Emmanuel Kwadwo

Kale Agyeman
email: emmanuel.agyeman@irt-jules-verne.fr

Denis Edelin

Damien Lecointe

Experimental Study of the Effect of a Cross Airflow on the Dynamics and Heat Transfer Performance of Impinging Circular Water Jets on a Concave Surface

In this study, the impingement of a concave surface by hot water jets is investigated. The jets are subjected to a cross airflow at ambient temperature in order to study the effects of the interactions between both fluids on the jet dynamics and the heat flux at jet stagnation area.

Different parameters such as the jet diameter, separation distance between two adjacent jets, Reynolds numbers of the jets and the Reynolds number of the airflow are varied. These studies reveal that imposing airflow in the annular space between the jet orifice and the impacted surface can increase the surface wetted area by 40% and can also enhance the heat transfer coefficient at the jet stagnation area by as much 105 %. It was also observed that reducing the jet to air mass flow ratio to values below 0.75 leads to the tilting of the water jets and the widest uniformly heated area among the flow parameters tested can be obtained with a ratio of the distance between the jet orifice and the impacted surface and the jet orifice diameter of 4.5 for a single jet impingement.

INTRODUCTION

During the cooling of injection and compression moulds via the circulation of fluids in channels, the progressive increase in the temperature of the fluid as it flows through the canal leads to a non-homogeneous cooling of the mould [START_REF] Marques | Design of conformal cooling for plastic injection moulding by heat transfer simulation[END_REF]. This is due to the fact that the heat flux is at its highest at the entrance of the canal and reduces progressively as the fluid heats up [START_REF] Tymen | Temperature mapping in a two-phase water-steam horizontal flow[END_REF]. This challenge tends to worsen when there's a phase change of the fluid since most of the fluid gets converted to vapour. Water is the preferred fluid for mould cooling but other fluids such as oil can also be used. A heterogeneous cooling of the mould could negatively affect the quality of the part being formed. An alternative to this cooling approach is making sure the surface is cooled simultaneously by a fluid having the same temperature along the entire surface being cooled as opposed to the scenario where the fluid entering the canal is colder or of a different phase than the fluid leaving it. For the cooling to be homogeneous, the surfaces of the canals need to be impinged simultaneously in order to ensure a uniform distribution of the heat flux. This could be achieved by the impingement of multiple jets along the entire surface of the cooling canals coupled with the imposition of airflow along the canals to uniformly distribute the water film on the impinged surface and to evacuate excess water and or steam when higher temperatures are involved. The aim of this study is thus to better understand the complex interactions between water impinging jets and a cross airflow in a confined cylindrical space in view of a potential application of this technology in the controlled and homogenous cooling of injection and compression moulds. The studies are limited to non-boiling conditions and are thus only applicable to scenarios involving relatively low surface temperatures (< 200 °C).

Liquid and air jets have numerous industrial applications in the manufacturing, aerospace and electronics industries. Some of the applications of water and air jets are in the quenching and controlled cooling of metals during their manufacture, jet engine turbines cooling and cooling of electronic devices to avoid the overheating of their circuits. Numerous experimental and numerical studies have been undertaken in order to better understand jet impingement and optimize its heat transfer performance.

Bouhadef [START_REF] Bouhadef | Étalement en couche mince d'un jet liquide cylindrique vertical sur un plan horizontal[END_REF] studied the hydrodynamics of the water film formed after the impingement of a circular jet on a flat surface. A theoretical model for the determination of the position of the flow front for different jet speeds was developed. This model proved to be accurate when compared to experimental results. Watson [4] developed a model for determining the radius of the hydraulic jump when a smooth jet of water falls vertically onto a horizontal plane.

Wang et al. [START_REF] Wang | Heat transfer between a circular free impinging jet and a solid surface with non-uniform wall temperature or wall heat flux-1. Solution for the stagnation region[END_REF] analytically studied the stagnation region heat transfer during the impingement of a surface by a circular water jet. Their studies revealed that the wall temperature or heat flux distribution have a considerable effect on the stagnation point Nusselt number. Elison and Webb [START_REF] Elison | Local heat transfer to impinging liquid jets in the initially laminar, transitional, and turbulent regimes[END_REF] investigated the effects of the jet flow regime on its heat transfer performance. Studies were performed on both free surface and submerged jets. Their results revealed that the Nusselt number was approximately correlated to Re 0.5 and Re 0.8 for initially laminar and turbulent jets respectively. Liu et al. [START_REF] Liu | Convective Heat Transfer by Impingement of Circular Liquid Jets[END_REF] developed correlations for the prediction of heat transfer without phase change on a surface impinged by a circular liquid jet. The impinged surface was divided into the stagnation, laminar, transition and turbulent zones all determined by the velocity profile of the fluid on the surface. The effects of the viscous and thermal boundary layers development on heat transfer performance during the impingement of a surface by a circular liquid jet were studied by Liu and Lienhard [START_REF] Liu | Liquid Jet Impingement Heat Transfer on a Uniform Flux Surface[END_REF]. They concluded that the maximum Nusselt number was located at some radius away from the stagnation point and that both the magnitude and the radial position of the maximum Nusselt number increase with the Reynolds number. Hu and Zhang [START_REF] Hu | Experimental and Numerical Study on Heat Transfer with Impinging Circular Jet on a Convex Hemispherical Surface[END_REF] investigated the water jet impingement of a convex surface. They concluded that the heat transfer coefficient on a convex surface is higher than that on a flat surface and is highest at the jet stagnation point.

The heat flux distribution on a plate impacted by two adjacent liquid jets was experimentally studied by Teamah et Khairat [START_REF] Teamah | Heat transfer due to impinging double free circular jets[END_REF]. They came to the conclusion that the Nusselt number values are higher at the jet stagnation zones, however, the Nusselt number drops as we move away from the jets. This is due to the thickening of the liquid film and the drop in its radial velocity resulting from the interactions between the fluids from both jets. Ishigai et al. [START_REF] Ishigai | Heat Transfer of the Impinging Round Water Jet in the Interference Zone of Film Flow along the Wall[END_REF] analyzed the heat transfer and hydrodynamics at the interference region formed by the interaction of two adjacent jets. They concluded that the type of flow at the interference region is dependent on the film Froude number while the heat transfer is dependent on both the Froude number and the Reynolds number. The heat transfer characteristics in a canal with an inclined heated surface impinged by a single array of staggered jets were studied by Al-Hadhrami [START_REF] Al-Hadhrami | Study of Heat Transfer Distribution in a Channel with Inclined Target Surface Cooled by a Single Array of Staggered Impinging Jets[END_REF]. Different nozzle configurations were tested and it was concluded that the outflow orientation in coincidence with the flow entry had a better average Nusselt number compared to the other configurations. No previous study involving the simultaneous use of water jets and a cross airflow for cooling or heating purposes was found in the literature.

EXPERIMENT AND METHOD

Experiment

The different components of the experimental bench are illustrated on the schematic diagram of Figure 1. It consists of two concentric cylindrical tubes, one in plastic (PMMA) and the other in borosilicate glass. The inner plastic tube is perforated in order to create circular holes that enable the water in the tube to escape once pressurized. The escape of the pressurized water in the tube via the perforations leads to the formation of jets that impact the internal surface of the outer tube made of glass. Glass was chosen for its optical properties (transparency in the visible spectrum) and for its opacity to infrared radiation. This enables the visualization of the hollow space within the tube and permits the use of an infrared camera to measure the temperature of its external surface from which the heat exchange on the impinged surface can be characterized by an inverse method. The inner tube is connected to a thermostat (Lauda Proline RP845, No.6) with an in-built reservoir and pump. The thermostat thus has the double function of pumping the water and regulating its temperature. The flow rate of the water is regulated by varying the power of the pump and by adjusting the opening of the valve between the thermostat and the inner tube. This flow rate is measured accurately by an ultrasonic flow meter (Atrato 740-V10 D) installed between the thermostat and the inner tube's inlet. The outer tube is connected to a reservoir of compressed air regulated by a valve while the air pressure at the outlet of the air reservoir is measured by a pressure gauge (Bosch 1827231010). The flow rate of the air was measured by an airflow meter (SMC PFMB7501). An HD camera was used to visualize the different phenomena that took place within the tube during the impingement of the jets and their interaction with the air that flows perpendicularly to them in the annular space between both tubes. For the experiments involving heat transfer, the temperature of the outer surface of the glass tube was measured by means of an infrared camera (Optris PI640). The experiments conducted are summarized on Table 1.

An image of the experimental bench with the dimensions of the tubes is shown on Figure 2.

Both tubes are 1000 mm long; the diameter of the inner tube is ∅12/10 mm while that of the outer tube is ∅33/30 mm. This leaves a distance of 9 mm (H) between the orifice and the internal surface of the outer tube. Different orifice diameters were tested and range from ∅ (1-3) mm. This gives orifice to surface distance and jet diameter ratios (H/dj) of 3, 4.5 and 9 respectively. The experimental work was divided into 2 phases; a visualization of the fluid dynamics phase and a heat transfer phase. Different flow rates for both fluids were tested in order to study their effects on the jet and on the water film formed on the glass surface. For each experiment, water was allowed to flow in the inner tube for approximately 10 s in order to get rid of all the air trapped in the tubes. The valve at the exit of the tube was then closed in order to generate a higher pressure within the tube. This leads to the escape of the water from the orifices in the form of jets. During the experiments involving water and airflow, the valve regulating airflow is opened first and the airflow is allowed to stabilize for a few seconds before the release of the water jets. For the single jet experiments, the surface area occupied by the water film formed during jet impingement for different flow parameters was measured from the images taken by the HD camera positioned above the tube.

Method

The area of the wetted area was measured by an open source image processing software known as ImageJ ® by tracing contours along its boundaries. Before recording each experiment, a ruler was placed to the side of the tube in order to establish a scale that enabled the conversion of the pixels on the image to metric units as illustrated on Figure 3. Due to the fact that the tube is cylindrical and thus has a curved surface, the areas measured on the software are just a 2D projection of the real area. In order to take the effects of the surface's curvature into account, the areas measured were multiplied by a factor obtained by taking the ratio of the area of the upper half of the cylinder to that of its projection as demonstrated by illustration of Figure 4. For each experiment, 20 measurements were made and the average value was taken.

Area of upper half of cylinder = πrL

(1)

Area of its projection = 2rL (2)
Ratio of both areas =

( ) (3)
The heat transfer phase of the experimentation involves heating the outer glass tube with hot water jets. The water is heated in the thermostat to the required temperature of 50 °C before being pumped to the perforated inner tube. During the impingement of the jets, the temperature of the external surface of the glass tube is measured by an infrared camera positioned directly above the surface of the tube along the jet's axis.

