J Malet

M Radosavljevic
email: marko.radosavljevic@irsn.fr

M Mbaye

D Costa

J Wiese

E Gehin
email: gehin@u-pec.fr

FLOW CHARACTERIZATION OF VARIOUS SINGULARITIES IN A REAL-SCALE VENTILATION NETWORK WITH RECTANGULAR DUCTS

Keywords: DUCT, VENTILATION, BEND, DEFLECTOR, T-JUNCTION, DAMPER

Flow characterization in ventilation ducts is important for adequate modelling of contamination transfer in various contexts. Turbulent flow through straight tubes with circular cross-section has, generally, been widely studied, but HVAC networks are quite unlike such ideal cases. Industrial ducts are of large scale, their sections can be rectangular, and include many singularities, such as bends, T-junctions, reducers, valves, etc., which can modify the flow pattern.

The objective of this paper is to study the effect of various singularities on flow in real-scale rectangular ventilation ducts. Flow measurements are performed in a 60 m-long industrial ventilation network (600 x 2 400 mm²) which includes over ten vertical and horizontal bends, one T-junction with a ventilation damper located in the secondary branch, and one section reducer. Horizontal velocity profiles are measured using hot wire anemometry. The effects on the flow of a deflector inserted in a bend, of a damper leak, and of a damper opening are presented using experimental measurement and numerical simulation using ANSYS/Fluent with second-order turbulence models (RSM) validated on a DNS case. These tests form an extensive database for flow measurements at industrial scale, useful for CFD validation, a necessary step before simulating gaseous and particulate flow in ventilation ducts.

INTRODUCTION

Flow characterization and modeling in ducts is important for various applications. The earliest application is probably the quality of the main flow-rate measurement which is dependent on the location of the velocity measurement points in the duct section. Recommendations exist for performing such measurements (international standards ISO 3966, ISO 7145, DIN EN 12599 [START_REF]Ventilation for buildings-Test procedures and measurement methods to hand over air conditioning and ventilation systems[END_REF], Dinardo et al. 2016 [START_REF] Dinardo | How to directly measure the mean flow velocity in square cross-section pipes[END_REF]), generally by taking the measurement in a zone where turbulent flow is assumed established. However, in real-scale applications, flow establishment is difficult to obtain, raising many questions regarding the representativeness of flow-rate measurements in duct flows. The same problem exists for aerosol sampling representativeness, which is still an open field of research.

The second main field of interest for duct flow studies are HVAC systems which are, obviously, the most direct application, whether regarding heat losses for energy consumption evaluation or noise reduction for residential/industrial comfort. HVAC design in the early stages of the building design process also implies a need for adequate modeling of HVAC systems. Indoor air quality, and more recently, with the Covid19 pandemic, SARS-CoV-2 propagation through typical offices and ventilation systems, are other kinds of applications in which duct flow is the basis of aerosol and/or droplet transport and dispersion.

Flow in ventilation ducts is also of primary importance for aerosol transfer in many other industrial applications and/or processes. In nuclear buildings and plants, transfer within ventilation ducts can lead to local accumulation of radioactive material by particle deposition in duct singularities, entailing a radiological risk during maintenance operations on or near these singularities. These deposited particles can also be resuspended and transferred through the same ventilation network, depending on many parameters, among which the turbulent flow characteristics are of primary importance. Quantifying the deposit makes it possible to better assess the impact of the aerosol on the filters by clogging as well. The modelling of aerosol deposition is a subject of many past studies (Sippola and Nazaroff, 2004 [3], Wu and Zhao, 2007 [4], Ben Othman et al. 2011 [START_REF] Othmane | Predicting cleaning time of ventilation duct systems in the food industry[END_REF], Jiang et al. 2011 [6], Lu and Wang, 2019 [START_REF] Lu | Particle deposition in ventilation ducts: A review[END_REF]) and remains a challenging task enhanced by the fact that deposition measurement is not a standard measurement technique (Costa et al. 2022 [8]). This accumulation and resuspension effect is also a concern for biological aerosols in ventilation ducts in food factories, making agribusiness another application for duct flow studies. Other industrial fields involving dust particulate matter transported through ventilation ducts also need adequate description of flow modeling, especially in singularities such as elbows, for risk assessment on sand erosion in the duct in local zones where sand particles mainly impact (Sommerfeld and Lain, 2018 [START_REF] Lain | Stochastic modelling for capturing the behaviour of irregular-shaped nonspherical particles in confined turbulent flows[END_REF]).

In coal-fired power plants which continuously supply pulverized coal to furnaces, coal particles are transported through ducts consisting in numerous bends and straight sections; these changes in flow direction, combined with the large size of the coal particles (10 to 1000 µm) lead to non-uniform particle concentrations, making it difficult to control the fuel droplet supply to individual burners.

Industrial accidents and fires are another type of situation for which good modeling of turbulent duct flow is needed, especially for soot particle transport under extreme temperature conditions which necessarily creates other flow patterns in the duct as well as in the singularities of the ventilation network.

All these applications generally lead to engineering models developed to simulate the performance or losses of a ventilation duct according to the specific case. Afram and Janabi-Sharifi (2014) [START_REF] Afram | Review of modeling methods for HVAC systems[END_REF] present a review of modeling methods for HVAC systems for numerous applications. The French Institute for Radiological Protection and Nuclear Safety (IRSN) develops the SYLVIA code (Chojnacki et al., 2019 [11]) enabling characterization of pressure losses and aerosol (radioactive or soot) deposition in ventilation ducts under normal and accident conditions (fire propagation). This type of engineering modeling requires validation of the various assumptions, hypotheses and simplifications of the phenomena. Validation is obtained through experiments which do not always allow exhaustive characterization of the flow inside the ducts, either because of difficult access to measurement zones, or because of the use of very local (point) measurements that do not allow multi-dimensional validation.

Computational Fluid Dynamics (CFD) can then be a complementary tool for validating the engineering codes, once they themselves have been validated using experimental data. Depending on the application, different types of measurement may be performed for CFD validation types: pressure loss, aerosol deposition, noise reduction, temperature measurements. All of these are sensitive to one main variable: flow velocities and the associated turbulence parameters. In other words, simulation of one of these parameters requires adequate simulation of the flow velocity to avoid errors relating to the simulated phenomena.

Consequently, velocity and turbulence measurements in ventilation ducts are of prime importance and are thus the focus of numerous studies, as will briefly be presented in the State-of-the-Art section below.

However, few such measurements are performed on real-scale ventilation networks comprising several rectangular straight lengths, horizontal and vertical bends of various shapes, T-junctions, reducers, circular-to-rectangular connections, etc.

In this paper, the work is based on a large-scale experimental test facility involving different straightlength ducts (shorter, medium, long), different types of bend (horizontal, vertical, U-shape, S-shape, with/without internal deflector), a T-junction, a symmetrical reducer and a ventilation damper. Part of this facility is designed especially devoted for the study of so-called -typical industrial systems‖, such as internal deflectors often installed in industrial bends, dampers, fire dampers, flexible sleeves, etc. Implementation of Pitot tube, hot wire anemometry, and PIV are available at various points in the facility.

The objective of this paper aims to contribute to flow characterization in large-scale industrial rectangular ducts by performing experiments and associated CFD simulations. The objectives of the measurements performed using such a large-scale facility are manifold:

-To characterize the flow in straight ducts at several points downstream of a singularity.

-To study the flow upstream and downstream of a singularity, such as a bend, a T-junction, and a reducer.

-To study the impact of so-called -typical industrial systems‖ on flow measurements, such as a bend deflector, a damper leak, or a standard ventilation damper in various positions. This paper starts with a presentation of the state of the art regarding past experimental measurements of velocity performed on ventilation ducts. In the second part, presentation of the experimental test bench and the numerical code with its associated preliminary verifications and validations will be given. Results will then be presented, first focusing on a standard geometrical configuration of a ventilation network (straight ducts, bend, T-junction and reducer). The second part of the discussion looks at typical industrial systems (bend deflector, residual leak from a flow damper and a standard ventilation damper).

STATE-OF THE -ART

Many studies exist on flow measurements in ducts but there are not many on large-scale rectangular ducts.

Indeed, such studies generally focus on one or two components (one straight duct, one bend, one convergent section). Most of these are symmetrical (either circular or square cross-section) and studies are generally performed at small scale (few centimeters). For rectangular sections, the focus is generally on large aspect ratios (Hinze, 1973 [12], Rokni et al. 1998 [13]). In addition to real-scale experimental studies, more DNS calculations are being performed, especially on secondary flows in various types of ducts; such results provide a wide range of valuable information (Huser et al., 1993 [30], Gavrilakis, 1992 [31] , Zhang et al. 2015 [START_REF] Zhang | Direct numerical simulation of a fully developed turbulent square duct flow up to Re τ = 1200[END_REF]) on small-scale fictitious ducts.

Table II. Experimental studies on square ducts involving detailed flow measurements

METHODS

This study is based on experimental measurements on a large-scale duct having several singularities such as various types of bends, T-junction and reducers, completed by numerical calculations that can be used to extrapolate the experiments for cases or locations for which experimental data are not available experimentally.

Experimental facility

The experimental facility (Figure 1) is constituted mainly of large-scale rectangular ducts. This network works under aspiration by two blowers (Outlet) allowing flowrates from Q = 3000 to 5000 m 3 /h for the smaller blower, and from 5000 to 12,000 m 3 /h for the larger one. The facility is on three different levels, in four different rooms, allowing for the connection of various instrumentation systems, as well as relatively easy permutations of different parts of the duct. There are three zones specifically designed for changing a given component: the -bend‖ zone, the -system and T-junction‖ zone, and the -reducer‖ zone.

Three flow inlets are available. Through Inlet1, the air is first filtered (H13 Camfil filters, 99.95% filtration efficiency for particles with diameter 0.1 µm); it can be dehumidified down to 20% RH and heated to 20°C above the ambient temperature. Inlet2 is used without filter and dehumidification, but a cm long honeycomb is installed upstream of the same heating system. Last, Inlet3 has only a metallic grid at its entrance (no honeycomb, no filter no dehumidification and no heating). Most of the duct is made up of rectangular sections measuring 40 x 60 cm 2 , the reducer zone allows us to study flow through a 20 x cm 2 duct section; circular sections available at different locations are of 50 cm internal diameter. The overall length is about 60 m. The duct is made of galvanized steel, except some elements which are made of Plexiglas in order to perform laser measurements as PIV.

