Carlos Guillamon

Romain Janodet

Léa Voivenel

Renaud Mercier

Vincent Moureau

Carlos Guillamon -

Romain Janodet -Léa

Voivenel -Renaud Mercier -

A novel methodology to simulate fuel injection in multipoint systems -Application to liquid jet in crossflow

Keywords: Multi-phase flows, Atomization, Lagrangian simulations, Jet-in-crossflow

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Simulations of aeronautical combustion chambers require an accurate description of the fuel liquid phase, as the injection and atomization processes have a strong influence on the flame. Nevertheless, computations comprising all the physical processes from injection to combustion cannot be achieved with one numerical formalism due to their different nature. In particular, modeling fuel injection needs special care due to the multi-scale nature of atomization. Approaches aiming at resolving primary atomization, such as diffuse or sharp interface methods, can accurately resolve the liquid-gas interface but become too expensive when many small droplets are present and cannot be used in reactive simulations. Other approaches, such as lagrangian methods, can be used for performing reactive computations at the expense of neglecting atomization. Consequently, they require a proper modeling of injection, which is often circumvented by injecting experimental distributions. In order to improve the modeling of fuel injection in multipoint systems, we have developed a new methodology to build injectors for lagrangian simulations. These injectors learn the spray from resolved atomization simulations and use it to inject lagrangian droplets in combustion simulations. The strategy is first developed on a non-reacting liquid jet-in-crossflow. The blockage effect from the liquid jet to the gas is characterized in the resolved simulations and modeled with the actuator line method (ALM) [START_REF] Sørensen | Numerical Modeling of Wind Turbine Wakes[END_REF]. A secondary atomization model is embedded in the lagrangian simulations. The models are then applied to the same jet in crossflow configuration and compared with existing experimental data. Relative influence of the modeling bricks (dense core potential effect, droplet injection assumptions) are also discussed.

Numerical setup and operating condition

The test case chosen to simulate fuel injection is a high-pressure kerosene liquid jet in crossflow experiment tested in [START_REF] Becker | Breakup and atomization of a kerosene jet in crossflow at elevated pressure[END_REF]. It is chosen for its application in multipoint injectors for aeronautical combustion chambers. The numerical domain replicating the test bench is shown in Fig. 1. It consists of a plenum where pressurized air (the crossflow) is injected through a gaseous inlet. Kerosene is injected perpendicularly to the crossflow through a tapered nozzle located at the bottom of the plenum. Fuel is injected through the liquid inlet specified in Fig. 1b following a Poiseuille profile. For crossflow injection, it is mentioned in [START_REF] Becker | Breakup and atomization of a kerosene jet in crossflow at elevated pressure[END_REF] that the boundary layer thickness at the lip of the injector is 5 mm. As the numerical domain is reduced with respect to the experimental bench, a velocity profile with a boundary layer following a 1/7 th power law is prescribed. The thickness of this boundary layer is calculated considering that the gas evolves from the inlet to the injector as a turbulent boundary layer along a flat plate [START_REF] White | Viscous Fluid Flow[END_REF]. Outside the boundary layer, the velocity follows a parabolic profile.

Noname manuscript No.

(will be inserted by the editor)

C2 -Restricted

The operating point of the jet in crossflow is governed by two main dimensionless numbers: the momentum ratio q and the gaseous Weber number Weg. The condition simulated is the baseline case reported in [START_REF] Becker | Breakup and atomization of a kerosene jet in crossflow at elevated pressure[END_REF], defined by q=6 and Weg =1470.

Resolved simulations of jet in crossflow atomization

Accurate Conservative Level-Set methodology

In order to solve for primary atomization, the interface capturing method known as Accurate Conservative Level-Set (ACLS) method has been used [START_REF] Desjardins | An accurate conservative level set/ghost fluid method for simulating turbulent atomization[END_REF]. This methodology distinguishes between phases by defining a level-set function ψ which is a hyperbolic tangent profile bounded between 0 and 1. The interface is denoted by the iso-level ψ = 0.5, lower values denote gas phase and larger ones indicate liquid phase. The pressure jump at the interface due to surface tension is accounted for with the Ghost-Fluid Method. Furthermore, in order to better resolve the interface dynamics and save computational resources, this method is complemented with an Adaptive Mesh Refinement (AMR) strategy to refine the mesh locally at the liquid-gas interface by specifying the element size Δxmin [START_REF] Leparoux | Primary atomization simulation applied to a jet in crossflow aeronautical injector with dynamic mesh adaptation[END_REF]. More details regarding this methodology can be found in [START_REF] Janodet | A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids[END_REF].

Results

Two mesh resolutions were simulated for the operating point previously specified: Δxmin = 20 µm (coarse mesh) and 10 µm (fine mesh). They can be specified with respect to the injector diameter as dinj/Δxmin = 22.5 and 45 respectively. Fig. 2a shows the trajectories obtained for both cases compared with an experimental correlation provided by [START_REF] Becker | Breakup and atomization of a kerosene jet in crossflow at elevated pressure[END_REF]. The trajectories correspond to the windward side of the jet and have been timeaveraged. Both numerical trajectories show a good agreement with the experimental one. The finest resolution trajectory is closer to experiments, while the coarsest resolution is slightly underestimated. Fig. 2b shows an instantaneous snapshot of the developed jet for the coarse mesh. The jet shows a good behavior: it leaves the nozzle and bends towards the crossflow direction as a consequence of its interaction with the air. Instabilities leading to primary atomization are seen in the windward side of the main jet column (column breakup mechanism), also known as dense core. Consequently, the jet will break into big blobs and ligaments that will keep on atomizing further downstream. At the same time, droplets are stripped-off the dense core closer to the injection nozzle due to the strong shear force (surface breakup mechanism).