Inverse heat conduction analysis

An inverse method was used to estimate the heat transfer coefficients and the heat flux at the jet stagnation area. The objective function which is the root mean square error between the numerical computations and the experimental measurements was minimized iteratively by the Nelder-Mead simplex algorithm [START_REF] Lagarias | Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions[END_REF]. The temperature was measured from a circular area with a 1 mm diameter on the external surface whose centre lies on the same axis as the jet. The direct problem is modelled as a 1D heat conduction problem across the thickness of the glass tube (Figure 5) and is solved by the finite element method (FEM). A transient natural convective heat transfer coefficient is imposed on the external surface of the glass tube. This natural convective heat transfer coefficient is calculated from the correlating equation for a horizontal cylinder by Churchill and Chu [START_REF] Churchill | Correlating equations for laminar and turbulent free convection from a horizontal cylinder[END_REF] by using the external surface temperature measurements obtained. The jet heat transfer coefficient to be estimated is imposed on the internal surface of the glass tube.

Using a 1D model is justified by the adiabatic conditions surrounding the jet stagnation area due to the uniform temperature distribution on the area occupied by the wetted area formed during jet impingement. Given that the jet stagnation area is small when compared to the wetted area (wetted area to stagnation area ratio of 600), heat conduction via the other axes is minimized.

The heat flux is then calculated from the values of h and of the internal surface temperature vector (T int -sur (t)) obtained as well from the inversion analysis. The minimization procedure is illustrated on the schematic diagram of Figure 6.

q * = ℎ . [T : -T <=5 _ ?@+ (𝑡)], on Γ1 ( 5)

q ) = ℎ E (𝑡). [T FG5 _ ?@+ -T E ] , on Γ2 (6)

Uncertainty analysis

The uncertainties on the different experimental parameters and calculations are presented. The uncertainties on the experimental measurements were obtained by dividing the values provided by the manufacturers by √3 while the uncertainties on the calculated parameters were estimated by means of the propagation of uncertainty method. The approach used to determine the errors from the use of the inverse method is also described. The uncertainty on the airflow rate measurements were estimated by the manufacturers as 3% of the reading over the flow rate range of 5 -500 l/min while the uncertainty on the water flow rate measurements were estimated as 1% of the reading over the flow rate range of 0.02 -5 l/min. With regards to the temperature measurements, the uncertainty is the higher of ±2 °C or ±2% of the reading over the range -20 -900 °C. Table 2 summarizes the uncertainties on the calculated parameters.

For the inverse method, the uncertainty on the estimated heat transfer coefficient with a confidence interval of 95% and 10 experimental samples was obtained from equation ( 7) [START_REF] Ozisik | Inverse Heat Transfer: Fundamentals and Applications[END_REF].

∆ℎ = 1.812 × αMvar(ℎ) (7)
A value of 𝛼 = 0.316 which represents the noise of the temperature measurements was used while the variance of the heat transfer coefficient (var (h)) was calculated from equation [START_REF] Liu | Liquid Jet Impingement Heat Transfer on a Uniform Flux Surface[END_REF].

var (h) = TS FG5_?@+ V S FG5_?@+ W X* (8)
where,

S FG5_?@+ = ⎣ ⎢ ⎢ ⎡ ,0 \]^_`ab,def ,g ⋮ ,0 \]^_`ab,d i ,g ⎦ ⎥ ⎥ ⎤ (9)
The uncertainty on the heat flux calculated was obtained by using the propagation of uncertainty method described by equation 10.

(∆q(t)) ) = n ∂q ∂h q ) (∆ℎ) ) + s ∂q ∂T : t

) T∆T : W ) + s ∂q ∂T ?@+_<=5 t ) T∆T <=5_?@+ (t)W ) [START_REF] Teamah | Heat transfer due to impinging double free circular jets[END_REF] ∆T <=5_?@+ (𝑡) = ∆ℎ. S <=5 _ ?@+ (t)

RESULTS AND DISCUSSION

Flow visualisation

Results for a single jet diameter that when there's no airflow in the annular space between both tubes, the wetted area increases progressively until a critical value is attained above which there's no further increase in the wetted area. This is due to the fact that most of the water splashes off the surface due to the relatively high jet velocity. Another observation that can be made is that airflow increases the wetted area for most jet Reynolds numbers (Rej) tested. The increase in the area by the airflow is

S <=5_?@+ = ⎣ ⎢ ⎢ ⎡ ,0 uv^_`ab,def ,g ⋮ ,0 uv^_`ab,d i ,g ⎦ ⎥ ⎥ ⎤ (11)
higher for lower jet Reynolds numbers (< 8000) when compared to the higher jet Reynolds numbers. However, for airflow Reynolds numbers (Rea) greater than 4000, there's a significant increase in the area of the water film for the entire range of jet Reynolds numbers tested.

Results for two adjacent jets

In addition to the studies performed on a single jet, the effects of the interactions between two adjacent jets were also studied. For a scenario with two adjacent water jets, an interference zone where the fluids originating from both jets meet is formed (Figure 9). This zone is characterized by a relatively lower heat flux when compared to the heat flux at the stagnation areas of both jets [START_REF] Teamah | Heat transfer due to impinging double free circular jets[END_REF]. Increasing the flow rates of both jets also increases the area of the water film formed on the tube's surface which can be observed by comparing the images of Figure 9 and Figure 10.

Effects of increasing the distance (s) between the jets are shown. Results presented are for a scenario with no airflow in the annular space. It can be observed that as the distance between the jets increases, a wider water film is formed and the interference zone between both jets gets wider.

Figure 11 shows us the effect of continually increasing the air mass flow rate for a given jet mass flow rate is shown. It's observed that as the jet mass flow rate to air mass flow rate ratio increases, the jets deflect progressively until getting to a point where the air starts penetrating the internal tube via the orifices. This prevents the exit of the jets from the orifices. The mass flow rate ratio is obtained from the expression below:

𝜎 = 𝑚 y ṁ { ̇ (13)

Influence of jet parameters on the temperature uniformity of the tube's external surface

Results for a single jet Different H/dj ratios were tested in order to study the effect of this parameter on the temperature uniformity of the heated surface. As illustrated on Figure 12, the temperature was measured on the external surface of the glass tube along its length and along half its circumference at the jet impact area. Figure 13a and Figure 13b illustrate the temperature distribution on the external surface of the tube along the tube's length and along its circumference for different jet diameters at times 10s, and 40s respectively is presented. The dimensionless temperature was obtained from the equation below:

T * = T -T } T : (14)
The ambient temperature during the experiments ranged from (22-27) °C and was assumed to be equal to the initial temperature of the tube. It can be observed from Figure 13 that a H/dj ratio of 4.5 has the widest uniformly heated area for the same jet mass flow rate of approximately 9.10 -3 kg.s -1 when compared to the other ratios. We also notice that the airflow tends to shrink the heated area before the jet stagnation point and expand the heated area after the jet stagnation point in the direction of the airflow. This phenomenon can be observed from the images of Figure 7. It's safe to assume that increasing the airflow further will widen the heated area due to an increase in the wetted area as illustrated on the graph of Figure 8. Another observation is the fact that some of the temperature profiles have negative values. This could be due to the evaporation of water droplets that splash unto the parts of the tube that are not directly impacted by the jet. The reason for this hypothesis is the fact that the temperature drops below the ambient temperature and the negative temperature values are obtained only from the parts of the tube's surface that were attained by water droplets. The airflow in the tube could be responsible for the high evaporation rates.

With regards do the temperature distribution along the upper half of the tube's circumference, a rather uniform temperature distribution is observed and the airflow doesn't affect the temperature distribution. The temperature measurement was limited to the range (-60° -+60°)

with the jet axis being the line of reference for the angle measurements. This limitation is due to the effect of the directional dependency of the tube surface emissivity as demonstrated in the study of Ibos et al. [16]. This therefore makes the measurements obtained from angles beyond 60° or -60° unreliable.

Results for two adjacent jets

In a similar manner to what was done during the tests performed on a single jet, the temperature distribution on the external surface of the heated tube was measured for a scenario involving the simultaneous impact of the tube's internal surface by two adjacent jets. This study was performed in order to identify the ideal spacing between the jets (dj = 1 mm) for a uniform temperature distribution along the impacted surface. The positioning of the jets is illustrated on Figure 14. Figure 15a and Figure 15b show us the temperature distribution on the external surface of the glass tube for different times during the impingement of the tube for a single jet Reynolds number of 8989. It's assumed that the total flow rate of the water is equally divided among the jets leading to identical Reynolds numbers. The reason for this assumption is the fact that the orifices are almost identical and the pressure of the water is uniformly distributed along the tube. It can be observed from the graphs that as the distance between the jets increases, a wider area is heated and the airflow tends to have the same effect observed in the previous study where the heated area before the first jet's stagnation area is reduced and that after the second jet's stagnation area in the direction of the airflow increases.

Influence of the Reynolds numbers of both fluids on the heat transfer at the jet stagnation area

The effect of different Reynolds numbers of both the jet and the airflow on the stagnation area heat transfer between the jet and the surface is studied. Figure 16 illustrates the zone where the temperature is measured on the external surface of the glass tube while Figure 17 shows the experimental measurements made. The heat transfer coefficients estimated are presented on Table 3 while the heat fluxes estimated (Figure 18a) are placed by the side of their estimated relative errors (Figure 18b). After analyses, it was observed that the differences between the temperature profiles obtained from the 3 highest Reynolds numbers are lower for the scenario with a cross airflow. However, for the lowest jet Reynolds number of 4753, the gap is widened.

This can be explained by the enhancement in the jet stagnation area heat transfer coefficient by the airflow for some combinations of jet Reynolds numbers to air Reynolds numbers. This enhancement was found to depend on the ratio of the Reynolds numbers of both fluids as illustrated on Figure 19. The enhancement in the heat transfer coefficient peaks at a ratio of 2.87 and tends to decrease progressively as the ratio increases. However, reducing the jet's Reynolds number to air Reynolds number ratio below 2.87 has a negative effect on the heat transfer coefficient which reduces from its original value obtained without airflow. The errors on the heat transfer coefficient were taken into account in the calculation of its percentage enhancement as described in equation [START_REF] Ozisik | Inverse Heat Transfer: Fundamentals and Applications[END_REF].

Enhancement in ℎ = ( g "… †i ‡ˆ‰ g Šˆ "… †i ‡ˆ‰ -1 ) × 100 (15)
The hypothesis proposed to explain this enhancement is the turbulence generated at the jet stagnation area due to the interaction between both fluids. The variations in the enhancement could be explained by the variations in the turbulence intensity which could depend on the ratio of the Reynolds numbers of both fluids. However, when the ratio is relatively low (< 2.87) the airflow tends to have a negative effect on jet heat transfer performance.

CONCLUSIONS

The influence of airflow on the hydrodynamics of an impinging jet and the water film formed on the surface after impact was visualized and its area measured for a single jet. The interaction between two adjacent jets with different separation distances between them was also visualized.

