A-M Gustafsson

L Westerlund

CFD-modelling of natural convection in a groundwater-filled borehole heat exchanger (CFD-modelling of a water-filled BHE)

Keywords: Natural convection, borehole heat exchanger, buoyant flow, numerical model, groundwater filled borehole, U-pipe

In design of ground-source energy systems the thermal erformance of the borehole heat exchangers is important. In Scandinavia, boreholes are usually not grouted but left with groundwater to fill the space between heat exchanger pipes and borehole wall. The common U-pipe arrangement in a groundwater-filled BHE has been studied by a threedimensional, steady-state CFD model. The model consists of a three meter long borehole containing a single U-pipe with surrounding bedrock. A constant temperature is imposed on the U-pipe wall and the outer bedrock wall is held at a lower constant temperature. The occurring temperature gradient induces a velocity flow in the groundwater-filled borehole due to density differences. This increases the heat transfer compared to stagnant water. The numerical model agrees well with theoretical studies and laboratory experiments. The result shows that the induced natural convective heat flow significantly decreases the thermal resistance in the borehole. The density gradient in the borehole is a result of the heat transfer rate and the mean temperature level in the borehole water. Therefore in calculations of the thermal resistance in groundwater filled boreholes convective heat flow should be included and the actual injection heat transfer rate and mean borehole temperature should be considered.

Borehole heat exchanger (BHE) systems use the ground as a heat source or sink for space conditioning in residential and commercial buildings. In Scandinavia groundwater is often used to fill the space between borehole wall and collector wall, while otherwise it is more common to backfill with some grouting material. The advantage of using water is cheaper installations and more easy access to the collector if needed. Grouting is on the other hand required in many counties by national legislation in order to prevent groundwater contamination or is used to stabilize the borehole wall. In Sweden the most common bedrock is crystalline granite with few fractures, as a result the use of groundwater filled boreholes is dominant.

This paper covers heat injection in a groundwater-filled BHE with a single U-pipe collector. During operation of the system a temperature gradient is developed in and around the borehole. When the temperature changes in the water a volume expansion or reduction is induced, resulting in changes in the density. Dense water will start to sink and less dense water to rise. The induced natural convective flow will result in a better heat transfer through the borehole water. It will depend on the mean temperature level in the borehole water and injection heat transfer rate the system is working with.

Most BHE calculation models are 1D or 2D using only conductive heat transfer [START_REF] Zeng | Heat transfer analysis of boreholes in vertical ground heat exchangers[END_REF][START_REF] Yavuzturk | Modeling of vertical ground loop heat exchangers for ground source heat pump systems[END_REF]. The thermal process is usually divided into two separate regions, the solid bedrock outside the borehole and the region inside the borehole. Since the aspect ratio is quite small, transient heat transfer in the bedrock is often modelled according to the 1D line-source or the cylindrical-source theory. Regarding long-term responses for the BHE, the dynamic temperature changes inside the borehole are small compared to those in the ground.

Therefore, the thermal process inside the borehole is commonly treated as steady-state heat transfer and described by a constant borehole thermal resistance, R b [K,m/W]. This includes heat transfer from the bulk heat carrier fluid through both the collector pipe and the filling material in the borehole.

Few models concern the convective heat transfer in the groundwater. Most of them are dealing with regional groundwater flow [e.g. [START_REF] Claesson | Analytical studies of the influence of regional groundwater flow on the performance of borehole heat exchangers[END_REF][START_REF] Chiasson | A preliminary assessment of the effects of groundwater flow on closed-loop ground-source heat pump systems[END_REF], which is shown not to influence the system except in porous ground or high fractured bedrock. Other studies have shown that during certain conditions regional groundwater flow may increase the heat transfer even for small Darcy flows [START_REF] Gehlin | Influence on thermal response test by groundwater flow in vertical fractures in hard rock[END_REF][START_REF] Witte | Geothermal response test with heat extraction and heat injection: examples of application in research and design of geothermal heat exchangers[END_REF]. There is also a study on thermosiphon effects where groundwater filled borehole in fractured rock experiences a convective flow through the borehole into connecting fractures, increasing the heat transfer in the bedrock as well as the borehole [START_REF] Gehlin | The influence of the thermosiphon effect on the thermal response test[END_REF].