Flowchart and submodels

The developed models are represented by the flowchart of Fig. 3. Resolved atomization simulations (see Section 3) are performed, spray characteristics (droplets sizes, flow rates, centroid location and velocities) are extracted and processed by the lagrangian injectors learning block to create the injectors and initialize lagrangian simulations. The injectors learning part performs the following steps:

• Spray sampling. Droplets are tracked by their centroid and accumulated in planes perpendicular to the crossflow direction (see Fig. 2b) • Spatial discretization. The accumulated spray is discretized into elements for an in-plane characterization (Fig 2c). Each element will compose a separate spray with different statistics of distributions (diameters, velocity) and scalars (mean velocities, fluxes, mean diameters). • Spray convergence is checked in order to know if enough droplets have been accumulated to build the features statistics. For that purpose, droplets size distribution is compared at several time instants.

Convergence is achieved when it does not change as more droplets are accumulated.

Once spray features are converged, lagrangian injectors can be built. As only one operating point has been simulated here, the learning process consists in a simple linear interpolation of the discrete statistics obtained at the same sampling location. An example of Sauter Mean Diameter (SMD), volume flux and mean axial velocity maps obtained for a sampling plane located at x = 10 mm (see Fig. 2b) which can be used for injection is shown in Fig. 4. The developed models are complemented with two extra submodels (top part of Fig. 3):

• Dense core learning for liquid jet/air interaction to replicate the blockage effect of the dense core in lagrangian simulations, where it is not taken into account a priori. ALM [START_REF] Sørensen | Numerical Modeling of Wind Turbine Wakes[END_REF] is used to substitute it by a body force applied to the gas that accounts for its presence. This body force, named actuator, is learnt from resolved simulations. • Secondary atomization models are plugged into the lagrangian simulations to account for further breakup of spherical droplets.

Conclusions

A new strategy to build lagrangian injectors has been proposed. A jet in crossflow test case has been simulated and processed to build the models. Injectors have been developed by studying the resulting spray from resolved atomization simulations. The models are complemented with refined physics such as secondary atomization models and liquid-air interaction. Finally, the obtained injectors have been tested in the same test case, showing a good prediction of the circular spray shape and the flux values. However, the maximum vertical flux location and the spray bounds are overestimated. Improvements will be done by a better determination of the injection velocities and by a more accurate modeling of the dense core blockage effect, which is thought to currently underestimate the force imposed by the actuator on the air flow. Further research includes a more accurate spatial discretization of the injectors by quad-trees [START_REF] Dezeeuw | An adaptively Refined Cartesian Mesh Solver for the Euler Equations[END_REF] and the implementation of subgrid dispersion models [START_REF] Gosman | Aspects of computer simulation of liquid-fueled combustors[END_REF]. In the long term, the models will be fed with more operating conditions and finally applied to an academic multi-staged fuel injector more representative of aeronautical injection systems [10].

Fig. 1

 1 Fig. 1 Numerical domain and boundary conditions of the experimental facility tested by [2]. a) Complete domain. b) Detailed view of injection nozzle. All dimensions are in mm

4. 2 .Fig. 3 Fig. 4

 234 Fig. 3 Flowchart of proposed models for lagrangian injection

Acknowledgments

This project has received funding from the European Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 765998 in the project ANNULIGhT. Computer resources have been provided by GENCI, France, under the allocation A0092B11072. The authors would also like to acknowledge Thierry Poinsot from CERFACS, France, for fruitful discussions on the methodology.


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

Brahim Abed

Amelie Danlos

Florent Ravelet

Richard Paridaens

Michael Deligant

Sofiane Khelladi

Farid Bakir

Cheikh Brahim
email: abedcheikhbrahim@gmail.com

Experimental study of a novel centrifugal compressor with two successive and independent rotors

Keywords: ], Z Number of blade,[-], γ Specific heat rate [-]

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

1 Introduction A counter-rotating system comprises two successive rotors designed to follow opposite directions of rotation. This configuration has been used in almost families of turbo machines including for axial, centrifugal or mixed type machines pump [START_REF] Fukutomi | Performance and internal flow of sirocco fan using contra-rotating rotors[END_REF][START_REF] Tosin | Exiperimental and numerical investigation of a counterrotating mixed-flow single stage pump[END_REF][START_REF] Sharma | A study of some factors affecting the performance of a contra-rotating axial compressor stage[END_REF][START_REF] Furukawa | Performance test and flow measurement of contrarotating axial flow pump[END_REF][START_REF] Chen | A study of speed ratio affecting the performance of a contra-rotating axial compressor[END_REF][START_REF] Shi | Experimental investigation of a counter-rotating compressor with boundary layer suction[END_REF][START_REF] Shigemitsu | Performance and internal flow of contra-rotating small-sized cooling fan[END_REF][START_REF] Luo | Design of 1 + 1 / 2 counter rotating centrifugal turbine and performance comparison with two-stage centrifugal turbine[END_REF][START_REF] Mao | Investigation of the casing groove location effect for a large tip clearance in a counter-rotating axial flow compressor[END_REF][START_REF] Sun | Design and performance analysis of a two-stage transonic low-reaction counter-rotating aspirated fan/compressor with inlet counter-swirl[END_REF]. The major advantage of the application of this system is the increase in power density. Many publications deal with using counter-rotating on turbomachine have been published including various patents [START_REF] Price | Counterrotating supercharger[END_REF][START_REF] Florjancic | Kreiselmaschine mit gegenlufigen laufrdern und verwendung der kreiselmaschine[END_REF], however, its application on a centrifugal compressors is not available in the open literature. In 2018, Dujour et al. [START_REF] Dejour | Assessment of a novel non-axial counter-rotating compressor concept for aero-engines[END_REF] assessed by numerical simulations a non-axial counter-rotating configuration which cannot be described as a "counterrotating centrifugal compressor" because the outlet flow is in the axial direction. This configuration gives a significant increase in pressure with almost no change in efficiency. The additional freedom offered by choosing of the two speeds of the upstream and downstream rotors allow further control and improve these counter-rotating machines performance over the extended operating range. The speed ratio is defined by the ratio of the upstream-rotor speed (N UR ) to the downstream-rotor speed (N DR ) was used to study this type of turbomachine.

