Olivier Coutier-Delgosha

Jean-Luc Reboud
email: reboud@enise.fr

Regiane Fortes-Patella

Numerical Study of the Effect o f t he Leading Edge Shape on Cavitation Around Inducer Blade Sections

Keywords: Numerical Simulations, Cavitation, Rocket Engine Turbo-Pumps, Inducers, Hydrofoils

A numerical study of the cavitation behaviour of two-dimensional hydrofoils simulating a section of an inducer blade is presented. Two leading edge shapes were chosen to approach rocket engine inducer designs. They were tested with respect to the development of sheet cavitation. The numerical model of cavitating flows is based on the 3D code FINE/TURBO™, developed by NUMECA International. The cavita tion process is taken into account by using a single fluid model, which considers the liquid vapour mixture as a homogeneous fluid whose density varies with respect to the static pressure. Numerical results are compared with experimental ones, obtained in the CREMHyG large cavitation tunnel(ll. Pressure distributions along the foil suction side and the tunnel walls were measured for different cavity lengths. Total pressure measurements along the foil suction side allow characterizing the effects of cavitation on the liquid flow. Influence of the leading edge shape on the cavitation behaviour and comparison between experiments and numerical predictions are discussed.

Introduction

The prediction of the cavitation behaviour is of first importance for the design of rocket engine turbo pumps.

Indeed, this phenomenon results in strong unsteady forces acting on the pump components, and it may lead to substantial performance losses. The analysis of the vapour occurrence in the pump, as well as the study of the unsteady effects related to cavita tion, could directly influence the pump inducer design. Total pressure measurements have been per formed using a 4 holes probe along 3 axes crossing the upper channel at 37%, 70% and 95% of the chord from the leading edge (Fig. 1).

Velocities have been deduced from the total and static pressure measure ments. Comparisons with LDA data acquired along the same axes were used to validate the method under non-cavitating and cavitating conditions. in which the interface is considered to be in dynamic equilibrium<6),(!s),(l4). The momentum transfer between the phases is thus strongly linked to the mass transfer.

In the present work the empirical barotropic law p(P) used is presented in Fig. 3. When the pressure is respectively higher or lower than the vapour pressure, the fluid is supposed to be purely liquid or purely vapour, according respectively to the Tait equation and to the perfect gas law. The two fluid states are joined smoothly in the vapour-pressure neighbour hood. It results in the evolution law characterized mainly by its maximum slope 1/Amin2, where Amin2= dP/dp. Amin can thus be interpreted as the minimum speed of sound in the mixture. (16), [START_REF] Choi | The Application of Preconditioning in Viscous Flows[END_REF]. It consists in multiplying the pseudo-time derivatives by a preconditioning matrix r-1. Such modifications have no influence on the converged result, since these terms are of no physical meaning, and converge to zero.

The discretization is based on a finite volume approach. We use a second order central scheme, which must be associated with two artificial dissipa tion terms, respectively of second and fourth order.

The first one is activated in the strong pressure gradi ent areas, such as shocks. The other one is used in the whole domain, and it results in a second order space accuracy. The pseudo-time integration is made by a four-step Runge-Kutta procedure.

The physical time-derivative terms are discret ized with a second order backward difference scheme that ensures a second order accuracy in time. Experimental results are also provided on these figures, to enhance comparison. We obtain a reliable agreement between numerical and experimental results, the case of the SLE foil at 4.5 degrees angle of attack needing nevertheless at particular treatment, as will be discussed hereafter. Figure 7 shows the density of the fluid obtained for the four cases, for the cavitation number corre sponding to a cavity length close to 15% of the chord.

It can be noticed that the high angle of attack leads to a faster growing of the cavity thickness downstream of the detachment point, and to a larger void ratio along the foil surface.

Quantitative comparisons are investigated be tween experiments and the numerical results in the case of the bevelled leading edge at high angle of attack. The static pressure evolution along the profile is represented in Fig. 8 for a cavity length increasing from 5% of the chord to 20% of the chord.

We observe a general good agreement between the numerical results and the experimental data : the charts confirm that the cavity length is correctly predicted. The pressure downstream of the closure area is a little over-estimated by the calculation, which is mainly an effect of the 2D simulation that do not take into account the obstruction effects linked to 8

--�-,-'"�--�---•-•--r-•------- 0 .
6 �==t==l:��::'j --------:--•"'" _____ -------,----o.6 -t----�---t---r--1-____, io;; ==:..l OA f---1---l---,b__,.�.... .,,........Ct@" -v "' o.z +---l, -_+--_ ----:. 1-rru-F�r---+---+-------c In non-cavitating conditions, the boundary layer appears almost symmetric on both sides of the chan nel. In cavitating condition, the important increase of

0 . 4 -l- 0 . 2 _.-a • u c. o _(). � •v 0 � - o.2 II - o .< �LI I---+----+---+--t----+-- -o .
0 o f-��� • �� � � v � �--+--�---t---'" 1 h ! -0 . 2 -1---t-'--t---+--+-- ----1 ---f----1,

Fig. 2 .Fig. 1

 21 Fig. 2. The first leading edge presents a parabolic shape, about 3 mm long, creating with the suction side

3 .Fig. 2

 32 Fig. 2 Geometry of the bevelled leading edge (BLE) and the sharp leading edge (SLE) . Angle of attack= 4.5 degrees

IFig. 3

 3 Fig.3The barotropic state law p(P)

5 .

 5 This numerical model was adapted to treat the cavitation process<9). The key point of this adaptation is the modification of the state law of the fluid. Our barotropic law implies the simultaneous treatment of two different cases : the fluid is highly compressible in the two-phase flow areas (the Mach number can be as high as 4 or 5) and it is almost incompressible in the pure vapour or pure liquid areas. So the main difficulty consisted in managing these two different states of the fluid, without creating any spurious discontinuity in the flow field. Besides, the cavitation consists in a very sharp and very rapid process. It means that the density time fluctuations and the density repartition must be smoothed, to avoid numer ical instabilities. Thus, we use an under-relaxation of the variations of the density to prevent too fast chang ing during one pseudo-time step. We also modified the switch between the two types of artificial dissipations. The second difference term is now also activated in the strong density gradient areas, such as cavitation sheet interface. Turbulence model We use for the calculations presented in this paper a classical Baldwin-Lomax turbulence model. Other calculations considering k-E turbulence models are in progress to improve the physical analyses. A more detailed study of the influence of the turbulence model on unsteady cavitation simulation is proposed in Ref. (18). It shows a major effect of the compres sibility effect modelling on the unsteady behaviour of cloud cavitation. Boundary conditions The boundary condition setting is based on a system of dummy cells. Classical incompressible types of boundary conditions are applied : imposed velocities at the inlet, and an imposed static pressure at the outlet. Numerical studies have been started in LEGI to improve these conditions, mainly by taking into account the test rig influence<'9l, but have not been applied in the cavitating case yet. Laws of the wall are applied along solid boundaries. Initial transient treatment First of all, a steady step is carried out, with a pseudo vapour pressure low enough to ensure no vapour presence in the whole computational domain. Then, this vapour pressure is increased progressively BLE during the early time steps, until the required cavita tion number !5 is reached. Vapour appears progres sively in the low static pressure regions during this transient. The cavitation number is then kept con stant throughout the computation. Two-dimensional Results 2D computations were performed on both geome tries, for the two experimental angles of attack of 4.1 and 4.5 degrees. A 10 000 cells mesh was applied in the four cases (Fig. 4), and a large range of cavitation numbers was considered, according to the experimen tal results. In the case of the SLE foil at 4.5 degrees incidence, a second mesh has been tested, more refined near the leading edge. In all computations a cavitation sheet appears on the suction side of the foil and completely stabilises as soon as the operating cavitation number is reached. Then, decreasing the cavitation number !5 in succes sive steps allows drawing the relationship: cavitation number !5 versus cavity length. Figures 5 ( a ) and ( b ) present the results for the two angles of attack, respectively in the case of the BLE and SLE foils.

