E Vinot

R Trigui

B Kabalan
email: bilal.kabalan@univ-eiffel.fr

Rule-Based Energy Management of Hybrid Electric Vehicles Focus on Load Following Strategy

Keywords: Energy management, Hybrid Electric Vehicle, Rule based management, Charge sustaining, Charge depleting

This chapter deals with the rule-based Energy Management Strategy (EMS) used for Hybrid Electric Vehicles (HEVs). Dierent methods are presented, with a special focus on the load following strategy. The choice of the system operations is presented for battery charge sustaining and charge depleting operations. A parallel hybrid architecture is chosen as a rst example. The case of a Power-Split Hybrid architecture is also developed presenting the management of the engine operations. The energy management in a hybrid vehicle with hybrid electric storage system (Battery plus Ultra Capacitor) is also detailed.

Power system energy management

Energy management plays a paramount role in every multi-sources power system from electricity grid to hybrid vehicles [START_REF] Roboam | Conception systémique pour la conversion d'énergie électrique 2: approche intégrée par optimisation[END_REF]). Since two or more power sources are present in such system, several energy paths exist. The supervision of the energy ow is called the energy management of the system. Its role is to decide which sources are involved and how much power they supply (or absorb) at each time step. This choice depends on the instantaneously required energy and on other criteria (state of stored energy in bidirectional sources for example). It also has to respect the constraints on the system and on the components (for example min/max power, torque or current ...) and could try to minimize (or at least improve) some objectives as the global energy consumption or the greenhouse gas emissions.

Rule based methods are commonly used to achieve this task. They can be based for example on frequency approach or power demand approach. However, to be ecient, these rules become complex and should be tuned or directly derived from optimal (or sub-optimal) energy management strategies.

In this chapter, we will focus on the case of Hybrid Electric Vehicles (HEVs) and simple rule-based energy management. The hybridization of a vehicle is a general concept achieved as soon as there is more than one sources of energy. Generally, unidirectional energy sources (gasoline, fuel cell, gas ...) are coupled with at least one bi-directional energy source (battery, ultra-capacitor UC, pneumatic storage ...). The concept is not only applied to ground vehicle, it is also used on other types of vehicles (train, boat ...).

This chapter deals with ground vehicles propelled by one engine (gasoline or diesel) and using one or two reversible sources (battery and UC) as main energy storage sources. However, the principle presented in the following section should generally be adapted to other energy sources and other types of vehicle.

The EMS of such vehicles are precisely dened in the previous chapter of this encyclopedia (Energy Management Strategies for HEVS: Introduction and Positioning). It presents the dierent EMS methods (Rule based, optimization based ...) and their classication.

Ground HEVs generally present a simple system as it is often composed of one main mechanical energy consumer (the vehicle itself) and two energy sources, with at least one bi-directional energy source. Figure 1 presents a general HEV architecture with one engine and one energy storage system (battery). An electrical energy consumer is often added to model the auxiliaries consumption. It represents the power demand of the accessories, including the air cooling system, when there is an electric compressor. For simplicity, it will be neglected in this chapter but can be easily considered by adding a requested power to the main consumer (in our cases: the vehicle). The mechanical and electrical connection between the motors; Internal Combustion Engine (ICE) and Electrical Machine (EM) can be of dierent types. This leads to dierent families of hybrid architectures (parallel, series, Power-Split...) see for example [START_REF] Guzzella | Electric and hybrid-electric propulsion systems[END_REF]. These connections can be composed of Planetary-Gear (PG), Gear-Boxes (GB), Final Gear (FG) ...

Vehicle

Engine

Battery

Hybrid architecture

Fuel tank

Mechanical Connections

Power electronic Converter(s) In the cases of HEVs the energy management will address the following points:

Choice of the operating modes of the vehicle : pure electric, or hybrid mode and the energy paths between the components (battery charge or discharge when engine ON, sec.3.1).

Managing the state of charge of the battery; charge sustaining (sec.3) or charge depleting modes (sec.4).

Choice of the gearbox ratio if relevant.

Choice of the engine operation point in a Power-Split Hybrid Electric Vehicle (PSHEV, sec.3.2).

The energy management rules make an instantaneous choice of the energy paths, however they have to respect long terms state of charge objectives. If the battery cannot be plugged to the grid, the vehicle operates in Charge Sustaining (CS) mode. The battery SoC (State of Charge) uctuates around a pre-chosen SoC and globally, only chemical energy (coming from fuel) is used. If the vehicle can be plugged to the grid (Plug in Hybrid Electric Vehicle: PHEV) it is operated in Charge Depleting (CD) mode until a SoC limit. Hence a part of the energy comes from the grid reducing the fuel consumption.

The objectives of this chapter are to present in a simple way the concept of Rule based EMS. More Specically we will focus on Load Following Strategy developed for the rst HEVs. It existed for many decades but is still used as it is a simple method, easy to implement in HEVs, well-known and presenting good performances.

In this chapter a short presentation of the Rule Based EMS principle based on the example of a parallel hybrid Vehicle is proposed (sec. 2). The cases of charge sustaining operation will then be treated presenting simple rule based energy management in CS mode (sec. 3.1) for a parallel architecture and then its modication for Power-Split architecture (sec. 3.2) to manage the choice of engine operation. A more complex case, with two energy storage sources is then presented to provide an example of energy management with three sources HEVs (sec. 3.3). Finally, the charge depleting operations are discussed (sec. 4) presenting the basic rules to manage the decreases of the SoC along the travel.

Rule Based EMS and energy ow : case of Parallel hybrid Vehicle

As in every system where multiple energy sources are involved, energy management rules are mandatory in hybrid vehicles [START_REF] Hofman | Rule-based energy management strategies for hybrid vehicles[END_REF]). They do the power and energy path choices in the vehicle, respecting the constraints of battery charge or discharge. As an example, the possible energy paths are presented g.2 in the case of a parallel hybrid architecture with two clutches. In such an architecture the Engine (ICE) and the Electrical Machine (EM) are mechanically connected to the wheels. The EM is connected directly to the engine or by means of a coupling device (CPL). A rst clutches (C1) allow to decouple the engine from the wheels in electrical operation. A Gear box (GB) is required, as in conventional vehicles to adapt the ICE speed depending on the wheel speed. A Second clutch C2 (if open) allows the EM to start the engine. GB is connected to the wheels by means of a Final Gear (FG) and dierential device (DIFF). The Electrical machine is connected to an Inverter (INV), Which is linked to the Battery (BATT).

Dierent parallel architectures exist depending on the place of the electrical machine, and other hybrid architectures also exist such as Power-Split architecture (sec.3.2). For more information on the dierent hybrid architecture see for example [START_REF] Guzzella | Electric and hybrid-electric propulsion systems[END_REF].

Several energy paths are possible in Parallel HEVs (and in HEVs in general). When the vehicle operates in electric mode, the power ows downstream from battery to the wheel (traction) or upstream from the wheel to the battery (regenerative braking). In hybrid mode, the engine and the EM provide power (orange and cyan arrow). Those powers are added in the coupling device and ow to the wheel (blue arrow). The electric ow can be positive (from the battery to the wheel: boost mode). It can also be negative, from the engine to the battery. A pure ICE ow, from the ICE to the wheels, can also be imagined with no electric ow. The energy management laws are thus in charge of choosing the directions and the values of these ows to provide the required power to the vehicle and the battery and generate the high level set-points to the component close loop controllers (set points of EM and ICE torque ...). These laws can be classied in two types : online (can be implemented directly in the vehicle computer unit) and o-line (need the knowledge of the entire speed prole), thus cannot be implemented directly online (for more complete classication of HEVs energy management see chapter: "Energy Management Strategies: Introduction and Positioning"). In this chapter, we focus only on simple online energy management laws and their principles.

In this type of energy management, we currently nd methods based on simple rules (sec. 3 and 4) [START_REF] Kimura | Drive force control of a parallel-series hybrid system[END_REF]; [START_REF] Akli | Energy management and sizing of a hybrid locomotive[END_REF]; [START_REF] Mayet | Inuence of an energy storage system on the energy consumption of a diesel-electric locomotive[END_REF]; [START_REF] Vinot | Model simulation, validation and case study of the 2004 ths of toyota prius[END_REF]; [START_REF] Poline | Contribution aux méthodes de conception et de gestion des systèmes énergétiques multisources par optimisation systémique. Application aux trains hybrides électrique autonomes[END_REF]).

