplates, less suction is generated as the three-dimensional interfaces in the boundary layers of these two regions arise tiny secondary instabilities on both sides that block the flow from it. To complete what is said so far, friction lines on the upper surface of the wing at 15 • incidence with flow control are also considered. It is found that the flow got back its streamwise direction in comparison to the baseline case. This is because the boundary layer is completely separated from the wall and reattach to the wing particularly in the mid-span region constraining the stream to flow downward to the trailing edge. Two thirds of the wing suction side are occupied by a pair of counter rotating vortices resulting from recirculation of the flow from high to low pressure. In addition of secondary instabilities close to the leading edge on both sides are generated the flow from the endplates interferes with the wing boundary layer, which yield it to partially stalled state. Finally, all these results conclusively show that passive control as uses here showed capability to delay full stall by 3 • . Furthermore, an enhancement in aerodynamic loads is also ensured with control. 21% of drag reduction and 23% in lift growth are effectively obtained.

Conclusion

In this paper a passive flow control approach for a pre-stalled and post-stalled airfoil is numerically in- . The longitudinal gap between the wing and rod together with rod's diameter are key parameters carefully considered in this study. Detailed RANS CFD calculations are carried out for both controlled and baseline cases to show the influence of the joint device on the flow control effectiveness. Friction lines are further analyzed to give information on the flow field behavior on wall surface and correlative pressure distribution. The diameter of the microcylindrical rod considered for this current study is d/c = 0.013, placed away from the wing leading edge at 3 times the diameter in the chordwise direction. For the baseline case, flow fields and average pressure coefficient distribution analysis made it possible to highlight the underlying physical phenomenology involved in laminar and turbulent boundary layer separation. It is shown that laminar boundary layer is particularly sensitive to pressure gradients induced by the wing at incidence. This caused premature separation of the flow followed by reattachment after transition to turbulent state accompanied by formation of the so-called laminar separation bubble (LSB). At the pre-stall flow condition (α < 13 • ), the bubble forms near the trailing edge of the wing. As the incidence increases the LSB significantly decreases in length while migrating upstream to stabilize in the vicinity of the leading edge. This feature is encountered between α = 2 • and α = 8 • . When the angle of attack is greater than 8 • , the airfoil exhibits presence of a second conventional bubble near the trailing edge as well as the LSB near the leading edge. At α = 12 • the laminar flow completely separates from the wing upper surface and forming a large recirculation zone; hence the wing is stalled. Any further increase in incidence results in the laminar separation bubble sudden burst leading to a heavy turbulent separation of the boundary layer subsequently to the important pressure gradient. Analysis of lift and drag forces with the LBS formed showed significant degradation in the overall aerodynamic loads pushing the wing to an abrupt stall. When the microcylindrical control device is introduced into the flow, a considerable influence on the behavior of the laminar separation bubble is induced. Presence of the rod revealed ability to partially eliminate the bubble by causing an early reattachment of the premature laminar separated boundary layer over a significant extent. The total length of the LSB is found to reduce by more than 75% and almost vanish for an incidence of 10 • . Furthermore, the vortex like generator deeply impacts the flow structure especially at stall and poststall conditions. At AOAs ranged between 10 • to 15 • , the control device acts similarly to a pumping system energizing the boundary layer on the airfoil counterbalancing the adverse pressure gradients. In fact, eddies generated in the cylinder wake interact with the boundary layer of the wing, ensuring convection of energy from freestream to near wall flow. The size of the downstream recirculation zone is significantly reduced for post-stall conditions. In other words, mean pressure contours and corresponding friction lines on the suction side are corroborating results for control effectiveness of the rod beyond stall conditions of the baseline wing. It was capable of maintaining attached flow for incidence of 15 • till 33% of the whole wing upper surface close to the midspan region, while the backflow took advantage in non-controlled configuration, hence a complete separation from the leading edge was noticed. Finally, for pre-stall regime, the controlled flow doesn't provide significant improvement in either lift and drag, but does show effectiveness in reducing the length of the laminar separation bubble leading to further understanding of the intricate involved dynamics influencing the wing aerodynamic performances. Meanwhile, at poststall regime presence of the rod close to the leading edge seems to effectively suppress or diminish and in most favorable case delay flow separation to higher angles of attack. This is advantageous to either lift enhancement or drag reduction, resulting respectively in a gain of 23% and a reduction of 73% as evaluated in this study.

Fig. 1

 1 Fig. 1 Schematic of the NACA-0012 wing of chord length c controlled by a micro-cylinder of diameter d placed at a distance L upstream of the leading edge

Fig. 2 (

 2 Fig.2(a) Schematic of adopted mesh topology for the domain(b) Structured mesh around the rod close to the airfoil, (c) Structured mesh close to the trailing edge of the airfoil.

Fig. 3 3 . 3 . 3

 3333 Fig.3CFD lift and drag coefficients for baseline case at varying AOAs.

Fig. 4

 4 Fig. 4 Process of LSB migration at low Reynolds number of 4.45 × 10 5 for NACA0012 wing; arrows highlights the LSB location (flow moving left to right).

Fig. 5

 5 Fig. 5 LSB characterisation at flow conditions of Re c = 4.45 × 10 5 and α = 8 • (flow moving top to bottom).

Fig. 6

 6 Fig. 6 Effect of microcylinder rod on LSB dimensions at α = 10 • ; (a) baseline case; (b) controlled case (flow moving left to right).

Fig. 7

 7 Fig. 7 Contours of pressure coefficient (upper column) and friction lines distribution (lower column) on wing suction side surface at flow conditions of α = 11 • and Re c = 4.45 × 10 5 ; (a) baseline case; (b) controlled case (flow moving top to bottom).

Fig. 8

 8 Fig. 8 Contours of pressure coefficient (upper column) and friction lines distribution (lower column) on wing suction side surface at flow conditions of α = 12 • and Re c = 4.45 × 10 5 ; (a) baseline case; (b) controlled case (flow moving top to bottom).