4 . 1 Fig. 4 0Fig. 5 5 - 2 +Fig. 6

 4145526 Fig. 4 Detail of the mesh near the leading edges : BLE and SLE foil

Fig. 7

 7 Fig. 7 Shape of the cavities with Lcav=15% Lref, (a) Bevelled leading edge -i=4.5", (b) Bevelled leading edge -i=4T, (c) Sharp leading edge -i=4.5", (d) Sharp leading edge -i=4.1"

6I

  .,..-_ --+--+---1-----+--+-----0 . 8 +-. --+----+---+---+-----+----;' .......0 --o .......: iU .O.C) beveled leading edge i=4.5' Lcav/Lref=1 0% 0 . 8 ---••-•••-

Fig. 8

 8 Fig. 8 Static pressure dis tribution on the profile : numerical and experimen tal results (BLE foil, Vref=16 m/s) the boundary layers developing along the sidewalls of the tunnel. Nevertheless, the most important discrep ancy concerns the pressure increase in the cavity closure area, which appears more pronounced in the calculations than in the experiments. This sharp elevation predicted by the model in the cavity wake can be related to the complete stabilization of the cavitation sheet. The real behaviour involves self oscillations of the cavitation sheet and the measured time-averaged pressure distributions downstream of the cavities appear smoothed. Velocity profiles across the upper channel are more closely studied. The velocity distribution along three axes almost perpendicular to the foil suction side, respectively at 37%, 70%, and 95% of the chord

1 2 0. 8 1 0. 2 ,Fig. 9 Fig. 10

 12812910 Fig. 9 Velocity profiles in three sections located respectively at 37%, 70%, and 95% of the chord. All values are divided by the mean velocity in the corresponding section in non cavitating condition. (BLE fo il at 4.5 degree, Vref=16 m/s). Non cavitating condition experimental points+; numerical result (fu ll line) ; Cavitating condition (Lcav/Lref=15%) experimental points .A ; numerical result (fu ll line) ; Difference between non-cavitating and cavitating conditions experimental e ; numerical result (fu ll line)

6 .

 6 Three-dimensional Computation A three dimensional calculation taking into account the complete experimental geometry was performed, to illustrate the 3D ability of the numerical code and to estimate the effect of 2D simplifications applied in the previous cases. A 106 cells mesh of the SLE foil at 4. 1 degrees angle of attack is used. The cavitation number is fixed to 0.2, which leads to a cavity length close to 5% of the chord. The cavity shape, shown in Fig. 10, is clearly three-dimensional, with an important influence of the sidewalls boundary layers, also visible on the streamlines drawn from the foil leading edge.

A

  numerical study of the cavitation behaviour of two-dimensional hydrofoils simulating a section of an inducer blade was presented. Two-dimensional com putations were performed in different cases : two different foil leading edge shapes, two different angles of attack. A good agreement with experiments is generally obtained for the cavity length at different cavitation numbers. In one case, namely the sharp leading edge foil at the higher angle of attack, the presence of a separated flow near the sharp leading edge, observed for non-cavitating conditions, creates the condition of a strong hysteresis phenomenon in the numerical result. Only the simulation performed by increasing the cavitation number from its minimum value provides a behaviour that conforms to experi mental observations. With this angle of attack, the cavity is larger than with the bevelled leading edge foil, in both experiments and simulations. The self oscillating behaviour of cavitation is not simulated at the present stage of the model. There is no effect of the leading edge shape at the lower angle of attack. Static pressure distributions along the foil suction side and velocity profiles in the cross sections of the foil suction side channel agree well with measurements. The presence of the cavitation sheet leads to the modification of the boundary layer all along the foil, with a probable effect on the trailing edge flow. A first 3D computation shows the influence of sidewall bound ary layers on attached cavity.

Acknowledgements

This work is supported by a doctoral grant from the Education French Ministry MERT, SNECMA Moteurs (Rocket Engine Division), and by the French space agency CNES.

The laboratory CREMHyG (Grenoble, France) provided experimental results.


Numerical Simulation of the Unsteady Cavitation Behavior of an Inducer Blade Cascade

Olivier Coutier-Delgosha, * Yannick Courtot, † Florence Joussellin, ‡ and Jean-Luc Reboud § Institut National Polytechnique de Grenoble, 38041 Grenoble Cedex 9, France

One source of unsteadiness in turbopump inducers consists in a rotating cavitation behavior, characterized by different cavity shapes on the different blades, which leads to super-or subsynchronous disturbances. This phenomenon is simulated for the case of a simple two-dimensional blade cascade corresponding to a typical fourblade inducer. A numerical model of unsteady cavitating flows was adapted to take into account nonmatching connections and periodicity conditions. Single-channel and four-channel computations were performed, and in the latter case, nonsymetrical unstable flow patterns were obtained. Limits of stability according to the mass flow rate and the cavitation number are presented. Qualitative comparisons with experiments, instability criterion, and the mechanisms of instabilities are also investigated.

I. Introduction

T O achieve operating at high rotational speed and low inlet pres- sure, rocket engine turbopumps are generally equipped with an axial inducer stage working in cavitating conditions (Fig. 1). Cavitation develops on suction side of the blades and at inducer periphery near the tip. Peripheral cavitation concerns all cavitating structures that appear near the shroud casing at the inducer inlet, as backflow of the pump [START_REF] Yokata | A Study on Swirling Backflow and Vortex Structures at the inlet of Inducer[END_REF] and cavitating tip vortices. [START_REF] Laborde | Tip Clearance Cavitation in an Axial Flow Pump[END_REF] The presence of vapor induces disturbances that can result in substantial performance losses. Moreover, when inlet pressure is decreased from cavitation inception to breakdown of the pump, unsteady phenomena may appear, associated with different blade cavitation patterns. Experimental results point out two main types of cavitation instabilities: a self-oscillation behavior of cavitation sheets, whose mechanism was studied in cavitation tunnels and analyzed in detail by many authors, [START_REF] Stutz | Experiments on Unsteady Cavitation[END_REF][START_REF] Kubota | A New Modelling of Cavitation Flows: A Numerical Study of Unsteady Cavitation on a Hydrofoil Section[END_REF][START_REF] Chen | Modeling Hydrodynamic Nonequilibrium in Cavitating Flows[END_REF] and a rotating cavitation behavior, mainly observed in inducers, which shows different sizes of cavitation structures in the different blade-to-blade passages of the machine and leading to super-or subsynchronous perturbations.

This last phenomenon strongly depends on the cavitation development in the machine. A typical example is given in Fig. 2: At cavitation inception, only a steady and balanced flow pattern with one short attached cavity on each blade is observed from flow visualizations. When the cavitation parameter is slightly decreased, a steady and alternate cavitating configuration appears (only on four blade inducers) with alternatively one short and one long cavity. For a lower cavitation parameter, [START_REF] Kamijo | An Experimental Investigation of Cavitating Inducer Instability[END_REF] just above breakdown, an unsteady flow pattern called rotating cavitation can be identified: Unbalanced attached cavities are observed in the different channels, their distribution rotating faster than the inducer, [START_REF] De Bernardi | Experimental Analysis of Instabilities Related to Cavitation in Turbopump Inducer[END_REF][START_REF] Pagnier | Conception and Experimental Study of an Inducer[END_REF] which leads to large radial loads on the shaft. [START_REF] Goirand | Experimental Investigation of Radial Loads Induced by Partial Cavitation with Liquid Hydrogen Induce[END_REF] Finally, near the breakdown of the inducer, a steady and balanced flow pattern with fully developed cavitation is observed.

These instabilities induce some strong radial forces that may perturb the rotor balance and important pressure fluctuations in the lines. They must be quantified and controlled to avoid any major effect on the global pump behavior.