These rules are sometimes optimized oine by tuning some parameters (power threshold for example) [START_REF] Bertram | Multi-objective optimization of a parallel hybrid electric drive train[END_REF][START_REF] Buerger | Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[END_REF]). Complex rules are also developed based on oine pre-calculation on an optimal process as Stochastic dynamic programming [START_REF] Leroy | Towards real-time optimal energy management of hev powertrains using stochastic dynamic programming[END_REF]). Fuzzy logic energy management [START_REF] Singh | Fuzzy logic and elman neural network tuned energy management strategies for a power-split hevs[END_REF] or "Equivalent Consumption Management Strategy" [START_REF] Li | Real-time energy management for commute hevs using modied a-ecms with trac information recognition[END_REF])) are also more and more developed. A lead of development of these laws now concerns predictive energy management laws based on the knowledge of future driving conditions (speed, trac slopes ...) [START_REF] Liu | Cooperative optimization of velocity planning and energy management for connected plug-in hybrid electric vehicles[END_REF]). Neural networks (often linked with charge depleting operation) and predictive energy management are also a recent lead of development [START_REF] Zhou | A novel energy management strategy of hybrid electric vehicle via an improved td3 deep reinforcement learning[END_REF]). For more information on these topics see other chapter and refer to chapter: Energy Management Strategies: Introduction and Positioning. These laws tend to respect a predened SoC objective (as explained in this chapter) but they also can try to improve other objectives. A compromise between fuel consumption and pollutants emission can be one of these objectives, improved by delaying or favoring the engine start at the beginning of the cycle avoiding catalyst pipe cold operations. The reduction of battery aging could also be an objective by reducing current or thermal stress [START_REF] Pham | Integrated online energy and battery life management for hybrid long haulage truck[END_REF]).

In the following, we mainly focus on simple but ecient rules managing only the battery state of charge in charge sustaining or charge depleting mode.

Charge sustaining case

The charge sustaining energy management is used in non plug-in hybrid vehicles. In this case, the only source of energy is the chemical energy contained in the fuel tank. The battery size is generally small in such vehicles (less than 5kWh). The battery SoC globally uctuates around a preferred value as it will be generally of no interest to charge or discharge it too much (except for example in mountain use conditions). The relatively small SoC window evolution improves the life span of the battery avoiding high and low SoC. This section presents simple rule based energy management to choose the vehicle operation (sec. 3.1) and the engine operation in case of Power-Splitt HEV vehicles (sec. 3.2). Section 3.3 deals with the case of HEVs with Hybrid Storage System (HSS).

Simple rules for operation mode choice

General presentation

In charge sustaining, the operating modes of the system and the battery operation (charge or discharge) can be managed with simple rules. The management presented in the following is highly derived from the one of the Toyota Hybrid System, at least those used in the Prius II [START_REF] Vinot | Model simulation, validation and case study of the 2004 ths of toyota prius[END_REF]; [START_REF] Kimura | Drive force control of a parallel-series hybrid system[END_REF]) and is commonly called power following strategy or load following strategy (LFS).

System Management

A LFS is presented in the following. Simple decision rules and the principle of the Energy Management deciding to start or not the Engine are described. In this rule based management, the owchart of decision principles is presented in gure 3 and is only based on two characteristics. A rst curve (g. 4) will x the choice of electric or hybrid mode (engine ON/OFF), a second (g. 5) provides the power required by the battery depending on its SoC. Using the curve (g.5), the required power by the battery P batreq is easily assessed depending on its state of charge.

On the rst curve (choice of operating mode characteristic, g.4), a threshold P startICE is determined using the curve, depending on the battery SoC. The required power P req is then evaluated summing the battery required power and the power requested by the driver to propel the vehicle. This power is evaluated knowing the driver's action on the throttle, which is transformed into a required torque (T req ) on the wheel shaft and multiplied by the rotation speed to provide a required power:

P req = T req • Ω wheel + P batreq (1)
If this value (P req ) is higher than P startICE the engine is started otherwise the powertrain will be operated in electric mode. In this case, the battery provides the necessary required power to propel the vehicle.

If the engine is started (P req > P startICE ), the variables hyb1/0 = 1 and elec1/0 = 0 (g. 3) and the required torque on the ICE is determined knowing its rotational speed (which can be measured or deduced from the wheel speed and gear ratio).

If the engine is OFF (P req < P startICE ), the variables hyb1/0 = 0 and elec1/0 = 1 , and the required torque on EM is assessed using its rotational speed (measured or known using the total gear ratio from wheel to EM). The power provided by the battery is then disconnected from the required one (P batt_req ).

For example, considering a SoC = 60%, and a required mechanical power T req • Ω wheel = 10kW . The battery required power is P batt_req = -1kW (5) corresponding to a battery recharge. The total required power is then of P req = 11kW when the threshold P startICE to start the engine is evaluated using g.4 and is equal to 10kW (for SoC = 60%). In this case; P req > P startICE thus the powertrain will operate in hybrid mode and the energy management law will tend to recharge the battery. With these two simple rules, the vehicle energy management (g. 3) xes the system operation and guarantees a charge sustaining mode. This can be seen in gure 6 where the state of charge of a vehicle (Toyota Prius II) is simulated with this energy management on the NEDC driving cycle for three initial SoC. It is clear that this management law tends to keep the SoC around a value of 56 %. If the starting SoC is around this value, the vehicle is globally operated with near zero battery energy balance (only fuel is consumed along the cycle). Starting at high SoC value, the battery is globally discharged and the engine is not too much used (g. 6) especially during the rst three hundred seconds. On the contrary, starting at really low SoC, the engine is highly used and is never OFF (including regenerative braking phases) during these three hundred seconds. This behavior is explained by the shape of the two curves (g. 4 and 5). When the SoC is low, the engine will be started for low required power P req and the battery request to be recharged with relatively high power (below 40 % SoC). On the other hand, for high SoC, the threshold to start the engine is high and the battery required power is negative (discharge cases). The hybrid mode is thus not much used favoring the electric mode (battery discharge except in regenerative braking) and hybrid mode with battery providing power to the wheel. These energy management rules tend to "naturally" bring the SoC around a value where the required power is around zero. Note that, due to the losses in the system (not taken into account in eq. 1) the SoC tends to a value with a small negative battery recharge requirement. For vehicle operation measurement and validation on this law in a real case (SoC, engine torque and speed, fuel consumption) one can refer to [START_REF] Vinot | Model simulation, validation and case study of the 2004 ths of toyota prius[END_REF]).

Supplementary rules are often added for the vehicle operations at high speed or when the engine and tail pipe are cold. At speeds higher than a certain threshold, the engine can be kept ON, even if in idle operation, favoring vehicle dynamic and driving comfort. In cold start conditions, the engine start can be favored in order to warm the catalyst converter to oxide the pollutants with a good eciency.

Concerning the ON/OFF engine choice, to avoid oscillations between hybrid and electric mode, the use of one curve is not enough. If the same characteristic is used to start or stop the engine a risk of oscillations between the two modes is high if the required power varies around the engine ON/OFF threshold. A simple way to solve this problem could be the addition of a minimum time spend in hybrid mode forcing the engine to be ON a minimum of time. Another solution could be to have a dierent threshold to stop the engine. A hysteresis should then be added on the engine ON/OFF laws (sec. 4) . These rules can be applied to any type of hybrid architecture (parallel, power-split, series ... ). In those with a gearbox, the gear shifting is done automatically. The gear choice can be based on the engine speed and possibly on the required torque. This globally tends to x the engine operating point in a good eciency area. For power-split (PSHEV), another curve is used to manage the engine operation choice as it can be made in a continuous manner (section 3.2). Among the hybrid vehicle architectures, the power-split hybrid electric vehicles (PSHEVs) have been proven to be among the most ecient. Several PSHEV architectures exist. The Toyota hybrid system (THS) based on planetary gear is the most known (g. 7). Opel uses another system based on planetary gear in the Ampera [START_REF] Vinot | Comparison of dierent power-split architectures using a global optimisation design method[END_REF]). Finally, PSHEV architectures with Electrical Variable Transmission (EVT) are currently studied in laboratories [START_REF] Hoeijmakers | The electric variable transmission[END_REF]; Verbelen et al. ( 2020)) but are not commercialized yet.