Fig. 9

 9 Fig. 9 Contours of pressure coefficient (upper column) and friction lines distribution (lower column) on wing suction side surface at flow conditions of α = 13 • and Re c = 4.45 × 10 5 ; (a) baseline case; (b) controlled case (flow moving top to bottom).

Fig. 10

 10 Fig. 10 Contours of pressure coefficient (upper column) and friction lines distribution (lower column) on wing suction side surface at flow conditions of α = 15 • and Re c = 4.45 × 10 5 ; (a) baseline case; (b) controlled case (flow moving top to bottom).

  vestigated. Flow response to placing a microcylindrical shaped rod near NACA-0012 wing-based profile at low chord-based Reynolds number of Re c = 4.45 × 10 5 is carefully examined. Particular focus is put on parietal pressure distribution on suction side surface along with flow field patterns with corresponding impart on the overall aerodynamic loads particularly high angles of attack ranging from 0 • to 24

Table 1

 1 Grid independence analysis

	Mesh	Nodes	on	c L	at	Error (%) with
		Aerofoil		10 •		previous mesh
	MESH-1	200		0.8636		-
	MESH-2	450		0.9035		4.59
	MESH-3	640		0.9086		0.56

Table 2

 2 Lift coefficient from CFD simulations and wind tunnel experiments c L at 10 • c L at 12 • c L at 14 •

	Present	0.9035	1.0613	1.0876
	work
	CFD [24]	0.8752	0.9801	1.025
	Error (%)	3.23	8.28	6.1
	Exp.	0.898	1.021	0.962
	Error (%)	0.61	4.0	13.05


Van-Thang Nguyen
email: thang.nguyen@ensam.eu

Amelie Danlos

Florent Ravelet

Michael Deligant

Moises Solis

Sofiane Khelladi

Farid Bakir

CFD Analysis to explain the Operating Range Extension observed during Operation in Corotation Mode of a Twin-impeller Centrifugal Compressor Stage

Keywords: centrifugal compressor, CFD, counter-rotating impellers, operating range extension

Centrifugal compressors are widely used in many industrial applications because of their advantages. However, these turbomachines suffer at a low-flow rate from instabilities, such as rotating stall and surge. That leads to operational failure, pressure fluctuations and vibrations of the thorough system. Many mechanical solutions minimize these instabilities and expand the operating range towards low-flow rates like active control of the flow path, variable inlet guide vane and casing treatment. Currently, our team has developed a new compressor composed of a twin-impeller powered by autonomous systems. We notice the performance improvement and instabilities suppression of this compressor experimentally. In this paper, a CFD study is presented to explain some of these experimental observations by analyzing the inside of twin-impeller, the flow structures and thermodynamic characteristics at low flow rates operating in a corotating mode. Numerical results and experimental measurements of compressor maps are consistent.

INTRODUCTION

Surge line and choke line always limit operating range of compressors. Choke is an unstable state that occurs if the discharge pressure is low and the flow rate is large. This leads to an increase in the flow velocity in the compressor. If the velocity reaches the speed of sound at the blade throat, the compressor then blocks the flow, consequently, high-frequency vibrations with small amplitudes in blades and stator vanes are generated which means the flow channels between blades suffer a blockage effect. The compressor operating in this state presents low performance and failure due to the material's fatigue effect over a long time. However, choke is more likely to occur in axial compressors than in centrifugal compressors because of the more considerable distance between the surge and choke limits of centrifugal compressors on the performance map. Therefore, a choking phenomenon in centrifugal compressors is often overlooked and it does not cause deep concern for researchers. Surge phenomenon is characterized by a strong backflow in the compressor. The pressure drops rapidly because the generated pressure does not overcome the downstream pressure gradient when the machine flow reduces below a certain minimum value. And then, the pressure and mass flow gradually increase. The equilibrium of the compressor is then re-established. This process is periodically repeated and formed a pressure oscillation cycle in the system. This oscillation creates strong impact pulses. Several internal components damage will occur if the compressor works for a long time in this state. Therefore, researchers focus on improving the surge limit to extend the compressor operating range towards low flow rates. Indeed, all compressors are controlled to avoid surge phenomenon to ensure safety. Compared to the choking phenomenon, the surge is easier to detect thanks to the pressure pulse signals in the system. As a result, solutions have been implemented to limit the occurrence of surge phenomenon such as using safety margin by selecting a control line that is far away from the actual surge line [START_REF] Botros | Developments in centrifugal compressor surge Control-A technology assessment[END_REF][START_REF] Dukle | Rotating equipment:Validating anti-surge control systems[END_REF], or using a variable inlet guide valve to allow the adjustment of inlet flow angle, one of the causes of surge [START_REF] Simon | Improvements in performance characteristics of single-stage and multistage centrifugal compressors by simultaneous adjustments of inlet guide vanes and diffuser vanes[END_REF]. The other methods were developed to suspend the surge phenomenon such as using the casing treatment method by adding grooves, slots, or holes in the casing of an inducer [START_REF] Koyyalamudi | Stall margin improvement in a centrifugal compressor through inducer casing treatment[END_REF][START_REF] Eynon | A study of the flow characteristics in the inducer bleed slot of a centrifugal compressor[END_REF][START_REF] Nikpour | Turbocharger compressor flow range improvement for future heavy duty diesel engines, Conference on thermo-and fluid dynamics processes in diesel engines[END_REF], active control method uses a plenum bleed valve and air injection method to minimize flow turbulence [START_REF] Willems | Modelling and Bounded Feedback Stabilization of Centrifugal Compressor Surge[END_REF][START_REF] Day | Active suppression of rotating stall and surge in axial compressors[END_REF]. These methods can improve the surge margin from 4% to 18%. This study introduces a novel generation of centrifugal compressors that use twin-impeller to improve surge margin based on the active control method. This compressor can operate in two modes: contra-rotating mode (the two impellers rotate in the opposite direction) and co-rotating mode (the two impellers rotate in the same direction).