The influence of the air/jet and jet/jet interactions on the heat transfer with no phase change between the jet and the surface was also studied. These studies revealed that:

1. Imposing airflow in the area between an impinging jet and the impacted surface spreads out the water film that forms on the surface thereby increasing its area for certain jet to air Reynolds numbers ratios. For the flow parameters tested, the wetted area could be increased by as much as 40 % by the airflow. This means that when cooling or heating a certain area by water jets, introducing a cross airflow could reduce the number of jets needed for a homogeneous cooling/heating of the surface. For values of σ < 0.75, the water jets start tilting under the force of the airflow until getting to a point where the jets are unable to exit the orifices.

2. The heat transfer coefficient at the jet stagnation area can be enhanced by as much as 114%

and depends on the jet to air Reynolds number ratio. This could be brought about by variations in the turbulence intensity which could be linked to the interaction between both fluids.

3. For a single jet, the optimum performance in terms of the size of the area that is heated uniformly was obtained with a H/dj ratio of 4.5. For two jets, uniform heating/cooling could still be achieved by increasing the s/dj ratio to 50.

ACKNOWLEDGEMENTS:

Rea

Reynolds number of airflow,

• " (•X' d'"" )

• "

Rej

Reynolds number of jet,

List of figures

Figure 7

 7 Figure7shows us the effects of varying the control parameters (jet and air mass flow rates)

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :Figure 9 :Figure 10 :Figure 11 :Figure 12 :Figure 13 :Figure 14 :Figure 15 :Figure 16 :

 12345678910111213141516 Figure 1: Schematic illustration of the experimental bench and of its different components

Figure 18 :Figure 1 :

 181 Figure 18: Heat flux at jet stagnation area: a) Evolution of the heat flux with respect to time,

Figure 3 :

 3 Figure 3: Measurement of area of water film by an image processing software

Figure 9 :

 9 Figure 9: Visualization of water film and of interference zone formed between two adjacent jets dj =1 mm, 𝑚̇5 = 11.33. 10 X› kg/s , s/dj = 20, a) Side view, b) Top view

Figure 10 :Figure 11 :Figure 17 :Figure 18 :

 10111718 Figure 10: Visualization of water film and of interference zone formed between two adjacent jets for different separation distances (dj =1 mm), a) ṁ5 = 13.67. 10 X› kg/s , s/dj = 10,

Figure 19 :

 19 Figure 19: Influence of the Reynolds numbers ratio on the heat transfer coefficient at jet

  The authors would like to thank Pierre Mousseau and Alain Sarda for their guidance during the experimental phase of this research and they are also grateful to Yannick Madeck and Erwann Paviot for their help during the assembly of the experimental bench.

	L	tube length, m
	𝑚̇	mass flow rate, kg.s -1
	PMMA	poly(methyl methacrylate)
	q	heat flux, W.m -2
	r	radius of canal section, m
	Re	Reynolds number
	NOMENCLATURE
	cp	specific heat, J.kg -1 .K -1
	D	canal diameter, m
	dj	jet orifice diameter, m
	dtube	external diameter of tube, m
	e	thickness of glass tube, m
	FEM	Finite element method
	g	gravity, m.s -2
	H	distance between jet orifice and tube's internal surface, m
	h	heat transfer coefficient, W.m. -2 K -1
	k	thermal conductivity, W.m -1 .K -1

Table 1 :

 1 Summary of different parameter values for the experiments on heat transfer

	• -' -
	• ‰

Table 2 :

 2 Uncertainties on experimental and calculated parameters

	Experiment	Number	Diameter	Mean jet	Jet exit	Jet	Mean	Air	Initial	Distance
	number	of jets	of orifice	flow rate	speed	Reynolds	airflow	speed	surface	between jets
			(mm)	(kg.s -1 ×	(m.s -1 )	number	rate	(m.s -1 )	temperature,	(mm)
				10 -3 )			(kg.s -1 ×		Ti (°C)
							10 -3 )
	1	1	1.05	6.17	7.85	8989	0	0	24.66	-
	2	1	1.05	9.01	11.50 13483	0	0	25.29	-
	3	1	1.05	6.17	7.85	8989	1.35 1.85	25.28	-
	4	1	1.05	9.01	11.50 13483	1.35 1.85	25.66	-
	5	1	2.10	9.83	3.11	6989	0	0	22.71	-
	6	1	2.10	7.83	2.49	5596	1.35 1.85	24.78	-
	7	1	3.17	10.05	1.41	4753	0	0	24.84	-
	8	1	3.17	7.50	1.06	3573	1.35 1.85	24.24	-
	9	2	1.05	6.17	7.85	8989	0	0	24.54	10.06
	10	2	1.05	9.01	11.50 13483	0	0	25.26	10.06
	11	2	1.05	6.17	7.85	8989	1.35 1.85	25.29	10.06
	12	2	1.05	9.01	11.50 13483	1.35 1.85	25.75	10.06
	13	2	1.05	6.17	7.85	8989	0	0	24.06	20.08
	14	2	1.05	9.01	11.50 13483	0	0	25.12	20.08
	15	2	1.05	6.17	7.85	8989	1.35 1.85	24.58	20.08
	16	2	1.05	9.01	11.5	13483	1.35 1.85	25.30	20.08
	17	2	1.05	6.17	7.85	8989	0	0	25.91	50.10
	18	2	1.05	9.01	11.5	13483	0	0	26.73	50.10
	19	2	1.05	6.17	7.85	8989	1.35 1.85	26.54	50.10
	20	2	1.05	9.01	11.5	13483	1.35 1.85	26.92	50.10

Table 3 :

 3 Estimated heat transfer coefficients at the jet stagnation area for different flow parameters

	Rej	4753	4753	6989	6989	8989	8989	13483	13483
	Rea	0	2437	0	2437	0	2437	0	2437
	h (W.m -2 .K -1 ) 489.98 446.92 439.06 899.12	665.96 1246.06 1020.96 1363.82
	Relative error
		2.44	2.44	2.25	2.82	3.03	3.57	2.56	3.34
	on h (%)


Amine Taguett

Thierry Aubert

Marc Lomello

Ouarda Legrani

Omar Elmazria

Jaafar Ghanbaja

Abdelkrim Talbi

HAL is

Ir-Rh thin films as high-temperature electrodes for surface acoustic wave sensor applications Amine Taguett 1 , Thierry Aubert 1,2 LGS) is currently the most appropriate candidate. It has been intensively studied, demonstrating a good stability at high temperature [START_REF] Hornsteiner | Surface acoustic wave sensors for high temperature applications[END_REF][START_REF] Bardong | Experimental and Theoretical Investigations of Some Useful Langasite Cuts for High-Temperature SAW Applications[END_REF]. However, it has to be noted that, under high-temperature vacuum conditions, LGS suffers from surface degradation related to gallium and oxygen losses [START_REF] Aubert | Iridium interdigital transducers for high-temperature surface acoustic wave applications[END_REF][START_REF] Seifert | RuAl thin films on high-temperature piezoelectric substrates[END_REF][START_REF] Seifert | Surface effects and challenges for application of piezoelectric langasite substrates in surface acoustic wave devices caused by high temperature annealing under high vacuum[END_REF]. Regarding the IDTs, the use of a material having good corrosion resistance seems required.

First studies naturally turned to platinum regarding its exceptional noble character and a melting temperature as high as 1773°C [START_REF] Firebaugh | Investigation of high-temperature degradation of platinum thin films with an in situ resistance measurement apparatus[END_REF][START_REF] Thiele | Platinum and Palladium High-Temperature Transducers on Langasite[END_REF]. However, it was observed that 100 nm-thick Pt thin films agglomerate at temperatures higher than 700°C [START_REF] Maskell | Agglomeration of thin platinum films on a zirconia substrate[END_REF][START_REF] Pereira Da Cunha | Enabling Very High Temperature Acoustic Wave Devices for Sensor & Frequency Control Applications[END_REF][START_REF] Aubert | Behavior of Platinum/Tantalum as interdigital transducers for SAW devices in hightemperature environments[END_REF]. Agglomeration is a phenomenon specific to thin films, related to their large surface tension, which transforms a continuous thin film in a more stable configuration from the thermodynamics point of view, namely in a collection of separate beads. Agglomeration kinetics depends both on the film thickness and the nature of the film material. The thicker is the film, the slower are agglomeration phenomena. On the other side, as agglomeration is driven by atomic diffusion phenomena, it is slower for metals with higher melting temperature and thus smaller diffusion coefficients. in air atmosphere [START_REF] Pereira Da Cunha | High Temperature Sensing Technology for Applications Up To 1000°C[END_REF]. Since then, new electrode materials and structures have been investigated by this group towards establishing stable operation of LGS-based SAW high-temperature sensors at 900°C and beyond [START_REF] Behanan | Thin Films and Techniques for SAW Sensor Operation Above 1000°C[END_REF].

In order to achieve electrodes that are able to operate in corrosive atmospheres at temperatures of 800°C and more, it could be relevant to replace platinum by a noble metal with lower intrinsic diffusion coefficients. In this context, iridium is an appropriate candidate as its melting temperature (2447°C) is significantly higher than that of platinum. First investigations on pure Ir electrodes were very promising, confirming the high resistance of iridium thin films to agglomeration phenomena [START_REF] Aubert | Behavior of Platinum/Tantalum as interdigital transducers for SAW devices in hightemperature environments[END_REF][START_REF] Aubert | In situ high-temperature characterization of AlN-based surface acoustic waves devices[END_REF]. However, these results were obtained under vacuum conditions as Ir transforms into volatile IrO 3 above 800°C in oxidizing environments [START_REF] Bao | Effects of thermal exposure on Ir-based alloys with and without Pt coating[END_REF]. This drawback could be overcome by alloying iridium with another element. Indeed, Osamura et al.

studied the high-temperature behavior of spark plug electrodes made of various Ir-based alloys, including Ir-W, Ir-Re, Ir-Mo, Ir-Ru, Ir-Hf, Ir-Pt, Ir-Pd, Ir-Ni and Ir-Rh [START_REF] Osamura | Development of New Iridium Alloy for Spark Plug Electrodes[END_REF]. Material challenges to face for this application are very similar to those encountered in the development of hightemperature SAW IDTs. Indeed, it is necessary to employ a conductive material with a high melting point to improve the sparking wear resistance. Moreover, as spark plugs are exposed to a hot environment (temperature can exceed 2000°C) containing large amounts of oxygen, it is important that the material from which spark plug electrodes are made be highly resistant to oxidation.

Osamura et al. found that among all the investigated Ir-based alloys, Ir-Rh alloys show the best performance in such conditions. In particular, Ir-Rh alloys show a far better resistance to oxidation than pure iridium above 800°C. This phenomenon was explained by the formation of a thin rhodium oxide passivation layer at the surface of the samples during annealing. In fact, Osamura et al. assumed that Ir atoms close to the surface transform into IrO 3 and fly off, so that only Rh atoms remain close to the surface. The latter also oxidize into Rh 2 O 3 which is a stable oxide that hinders O diffusion deeper inside the sample. Unfortunately, the thickness of the Rh 2 O 3 passivation layer is not given in this study. Note that the Rh protection effect is maximized as soon as the Rh content reaches 10 wt%. Very few other studies were dedicated to Ir-Rh alloys and none of them to Ir-Rh thin films with a thickness in the range of some hundreds nanometers.