In the THS, the architecture is composed of one engine two EMs and one PG. The engine is linked to the Planet Carrier and EM2 to the Sun gear. The ring is connected to the wheels and EM1. No gearbox is needed as PG and EM2 allow the adaptation of engine speed on a continuous manner. For a complete explanation of the THS and its operating modes see for example [START_REF] Vinot | Model simulation, validation and case study of the 2004 ths of toyota prius[END_REF]; [START_REF] Guzzella | Electric and hybrid-electric propulsion systems[END_REF].

By splitting the engine power in a combined serial and parallel way and decoupling the engine and wheel speeds, such architectures allow a fuel consumption reduction which can reach 40% in urban driving conditions compared to a conventional vehicle. A degree of freedom is added to the management of the powertrain. For a required engine power, the operating point of the engine can be chosen quite independently of the other parameters of the system (vehicle speed ...) along a given power hyperbole (g. 8).

Engine operation Management

To manage the engine operation (g. 10), a rule is added to the two previous rules presented in (sec. 3). A preferred engine operation curve is then often used (in cyan g.8) to x the engine torque and speed. It is predened to match the best specic fuel consumption area (best eciency). The operating point is then the intersection between this curve and the hyperbole of required power. Once the engine operating point is chosen, and knowing the wheel speed and required torque, the operation point of the others components (Planetary gear, Electric machines ...) can be deduced and the closed control generated (see for more details [START_REF] Vinot | Improvement of an evt-based hev using dynamic programming[END_REF]; [START_REF] Chen | Global modeling of dierent vehicles[END_REF]).

Simulation Results

An example of the engine operation is presented in gure 9 on the WLTP cycle for a simulated Prius-II vehicle. It is clear on the gure that the engine operation points (in blue on the gure) mainly concentrate around the predened engine operating curves (except in dynamic phases).

Load following rule based energy management (LFS) has been presented in the charge sustaining cases (sec. 3.1.2). The used curve can be simpler (uses constant threshold for example, see sec. 4) or more complex [START_REF] Kim | Power management and design optimization of fuel cell/battery hybrid vehicles[END_REF]; [START_REF] Romaus | Optimal energy management for a hybrid energy storage system for electric vehicles based on stochastic dynamic programming[END_REF]; [START_REF] Liu | Modeling and control of a power-split hybrid vehicle[END_REF]). Their shape could be optimized to improve the fuel consumption (see for example [START_REF] Vinot | Optimal energy management of hevs with hybrid storage system[END_REF]). Other parameters could also be managed and particularly the DC bus voltage when a DC-DC converter is used between the battery and the inverters (for more details refer to [START_REF] Verbelen | Comparison of an optimized electrical variable transmission with the toyota hybrid system[END_REF]). In order to reduce the stress on the battery or to increase the capability of the storage system to better handle the power peaks, one can imagine to use hybrid storage systems [START_REF] Vinot | Optimal energy management of hevs with hybrid storage system[END_REF][START_REF] Trovao | A real-time energy management architecture for multisource electric vehicles[END_REF][START_REF] Castaings | Comparison of energy management strategies of a battery/supercapacitors system for electric vehicle under real-time constraints[END_REF]). Such systems will commonly associate two sources with dierent characteristics; one mainly oriented on energy capacity and one able to absorb high peaks of power with small storage energy capability.

The association of a battery and an ultra-capacitor (UC) is probably the most studied hybrid storage system. In such a system, the energy management has an additional role: it has to manage the electrical power sharing between the battery and the ultra-capacitor.

An example of such architecture is presented in gure 11, where a DCDC converter is connected to the UC bus to adapt its voltage to those on the battery. The choice of the number and place of DCDC converter can be dierent. DCDC converters can be placed on the DC bus (before the inverter) or connected to the battery [START_REF] Allègre | Flexible real-time control of a hybrid energy storage system for electric vehicles[END_REF][START_REF] Castaings | Gestion d'énergie de véhicules multi-sources électriques et hybrides au travers de la représentation énergétique macroscopique[END_REF]).

To manage such a vehicle, the rules presented in section 3 can be applied with a supplementary law to manage the power sharing between the battery and the UC. This can be managed in a relatively simple manner using frequency based principle. The high frequency electrical power is aected to the UC and the low frequency to the battery. For that, a rst order lter could be added to the required electrical power (g. 12).

In electric mode, the required electric power P req_elec is deduced from the required torque T req . In hybrid mode, a required battery power P req_batt is added to the necessary power to drive the vehicle. The engine has to provide the sum of these two powers P req_ice .

In both modes, a rst order low pass lter with a cut-o frequency f c is used on P req_elec to compute the battery target power P targ_batt . Taking into account the available UC power, the UC is then used to provide the dierence betweenP targ_batt and P req_elec . If the desired UC power exceeds the available UC power (maximum/minimum current and/or voltage), the battery is used to provide the necessary additional power to fulll P req_elec . Overall, with this strategy the battery satises the mean required power while high frequency power peaks are provided by the UC. Moreover, if P req_batt is correctly tuned, the charge sustaining mode is guaranteed for the battery even if the battery does not provide exactly its required power.

However, due to the losses in the systems, this management does not guarantee the State of charge sustaining of UC. In order to avoid long-term supercapacitors discharge, an adaptive controller can be added based on dierent techniques such as PI controller [START_REF] Hussain | A real-time biadaptive controller-based energy management system for batterysupercapacitor hybrid electric vehicles[END_REF]), fuzzy logic [START_REF] Snoussi | Auto-adaptive ltering-based energy management strategy for fuel cell hybrid electric vehicles[END_REF], Linear quadratic regulation [START_REF] Sadeq | Linear quadratic regulator control scheme on hybrid energy storage system[END_REF]).

Simulation Results

Applying such rules for the energy management on a parallel hybrid architecture, gure 13 presents the battery and UC current and the battery SoC that can be obtained along a NEDC cycle for two dierent values of cutting frequency f c (0.06 Hz and 0.0005 Hz). This gure highlights the eect of the cut-o frequency of the rst order lter on the battery current. The battery current peak and the corresponding battery current stress are drastically reduced when the cut-o frequency is small (0.0005 vs. 0.06 Hz). The overall strategy does not change so much. The electric mode is mostly used in the rst 800 s of the cycle and for the rest of the cycle the engine is used to charge the battery to achieve charge sustaining operation over the cycle. For more details (parameters of the use cases and deeper explanation see [START_REF] Vinot | Optimal energy management of hevs with hybrid storage system[END_REF]).

The rule based management laws in cases of hybrid architectures were presented in the previous sections. The case of power split functionality was treated in section 3.2. The management of hybrid electric vehicle with hybrid storage system was presented in section 3.3. All these rules and laws are applied in the charge sustaining case. The case of plugin vehicle and the battery discharge management (charge depleting) are presented in the following section. In a plug-in vehicle, the battery has to be discharged in order to replace a part of the fuel energy consumption by electrical energy consumption. The on-board computer unit has thus another parameter to manage: the global discharge of the battery. Three dierent modes of energy management can be dened (g.14).

A pure electrical mode. Only the battery provides energy to the wheels and the accessories. It needs a battery and electrical machine(s) with enough power (tens of kw).

A blended mode. The vehicle is managed in hybrid mode. The engine is ON or OFF depending on rules, which can be close to those on charge sustaining mode, but aims to discharge progressively the battery.

The charge sustaining mode. Generally triggered when a low battery SoC is reached and which can be managed as previously presented (sec.3).

The pure electric mode and blended mode can be present or not depending on the strategy adopted and on the size of the battery. Some manufacturers choose for example to switch directly from pure electric mode to charge sustaining mode.

The switching choice between these modes can be done in a simple manner as presented in (g.14) by progressively discharging the battery until charge sustaining operation. In this case the SoC is the main parameter of decision. However more and more predictive energy management strategies are studied for PHEVs and try to use the complete or at least partial knowledge of the future driving mission. Depending on this knowledge, the choice of the operating mode can be modied. As an example, if urban conditions will follow highway conditions, a charge sustaining mode can be chosen in prevision of pure electric mode in urban conditions. As explained before three main modes are generally used for rule based energy management of PHEV, namely electric mode (EL), hybrid mode where the ICE is on (called also blended mode, BL) and charge sustaining mode (CS). In the present example the mode selection is based on SoC thresholds.