The measurements obtained with our experimental device reproduce the characteristics of a singleimpeller centrifugal compressor, design with the same size, by varying the speed of each impeller independently [START_REF] Nguyen | Experimental study of the rotor-rotor aerodynamic interaction of a counter-rotating centrifugal compressor[END_REF]. The combination of the rotation speed of the upstream impeller and downstream impeller can improve the surge margin in comparison with the single impeller compressor as shown in figure 1. Especially, by changing the rotational direction of the upstream rotor (in co-rotating mode) with a speed of about 50%, the surge margin can shift about 22% towards a lower flow rate.

CFD MODEL

Computational Fluid Dynamics (CFD) plays an important role in the design and performance evaluation of turbomachinery. In this study, the twinimpeller centrifugal compressor has been simulated three-dimensionally using the commercial CFD software Star CCM+ 13.06. The compressor was modeled into seven domains: inlet pipe, inlet elbow, upstream-impeller, downstream-impeller, cavity, volute, and outlet pipe (Figure 2). The inlet and outlet pipe domains were extended to 5-diameter-long to reduce the effect of boundary conditions [START_REF] Broatch | Simulations and measurements of automotive turbocharger compressor whoosh noise[END_REF].

Polyhedral grids are used to discrete because of higher accuracy when the second flow is relevant [START_REF] Galindo | Set-up analysis and optimization of CFD simulation for radial turbines[END_REF]. In addition, a prism layer mesh was applied to increase the near-wall region to obtain the y+ value close to the unity on the blade surface of the impellers. The details of the mesh model are shown in figure 2.

Model parameters:

The simulation has been conducted in the steady-state and unsteady state, segregated implicit solver, ideal gas model. The k- SST turbulence model has been applied, the secondorder discretization in space has been used. In the unsteady state simulation, a time step T=2.143e-5 was selected. The chosen value corresponds to 1.29deg turning of the impeller per time step. For each time step, all maximal residuals are converged to 10e-5 after 20 internal iteration loops.

Boundary conditions:

The outlet pressure was imposed as the atmospheric pressure of 101325Pa.

The mass flow rate normal to the boundary was used as the inlet boundary condition. At the inlet, total temperature was imposed according to the value of experimental measurements. The interfaces between fluid domains are frozen rotors. The walls are adiabatic.

Mesh dependency:

Choosing the right mesh model for the computation plays an essential role in saving computational resources while ensuring accuracy. Selection of the finest mesh is done through mesh independence test by constructing various mesh models. In this study, we have made three grid models to investigate the influence of mesh resolution on the performance of the compressor. More details of these mesh sets are summarized in table 1. The simulation was performed at the speed N1 = -11000rpm, N2 =11000rpm and was compared to the experimental results [START_REF] Nguyen | Experimental study of the rotor-rotor aerodynamic interaction of a counter-rotating centrifugal compressor[END_REF]. Three performance curves corresponding to three mesh sets are shown in figure 3. It is easy to see that all models give nearly the same results however, mesh 2 and 3 produce predictive results with smaller deviation than mesh 1. The deviation between simulation results and experimental measurements is below 5%, which is entirely acceptable. Mesh 2 and 3 show nearly the same results in BEP and low flow regions, consequently, mesh 2 was selected to save resources and computation time. At NSP, it is easy to see the large differential pressure between the exit cone region and the inlet volute tongue. Especially, a local high-pressure region appears at the pressure surface of the downstream impeller. The cause of this phenomenon is that these blades face the backward pressure gradient from the exit cone. It is being developed inside the volute due to the decrease in compressor flow. If the mass flow of the compressor continues to decrease, a back and strong flow is generated. Consequently, the compressor falls into the surge phenomenon. In order to help the compressor to operate at a lower flow rate than NSP with the same pressure ratio, the speeds of the two impellers had to change. Specifically, the speed of the upstream impeller decreases and the speed of the downstream impeller increases intending to modify the inlet condition of each impeller. ESP is the working limit point of the compressor, at which the upstream impeller rotates in a similar direction as the downstream impeller (in co-rotating mode). In this way, the compressor can operate stably at very low flow rates while keeping the compression ratio unchanged. It can be noted that the pressure distribution at ESP is virtually identical to NSP. However, the local pressure area on the downstreamimpeller pressure surface is higher due to the impact of the fluid flowing out from the adjacent blade passage.

Figure 4

Pressure distribution on an equipotential surface at 0.5span of three operating points

Figure 5 shows the static pressure distribution on a pressure side (PS) and a suction side (SS) of the two impellers along the stream-wise direction from the leading edge to the trailing edge. It can be seen the pressure difference between the PS and SS of both impellers. This shows that the flow in the blade passage is homogeneous and the compressor works with the highest efficiency. However, there is a difference in the pressure distribution between the two impellers at NSP. The upstream impeller still has a clear distinction between PS and SS; meanwhile, the downstream impeller has a small pressure difference between these two sides, which means the turbulence appeared in the blade passage.