Over the past few years, numerical models have been developed to predict the cavitation instabilities in inducers. They are based on stability analyses and linear approach and take into account the total flow rate variations through a cavitating blade-to-blade channel, [START_REF] Tsujimoto | A Theoretical Analysis of Rotating Cavitation Inducers[END_REF][START_REF] Joussellin | Analytical Modelling of Instabilities in a Cavitating Turbopump Inducer[END_REF] or calculate the flow around attached cavities. [START_REF] Pilipenko | Theoretical and Experimental Computational Methods for Determining Volume of Cavities and Coefficients of Dynamic Equation of Cavitation Cavities[END_REF][START_REF] Watanabe | Linear Analyses of Cavitation Instabilities[END_REF] To improve the understanding and the prediction capability of cavitation instabilities, numerical and experimental analyses are carried out in France through collaborations between the Laboratoire des Ecoulements Géophysiques et Industriels, the Rocket Engine Division of Fig. 2 Cavitation patterns and performance evolution as the cavitation number decreases in four-blade inducer. [START_REF] De Bernardi | Experimental Analysis of Instabilities Related to Cavitation in Turbopump Inducer[END_REF] SNECMA Moteurs and the French space agency Centre National d'Etudes Spatiales. A two-dimensional model was developed [START_REF] Reboud | Two-Phase Flow Modeling of Unsteady Cavitation[END_REF][START_REF] Reboud | Two Phase Flow Structure of Cavitation: Experiment and Modeling of Unsteady Effects[END_REF][START_REF] Coutier-Delgosha | Numerical Simulations in Unsteady Cavitating Flows[END_REF] to simulate unsteady cavitation phenomena in inducers, such as pulsating cavities or vapor cloud shedding. The liquid/vapor mixture is considered in this model as a single fluid whose density varies from the liquid density to the vapor density, with respect to the local static pressure. The model has been validated on numerous cases, such as venturi-type sections or hydrofoils in cavitation tunnels, and the results demonstrated a good agreement with experiments. Its specificity is a reliable simulation of the cyclic behavior of self-oscillating cavities. [START_REF] Coutier-Delgosha | Numerical Simulations in Unsteady Cavitating Flows[END_REF][START_REF] Lohrberg | Numerical and Experimental Investigation on the Cavitating Flow in a Cascade of Hydrofoils[END_REF] In the present paper, the numerical model is applied to the simulation of the other instability observed in inducers, namely, the nonsymmetrical cavitation pattern. This first attempt is performed in a two-dimensional blade cascade corresponding to a four-blade inducer. The main objective was to take into account the interaction phenomena between the different blade-to-blade passages and to evaluate their effect on the unsteady behavior of the cavitation sheets on each blade. We focus in the present study on the ability of the numerical model to distinguish stable configurations from unstable ones, with a special attention paid to the mechanisms of instabilities.

The computational domain is the blade-to-blade geometry, that is, a (m, r θ) representation, where m is the meridian coordinate, r the radius (here constant), and θ the revolution angle. The twodimensional blade-to-blade channels were drawn by cutting the three-dimensional inducer geometry at constant radius R c equal to 80% of the tip radius R (Fig. 3). The computational grids of the four channels must be identical to ensure a precise detection of unstable cavitating behaviors. Indeed, different grids would induce spurious numerical errors that could be held responsible for the appearance of instability in the flowfield. Unfortunately, this condition cannot be imposed with a single mesh applied to the whole geometry because of the orthogonality of the cells that is required by the numerical model in the computational domain. Therefore, four identical separate grids are used for the four channels with three connections and one periodicity condition. It can be seen in Fig. 4 that it is quite impossible to obtain matching cells at these boundaries because of their curvature due to the high inclination of the blades in the (m, r θ) representation. Therefore, a new method to treat nonmatching boundaries is presented in this paper. It is based on an interpolation technique that guarantees, through its integration inside the algorithm, both mass and momentum conservation.

Computations were performed with different values of the cavitation number σ ,topoint out stable or unstable cavitating flows. Our present objective is to demonstrate the capability of the numerical model to simulate the mechanisms of nonsymmetrical flow arrangements. Results of the calculations are also compared to experimental observations performed previously at the Centre de Recherches et d'Essais de Machines Hydrauliques de Grenoble (CREMHyG) laboratory.

II. Physical Model

The cavitation model is based on a single-phase flow approach, which assumes that only one fluid is considered. [START_REF] Delannoy | Two Phase Flow Approach in Unsteady Cavitation Modeling[END_REF] This fluid is characterized by a density ρ that varies in the computational domain with respect to a state law. When the density in a cell equals the liquid density ρ l , all of this cell is occupied by liquid, and if it equals the vapor density ρ v , the cell is full of vapor. Between these two extreme values, the cell is occupied by a water/vapor mixture that we still consider as one single fluid. The void fraction α v = (ρρ l )/(ρ v -ρ l ) can be defined as the local ratio of vapor contained in this mixture. If the cell is full of vapor, then α v = 1. However, if a cell is totally occupied by liquid, α v = 0.

Through this simple model, linking the void ratio α v to the state law, we implicitly treat the fluxes between the phases, without the supplementary assumptions required in the case of a two-phase model.

With regard to the momentum fluxes, our model assumes that locally (in each cell) velocities are the same for liquid and for vapor: In the mixture regions, gas structures are supposed to be perfectly carried along by the main flow. (The friction forces are high, compared to the buoyancy forces.) That hypothesis is often assessed for this problem of sheet-cavity flows, in which the interface is considered to be in dynamic equilibrium. [START_REF] Merkle | Computational Modeling of the Dynamics of Sheet Cavitation[END_REF][START_REF] Kunz | Multi-Phase CFD Analysis of Natural and Ventilated Cavitation About Submerged Bodies[END_REF] The momentum transfers between the phases are, thus, directly linked to the mass transfers.

Vaporization and condensation processes are managed by a postulated barotropic state law that links the density to the local static pressure. The fluid is supposed to be purely liquid or purely vapor when the pressure is higher or lower than the vapor pressure, respectively. The two cases are joined smoothly in the vapor-pressure neighborhood. It results in the state law presented in Fig. 5, whose only parameter is the maximum slope 1/A 2 min , where A 2 min = ∂ p/∂ρ. A min can, thus, be interpreted as the minimum speed of sound in the mixture. Its calibration was performed in previous studies [START_REF] Reboud | Two Phase Flow Structure of Cavitation: Experiment and Modeling of Unsteady Effects[END_REF][START_REF] Coutier-Delgosha | Numerical Simulations in Unsteady Cavitating Flows[END_REF] in the case of unsteady self-oscillation behavior of sheet cavitation. The optimal value was found to be independent of the hydrodynamic conditions and is about 2 m/s for cold water, with p vap = 0.023 bar, and corresponds to p vap ≈ 0.06 bar (Fig. 5). The use of this state law implies that no delay to vaporization or condensation can be considered: Density directly depends on the pressure. Nevertheless, other models including this physical feature [START_REF] Kunz | Multi-Phase CFD Analysis of Natural and Ventilated Cavitation About Submerged Bodies[END_REF] have been also implemented and tested. If the vaporization/condensation terms are correctly tuned, that is, the delay parameters are optimized, then very similar results are obtained. In the present case, we try to simulate large-scale fluctuations of the whole cavitation sheets attached to the blades. To obtain numerically smooth cavities, we use a nondimensional ratio A min /(R c ) of 0.1. Rotation speed corresponding to a celerity of sound of 2 m/s is then lower than the experimental value.

The main numerical problem of our single-fluid approach results from the difficulty to manage different flow behaviors: incompressible flow in the areas containing pure liquid or pure vapor and a highly compressible flow in the areas of transition between liquid and vapor.

III. Numerical Model

To solve the time-dependant Reynolds-averaged Navier-Stokes equations associated with the barotropic state law presented earlier, the numerical code applies the SIMPLE algorithm on twodimensional structured curvilinear-orthogonal meshes, with modifications to take into account the cavitation process. The details of the numerical resolution were presented by Coutier-Delgosha et al. [START_REF] Coutier-Delgosha | Numerical Simulations in Unsteady Cavitating Flows[END_REF] It is based on an implicit method for the time discretization, and the HLPA nonoscillatory, second-order convection scheme proposed by Zhu. [START_REF] Zhu | A Low Diffusive and Oscillation-Free Convection Scheme[END_REF] A complete validation of the method was performed, and the influence of the numerical parameters was widely investigated. The results are reported in Ref. 16.