Velocity profiles are measured by a standard Pitot tube (Pitot tube, KIMO pressure transducer) and a standard industrial hot wire anemometer (KIMO Sauermann) providing the main velocity component.

The locations where the velocity profiles are performed as shown in Figure 1 (right). All the measured profiles are horizontal transverse profiles at mid-height. The number of measurement points per profile is around 30 with refinement on the walls. Each measurement point is averaged over 150 s and sampled at

Hz. The standard deviation on the time average is calculated on each point. Velocity profiles are obtained using a motorized displacement rail for the probe, ensuring the non-rotation of the latter by a manipulator.

Each profile is reproduced at least once for at least one ventilation flowrate. About a hundred profiles have been measured, already providing a large database of results. To our knowledge, despite the simplicity of hot wire measurement, there are no experimental facilities of the same type affording so many velocity profile measurements.

Static pressure measurements are also available at many locations in the facility. Depressions in the ducts can be rather high, up to -3000 Pa in the reduced section LD11.2 downstream of experimental measurement section of the network in order to reproduce real-scale situations. Gas tracer technique is used to calibrate the ventilation flow-rate, by measuring helium concentration using a mass spectrometer: pure helium is injected at a specific location (injection points shown on Figure 1) with a calibrated flowrate, negligeable compared to the main duct flowrate, so that helium is considered as a trace gas and no buoyancy effect occurs; after a mixing zone, helium is considered homogeneous in the duct (this is verified experimentally), so that its concentration at one point can be used, by performing a mass balance,

to

Numerical calculations

The numerical simulations are carried out using the ANSYS / Fluent 19.2 code. The geometry is done using SpaceClaim. The air handling unit and the fan casemate are not integrated in this geometry. The rest of ducts are simulated according to the construction plans. The mesh produced with ANSYS / Meshing is of 17 million elements, the meshes are 6 to 11 mm in length depending on the direction considered, with refinement at the walls. The calculation is carried out for isothermal conditions.

Regarding turbulence, RANS models are known to be inefficient for the characterization of secondary flows, the origin of which is known from turbulence anisotropy. This is illustrated using the standard turbulence models RANS/k- (RNG, Realizable) and RANS/K- models based on preliminary calculations of the DNS case in Zhang et al. (2015) [START_REF] Zhang | Direct numerical simulation of a fully developed turbulent square duct flow up to Re τ = 1200[END_REF]. This case studies flow under a friction Reynolds number Re  of 1200 in a square duct. With these RANS models, close agreement is obtained for the longitudinal flow, but the secondary flows are not recovered. Using RSM modeling, good results for the transverse velocity profiles are obtained (without any dedicated wall modeling, just the -enhanced wall treatment and some dedicated pressure effects‖ of FLUENT), as shown in Figure 2. As a result, RSM modeling is used in the calculations presented here. However, in this paper, our only concern is analysis of the average flow.

Steady state is reached between 6 and 21 s depending on the flow rates. The convergence of the residuals varies between 10 -3 and 10 -4 for the le ss efficient of the equation's highest residuals (generally from continuity equation solving), the other residuals being 10 to 100 times weaker. A Grid Independence

Study was performed once on the whole facility.

RESULTS AND DISCUSSION

General flow considerations

Establishment Length

There are many studies on the length of flow establishment, geared to specific applications. In industry (in ventilation ducts, in chimneys), for positioning instrumentation such as Pitot probes (NFX10-112, ISO 4053-1) or for injecting a tracer for specific characterization (NF X 10-141 [START_REF]Measurement of gas flow in conduits -Tracer methods[END_REF]), the recommended Horizontal profiles of the longitudinal velocity at mid-height are obtained experimentally at location LD10 situated after almost 50 m length of ducts and 9 horizontal/vertical bends and at L/D h = 15.4 downstream of the last bend, (Figure 3). The dissymmetry of this profile at this location is explained by the fact that the flow is not, theoretically, fully developed for all the Reynolds numbers studied. This is observed experimentally as well as in the numerical simulation. However, this location is the point where the mean velocity profile is the closest to the initial flat profile. Figure 4 provides a comparison of this profile (red curve) with that obtained after a straight duct situated upstream of the first bend (yellow curve -given at a different Reynolds number than that one of Figure 3, but the flow similarity is demonstrated on many locations of the facility (see for example Figure 9, bottom figure) : the latter is the location having the longest straight lengths of duct upstream and downstream. For example, the zone L/D h = 18.8 located downstream of the first bend (blue curve in Figure 4) presents a less flat velocity profile than that obtained at L/D h = 15.4 downstream of the entire duct network (red curve in Figure 4). These results simply exhibit the influence of downstream singularities on the flow, which is generally well known, but not always studied in detail.

Bend flows

It has been seen in the previous section how a bend can influence the horizontal component of the mean velocity, even 15D h to 19D h downstream. The detailed evolution of the change in velocity profile downstream of a horizontal bend is given by the numerical calculations in the upper part of Figure 5. Two main parts upstream of a bend can be considered: up to a length of 3D h , where the flow in the inner curvature zone (the so-called intrados) changes downstream of the recirculation zone, and from 3D h , where the velocity profile very slowly returns to a flat profile. These numerical results downstream of a Considering the flow upstream of a bend, the influence is less significant but should also be noted, as presented in Figure 6 for simulations and experiments. The maximum velocity shifts from one side of the duct (intrados) to the other (extrados). Again, the numerical results are in close agreement with the experiments. It should also be emphasized that, compared to a square duct or a circular pipe, these results on the influence of a horizontal bend are given here for the horizontal profile of the velocity at mid-height and cannot be extrapolated to the vertical profiles (no symmetry). This is confirmed by analyzing the results of a horizontal profile immediately downstream of a vertical bend (Figure 7). In both the simulation and the experiments, the velocity profile remains almost flat. The vertical profile could not be measured at that point, but it should, for symmetry and self-similarity reasons, be, very close to the bottom left one of

T-junction flows

The flow in a horizontal T-junction (Figure 8) can also be studied in this facility, considering one main incoming branch (MInB), a perpendicular secondary incoming branch (SInB) and the outlet branch (OutB). Numerical results as well as one code-experiment comparison are presented in Figure 9. It is interesting to see some similarity for the flow in a bend and the one in a T-junction : this can be observed by comparing left graph of Figure 9 for the flow downstream of a T-junction and the left graph of Figure 5 for the flow downstream of a horizontal bend. The effect of the velocity sink due to the curvature of the duct is observed on a larger transverse zone (up to X/X max = 0.2) for the bend than for the T-junction (up to X/X max = 0.1): in the latter, the flow of the incoming branch avoids the larger effect observed in a bend. This observation is made for all incoming flows and is found to be self-similar in the simulations as well as in the experiments (Figure 9 In the case of gas transfer in the main line of the T-junction, the secondary junction involves a change in the gaseous concentration. A heterogeneous concentration field can then be obtained, as illustrated in

EXP -Q1 EXP -Q2 EXP -Q3 EXP -Q4 EXP -Q1 -R EXP -Q2 -R EXP -Q3 -R EXP -Q3 -R Profil transverse horizontal X/Xmax (-) U/Umax (-) 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1 1.2 EXP -Q1 EXP -Q2 EXP -Q3 EXP -Q4 EXP -Q1 -R EXP -Q2 -R EXP -Q3 -R EXP -Q3 -R Profil transverse horizontal X/Xmax (-) U/Umax

Reducer flow

The last part of this facility comprises a reducer section with the duct narrowing from 0.4 m x 0.6 m cross-section (D h = 0.48 m) to 0.2 m x 0.3 m cross-section (D h = 0.24 m). The reducer component is symmetrical, centered on the centers of the upstream and downstream sections, and at a 45° angle with the axis of the duct. Since the velocity profile upstream of this reducer is almost flat for a flow Reynolds number of 3.4 10 5 (Figure 3), the profile downstream of the reducer (L/D h = 5.7) remains flat, as presented in Figure 12. Even if this result can be considered as expected, it should be emphasized that the reducer section does not result in any enhancement of the slight dissymmetry present upstream of the reducer.

Influence of specific industrial features on the flow

In this section, typical industrial features, such as an inner bend deflector or a ventilation damper as well as a T-junction (Figure 13) will be studied and their influence on the flow discussed.

Bend deflector

In industrial ventilation networks, it is generally considered that a so-called deflector (Figure 13), inserted in a duct, is favorable to ensuring turbulence and mixing of the flow. Several bends with a deflector are

1.2 U -LD11-2 -Q = 3200 Nm3/h -03112021_1 X/Xmax U/U_max
available in this facility. Experimental measurements are performed just downstream the deflector (Figure 14) and numerical calculations are given at the same location but without a specific modeling of the deflector. Experimental results show a clear effect of the deflector, and the effect is found to be selfsimilar. It can also be noticed that the effect of the deflector on the mean flow is no longer observed at L/D h = 8 downstream (Figure 15).

Leak in a ventilation damper

Various classes of ventilation dampers (Figure 13) can be found in ventilation networks, classed according to intrinsic leakage level. In this facility, a Class C damper (EN 1751 standard) is tested in order to evaluate the flowrate, and as a result the velocity obtained downstream of a closed damper located upstream of the secondary branch of the T-junction. Results are presented in Figure 16, for the minimum and maximum flowrates studied here, i.e., for different depressions occurring inside the Tjunction and involving aspiration through the closed damper. It can be seen that the residual leakage velocities are non-negligible and that the flow is highly fluctuating. To confirm the orientation of this leakage, helium is injected upstream of the damper and the measured helium concentration profile is almost a flat profile for the highest ventilation flowrate in the main incoming branch of the T-junction (Figure 17). These helium concentration measurements, knowing the injection flowrate of 20 l/min at the entrance of the T-junction allows also to calculate the duct ventilation flowrate in the secondary incoming branch, i.e., the leakage flowrate. This is done using the gas tracer technique described in Section 3.1. The damper leakage flowrate found from those helium concentration measurements is the used for numerical simulations. Figure 18 shows the code-experiment comparison of the velocity in the secondary incoming branch: the numerical simulations performed with a leakage flowrate through the damper are in better agreement with the experimental data than the ones considering a tight damper.