Generally the PHEV charged at 100% of SoC begins with all electric mode. Some strategies suggest to use this mode until the minimum SoC corresponding to charge sustaining mode enabling (SoC_CS). In this case the blended mode is never selected (only for the cases where electric drive power is lower than the required power). This kind of strategy is basic and allows to maximize the electricity use whatever the trip distance and duration are. However when the trip is long, it leads to intensive use of the CS mode which is not the most ecient for a PHEV.

In the presented method here, we suggest to use appropriate SoC_BL as a threshold to enable Blended mode. The variation of this threshold makes it possible to adapt the use of the battery during the trip and thus to have long or short blended mode (we can decide in the opposite of the former case to enable the Blended mode from the beginning of the trip and never select the EL mode).

In all cases when the CS mode is selected, one can use a charge sustaining strategy using load following strategy (LFS) like explained in section 3.

For the Blended mode, simple rules could be adapted from the LFS strategy.

When the power demand is higher than a constant threshold (P_h) and lower than the optimal ICE power, the ICE is ON and provides the requested power. Therefore, unlike in CS mode, the battery is not recharged in this case so that globally (in the BL mode) its charge continue to deplete.

When the power demand is higher than the optimal ICE power, the ICE is ON and provides its optimal power. The battery provides the dierence between the required power and the ICE optimal power.

When the power demand is lower than a constant threshold (P_l), the ICE is OFF. The margin between P_h and P_l provides a hysteresis band to prevent modes oscillation.

When the power demand is negative (vehicle deceleration/braking) the ICE is OFF (electric mode) and regenerative braking is maximized.

These rules have been implemented in a parallel PHEV model and tested on a succession of six driving cycle of extra-urban road type. The vehicle characteristics and the thresholds used are summarized in table 1. Simulation results [START_REF] Buerger | Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[END_REF] show the succession of the modes selection according to the SoC planed thresholds. The expected behavior of the SoC and the ICE vs EM use (Torques graph) is in accordance with the strategy. When varying the parameter values of the rule based EMS, the fuel consumption of the PHEV could be dierent for the same SoC variation along the use. This leads to the idea of a possible optimization of these values that could be done by simulation considering a representative use of the vehicle that includes dierent types of driving cycles.

Conclusion

Due to the presence of more than one energy source and energy path in Hybrid Electric Vehicles (HEVs), an energy management strategy (EMS) is required. The objective of this chapter is to present in a simple way the well-known Rule-based EMS and how they are implemented in dierent cases of HEVs. For this, the general problem of energy management in HEVs is rst explained: the instantaneous decisions to make, the state constraints to respect, and the objectives to optimize, if any. In the second section, this problem was explained in the case of a parallel HEV. After this, the application of rule-based EMS in charge sustaining operation is done for 3 examples: a parallel architecture, a Power-split architecture and a 3 sources HEV with hybrid energy storage system. For each example, the rules are described and the simulation results of the system operation are shown. Finally, rule-based EMS are applied in the case of charge depleting operation (plug-in hybrid vehicle). The simulation results and the vehicle operation are presented. It is clear that dierent parameterization of the rules leads to dierent results, which emphasizes the importance of optimizing these rules.

Figure 1 :

 1 Figure 1: Hybrid electric vehicle architecture with two sources

Figure 2 :

 2 Figure 2: Energy path in hybrid parallel architecture

Figure 3 :

 3 Figure 3: Rule based management in HEV vehicle

Figure 6 :

 6 Figure 6: SoC evolution and engine speed along NEDC cycle

Figure 8 :

 8 Figure 7: Toyota Hybrid System

Figure 10 :

 10 Figure 10: Rule based management in PSHEV vehicle

  Figure 11: Hybrid parallel architecture with battery and UC

Figure 12 :

 12 Figure 12: Rule based management in HEV vehicle with hybrid storage system

Figure 14 :

 14 Figure 14: SoC evolution in PHEV vehicle

Figure 15 :

 15 Figure 15: Energy management in CD operations

Table 1 :

 1 Vehicle characteristics and thresholds

	Variable	Value/threshold
	Vehicle mass 1350 kg
	Electric power 60 kW
	ICE power	80 kW
	SoC_BL	40%
	SoC_CS	20 %
	P_l	18 kW
	P_h	24 kW


Arbia Ben Khodja
email: arbia.ben-khodja@michelin.com

Serge Simoëns
email: serge.simoens@ec-lyon.fr

Marc Michard
email: marc.michard@ec-lyon.fr

David Le Touzé
email: david.letouze@ec-nantes.fr

Corentin Hermange
email: corentin.hermange@michelin.com

Clément Poncet
email: clement.poncet@michelin.com

Guillaume Oger
email: guillaume.oger@ec-nantes.fr

Serge Simo Ëns

David Le Touz É3

R(refracted)-PIV measurements of water film flow: application to flow under a rolling tire

Keywords: Hydroplaning, flow visualization, Particle Image Velocimetry, complex geometry, tire tread

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

Introduction

The hydroplaning is a situation well-known by car drivers that may lead to fatal accidents. It is a gradual phenomenon directly linked to the vehicle velocity where the tire loses its contact with the ground under rainy conditions [1]. Because of the high speed, the tread grooves are not able to drain water quickly enough anymore, leading to an increasing pressure of the fluid in contact with the tire. The fluid lift is therefore increased as well, deforming the tire, and reducing its contact area with the ground [START_REF] Maycock | Second paper: Studies on the skidding resistance of passenger-car tyres on wet surfaces[END_REF] [START_REF] Meades | Braking force coefficients obtained with a sample of currently available radial ply and crossed ply car tyres[END_REF]. Numerical studies have been made in the purpose of better understanding this complex problem and seeking in the end an optimization of the tread design [START_REF] Jenq | Transient hydroplaning performance of inflated radial tire with V-shape grooved tread pattern using lsdyna explicit interactive fsi scheme[END_REF] [START_REF] Okano | Hydroplaning simulation using MSC. dytran[END_REF] [6] [START_REF] Gillard | An efficient partitioned coupling scheme for tire hydroplaning analysis[END_REF]. Combined experimental and numerical works have also been conducted focusing on the comparison of global parameters like the skid resistance and the hydroplaning speed [START_REF] Ong | Wet-pavement hydroplaning risk and skid resistance: modeling[END_REF] or also the evolution of footprint shapes with the velocity [START_REF] Donatellis | Virtual treaded tire simulation as a design predictive tool: Application to tire hydroplaning[END_REF]. In the late 60s, testing facilities for the hydroplaning investigation helped showing the importance of the tread pattern by comparing breaking force coefficient of smooth tires with treaded ones [START_REF] Allbert | Tires and hydroplaning[END_REF]. More recently, experimental investigations have been performed involving different water heights, tread depths and inflation pressures leading to the comprehension of the main factors leading to the loss of the contact surface [START_REF] Hermange | Experimental investigation of the leading parameters influencing the hydroplaning phenomenon[END_REF]. However, the first local quantitative velocity investigation during situations that could lead to to hydroplaning has been experimentally proposed by Cabut et al. [START_REF] Cabut | PIV measurements using refraction at a solid-fluid interface[END_REF] based on an extended Particle Image Velocimetry (PIV) technique, the so-called r(refracted)-PIV. This dedicated measurement method opens the possibility of a deeper investigation of the water flow inside the grooves located in the CPA and also in the region around the CPA during the rolling of a tire over a water film. For this aim and to analyse their first results obtained with such a method, Cabut [START_REF] Cabut | Characterisation of the flow in a water-puddle under a rolling tire with refracted piv method[END_REF] and Cabut et al. [START_REF] Cabut | Particle image velocimetry (PIV) measurements in a water film, application to a tire rolling through a puddle[END_REF], [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] defined some first parameters to describe quantitatively flows inside grooves and outside the CPA. In [START_REF] Cabut | Particle image velocimetry (PIV) measurements in a water film, application to a tire rolling through a puddle[END_REF] they focused on the water-bank (region in front of the tire) and shoulder zones whereas in [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] they focused their interest on flows inside the longitudinal grooves of a summer tire (Michelin Primacy 4). Furthermore, for a given transverse groove, Cabut [START_REF] Cabut | Characterisation of the flow in a water-puddle under a rolling tire with refracted piv method[END_REF] developed a velocity averaged (inside the groove domain) parameter and plot it as a function of the longitudinal location of this transverse groove (barycenter of the integration domain). Such result, never published, show how water ejection from the CPA, is dependant on the location of the groove inside the CPA during the rolling process. This major result is carried 1 INTRODUCTION 3 on in the current study for a different type of tire tread. In so, the exact same experimental set up as in Cabut and partners' work, but with a different tire with a different zone complexity is used here to lead this groove analysis. In the present work, the local velocity inside the grooves is calculated through a segmentation process adapted to the complexity of the studied tread design.