When the compressor operates at a lower flow rate with a co-rotating mode (ESP), it is clear that the upstream impeller has no pressure difference between PS and SS. It can be noted that the pressure at the trailing edge slightly decreases relative to the leading edge. This shows that the co-rotating effect changes the working condition slightly at the leading edge of the downstream-impeller and makes it better compatible with a low flow rate in case of dropped flow rate, and then limits the occurrence of the surge. The presence of turbulence within the blade passages at NSP and ESP rapidly reduces the compressor performance due to increased losses. The eddy regions increase entropy within the impellers. This increase can be seen clearly at ESP as shown in Figure 6. At BEP, the entropy distribution is uniform, which shows that the compressor operates at the highest efficiency and least loss. The uneven distribution of entropy within the downstream impeller of NSP and ESP due to eddies increases entropy rapidly inside the blade passage. The most increase of entropy can be observed inside the blade passage near the volute tongue of ESP, where the entropy value is tripled compared to the BEP. This shows that the compressor operating at this point suffers many losses, so its performance is low. This is completely consistent with the performance curve shown in Figure 1. Asymmetry effect: Due to the unique structure of twin-impeller compressors, the inducer has to use an inlet elbow so that the inlet becomes asymmetric. This also affects the compressor performance as well as the surge limit point. Figure 8 compares the flow structure on the inlet elbow cross-section of the three selected operating points. It is clear that the inducer asymmetry does not seem to have a significant effect on the inlet flow structure at BEP. However, the effect of asymmetry at NSP and ESP is clearly visible because of the decrease in mass flow. At these points, the downstream pressure gradient increase leads to make a reserved flow at the impeller tip. In addition, the change in pressure from the small to the large radius sides due to the asymmetry of the elbow combined with the reserved flow creates vortex regions with different sizes on both sides of the inducer. The size of the vortex increases as the flow decreases. It can develop about 50% of the area of a large radius at ESP. The asymmetry inlet causes the surge to appear earlier by increasing the incidence angle. The eddy zones decrease in size over time steps. A vortex is marked, for example, that appears in the blade passage as shown in Figure 9. This vortex size shrinks gradually over time steps and disappears after 60 time steps. However, the simulation results over 1s show that the appearance and disappearance of the vortex regions are repeated many times. This phenomenon shows that this is the limit of stability of the compressor at this rotation speed.

With co-rotating mode, twin-impeller compressors can operate at a lower flow rate than the limit flow in contra-rotating mode (NSP) but still maintain a good compression ratio. Figure 10 shows the streamline structure inside the compressor at ESP in 80 time steps with the rotational speed of the two impellers respectively N1 = 6240rpm and N2 = 12000rpm. It can be seen that the eddies within the blade passages change in size as the relative position between the blade rows changes. However, because the machine flow rate is low, these eddies do not disappear and eternally exist within the blade passages. In addition, some blade passages present a flow pattern quite uniform. This shows that the fluid flow is still circulating normally through these blade passages to maintain compressor stability. At BEP, the flow pattern and the pressure distribution within the impellers as well as in the volute are quite homogenous. This explains why the compressor has the highest performance at this point. However, the eddies can be observed at NSP. They are localized in some blade passage of the downstream impeller near the volute tongue. The eddies decrease in size in the adjacent blade passage towards the opposite rotational direction of the downstream-impeller. The blade passages are partly or completely blocked by these eddies and generate the local high pressure region on the blade surface. The same thing happens at ESP, where more eddies appear in blade passages in both impellers. However, some blade passage still maintains a uniform flow structure that allows fluid to pass through to keep the compressor from falling into a surge state. The presence of eddy zones within the impellers increases the local entropy causing an increase in losses. Therefore, the compressor efficiency at these points is quite low.

CONCLUSIONS

The unsteady simulation illustrates that the change of blade row position does not affect the flow pattern at BEP. Nevertheless, it greatly influences the flow structure at NSP and ESP. According to the relative position of the blade row, the decrease in size of the eddies zone is observed at NSP. In addition, these eddies always exist within impellers at ESP. At this point, the compressor operates stably at a very low flow rate thanks to the co-rotating effect.

Figure 1

 1 Figure 1 Experimental characteristics of twin-impeller (red solid line) compared to single-impeller centrifugal compressor (blue dash line) at the rotation speed of 11000rpm

Figure 2

 2 Figure 2 Mesh details of twin-impeller centrifugal compressor

3

 3 Simulation results different mesh size in comparison with experiment at the speed of N1=-11000rpm, N2=11000rpm: Pressure ratio (a) and polytropic efficiency (b) Flow analysis: Figure4shows the pressure distribution inside the compressor on an equipotential surface at 0.5span. At BEP, the pressure increases gradually from the leading edge to the trailing edge of each impeller and from the volute tongue to the exit cone region.

Figure 5

 5 Figure 5 Blade loading at 0.5span of three operating points

Figure 6

 6 Figure 6Relative velocity vector distribution an equipotential surface at 0.5span of three operating points

Figure 7

 7 Figure 7Entropy distribution an equipotential surface at 0.5span of three operating points

7

 7 Figure 7Flow structure at the compressor inlet at three operating points

Figure 8

 8 Figure 8 Various streamline pattern according to the timestep on a half span at BEP

  Numerical simulation studies have been conducted to further investigate the fluid flow characteristics inside the twin-impeller centrifugal compressor. Based on the experimental results, the simulation has been conducted in a steady and unsteady state. Two points in contra-rotating mode are included: BEP and NSP and one point in corotating mode has been chosen to analyze the flow structure inside the compressor. The results indicate that:

-10000/10000 -6240/10920

								In this paper,
	we introduce CFD results to analyze the flow
	structure inside the compressor at three special
	points: Best Efficiency Point (BEP), Near Surge
	Point (NSP), and Extended Stability Point (ESP).
	Pressure ratio ( s )	1.12 1.14 1.16 1.18 1.20	1.178 1.171 0.08kg/s Extended zone 0.206kg/s 6240/12000 ESP	NSP	BEP	single-impeller 1.141 1.158 twin-impellers
		1.10	0.0 36.2% 45.3% 0.1	70%	0.2	0.3 73.1%	0.4	0.5 0.543kg/s 0.6 0.648kg/s 0.7	0.8	30 40 50 60 70 80	Polytropic efficiency ( p %)
					Corrected mass flow rate (kg/s)

Table 1

 1 Details of mesh sets used for mesh sensitivity study

		Mesh 1	Mesh 2	Mesh 3
	Inlet pipe	74880	185760	308160
	Inlet elbow	97737	227858	366104
	impeller 1	309151	697922	1373753
	Impeller 2	635511	1273090	2139742
	Cavity	188911	342755	518865
	Volute	70711	155067	311061
	Outlet pipe	74880	101340	212220
	Total	1430541	2983792	5229905
	RESULTS AND DISCUSSION
	Steady state simulation: The steady-state method
	uses the moving reference frame technique applied

on impeller regions while the grid is not moving. In this technique, the Coriolis and centrifugal forces are added to the momentum equations so even though the mesh does not rotate, the impeller motion is still modeled. For the first step, a steady-state simulation has been performed to analyze the flow structure inside of twin-impeller compressor. Three particular points: BEP, NSP, ESP have been simulated with the working parameters based on experimental results and listed in Table

2

.