Impact of a ventilation damper on the flow

A ventilation damper (Figure 13) is made up of different blades to form a specific angle with the duct axis, between 90° (closed damper) and 0° (fully open damper). Its purpose is to modify the flowrate by increasing the pressure loss when this angle is changed. Despite the fact that the damper blades should generate strong turbulence and mixing, the opposite effect is observed in our experiments. A tracer gas is injected (see the injection points on Figure 1) over a 10 mm internal diameter tube centered on the duct section in a co-current manner. Concentration profiles are measured at around 10D h upstream of the injection point. It can be observed that, downstream of the ventilation damper, the turbulent fluctuations are much higher than at all other measurement locations (Figure 20) and that the expected almost-flat profile is hard to obtain. This result probably depends on the type of damper, i.e., on the number of blades, shape, and the flowrates, etc. The conclusion from these first results is that attention should be paid to the flow downstream of a damper since heterogeneity can be obtained at a much higher rate than expected.

CONCLUSION

In this paper, we have studied the characterization of the flow in various singularities of large-scale industrial ducts. The first specific feature of our study, in addition to the size of the real-scale experimental facility with 0.6 m x 0.4 m ducts measuring over 60 m in length, is that it is based on numerous experimental measurements combined with CFD simulations of the flow performed using second-order turbulence modeling (RSM), which enables anisotropy to be taken into account. In this paper, the focus is mainly on mean variables, but the metrology of this facility makes it possible to go further in the future and include PIV and high-frequency hot wire anemometry. The simulations have first been validated for a DNS case, and numerous code-experiment comparisons are given in this paper, enabling CFD calculations with RSM turbulence modelling to be used as a prospective tool for investigating flow in zones without instrumentation.

A specific study on straight lengths shows that in such real-scale applications, flow establishment is never rigorously obtained because of both upstream and downstream singularities. However, the velocity profile at 15D h is found to be almost flat in this facility. Flow downstream of a bend is also studied in this paper.

Even if many other studies can be found in the literature on bend flows, this is, to our knowledge, the first research at such a scale and with such detailed measurements, on horizontal as well as vertical bends. The influence of a specific industrial component, the deflector inserted inside a bend, is shown experimentally and the velocity profiles are found to be strongly impacted by such a deflector up to 8D h . This result is not found in previous studies. Considering, for example, that some measurement components, such as Pitot Industrial Probes, can be installed in a shorter zone downstream of a bend with a deflector, numerous errors can be obtained in flow measurements in the presence of a deflector. A horizontal T-junction is another singularity investigated in this paper, which is rather a rare component to be studied in ventilation ducts. Flow measurements in T-junction outlets exhibit some similarity with a bend outlet; this observation could be used in future studies on engineering modeling of such flows, even if the flow distribution between the T-junction branches should be a further parameter to consider. The last singularity considered in this paper is a ventilation damper which, first, is found to have a consequent impact on the downstream flow pattern when closed (a damper is never perfectly sealed), and second, shows significant variations in concentration homogeneity downstream.

The database of experimental data acquired using this large-scale ventilation duct is important and is continuously growing. It can also be used for benchmarking activities in the field of flow simulation for mechanical ventilation. The code-experiment validations presented in this paper give some confidence in prospective use of the numerical simulations to study in more detail specific features, such as the effects of the bend curvature or the flow repartition in a T-junction. The results can also serve as the basis for flow validation before studying many other physical phenomena which depend on the flow, such as gas dispersion and aerosol deposition in ventilation ducts. This database could be enlarged with turbulence variables using transparent singularities coupled with PIV measurements.

  U m , I turb U m at 1 mm from the walls U m : mean velocity, U velocity, I turb turbulence intensity, SD : Straight Duct, R c : turning radius, CB : curved bend, SF: secondary flows, HW: Hot Wire, PT: Pitot TubeTable III. Experimental studies on rectangular straight ducts involving detailed flow measurements U long , vorticity, vector-files U transv S: surface of the cross-section

  Figure 7 for LD6.1, and Figure 10 for LD6.4. Self-similarity of the longitudinal component of the mean

Figure 1 :

 1 Figure 1: Overall view of the experimental facility (up) and location of the measurement zones (down) -see also Figure 8 for the T-junction zone

Figure 2 :

 2 Figure 2 : Zhang et al. (2015) [32] DNS test case compared to two RANS modeling and the RSM

Figure 3 : 3 .4 10 5 Figure 4 :

 3354 Figure 3: Horizontal profiles of the longitudinal velocity at mid-height at L/D h = 15.4 downstream of the last bend CD9 (LD10): code-experiment comparison (left), repeatability study (right) -Re = 3.4 10 5

Figure 5 :

 5 Figure 5: Horizontal component of the mean velocity profile at different distances downstream of a horizontal bend at mid-height at Re = 3.4 10 5 : upper figures, simulations downstream CD2, bottom figures, codeexperiment comparison downstream of CD1 at LD2.1 (L/D h = 0.26) and LD2.2 (L/D h = 2.5), IC 95%

Figure 6 :

 6 Figure 6: Horizontal component of the mean velocity profile at different distances upstream of a horizontal bend CD1 -left, simulation at LD1.4av: L/D h = -7.8, LD1.4am = L/D h = -0.26, LD1.1: L/D h = -10.2), right: code-experiment comparison at L/D h = -7.8; Re = 3.4 10 5 , IC 95%

Figure 5 .

 5 Figure 5.

Figure 7 :

 7 Figure 7: Horizontal component of the mean velocity profile at LD6.1: L/D h = 0.26 downstream of a vertical bend, code-experiment comparison, Re = 3.4 10 5 , IC 95%

  , bottom figure). Changing the flow in the SInB results in a change to this -typical bend flow profile‖ in the so-called ‗intrados' (inner part of the flow curvature) between the SInB and the OutB. Such results indicate how complicated the flow in a T-junction can be, depending on the main incoming branch, the characteristics of the bend formed from the SInB and the OutB of the Tjunction, and the flow repartition between the MInB and the SInB.

Figure 8 :Figure 9 :

 89 Figure 8: T-junction representation (left) and simulated field of the velocity magnitude at mid-height of the duct section (right)

Figure 10 :

 10 Figure 10: Horizontal component of the mean velocity profile for different flow repartition in the SInB of the T-junction; Left : Re MInB = 3.2 10 5 and Re SInB = 1.8 10 5 , Right : Re MInB = 8.9 10 4 and Re SInB = 3.4 10 5 -profiles measured at LD6.4: L/D h = 2

Figure 11

 11 Figure 11.

Figure 11 :

 11 Figure 11: Effect of a secondary branch of a T-junction on gaseous concentration profile: concentration profile upstream of a T-junction at LD6.1 (L/D h = 0.26) on the left and downstream at LD6.4 (L/D h = 2) on the right

Figure 12 :

 12 Figure 12 : Horizontal component of the mean velocity profile downstream of the reducer section (LD11.2 -L/D h = 5.7)

Figure 13 :

 13 Figure 13: Inner deflector in an industrial horizontal bend CD2 (left) and ventilation damper in an open position (right)

Figure 14 : 26 Figure 15 :

 142615 Figure 14: Horizontal component of the mean velocity profile downstream of the bend, showing the experiment with an inserted deflector in the bend on the left, and the simulations without any bend on the right -LD9 at L/D h = 0.26

Figure 16 :Figure 17 :Figure 19 :

 161719 Figure 16: Horizontal component of the mean velocity profile downstream of a closed Class C

Figure 20 :

 20 Figure 20: Effect of a damper on concentration fluctuations: top: at LD1.1, without damper upstream, bottom left: at LD12 (L/D h = 10) with a damper half open upstream bottom right: at LD12 (L/D h = 10) with a damper 100% open

  dimensional distance in the duct, having its origin at the outlet of the singularity located just upstream/downstream of the considered length MInB : indices for Main Incoming Branch of a T-junction OutB : indices for outcoming Branch of a Tbased on the duct hydraulic diameter and the duct mean velocity Re  : Reynolds number based on the duct hydraulic diameter and the friction velocity

Table I

 I

	duct is measured by Geropp and Odenthal (2002) [14] in order to compare the results to a velocity law.
	Sudo et al. (1998) [15] and Kalpakli and Orlu (2013) [16] performed measurements of velocity profiles
	inside a bend, at various locations, with the objective of observing secondary flows by measuring
	transverse components. Circular U-bend studies are presented in Azzola et al. (1986) [17] and Sudo et al.
	(2000) [18] where longitudinal measurements are performed. Other studies focus on more complex bend
	singularities, such as Caré et al. (2014) [19] who study co-planar and non-co-planar bends, and Sleiti et
	al. (2017) [20] who work on close-coupled bends. A wide range of measurement techniques is used in
	these studies, Pitot tube, hot wires, laser Doppler velocimetry, and Particle Image Velocimetry (PIV).
	presents several experimental studies involving detailed flow characterization performed on
	circular ducts of sizes generally lower than 20 cm diameter. A longitudinal velocity profile in a straight

Table I . Experimental studies on circular ducts involving detailed flow measurements Authors Duct shape Duct size (D h R c , L) Exp. method Reynolds Location of measurements Enayet et al. (1982) [21]

 I

	SD, L = 0.48 m,	D h = 4.8 cm	LDA	4.3 10 4	U Profiles at 45° and 90° of a
	90-bend	R c = 3.4 cm			CB

Azzola et al. (1986) [17]

	U-bend	AR=6.75	LDA	5.74. 10 4	over z, between 90° to z/D =
				11. 10 5	5

Sudo et al. (1998) [15] 90

	-bend, L u =10	D h =10.4 cm	HW	6.10 4	z/d=-1  z/d=5
	m, L d = 4.2 m	R c =20.8 cm	SP on
			walls

Sudo et al. (2000) [18]

	U-bend	D h =10.4 cm	HW	6.10 4	21 points inside the U
		R c =20.8 cm

Geropp and Odenthal (2002) [14]