A standard k-epsilon RNG model of turbulence is used. This model does not allow any simulation of the self-oscillation behavior of sheet cavitation, as reported by Coutier-Delgosha et al. [START_REF] Coutier-Delgosha | Evaluation of the Turbulence Model Influence on the Numerical Simulations of Unsteady Cavitation[END_REF] The effects of the two-phase mixture compressibility on the turbulence structure must be taken into account to simulate this phenomenon correctly. A modification of the standard model was proposed in Refs. 15 and 16 to solve this problem efficiently. In the present study, only the rotating cavitation pattern is investigated. This is a first attempt to predict numerically the cavitating coupling between the channels, and so the interaction of its mechanisms with the self-oscillation of each cavity is not suitable. Thus, the standard turbulence model is applied.

IV. Connection of Nonmatching Boundaries

The boundary condition setting is based on two rows of dummy cells generated around the computational domain. Connections or periodicity conditions between two frontiers are obtained by transferring variables from inner cells to dummy cells. In matching boundary cases (identical grids on the two sides of the frontier, Fig. 6a), no interpolation is necessary, and the procedure involves no supplementary numerical error. In nonmatching boundary cases (Fig. 6b), special care must be paid to constrict the errors introduced by the interpolations and to respect the conservative character of the resolution. Indeed, the spurious generation of mass or momentum inside the domain, through connections or periodicities, would be very prejudicial to the rate of convergence.

We present here the general features of the process indicated in Fig. 6b. It consists in transferring the information from rows A1 and A2 to rows B1 and B2 and from rows A ′ 1 and A ′ 2torowsB ′ 1 and B ′ 2.

A. Geometry of Dummy Cells

In the case of connections or periodicity conditions, the shape of the dummy cells is of first importance because their width, their length, and their curvature strongly affect the computation. Any geometrical difference between the dummy cells and the inner corresponding ones would enhance the numerical errors by creating some spurious mass and momentum flow rates. Therefore, these cells must be as similar as possible to the cells of the original corresponding row.

B. Interpolations of Variables

All variables are transported from the computational domain to the dummy cells, that is, from A rows to B rows, through interpolations. The kind of interpolation depends on the transmitted variable. The transfer aims to ensure the conservation of both mass and momentum. In other words, the mass quantity passing through one of the two frontiers must be as close as possible to the mass quantity passing through the second one. The same conditions are required for the momentum fluxes.

1) The velocity component u (tangential to the frontier) and the pressure P are linearly interpolated.

2) The density ρ is transmitted so that the quantity of mass ρ S in each cell of the final row equals the sum of quantities ρ i S i in the cells or part of cells of the original row (Fig. 7). 3) The transmission of the velocity component v (normal to the frontier) is a little more complex because it must satisfy the conservation of both mass and momentum. Because staggered grids are used, v is not located at the center of the cells, but on their northern and southern frontiers. As can be seen in Fig. 8a, v is transmitted from lines 3 ′ ,4 ′ to lines 1 ′ ,2 ′ and from lines 1, 2, 3 to lines 4, 5, 6. Note that v is calculated only on one of the two frontiers, here on line 1, and the result is transmitted to the other one, line 4. The procedure guarantees the equality of fluxes on these two lines, without altering the convergence rate. Unfortunately, mass and momentum conservations cannot be both obtained with only one variable v.T osolve this problem, we took advantage of the specificity of the pressure correction algorithm, which is based on two separated resolutions of momentum and continuity equations.

C. Integration in the Algorithm

The velocities must be transmitted each time they are modified inside the computational domain, that is, two times per iteration: after the resolution of the momentum equations (step 1) and after the velocity correction involved in the pressure-correction method (step 2).

We considered that the first step was based on equilibrium between the momentum fluxes and the pressure gradients. Thus, the equality of the momentum fluxes on the connected frontiers must be verified during this step, and a B transfer (Fig. 8b) is performed just before. However, the second step is based on equilibrium between mass fluxes. These have to be equal on the two frontiers during this step, and an A transfer is performed immediately before.

V. A pplication to a Two-Dimensional Blade Cascade

The numerical model presented was applied to the calculation of the cavitating behavior of a four-blade cascade representing a complete rocket engine turbopump inducer. The objective was the simulation of the four sheets of cavitation attached to the blades and their unsteady coupled behavior.

A. Single Channel Computation

First only one blade-to-blade channel was considered. The uniform flow velocity imposed at the mesh inlet is deduced from the flow rate, and a periodicity condition is applied between the two sides of the channel (Fig. 9), according to the procedure presented in the preceding section. A uniform static pressure is imposed at the domain outlet, far enough from the trailing edge to avoid any influence of the boundary condition on the pressure field around the blade. Possible effects of the lines upstream and downstream from the inducer on its cavitating behavior are not taken into account in this approach.

A 190 × 30 structured mesh is used (Fig. 10). A special contraction of the grid is applied in the expected cavitating areas, that is, around the leading edge in the axial direction and on the suction side of the blade in the transverse direction. Along the solid boundaries, the k-ε turbulence model is associated with standard laws of the wall, and so a grid contraction is applied on both sides of the blade to constrict y+ at the first grid point between 35 and 120 for the Reynolds value used. The study of the influence of the Reynolds number would need a remeshing near the blades surfaces and was not performed for that first application.

To characterize the flow around the blade, a slow decrease of the cavitation number is simulated. First, a stationary step is performed, which imposes the reference flow rate and an outlet static pressure high enough to avoid any presence of vapor in all of the computational domain. During the following time steps, this pressure is decreased progressively, and vapor appears on the blade suction side. Large time steps ( t = 0.1T ref ) are imposed during that slow transient, to minimize the time-dependent terms in the equations and to obtain quasi-steady flowfields. Figure 11 shows the flow characteristics obtained for a cavitation number equal to 0.1. It can be seen that the shape of the sheet of cavitation is directly governed by the pressure field. The obstruction generated by the cavity in the flow also clearly appears on the streamlines representation. This obstruction increases when the cavitation number is still lowered, and it finally results in the drop of the blade performance, that is, an increase of the pressure inlet in the present case.

The entire behavior is recapitulated in Fig. 12, which shows the evolution of the blade performance as the cavitation number is lowered from initial noncavitating conditions down to the final performance drop. It consists successively in a quite stable evolution (for σ>0.2),afirst pronounced drop at σ = 0.2, and then a sudden increase of the head (σ = 0.1) just before the final blockage.

Although a large time step was used, the chart strongly fluctuates, which indicates that the cavitating flow is fundamentally unstable. Moreover, some numerical instability is observed when reaching the final head drop: The flow rate is imposed strictly at the inlet and the cavitation blockage is, thus, especially abrupt. The simulation was also performed with t = 0.025T ref and t = 0.4T ref to investigate the influence of the time step. The more t is decreased, the more the sheet of cavitation fluctuates, but no noticeable difference can be observed for the mean performance evolution. The influence of the mesh on this mean performance was also tested [START_REF] Courtot | Instabilités de Cavitation dans les Inducteurs: Analyse et Modélisation de l' Écoulement Instationnaire en Grilles d'Aubes[END_REF] with a finer grid composed of 220 × 35 cells, and less than 2% of difference with the standard grid was obtained in cavitating conditions (σ<0.4).

The decrease/reincrease of the performance (0.025 <σ <0.1) was more closely investigated, to understand the mechanisms of this surprising behavior. Observation of the velocity fields indicates that this phenomenon is due the interaction between the attached sheet cavitation and the boundary layer on the blade: Figure 13 shows the modifications due to cavitation of the relative velocity W on the suction side of the blade. Velocities are reported in two sections located at midchord and at the trailing edge, respectively. Because of the blade orientation, the variations of W are almost consistent with the evolution of the tangential relative velocity W u .