Michael Pereira

Florent Ravelet

Kamel Azzouz

Tarik Azzam

Hamid Oualli

Smaïne Kouidri

Farid Bakir

ICCHMT2021

Keywords: Axial flow fan, CFD, Leakage flow rate, air injection, hollow blade, rotating shroud

Axial flow fans are used in many fields in order to ensure the mass and heat transfer from air, chiefly in HVAC industry. A more proper understanding of the airflow behavior through the systems is necessary to manage and optimize the fan operation. Computational Fluid Dynamics (CFD) represent a real tool providing the ability to access flow structures in areas where measuring equipment cannot reach. Reducing the leakage flow rate, inherent in operation by synthetic-jet techniques improves performance. This paper presents the CFD results performed on a hollow blade fan developed by our team. The leakage flow is controlled by blowing air from 16 designated circular holes and arranged on the fan shroud. We discuss the results for two rotational speeds (1000 and 2000 rpm) and two injection rates (0.4 and 0.8). The numerical results consistent with the experimental show, for the low rotation speed and high injection ratio, significant gains in power (53%), torque (80%) and leakage flow rate (80%).

Nomenclature

relative position between the fan and the carter (m) 𝑥 ℎ𝑜𝑙𝑒𝑠 position of the injection holes on the casing (m)

Introduction:

The leakage flow rate developed in the operating set has shown a great influence on the turbomachines. This flow induced by the pressure difference either between the upper and lower surfaces of the blades, or between the upstream and downstream side of the device, is responsible for the energy losses and the generation of noise. It is in this context that the authors plan to analyze the mechanisms generated by such devices. Boudet et al. [START_REF] Boudet | Zonal large eddy simulation of a fan tip-clearance flow, with evidence of vortex wandering[END_REF] have numerically and experimentally investigated the leakage flow rate for an axial fan. They showed that the major contribution of sound emission is induced by the tip vortex. For a turbine, Fischer et al. [START_REF] Fischer | Investigation of the tip leakage flow at turbine rotor blades with squealer cavity[END_REF] were managed to characterize the structure of the tip vortex by using a modulable frequency Doppler Effect velocity meter with high temporary resolution. Pogorelov et al. [START_REF] Pogorelov | Effects of tip gap width on the flow field in an axial fan[END_REF] attempted to identify this structure for an axial fan. It shows that the reduction in the dimension of the tip clearance leads to the reduction in both the size of the tip vortex and the amplitude of the noise. Throughout an LES investigation, You et al. [START_REF] You | Effects of tip-gap size on the tip-leakage flow in a turbomachinery cascade[END_REF] emphasized and confirmed that the effect of this dimensions on noise generation and vibration. Lee et al. [START_REF] Lee | Aerodynamic performance of winglets covering the tip gap inlet in a turbine cascade[END_REF] discussed the influence of the height of the squealer rims for a turbine. A reduction of around 11.6% was obtained for the total pressure drop coefficient.

To reduce the leakage flow rate, various geometric solutions have been proposed. Wallis et al. [START_REF] Wallis | The control of shroud leakage flows to reduce aerodynamic losses in a low aspect ratio, shrouded axial flow turbine[END_REF] have dealt with the extraction of the work during the passage of the leakage flow through small vanes bladelets or turning device placed on the shell in the presence of radial barriers fixed on the casing. They managed to reduce the tangential component of the leakage flow. However, they highlighted the unsteadiness and complex structural effects of the flow at the tip clearance. Corsini et al. [START_REF] Corsini | Development of improved blade tip endplate concepts for low-noise operation in industrial fans[END_REF] studied the shape of the endplats placed at the end of the blades in order to change the orientation and the formation of the tip vortex. Aktürk et al [START_REF] Akturk | Axial flow fan tip leakage flow control using tip platform extensions[END_REF] improve the performance and reduction of leakage flow rate of an axial fan by means of the study of the five platform extensions of the profile on the lower surface.