	SD, L = 6.08 m	D h =7.6 cm	LDA, SP	1.49 10 5 1.86 10 5

Longitudinal profile Kalpakli and Orlu (2013) [16]

	bend	D h =6.03cm	Stereo PIV HW	1.4 10 4 to 3.4 10 4
		R c =1.58 D h

Three profiles and transverse fields Caré et al. (2014) [19]

	2 co-planar and 2	D h =20 cm	PT	2 10 5	10-point profiles at z/d = 1,
	non-coplanar
	bends				4, 10 and 45

Sleiti et al. (2017) [20]

	components are available in the open literature, but there are only a few experiments on the experimental
	characterization of secondary flows. Demuren and Rodi (1984) [22] synthetize most of the very first
	experimental studies on secondary flows in non-circular ducts. Launder et al., (1972) [23], Gessner et al.,
	(1979) [24] and Kliafas and Holt (1987) [25] and others listed in Table II present experimental data,
	generally for straight ducts but also sometimes correlated with bend flow studies. Further studies on
	rectangular ducts are detailed in Table III, such as Melling and Whitelaw, (1976) [26], Fujita et al., (1989)
	[27], Knight et al., (1985) [28], Maeda et al., (2005) [29]. Regarding the configurations of the rectangular
	channels, studies are rather limited in number over the last forty years: experimental studies either focus
	on straight length or on one bend: none of the experiments consider several singularities in the same
	Close-coupled bends (Z and U-	D h =30.5 cm R c =1.5 D h	PT -Five-hole U-	3.3 10 5 to 3.6 10 5
	shape)		probe
	Key --AR: Aspect Ratio, PIV: Particle Image Velocimetry, LDA: Laser Doppler Anemometry, HW: Hot Wire, PT:
	Pitot Tube, SP: Static Pressure measurement, L u : upstream Length, L d : downstream Length, D h : hydraulic Diameter, R c :
	curvature Radius, z: longitudinal direction, r: radial direction
	Experimental studies in square ducts and rectangular ducts (Table II and Table III) are mainly performed
	with hot wire and LDA measurements. It can also be noted that measurements of the longitudinal flow

facility. Furthermore, these experimental studies are performed on academic scales, ranging between a few centimeters up to 15-25 cm.

Table 4 : Parameters of the different tests and flow establishment lengths

 4

	Q codification name	Q (m 3 /h)	U m (m/s)	Re (-)	L e (m)	L e / D h
	Q4	3100	3.6	1.1 10 5 11.7	24
	Q1	5050	5.8	1.9 10 5 13.2	27
	Q2	7850	9.1	2.9 10 5 14.7	31
	Q3	9272	10.7	3.4 10 5 15.4	32

Acknowledgements

The authors would like to thank the R. Rossignol and D. Hare for their contribution to some of the Tjunction characterization data.

Impact of flow repartition in a T-junction

Considering that numerous simulations of the flow in this duct network have already been well validated on experimental data (part of them are presented in this paper), numerical simulations have been used to study the influence, on the velocity profile, of the flow repartition between the main incoming branch and the outcoming branch of a T-junction.

It can be observed in Figure 19 that when the flowrate in the secondary incoming branch becomes higher than the flowrate in the main incoming branch (Q OutB = 3 Q MInB , so that Q SInB = 2Q MinB ), the typical bend recirculation zone (Figure 5) is observed, as already discussed in section 4.1.3 (Figure 9). It can be concluded that the flow in a T-junction is a clear mixing of a bend flow and a straight flow and that this mixing depends on the flow distribution. A more detailed study on T-junction flows is thus needed in order to consider the shape of the T-junction as well as flow distribution in the branches.


est destinée au dépôt

  Estimation of the diffusion coefficient of hygroscopic materials using a contactless transient THz water vapour content imaging and excitation device M. Bensalem, Alain Sommier, Jean-Christophe Mindeguia, Jean-Christophe Batsale, Christophe Pradere To cite this version: M. Bensalem, Alain Sommier, Jean-Christophe Mindeguia, Jean-Christophe Batsale, Christophe Pradere. Estimation of the diffusion coefficient of hygroscopic materials using a contactless transient THz water vapour content imaging and excitation device. International Journal of Heat and Mass Transfer, 2023, 208, pp.124064. 10.1016/j.ijheatmasstransfer.2023.124064. hal-04099768


Adrien Berquer

Vincent Bretagnolle

Olivier Martin

Sabrina Gaba
email: sabrina.gaba@inrae.fr

Disentangling the effect of nitrogen input and weed control on crop-weed competition suggests a potential agronomic trap in conventional farming

Keywords:

Weeds are commonly assumed to induce yield loss because of resource competition. However, there is growing empirical evidence that the picture is much more complex, because fertilizer inputs, by modifying the level of resources and weeding by removing some weed species, affect the outcome of crop-weed interaction. We assess how two important crop production inputs -nitrogen (N) fertilization and weed-control -affect a fundamental non-chemical means of weed management, the outcome of crop-weed competition, in real field conditions in 56 winter cereal fields, of which 23 were organically farmed. We used a factorial design with two levels (absence/ presence) of nitrogen input and weed control inputs, but in our case, the "control" (i.e., presence level) for both practices was the usual practice of the farmer (which therefore varied). We found that crop aboveground biomass and grain yield were positively related to the amount of N total (N soil plus N fertilizer), while weed species assemblages were negatively affected, showing lower species richness and weed abundance (i.e., number of plants). We also detected a contrast between farming systems: conventional fields (CF), managed with higher amount of total N and weed control, showed higher crop biomass and grain yield, and lower weed abundance compared to organically farmed fields (OF). Importantly, the findings showed that the outcome of the competition between crops and weeds was largely in favor of the crop plants in CF fields, even in the absence of weed control. In OF fields, the outcome of the competition between weeds and crop plants was still largely in favor of the crop, but at a lesser extent than in CF fields. The patterns were similar in unfertilized plots, though weed control in CF fields was more effective at low amounts of N, suggesting that more intense weed control is required in N-rich fields to maintain crop production. Overall, we argue that these results may underlie an agronomic trap: while an increased supply of nitrogen generally increases crop yield, it also benefits to weeds, requiring more efficient weed control.

Introduction

A major priority in the agroecological transition concerns pesticide reduction, since pesticides negatively affect agroecosystem biodiversity [START_REF] Geiger | Persistent negative effects of pesticides on biodiversity and biological control potential on European farmland[END_REF]. But despite numerous government incentives, pesticide useand especially herbicideshas not significantly decreased over the last ten years [START_REF] Möhring | Pathways for advancing pesticide policies[END_REF], hence impeding any major recovery of biodiversity in agroecosystems. Indeed, weeds can also play an important role in maintaining ecosystem services such as pollination and biological control [START_REF] Bretagnolle | Weeds for bees? A review[END_REF][START_REF] Marshall | The role of weeds in supporting biological diversity within crop fields[END_REF]. One reason for persistent herbicide use is that weeds have long been viewed as a limiting factor in crop production.

They are considered as major pests as weeds can reduce wheat yields by 23 % (potential loss) or 7 % (actual loss), depending on weed species [START_REF] Oerke | Crop losses to pests[END_REF]. Thus weeds are intensively managed by farmers with a combination of agricultural techniques, including tillage and, above all, herbicide application [START_REF] Tilman | Agricultural sustainability and intensive production practices[END_REF]. The latter has environmental costs on ground and surface water [START_REF] Kudsk | Herbicidesa two-edged sword[END_REF], biodiversity [START_REF] Geiger | Persistent negative effects of pesticides on biodiversity and biological control potential on European farmland[END_REF] and human health [START_REF] Wilson | Why farmers continue to use pesticides despite environmental, health and sustainability costs[END_REF]. Therefore, reducing the use and risk of herbicides is a complex issue, currently stifling the agroecological transition, i.e., moving towards farming systems that enhance natural regulations (i.e. natural pest control) and ensure for food security, farmers welfare and biodiversity conservation [START_REF] Altieri | Agroecology: The Science of Sustainable Agriculture[END_REF].

Weed regulation through crop competition may be a sustainable alternative option to herbicides [START_REF] Sardana | Role of competition in managing weeds: an introduction to the special issue[END_REF], but relies on better knowledge of crop-weed competition. For long studies have focused on reducing the impact of weeds on crop production, i.e., the effects of crop-weed competition on the crop [START_REF] Zimdahl | Definition of plant competition[END_REF]. In arable fields, crop plants are dominant competitors, are enhanced by nitrogen (N) supplywhich improves their competitive ability -, establish early in the season, and are sown at very high density [START_REF] Gaba | Agroecological weed control using a functional approach: a review of cropping systems diversity[END_REF]. Studies that have investigated crop-weed competition from the crop viewpoint have mostly used pairwise crop-weed species interactions involving generally only one weed species [START_REF] Kristensen | Crop density, sowing pattern, and nitrogen fertilization effects on weed suppression and yield in spring wheat[END_REF][START_REF] Olsen | Increased density and spatial uniformity increase weed suppression by spring wheat[END_REF]; but see [START_REF] Gibson | The weed community affects yield and quality of soybean (Glycine max (L.) Merr.)[END_REF]Gaba et al., 2018 for exceptions). However, in reality, crop plants in arable fields interact with multiple weed species, and the competitive interactions between the crop and weeds are diffuse and vary with the competitive ability of the weed species [START_REF] Blackshaw | Nitrogen fertilizer timing and application method affect weed growth and competition with spring wheat[END_REF][START_REF] Blackshaw | Nitrogen fertilizer rate effects on weed competitiveness is species dependent[END_REF]. Furthermore, few studies were conducted in real fields, monitoring weed flora and using experimental designs allowing to assess crop-weed competition [START_REF] Colbach | The pitfalls of relating weeds, herbicide use, and crop yield: don't fall into the trap! A critical review[END_REF], and even fewer were conducted with farmers in their real farmed conditions [START_REF] Gaba | Social-ecological experiments to foster agroecological transition[END_REF]. However, results from experimental research units are likely to differ from those from real farms since they do not account for variability in farmers' decision-making, local pedo-climatic conditions or landscape context.