The curves corresponding to σ = 0.12 show a diminution of W inside the boundary layer, and an increase of W outside, compared with very low cavitating conditions (σ = 0.4). The predominant effect at this stage is the increase of W in the main part of the section, which leads to the progressive decrease of the blade performance. For σ = 0.08, an opposite effect appears at midchord: W is increasing inside the boundary layer, while decreasing outside. Nevertheless, this effect is not strong enough to propagate to the trailing edge, where W is still globally increasing, which explains the important drop of the performance. For σ = 0.024, it can be observed that the earlier effect has propagated all along the blade, and it was also amplified: W has much decreased in the major part of the sections (leading to a better pressure rise), although it notably increased close to the blade.

The progressive growth of the sheet of cavitation is responsible for these variations of W. Figure 14a shows a scheme of this mechanism in the case of two consecutive blades, instead of the present periodicity condition. As σ is lowered, the cavity width expands and the fluid at the blade leading edge is pushed upstream. This fluid is then moved by a part of the main flow toward the bottom of the channel and highly accelerated. It induces a jet effect on the suction side of the adjacent blade, which constricts the boundary layer closer to the blade. The result is an increase of the velocity close to the wall and a decrease in the other part of the section.

When σ still decreases (Fig. 14b), this effect disappears because of the obstruction generated by the cavity: This explains the final performance drop.

B. Four-Blade Cascade Computation: Steady Behavior

Time-accurate computations are performed on the four-blade mesh composed of four connected earlier grids, that is, 28,000 cells. The periodicity condition is then applied between the fourth and first channels, as in the real runner. The time step was chosen to put emphasis on the investigation of the low-frequency fluctuations of the attached cavity, without being perturbed by the local unsteadiness in each cavitation sheet wake (cloud shedding): therefore, it is fixed equal to 1% of the blade passage time T ref . Thus, the self-oscillation behavior of the cavities is not simulated. Successive time-accurate computations are performed at fixed cavitation number and nominal flow rate coefficient.

First cases with quite high cavitation number (σ ≈ 0.175) lead to stable and symmetrical small cavities attached on each blade (Fig. 15a). The coupling between the four channels does not generate in that case any supplementary unsteady effect: The four cavities remain identical, and their shape becomes constant in time after the initial transient, as in the single-channel computation. This behavior is shown in Fig. 15b, which presents the time evolution of the cavity in the first channel: It completely stabilizes after the initial fluctuations. (This transient from t/T ref = 0t o1 0corresponds to the growing of the attached cavity from the noncavitating initial condition.) Figure 16 shows only small oscillations in the mass flow rate through each passage. Therefore, in this configuration the four-channel coupling has only a very small effect on the cavitation unsteady behavior.

C. Four-Blade Cascade Computation: Unsteady Behavior

When the cavity length is increased (σ = 0.15),anunsteady configuration spontaneously appears. cavities are then different on the successive blades: three large cavities and a little cavity are simulteously obtained. This unbalanced cavitating structure propagates from blade to blade in time. That phenomenon takes place spontaneously, only from the very small perturbations due to numerical errors of truncation.

Figure 19 shows the repartition of the mass flow rate in the cascade. After the initial transient, periodic fluctuations take place with different phases in the four channels. Their amplitude increases when the cavitation number is slightly decreased from 0.15 to 0.135. Visual observation (Fig. 17) and a fast Fourier transform analysis of cavity length fluctuations signal (Fig. 20) show that in the stator frame the phenomenon is about 50% faster than the inducer rotation speed. As observed in the experiments, this value slightly decreases with cavitation parameter. However, the numerical frequencies of that supersynchronous phenomenon remain about 25% larger than experimental values, as already observed in analytical models by Tsujimoto et al. [START_REF] Tsujimoto | A Theoretical Analysis of Rotating Cavitation Inducers[END_REF] and Joussellin and de Bernardi. [START_REF] Joussellin | Analytical Modelling of Instabilities in a Cavitating Turbopump Inducer[END_REF] Foralower cavitation parameter (σ = 0.08),astable configuration appears (Fig. 21), with alternate long and short cavities on the blades and different flow rates in the successive channels. Such a configuration is observed experimentally but at a cavitation number higher than the supersynchronous range (Fig. 2).

Figure 22 shows the cavitating performance computed by averaging the head coefficient obtained with the four-channel simulations at fixed cavitation number and nominal flow rate coefficient (points △).I nthe whole range of nonsymmetrical sheets of cavitation, the head coefficient is larger than the one obtained from the single-channel computation: the hollow in the chart is considerably reduced. This means that these special patterns of the flowfield (rotating supersynchronous cavitation and alternate cavitation) result in a diminution of the averaged losses in the blade cascade.

This effect can be interpreted on the basis of the analysis performed earlier in the case of the single-blade calculation. Indeed, rotating and alternate cavitation lead to the enlargement of some of the sheets of cavitation, compared to the stable configuration. The growth of these cavities pushes the fluid upstream at the leading edge. This fluid is then accelerated by the incoming flow, which results in the jet effect observed on the blade suction side in the adjacent channel (Sec. V.A). Thus, the flow in this channel is accelerated in the boundary layer, and decelerated above, which globally boosts the performance of the cascade. Nonsymmetrical flow patterns can, thus, be considered as a self-adaptation of the flow to reduce the losses in the blade-to-blade channels.

On the other hand, the final head drop is reached at higher σ because of the lack of symmetry: The biggest of the cavities are larger than the one obtained in the case of a single-grid computation at the same cavitation number.

D. Comparison with Experiments

Quantitative comparison between the three-dimensional inducer and the two-dimensional blade cascade is not directly available because of three-dimensional effects and the variation of the hub-toshroud ratio that is not taken into account. However, computations were performed at different operating conditions, by the varying of the cavitation number and the flow coefficient between 0.9 ref and 1.2 ref . The results are compared to experimental data in a qualitative way. The performance charts obtained are given in Fig. 23 with the limits of all nonsymmetrical flow arrangements, that is, rotating cavitation and alternate blade cavitation. For each flow rate, these limits are defined by two extreme values on a σ scale, respectively σ + and σ -.

In all cases, the final head drop is predicted by the model at a too high σ with to the experimental value (0.06 instead of 0.02). The cavitation parameter range of rotating cavitation σ = (σ + -σ -) increases when the flow rate coefficient decreases. That result agrees with experimental observations performed by Pagnier et al. [START_REF] Pagnier | Conception and Experimental Study of an Inducer[END_REF] and Yokata et al. [START_REF] Yokata | A Study on Swirling Backflow and Vortex Structures at the inlet of Inducer[END_REF] At reference flow coefficient φ ref , the experimental range of nonsymmetrical flow configurations is about σ exp = 0.07 (Fig. 2). Numerical results of σ are plotted with respect to the flow rate coefficient in Table 1: The comparison shows that the experimental range corresponds to the numerical result at φ/φ ref between 1 and 1.05. That result can be explained qualitatively by an important difference in inlet conditions between experiments and the numerical prediction: In the experiments, a partial obstruction of the inlet section due to a backflow area in the vicinity of the casing is observed. This particular flow pattern is shown in Fig. 24 (see Ref. 24), with S flow indicating a whole cross section, S back the size of the backflow, and S cav the area occupied by cavitation near the shroud. This phenomenon is not taken into account in the present simulations, which modifies the cascade inlet condition: In experiments at nominal flow rate the obstruction leads to a higher component C m of the velocity than in the simulation. For a higher simulated flow rate, inlet conditions are recovered, and σ is consistent with σ exp .

A comparison between the experimental breakdown chart at nominal flow rate and the one obtained by the four-channel computation is presented in Fig. 25. Although the present model, mainly because of the passage from three dimensional to two dimensional, cannot precisely quantify the location of breakdown and instability, a general correct agreement is obtained with experiments.

E. Instability Criterion

The evolution of the instability range according to the mass flow rate was investigated, to improve the understanding of the mechanisms that govern the onset and the conclusion of nonsymmetrical flow pattern.