Based on Osamura's study, it appears that Ir-Rh thin films could be good candidates for SAW applications taking place in high-temperature oxidizing atmospheres. Consequently, the goal of this study is to make a first investigation on the high-temperature behavior of such Ir-Rh thin films, to determine their relevance for the targeted application.

II. EXPERIMENTAL

Ir-Rh thin films were deposited on Y and Y+50°-cut LGS substrates (Witcore Co. Ltd., Jinan, China) by one-gun electron-beam evaporation method (Edwards Auto 306). The base pressure was 3•10 -8 mbar. From Ir 70 Rh 30 alloy pellets, 150 to 300 nm-thick Ir-Rh alloy thin films were deposited without and over a 10 nm-thick Cr adhesion layer (on Y-cut LGS substrates).

From pure Rh and Ir pellets, 120 nm-thick multilayers films (6 to 24 layers) were deposited without adhesion layer (on Y+50°-cut LGS substrates).

SAW delay lines operating at 97 MHz were achieved using photolithography process and ion beam etching, from the Ir-Rh alloy thin films with Cr adhesion layer. The SAW direction was Y-X. The spatial period of the IDTs was 24 µm.

Unprocessed thin films and SAW devices were annealed in air for 4 days at 800°C. After annealing, the samples were cooled down to room temperature. As-deposited and annealed samples were investigated by various methods. The morphology was observed by scanning electron microscopy (SEM -Zeiss SupraTM 55VP). Phase composition and microstructures were obtained by X-ray diffraction (XRD) in Bragg-Brentano geometry (Bruker D8 advance -CuK α1: λ = 1.54056 Å) and transmission electronic microscopy (TEM -JEOL ARM 200F). TEM lamellas were prepared using focused ion beam (FIB) etching. The chemical composition was determined by scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS).

The resistivity of as-deposited and annealed films was measured by the four-points probe method.

SAW devices were electrically characterized at room temperature, before and after annealing, using a network analyzer (PNA 5230a, Agilent Technologies Inc., Santa Clara, CA) and an RF prober station (S-1160, Signatone Corp., Gilroy, CA).

III. RESULTS AND DISCUSSION

A. Preliminary study: Ir-Rh alloy film deposition

As mentioned in the introduction section, Osamura's study revealed that Ir-Rh bulk alloys resistance to oxidation is maximized from a rhodium weight concentration of 10 % [START_REF] Osamura | Development of New Iridium Alloy for Spark Plug Electrodes[END_REF].

However, the behavior of Ir-Rh thin films regarding oxidation is unknown. Consequently, in order to secure the Rh protective effect, first evaporations were made from Ir-Rh pellets containing 19 wt.% (30 at.%) of rhodium. Fig. 1 shows the TEM cross-section image of a The deposited alloy films showed very poor adhesion properties on bare LGS substrates. As the first deposited layers are nearly Rh layers, this means that rhodium element has not enough affinity for oxygen to form firm bonds with an oxide substrate, such as LGS. Thereafter, a 10nm-thick chromium adhesion layer was successfully employed to enhance the adhesion quality between the Ir-Rh alloys films and the LGS substrates.

B. Ir-Rh multilayers film deposition

As described hereinabove, the control of the stoichiometry of Ir-Rh alloy thin films deposited by one-gun electron-beam evaporation is very tricky. Consequently, the rest of the study was dedicated to multilayers films composed by Ir and Rh nanolayers alternately evaporated from pure Ir and Rh pellets respectively. Thereby, the overall film composition depends on the thickness ratio between the successive Ir and Rh nanolayers.

Let us call n the number of moles in one nanolayer, m the mass of the nanolayer, M the molar mass of the element constituting the nanolayer, ρ the density of the nanolayer, S the surface of the substrate and t the thickness of the nanolayer. Thus, n can be expressed as:

Finally, the atomic ratio between rhodium and iridium elements in the multilayers film is:

Thereafter, the targeted atomic ratio was 1 (in order to obtain Ir 50 Rh 50 multilayers films), so Ir and Rh nanolayers of same thickness were successively deposited. As Sakharov et al. reported that Ir thin films adhere well to LGS substrates [START_REF] Sakharov | Optimization of wafer orientation and electrode materials for LGS hightemperature SAW sensors[END_REF], all multilayers films were successfully deposited starting by an Ir nanolayer. In the same way, the films were ended by an Rh nanolayer in order to take advantage of the Rh 2 O 3 passivating layer that could form at the surface. The total thickness of the deposited films was 120 nm. Three kinds of film nanostructure were investigated, depending on the number of nanolayers successively deposited (Tab II). Fig. 2 shows the TEM cross-section image of an as-deposited 12x10 nm multilayer film.

nm

LGS Substrate

C. High-temperature behavior

Fig. 3 shows the XRD patterns of the Ir 10 Rh 90 , Ir 30 Rh 70 alloy and Ir 50 Rh 50 multilayers films before and after a 4-days annealing period at 800°C. Based on the calculated Ir-Rh phase diagram available in the literature [START_REF] Tripathi | The Ir-Rh (Iridium-Rhodium) System[END_REF], in which no intermetallic compound can be found, we assume that the alloy films are solid-solution-type. All kinds of as-deposited films crystallized in the face centered cubic (fcc) phase, being textured in the [111] direction. Ir x Rh 1-x (111) XRD peaks are not visible anymore on the XRD patterns of annealed samples.

They are substituted by peaks related to several oxides phases. Some peaks can surely be identified as orthorhombic Rh 2 O 3 (noted as o-Rh 2 O 3 in Fig. 3a) in the case of alloy films and as rhombohedral Rh 2 O 3 (noted as rh-Rh 2 O 3 in Fig. 3b) in the case of multilayer films. This difference is unexplained. The remaining peaks could be attributed either to IrO 2 or RhO 2 which are both tetragonal form. The theoretical peaks of these two phases are very close and none of them coincides exactly with the experimental reflexes. By adjusting the lattice parameters of IrO 2 (or RhO 2 which comes to the same thing), a good match was obtained. Consequently, we assume that the actual tetragonal phase is Ir x Rh 1-x O 2 rather than IrO 2 or RhO 2 . This assumption is strengthened by the fact that the lattice parameters of the hypothetical Ir x Rh 1-x O 2 phase were found to follow well the Vegard law.

The resistivity of the as-deposited Ir 10 Rh 90 and Ir 30 Rh 70 alloy films is one order of magnitude higher than conventional values for metallic thin films (Tab. III). On the other hand, the electrical resistivity of the as-deposited multilayers films is comprised between 25 μΩ•cm for the 24x5nm sample and 40 μΩ•cm for the 6x20nm one.

The effect of the annealing process on the electrical properties of the different films is highly dependent of their composition. In the case of the Ir 10 Rh 90 alloy films, the electrical resistivity gained two orders of magnitude, reaching the value of 21000 μΩ•cm. The Ir 30 Rh 70 alloy films showed a much smaller rise, as the post-annealing resistivity is equal to 400 μΩ•cm. Regarding the Ir 50 Rh 50 multilayers films the final resistivity is lower than 200 μΩ•cm, independently from the film nanostructure.

The decrease of the resistivity with the Ir rate can be explained by the large difference in the electrical proprieties between rhodium oxides and IrO 2 . Indeed, Hämäläinen et al. reported an electrical resistivity between 5000 and 11000 μΩ•cm for films mixing RhO 2 and Rh 2 O 3 grains [START_REF] Hämäläinen | Study on Atomic Layer Deposition of Amorphous Rhodium Oxide Thin Films[END_REF]. On the other hand, IrO 2 shows an exceptionally low resistivity for an oxide. El Kahkani et al. found a bulk value equal to 42 μΩ•cm [START_REF] El Khakani | Highly Conductive and Optically Transparent Polycrystalline Iridium Oxide Thin Films Grown by Reactive Pulsed Laser Deposition[END_REF], while values between 47 and 300 μΩ•cm were measured for IrO 2 thin films [START_REF] Lisker | Effect of annealing in oxygen atmosphere on morphological and electrical properties of iridium and ruthenium thin films prepared by liquid delivery MOCVD[END_REF][START_REF] Pinnow | Preparation and properties of dc-sputtered IrO2 and Ir thin films for oxygen barrier applications in advanced memory technology[END_REF]. Consequently, we assume that the conductivity of the Ir x Rh 1-x O 2 phase increases with the stoichiometric coefficient x. Moreover, one can observe in The influence of the annealing process on the nanostructure of the multilayers films was examined by TEM analyses (Fig. 4). It can be observed that the multilayered structure was lost during annealing while a surface layer formed. The latter is completely Ir-depleted as evidenced by the STEM-EELS maping (Fig. 5). Quantitative EELS measurements reveal the Rh 2 O 3 nature of this layer (Tab. IV). In other words, this result fully confirms Osamura's observations on Ir-Rh bulk alloys: an Rh 2 O 3 mantle forms at the surface of the films during annealing [START_REF] Osamura | Development of New Iridium Alloy for Spark Plug Electrodes[END_REF].

The thickness of the Rh 2 O 3 surface layer depends on the initial nanostructure of the multilayers films: about 30 nm for the 24x5 nm sample (Fig. 4a) while it is close to 50 nm for the 12x10 nm one (Fig. 4b). The inner part of the film is Rh-depleted, which means that Rh atoms diffuse towards the surface layer during annealing (Tab. IV).

LGS IDTs are fully oxidized after this annealing process, their resistivity reaching 21000 μΩ•cm, as described in the previous section. For that no signal has been registered after annealing. On the contrary, the SAW measurements performed on devices based on 150 nm-thick Ir 30 Rh 70 alloy films show that a SAW signal is still clearly visible after annealing (Fig. 6). Insertion losses increased by 8 dB during heating, which is certainly related to the threefold increase of the film electrical resistivity (Tab. III). In the same time, the operating frequency shifted towards lower values. The origin of this phenomenon could be mass loading effect, since the mass of the IDTs increased during oxidation process. No agglomeration phenomena can be observed on the IDTs after the 4-days annealing period (Fig. 7). However, some blisters are visible and the finger edges are peeling off. These phenomena could indicate the unsuitability of the Cr adhesion layer for high-temperature applications. Various studies will have to be done in order to confirm these first promising results. Longer annealing periods at 800°C will be performed in order to determine the time-evolution of the Rh 2 O 3 overlayer observed on the multilayers films after annealing. In the same way, the behavior of the films at higher temperatures, for which pure Ir volatilizes in IrO 3 , will be investigated.

Finally, Ir-rich multilayers film will be investigated in order to optimize the IDTs electrical behavior.