θ = N UR N DR (1)
Sharma et al. [START_REF] Sharma | A study of some factors affecting the performance of a contra-rotating axial compressor stage[END_REF] studied many parameters that affect the performance of counter-rotating axial compressors, including speed ratios. Their results showed that if the downstreamrotor rotates 50% faster than the upstream-rotor, the rotation stall on the upstream-rotor is suppressed. In 2007, Furukawa et al. [START_REF] Furukawa | Performance test and flow measurement of contrarotating axial flow pump[END_REF] conducted an experimental study of counter-rotating axial pumps. They found that the maximum efficiency could be archived at different mass flow rates when the speed ratio changed and the speed of the upstream-rotor is constant. The authors concluded that using the counter rotating component could give a wider operating range and a higher efficiency according to the speed ratio. To emphasize the effect of the speed ratio on the efficiency of the axial counterrotating compressor, the work of Chen et al. [START_REF] Chen | A study of speed ratio affecting the performance of a contra-rotating axial compressor[END_REF] pointed out that with a speed ratio of 1.143, the compressor can achieve the highest efficiency with a slight reduction of the total pressure ratio and the working margin. They concluded that if the speed ratio is inferior to one, a stable range of the compressor becomes smaller and decreases when the speed ratio decreases. In 2012, the study of Limin et al. [START_REF] Limin | The Effect of Speed Ratio on the First Rotating Stall Stage in Contra-Rotating Compressor[END_REF] presented that with a speed ratio higher than 0.9, the first stall stage appears in the downstream-rotor with a reduction of mass flow rate. In contrast, when the downstream-rotor rotates slower than the upstream-rotor, the tip leakage flow of the downstream-rotor decreases significantly with the decrease of the speed ratio. The stall phenomenon firstly occurs in the upstream-rotor. The study of Mistry et al. [START_REF] Mistry | Effect of variation in axial spacing and rotor speed combinations on the performance of a high aspect ratio contra-rotating axial fan stage[END_REF] on an axial counter-rotating fan showed that the speed ratio plays an important role in terms of overall pressure rise. When the downstream-rotor rotates faster than the first one, the suction effect is generated stronger. This improves the fan performance. Similarly, the study conducted by Nouri et al. [START_REF] Nouri | Experimental Study of the Instationary Flow Between Two Ducted Counter-Rotating Rotors[END_REF] showed that the low-speed ratios give lower performances.

Increasing the speed ratio within the range of [0.8 1.2] results in a slight increase in performance. The efficiency can reach a maximum value if it is in a range of [1.05 1.15]. The work of Subbarao et al. [START_REF] Subbarao | Effect of speed ratio on the performance and flow field of a counter rotating turbine[END_REF] on the speed ratio of a counter-rotating turbine shows that the overall efficiency is improved with a speed ratio greater than one. In addition, they identified that the losses vary with the speed ratio and that performance can be improved by adjusting the rotation speed of the rotors. In 2015, the experimental study of the counter-rotating mixed-flow pump was conducted by Tosin et al. [START_REF] Tosin | Exiperimental and numerical investigation of a counterrotating mixed-flow single stage pump[END_REF] showed that the speed ratio has a powerful effect on the modification of entire pump characteristics. Their study focuses on the improvement of the head and on the optimization of the efficiency by changing the speed ratio.

Ԧ 𝐶 𝑟1 𝑪 𝒓𝟒 𝑪 𝒓𝟑 𝑾 𝟏 𝑾 𝟐 𝑾 𝟐 Ԧ 𝐶 3 𝑊 3 𝑾 𝟒 𝑼 𝟒 𝑪 𝟒  3  2  4  1  2  1 2
Experimental results showed that the head is changed from 12 to 26 m when the rotor has a higher rotation speed. The efficiency of the pump is almost constant at 80%. They also emphasize that the head rise is significantly improved by increasing the speed of the downstream-rotor while reducing the speed of the upstream-rotor. In this paper we present, for the first time in the literature, a design method for the two rotors of a CRCC. The experimental results obtained on a designed and produced machine in the laboratory are analyzed. This compressor confirms its superiority in power density and efficiency values over a wide operating range. A comparison with the available experimental characteristics of another conventional centrifugal compressor of the same size is provided in order to illustrate the superiority of CRCC.

2 Design of CRCC rotors 2.1 Velocity triangles of CRCC The first step in the design method for CRCC is the presentation of the velocity triangles which are shown in figure 1. Apply the Euler equation for this case to determine the enthalpy of each rotor as well as the total enthalpy of the compressor as following relations:

∆h 1 = U 2 C u2 -U 1 C u1 (2)
∆h 2 = U 4 C u4 -U 3 C u3 (3)
Because of the counter-rotating effect, the component C u3 is negative and the upstream-rotor is considered no prewhirl (C u1 = 0). Consequently, the total enthalpy of CRCC is determined as:

∆h total = U 4 C u4 +U 3 C u3 +U 2 C u2 (4)
Obviously, the total enthalpy of CRCC is consistently higher than that of SRCC because two components U 3 C u3 and U 2 C u2 were added. As a result, CRCC configuration gives more pressure rise.

However, the main disadvantage of CRCC compared to SRCC is the relative velocity at the leading edge of the downstream-rotor. Indeed, this velocity increase dramatically by the counter-rotating effect as described in equation 5. The increase of this velocity can induce the choke of CRCC, and it should be paid attention in the design process considering the desired choke margin.

W u3 = U 3 +C u2 , W 3 = C m3 2 +W u3 2 (5)
The designer should pay attention to this problem in CRCC design step to avoid the stage chocking and having an acceptable chock margin.

Design method for CRCC

In this study, the meridional shape of CRCC is kept the same as that of SRCC with the same volute for a fair comparison. Also, the leading and trailing edges of CRCC are The key to designing CRCC when its leading and trailing edges are fixed is to determine the position of the interface between the rotors, the trailing edge of the upstreamrotor and the leading edge of the downstream-rotor. To design CRCC, the single rotor of SRCC is divided into two separated rotors (upstream-rotor and downstream-rotor). The position of the interface between upstream and downstreamrotor is determined by the meridional Length Ratio (LR) which is defined by the following relation:

LR = L UR L m (6)
This parameter indirectly specifies the amount of the specific head that each rotor should deliver according to the total head offered by CRCC. Once LR is fixed, the upstream and downstream rotors can be calculated taking into account that the upstream-rotor inlet, the downstream-rotor outlet, and their meridional shape is already known. The downstream-rotor is directly determined after calculating the upstream-rotor by considering zero-incidence at the downstream-rotor leading edge by using equation 5.