A commercial winter tire with transversal grooves and a central zigzag part is considered. At the best of our knowledge, the splitting of the groove geometry, for local average, is an analysis that has never been published before and even more never applied to flow analysis of transversal grooves. To conclude, this work is the continuity of Cabut's work with the permanent research of a specific universal behavior whatever the tread design. Such approach is necessary for a quantitative description of the flow circulation inside a specific tire tread and will eventually help us improve our knowledge of the complex mechanism that lead to the hydroplaning situation.

The layout of the present paper is as follows. In section 2 we present the experimental setup, with a focus on a specific r-PIV arrangement using refraction at a solid/liquid interface. Some specific tools for data and image processing are described in order to consider the random position of the tire when performing a set of independent measurements. Some specific features of the flow inside directional grooves, as well as in the water-bank located in front of the contact patch area are given and discussed in section 3. Finally, some conclusions and perspectives are drawn in section 4.

Abbreviations and notations

A6: MICHELIN Alpin 6 205/55 R17 commercial tire CPA: Contact patch area H w : Depth of the water film (in mm) L x : Length of the contact patch area in X-axis direction (in mm) N : Number of runs given one set of operating parameters (V 0 ,H w ) V 0 : Car speed (in m.s -1 ) V * = V /V 0 : Dimensionless velocity WB: Water-bank x * = x/L x : Dimensionless abscissa

About the tread design

In this work we focus on a commercial winter tire currently designated as A6.

We consider a worn state of the tire leading to a remaining tread depth of 2mm, while for a new tire it is about 8mm. We give in Fig. 1 a depiction of the A6 tread in both new and worn states with some dimensions to give the reader an order of magnitude concerning the tread design. The central groove has a zigzag shape connected to directional grooves extending from the center to the shoulder of the tire and segmented into three nearly straight segments. Note that for acoustic issues the actual width and spacing of directional grooves is not strictly equal for all of them, and dimensions given on the left in Fig. 1 are averaged typical values. Moreover, some segments of the directional grooves have a worn indicator producing periodically a local geometric restriction of the flow in the groove as the car is rolling. Nevertheless, these indicators do not appear to influence the flow inside the central groove and are rarely located in the directional grooves in our database. In comparison, such indicators are of first order importance inside longitudinal grooves for summer tires as the one investigated by Cabut et al. [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF]. The third kind of grooves of interest are the ones between two adjacent directional grooves, herein after simply identified as "connecting grooves". Finally, the tire has what is known as an "evolving" tread, which results in the progressive appearance of sipes during the wear process among other modifications. Nevertheless, the spatial resolution of PIV measurements is not sufficient for capturing the flow inside these sipes because of their reduced width. Therefore, in this work we only focus on the flow in the central, directional and connecting grooves. The PIV technique has been previously used for the measurement of the air flow around the tire in the aim of aerodynamic drag study [16][17]. However, to the best of our knowledge, the PIV has been used for the first time in a hydroplaning application including a liquid phase by Cabut et al. [START_REF] Cabut | PIV measurements using refraction at a solid-fluid interface[END_REF]. The authors derived a specific method from the classical planar PIV, the so-called r-PIV (refracted-PIV), for application to a tire of a real car rolling through a puddle of water. In this section we introduce the experimental facility used in this work, then we present some specific processing tools of PIV images for such a complex tread pattern.

Experimental set-up

Measurements are performed on an in-situ track at Michelin Technology Center of Ladoux (Cébazat, France). The dedicated area is a dry straight road with a transparent portion made of a thick PMMA block that is embedded to the ground and was used for previous studies [11] [14]. The studied tire will roll on this transparent window, on which a water film is initially at rest, delimited by a seal and height controlled. For safety issues all emitting and receiving optics are located under the ground level in a dedicated room. Therefore, it is not possible to generate a planar light sheet parallel to the ground as should be done with a standard 2D PIV measurement system and a specific optical arrangement is needed for the targeted application. The overall scheme of the installation is presented in Fig. 2(a).

Emitting optics characteristics

The experimental setup has previously been detailed by Cabut et al. [START_REF] Cabut | Particle image velocimetry (PIV) measurements in a water film, application to a tire rolling through a puddle[END_REF], [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF]. Let us only recall that the source light is a dual cavity pulsed laser emitting at a wavelength of 532nm. The light sheet generated at the exit of the emitting device is directed towards the inclined face of the transparent window depicted in Fig. 2(b). The angle θ is equal to the theoretical angle predicted by Snell-Descartes laws for full refraction at the PMMA/water interface for an incoming light sheet normal to the inclined face. A small angle of the light sheet with the normal allows, after refraction, the propagation of the light sheet inside the liquid film, with a high spreading rate. Therefore, for a small thickness of the water film, the vertical intensity profile I(z) of illumination is nearly uniform in the area of interest, and the liquid film is illuminated in the volume, introducing 2.1 Experimental set-up some bias in velocity measurements for inhomogeneous actual velocity profiles in the vertical direction. Such bias due to both emitting and receiving optics have been analyzed by Cabut et al. [START_REF] Cabut | PIV measurements using refraction at a solid-fluid interface[END_REF].

R-PIV seeding

The tracers used in this application are fluorescent particles doped with Rhodamine B allowing a high signal-to-noise ratio, as soon as a narrow-band filter centered around 584nm with a bandwidth of ± 10nm is mounted on the camera lens. The particles are rather spherical with a nearly Gaussian diameter distribution with a mean value of d p = 35µm and a standard deviation of about 5µm. To quantify inertia effects of particles, we have evaluated their Stokes number St = τp τ f where τ p is the particle response time and τ f = L0 U0 the the characteristic time scale of the flow. Inside the CPA (contact patch area: region where the tire is in contact with the ground), L 0 can be taken as the CPA length L x and U 0 as the steamwise velocity V x inside the grooves. The relaxation time is calculated as τ p = ρpd 2 p 18µ where ρ p = 1.19kg/m 3 is the particles density and µ ≈ 1.10 -3 P a.s (20 °C) the water dynamic viscosity. We can find that St < 10 -5 which is small enough and we can then consider that the particles perfectly follow the fluid.

Receiving optics characteristics

Pairs of images are recorded with a double frame sCMOS camera with a resolution of 2560 x 2160 pixels in the streamwise and spanwise directions respectively. The dimensions of the field of view are 224mm x 190mm, and the calibration factor is 0.09 mm per pixel. The focal distance is equal to 100mm, the working distance between camera lens and the water film has been fixed to nearly 1150mm and the lens aperture fixed to 5:6.

Synchronization of the acquisition

To ensure the synchronization of the laser and the camera with the rolling of the tire on the window, a programmable timing unit (PTU) is used in combination with the commercial software DaVis 8. Optical sensors located some meters before the water puddle calculate the actual car's speed V 0 and generate a trigger signal with a time delay. This delay is computed with a real-time processor and adjusted in order to trigger the PIV system when the tire is at a pre-defined location inside the camera's field of view, whatever the value of V 0 . The time-delay δt between the two-pulses of the laser is adjusted to the vehicle speed, e.g., δt = 225µs for V 0 = 11.11m.s -1 . Before each run, the driver sets the car in position in the beginning of the track and waits for the water film to reach its targeted value H w . When the test starts, a process of rolling, illuminating, and image recording is achieved. For the analysis of the flow repeatability, since PIV measurements are not time-resolved with the system, the overall procedure is repeated over a set of N independent runs for a fixed couple of operating parameters V 0 and H w .

Water depth

The water film depth is regulated by an ultrasound probe located on the track. The standard deviation of H w over the set of N runs is around 3% for low wind conditions. We choose H w = 1.5mm in the present r-PIV experiments; this height is a good compromise between European regulations for breaking tests on wet roads and the homogeneity of the water depth on the window. We note that a higher water depth is more penalizing from the hydroplaning perspective.

Image acquisition and processing

The velocity field is generated using the commercial software DaVis. The cross-correlation between a pair of images is performed with an iterative process using interrogation areas of decreasing size. The initial size 96x96 pixels is dictated by the maximum displacement of seeding particles. The final size 32x32 pixels with an overlapping factor of 75% results of a compromise between signal-to-noise ratio and spatial resolution. The minimum interrogation window size is therefore comparable to half the width of the central groove, and the mesh grid obtained for the selected overlapping factor is 0.7mm. Note that due to the presence of geometric masks as windows are shifted (for overlapping) to the border of a groove, the spatial resolution is locally improved. For some regions of the images, tests were done to ensure that a smaller window size, down to 16x16 pixels, does not change or improve the results obtained with the present parameters.