Abstract-

  The achievement of surface acoustic wave (SAW) devices stable in hightemperature oxidizing atmospheres requires the development of conductive thin film electrodes that can withstand such harsh conditions. Recent studies have demonstrated the suitability of Pt-based alloys, multilayers or nanocomposite films for temperatures up to 800°C. Electrodes based on new materials and structures still have to be developed for applications taking place at higher temperatures. In this perspective, thin films based on iridium could be good candidates regarding the high melting point, and thus the low diffusion coefficients of this noble metal. In particular, Ir-Rh bulk alloys have shown superior performance as spark plug electrodes, which have to resist concurrently to physical and chemical wear such as high-temperature SAW electrodes. Consequently, this paper deals with the high-temperature behavior of Ir-Rh thin films. Ir-Rh alloys and multilayers films, with an Ir atomic ratio between 10 and 50%, are deposited by one-gun electron beam evaporation method. The impact on the films of a 4-days annealing treatment at 800°C in air is studied by X-ray diffraction, scanning and transmission electron microscopy, electron energy loss spectroscopy and four-points probe resistivity measurements. It turns out that all the films oxidized during the annealing period. The post-annealing electrical properties are highly dependent of the initial composition of the film: the higher is the Ir rate in the film, the lower is the electrical resistivity after annealing. Moreover, an Rh 2 O 3 overlayer, with a thickness of some tens of nanometers, forms at the surface of the film, confirming previous observations made on Ir-Rh bulk alloys. First SAW measurements made on devices based on Ir 30 Rh 70 alloy electrodes are very promising as a SAW signal is still clearly visible after the 4-days annealing process, while no agglomeration phenomenon can be observed.Index Terms-high-temperature; SAW; Ir-Rh electrodes; multilayers filmI. INTRODUCTIONThere is currently a strong industrial request to develop wireless measurement solutions for a variety of industrial applications taking place between 200°C and 1000°C that cannot be addressed by wired sensors. For instance, in metallurgy domain, such sensor could allow an accurate monitoring of the temperature at different positions on a steel band undergoing a thermal annealing treatment cycle, and thus a better adjustment of the annealing line parameters. Surface acoustic wave (SAW) technology could meet this need as SAW devices are passive components, thus requiring neither embedded electronics nor power source to be wirelessly interrogated.These devices are composed of a piezoelectric substrate on which are built interdigited conductive electrodes called interdigital transducers (IDTs). The typical thickness of the thin film from which the IDTs are lithographed is one hundred nanometers. One of the main challenges to face in order to achieve high-temperature wireless SAW sensors is the development of the constitutive materials able to withstand elevated temperatures up to 1000°C and corrosive atmospheres, starting with hot air. Concerning the piezoelectric substrate, langasite (La 3 Ga 5 SiO 14 ;

Figure 1 :

 1 Figure 1: Cross-section bright-field TEM image of an as-deposited 300 nm-thick Ir 10 Rh 90 thin film. Red points indicate the EELS measurements locations.

Figure 2 :

 2 Figure 2: Cross-section bright-field TEM image of an as-deposited 12 x 10 nm Ir 50 Rh 50 multilayers thin film.

Figure 3 :

 3 Figure 3: As-deposited and post-annealing XRD patterns of Ir 10 Rh 90 alloy film, Ir 30 Rh 70 alloy film (a) and Ir 50 Rh 50 multilayers films (b).

Fig. 3

 3 Fig. 3 that the relative intensity of Rh 2 O 3 reflexes (compared to the intensity of Ir x Rh 1-x O 2 peaks)

Figure 4 :

 4 Figure 4: Cross-section bright-field TEM image of 24x5nm (a) and 12x10nm (b) Ir 50 Rh 50 multilayers films after 100 hours of annealing at 800°C in air. Red points indicate the EELS measurements locations.

Figure 5 :

 5 Figure 5: STEM-EELS mapping of the 12x10nm multilayered films after 100 hours of annealing at 800°C in air: Ir (orange), Rh (green) and O (blue).

Figure 6 :

 6 Figure 6: Frequency response (S 21 magnitude) of a SAW device based on LGS substrate and 150 nm-thick Ir 30 Rh 70 alloy thin film before and after a 4-days annealing period at 800°C in air.

Figure 7 :

 7 Figure 7: SEM image of Ir 30 Rh 70 alloy IDTs after 100h at 800°C in air.

  , Marc Lomello 1 , Ouarda Legrani 2 , Omar Elmazria 3 , Jaafar Ghanbaja 3 , Abdelkrim Talbi4 Laboratoire SYMME, Université Savoie Mont Blanc, 74944 Annecy-le-Vieux, France

Laboratoire Matériaux Optiques, Photonique et Systèmes (LMOPS), CentraleSupélec-Université de Lorraine, 57070 Metz, France Institut Jean Lamour (IJL), UMR 7198 Université de Lorraine-CNRS, 54506 Vandoeuvre-lès-Nancy, France LIA LEMAC/LICS -IEMN, UMR 8520, EC Lille-CNRS, 59652 Villeneuve d'Ascq, France.

Table I : Ir & Rh relative rates in Ir-Rh alloy films as given by EELS measurements. Measurement locations are shown on Fig. 1

 I

	Measurement location number	1	2	3	4
	Rh (at.%)	98	96	91	89
	Ir (at.%)	2	4	9	11

Table II : Description of the three investigated nanostructures.

 II

	Sample number	1	2	3
	Number of
	deposited	6	12	24
	nanolayers
	Nanolayer thickness (nm)	20	10	5

Table III : Specific electrical resistance (in μΩ•cm) of the different samples before and after annealing.

 III

		Ir 10 Rh 90 alloy film	Ir 30 Rh 70 alloy film	Ir 50 Rh 50 multilayer film (6x20nm)	Ir 50 Rh 50 multilayer film (12x10nm)	Ir 50 Rh 50 multilayer film (24x5nm)
	As-deposited	125	116	39.6	34.6	25.5
	After
	100 hours	2.1•10 4	400	189	188	186
	@ 800°C

Table IV : EELS relative chemical composition of the 12x10nm multilayered films after 100 hours of annealing at 800°C. Measurement locations are shown on Fig. 4b

 IV

	Measurement location number	1	2	3	4
	Rh (at.%)	39.9 20.7 8.0 14.6
	Ir (at.%)	0.3	17.2 26.5 23.6
	O (at.%)	59.8 62.1 65.5 61.8

First SAW measurements were realized on devices based on 150 nm-thick Ir 10 Rh 90 alloy films with Cr adhesion layer, before and after a 4-days annealing period at 800°C. As a reminder, the

Cover layer Rh 2 O 3 Ir x Rh 1-x O 2

Acknowledgement. This work was financially supported by the Lorraine Regional Council. We are also grateful to Dr. Pascal Boulet for fruitful discussions concerning the XRD results.


Emmanuel K K Agyeman
email: emmanuel.agyeman@irt-jules-verne.fr

Pierre Mousseau
email: pierre.mousseau@univ-nantes.fr

Alain Sarda
email: alain.sarda@univ-nantes.fr

Damien Lecointe
email: damien.lecointe@irt-jules-verne.fr

Homogeneous and automated cooling of a mould segment by multiple water jet impingement and a cross air flow

Multiple water jets and a cross air flow are used to cool a mould segment in a homogeneous and automated manner. The test segment was cooled from an initial temperature of 573 K. An average temperature difference of less than 3 K and a maximum temperature difference of less than 6 K were obtained along the length of the surface of the test segment during the entire duration of the cooling process as opposed to the traditional channel cooling approach where the mean and maximum temperature differences increase over time. The top surface of the test segment represents the mould/part interface which is of interest in this study. Using model predictive control (MPC) and a data driven predictive model, the cooling speed of the test segment's top surface was able to be maintained within ± 5 K of the cooling ramp imposed. The results were compared to the results obtained when using a simpler On/Off algorithm for automated cooling. Compared to the simpler On/Off algorithm, there was an improvement in the accuracy of the cooling ramp with respect to its reference value of over 30 % for most cooling ramps tested (5 -25 K/min). A parametric study on the influence of the flow rates of the fluids on the cooling speed of the test segment's surface was also conducted.

Introduction

The uniform and controlled cooling of injection and thermoforming moulds is essential for the quality of the parts formed as demonstrated by the studies of Gombos et al. [START_REF] Gombos | Thermo-Mechanical Behaviour of Composite Moulding Compounds at Elevated Temperatures[END_REF]. A non-homogeneous cooling of the mould could lead to undesirable defects of the part such as hot spots, sink marks, thermal residual stress, differential shrinkage and warpage [START_REF] Chen | Analysis of Thermal Residual Stress in Plastic Injection Molding[END_REF][START_REF] Wang | Study on Residual Stresses of Thin-Walled Injection Molding[END_REF]. A lot of progress has been made on the use of conformal cooling channels [START_REF] Arrizubieta | Case Study: Modeling of the Cycle Time Reduction in a B-Pillar Hot Stamping Operation Using Conformal Cooling[END_REF][START_REF] Deepika | Plastic Injection Molded Door Handle Cooling Time Reduction Investigation Using Conformal Cooling Channels[END_REF][START_REF] Dimla | Design and Optimisation of Conformal Cooling Channels in Injection Moulding Tools[END_REF][START_REF] Marques | Design of Conformal Cooling for Plastic Injection Moulding by Heat Transfer Simulation[END_REF] for the homogenous cooling of moulds. As opposed to straight drilled cooling channels, conformal cooling channels can adopt complex flow paths, hence are better suited for cooling parts with complex geometries. However, the cooling of injection and thermoforming moulds with water which is readily available and relatively cheap poses some complications when the mould's initial temperature is relatively high (> 473 K) and when the mould is large in size because of the relatively low boiling point of water. For some materials, the required temperature necessary for the forming process can be as high as 673 K [START_REF] Gombos | Thermo-Mechanical Behaviour of Composite Moulding Compounds at Elevated Temperatures[END_REF]. As a result of these high initial temperatures, when the water flows into the cooling channels, it boils and changes phase immediately [START_REF] Yan | Subcooled Flow Boiling Heat Transfer of Water in a Circular Tube under High Heat Fluxes and High Mass Fluxes[END_REF] thereby leading to a non-homogeneous distribution of phases along the cooling channels with the liquid phase dominating at the entrances of the channels while the gaseous phase dominates at the channel exits. This heterogeneity in phase distribution tends to worsen for longer and wider moulds and for cooling channels that are connected in series as opposed to parallel cooling channels due to the fact that when the channels are connected in series, the water spends more time in the mould, hence a larger quantity of the liquid gets converted to the vapour phase. This phenomenon has a major impact on the heat transfer with a reduction in the heat flux the further we move away from the channel entrance [START_REF] Tymen | Temperature Mapping in a Two-Phase Water-Steam Horizontal Flow[END_REF]. The progressive reduction in the heat flux along the channel can be explained by the formation of vapour pockets between the channel surface and the remaining liquid as the distance from the channel entrance increases. These vapour pockets slow down the heat transfer due to their relatively low thermal conductivity while the cooling channel entrances experience high heat fluxes brought about by the vaporization of the water which is known for having a high latent heat of vaporization. This disparity in cooling speeds across the mould leads to a heterogeneous temperature distribution which could have a negative impact on the quality of the part being fabricated. Additionally, the progressive heating of the fluid as it flows through the channel leads to a reduction in the heat flux. A potential solution to this problem is the use of multiple jet impingement and a cross air flow as opposed to the traditional channel flow approach. A wide collection of studies on jet impingement can be found in the literature with applications in the manufacturing, electronics and aeronautics industries. Some relevant studies on single and multiple liquid jets impingement cooling of hot surfaces are summarized below.