Crop-weed competition is affected by farming practices, such as weed control (including both herbicide application or mechanical weeding) or the increase of N availability, since weed control and nitrogen fertilizers affect weed diversity [START_REF] Fried | Environmental and management factors determining weed species composition and diversity in France[END_REF][START_REF] José-María | Effects of agricultural intensification on plant diversity in Mediterranean dryland cereal fields: agriculture intensity & plant diversity[END_REF][START_REF] Moss | Symposium The Broadbalk long-term experiment at Rothamsted: what has it told us about weeds[END_REF]. High level of N supply may favor weeds over crop plants since fertilizers promote nitrophilous weeds with strong competitive ability [START_REF] Berger | Does soil nitrogen affect early competitive traits of annual weeds in comparison with maize[END_REF][START_REF] Iqbal | Effects of nitrogen supply on competition between wheat and three annual weed species[END_REF][START_REF] Moreau | The ecophysiological determinants of nitrophily in annual weed species[END_REF]. However, there is no consensus on how nitrogen input affects the crop-weed competition. Several studies revealed a disadvantage of weeds in N-rich environments [START_REF] Blackshaw | Nitrogen fertilizer rate effects on weed competitiveness is species dependent[END_REF][START_REF] Di Tomaso | Approaches for improving crop competitiveness through the manipulation of fertilization strategies[END_REF][START_REF] Iqbal | Effects of nitrogen supply on competition between wheat and three annual weed species[END_REF][START_REF] Van Delden | The influence of nitrogen supply on the ability of wheat and potato to suppress Stellaria media growth and reproduction[END_REF] while others showed that excessive N input may translate into higher potential yield loss [START_REF] Moss | Symposium The Broadbalk long-term experiment at Rothamsted: what has it told us about weeds[END_REF], i.e., weeds acquiring N at higher rate than the crop [START_REF] Blackshaw | Differential response of weed species to added nitrogen[END_REF][START_REF] Harbur | Response of three annual weeds to corn population density and nitrogen fertilization timing[END_REF]. The rate, the timing and application method of N input can affect crop competitive ability, hence the potential for crop plants to regulate weeds [START_REF] Abouziena | Effect of nitrogen rates and weed control treatments on maize yield and associated weeds in sandy soils[END_REF][START_REF] Cathcart | Nitrogen management will influence threshold values of green foxtail (Setaria viridis) in corn[END_REF][START_REF] Primot | Predicting the risk of weed infestation in winter oilseed rape crops[END_REF].

Weed control, either chemical or mechanical, removes weed plants or injures weed seedlings, and is thus expected to favor crop plants [START_REF] Chauhan | Effect of tillage systems and herbicides on weed emergence, weed growth, and grain yield in dry-seeded rice systems[END_REF][START_REF] Melander | Integrating physical and cultural methods of weed controlexamples from European research[END_REF]. However, weed control may enhance the abundance of competitive weeds by filtering species [START_REF] Fried | Trajectories of weed communities explained by traits associated with species' response to management practices[END_REF][START_REF] Gaba | Herbicides do not ensure for higher wheat yield, but eliminate rare plant species[END_REF] hence increasing the magnitude of the competition of weeds on crop plants. Finally, the efficacy of weed control may vary with N input. The relative competition ability of oilseed rape against weeds was shown to be improved by herbicide application especially at higher N levels [START_REF] Wang | Herbicide and nitrogen rate effects on weed suppression, N uptake, use efficiency and yield in winter oilseed rape (Brassica napus L.)[END_REF]. Better understanding how weed control and N fertilization affect the outcome of crop-weed interactions can help farmers enhance crop competition as a means of non-chemical weed management. Studying competition in real field conditions is however complex, and requires to tease apart potential confounding factors.

In this study, we experimentally explored crop-weed competition and how it is affected by the presence and absence of fertilizer input and weed control in 56 farmed winter-cereal fields selected along a gradient of management intensity, based on the amount of nitrogen provided by farmers and their weed control intensity (i.e., number of herbicide applications and/or of mechanical weeding). Our design included organically and conventionally farmed fields to cover a wide gradient of management intensity and to understand the differential effects of chemical and mechanical weed control on crop-weed interaction. In each field, we implemented a factorial experimental design, combining the presence or absence of nitrogen input during crop growth with the presence or absence of weed control. In each experimental plot, we quantified the separate and combined effects of weed control and fertilizer input on the competitive outcome between the dominant species (the crop) and the weed species assemblage (i.e., all the species that were found in a plot), as well as its consequences on yields. We first explored changes in crop biomass, weed diversity, weed abundance and weed biomass along the gradient of the amount of N both in the presence and absence of weed control at two key periods of the cropping season: crop flowering and crop harvest. Second, by using different indices to measure competitiveness, either on the side of weeds or crop plants, we quantified relationships between the competitive outcome and the N resource interacting with weeding pressure. Finally, in order to disentangle the effect of N input from the effect of weed control, we focused on the unfertilized plots and analysed changes in crop biomass, weed diversity, abundance and biomass, as well as weed-crop interaction along a gradient of the amount of N in soil, in the presence or absence of weed control.

Material and methods

Study site and experimental design

The study was performed in 2013 and 2014 in winter cereal fields in the Long-Term Social-Ecological Research (LTSER) 'Zone Atelier Plaine & Val de Sèvre' located in the south of the Deux-Sèvres district (46 • 23 ′ N,0 • 41 ′ W) in the Nouvelle-Aquitaine region in France [START_REF] Bretagnolle | Description of long-term monitoring of farmland biodiversity in a LTSER[END_REF]. This agricultural landscape is dominated by intensive cereal production, as well as winter oilseed rape, maize and sunflower. Crops grown are mainly winter cereals (38.2 %) with 34.8 % wheat and 3.5 % barley, winter oilseed rape (8.3 %), corn (9.6 %), sunflower (10.4 %), but also meadows and alfalfa fields (12.3 %) and about 10 % of woods and built-up. We chose to conduct the study in real farming conditions to evaluate the studied effects over a wide range of weed species assemblages and farm management strategies. The fields and farms were selected to provide a representative range along a gradient of management intensity depending on farming practices that included N fertilizer application and weed control (see also [START_REF] Gaba | Crop competition in winter wheat has a higher potential than farming practices to regulate weeds[END_REF]. The experiment was conducted in 56 farmed fields (16 in and 40 in 2014), of which 23 were farmed organically. Four winter cereals with similar agronomic characteristics were used by farmers i.e., winter wheat (42 of which ten were farmed organically), barley (one in conventional farming and four in organic farming), spelt (four in organic farming) and triticale (four in organic farming). Within each field, in addition to the farming intensity gradient, we set up a two-factor experimental design to manipulate the presence or absence of nitrogen input and the presence or absence of weed control (i.e., herbicide sprayed in CF fields, and mechanical weeding in OF fields). The farmers themselves implemented the treatments, following their standard practices. Therefore, in plots receiving N or weed control in a given field, the amount of N applied and the type and intensity of weed control were that used by the farmer in the rest of the field [START_REF] Gaba | Social-ecological experiments to foster agroecological transition[END_REF]. Otherwise, in plots not receiving N or weed control, farmers cut the spreader/sprayer, or lift the harrow on the corresponding plots. The experimental area varied between 150 and 200 m 2 and was divided in four areas corresponding to each experimental modality alone and in interaction (Fig. 1d). In 2013, the experimental plots were in the first m of the field, and in 2014 in the center of the field (for further details see [START_REF] Catarino | Experimental and empirical evidence shows that reducing weed control in winter cereal fields is a viable strategy for farmers[END_REF][START_REF] Gaba | Crop competition in winter wheat has a higher potential than farming practices to regulate weeds[END_REF][START_REF] Gaba | Social-ecological experiments to foster agroecological transition[END_REF]. The experiment started each year when the crops were sown and ended at crop harvest. At the end of the experiment, we interviewed the farmers to collect data on their agricultural practices: the amount and type of agrochemicals (fertilizers and pesticides) applied and the number and type of soil operations. Inorganic nitrogen is rapidly available to plants, hence the quantity of nitrogen used was directly calculated according to the fertilizer composition and the respective quantity applied. Organic fertilizer sources were of various forms of organic fertilizers: organic liquid or solid manure, litter, compost, animal by-products. Since organic nitrogen has to go through mineralization in order to be converted into its inorganic forms, the quantity of nitrogen mineralized in the organic fertilizers was calculated following [START_REF] Jeuffroy | Azodyn: a simple model simulating the date of nitrogen deficiency for decision support in wheat fertilization[END_REF]. The soil characteristics (% of clay, sand and silt; content of organic matter) and the amount of nitrogen content in the soil (N soil) were estimated from soil samples (mixture of three soil cores 15-20 cm in depth) collected at the end of January in each experimental plot. Analyses were carried out by the accredited INRAE Soil Analysis Laboratory (Arras, France: COFRAC accredited). We defined available N as the sum of N present in the soil in late January (as measured in soil samples) plus N input provided by the farmer during crop growth (after January). Because crop plants were sown late October, our estimate of N present in the soil in January therefore accounted for the uptake of crop plants between October and January, though it is limited (i.e., crop plants being at tillering stage).

Weed and crop sampling

In each of the four experimental areas, two 1 m 2 sampling plots were placed 2 m from the edge to avoid border effect. At crop flowering (end of May) and at harvest (early July), weed species identity and abundance were recorded in one of the sampling plots (Fig. S1; see also details in [START_REF] Gaba | Crop competition in winter wheat has a higher potential than farming practices to regulate weeds[END_REF]. At crop flowering, weed and crop aboveground biomass were estimated by harvesting 0.36 m 2 in one of the two sampling plots at crop flowering. At harvest, weed aboveground biomass and crop grain were sampled in the entire 1 m 2 plot in the remaining sampling plot. Both dead and living weed plants were collected. Plant samples were oven-dried at 80 • C for 48 h and weighed for biomass estimation. The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively. Because of nestedness, we cannot separate whether the effect comes from the intercept or the covariance. The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). (C) Predicted values of crop biomass and grain yield in CF (blue) and OF (green) fields for the threshold value of 120 kg.ha -1 of N fertilizer. SEs are shown. (D) Schematic representation of the experiment with the four treatments presented.