For the design of the upstream-rotor, the iterative method of Aungier [START_REF] Aungier | Centrifugal compressors: a strategy for aerodynamic design and analysis[END_REF] is applied and coupled with the performance prediction method utilizing a combination of loss models. This method uses an empiric prediction of the Cordier line for optimum machines as a function of flow coefficient to predict the total head and calculate iteratively the blade angle and blade number based on a criterion on the global blade loading. The prediction of the Cordier optimal line is quite accurate compared to another empiric method as shown by Casey et al. [START_REF] Casey | The cordier line for mixed flow compressors[END_REF]. Pakle et al. [START_REF] Pakle | Design of a highperformance centrifugal compressor with new surge margin improvement technique for high speed turbomachinery[END_REF] have successfully implemented this method in order to design a highperformance centrifugal compressor. This method was also coupled with optimization techniques and used to optimize turbochargers as shown in Ref. [START_REF] Bourabia | Aerodynamic prelim-inary design optimization of a centrifugal compressor turbocharger based on a one-dimensional mean-line model[END_REF]. Table 2 and3 show a validation of the design code against two known existing single rotor stages. Figure 3 shows a validation of the loss model collection used in this study against experimental data of an open-source conventional centrifugal compressor and compared with the Oh's model [START_REF] Oh | An optimum set of loss models for performance prediction of centrifugal compressors[END_REF]. Thereby, the iterative design method is implemented for the upstream-rotor as:

φ = ṁ πρ t1 r
I = ∆h U 2 2 = 0.68 - φ 0.37 3 + 0.002 φ (8)
The parasitic losses are given by:

I par = 0.002 φ (9)
The internal polytropic efficiency of the rotor is given by:

η p = 0.95 - 0.0005 φ (10)
Absolute flow angle at trailing edge is determined as:

tan(α 2 ) = 1 0.26 + 3φ (11)
Assuming zero pre-swril at the inlet of upstream-rotor, the tangential and meridional components of absolute velocity can be calculated respectively as:

C u2 = U 2 (I -I par ) (12)
C m2 = C u2 tan(α 2 ) (13)
The outlet total and static temperatures are calculated as:

T t2 = T t1 + ∆h C p (14)
T 2 = T t2 - C 2 2 2C p (15)
The outlet total and static pressure are calculated as:

P t2 = P t1 1 + η p (I -I par )U 2 2 C p T t1 γ γ-1 (16)
P 2 = P t2 T 2 T t2 γ γ-1 (17) ρ 2 = P 2 RT 2 (18)
Blade loading and blockage factor at the outlet of the rotor are used to determine in an iterative manner, the number of blades and corresponding outlet blade angles:

λ = 1 1 -B 2 ( 19
)
where B 2 is a blockage factor of the flow area at the rotor tip. λ is calculated as:

λ = K λ + 0.00175 φ 2 + 0.0015 φ -0.22 ln(φ) (20)
The factor K λ depends on several parameters. These include not only the blade angle β b and passage area A at both inlet and outlet, but also the passage width b 2 at the outlet and the blade mean camber line length L UR . L UR and b 2 make the calculation procedure somewhat difficult since the blade camber line length and blade number Z UR are unknown until the rotor geometry is determined:

K λ = 1 + 0.3 + b 2 L b,UR 2 b 2 A 2 2 cos β b2 2 L b,UR A 1 2 cos β b1 2 (21) b 2 = (1 - Z UR t b 2π cos β b2 r 2 )b 2,SRCC (22)
L B = L axUR 0 m(z) cos β b (z) dz (23)
The blade angles distribution are implemented by using the following equations:

β bs = β b1s + (β b2 -β b1s )(3ζ 2 -2ζ 3 ) (24)
Copyright c by ASME

β bh = β b1h + Aζ + Bζ 2 +Cζ 3 (25) A = -4(β b2 -β h + β b1h ) (26)
B = 11β b2 -16β h + 5β b1h (27)
C = -6β b2 + 8β h -2β b1h (28)
β h = 90K + (1 -K)(β b2 + β b1h ) 2 (29) ζ = m 2 -m(z) m 2 -m 1 (30) m(z) = z 0 1 + dr(z) dz 2 dz (31) m 2 = L axUR 0 1 + dr(z) dz 2 dz ( 32
)
Axial distance is calculated as:

L ax = min(L ax,SRCC , 2r 2 [0.014+0.023r 2 /r h1 +1.58φ]) (33)
m(z) is calculated numerically using Gauss method [START_REF] Robert | Pompes rotodynamiques-similitude et conception des pompes centrifuges[END_REF]. The range value of the parameter K is between 0 -1 to adjust the rake angle. Finally, the wrap angle of blades is calculated as:

θ(z) = m 2 m 1 tan β b (z) r(z) dm(z) (34)
θ(z) is initialized to have a zero value at the trailing edge at the hub (blade stacking condition) and adjusted at shroud to have the same rake angle as that of the SRCC impeller. Note that the blade number is calculated also by an inner iterative procedure. This design method is originally performed by a several iterative loops one in another to compute meridional and blades according to the limitation on blade loading defined. But in this study, the meridional shape is already known for both upstream and downstream rotors. The global blade loading is calculated from Ref. [START_REF] Aungier | Centrifugal compressors: a strategy for aerodynamic design and analysis[END_REF] as:

BL = ∆W W 1 +W 2 ≤ 0.9 (35) ∆W = 4πr 2 U 2 (I -I par ) Z UR L B,UR (36)
Then, the tangential component of absolute velocity at the tip is recalculated (in an inner loop to determine λ) as:

C u2 U 2 = (I -I par ) = σ 1 - λ ṁtan β b2 ρ 2 A 2 U 2 (37)
σ is the slip factor. There are many empiric formulas for the slip model. The most recent one is given by Qiu et al. [START_REF] Qiu | Analysis and validation of a unified slip factor model for impellers at design and off-design conditions[END_REF] and is employed. For simplicity and numerical stability, only the radial and turning terms in this model are implemented. The passage term is very small compared to other terms (see Ref. [START_REF] Qiu | Analysis and validation of a unified slip factor model for impellers at design and off-design conditions[END_REF]) and difficult to implement. The design process is resumed as a flowchart shown in figure 4. Four values of LR are specified, and then four corresponding CRCC configurations are built by the design method described precedent at the design mass flow rate of 0.73 kg/s with N UR = -N DR = N SRCC = 16000 rpm [START_REF] Nguyen | Study of the Effect of the Contra-Rotating Component on the Performance of the Centrifugal Compressor[END_REF]. These four CRCC configurations are analyzed by CFD and their performances in terms of pressure ratio and polytropic efficiency are shown in table 4.

CRCC design done

The C1 configuration is therefore chosen to be manufactured because it delivers the highest efficiency and the closest pressure ratio to that of SRCC. Also, C1 aligns with the statement of Tosin et al. [START_REF] Tosin | New approach for multi-rotor mixed-flow pump design and optimization[END_REF] in which they show that having the lowest value of LR (indirectly equivalent to the load factor) will give the highest efficiency machine. The geometric parameters of two counter-rotating rotors are resumed in table 5 and table 6. It can be noted that CRCC and SRCC have the same size and use the same volute to facilitate the performance evaluation. The structure of the test bench is presented in the figure 5. We discuss in this paper the first part of the experimental results of the CRCC global characteristics and compare them with those of the corresponding SRCC at the selected speeds, as shown in figure 2. It can be noted that the selected speed is lower than the design speed because of the electrical resource limitation.

Experimental setup

CRCC test bench works in suction application, the pressure outlet is the atmospheric pressure. Because CRCC uses two independent electric motors so its inlet form was changed by using a curved pipe type with an angle of 90 • . The speed of two rotors: N UR for the upstream-rotor and N DR for the downstream-rotor, can vary independently by two inverters. The test platform consisted of a CRCC compressor connected to an open-loop system and driven by two independent electric motors. A locked valve located upstream of a storage tank is used to adjust the airflow into the system. The storage tank is then connected to a 3.5m long pipe to stabilize the flow. In the downstream of the compressor, a muffler was installed to reduce the noise of the system. The operating parameters of the compressor are measured by a sensor system that has been installed and described in figure 6.

The mass flow rate is determined based on measuring pressure differentials on the Flo-Bar Averaging Pitot tube. The manometer FCO16 with an accuracy of ±1% was connected with the Pitot tube to measure the pressure differentials. The value of the mass flow rate is then calculated according to the calibration equation 38. Four Pt100 thermocouples with an accuracy in the range of 0.02 • -0.04 • were used to determine the inlet and outlet temperatures. One thermocouple was placed at the inlet and three other ones were installed at the downstream pipe of the compressor. Four pressure taps distributed on the circumferential inlet tube were connected to a manometer FC332 with an accuracy of 0.5%, use to measure the average static pressure. Two Kisler 4005B highly sensitive instantaneous pressure sensors were used to measure the dynamic pressure in the system. By analyzing the dynamic pressure of these sensors, the fluctuations in pressure inside the system determine can be detected that determine the surge phenomenon. These two sensors are located in the inlet and the area between the two rotors. The pressure ratio is calculated by the static pressure at the inlet of the upstream-rotor and outlet of the volute and it is defined as:

Π s = P atm P 1 (40)
The polytropic efficiency used in this study is calculated with the equation 41:

η p = γ -1 γ ln P atm P 1 ln T out T 1 (41)

Results and discussions

As mentioned above, CRCC uses two independent rotors, which means one more degree of freedom was added in the system as the speed of the second rotor. Increasing the degree of freedom of the compressor makes the design process more complicated. Therefore, it is essential to conduct experiments to explore the characteristics of the compressor type based on combining the speed of the rotors independently. Two cases of operation are considered for testing its impact on the CRCC performances.

Case 1: The upstream-rotor is freely rotated around its axis; the downstream-rotor rotates at a constant speed of 11k rpm. In this case, the speed of the upstream-rotor depends on the mass flow rate through the compressor (N UR = f ( ṁ)).

Case 2: The two rotors are driven simultaneously in the opposite directions (N UR = -N DR ), called counterrotating mode. The global performances of CRCC are then compared to that of SRCC at the same rotation speed of 11k rpm.

Case 1-Behavior of CRCC with the upstream rotor

is freely rotated In this operating mode, the upstream-rotor is not driven by the electric motor, it rotates freely. The flow streamlines in figure 7 show how they pass the compressor. Due to the gradient-pressure between the compressor inlet and outlet, the fluid flow passes the upstream-rotor within the blade row. The high-velocity flow produces the gradient pressure on the rotor blade surface due to the airfoil shape of the rotor blade. The surface side with higher-pressure called Pressure Side (PS) and the other side with lower pressure called Suction Side (SS). The gradient pressure generates a torque which drives the upstream-rotor to rotate. It depends on the flow velocity or flow rate through the compressor. The rotational direction of this rotor is always contrary to the downstreamrotor direction. The flow out of the upstream-rotor was transferred energy by the downstream-rotor to accelerate and compress. After that, it was delivered to the outlet pipe. As a result, the upstream-rotor works like a turbine. The energy consumes by this rotor decrease slightly the head of the compressor. The head rise of the CRCC is generated only by the work of the downstream-rotor.