Noted in Fig. 23 that the ending of instability occurs just at the beginning of the final drop of the cascade performance. Indeed, it has already been said (Sec. V.A) that this drop was due to the obstruction of the blade-to-blade channels by the sheets of cavitation. Thus, a critical size of the cavities could be directly responsible for the conclusion of the alternate blade cavitation. This assumption is confirmed in Fig. 26a, which presents the same six head drop charts as functions of the classical parameter σ/2α, which is usually considered as the key parameter to determine the length of the cavity in a given configuration. For all of the mass flow rates, instability vanishes for σ/2α ≈ 0.5/0.6. This value is fully consistent with the criterion obtained by Tsujimoto et al. [START_REF] Tsujimoto | Linear Analysis of Cavitation Instabilities of Hydrofoils and Cascade[END_REF] in the case of experimental results obtained with a three-blade inducer.

With regard to the onset of instability, this criterion cannot be applied, as can be seen in Fig. 26a. Indeed, according to the model, rotating cavitation appears earlier, that is, for a smaller length of cavitation sheets, when the mass flow rate decreases. This effect could be related to the increase of angle of attack, which enhances the flow separation at the blade leading edge and, thus, increases the obstruction generated by cavities, even for very small cavities. Thus, the inception of rotating cavitation would allow reducing the losses, as noted in Fig. 22. This additional influence of the flow incidence at the leading edge is confirmed by the instability map as a function of σ/α 3 (Fig. 26b). An almost constant value of σ/α 3 = 350 is obtained, which could be a criterion for instability inception in blade-to-blade calculations.

VI. Conclusions

We have presented two-dimensional computations performed on a four-blade cascade geometry representative of the behavior of a real three-dimensional inducer. This work implied the development of a nonmatching connection treatment, based on an interpolation process adapted to the SIMPLE algorithm. Attention was focused on the study of nonsymmetrical flow patterns that occur in inducers, that is, rotating supersynchronous cavitation and alternate cavitation. These two flow configurations were successfully predicted by the numerical model at several mass flow rate conditions. Comparisons between single-channel and four-channel computations revealed that nonsymmetrical flow patterns allow suppressing the hollow in the blade cascade performance before the final breakdown. The analysis of the velocity field on the blade suction side in the case of a single-blade computation suggests that this reduction of the losses could be linked to an important acceleration of the flow in the channels where the cavity is small. This jet effect modifies the boundary layer on the blade suction side, which globally leads to a decrease of the losses for the whole cascade. Instability criteria independent from the flow rate were found, for instability inception and conclusion.

This work is pursued to clarify the effects of rotation speed and fluid parameters and to assess the prediction capability of the model. We intend more particularly to take into account the mentioned three-dimensional effects. Therefore, a full threedimensional model is developed to predict cavitating flowfields in inducers. The final objective is to apply the numerical method presented in the present paper to three-dimensional computations, to predict the unsteady effects associated with cavitation in the real three-dimensional geometry.

  NomenclatureA min = minimum speed of sound in the two-phase mixture, m/s C(C m , C u )= v elocity vector in fixed frame, m/s C p = dimensionless static pressure, ( pp ref )/( 1 2 ρU 2 ) P = total pressure, P + 1 2 ρC 2 ,Pa P 1 , P 2 = total pressure at inlet and outlet, Pa p = local static pressure, Pa p ref , p vap = reference pressure (inlet pressure), vapor pressure, Pa p 1 , p 2 = static pressure at inlet and outlet, Pa r, R c , R = inducer radius, radius corresponding to the blade cascade, tip radius, m S = nondimensional surface of a grid cell S flow = cross section of the blade-to-blade channel, m 2 T ref = time corresponding to the passage of one blade in the fixed frame, s U = training velocity at inducer radius R c , R c , m/s W(W m , W u ) = relative velocity vector, m/s α =fl ow incidence at the blade leading edge, rad α v = local void fraction ρ l ,ρ v ,ρ = nondimensional density of the liquid, of the vapor, of the mixture ρ ref = reference density ρ l σ =c a vitation number, ( p 1 -p vap )/( 1 2 ρU 2 ) , ref =fl ow coefficient, C m /(U ), and reference flow coefficient

Fig. 1

 1 Fig. 1 Rocket engine four-blade turbopump inducer.

Fig. 3 Fig. 4

 34 Fig. 3 Passage from three-dimensional real geometry to blade cascade.

Fig. 5

 5 Fig. 5 Barotropic state law ρ(P).

Fig. 6

 6 Fig. 6 Information transfer between segments 1 and 2 in case of a) matching and b) nonmatching boundaries.

Fig. 7 Fig. 8

 78 Fig. 7 Density transfer.

Fig. 9 Fig. 11

 911 Fig. 9 Boundary conditions for a single-channel computation.

Fig. 12 Fig. 13

 1213 Fig. 12 Single-channel computation; cavitation characteristic of the cascade at φ = φ ref and associated length of the attached cavity (ratio 5:1 between horizontal and vertical scales).

FigFig. 15

 15 Fig. 14 Origin of variations.

Fig. 16 Fig. 17

 1617 Fig. 16 Mass flow rate repartition in the four channels; σ = 0.175.

Fig. 18 Fig. 19 Flow

 1819 Fig. 18 Cavity length evolution on the four blades: amplification of the unsteady coupling and phase shift (σ = 0.15).

Fig. 21 Fig. 22

 2122 Fig. 21 Flow rate repartition in the four channels; φ = φ ref , σ = 0.08.

Fig. 23 Fig. 24

 2324 Fig. 23 Effect of the flow rate on the cavitation characteristic and on the instability range: --, limit of nonsymmetrical arrangements and , experimental instability range Φ = Φ ref .

Fig. 25

 25 Fig. 25 Comparison between the experimental performance chart and the result of the four-channel computation at nominal flow coefficient.

Fig. 26

 26 Fig. 26 Limit of nonsymmetrical flow patterns according to σ/α and σ/α 3 .

Table 1 Instability range vs flow coefficient

 1

	φ/φ ref	σ
	0.90	0.16
	0.95	0.125
	1.0	0.08
	1.05	0.065
	1.1	0.04
	1.2	0

Acknowledgments

The authors thank SNECMA Moteurs (Rocket Engine Division) and the French space agency Centre National d'Etudes Spatiales for their support of the present work. We are also grateful to the CREMHyG laboratory (Grenoble, France), who provided the experimental results.


Margot Mieskes
email: margot.mieskes@h-da.de

Karën Fort
email: karen.fort@sorbonne-universite.fr

Aurélie Névéol
email: neveol@limsi.fr

Cyril Grouin
email: cyril.grouin@limsi.fr

Kevin B Cohen
email: kevin.cohen@gmail.com

NLP Community Perspectives on Replicability

Introduction

"As a community, we need to know where our approaches fail, as much -if not more so -as where they succeed." Despite this statement by [START_REF] Fokkens | Offspring from Reproduction Problems: What Replication Failure Teaches Us[END_REF], we are still aiming at higher, faster, better results with little outside verification. And although it has become good practise to share code, data and parameters, previous work and experience indicate that sharing is still not as common as one would hope for. Call for Papers in major conferences encourage to submit or reference data and to submit code, i.e., in supplemental material 2 . But recent work indicates that this is not done thoroughly enough [START_REF] Mieskes | A Quantitative Study of Data in the NLP community[END_REF][START_REF] Bretonnel Cohen | Reproducibility in Biomedical Natural Language Processing[END_REF][START_REF] Wieling | Squib: Reproducibility in Computational Linguistics: Are We Willing to Share?[END_REF]. Other factors mentioned by [START_REF] Fokkens | Offspring from Reproduction Problems: What Replication Failure Teaches Us[END_REF], such as preprocessing methods, experimental setup, system variation, etc., are rarely reported. [START_REF] Pedersen | Empiricism Is Not a Matter of Faith[END_REF] urges to not fear any dispossession of a tool, and highlights that sharing code will result in its use in new systems and citations of the work describing this code. Moreover, we should consider sharing software as a way to improve it more efficiently. In recent years, we have seen a rise in attention targeted towards the task of replication for example in the COLING 2018 selection criteria3 , the LREC 4REAL Workshops (Branco et al., 2016(Branco et al., , 2018) ) and the recent LREC initiative for replication. 4 But so far the task of replicating previous results has little merit in itself, but is rather only a (baseline) part in a paper. Additionally, normally it only gets reported in successful or mainly successful cases. Following the argument by [START_REF] Fokkens | Offspring from Reproduction Problems: What Replication Failure Teaches Us[END_REF], the cases where it fails, hardly ever get reported, despite Calls for Papers encouraging negative results5 and although they might be equally or even more important than the successful replication.