Before generating the velocity field of each run, a geometric virtual mask is applied on the raw images. The mask generation is one possible source of variability in the results presented in section 3. It is a sensible task since from one image to another not only the tire deformation is not the same due to the dynamics of the fluid, but also the image illumination changes. The purpose of the mask is primary to remove regions without seeding particles (out of fluid flow regions), but also to enhance the cross-correlation quality near the groove's borders. The mask is generated using our own image processing algorithm based on binarization, Gaussian blurring as well as other morphological operations, e.g., closing and dilation. We give in Fig. 3(a) an example of a raw image, the corresponding image with its geometric mask in Fig. 3(b) and the velocity field obtained by cross-correlating a pair of masked images recorded for a given run in Fig. 3(c).

This mask determination method is different from Cabut's work in which a manual process is adopted [START_REF] Cabut | Characterisation of the flow in a water-puddle under a rolling tire with refracted piv method[END_REF]. The present procedure should remove the uncertainty introduced by the operator factor. In addition, despite the driver's skills, the location of CPA inside the field of view can undergo some disparity from one run to the other. We show in Fig. 4 raw images for four different runs to highlight the difference of positioning of the tire on the window. The 2.3 Generation of (X,Y)-offsets for CPA collapse variability appears to be mainly in the spanwise direction Y; a small jitter in the X location of the CPA can be explained by small departures of the actual water film depth from the targeted one. At this stage the origin O is the one resulting from the calibration of the camera, and its location inside the field of view is arbitrary.

Generation of (X,Y)-offsets for CPA collapse

We intend to analyze the flow in the water-bank (highlighted in blue in Fig. 3(a)) and inside the grooves for a set of independent runs. Therefore, the location of the CPA, or at least its leading edge, needs to be collapsed to define a common coordinate system for all the velocity fields, with a common origin O with some physical relevance with the flow structure around the tire and inside the CPA . For a reference run, the image Img 0 is first chosen, then the (X,Y) offsets of the other images (runs), relatively to Img 0 , need to be computed against Img 0 . Two different strategies are proposed to generate the X-offset:

Intensities (or grey level)-based strategy: The main idea is to use the grey-level intensity distribution inside raw images. This method has previously been used by Cabut et al [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] for a tire model with four central longitudinal grooves. In that case, the X-offset for different runs was deduced from the grey-level profile along a narrow band including the central rib with straight edges; such profile is nearly uniform with a very low noise level for the region located inside the CPA and presents a strong gradient near the front edge of the CPA due to the contribution of seeding particles present in the liquid phase, just in front of the central rib.

Velocity-based strategy: This method is based on a quite different idea.

The different tires present the common property to push the liquid to the front, with the appearance of the so-called water-bank with a peak value on the V x velocity profile, bounded by relatively sharp falling and raising edges. . Most of the existing tire models also generate locally a plateau in the V x profile behind the tire, with a zone of sharp gradient near the CPA trailing edge, as depicted in Fig. 5. The X-offset is then deduced from the displacement corresponding to the peak value of the cross-correlation between V x velocity profiles. The main assumption for this method is that the global shape of the velocity profile remains nearly similar from one run to the other.

Therefore, variations due to potential turbulence or two-phase flow influences are hypothesized negligible compared to velocity field determination error levels.

For the tire considered in this study, its complex groove shapes (zigzag and directional grooves) leads to much noisier grey-level profiles inside raw images in the X-direction near the tire mid-plane, than for a tire with longitudinal grooves. Therefore, the peak-detection of the cross-correlation between 2.3 Generation of (X,Y)-offsets for CPA collapse grey-level profiles is somewhat difficult to obtain. Hence the choice to apply the second strategy based on the analysis of velocity profiles.

The first step is to determine the Y-offsets over the N runs. An easily identifiable point on each image is selected using the tread pattern of the tire, e.g. the top of the central zigzag groove depicted with red dots in Fig. 4. The Y-offsets are calculated via the rule: Y-offset j =Ycoordinate Img0 -Ycoordinate j for 0 ≤ j ≤ N -1 At this point, we are able to collapse at the best the N images along the Yaxis. The X-offsets are then determined as follows. We note V jI the Y-shifted velocity field of the run j that is computed for masked images according to Sec. 2.2. In order to remove some potential small-scale noise, the velocity field is then spatially averaged along Y in a band centered around y = 0, as shown in green in Img 0 (Fig. 5(a)). The resulting spatially Y-averaged velocity V jII (x) is related to V jI (x, y) by the relation:

V jII (x) = 1 y 2 -y 1 y2 yi=y1 V jI (x, y i ) (1)
Then comes the actual correlation step between the V jII (x) profiles and the V 0II (x) one. The curves of V jII (x) are plotted together on Fig. 5(c), this for each j (0 ≤ j ≤ N -1). X-offset j are determined corresponding to the maximum of correlation for each case. Each offset corresponds to the translation for the best curve shape matching. Therefore, this method tends to overlay the images according to the position of their water-bank. In case of the A6, the Fig. 5(d) indicates the final shifting; even if the peak value of the profiles undergoes some variations from one run to the other, the collapse of the positions of the rising and falling edges of velocity profiles is very satisfactory. At this stage, the location x = 0 is common for all runs but remains somewhat arbitrary. In Fig. 5(b) the CPA region is bounded by the dashed vertical lines in the intensity profile along X-axis, it corresponds to the area where the illumination is the lowest since the tire is in contact with the ground. We decide to define x = 0 as the location of the right dashed line where the grey-level gradient increases suddenly. Concerning the position of y = 0 it has been chosen so that it corresponds to the center of the middle zigzag groove. With this choice, we introduce a natural separation between the flow inside the grooves of the CPA (x < 0), and in the water-bank in front of the tire (x > 0) which is the region where the water velocity and the pressure are the highest. This last region is responsible for the main part of the fluid lift and therefore of the reduction of the CPA when the car velocity increases. In the rest of this document, V *

x denotes V II /V 0 . We present in this section results obtained for the A6 tire in a worn state at V 0 = 11.11m.s -1 (40km/h) and H w = 1.5mm. Our objective in this part is to see in what extent parameters and normalized quantities could be used for studying another tread design tire, and in what extent they could help understanding flow circulation inside and outside the CPA zone.

Single run

We give in Fig. 6 the velocity magnitude | V | for one run of the A6 tire. In this section we will study the water flow in different zones of the CPA in order to estimate the preferential directions of the water inside the grooves and the evolution of the velocity inside a directional groove depending on its position in the CPA. The objective being first to have an idea about the flow structure along the different grooves and how water is moving from the head of the CPA to the rear or to the shoulders.

Flow inside the central zigzag groove

We start to analyze the velocity inside the central groove. We show in Fig. 7 the field of velocity magnitude inside this groove from the previous shown global velocity field (Fig. 6(b)). The intensities are deduced from the colormap. We focus here on the area between x = -115mm and x = 0 which corresponds to L x , the length of the CPA (highlighted in Fig. 6(a)). We normalize the X-axis by L x and we note x * = X/L x the dimensionless abscissa. Note that this length is chosen following the first work done by Cabut et al. [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] demonstrating its use for self-similarity trends for velocity profiles along straight groove. This is the first attempt to use the same kind of analysis for a tire that has a complex central groove. Identically, the velocity is normalized by V 0 as in Cabut's work. First, we can see that we have a rather good resolution and the flow is well captured despite the complex geometry of the tire tread. Second, we observe that the flow is evacuated mainly from the front of the CPA (x * = 0%) to its rear (x * = -100%), and it is accelerating near the end. We give in Fig. 8 the values of V * x = V x /V 0 and V * y = V y /V 0 space Y-averaged in the central groove (-7mm ≤ y ≤ 7mm) and plotted along the X direction. The Y-averaging is used to show the velocity trends inside the groove. As stated, the flow is accelerated till the rear of the CPA and V *

x reaches around -0.3 near x * = -85% while V * y reaches 0.2 in the same position. However, the peak values of V * y decrease from the rear to the beginning of the CPA. This can be due to the deformation of the tire when it leaves the CPA, the tread portions are suddenly relaxed and widen the central groove, accelerating the water flow to the end of the CPA. Furthermore, we can see in Fig. 8(b) how the flow is disturbed due to the connections between this central groove and the directional grooves (highlighted with arrows) especially near x * = -90% and x * = -70%. This disturbance is well captured in the upper half of the central groove while it seems weaker in the lower part. This gives us some first quantitative and absolute information on the groove flow. It is clear that more quantitative analysis has to be conducted and more particularly a referential linked to the variable axis along the groove and its corresponding perpendicular counterpart has to be defined. Note that for this present work we will do such analysis in section 3.1.4. Nevertheless, we will now present some description for another zone in order to have a final coarse description of the flow in the whole CPA region.