Incropera et al. [START_REF] Incropera | Single-Phase, Liquid Jet Impingement Cooling of High-Performance Chips[END_REF] investigated the use of circular liquid jets for the extraction of high heat fluxes from electronic components. They concluded that chip to coolant resistances as low as 0.3 K.cm 2 /W could be achieved with flow rates as low as 17 g/s. Better cooling performances were also achieved with confined jets compared to free surface jets. With confined jets, the fluid flow is directed by the use of walls. Karwa et al. [START_REF] Karwa | Experimental Investigation of Circular Free-Surface Jet Impingement Quenching: Transient Hydrodynamics and Heat Transfer[END_REF] studied the hydrodynamics and temporospatial heat flux distribution on an extremely hot steel plate (1173 K) impinged by a circular water jet. They observed that the liquid wetting front radius increased slowly over time and that the maximum heat flux increased with jet velocity and subcooling. Baonga et al. identified the formation of 3 distinct zones after the impingement of a circular liquid jet on a hot circular disk. The zones were called impingement zone, parallel flow zone and hydraulic jump zone. It was concluded that for each zone the heat transfer coefficient depends on the fluid flow rate.

The following authors studied jet impingement cooling with two or more jets. Wei et al. [START_REF] Wei | Experimental Characterization and Model Validation of Liquid Jet Impingement Cooling Using a High Spatial Resolution and Programmable Thermal Test Chip[END_REF] observed that a lower thermal resistance and a better temperature homogeneity could be achieved with multiple liquid jets impingement as opposed to single jet impingement. The influence of nozzle geometry, orifice to surface spacing and jet Reynolds number on the heat transfer coefficient of jets was studied by Whelan and Robinson [START_REF] Whelan | Nozzle Geometry Effects in Liquid Jet Array Impingement[END_REF] who concluded that confined submerged jets yield a better heat transfer coefficient than free surface jets. Lee et al. [START_REF] Lee | Quench Subcooled-Jet Impingement Boiling: Two Interacting-Jet Enhancement[END_REF] undertook a similar study where a flat extremely hot (1173 K) horizontal surface was impinged by 2 adjacent circular water jets. Their results were in agreement with those of Teamah et Kheirat [START_REF] Teamah | Heat Transfer Due to Impinging Double Free Circular Jets[END_REF] with a higher heat transfer coefficient observed at the impingement zones when compared to the interaction zone where the fluids from both jets merge. Lu et al. performed a numerical study on a rotating liquid jet impingement cooling system. Their studies revealed that the uniformity of the heat removal was enhanced with the jet orifice rotation speed. No study involving the simultaneous use of multiple impinging circular water jets and a cross air flow for cooling purposes was found in the literature.

This paper explores an alternative approach to mould cooling that could not only largely improve upon the homogeneity in temperature of high temperature composite and polymer forming moulds, but enable a precise control of their cooling speeds. The explored approach consists of the simultaneous use of multiple circular water jets impingement and a cross air flow in the annular space between the pipe generating the jets and the channel surface (Fig. 1). With this method, the entire channel surface is impinged by the water jets simultaneously, thus limiting the heterogeneities in phases along the channel created by the flow of the water from one end of the cooling channel to the other. In addition to an improvement in mould temperature homogeneity, a precise control of the mould cooling speed could be achieved by the intermittent impingement of the jets whose impingement durations can be varied in order to achieve the desired cooling speed. The formula applied by Menges et al. [START_REF] Menges | How to Make Injection Molds[END_REF] and Rao et al. [START_REF] Rao | Design Formulas for Plastics Engineers[END_REF] reveals that the cooling time of a part being fabricated depends on its thermal diffusivity, its thickness, its melt temperature, its ejection temperature and the temperature of the part/mould interface. The main aim of this study is thus to propose a method for the accurate control of the temperature evolution at the mould/part interface by multiple water jets cooling beginning with a simplified study that involves the control of the surface temperature of a mould segment before expanding the studies to a complete mould prototype. Materials and Methods

Materials

The experimental bench consists principally of an instrumented stainless steel block (grade 316L) referred to as the test segment with dimensions 200×100×90 mm and a cylindrical channel of a ∅30 mm diameter bored centrally along its length (Fig. 2). The distance between the surface of interest and the channel (Fig. 3a) is 30 mm. For heating purposes, 8 circular holes with a diameter of 10 mm were bored along the test segment's width in order to create space for the placement of the cylindrical cartridge heaters. The test segment's internal temperature was monitored by 9 type K thermocouples with a diameter of 3 mm inserted at a depth of 50 mm along the test segment's width (Fig. 3a). The test segment's top surface is representative of the mould/part interface and is monitored by 25 type K thermocouples with a diameter of 0.5 mm as illustrated on Fig. 3b. The red dots represent the hot junctions of the thermocouples while the black lines represent the positions of the grooves used to hold the thermocouples in place. For the channeling of the air flow, water vapour and the remaining liquid water, 2 cylindrical quartz tubes with a diameter of ∅33/30 mm and length of 400 mm are attached to both ends of the central channel. The air passes through a compressed air dryer before flowing through the cooling channel (Fig. 2). The joints are rendered airtight by the use of a silicon seal. A perforated stainless tube with a length of 1000 mm and diameter of ∅12/10 mm is inserted along the central axis of the test segment's channel and of both cylindrical tubes attached to the test segment's sides. The perforations were made on the side of the tube facing the top surface (opposing gravity) of the test segment's channel and consist of 7 orifices with a diameter of ∅1 mm. There's a distance of 30 mm separating adjacent orifices with the first orifice being at a distance of 10 mm from the channel's entrance. All the sides of the test segment are insulated by a 50 mm thick fiberglass material as illustrated on Fig. 4. For the monitoring of the fluid temperatures, thermocouples are inserted into the entrances and exits of the central tube and the cylindrical glass tubes. The temperature of the water entering the central tube is measured by a 3 mm rigid type K thermocouple whose hot junction is positioned at the center of the flow (Fig. 2). The same approach is used to measure the temperature of the air entering the quartz tube attached to the entrance of the test segment's channel and to measure the temperature of the mixture of air, water vapour and liquid water exiting the test segment (Fig. 2). All temperature acquisitions are made centrally on a National Instruments ® acquisition card (NI TB-4353) inserted into an NI PXIe-1073 chassis and the temperatures are monitored in real time on LABVIEW ® .

The flow rates of the water and air are controlled by electronic valves installed at the entrances of the central steel tube and the quartz tube respectively. The flow rate of the water is controlled by a type 6223 Burkert electronic valve while the flow rate of the air is controlled by a type 3280 Burkert electronic valve. In order to measure the flow rates of both fluids, flow meters are installed after the electronic valves. The flow rate of the water is measured by an ultrasonic flow meter (Atrato 740-V10-D) while that of the air is measured by an SMC PFMB7102 flow meter. Both electronic valves are controlled by (0 -10 V) signals generated by an NI-6229 National Instruments ® command card controlled from LABVIEW ® .

During each experiment, the test segment is heated for approximately 1200 s by a total power of 2160 W to a temperature of 593 K and allowed to cool naturally to the desired initial cooling temperature of 573 K. This approach improves upon the test segment's temperature homogeneity before the cooling phase is commenced (maximum temperature difference of 6 K on the test segment's surface) due to the transfer of heat from the hotter zones to the colder zones. Once the required initial temperature is attained, the cooling phase is initiated by releasing both fluids into their respective tubes, done by opening the electronic valves that regulate their flow rates. The exit of the central tube is closed by an SMC VXED2140 electronic valve in order to generate a higher pressure within the tubes and to direct all the water towards the orifices.

Fig. 2 Schematic illustration of experimental bench

Uncertainty analysis

The parametric studies involved 5 water flow rates and 5 air flow rates. The exact values of the water flow rates expressed as the mean and the standard deviation (SD) of the values measured over the duration of the experiments are displayed on Table 1. The values of the air flow rates on the table are also time averaged with their standard deviations ranging from (0.04 -0.1) g/s. For all the experiments, the temperature of the water stayed within the range of (289 -294) K while the temperature of the air stayed within the range of (294 -296) K. The uncertainty on the water flow rate measurements was estimated by the manufacturers at 1% over the flow range (0.3 -83) g/s while that on the air flow rate measurements was estimated at 3% over the flow range of (0.1 -9.8) g/s. The temperature measurement uncertainty linked to the temperature acquisition system (cold junction compensation and thermal EMF) was estimated at ±0.38 K while the uncertainty of the type K thermocouples is the higher of ±2.5 K or ±0.75 % of the measured value according to the manufacturer. Assuming a confidence interval of 95 %, this value was divided by 1.96 to give a standard uncertainty of ±1.28 K. This gives us a global uncertainty on the temperature measurements of ±1.66 K Table 2 shows us the Reynolds numbers and velocities of the air flow and the water jets. The flow rate of each individual jet was measured by means of a chronometer and a scale balance and the flow rates measured were found to lie within a range of ±10% of the reference value. In the calculation of the jet exit velocities and Reynolds numbers, the mean of the flow rates of the 7 individual jets was used. The uncertainties on the calculated parameters obtained by propagating the uncertainties on the measured parameters are presented on Table 3.

Methods

Evaluation of the temperature homogeneity of the test segment's top surface along its length

The temperature homogeneity along the test segment's length was evaluated by taking the mean and the maximum values of all the temperature differences between the 13 centrally aligned thermocouples at each time step. The heterogeneities in temperature brought about by the heating phase were accounted for by subtracting the initial temperature value at the onset of cooling for each thermocouple from all the subsequent temperature measurements (Eq. ( 1)) before proceeding to the calculation of the mean (Eq. ( 2)) of the temperature differences at each time step.

Ti (t) = Yi (t) -Yi (t=0) (1)
Mean (E

' (t)) = ∑ ∑ ( ,- ./01, |3 0 (4)53 . (4)| ,6 0/, ) 7 (2)
where i = thermocouple number starting from the left and n = total number of temperature differences

The spatial mean temperature of the entire segment surface was obtained by averaging all the 25 temperature measurements made on the surface (Fig. 3b).This mean was used to monitor the temperature and the cooling speed of the entire surface.