Statistical analysis

In a first step, we examined the effects of N total (N input plus N soil ), as a continuous variable, on crop and weed plants using linear models, in presence or absence of weed control treatment (one model per modality). We first tested these effects on crop aboveground biomass and grain biomass, respectively collected at crop flowering and at harvest in fertilized plots. We accounted for the type of farming system (OF vs CF) by including N total statistically nested within the farming system in the models. As we found N total in OF to be much lower compared to that N total in CF (see 'Results'), we compared the estimated crop aboveground production and grain yield at a value of 120 kg.ha -1 corresponding to a value observed in both farming systems using the estimates of the model parameters. This value being selected arbitrary, we also estimated crop aboveground and grain yield at four other values to check for the robustness of our results (see Fig. S2). Then we examined how weed species richness, abundance and biomass varied with the amount of N total , in the presence or absence of weed control, again using data collected in fertilized weedy or weeded plots at flowering and harvesting periods. The same model was used for crops and weeds.

In a second step, to disentangle the effect of weed control from those of N fertilization on crop and weed plants, we tested the impact of weed control in unfertilized plots at crop flowering and at harvest, on crop aboveground biomass (or grain yield at harvest), weed species richness, weed abundance and weed aboveground biomass. We used two linear models, one for each weed control treatment (presence of absence), with the soil N content (N soil , without any N input) alone and nested within the farming system.

The third step of our analyses consisted in exploring how Weed Control Effect on the crop (WCE crop ) or Weed Control Effect on weeds (WCE weed ) vary with the amount of N soil or N total . To measure the effect of weed control, we used an index that is computed as the percentage difference, in the presence or absence of weed control, in crop aboveground biomass or in weed aboveground biomass, abundance or richness. The percentage differences were computed symmetrically for the crop and weeds to illustrate the expected effect of weed control, i.e. positive for crops and negative for weeds:

Forthecrop, WCE crop = X i WC1 -X i WC0 X i WC1 + X i WC0 (1) Forweeds, WCE weed = X i WC0 -X i WC1 X i WC0 + X i WC1 (2)
where X i WC1 and X i WC0 are the crop or weeds response variables in the presence (WC 1 ) or absence (WC 0 ) of weed control. The values range from -100-100%, with positive values indicating a positive effect of weed control in crop and negatives values indicating an efficient decrease of weeds (either in terms of richness, abundance or biomass depending on the response variable). Response variables for the crop included biomass or grain, while for weeds it included biomass, abundance or richness. In the five cases, the same model structure was used. The amount of N was either N total or N soil , depending on whether data were collected in fertilized or unfertilized plots.

Finally, after analysing the crop and weeds separately, we replicated our analytical framework to investigate crop-weed interaction in relation to N amount (N total , or N soil only) and weed control. We used a metric of competition, the Competitive Balance Index (CBI), inspired of the relative interaction index (RII) recommended to explore competition [START_REF] Armas | Measuring plant interactions: a new comparative index[END_REF]. This metric is better suited to examining how the competition outcome between weed and crop plants varies with the amount of N, and is computed as the contribution of crop aboveground biomass over the total amount of plot aboveground biomass (from crop and weed plants):

CBI = B crop -B weed B crop + B weed (3)
This competition index, CBI, was computed in the presence and absence of nitrogen, using biomass data from fertilized plots when exploring the effect of N total , or unfertilized plots when exploring the effect of N soil , and in presence and absence of weed control using biomass data from non-weeded and weeded plots. The variation of CBI indexes was assessed using the same model as for WCE indexes.

All analyses were conducted for two time periods, crop flowering (in May) and harvest time (late June/early July). We checked for the prerequisites of homogeneity of variances, normality of the residuals, and collinearity of all models. Crop biomass, weed abundance and biomass were log-transformed. All statistical analyses were performed with R software (R Core Team, 2020).

Results

Crop response to nitrogen input

The amount of N total (i.e., N soil plus N input ) varied strongly across fields (from 8.3 to 264.6 kg.ha -1 ), which resulted in strikingly different resource levels for crops and weed species assemblages between fields (Fig. 1). N total was significantly lower in OF fields compared to CF fields (mean±sd: OF = 63.2 ± 38.9 kg.ha -1 and CF = 180.4 ± 39.5 kg.ha -1 ; Wilcoxon test: W=3008, p-value<0.0001).

At crop flowering, in fertilized plots, crop aboveground biomass was significantly and positively related to the N total (Fig. 1a, Table 1). Similar results were observed at harvest, with an overall positive effect of the N total on grain yield (Fig. 1b). As expected, at both periods, crop and grain biomass were significantly higher in CF fields compared to OF fields (Table 1, Fig. 1a-b), though this could result either from difference in farming system or a difference in N input (in the statistical model, N input was nested within farming system, thus the relative effect of two factors could not be statistically teased apart). By setting N total at 120 kg. ha -1 for both farming systems (a value of input that existed for both farming systems, Fig. 1a-b), and estimating crop and grain biomass at this N threshold for each farming system based on their individual equation derived from Fig. 1, we found that at both crop flowering and harvest, there was a significant difference between farming systems. CF exceeded by about 20 % OF system yield at 120 kg.ha -1 N (Fig. 1c). As a difference between farming systems was clearly observed despite N input being set at an equal value (for a robustness analysis in regard to the threshold value, see Fig. S2), we looked for possible differential effects of weeds and/or weed control between the two farming systems.

Weed response to nitrogen input

In fertilized plots, the amount of N total had a negative effect on weed species assemblages at both crop flowering and harvest (Fig. 2). In particular, at crop flowering, weed species richness and weed abundance significantly decreased with N total (Fig. 2b-c; Table 1), with richness being three times lower in fields with a high amount of N compared to those with the lowest N amount. Weed aboveground biomass production also decreased with N total , although the effect of N was only significant at crop flowering (Fig. 2a, Fig. 2d; Table 1) and actually only in the case of CF when herbicides were applied (Fig. 2a). On average, weed species richness was slightly higher in OF than CF fields (Fig. 2b), but the largest difference between farming systems was observed for weed abundance in weeded plots, which was about twice as high in OF fields as in CF fields (Figs. 2c and2f, Table 1).

Crop and Weed responses to weed control and its impacts on crop-weed competition

Weed control had no significant effect either on crop aboveground biomass production at crop flowering (Figs. 3a, 3e; 639.9 ± 372.6 g/m 2 in weeded plots and 625.8 ± 327.2 g/m 2 in non-weeded plots; paired Wilcoxon test: V = 468, p-value = 0.64) or on grain yield (Fig. S3a, S3e; 42.97 ± 25.27 g/m 2 in weeded plots and 48.18 ± 28.51 g/m 2 in nonweeded plots; V = 491, p-value = 0.44). Conversely, we detected significant negative effect of weed control on weed species richness (Fig. 3c; average in fertilized non-weeded plots: 8.4 ± 3.6 species/m 2 and in fertilized weeded plots: 6.7 ± 3.9 species/m 2 ; V = 221, p-value = 0.011), weed aboveground biomass (Fig. 3b; average in fertilized nonweeded plots: 88.02 ± 105.91 g/m 2 and in fertilized weeded plots: 45.16 ± 71.48 g/m 2 ; V = 162, p-value <0.0001), and weed abundance (Fig. 3d; average in fertilized non-weeded plots: 74.99 ± 86.2 plants/m 2 and in fertilized weeded plots: 63.22 ± 80.21 plants/m 2 ; V = 309.5, pvalue = 0.0118) at crop flowering.

The effect of weed control on both the crop and weeds further varied with the amount of N. In CF, the effect of weed control on crop biomass (evaluated with WCE crop ) decreased significantly with N total (Fig. 3a). In addition, weed control effect (evaluated with WCE weed ) on weed aboveground biomass significantly increased with N total (Fig. 3b). However, the trend was opposed between OF and CF fields, i.e., the effect of weed control on weed aboveground biomass increase with N total in OF fields and decrease with N total in CF fields (Fig. 3b). The opposite overall pattern was observed with N soil , i.e., WCE weed significantly decreased with N soil , especially in CF fields (Fig. 3f), suggesting a decrease in weed control efficacy with increasing N.

At crop flowering, most of the biomass was produced by crop plants (high positive CBI values), indicating that the competitive balance was largely in favor of crop plants in fields (Fig. 4a). The high dominance of crop plants was noticeable when N total was higher than 120 kg.ha -1 , but was more variable below this threshold value (Fig. 4). In the fields with a lower N total , weed aboveground biomass accounted for some 20 % of the total aboveground biomass production, whereas in the former it was always lower than 10 %. This pattern was almost similar in weeded (Fig. 4a) and non-weeded (Fig. 4b) plots. Indeed, when comparing CBI values computed in weeded and non-weeded plots, very few differences could be observed confirming the absence of weed control effect (Fig. 4a,b). Such pattern was even more pronounced at crop harvest (Fig. 4c-d). The magnitude of the weed control effect was hardly noticeable because weed biomass was generally low in non-weeded plots, especially compared to the crop biomass. CBI also increased significantly with N, either N total or N soil (Fig. 4), indicating that N supply increases crop biomass at the expense of weed biomass, though this effect decreases with increasing N, and is negligible at very high N levels. Similar patterns were found at harvest (Fig. 4c-d, Fig. 4g-h).

In summary, our results reveal contrasted patterns below and above 120 kg.ha -1 of N total , i.e. between OF and CF fields, since fields with an amount of N total lower than this threshold value were generally OF fields. In OF fields, weed abundance was higher, the competitive balance between weed and crop plants was in favor of the crop and weed control was less efficient than in CF fields. Moreover, opposite patterns of the effect of weed control with N were observed between CF and OF both with N soil and N input . These patterns further suggest that the effect of weed control increased at higher N in OF, while its decreases in CF fields. However, we were not able to disentangle the effect of different types of weed control (mechanical weeding vs herbicides) from the effect of N amount.