In the directional grooves

We are interested here in analyzing the velocity field V y in the directional grooves (those leading from the previously studied center groove to the tire shoulders) in order to show how water could be evacuated from the central zone. We call this region Area 2 (highlighted in green in Fig. 9(b)). We can see in Fig. 9(a) that along the CPA, y-averaged V * y goes from -0.2 for x * ≈ -95% to nearly zero between x * = -60% and x * = -10%. Note here that as the Y-averaging is done over all Area 2 width, V * y is determined whatever the x * location. Such results couldn't be compared to Cabut's results in the same region as in the present case contribution of velocity field comes exclusively from the transverse grooves. For this reason, such analysis is difficult to consider for a comparison with other tire treads in order to determine the drainage process. This actually requires the use of a parameter accounting for averaging 3.1 Single run in the axial groove direction (or perpendicularly). This is what will be defined in part 3.1.4. In describing the instantaneous run, we show in Fig. 10 an enlargement of the directional grooves, one close to the end of the CPA (pink dashed) and another close to the water-bank (orange dashed). We can clearly see how the water flow is directed to the central groove in the first case and how it is nearly stopped in the second one. This can partly explain the acceleration of the flow in the central groove that we have observed close to the end of the CPA (Fig. 7 and Fig. 8). The directional grooves supply the central one in this region of the CPA. Close to the water-bank it is rather the opposite, and the water flow goes from the central groove to the directional groove, but the velocity is rather low (less than 1m.s -1 ). Such coarse analysis shows the necessity to define a local referential for the grooves. At the best of our knowledge, this will be done for the first time in the part 3.1.4 for all present grooves of the same tire, separating the central zone from the border ejection zone.

Near the shoulders

To focus on the flow close to the shoulders, we define as previously a longitudinal band delimited transversally that we call Area 3 (Fig. 11(b)). In Fig. 11(a) we note that the zero velocity corresponds to the zone outside the grooves. The water is channeled inside the central groove (V * y < 0) in the rear of the CPA at a maximum velocity around -2m.s -1 . But for x * ≥ -70%, it is directed from the CPA to the outside (V * y > 0). This flow dynamics have also been observed in the case of the Primacy 4 tire in a new state in the work of Cabut et al. [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] considering the analysis of C-type transverse grooves. The authors showed a correlation between the location of the groove along the X-axis and the velocity inside the groove : water is ejected outside for a groove located at the beginning of the CPA and sucked inside at the end of the CPA. This Finally, the directional groove at x * = -55% of L x (number 2 in Fig. 11) does not really play a role of drainage here considering the very low velocity 3.1 Single run inside it (around 0.5m.s -1 ). We give in Fig. 12 an enlargement of the two rear directional grooves where we can see the difference of the flow dynamics from one groove to the other. We can note a difference in the grooves' width. This can be explained by the difference that exists in the tread pattern to reduce tire noise.

Definition of a local referential inside grooves

We now will generalize the local average parameter defined by Cabut [START_REF] Cabut | Characterisation of the flow in a water-puddle under a rolling tire with refracted piv method[END_REF] simultaneously for all transverse grooves involved in the drainage process from the CPA zone to outside. One of the main issues is to determine if the flow is sucked inside a groove or pushed outside it, depending on its x-position along the CPA. For that purpose, in a first step we define a new local referential ( u, v) that follows the directional groove direction. We split each groove inside the CPA into three straight segments following roughly their change in direction from the shoulder to the central part of the CPA. We give in Fig. 13(a) an example of the segments' definition for one of the directional grooves where u k (k = 1, 2, 3) is the vector defining the orientation of segment k. From now on we call simply u the unit direction vector of the groove, and we focus on the velocity component V u = V . u. As shown in Fig. 13(a), we have five directional grooves for each run. We call Groove 1 the directional groove near the end of the CPA till Groove 5 the directional groove near the water-bank following the X-axis orientation. A similar segmentation of the zigzag central groove is performed using nine elementary straight segments (Fig. 13(b)). In a second step, we define inside each segment a characteristic fluid velocity V umean as the value of V u spatially averaged along its width and length. If we have in mind that every velocity vector measured with the r-PIV technique is in fact the result of seeding particles which are randomly located and illuminated at different Z altitudes, we can consider that V umean is a global indicator of the velocity inside the volume corresponding to a segment. Finally, in a third step we define the location x of a segment as the x-value of the geometric barycenter of the segment under consideration. The evolution of V * umean = V umean /V 0 with X/L x inside the CPA is shown in Fig. 14, for directional grooves (Figures 14(a), 14(b) and 14(c)), and for the central zigzag groove (Fig. 14(d)). The results are remarkable, mainly for segment 1 of the directional grooves. Despite the small number of runs, the characteristic fluid velocity V * umean of the fluid inside segment 1 is clearly correlated with X/L x . The flow is pushed out of the groove at the beginning of the CPA, and sucked inside the segment at the end of the CPA; the maximum value of V * umean is around 0.6. Such a correlation between fluid velocity inside a transverse groove and its location inside CPA has previously been established by Cabut et al. [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF] considering the analysis of transverse type C-type grooves of a summer tire with four longitudinal grooves. In that case the correlation was nearly linear, there was no suction for grooves located at the end of the CPA, and the maximum normalized velocity was around 0.2, a value much smaller than the present one. The authors linked this behavior with the compression and relaxation of the rubber in the inlet and the outlet of the CPA, highlighting a parabolic distribution of the pressure at the shoulder [START_REF] Heinrich | Rubber friction, tread deformation and tire traction[END_REF]. A correlation between V * umean and X/L x is also clear for segments 1 and 2. For the central zigzag groove, the evolution of V * umean with X/L x shows a monotonic variation illustrating the accumulation of water from the front end of the CPA until its rear end. 3.2 Ensemble averaged velocity field As a conclusion of this section, the discrepancies between winter-type and summer-type tires suggest that the different V * umean profiles can be considered inside CPA as the hydrodynamic signature of the particular tread design considered. After studying the water flow inside the CPA, another region is of interest in this study, the water-bank. We draw the reader's attention to the random positioning of directional grooves inside the CPA. This adds an extra difficulty to consider averaged quantities inside this region. However, as stated in section 2.3, the overlapping of the N images has been done based on the position of the water-bank, thus our interest in averaged parameters in this last region of interest.

Ensemble averaged velocity field

In this section we analyze the velocity field of the ensemble averaged data for N = 7, V 0 = 11.11m.s -1 and H w = 1.5mm to study the evolution of the velocity in the water-bank (WB). The areas of averaging are defined in such a way to detect the change in the global flow behavior as a function of the position inside the WB. In particular, we want to check if there is some visible impact of the groove design on this part of the flow as a signature of the grooves.

Large scale movement inside the water-bank

The WB starts from x = 0 as indicated in Fig. 5(b). To further analyze the evolution of V *

x from the central region to the shoulders, we can plot it Xaveraged in three zones splitting the WB between x 1 =0mm and x 2 =49mm as depicted in Fig. 15(a). Such bands are chosen to cover the parts i)D x 1 : from the WB beginning to before the peak of the longitudinal velocity shown in Fig. 5(d), ii)D x 2 around the peak value and iii)D x 3 after such peak. The three regions are of equal width (Fig. 15(a)). This allows us to study the evolution of the velocity profiles V *

x (y) and V * y (y) at different x-positions as D x 1 is the closest one and D x 3 the furthest. We can hope to bring out some influence of the tread design on such profiles. The error bars represent the standard deviation over the N runs. First we note that the profiles are not perfectly symmetric against y = 0. This is partly due to the asymmetry of the tread design in the transverse 3.2 Ensemble averaged velocity field direction. It can also be explained by the lack of repetitions that increases the noise in our signals. Second, for the three subregions D x i, two humps exist for V *

x (Fig. 15(b)), reached around y = -25mm and y = 25mm. The maximum of V *

x is reached in D x 2 and it exceeds 0.7. Concerning V * y (Fig. 15(c)), we can see that at a large scale (tire width scale), the evolution is rather linear in the three subregions D x i and the highest values are reached in D x 1. This is mainly due to the shape of the grooves that drain water to the shoulders rather than to the center. However, we can assimilate the disruptions specially seen in D x 1 to a smaller scale phenomena.