Figure 8 illustrates the overall experimental characteristics of CRCC at three different speeds of 9k rpm, 10k rpm, 11k rpm, and the free rotational speed of the upstream-rotor. It is easy to see that the speed of the upstream-rotor reduces according to a linear relation of the mass flow rate. The highest speed of the upstream-rotor achieves -7.2k rpm when the lock valve opens maximum corresponding to a flow rate of 0.746kg/s. The speed of the upstream-rotor decreases gradually as the control lock valve closes continuously to diminish the flow into the compressor. It is no longer rotate at the mass flow of 0.191kg/s because at this flow rate the torque which is generate by the pressure differentials between PS and SS of the blades does not overcome the resistance torque of the drive system (figure 8a). It can be noted that the pressure ratio of the CRCC increases with increasing speed while the efficiency of the compressor is always stable at 72 ± 1.2% (figure 8b). On a wide range of flow rates, the CRCC exhibits slightly smaller pressure ratios than the SRCC at the observed speeds due to the energy dissipated in the upstream rotor. Nevertheless, for identical operating points based on pressure-flow rates, the CRCC demonstrates better efficiency every time than the SRCC. For example, for two points, P1 and P2, are marked in figure 9, the efficiency value goes, respectively, from 69±1.2% to 72,6±1.2% and 64±1.2% to 70±1.2%. This can be explained by the compatibility of the fluid flow with the rotors. When the upstream-rotor rotates freely, the fluid flow is well guided to the downstreamrotor. As a result, there is less loss by the inlet incidence. A downside, however, the operating points of the CRCC are obtained for slightly higher downstream-rotor rotation speeds (10k rpm for CRCC and under 10k rpm for SRCC). The CRCC requires a higher speed to be able to achieve the same pressure ratio in this case because it has to compensate for the lost energy in the upstream rotor. For indus-trial applications, in case of the cost and space are considered, the upstream-rotor freely rotating rotor can be used as a pre-rotating inlet guide vane to improve the efficiency of the compressor.

Case 2 -Behavior of the CRCC with the upstream

rotor motor powered In this case, both rotors are driven simultaneously (counter-rotating mode). For this mode, the speed of the rotor can be the same or different. The ratio of the upstreamrotor speed to the downstream-rotor is defined as the speed ratio (θ) used to evaluate the compressor behavior. Firstly, the compressor behavior was analyzed at the same speed of 11k rpm (θ= 1). Next, the speed of the downstream-rotor is kept constant at three different speeds of 9k rpm, 10k rpm and 11k rpm; the speed of the upstream-rotor varies corresponding to the speed ratio changes in the range of [-0.7 -1.3].

Performance of CRCC at the speed ratio θ = -1

Figure 10 presents the comparison of the global performance between CRCC (in counter-rotating mode) and SRCC at the speed of 11k rpm. Obviously, the pressure ratio of CRCC is always higher than that of SRCC with the same tip-speed (figure 10a). It can be noted that the pressure deviation between CRCC and SRCC increases as the mass flow rate decreases. At the best efficiency point, the pressure ratio of CRCC is 1.194, which increases by about 4.6% compared to 1.141 of SRCC. It can be interpreted by the increase of the kinetic energy of the fluid flow. When the upstream-rotor is driven, the shaft power is transferred to the fluid flow lead to increase the relative velocity at the downstream rotor inlet. According to the velocity triangle as mentioned in section 2.1, the total enthalpy rise of CRCC increase due to the counter-rotating effect.

The comparison of polytropic efficiency between CRCC and SRCC is illustrated in figure 10b. It is clear that the CRCC efficiency is always higher than SRCC within the mass flow rate range of [0.4 0.7] kg/s. At the best efficiency point, the efficiency of CRCC increase by about 3.6% compared to SRCC. It can be remarked that this point is shifted to a lower mass flow rate at 0.584kg/s instead of 0.648kg/s for SRCC. However, the limit point of CRCC seems to be shifted to a higher mass flow rate. That means the surge phenomenon of CRCC appears early. This could be explained by the more sensitive incident angle at the downstream-rotor inlet. As stated by the velocity triangle, the inlet incidence angle increase quickly at the low flow rate due to the counterrotating effect. Therefore, the separation region appears in the blade passage of the rotors and generates a stall cell. The instability appears when the stall cells are developed in the entire rotors.

Figure 10c shows the total power consumption of CRCC in comparison with the SRCC one. The red solid line and the green solid line represent the power consumption of the upstream-rotor CR(P1) and the downstream-rotor CR(P2), respectively. The black solid lines and black dashed lines are respectively the total power consumption of CRCC and It is easy to see the power consumption of the downstream-rotor is approximately equal to the power consumption of SRCC. This shows that the fluid is mainly compressed in the downstream-rotor because it has a large variable diameter from the inlet to the outlet. The consumption of the upstream-rotor is small and increases as the flow decreases, which is almost the characteristic of axial turbomachinery. Upstream-rotor mainly speeds up the fluid flow to the downstream-rotor. Consequently, the total power consumption of CRCC is always higher than that of SRCC because of the high-pressure rise and mechanical losses in the upstream-rotor drive system.

Influence of the speed ratio on the performance

The previous results illustrate the counter-rotating mode provides higher performance and produces more pressure ra- tio rise than SRCC at the same tip-speed. To investigate the effect of the speed ratio in the counter-rotating mode, the speed of the upstream-rotor varies with each fixed speed of the downstream-rotor. The variation of speed ratios is then conducted to evaluate its ability to reproduce the performance and the operating selected of SRCC at a lower tip-speed. The performance of SRCC is constructed at five main speeds of 9k rpm, 10k rpm, 11k rpm, 12k rpm, and 13k rpm as shown in figure 2. Three main speeds of the CRCC downstream-rotor of 9k rpm, 10k rpm and 11k rpm are selected in this study. At each speed of the downstreamrotor, the speed of the upstream rotor varies corresponding to the speed ratio in a range of [-0.7 -1.3] (the minus sign represents two rotors rotating in the opposite directions). Seven speed-ratios of θ 1 =-0.7, θ 2 =-0.8, θ 3 =-0.9, θ 4 =-1, θ 5 =-1.1, θ 6 =-1.2 and θ 7 =-1.3 are used to construct the characteristics of CRCC in order to the comparison. In this study, the results of the downstream-rotor speed at 11k rpm are illustrated to analyze the effect of speed ratio on the performance. Fig-