Model predictive control of the cooling speed of the test segment's top surface

Model predictive control (MPC) is an advanced control method that can be used to predict the behavior of linear and non-linear systems. One of the major advantages of model predictive control when compared to other control techniques such as PID (Proportional Integral Derivative), LQR (Linear Quadratic Regulator) and LQG (Linear Quadratic Gaussian) is the fact that it can be used to optimize multivariable objective functions with or without constraints. MPC also works best for systems with relatively high response times.

Figure 5 shows us the operating principles of MPC which consists principally of an optimization algorithm and a predictive model. MPC seeks to minimize the errors between the values predicted by the predictive model and the reference values which are imposed. It does this by optimizing a sequence of plant inputs by means of an optimization algorithm. The measured outputs from the plant are also used by the MPC in real time in order to update its current state. The objective function optimized by the algorithm is illustrated by Eq. (3) while Eq. ( 4) illustrates the sequence of the plant inputs. Some other important parameters to take into account when setting up MPC are the prediction horizon, the control horizon and the sampling time. The selection criteria for these different parameters are explained by Alberto et al. [START_REF] Bemporad | Model Predictive Control Toolbox -User's Guide[END_REF]. For this study, a prediction horizon of 25, control horizon of 2, and sampling time of 2 s were used.

Fig. 5 Schematic illustration of model predictive control

J(u : ) = < < = w ?,A s A CT E,A (k + i) -T J,A (k + i)KL M J NOP 7 QOP (3) z : 3 = [u(k) 3 u(k + 1) 3 … u(k + hp -1) 3 ] (4)
Where k = current control interval, z = quadratic program (QP) decision, n = number of plant output variables, sj = scale factor of jth plant output in engineering units, wi,j = tuning weight for jth plant output at ith prediction time step (dimensionless), p = prediction horizon

In this study, model predictive control was applied to control the cooling speed of the test segment's surface by optimizing the sequence of the opening and the closure of the electronic water valve. The predictive model used was a data driven polynomial model known as ARMAX [START_REF] Simpkins | System Identification: Theory for the User, 2nd Edition[END_REF] while the optimization algorithm used by the MPC is known as KWIK [START_REF] Schmid | Quadratic Programming Methods for Reduced Hessian SQP[END_REF]. Both the predictive model and the MPC are contained in the model predictive toolbox and the system identification toolbox of MATLAB ® which was used for this study. Given the fact that ARMAX is a data driven model, the model had to be fed with experimental data (Table 4) that is representative of the system's dynamics (heat transfer within the test segment). Some of the data was used to estimate the model parameters (Fig. 6) while the rest of the data was used to validate the model created. The cooling speeds of Exp4 -Exp7 (Table 4) were obtained from a simpler automated cooling approach illustrated by Fig. 7 where the spatial mean surface temperature of the test segment's surface (spatial mean of 25 temperature measurements) is compared to a reference temperature at each time interval and the opening and closure of the water valve is determined by the difference between both temperatures. The limitation of this approach is the fact that the heat diffusion response time of the test segment isn't taken into account. Hence the measured temperature tends to deviate from the reference temperature due to the late closure of the water valve. The input takes a value of either 0 or 1 where 0 represents a closed water valve and 1 represents an open water valve. The orders of the different polynomials of the ARMAX model used are [7 5 4 3]. These values were determined by optimizing the objective function represented by Eq. ( 5).

RSE =Y∑

∑ ZT [ \]^,_ -T `\]^,_ a M b cdefg bOh Ph ij`Ok (5)

Table 4 Summary of different experiments used to determine the optimal orders and coefficients of the predictive model

Experiment Description Exp1

Continuous and simultaneous cooling by air and water (Qw = 10 g/s, Qa = 6.9 g/s) Exp2

Cooling by air only (6.9 g/s) Exp3

Random The results of the evaluation of the accuracy of the model created are illustrated on Fig. 8. The accuracy of the model was evaluated by taking the root mean square error (RMSE) and the absolute value of the temperature difference (dT) between the measured output and the model output at each time interval evaluated by Eq. ( 6) and Eq. ( 7) respectively. We observe from Fig. 8 that the accuracy of the model created is satisfactory for the desired application.

RMSE = Y ∑ Z3 l (4)5 3 m (4)a 6 _ n _/o 7 (6) dT(t) = pT [ (t) -T J (t)p (7)
Fig. 8 ARMAX model validation results

Results and discussion

Influence of the flow rates of the fluids on the cooling speed of the test segment's top surface

The effect of varying the flow rate of the water and that of the air was studied. Fig. 9 shows us the evolution of the spatial mean temperature (Fig. 9a) and of the cooling speed (Fig. 9b) of the test segment's top surface with respect to time for different water flow rates and a constant air flow rate of 1.8 g/s while Fig. 10 shows us the evolution of the spatial mean temperature (Fig. 10a) and of the cooling speed (Fig. 10b) for different air flow rates and a constant water flow rate of 27 g/s. For all the scenarios tested, it can be observed that the cooling speed peaks after approximately 50 s and then reduces progressively over time. A possible explanation for this is the change of boiling regimes from the transition boiling regime to the nucleate boiling regime. The same transition can be seen in the literature [START_REF] Ishigai | Boiling Heat Transfer for a Plane Water Jet Impinging on a Hot Surface[END_REF] for a similar temperature range. The progressive decrease in the cooling speed can be explained by the fact that the heat flux at the impinged surface is dependent on its temperature [START_REF] Schmid | Quadratic Programming Methods for Reduced Hessian SQP[END_REF][START_REF] Ishigai | Boiling Heat Transfer for a Plane Water Jet Impinging on a Hot Surface[END_REF] and decreases progressively with the decrease in temperature. Another observation is that there's a slight increase in the cooling speed of the test segment's surface with an increase in the flow rate of the water (Fig. 9) with a maximum cooling speed of 46 K/min for a 10 g/s flow rate and maximum cooling speed of 52 K/min for a flow rate of 58 g/s. This can be explained by the fact that increasing the flow rate of the water increases jet velocity for fixed orifice diameters and a positive correlation can be found between jet velocity and heat flux [START_REF] Karwa | Experimental Investigation of Free-Surface Jet Impingement Quenching Process[END_REF]. It can also be observed that the cooling speeds for all the flow rates converge at a time of about 300 s. At this point, the temperature of the channel's surface is less than 373 K [START_REF] Agyeman | Etude Thermique Expérimentale de l'impact d'un Jet d'eau sur une Surface Métallique Concave[END_REF] and there's no phase change of the water. This means that in the absence of phase change (boiling and evaporation) increasing the flow rate of the water beyond the lowest value of 10 g/s has no major impact on the cooling speed of the test segment's top surface. Furthermore, there's no significant difference between the cooling speeds obtained for water flow rates of 43 g/s and 58 g/s. This could indicate that increasing the water flow rate further beyond this value wouldn't lead to a significant increase in the cooling speed. Additionally, it can be observed from Fig. 10 that the air flow has no significant effect on the cooling speed of the test segment's top surface. Similar trends were observed for the other combinations of water and air flow rates.

3.2

Influence of the flow rates of the fluids on the temperature homogeneity of the test segment's top surface along its length For different flow parameters, the homogeneity of the temperature along the length of the test segment's surface was evaluated by Eq. ( 2) and the maximum temperature difference among all the temperature differences calculated for a given time step was also analyzed. The results obtained for a water flow rate of 10 g/s are illustrated on Fig. 11. It can be observed from Fig. 11 that increasing the air flow rate tends to worsen the temperature homogeneity along the length of the test segment.

Figure 12 shows us the temperature distribution along the length of the test segment's surface at different times for a water flow rate of 10 g/s and an air flow rate of 1.1 g/s. We can observe from the figure that the temperature distribution is relatively uniform except for the presence of some temperature peaks along the surface during the first 500 s of cooling indicated by the red broken lines. These peaks are caused by the presence of the cartridge heaters at those positions. The difference in thermal properties between the cartridge heaters and the test segment coupled with the thermal contact resistance between them slows down the transfer of heat from the test segment's surface. the temperature uniformity along the length of the test segment's surface for a water flow rate of 27 g/s and different air flow rates while Fig. 15 and Fig. 16 evaluate the temperature uniformity for a water flow rate of 58 g/s and different air flow rates. For the higher water flow rates of 26.7 g/s (Fig. 13) and 58 g/s (Fig. 15), increasing the air flow rate has a lesser influence on the temperature homogeneity of the test segment's top surface. This could be due to the fact that for the lower water flow rate of 10 g/s, the more the air flow rate is increased, the more the jets tend to tilt under the force of the air flow, hence the water film formed on the channel's surface during jet impingement is not uniformly distributed along the impinged surface. The temperature distribution at different times for the water flow rates of 27 g/s (Fig. 14) and 58 g/s (Fig. 16) is similar to that obtained with a water flow rate of 10 g/s. A noticeable advantage of this cooling approach is the fact that the temperature homogeneity doesn't get worse over time and the mean temperature difference happens to stabilize within the range of (1-2.5) K and the maximum temperature difference within the range of (2.5-6) K for a water flow rate of 10 g/s and air flow rate of 1.1 g/s. This is not the case when cooling is done via the traditional channel flow approach for the reason that the fluid tends to heat up as it flows through the channel, resulting in the progressive reduction of the heat flux along the channel. Additionally, when boiling is involved, the formation of vapor pockets tends to worsen the heat flux disparity along the channel. This phenomenon was demonstrated by the studies of Tymen et al. [START_REF] Tymen | Temperature Mapping in a Two-Phase Water-Steam Horizontal Flow[END_REF] and Yin et al. [START_REF] Yin | Experimental Study on Flow Patterns for Water Boiling in Horizontal Heated Tubes[END_REF]. Due to the reasons stated above, the temperature homogeneity of a tool cooled via the channel flow approach gets worse over time.

3.3

Automatic control of the cooling speed of the test segment's surface The test segment was cooled automatically with the MPC designed by the approach described in section 2.2.2. The results obtained were compared to those gotten from the simpler automated cooling approach illustrated on Fig. 7. During the automated cooling of the test segment, a constant water flow rate of 10 g/s and air flow rate of 6.9 g/s were used. The air flow control valve was opened permanently for the entire duration of the cooling in order to remove the excess liquid from the channel while the opening of the water valve was controlled by the automated cooling algorithms. The reason for using the lowest water flow rate of 10 g/s for the automated cooling was to limit the cooling speed, especially within the first 120 s, in order to reduce the amplitude of the deviation of the measured temperatures from the reference temperatures during the impingement of the water jets. Different cooling ramps were imposed and the results obtained for cooling ramps of 5 K/min, 10 K/min, 15 K/min, 20 K/min and 25 K/min are illustrated on Fig. 17 We observe from the figures above that compared to the simpler On/Off cooling algorithm, the MPC improves upon the accuracy of the measured temperatures with respect to the reference cooling ramp imposed. Table 5 summarizes the RMSEs obtained for the different algorithms and cooling ramps used. Another observation is that for the highest cooling speeds of 20 K/min and 25 K/min, due to physical cooling speed limitations, after a certain duration (350 s), the cooling speed of the test segment is unable to keep up with the ramp imposed. The reason for this is that the heat flux at the channel surface isn't high enough to maintain the desired speed. Such limitations can be accounted for at the mould design stage by choosing the appropriate material and mass for the mould, the number of cooling channels and the distance between the channels and the mould/part interface.