Our contribution therefore is to identify how the community views the topic of replication and what role each individual plays as an author, as a reviewer and as part of the NLP community. In conducting a survey, which drew answers from over two hundred respondents, we get a better picture of the factors that support or hinder making repli-cation more visible and how the three factors described above influence this. Our results indicate that the participants in general regard replication as an important issue and that the NLP community could do more to support replication, which would strengthen the field as a whole.6

Related Work

One of the earliest reports of a replication effort addresses manual word-sense disambiguation based on four words, representing different degrees of difficulty [START_REF] Kilgarriff | 95% Replicability for Manual Word Sense Tagging[END_REF]. The author reports that humans agree in this task on average in 95% of the cases. Following [START_REF] Fokkens | Offspring from Reproduction Problems: What Replication Failure Teaches Us[END_REF], others look into parameters that influence the replicability of results. [START_REF] Dakota | Towards Replicability in Parsing[END_REF]; [START_REF] Marrese | Replication issues in syntax-based aspect extraction for opinion mining[END_REF] and [START_REF] Horsmann | Do LSTMs really work so well for PoS tagging? -A replication study[END_REF] report various parameters and problems with replication experiments for morphology and syntax.

In the field of biomedical NLP, Olorisade et al. ( 2017) assess the reproducibility of findings published in 33 papers. They notice that data sets were missing, making it impossible to reproduce results for 80% of the papers. These figures are in line with results reported by [START_REF] Mieskes | A Quantitative Study of Data in the NLP community[END_REF]. They consider that a permanent link to the resources (data set, software, etc.) must exist along with published papers. As part of a NLP challenge, [START_REF] Névéol | Replicability of Research in Biomedical Natural Language Processing: a pilot evaluation for a coding task[END_REF] report results on replicating experiments from three systems submitted to the CLEF eHealth track. They show that replication is feasible although "ease of replicating results varied". They suggest the allowance of extra pages for papers, where information required to replicate an experiment could be reported. [START_REF] Moore | Bringing replication and reproduction together with generalisability in NLP: Three reproduction studies for Target Dependent Sentiment Analysis[END_REF] illustrate how to publish relevant details to reduce efforts in repeatability and generalisability. Suggestions include using only open data, open source code and providing extensive documentation in the code. [START_REF] Wieling | Squib: Reproducibility in Computational Linguistics: Are We Willing to Share?[END_REF] describe one example where exact replication was possible and the authors list the parameters that allowed them to do so: a virtual image, containing all code and all data or providing CodaLab worksheets. Their study, which compared the situation in sharing research artefacts between 2011 and 2016 indicates that, while the situation has improved and the availability of data is high, access to code is less so and requesting code is unsuccessful in most of the cases. Based on results of their actual replication experiments, at most 60% of the studies are replicable, but only if the need for exact replication was relaxed. [START_REF] Fares | Word vectors, reuse, and replicability: Towards a community repository of largetext resources[END_REF] present a repository and infrastructure containing texts, tools and embeddings for English and Norwegian. Their aim is to facilitate replicability and testing of previous results. [START_REF] Dror | Replicability Analysis for Natural Language Processing: Testing Significance with Multiple Datasets[END_REF] propose a "replicability analysis framework" and demonstrate its use on various tasks such as part-of-speech tagging or cross-domain sentiment classification. They specifically target cases where algorithms are compared across multiple data sets. The results indicate that testing on a range of data sets is only beneficial if the data sets are heterogeneous.

Survey Design

Our survey has 18 questions, of which many were conditional and show only if they apply to the respondent. Thus, not all questions have been answered by all participants, while most multiplechoice questions allow for several answers, resulting in more answers than participants for these questions. Questions are grouped into three categories: (i) replication work in general, (ii) replicating one's own work and (iii) replicating others' work.

General questions quiz participants on their perception of replication work. We also inquire about their current position to investigate potential correlation with other aspects of the survey. Questions addressing participants' replication experience specifically enquired about research artefacts availability (data, code, parameters, etc.) and about the timeline of the replication experience in order to assess attrition.

The survey was advertised on professional mailing lists (BioNLP, Corpora, LN and GLCL 7 ) and social network (LinkedIn). The appendix gives details on the progression of responses. With respect to sensitive data, only e-mail addresses were provided, on a voluntary basis, and we follow the ACM Code of Ethics and Professional Conduct 8 , specifically sections 1.6 and 1.7.

Figure 1 illustrates the flow of the questionnaire. If a person did neither replicate their own or someone elses work, they only had to answer the blue marked questions. If a participant tried to replicate his/her own work, but not someone elses work, they only had to answer the blue and the orange questions. Only persons who have experience in replicating their own and someone elses work had to go through the whole questionnaire, including the green questions. 9 This flow in addition to the possibility to give more than one answer in some questions results in different numbers of answers for each question.

Results

We received 225 responses and the two biggest groups of participants in our study identify themselves as graduate students and postdocs.

With respect to when work on replication has been done, 36 participants (16%) gave more than one anwer, indicating that they did work on replication at various stages of their career. Most answers (50.3%) state that replication was done on MSc or PhD level, less on PostDoc level (20.7%) and slightly more as Faculty members (24.3%). However, we did not find strong correlations between the respondents' position and opinion on the importance (or lack thereof) of reproducibility. Figure 2 shows the absolute numbers for this question, while Figure 3 shows the numbers for the participants current position.

General Stance towards Replicability

The answers show that in 56.4% of the cases, work on replication is considered "Important" and another 7.5% state that it is "Somewhat Important". Only 2 answers indicate that this work is "Unimportant". 20% of the answers regard work on replication as publishable, while 11.8% deem it unpublishable. 87 participants gave more than one answer. The majority (49) consider work on replication as important and publishable, while 26 of them consider it important but not publishable (see Figure 4 for the absolute numbers).

Replicating one's own work

Roughly 70% (156) of the participants declare they have tried to replicate their own work while about 30% have not tried (total 225). 9 Please note that only the most important questions are illustrated here and some questions have been left out.

With respect to how often replication of the same experiment was tried, 15 participants gave more than one answer, giving us 172 answers (see Figure 5 for the detailed figures). Of these, 28.5% indicate that replication was tried only once, while 38.4% tried 3 times or more.

When looking at the last attempt (total answers 234), nearly half (47.0%) report that they reached the same general conclusions, while 23.1% state that they reached the same figures. A little less than 10% report that they managed to reimplement the system, but got significantly different results. Another 14.9% could not find either the code or the data or the parameters used for the experiment (see Figure fig:resultsOwn for the absolute numbers). 52 participants gave more than one answer of which 25 report that they reached the same general conclusions and the same figures. Overall, the results indicate that even in the case when researchers try to replicate their own work, they fully succeed in only 23.1% of the cases.

Replicating others' work

About 60% (total 130) of the participants report that they tried to replicate someone else's work (see Figure 7 for detailed, absolute numbers). 51 respondents gave more than one answer with respect to the results achieved when replicating somebody else's work, resulting in 211 answers. Approximately 40% of the answers state that they reached the same general conclusions or figures, while another 33.6% of the answers state that they managed to re-implement or re-run the system, but with significantly different results. Nearly 23.1% of the responses state that re-implementation or re-runnning of experiments was not achieved (see Figure 8 for the absolute responses for this question). This means that over half of the replication experiments failed, either early on or at the level of results achieved.