Map characteristics in counter-rotating mode

Two other speeds of the downstream-rotor of 9k rpm and 10k rpm are conducted with a similar method. The results of three speeds are then used to construct the characteristic map of CRCC as shown in figure 12. The contour of the SRCC map (blue dashed line) is also illustrated in this figure to compare with the CRCC one. It reveals that the operating range of the two compressors is almost the same. In addition, the high-efficiency region (red zone) of CRCC is broadened and becomes larger than that of SRCC (the comparison between figure 2 and figure 12). This region is shifted to a lower mass flow rate compared to SRCC's region. Furthermore, the higher efficiency region ≥ 70% brown zone) can be seen clearly in the CRCC map. Besides, there are many ways to obtain the same pressure ratio characteristic in counter-rotating mode by simultaneously changing the speed of two rotors. In the selected speed, there are two regions where different speed ratios produce the overlap of the identical flow-pressure ratio curves. These curves have a slight difference in efficiency, and it depends on the speed of each rotor. The Higher Efficiency Points (HEP) are marked in figure 12 by selecting the higher efficiency point of two identical flow-pressure ratio curves. Two comparisons of efficiency between two identical flow-pressure ratio curves, for example, are shown in figure 13 and figure 14.

In the first one, the efficiency curve of θ 2 = -8k rpm 10k rpm = -0.8 is slightly higher than that of θ 6 = -10.8k rpm 9k rpm = -1.2 (figure 13). The surge limit point has been shifted slightly towards the lower mass flow rate if the upstream-rotor speed is lower than the downstream-rotor. As a result, the efficiency can be improved with the same pressure ratio if the downstream-rotor speed is higher than the upstream-rotor speed. In contrast, the efficiency of θ 1 = -7.7k rpm 11k rpm = -0.7 is a bit smaller than θ 5 = -11k rpm 10k rpm = -1.1 in the second one (figure 14). Nonetheless, the surge limit point is always enhanced if the downstream-rotor rotates faster than the upstream-rotor. Consequently, CRCC can give almost the same characteristic as SRCC at lower tip-speeds and higher efficiency but the surge phenomenon occurs slightly earlier than SRCC.

Conclusions

In this paper, the design method based on the loss model was presented. This method permit determining the geometry of the rotors from a reference rotor which has the same dimensions. The results of this method were validated with the existing data base in the open literature. After that, an experiment was conducted to investigate the influence of the speed ratio on the performance of CRCC against SRCC. The results show that:

1. Case 1-Upstream-rotor rotates freely: CRCC can improve the efficiency up to 3.5% due to the fluid flow was well adapted to the rotors. The inlet loss was minimized in this case. However, the pressure ratio was slightly reduced because the energy loss to drive the upstream-rotor. It can be remarked that CRCC efficiency is always higher than SRCC at the same pressure ratio and flow rate but the tip-speed of CRCC increases slightly. In some case of industry application, it can be helpful to improve the compressor efficiency and the upstream-rotor works as a pre-rotating inlet guide vane.

2. Case 2 -The two rotors are driven simultaneously in the opposite directions (N UR = -N DR ): CRCC can increase the pressure ratio up to 4.6% in comparison with SRCC at the same tip-speed. The polytropic efficiency is also improved by about 3.5%. The influence of the rotor speed on the performance of CRCC is then considered. The experimental results reveal that the speed ratio has a great influence on the pressure ratio of CRCC. The pressure ratio increases linearly with the speed ratio while the maximum efficiency seems to be stable. The pressure ratio can be increased up to 6.7% if the speed ratio goes up to -1.3. This can be explain by the increase of the flow kinetic energy which was provide by the upstream-rotor. It is worth noting that the best efficiency points of CRCC take place at the different mass flow rates when varying the speed ratio. At each speedcouples, the compressor has a minimum inlet loss at a specific flow rate due to the incidence angle modification according to the velocity triangles. The set of these points indicates the effective working area of CRCC. As a result, CRCC can give a more flexible operating range in comparison with SRCC to meet the various working conditions. Furthermore, CRCC can work at a lower tipspeed than SRCC to obtain the same performance and operating range.

However, the instability limit of CRCC is shifted to a higher mass flow rate. That means the surge occurs early in the CRCC configuration due to the higher sensitivity of the downstream inlet incidence angle. Fortunately, this problem can be resolved by changing the speed and the rotation direction of the upstream-rotor to extend the operating range of the compressor. This content will be presented in other publication.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Fig. 1 .

 1 Fig. 1. Velocity triangle (a) and a meridional contour (b) were used to design CRCC. Points 1 and 2 represent the inlet and outlet of the downstream-rotor,respectively, and points 3 and 4 respectively stand for the inlet and outlet of the downstream-rotor. Points 5 represents the volute outlet

Fig. 2 .

 2 Fig. 2. Performance map of SRCC with N ∈ [9k rpm, 13k rpm]

Fig. 3 .

 3 Fig.3. Loss model validation against experimental data of KIMM SRCC and Oh's model[START_REF] Oh | An optimum set of loss models for performance prediction of centrifugal compressors[END_REF]

  Fig. 4. CRCC design flowchart

Fig. 5 .

 5 Fig. 5. Structure of a counter-rotating centrifugal compressor (CRCC) (a) and single rotor centrifugal compressor (SRCC) (b)

Fig. 6 .

 6 Fig. 6. Scheme of the counter-rotating centrifugal compressor (CRCC) test bench

Fig. 7 .

 7 Fig. 7. The Pressure Side (PS) and Suction Side (SS) on the blade surfaces in case 1

Fig. 8 .

 8 Fig. 8. Overall experimental-characteristics of CRCC at three speeds, 9k rpm, 10k rpm and 11k rpm of downstream-rotor and in freerotation of upstream-rotor: (a) Pressure ratio, upstream-rotor speed and (b) polytropic efficiency.

Fig. 9 .

 9 Fig. 9. Comparison of characteristics map between CRCC (left figure) and SRCC (right figure) at the three-rotation speed of 9k rpm, 10k rpm, and 11k rpm

Fig. 10 .