Local or small scale groove influence inside the water-bank

We can see in the profile of V * y in D x 1 (Fig. 15(c)) that three "peak/hole" (P/H) events exist at y = -48mm, y = 0 and y = 48mm (dashed blue line in Fig. 15(c) for this last location). These disruptions correspond to the influence of the zigzag and the two connecting grooves on the flow in the WB. We emphasize that the subregion D x 1 is outside the CPA, the tire is not in contact with the ground anymore and the flow in this region is therefore not enforced to channel inside the grooves. Such P/H characterizes the efficiency of the tread design to draw the water by the central and connecting grooves. At the present vehicle velocity V 0 , the P/H is no more present on the furthest bands D x 2 and D x 3. Note that the influence of the groove inlets is also visible on the longitudinal velocity profile for D x 1 (Fig. 15(b)), where we can observe a large velocity deficit. This loss is also visible in D x 2 for which a plateau is present around y = 0. With more runs, the two other deficits could probably be determined at least for the band D x 1. Such deficits in the two velocity profiles could be studied more precisely in the future to characterize water drained under the WB compared to the one ejected at the shoulders. Their global velocity evolution as a function of the car velocity will probably help in the design of tread efficiency.

Velocity magnitude inside the water-bank

We give in Fig. 15(d) the evolution of the velocity magnitude | V | * spatially averaged along X between x 1 and x 2 . Globally, it has a shape close to V * x only that between y = -50mm to y = 50mm, | V | * is rather homogeneous, meaning that in the region in front of the tire the direction of the water ejection changes from the center to the shoulders, but not its modulus. The deficit holes are more visible than for longitudinal velocity profiles but are less significant than for transverse velocity profiles. Nevertheless it seems that they are still present in the second band D x 2 in location continuity with those in the band D x 1. More runs will probably increase the trends.

In conclusion to this part, the transverse velocity profiles are more sensible to the tread design at local scale but the modulus is probably more robust 21 for the detection of their impact. At large scale, two humps exist around the center zone for the longitudinal velocity profiles only (not for the transverse velocity profiles) and are significantly maintained in all subregions D x i. The linearity of V * y is also clear and maintained in all the WB width. However, at a small scale the grooves impact only the velocity profiles in the first band D x 1.

Conclusion

In this work, we present some elements of a local investigation of the velocities involved during the rolling of a tire over a water film. We had a principal objective to refine the work by Cabut in order to obtain 1) parameters able to improve our knowledge about transition to the hydroplaning situation, 2) parameters able to highlight universal behaviors allowing tire comparison whatever the tread design studied. The r-PIV measurement technique has proven its efficiency in front of a rather complex tread design with inclined directional grooves and a central zigzag groove. The collapse over several independent runs of the velocity fields inside the water-bank is performed with a cross-correlation technique and allows to define a common coordinate system in which the position of the contact patch area is fixed, while the locations of the different grooves inside the contact patch area undergo from one run to the other a random spatial jitter parallel to the car motion. A segmentation of the directional and central zigzag grooves into elementary straight segments is performed and allows to deduce, for each element, from PIV measurements and for every run, a dimensionless characteristic velocity V * umean . Results highlight a clear correlation between V * umean inside an elementary segment and its dimensionless coordinate X/L x where L x is the contact patch length for the selected couple of operating parameters (V 0 , H w ). This correlation is remarkably clear for the segments of the grooves close to the shoulders, with an ejection of water outside the grooves (V * umean > 0) for segments near the leading part of CPA, and a suction phenomenon (V * umean < 0) towards the grooves for segments located at the end of the CPA. However, the present results show some discrepancies with the case of a summer tire in a worn state with four longitudinal grooves and perpendicular transverse grooves for the sign and maximum value of V * umean [START_REF] Cabut | Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry[END_REF]. Finally, the velocity inside the water-bank has been studied using a statistical averaging over numerous trials, leading to specific hydrodynamic signature, at large and small scales, of the studied tread design. In the present work, for analyzing flow drainage from the center CPA zone to the CPA borders, we have shown extending Cabut's work that velocity averaged parameters (3.1.4 and 3.1.2) have to combine simultaneously both directional averaging in a flow zone of interest and longitudinal localization inside a transverse groove. In the future, a parametric study should be carried out increasing car speeds until the appearance of hydroplaning. The interest of such a parametric study is twice. First, inside the CPA, it is of interest to study the evolution of V * umean along the position X/L x and see if there is a breaking point when reaching the hydroplaning situation. Second, in the water-bank, the identification of suitable parameters e.g., the width of the WB allows us to study the efficiency of the tread until reaching its full capacity of drainage. The influence of H w has also to be understood. Moreover, other tread designs should be included in further studies in order to examinate designs' efficiency on a very local level. Last but not least, in parallel to the experimental approach, a numerical investigation is conducted in order to perform comparisons with experimental data concerning the different zones of interest [START_REF] Ben Khodja | Validation of coupled SPH-FE hydroplaning simulations using PIV measurements[END_REF].

Fig. 1 :

 1 Fig. 1: Details of the A6 tread design in a new (left) and worn (right) state

Fig. 2 :

 2 Fig. 2: Scheme of the in-situ r-PIV installation (a) and detail of the refraction processes of the laser sheet at the air/PMMA and PMMA/water interfaces (b)

Fig. 3 :

 3 Fig. 3: Raw intensity image of run 1 from r-PIV acquisition with a highlight of the water-bank region (a), then the same image on which we apply a binary image called a mask (b) and the velocity field associated generated from the cross-correlation processing (c) of the A6 tire in a worn state at V 0 = 11.11m.s -1 and Hw=1.5mm

Fig. 4 :

 4 Fig. 4: Raw intensity images (Frame 0) for four independent runs. The red dot on images shows the relative position of a given arbitrary point located on the edge of the central zigzag groove.

Fig. 5 :

 5 Fig. 5: Area 1 highlighted in green on raw image of the A6 at V 0 =11.11m.s -1 and Hw = 1.5mm (a), image intensities space averaged along Y-axis in Area 1 (b) and V *x space averaged along Y-axis in Area 1 before (c) and after (d) X-offsetting

Fig. 6 :

 6 Fig. 6: Raw r-PIV image (a) and its associated velocity field | V | (b) (run 1)

Fig. 7 :Fig. 8 :

 78 Fig. 7: Visualization of | V | field inside the central groove (run 1)

Fig. 9 :

 9 Fig. 9: Evolution of V * y (velocity y-averaged in the region Area 2) (a) and highlight of this region on raw image of run 1 (b)

Fig. 10 :

 10 Fig. 10: Enlargement of the directional grooves at the rear (left) and at beginning (right) of the CPA

.

Fig. 11 :

 11 Fig. 11: Evolution of V * y that is obtained from the velocity Y-averaged in the region Area 3 (a) and highlight of region Area 3 on raw image (b) (run 1)

Fig. 12 :

 12 Fig. 12: Enlargement of the two transversal grooves at the end of the CPA (number 1 and 2 in Fig.11)

Fig. 13 :

 13 Fig. 13: Definition of the segments cutting and highlight of the new referential axis in each segment in Groove 2 (a) and segmentation of the zigzag central groove (b)

Fig. 14 :

 14 Fig. 14: Evolution of V * umean over the grooves in the CPA in segment 1 (a), segment 2 (b), segment 3 (c) and zigzag groove (d) for N =7 runs, V 0 = 11.11m.s -1 and Hw = 1.5mm

Fig. 15 :

 15 Fig. 15: The WB is divided here into three subregions of equal width Dx1, Dx2 and Dx3 highlighted in (a). The evolution of V * x (b), V * y (c) and | V | * (d) the velocity space X-averaged between x 1 and x 2 (a) is represented.

Acknowledgments. This work is partly funded by the French government through the Association Nationale de la Recherche et de la Technologie (CIFRE grant agreement 2019/0949).