Effects of N soil and weed control in unfertilized plots

Weed control intensity (estimated by the treatment frequency index of herbicides, or TFI, or the number of mechanical weeding operations) was unrelated to N soil (Spearman correlation test: r s = -0.024, p-value = 0.864), in contrast to N total , the latter being significantly, highly and positively related to weed control intensity (r s = 0.834, p-value < 0.0001). We therefore explored the effect of weed control on weed and crop plants as well as the outcome of competition in the absence of N fertilization. In contrast to N total , we observed no significant differences in N soil (amount of N in the soil at the end of January) between OF and CF fields (Wilcoxon test: W = 1668, p-value = 0.38). In such unfertilized plots, grain yield increased significantly with the amount of N soil (Fig. 5b, Table 2), as it did in fertilized plots, although crop biomass, one month earlier, did not (Fig. 5a). In regard to weeds, N soil had a similar effect as N total on weed species richness and weed abundance, which both decreased significantly in OF and CF fields at flowering (Fig. 5d-e) while a significant decrease was only observed for weed species richness at harvest (Fig. 5g-h; Table 2). In contrast, no effect was detected on weed aboveground biomass (Fig. 5c, Fig. 5f). This suggests that at crop flowering the species or individuals in the fields with a higher amount of N soil produce more biomass per individual plant.

Similarly, in unfertilized plots, weed control had almost no effect on the crop, and little effect on weed plants, except for biomass (Table 2; Fig. 3e-h), as was found in fertilized plots. The only difference concerned weed aboveground biomass (Fig. 3f), which significantly decrease with increasing N, an opposite trend to that observed in fertilized plots (i.e., positive relationship; Fig. 3b). In OF fields, the effect of weed control on crop biomass decreased with N soil, highlighting the efficacy of mechanical weeding in fields with a lower amount of N soil (Fig. 3e).

Overall, weed control appeared more efficient in CF fields compared to OF fields, both for weeds and the crop (Fig. 3). This translated into the competitive balance, which was always largely in favor of the crop in CF fields compared to OF fields (Fig. 4e). In addition, the competitive balance in weeded and non-weeded plots were very similar, and crop advantage increased with the amount of N soil (Fig. 4e-f), suggesting that an increase of N availability provided a higher benefit to crop plants, which in turn produced more biomass at the expense of weeds. In both CF and OF fields, the increase of N soil differentially benefitted crop plants, regardless of weed control. Weed control in CF fields was, however, more efficient on crop biomass in fields with lower N soil (Fig. 3a). This pattern was not observed in OF fields, suggesting a qualitative difference between weed control in CF (chemical weeding) and OF fields (mechanical weeding).

Discussion

The aim of this study was to explore, experimentally, the importance of competition between weeds and winter cereal crop plants, and how nitrogen and weed control affect such competition in real farming conditions. Using an 'existing' gradient of nitrogen as provided by farmers, in addition to the experimental removal of weed control and N fertilization in organic and conventional farming fields, we were able to tease apart the effect of nitrogen and weed control on the competitive outcome between crop and weed plants, and the consequences on yield. We found that N supply (i.e., referring to N total in our study) had a prominent effect, increasing yields but decreasing weeds. We also found that although weed control had some effect on weeds, it had no effect on crop yield and on the competitive outcome between weeds and crop plants, because, all experimental treatments combined, weeds only contributed to around 10-20 % of the total plant biomass in conventional fields. However, by comparing fertilized and unfertilized plots, as well as organically and conventionally farmed fields, we found that N supply interacted with weed control: first, mechanical weeding appeared less efficient compared to herbicides, and second, while weed control did not affect yield at low N levels, it was apparently needed at high N levels to avoid a decrease in crop biomass. In the latter situation (i.e., high N levels), without herbicide application, weed biomass remained stable whatever the N applied level, while herbicide application suppressed a larger part of weed biomass with increasing N application (Fig. 2a). The relative efficacy of weed control in CF however decreased with N, being it N soil or N total (Fig. 3a-e). The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system).The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively.

Crop-weed relationships in relation to N supply

In fertilized and weeded plots, the results provide strong evidence that with more nitrogen the crop largely outcompetes weed plants, and that the crop-weed competitive balance favors crop plants. Increasing the resource supply (i.e. N supply) increases crop biomass at the expense of weed biomass. These findings align with previous results showing the high competitive ability of cereals over weeds [START_REF] Gaba | Crop competition in winter wheat has a higher potential than farming practices to regulate weeds[END_REF][START_REF] Lutman | A review of the effects of crop agronomy on the management of Alopecurus myosuroides[END_REF][START_REF] Stefan | Crop-weed relationships are contextdependent and cannot fully explain the positive effects of intercropping on yield[END_REF][START_REF] Van Der Meulen | A review of weed management in wheat using crop competition[END_REF]. For instance, [START_REF] Gaba | Crop competition in winter wheat has a higher potential than farming practices to regulate weeds[END_REF] found that in the absence of crops, weed biomass increased with N supply, but in the presence of crops and given the latter's competitive advantage, the expected increase in weed biomass was suppressed. In our studied fertilized plots, weed biomass represented less than 15 % of the total plant biomass (both crop and weeds) produced at crop flowering and at harvest in CF fields, whatever the N amount. In situations of lower N supply, i.e. in OF systems or in CF/OF unfertilized plots, the competitive balance was not so uneven, although still largely in favor of the crop both at crop flowering and harvest. The pattern was virtually unchanged without weed control since the competitive balance was similar between weeded and non-weeded fertilized plots in both farming systems, except at highest levels of N input. In unfertilized plots, weed control had no effect on competitive balance, still strongly biased in favor of crop plants in CF fields, with only slight variation between weeded (82.8 % ± 22.3 %) and non-weeded (77.7 % ± 21.0 %) plots. Although biomass (and also abundance) of weeds would be expected to increase with N input, the reverse was found in CF, both at crop flowering and harvest, indicating that the presence of the crop alone can reverse expected patterns, although the magnitude of this effect was lower in high N conditions. In all situations, OF or CF, increasing N (whether N total or N soil ) resulted in lowering weed species richness. Increasing the N supply therefore enhanced the competitiveness of crop plants against weeds in almost all contexts, confirming the higher ability of cereal crop plants to take up N over weed plants [START_REF] Andrew | A review of the potential for competitive cereal cultivars as a tool in integrated weed management[END_REF][START_REF] Blackshaw | Fertilizer application method affects nitrogen uptake in weeds and wheat[END_REF][START_REF] Blackshaw | Nitrogen fertilizer rate effects on weed competitiveness is species dependent[END_REF][START_REF] Mohler | Enhancing the competitive ability of crops[END_REF][START_REF] Ruisi | Nitrogen uptake and nitrogen fertilizer recovery in old and modern wheat genotypes grown in the presence or absence of interspecific competition[END_REF].

Difference in weed abundance and biomass in conventional and organic farming

While there were no significant differences in weed species richness, weed abundance and biomass were twice as high in OF fields compared to CF fields. This may be related to the different types of fertilizer between the two farming systems, only compost and organic manure in OF, and mainly inorganic manure in CF. However, the effect of the type of fertilizer in our study cannot be confirmed. Previous studies have revealed contrasting effects of organic fertilizer on weeds [START_REF] Rotchés-Ribalta | Responses of rare and common segetal species to wheat competition and fertiliser type and dose[END_REF][START_REF] Rotchés-Ribalta | Reduced crop sowing density improves performance of rare arable weed species more effectively than reduced fertilisation[END_REF], showing negative [START_REF] Dyck | Crop-weed interference as influenced by a leguminous or synthetic fertilizer nitrogen source: II. Rotation experiments with crimson clover, field corn, and lambsquarters[END_REF], positive [START_REF] Blackshaw | Nitrogen fertilizer, manure, and compost effects on weed growth and competition with spring wheat[END_REF] or neutral effects [START_REF] Cordeau | Long-term soil nutrient management affects taxonomic and functional weed community composition and structure[END_REF] on weed biomass when comparing organic and mineral fertilizers. Weed control strategy also differs between CF and OF, and mechanical weeding appears to be less effective than herbicides as revealed by our comparison of the two farming systems in unfertilized plots. Our results further suggest differences in the ability of the crop plants to suppress weeds between CF and OF. In our fields, OF and CF differed in their cereal species or cultivars, which are known to vary in their ability to take up N and in their competitiveness [START_REF] Andrew | A review of the potential for competitive cereal cultivars as a tool in integrated weed management[END_REF][START_REF] Storkey | Agricultural intensification and climate change have increased the threat from weeds[END_REF]. Crops in organic agricultural systems are generally less sensitive to weed competition compared to corresponding conventional systems [START_REF] Ryan | Weed-crop competition relationships differ between organic and conventional cropping systems: weed-crop competition in organic and conventional systems[END_REF], and organic farmers sow cereals at lower density with larger row spacing to facilitate mechanical weeding. Higher weed abundance and biomass in OF fields may therefore be the result of lower crop competition on weeds compared to CF fields, mainly due to lower competition for light because of larger row spacing. This mechanism may also explain the lack of an effect of weed control on production in OF fields, even though weed biomass is high.

Weed control effect and efficacy

Overall, weed control had a small effect, whether on crop yield, weed species assemblage, or crop-weed competition. Weed control decreased weed biomass by some 20 % in CF and decreased weed species richness in both farming systems, independently of availability of N, but did not affect statistically weed abundance in any system, either at crop flowering or harvest. A comparison of the effect of weed control between organic and conventional fields suggested that there is a qualitative difference in weed control efficacy between these two farming systems, with chemical weeding being more effective than mechanical weeding in controlling weeds [START_REF] Pannacci | Effects of mechanical and chemical methods on weed control, weed seed rain and crop yield in maize, sunflower and soyabean[END_REF]. However, this qualitative difference was expressed only at high N input. In situations of limited N (i.e., unfertilized plots when only N soil was available), there was no effect of weed control on weed species assemblage (abundance, richness or biomass) (Fig. 4c-d-e). This underlines an interactive effect between N input and weed control method. These results, obtained in real farming conditions, extend previous experimental studies by revealing lower herbicide efficacy at low levels of nitrogen [START_REF] Kim | Modelling interactions between herbicide and nitrogen fertiliser in terms of weed response[END_REF][START_REF] Singh | Herbicide and nitrogen application effects on weeds and yield of wheat[END_REF][START_REF] Sønderskov | Influence of nitrogen rate on the efficacy of herbicides with different modes of action: Impact of nitrogen rate on herbicide efficacy[END_REF][START_REF] Wang | Herbicide and nitrogen rate effects on weed suppression, N uptake, use efficiency and yield in winter oilseed rape (Brassica napus L.)[END_REF].