Pardowitz et al. [START_REF] Pardowitz | Experimental identification of rotating instability of an axial fan with shrouded rotor[END_REF] employed a rotating shroud for clearance vorticity suppression. Longhouse [START_REF] Longhouse | Control of tip-vortex noise of axial flow fans by rotating shrouds[END_REF] was able to reduce noise and improve efficiency by using a rotating shroud attached to the blade tips. This device prevents the formation of the vortex tip. In addition, it is a solution envisaged in so far as we want to maintain a fairly large clearance between the fan and the housing. For electric motors, cooling is generated by a centrifugal rotor, Vad el al. [START_REF] Vad | Aerodynamic and aero-acoustic improvement of electric motor cooling equipment[END_REF] redesigned the reference rotor by adding a shroud. For the same cooling performance, it reduces fan noise and power consumption. In addition, some geometric solutions focus on optimizing labyrinthine joints. Schramm [START_REF] Weigl | Active stabilization of rotating stall and surge in a transonic single stage axial compressor[END_REF] presented an optimization method for the labyrinth seal in the aim of reducing the leakage flow. This article is dedicated to the study of the leakage rate for an axial cooling fan of an automobile engine. We study flow control by injection. Several authors have sought to improve the performance of turbomachines by means of this technique. By injection upstream of the rotor of a transonic compressor, Weigl et al. [START_REF] Rhee | Analysis of a jet controlled high-lift hydrofoil with a flap[END_REF] succeeded in stabilizing the rotary stall and surge with an expansion of the operating range. Even at the profile scale, Rhee et al. [START_REF] Eberlincm | Experimental investigation of the interaction of two flows on the axial fan hollow blades by flow visualization and hot-wire anemometry[END_REF] increased the lift of an injection hydrofoil near the trailing edge. Eberlinc et al. [START_REF] Eberlinc | Modification of axial fan flow by trailing edge self-induced blowing[END_REF][START_REF] Eberlinc | Numerical and experimental investigation of axial fan with trailing edge self-induced blowing[END_REF][START_REF] Neuhaus | Active control to improve the aerodynamic performance and reduce the tip clearance noise of axial turbomachines with steady air injection into the tip clearance gap[END_REF] managed to increase the coefficient of the total pressure by 6% of an axial fan composed of hollow vanes by injection near the level of the trailing edge at the end. The jet, which is caused from the hub by an internal flow line, allowed the control of the boundary layer by increasing the local velocity and reducing the effect of the adverse pressure gradient. Neuhaus et al [START_REF] Foss | An aerodynamic shroud for automotive cooling fans[END_REF] manage to reduce the leakage rate and improve performance with an injection rate of 0.8%. In addition, these improvements were noted for a pulsed injection synchronized with the rotation of the fan. They achieve with an injection rate of 1.5% to widen the operating range of the fan by 62% by pushing the stall point towards low flow rates. At the displaced point, the improvement in pressure is approximately 40%. The study by Morris and Foss [START_REF] Niu | Experimental and numerical investigations of tip injection on tip clearance flow in an axial turbine cascade[END_REF] was devoted to the automobile cooling fan with a large clearance dimension (2.5 cm). Performance improvements were obtained for large flow rates by injection air from fixed shroud to the tip clearance. Niu et al [START_REF] Wadia | Inner workings of shrouded and unshrouded transonic fan blades[END_REF] obtained a reduction in the leakage rate using the effect of injection from different configuration of a row of 10 equidistant holes, oriented 45 ° to the end face of a turbine blades. For shrouded fan, Buisson et al [START_REF] Sarraf | Experimental study of blade thickness effects on the overall and local performances of a controlled vortex designed axial flow fan[END_REF] study a new casing treatment, which consists on helicoidal grooving of casing. The obtained results show reduction both of 45% in leakage flow rate and 2.3% in static efficiency, and the increase of 0.4% in torque.

In this study, we investigate experimentally and numerically the effect of the active flow control by air injection in the tip clearance of axial flow cooling fan. This fan is obtained with the rotational molding process, which involve hollow shape for the whole fan (hub, blades and shroud ring). The main aim of this work is to use the hollow shape induced by this process in order to exploit it in the control of tip clearance flow by steady air injection through rotating shroud ring, which is composed of injection holes oriented in such a way to reduce both of leakage flow rate and of the torque. With specific drive system realized at the LIFSE laboratory of Arts et Metiers Institute of Technology and adequate CFD modeling, the obtained results show reduction in leakage flow and gain in the torque.

Experimental setup

Blade geometry

In this study, we use an axial-flow cooling hollow fan developed by the rotational molding process using polyethylene material (figure 1) [START_REF] Azzam | Experimental investigation of active control by steady air injection in the tip clearance gap of an axial fan[END_REF][START_REF] Azzam | Experimental investigation of an actively controlled automotive cooling fan using steady air injection in the leakage gap[END_REF], where the preliminary researches have been developed at Arts & Metiers. This fan was generated following a controlled vortex designed axial-flow [START_REF] Sarraf | Experimental study of blade thickness effects on the overall and local performances of a Controlled Vortex Designed axial-flow fan[END_REF]. It has six blades, tip radius Rmax=179mm, hub-to-tip radius ratio (Rint/Rmax) equal to 0.337. A hollow circular shroud ring of 31mm length and 9mm thickness was added to ensure the increase of the fan solidity. The leakage gap is about 4mm. Figure 2 present the position of the injection holes at the middle of the shroud ring and the position between the fan and the carter (xfan=0) used in this study. these positions was investigated and their impact on the fan characteristics are not presented in this paper. The casing has a thick 46 mm. For injection operating condition, we use the injection rate 𝜉, defined as : 𝜉 = 𝑞 𝑖𝑛𝑗 𝑞 𝑚𝑎𝑥 ⁄ , where 𝑞 𝑖𝑛𝑗 is the injection rate delivered by the drive system and 𝑞 𝑚𝑎𝑥 = 1000 𝑙/𝑚𝑖𝑛 is the maximum injection rate for the fan resistance to the internal flow. Test bench and drive system

The drive system and the test bench was reported in [START_REF] Azzam | Experimental investigation of active control by steady air injection in the tip clearance gap of an axial fan[END_REF][START_REF] Azzam | Experimental investigation of an actively controlled automotive cooling fan using steady air injection in the leakage gap[END_REF]. In brief, figure 3 present the test bench used to determine the global performance which is built at the LIFSE laboratory of Arts et Metiers Institute of Technology and developed according to the ISO-5801 standard. The airflow rate is set and measured according to ISO-5167 norm. The elevation pressures are measured with an absolute precision of 0.1 Pa. For the torque, the uncertainty of the measurements is 0.1% of the full scale equal to 5 N.m.

Initially, in order to investigate the behavior of the fan over a wide range of operating flow conditions, ten diaphragm diameters are tested (Table 1). The measurements taken show that for a diameter 𝛷 ≥ 238 𝑚𝑚 the aeraulic power exhibits notable improvements in proportion to the diameters of the diaphragm.