Accessibililty of Research Artefacts

For finding research artefacts such as code, data and parameters, respondents gave several answers, resulting in 250 answers for where the code can be found, 260 answers for finding data and resources and 233 answers for finding the experimental parameters. GitHub is by far the most popular (36.4% of the answers) for accessing code, but more than 23.6% of the answers state that code is found on the authors' personal webpage, which does not guarantee availability beyond that person maintaining his/her webpage. More than 14% of the answers report that the code could not found. Data is also primarily published via GitHub or personal webpages (25% and 25.7% of the answers respectively). 11.1% report that the material used for the experiments could not be found. Parameters for experiments are primarily found in the respective publications (40.3% of the answers), while 21.9% of the answers state they could be found on GitHub as well. 13.7% report that they could not find parameters at all. Concerning these three elements, the text box associated with "Other" very frequently mentions "personal communication" or "e-mail" as a way of obtaining necessary information. This gives rise to a range of further issues, legal, ethical and in terms of transparency. Besides, it is only possible if authors actually answer such e-mails. In our survey, 40% of the participants report that they tried to get in touch with the authors (see Figure 12), but only in about 30% of the reported cases received a helpful answer (164 answers received, as 41 participants gave more than one answer). Approximately 20.1% mention that unhelpful answers were received and almost 23.8% never received any answer. Due to evolution of careers, 13.4% found out that the person had left the lab or the e-mail bounced, resulting in almost 40% of examples where authors were unreachable (see Figure 13).

Discussion

The survey results suggest that replicability is perceived as an important issue by a majority of responses (≥ 60%). It is difficult to compute an accurate response rate for the survey, because we do not know the extent of the population comprised by subscribers to the mailing lists and professional networks that we reached out to. However, if we approximate the target population using the average participation in a *ACL confer- ence (N=1,000), we can estimate the response rate at about 20%. This has previously been described as an "acceptable" response rate for online surveys. 10 While the responding population includes researchers with a wide range of seniority as well as members of academia and industry, it could be biased by their interest in replication. The results, and especially the comments, indicate that this is most likely not the case as some participants do not see the value in replicating previous results. They state that replicating previous work is only an "exercise" and actually an "overload" on the already busy researchers' schedule. One comment states that "10 year old systems are irrelevant" and "ML is moving so fast", which renders replicability studies essentially worthless. This could explain why the two largest groups performing replicability studies are on PhD or PostDoc level.

What does this mean for replicability? Responses indicate a variety of views on how replicability should be facilitated. One comment states that there is already a culture of sharing and publishing data and code and this should be enough. Another participant states that in industrial research publishing data or code is difficult, but suggests that the validity of an approach can be proven by applying the method to other data and in reaching the same general conclusions. Some participants support the idea of giving more visibility to replicability by making it a prominent topic at major conferences and by enforcing reporting guidelines towards reproducibility. Some participants mention that replicability is crucial to be taken seriously as a scientific field, even stating that the field is "suspect" if replication fails. One participant suggests that "every paper cited enough times should be replicated".

Conclusions and Future Work

Based on a survey we gave insight into the NLP community's view on replicability. We targeted three different facets of this topic: Authors publishing their work, Researchers building on top of other researchers' work and the Community, supporting such efforts. Our results show that on the authors' side more information has to be shared openly, rather than via personal communication. The use of reporting guidelines formalized into a protocol has been suggested recently for clinical NLP [START_REF] Velupillai | Using clinical Natural Language Processing for health outcomes research: Overview and actionable suggestions for future advances[END_REF]. Earlier studies from the clinical domain suggest that adherence to such guidelines is suboptimal [START_REF] Samaan | A systematic scoping review of adherence to reporting guidelines in health care literature[END_REF] and methods to improve adherence are being investigated [START_REF] Blanco | Interventions to improve adherence to reporting guidelines in health research: a scoping review protocol[END_REF]. The task of creating guidelines falls to the community and the adherence of such guidelines could become part of the reviewing process.

Experiments in replication fail more often than not. If we document and store all relevant information so that results could be reproduced by ourselves (e.g., before the final paper submission), the package could be published completely. Results by [START_REF] Wieling | Squib: Reproducibility in Computational Linguistics: Are We Willing to Share?[END_REF] indicate that images containing all the material or technical lab books published on CodaLab might be a way to proceed. Additionally, failure to replicate previous work (i.e. not achieving the same results and/or not being able to draw the same conclusions as previously reported), should be publishable in a way that gives us scientific merit and could be encouraged more.

Based on the comments, each of us, in all of our individual roles can improve the situation: As authors, we can be more diligent when reporting our experiments and experimental setup-even testing the replicability of our experiments ourselves. As reviewers, we can be more careful to check the supplementary material for relevant information, pointing out missing elements. As a community, we can appreciate replication more and develop guidelines both for authors and for reviewers.

Future Work

The next steps include, but are not limited to, analyzing whether the supplementary material and appendices actually do improve replicability, as stated by [START_REF] Névéol | Replicability of Research in Biomedical Natural Language Processing: a pilot evaluation for a coding task[END_REF]. Furthermore, evaluating the repository offered by [START_REF] Fares | Word vectors, reuse, and replicability: Towards a community repository of largetext resources[END_REF], whether other researchers actually build on top of it and with what results. NAA-CL recently initiated a "test of time" award. This could be extended to consider experimental work that has been cited often and gained influence on a shorter time-scale. This work could be verified for a follow-up conference. Replicability could also become a factor in the best paper awards.

Figure 1 :

 1 Figure 1: Illustration of the questionnaire flow.

Figure 2 :

 2 Figure 2: Position of the participants at the time they were doing replication experiments.

Figure 3 :

 3 Figure 3: Position of the participants at the time of the survey.

Figure 4 :

 4 Figure 4: Importance of Replication in General.

Figure 5 :

 5 Figure 5: Participants who tried to replicate their own work.

Figure 6 :

 6 Figure 6: Results achieved when trying to replicate own work.

Figure 7 :

 7 Figure 7: Participants who tried to replicate someone elses work.

Figure 8 :

 8 Figure 8: Results achieved when replicating someone elses work.

  Figure 9 illustrates the absolute numbers concerning the availability of code, while Figure 10 and Figure 11 illustrate them for other resources and parameters respectively.

Figure 9 :

 9 Figure 9: Sources for Accessing the Code for replication.

Figure 10 :

 10 Figure 10: Sources for Accessing Data and other Resources.

Figure 11 :

 11 Figure 11: Sources for Accessing Parameters for Replication.

Figure 12 :

 12 Figure 12: Participants who state that they reached out to original authors.

Figure 13 :

 13 Figure 13: Quality of Answers by original authors.

We use replication to describe related efforts, regardless of the exact aim (see(Cohen et al.,

2018))2 see for example http://www.acl2019.org/EN/ call-for-papers.xhtml "ACL (. . .) encourages the submission of supplementary material to report (. . .) details necessary for the replication of the experiments."

See: https://coling2018.org/ paper-types/.

This call occurred

weeks after we posted our call and are unrelated, but the latter might be inspired by our survey, see http://wordpress.let.vupr.nl/ lrec-reproduction/.5 "A negative result" http://www.acl2019.org/ EN/call-for-papers.xhtm (Short Papers)

The complete results of the survey are available at https://github.com/replicateNLP/ Survey-RANLP2019. Please note, that due to privacy regulations, we had to remove some free text answers that contain personal information, such as E-Mail addresses, which were given on a voluntary basis.

Biomedical NLP, French and German NLP.

https://www.acm.org/code-of-ethics

http://socialnorms.org/what-is-an-acceptable-surveyresponse-rate/


Jean-Frédéric Brun

Emmanuelle Varlet-Marie

Marlène Richou

Jacques Mercier

E Raynaud

Blood rheology as a mirror of endocrine and metabolic homeostasis in health and disease1