Given the minor effect of weed control on weed species assemblage, one would expect little effect as well on the competitive outcome between weeds and crop plants. Our two measures of competition between weeds and crop plants confirmed this prediction. At low N input (unfertilized plots), in both farming systems, weed control had no effect on the competitive balance (CBI). However, with increasing N input, we found that the crop significantly benefitted from weeding (Fig. 4e-h). This can be explained by the decrease of the magnitude of the regulation of weeds by crop competition that was observed in high N fields. Indeed, in CF fields, we found a positive relationship between weed control intensity (estimated by TFI) and N input. Increased weed control in N-rich CF fields resulted in lower weed biomass, but this did not translate into a significant gain of crop biomass.

Nitrogen input and herbicide use, an agronomic trap in conventional farming?

We detected a strong positive relationship between the amount of N input and of herbicides applied in CF fields. While a high amount of N was related to higher yields, the presence of weed control was not significantly related to an increase in yield, although yield was on average 10% higher in the presence of weed control. This gain, however, decreased with the amount of N input and, hence, with the amount of herbicide applied (these being positively correlated), the latter being relatively less efficient at high N input. Indeed, the negative relationship between the weed control effect (WCE) on crop biomass and the amount of N total in CF fields (Fig. 3a), despite an apparent higher increase in crop biomass with increasing N total (Fig. 1a), also suggests that the efficacy of herbicides decreased with increasing N. This suggests that higher crop production in the presence of high N input may only be achieved with an increase in the amount of herbicide applied, a pattern that suggests a decisional cascade in which increasing N supply to increase crop yield, also benefits to weeds whose management required a more intense weed control to maintain the yield at the same level. This can be seen as an agronomic trap requiring a high reliance on agronomic inputs.

By suggesting such agronomic trap in conventional farming, our experimental results point to a possible pathway (i.e., a combined reduction of N input and weed control) for sustainable weed management in the meantime, in line with growing empirical evidence that reducing weed control in the short term does not necessary relate to higher yield loss and may even result in higher income for farmers [START_REF] Catarino | Experimental and empirical evidence shows that reducing weed control in winter cereal fields is a viable strategy for farmers[END_REF][START_REF] Gaba | Herbicides do not ensure for higher wheat yield, but eliminate rare plant species[END_REF][START_REF] Lechenet | Reducing pesticide use while preserving crop productivity and profitability on arable farms[END_REF]. Our study confirms a more complex picture than straightforward crop-weed competition. Indeed, diverse crop and weed species assemblage may show no negative effects [START_REF] Epperlein | Reintroduction of a rare arable weed: competition effects on weed fitness and crop yield[END_REF][START_REF] Gaba | Herbicides do not ensure for higher wheat yield, but eliminate rare plant species[END_REF], or even a positive relationship between crop and weed diversity or biomass [START_REF] Adeux | Diversified grain-based cropping systems provide long-term weed control while limiting herbicide use and yield losses[END_REF][START_REF] Ryan | Weed-crop competition relationships differ between organic and conventional cropping systems: weed-crop competition in organic and conventional systems[END_REF]. Further studies are needed to confirm our results especially in other contexts with crop types with a lower potential to cope with weeds than winter cereals. The study over a longer term of reduced weed control is also of high importance to determine whether crop competition is sufficient to avoid a significant increase of propagules in the seed bank. Overall, our results offer insights that open new avenues for designing more sustainable weed management strategies to foster the agroecological transition. The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively.

Fig. 1 .

 1 Fig.1. Relationship between N total (kg.ha -1 ; sum of N soil and N input ) and crop aboveground biomass production at crop flowering (A) and grain yield at harvest (B). Data was collected in the presence of fertilizer. Circles show raw data. Light or dark green indicates data collected in OF fields in the absence (light) or presence (dark) of weed control. Light or dark blue indicates data collected in CF fields in the absence (light) or presence (dark) of weed control. The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively. Because of nestedness, we cannot separate whether the effect comes from the intercept or the covariance. The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). (C) Predicted values of crop biomass and grain yield in CF (blue) and OF (green) fields for the threshold value of 120 kg.ha -1 of N fertilizer. SEs are shown. (D) Schematic representation of the experiment with the four treatments presented.

Fig. 2 .

 2 Fig. 2. Relationship between N total (kg.ha -1 ; sum of N soil and N input ) and weed biomass (A;D), weed species richness (B;E) and weed abundance (C;F) at crop flowering (A-C) and at harvest (D-F). Data was collected in the presence of N fertilizer. Circles show raw data. Light or dark green indicates data collected in OF fields in the absence (light) or presence (dark) of weed control. Light or dark blue indicates data collected in CF fields in the absence (light) or presence (dark) of weed control.The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system).The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively.

Fig. 3 .

 3 Fig. 3.The effect of weed control on the crop (WCE crop ) and the weeds (WCE weed ) in fertilized (A-D) and unfertilized (E-H) plots at crop flowering. WCE crop is computed on crop biomass (A; E), while WCE weed is computed on weed biomass (B; F), richness (C; G) and abundance (D; H). The OF and CF fields are shown in green and blue respectively. The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The black lines show the predicted relationships without accounting for the farming system. The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). (A-E) Positive effect of weed control on crop plants (WCE crop ) indicates that crop aboveground biomass is higher in the presence than in the absence of weed control. (B-D;F-H) Positive effect of weed control on weed plants (WCE weed ) indicates that weed aboveground biomass (richness or abundance) is higher in the absence (non-weeded plots) than in the presence of weed control (weeded plots).

Fig. 4 .

 4 Fig. 4. The effect of N total (kg.ha -1 ; A-D) and N soil (kg.ha -1 ; E-H) on the competitive balance (CBI) between crop and weed plants in weeded (A,C,E,G) and nonweeded (B,D,F,H) plots. Data was collected at crop flowering (first two columns) and at harvest (third and fourth columns). The OF and CF fields are shown in green and blue respectively. The lines represent the predicted values of the linear models (solid when significant, dashed otherwise). The black lines show the predicted relationships without accounting for the farming system in the presence or absence of weed control, respectively. The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). Positive CBI weeded and CBI non-weeded values indicate that crop plants contribute more to biomass production than weeds, while negative values indicate that weed plants contribute more than crop plants.

Fig. 5 .

 5 Fig. 5. Relationship between N soil and crop aboveground biomass production at crop flowering (A) and grain yield at harvest (B), as well as with weed biomass (C; F), weed species richness (D;G) and weed abundance (E;H) at crop flowering (second row) and at harvest (third row). Data was collected in the absence of N fertilizer. Circles show raw data. Light and dark green indicate data collected in OF fields in the absence (light) or presence (dark) of weed control. Light and dark blue indicate data collected in CF fields in the absence (light) or presence (dark) of weed control. The lines represent the predicted values of the linear models.The significance level of the effect of N within the farming system was thus obtained by separate models (one per farming system). The black and gray lines show the predicted relationships without accounting for the farming system in the presence and absence of weed control, respectively.

Table 1 Summary of the linear models.

 1 Effects of available nitrogen (N) on biomass of crops and weeds, and weed species richness and abundance at two periods were explored in fertilized weedy and weeded plots. Significant effects are in bold.

		At flowering						At harvest
		with Weed Control		without Weed Control	with Weed Control		without Weed Control
		F value	Df	Pr (>F)	F value	Df	Pr (>F)	F value	Df	Pr (>F)	F value	Df	Pr (>F)
	(A) Crop
	N total	39.24	1	> 0.0001	52.90	1	> 0.0001	37.01	1	> 0.0001	35.12	1	> 0.0001
	N total: Farming system	4.42	1	0.0412	2.75	1	0.1045	4.26	1	0.0441	2.77	1	0.1022
	Residuals		44			44			51			51
	(B) Weed aboveground biomass
	N total	8.02	1	0.0070	1.14	1	0.2926	2.72	1	0.1056	1.43	1	0.2375
	N total: Farming system	0.34	1	0.5645	0.09	1	0.7629	3.05	1	0.0870	0.81	1	0.3732
	Residuals		44			44			48			51
	(C) Weed species richness
	N total	19.17	1	> 0.0001	11.53	1	0.0014	14.06	1	0.0005	5.83	1	0.0195
	N total: Farming system	1.96	1	0.1682	0.09	1	0.7660	0.36	1	0.5491	0.05	1	0.8264
	Residuals		47			48			48			50
	(D) Weed abundance
	N total	15.33	1	0.0003	16.20	1	0.0002	11.25	1	0.0016	8.26	1	0.0059
	N total: Farming system	2.27	1	0.1385	3.84	1	0.0560	8.40	1	0.0057	8.47	1	0.0054
	Residuals		45			48			46			50

Acknowledgments

We would like to thank the farmers in the LTSER "Zone Atelier Plaine & Val de Sèvre"; E. Cadet, P. Deroulers, T. Fanjas-Mercere, M. Liaigre, R. Perronne and E. Tedesco and several students for their help with setting up and managing the experiment and sampling; J. Caneill for designing the farmers' survey; and B. Nicolardot, C. Ducourtieux, F. Lombard, and E. Pimet for the soil sampling and soil analyses. We appreciate the very useful comments made by the two anonymous referees as well as the editor. The English was revised by Elise Bradbury.

Funding

This study was supported by the French Ministry of Ecology in the framework of the 'Pollinisateurs' program, the French National Research

Data availability

Data will be made available on request.

CRediT authorship contribution statement

VB and SG coordinated the research project and designed the experiment. VB supervised the experiment. SG, OM and AB analysed the data. SG and VB wrote the first draft of the manuscript. All authors contributed to the writing of the final version of the manuscript,

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.agee.2022.108232.

Table 2

Summary of the linear models. Effects of nitrogen (N) in the soil on biomass of crops and weeds, and weed species richness and abundance at two periods were explored in unfertilized weeded and non-weeded plots. Significant effects are in bold.