Torque measurement:

The experimental set-up carried out herein, the different components used for the mechanical transmission such as the motor shaft, coupling, torque meter, belt, pulley, bearing, rotary joint generate an elementary resistive torque, hence it is difficult to estimate them separately. Our goal is to characterize the operation of the fan alone for the different control configurations to get the static efficiency.

For a given speed of rotation, this amounts to estimating its resistive torque. To do this, we proceeded first to determine the two torques, at no load 𝐶 0 (fan removed) and that in presence of fan denoted by 𝐶.

The net torque will then be given as follow:

𝐶 𝑛𝑒𝑡 = 𝐶 -𝐶 0
During the tests, we noticed that the noload torque 𝐶 0 depends on the engine speed and the injection rate. The figure 4 below shows that for 1500 and 2000 rpm, the couple 𝐶 0 stabilizes from an injection rate in the order of (𝜉 = 0.4). It can be said that there is a saturation of the internal friction generated in the two rotating parts of the mechanical circuit (including the rotary joint and the hollow shaft). However, this phenomenon is not yet achieved for a rotation speed of 1000 rpm.

CFD modeling and grid generation

The research carried out in numerical modeling has shown that it is difficult to determine all the structures generated in the flow, because it requires time and heavy computational resources. In the field of rotary flows, to simplify the problem, the periodicity condition is often used in order to carry out a detailed study on the area of interest.

On the other hand, with reference to our experimental study, the periodicity studying a single blade is not applicable due to the number of holes used [START_REF] Eberlinc | Numerical and experimental investigation of axial fan with trailing edge self-induced blowing[END_REF]. However, in order to compare the experimental results obtained with those of the CFD, it was judged that it is preferable to study the complete geometry of the test bench. In order to estimate the size of the grid of the complete domain, the geometric parameters will be deduced from the study of the sensitivity of the mesh carried out for the 1/6 of the complete domain considered as cylindrical shape. The study of the mesh is not presented in this work.

The generation of structured mesh presents a particular difficulty in the areas close to the settling chamber, the hollow area of the fan and especially at the level of the injection holes. For this, we opted for a polyhedral mesh recognized by these advantages. The refinement criteria were carried out with appropriate control volumes size (boundary layer, wake, pressure gradients...). Figure 6 presents the complete numerical domain generated in polyhedral mesh.

In our work, we use ANSYS-Fluent code with the finite volume discretization. Our approach is based on the study of the steady viscous incompressible flow with k -ω SST turbulent model. The Moving Reference Frame (MRF) or Frame motion method is used to model the fan motion.

For velocity-pressure coupling, SIMPLE algorithm is used with MUSCL Third order for the momentum equation and the second order for the rest of equations. For boundary conditions, both of inlet and outlet are maintained at atmospheric pressure. For the controlled flow configuration, the air injection is defined by mass flow inlet condition inside the hub as shown in figure 7.

RESULTS

The main findings are presented in term of gain in fan power, torque and leakage flow for the following operation conditions: 16 injection holes, two rotation speeds rpm=1000 rpm and 2000 rpm and two injections rate 𝜉 = 0.4 and 0.8.

Aeraulic power:

We define the power gain as follow: 𝐺𝑎𝑖𝑛 = (𝑃 -𝑃 0 ) 𝑃 0 ⁄ , where 𝑃 = 𝑞 𝑣 ∆𝑃 is the delivered power for the controle configuration and 𝑃 0 is the power delivered for 𝑞 𝑖𝑛𝑗 = 0. We discussed the influence of the diaphragm diameter, rotationnal speed and the number of the injection holes (16 and 32) where the active control improves the delivered power nearly up to 40% [START_REF] Azzam | Experimental investigation of active control by steady air injection in the tip clearance gap of an axial fan[END_REF][START_REF] Azzam | Experimental investigation of an actively controlled automotive cooling fan using steady air injection in the leakage gap[END_REF]. Other measurements carried out for a series of fans have shown that the optimum gain in fan power varies between 30% and 53%. This wide range of variation results mainly from the operating conditions of the rotational molding and from the manufacturing defects of the fan. The figure 5 shows the maximum gain (53%) obtained for diameter diaphragm of 𝛷 = 375 𝑚𝑚, rotation speed of 1000 rpm and 16 injection holes. Figure 8 shows the evolution of the torque developed by the fan for numerical and experimental cases. The values obtained are practically low for the two rotational speeds and seem independent of the diaphragm diameter 𝛷. However, with a high speed of rotation, these low values have a significant influence on the motive power and therefore the static efficiency.

From the obtained results for the experimental study it is possible to conclude that for a control by 16 holes a maximum reduction of the torque of about 19% is reached for the speed conditions of 1000 rpm, of the diameter 𝛷 = 300 mm and of the injection rate 𝜉 = 0.8. The explanation is that the fan is in a rotating sprinkler configuration. The torque becomes important for a high speed of rotation (2000 rpm). In the operating tip clearance, friction remains predominant because the contribution of the blowing in terms of reducing the resistive torque remains minimal.

In the numerical simulation, the maximum torque reductions are estimated at :  80% for (1000 rpm, 𝜉 = 0.8 and independently of the diaphragm diameter).

 8% for (2000 rpm, 𝛷 = 300 mm and

𝜉 = 0.8).
It is noted that the gain in torque obtained experimentally (19%) is relatively low compared to the value of the gain resulting from the simulation (80%). This could be due to several experimental factors including:

-Sensitivity of the torque meter used (HBM 5 N.m). The measurement range seems important relative to the values that have been measured which are quite small. It is desirable to equip the experimental setup with a more suitable torque meter. In addition, the measurements are not direct due to the size constraint of the assembly. The possibility of positioning the torque meter upstream of the fan (inside the box) has been abandoned due to disturbances induced in the upstream suction flow. In the event that the assembly is carried out downstream of the fan, the torque meter must be equipped with a hollow shaft (to ensure the control of the main flow) with sealed couplings to remedy leaks in the injection flow. -Difficulty in determining the elementary torques of assembly components (belt transmission, coupling, rotating joint, etc.). We considered the net torque approach (without and with fan) with the hypothesis that with or without control, the elementary torques remains invariable.