Conclusion

An approach to automatically and accurately control the cooling speed and the temperature distribution along a mould/part interface is proposed. The simultaneous use of multiple impinging water jets and a cross air flow is used instead of channel flow in order to improve upon the temperature homogeneity along the length of the test segment. These studies revealed that:

• By using a combination of water jets and a cross air flow, a homogenous surface temperature along the length of a mould segment can be maintained. For the specimen studied, the mean temperature was able to be maintained within the range of (1 -2.5) K while the maximum temperature difference was maintained within the (2.5 -6) K range during the entire duration of the cooling under certain fluid flow conditions. This isn't the case with the traditional cooling approach of channel flow where the temperature homogeneity gets worse over time. • Model predictive control can be used to accurately (within ± 5 K of the imposed cooling ramp) control the cooling speed of a mould segment under boiling conditions within the physical cooling speed limitations of the system. The major advantage of this approach is that it can be adapted to a variety of cooling systems by using appropriate experimental measurements that represent the dynamics of the system for the construction of the data driven model (predictive model). • During the simultaneous use of water jets and a cross air flow for heat extraction, increasing the air flow rate has no significant effect on the cooling speed of the test segment's top surface. However, for relatively lower water flow rates (<16.7 g/s for the experimental conditions described), increasing the air flow rate tends to worsen the temperature homogeneity of the test segment's top surface.

In perspective, the application of this technology on a complete mould prototype with multiple channels and a real part could be studied.

Acknowledgement

This research was supported by financing from the PERFORM program of the Institut de Recherche Technologique Jules Verne. The authors are grateful to Yannick Madec and Erwann Paviot for their help during the fabrication and assembly of the experimental bench. Experimental data used for the determination of the predictive model's coefficients 8 Fig. 7 On/Off cooling speed control algorithm without MPC 8 Fig. 8 ARMAX model validation results 9 Fig. 9 Effect of the flow rate of the water on the cooling speed of test segment's top surface for a constant air flow rate of 1.

Nomenclature

Fig. 1

 1 Fig. 1 Illustration of the cooling approach

Fig. 3

 3 Illustration of the dimensions and the positions of the cartridge heaters and the thermocouples, a) Side view, b) Top view a) b) Fig. 4 Images of test segment: a) View of instrumented test segment from above, b) View of insulated test segment

Fig. 6 Fig. 7

 67 Fig. 6 Experimental data used to determine the predictive model's coefficients

Fig. 9

 9 Effect of the flow rate of the water on the cooling speed of test segment's top surface for a constant air flow rate of 1.8 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time a) b) Fig. 10 Effect of the air flow rate on the cooling speed of test segment's top surface for a constant water flow rate of 27 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time

  Fig. 12 Temperature distribution along length of test segment's surface for Qw=10 g/s and Qa=1.1 g/s Figures 13 and 14 evaluate the temperature uniformity along the length of the test segment's surface for a water flow rate of 27 g/s and different air flow rates while Fig. 15 and Fig.16evaluate the temperature uniformity for a water flow rate of 58 g/s and different air flow rates. For the higher water flow rates of 26.7 g/s (Fig.13) and 58 g/s (Fig.15), increasing the air flow rate has a lesser influence on the temperature homogeneity of the test segment's top surface. This could be due to the fact that for the lower water flow rate of 10 g/s, the more the air flow rate is increased, the more the jets tend to tilt under the force of the air flow, hence the water film formed on the channel's surface during jet impingement is not uniformly distributed along the impinged surface. The temperature distribution at different times for the water flow rates of 27 g/s (Fig.14) and 58 g/s (Fig.16) is similar to that obtained with a water flow rate of 10 g/s.

  Figures 13 and 14 evaluate the temperature uniformity along the length of the test segment's surface for a water flow rate of 27 g/s and different air flow rates while Fig.15and Fig.16evaluate the temperature uniformity for a water flow rate of 58 g/s and different air flow rates. For the higher water flow rates of 26.7 g/s (Fig.13) and 58 g/s (Fig.15), increasing the air flow rate has a lesser influence on the temperature homogeneity of the test segment's top surface. This could be due to the fact that for the lower water flow rate of 10 g/s, the more the air flow rate is increased, the more the jets tend to tilt under the force of the air flow, hence the water film formed on the channel's surface during jet impingement is not uniformly distributed along the impinged surface. The temperature distribution at different times for the water flow rates of 27 g/s (Fig.14) and 58 g/s (Fig.16) is similar to that obtained with a water flow rate of 10 g/s.

  Fig. 14 Temperature distribution along length of test segment's surface for Qw=27 g/s and Qa=1.1 g/s

  , Fig. 18, Fig. 19, Fig. 20 and Fig. 21 respectively.

Fig. 17

 17 Fig. 17 Cooling ramp of 5 K/min

Fig. 1 Illustration of the cooling approach 3 Fig. 2 Schematic illustration of experimental bench 4 Fig. 3

 13243 Fig.1Illustration of the cooling approach 3 Fig.2Schematic illustration of experimental bench 4 Fig.3Illustration of the dimensions and the positions of the cartridge heaters and the thermocouples, a) Side view, b) Top view 5 Fig.4Images of test segment: a) View of instrumented test segment from above, b) View of insulated test segment 5 Fig.5Schematic illustration of model predictive control 7 Fig.6Experimental data used for the determination of the predictive model's coefficients 8 Fig.7On/Off cooling speed control algorithm without MPC 8 Fig.8ARMAX model validation results 9 Fig.9Effect of the flow rate of the water on the cooling speed of test segment's top surface for a constant air flow rate of 1.8 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time 10 Fig. 10 Effect of the air flow rate on the cooling speed of test segment's top surface for a constant water flow rate of 27 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time 10 Fig. 11 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 10 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 11 Fig. 12 Temperature distribution along length of test segment's surface for Qw=10 g/s and Qa=1.1 g/s 11 Fig. 13 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 27 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 12 Fig. 14 Temperature distribution along length of test segment's surface for Qw=27 g/s and Qa=1.1 g/s 12 Fig. 15 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 58 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 12 Fig. 16 Temperature distribution along length of test segment's surface for Qw=58 g/s and Qa=1.1 g/s 13 Fig. 17 Cooling ramp of 5 K/min 14 Fig. 18 Cooling ramp of 10 K/min 14 Fig. 19 Cooling ramp of 15 K/min 15 Fig. 20 Cooling ramp of 20 K/min 15 Fig. 21 Cooling ramp of 25 K/min 16

  Fig.1Illustration of the cooling approach 3 Fig.2Schematic illustration of experimental bench 4 Fig.3Illustration of the dimensions and the positions of the cartridge heaters and the thermocouples, a) Side view, b) Top view 5 Fig.4Images of test segment: a) View of instrumented test segment from above, b) View of insulated test segment 5 Fig.5Schematic illustration of model predictive control 7 Fig.6Experimental data used for the determination of the predictive model's coefficients 8 Fig.7On/Off cooling speed control algorithm without MPC 8 Fig.8ARMAX model validation results 9 Fig.9Effect of the flow rate of the water on the cooling speed of test segment's top surface for a constant air flow rate of 1.8 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time 10 Fig. 10 Effect of the air flow rate on the cooling speed of test segment's top surface for a constant water flow rate of 27 g/s: a) Evolution of the surface temperature with respect to time, b) Evolution of surface cooling speed with respect to time 10 Fig. 11 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 10 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 11 Fig. 12 Temperature distribution along length of test segment's surface for Qw=10 g/s and Qa=1.1 g/s 11 Fig. 13 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 27 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 12 Fig. 14 Temperature distribution along length of test segment's surface for Qw=27 g/s and Qa=1.1 g/s 12 Fig. 15 Influence of the air flow rate on the homogeneity in temperature along the test segment's length for a water flow rate of 58 g/s: a) Evolution of the mean temperature difference with respect to time, b) Evolution of the maximum temperature difference with respect to time 12 Fig. 16 Temperature distribution along length of test segment's surface for Qw=58 g/s and Qa=1.1 g/s 13 Fig. 17 Cooling ramp of 5 K/min 14 Fig. 18 Cooling ramp of 10 K/min 14 Fig. 19 Cooling ramp of 15 K/min 15 Fig. 20 Cooling ramp of 20 K/min 15 Fig. 21 Cooling ramp of 25 K/min 16

Table 1 Exact values of the water flow rates for the different sets of experiments conducted

 1

						Water flow rate (g/s)
		10		20		27		43		58
	Air flow rate (g/s)	Mean value	SD	Mean value	SD	Mean value	SD	Mean value	SD	Mean value	SD
	1.1	9.3	1.8	18.7	3.3	26.8	3.0	45.3	5.0	53.8	5.0
	1.8	9.0	1.8	20.0	1.8	27.2	4.5	46.0	4.5	60.8	5.3
	2.9	11.3	1.8	20.2	2.2	26.8	3.8	44.3	5.3	60.0	5.7
	4.9	9.5	1.2	19.8	2.7	25.8	3.2	45.2	4.5	58.3	5.7
	8	11.3	1.3	20.3	1.7	25.0	3.0	43.7	4.2	55.5	5.8

Table 2 Reynolds numbers of the fluids for the ranges of flow rates tested

 2

	Air flow rate	Velocity of air	Reynolds number	Total water	Jet exit	Reynolds number
	(g/s)	flow (m/s)	of air flow	flow rate (g/s)	velocity (m/s)	of jets
	1.1	2.1	2136	10	1.9	1880
	1.8	3.3	3314	20	3.9	3750
	2.9	5.4	5524	27	5.2	5000
	4.9	9.1	9206	43	8.5	8130
	8	14.9	15099	58	11.4	10900

Table 3 Uncertainty on calculated parameters

 3

	Calculated parameter	Uncertainty (%)

Table 5 RMSE in K for different automated cooling algorithms and cooling ramps Cooling ramp (K/min) Automated cooling approach 5 10 15 20 25

 5

	MPC	1.98	5.49	3.57	4.38	15.36
	On/Off Algorithm	11.43	10.35	5.38	6.76	18.63

List of tables

Table 1 Exact values of the water flow rates for the different sets of experiments conducted 5 Table 2 Reynolds numbers of the fluids for the ranges of flow rates tested 6 Table 3 Uncertainty on calculated parameters 6 Table 4 Summary of different experiments used to determine the optimal orders and coefficients of the predictive model 7 Table 5 RMSE in K for different automated cooling algorithms and cooling ramps 16

List of figures