 10 Fig. 10. Comparison of performance between CRCC in counterrotating mode (case 2) and SRCC at the speed of 11k rpm:(a) pressure ratio, (b) efficiency, and power consumption (c)

Fig. 11 .

 11 Fig. 11. Overall experimental-characteristics of CRCC with different speed ratios at the downstream-rotor speed of 11k rpm: (a) pressure ratio and (b) efficiency

Fig. 12 .

 12 Fig. 12. Performance map of CRCC with N DR ∈ [9k rpm 11k rpm], N UR ∈ [-6.3k rpm -14.3k rpm]

θ 6 =Fig. 13 .

 613 Fig.[START_REF] Dejour | Assessment of a novel non-axial counter-rotating compressor concept for aero-engines[END_REF]. Variation of efficiency between two speed ratios (θ 2 = -8k rpm/10k rpm = -0.8 and θ 6 = -10.8k rpm/9k rpm = -1.2) that give the identical flow-pressure ratio

θ 1 =Fig. 14 .

 114 Fig. 14. Variation of efficiency between two speed ratios (θ 1 = -7.7k rpm/11k rpm = -0.7 and θ 5 = -11k rpm/10k rpm = -1.1) that give the identical flow-pressure ratio

ṁ

  Mass flow rate, [kg/s]; θ Speed ratio, [θ= N UR N DR ]; β Relative fluid flow angle, [ • ]; α Absolute fluid flow angle, [ • ]; β b Blade angle, [ • ]; φ Stage flow coefficient, [-]; η Efficiency, [-]; I Work input coefficient, [-]; L B Blade camberline length, [m]; m Meridional length, [m]; ζ Non-dimensional meridional length, [-]; L ax , z Axial length, axial coordinate, [m];

	b Blade height, [m];
	t b Blade thickness, m;
	A Area, m 2 ;
	BL Blade loading, [-];
	B Blockage factor, [-];
	σ Slip factor, [-];
	R Gas constant,[J/kgK];
	C p Heat capacity,[J/kgK];
	Subscripts
	m Meridional direction;
	u Peripheral direction;
	u Peripheral direction;
	re f Reference condition;
	cr Corrected condition;
	u Peripheral direction;
	h Hub;
	s Shroud;
	t Total condition;
	1 Compressor inlet;
	2 Upstream-rotor outlet;
	3 Downstream-rotor inlet;
	4 Downstream-rotor outlet;
	5 Volute outlet;
	b Blade;
	par Parasitic;
	p Polytropic condition;
	atm Atmospheric;
	abbreviation
	CRCC Counter-Rotating Centrifugal Compressor;
	UR Upstream-Rotor;
	DR Downstream-Rotor;
	SRCC Single Rotor Centrifugal Compressor;
	HEP High Efficiency Point;
	BEP Best Efficiency Point;

Table 1 .

 1 Geometric parameters of SRCC

	Parameter	Value	Parameter	Value
	d 1h	59.5 mm	β b1h	45.3 •
	d 1sh	161 mm	β b1sh	69.8 •
	d 2	286 mm	β b2	64 •
	b 2	29.7 mm	Z	7+7
	N	16000 rpm L m	104.5 mm
	also the same as that of SRCC, so only the counter-rotating
	effect will be properly investigated. The geometric parame-
	ters and the performance map of SRCC are shown in table 1
	and figure 2.

Table 2 .

 2 Geometrical parameters comparison between the developed code and the original centrifugal compressor-GT15V44[START_REF] Deligant | 3d cfd simulation of a turbocharger compressor used as a turbo expander for organic rankine cycle[END_REF]

	Description	Parameter Original	Code
	Shroud radius r Outlet blade angle β b2	-45 •	-45.339 •
	Blade number	Z	6/6	12

s1 15.55 mm 14.155 mm Shroud inlet blade angle β bs1 -60 • -56.8 • Outlet radius r 2 22 mm 21.135 mm Outlet blade height b 2 2.66 mm 2.511 mm

Table 3

 3

	Description	Parameter	Original	Code
	Shroud radius	r s1	105 mm	107.32 mm
	Shroud inlet blade angle	β bs1	-56, 536 • -55.625 •
	Outlet radius	r 2	215.5 mm	210.7 mm
	Outlet blade height	b 2	17 mm	17.4 mm
	Outlet blade angle	β b2	-50 •	-46.734 •
	Blade number	Z	15/15	20

. Geometrical parameters comparison between the developed code and the original centrifugal compressor-NASA CC3

[START_REF] Mckain | Coordinates for a high performance 4:1 pressure ratio centrifugal compressor[END_REF]

Table 4 .

 4 Performance comparison between four CRCC configurations by CFD calculations, N UR = -N DR = 16000 rpm at the design mass flow rate of 0.73 kg/s[START_REF] Nguyen | Study of the Effect of the Contra-Rotating Component on the Performance of the Centrifugal Compressor[END_REF]

	Configuration LR Pressure ratio (s-s) Polytropic efficiency (s-s)
	C1	0.3	1.31	78%
	C2	0.4	1.34	69%
	C3	0.5	1.38	65%
	C4	0.6	1.36	71%

Table 5 .

 5 Upstream-rotor geometric parameters

	Parameter	Value	Parameter Value
	d 1h	59.5mm	β b1h	45.3 •
	d 1sh	161mm	β b1sh	69.8 •
	d 2h	118mm	β b2h	53.6 •
	d 2sh	176mm	β b2sh	68.4 •
	N UR	-16000 rpm Z UR	7
	L UR	31.9 mm

Table 6 .

 6 Downstream-rotor geometric parameters

	Parameter	Value	Parameter Value
	d 3h	128.5mm	β b3h	72.7 •
	d 3sh	183mm	β b3sh	77 •
	d 4	286mm	β b4	64 •
	N DR	16000 rpm Z DR	9

Acknowledgements

The authors would like to thank LIFSE laboratory, the Mauritanian and Vietnam governments with all support for this study. Special thanks to Sebastien PORCHERON, lab's engineer, for helping us assemble the test bench.