Leakage flow :

The reduction of the leakage flow with evaluation of its influence on the different fan powers constitutes one of the primary objectives of this study [START_REF] Azzam | Experimental investigation of an actively controlled automotive cooling fan using steady air injection in the leakage gap[END_REF]. From this perspective, numerical simulation provides access to the evolution of the flow in areas with experimental measurement difficulties. The leakage rate generated in a limited space of 4 mm is a typical illustrative example, where it takes sources from air deviation at the exit blade or the aspiration from the stagnation ambient air. In our work, this flow is calculated at 25% at the exit surface of the leakage flow as shown in figure 9. In order to estimate the inherent variation of this flow relative to the nominal case, we define the gain in leakage flow as follows:

𝐸 𝜏 (%) = 100 .

(𝑚̇𝑔 𝑎𝑝_0 -𝑚̇𝑔 𝑎𝑝 ) 𝑚̇𝑔 𝑎𝑝_0 Where 𝑚̇𝑔 𝑎𝑝_0 , is the leakage flow rate calculated for the nominal case and 𝑚̇𝑔 𝑎𝑝 for the controlled case. From the two figure 10, the results are presented as follows:

 For the speed of 2000 rpm and an injection rate of 𝜉 = 0.4, a specific reduction of about 20% of the leakage flow.  For the rest of the curves relating to the cases checked, a reduction between 50% and 80% of the leakage rate is achieved. The maximum reduction is obtained for low rotation speed (1000 rpm) and high injection rate 𝜉 = 0.8

Conclusion

An automative cooling fan was built with rotational molding process which induces a hollow shape for the whole fan. This latter is used to drive air injection from hub to the tip clearance through a shroud ring to control the leakage flow, which is considered a source of energy dissipation. The internal flow generated by a specific drive system exits at the fan periphery by 16 holes. Numerical and experimental studies were carried out, especially in this study, for the two rotational speeds 1000 rpm and 2000 rpm, and two injections rate 𝜉 = 0.4 and 0.8.

In experiment, after a series of tests on rotomolded fans, the obtained results

show that the maximum gain in fan power is about 53%. The variation of this maximum is related to the operating conditions of the rotational molding process and its manufacturing defects.

For both studies, CFD and experiment, the control by air injection leads to an improvement in terms of reducing of leakage flow rate and fan torque.

With CFD, we reach reduction about 80% for leakage flow rate and torque at low rotation speed 1000 rpm and high injection rate 𝜉 = 0.8. However, for the experimental, the gain in torque reduction is about 19% which is relatively low compared to the numerical result.

As perspectives, the authors plan to consider the effect of the rotational molding process parameters to further improve the gain in fan power. Also, try to estimate the gain in torque especially in the presence of the internal flow with the remaining parts of the drive system.

Figure 1 :

 1 Figure 1: Hollow fan obtained with rotational molding process,

Figure 2 :

 2 Figure 2: on the left, position of the injection holes on the shroud ring, on the right, Position of the fan in the carter

Figure 3 :

 3 Figure 3: Experimental setup : (a) the fan drive system, (b) ISO-5801 test bench (dimensions 1.3mx1.3mx1.8 m).

Figure 4 :

 4 Figure 4: No-load torque variation 𝐂 𝟎 : () 1000 rpm, (•) 1500 rpm, (▲) 2000 rpm.

Figure 6 :Figure 7 :

 67 Figure 6: Grid generation for the test bench ISO 5801

Figure 5 :

 5 Figure 5: Experimental results The power gain added by the control for : diaphragm diameter Φ = 375 mm, rotation speed 1000 rpm, +: results for 16 injection holes. o: results for 32 injection holes.

Figure 8 :

 8 Figure 8: Evolution of the fan torque: (a) 1000 rpm et (b) 2000 rpm. Experimental results () baseline, (•) 𝝃 = 𝟎. 𝟒, (▲) 𝝃 = 𝟎. 𝟖, CFD results () with control, () 𝝃 = 𝟎. 𝟒, (∆) 𝝃 = 𝟎. 𝟖,

Figure 9 :

 9 Figure 9: leakage flow, evaluation and these sources

Figure 10 :

 10 Figure 10: Evolution of the gain in leakage flow by simulation (16 injection holes): 1000 rpm : () 𝝃 = 𝟎. 𝟒, () 𝝃 = 𝟎. 𝟖, 2000 rpm : () 𝝃 = 𝟎. 𝟒, () 𝝃 = 𝟎. 𝟖, It can be seen from figure 11 characterizing the nominal case, that the leakage flow behavior at tip clearance as well as both of upstream and downstream of the fan, is with high complexity including intense zones of swirling motion. Whereas, when the flow control is imparted to the fan (figure 12) at the flow conditions 𝜉 = 0.8, rotation speed 2000 rpm and diaphragm diameter Φ = 375 mm, important phenomenon is observed at the tip clearance between the casing and the shroud ring at the injection zone. It consists of two dead counterrotating air regions leading to formation of two eddies besides the injection stream. Resulting in a blockage of the ambient air aspiration toward the fan portside induced by the pressure drop (figure 9).

Figure 11 :Figure 12 :

 1112 Figure 11: Flow structure near the leakage gap, rotation speed 2000 rpm, diaphragm diameter 𝚽 = 𝟑𝟕𝟓 𝐦𝐦,

Table 1 : Diaphragm's diameters tested.

 1

	𝛷 (mm) 77 151 169 190 220 238 267 300 336 375