None of these models concern natural convection in groundwater filled borehole situated in solid rock without any larger fractures, which is a common situation in Sweden.

Water has a thermal conductivity of approximately 0.6 W/m,K, which would result in a rather high borehole thermal resistance, R b ~0.15 to 0.2 K,m/W (including heat transfer through the U-pipe and circulating fluid) in a common single U-pipe borehole heat exchanger. However, the induced convection increases the heat transfer and most measurements in the groundwater-filled single U-pipe BHE result in a borehole thermal resistance R b ~0.06 to 0.08 K,m/W during heat injection. A larger borehole thermal resistance results in a larger temperature difference between the borehole wall and mean fluid temperature. For a certain undisturbed ground temperature and a specific heat injection rate a larger R b will result in a higher fluid temperature up to the heat pump. For a heat pump injecting heat a high return temperature from the ground decrease the performance of the heat pump resulting in a higher electricity demand. It is therefore always desirably to have as low thermal resistance in the borehole and ground as possible.

As mentioned, the temperature-dependent natural convection in the groundwater is not modelled in current simulation tools and commercial software for BHE systems. Instead the borehole's thermal resistance is usually measured during a thermal response test (TRT) for a certain heat transfer rate injection or an assumed representative value for the given loading conditions is used. Thermal response tests are performed during approximately 72 hours in Sweden, after it is assumed to be steady-state conditions.

During a year of operation the heat transfer rate achieved and the temperatures received by the system differs depending on the season. The convective heat transfer will therefore change during the year which will result in different borehole thermal resistances. This study concerns the influence of natural convection on the borehole's thermal resistance for different heat transfer rates and temperature levels in solid bedrock without fractures. The results from the model are compared to other published numerical model and laboratory experiments.

Simulation models

Two different 3D, steady-state models were built and simulated in the CFD-software Fluent. The software uses a finite volume method to convert the governing equations to numerically solvable algebraic equations [START_REF]Fluent User's guide volume 1-5[END_REF]. A commonly investigated convection model in the literature is the annulus model. Such model (M a ) was constructed (Fig. 1a) to compare the result with published experimental result and numerical simulation, described in section 3. The second model (M u ) is a section of a U-pipe in a groundwater-filled borehole with surrounding rock (Fig. 1b). This model is used to investigate how the borehole thermal resistance (R b ) is affected by the convective flow. Of interest is how the R b change for different temperature conditions in the borehole water and heat transfer rates.

It is also compared with experimental results, section 4.

The annulus model (M a ) consists of two 1 m long cylinders with water filling the space between them (Fig. 1a). The outer radius was set to the same value as the borehole radius (r bhw ) and the inner radius (r po ) was chosen so that the conditions were similar to these in the published papers [START_REF] Keyhani | Free convection in a vertical annulus with constant heat flux on the inner wall[END_REF][START_REF] Littlefield | Buoyant laminar convection in a vertical cylindrical annulus[END_REF]. The numerical mesh consists of a total of 91000 cells of hexahedron and wedge-shaped volume elements in the borehole. A constant heat flux is given at the inner cylinder (q" po ) and a constant temperature at the outer cylinder (T bhw ).

The bottom and top boundaries are treated as adiabatic surfaces.

The U-pipe model (M u ) consists of a 3 m long and vertical groundwater-filled borehole containing a single U-pipe collector (Fig. 1b). The cylindrical region outside the borehole consists of solid bedrock with material parameters similar to granite (ρ br =2360 kg/m 3 ; c p,br =775 J/kg,K; λ br = 3 W/m,K) extending to a radius of 1 m. Due to the U-pipe configurations, the heat flow close to the pipes will not be radial. The volume between the borehole wall and the U-pipe is water-filled with material parameters according to Table 1.

All the material parameters except the density are kept constant for each simulation. In this model a constant temperature is set at the outside of the pipe wall (T po ) which should be an acceptable approximation for a 3 m long borehole at steady-state conditions. For the other boundary conditions, the outer vertical bedrock boundary is set to a constant temperature (T brb ) and the bottom and top boundaries are treated as adiabatic surfaces.

The numerical mesh consists of hexahedron and wedge-shaped volume elements, in total about 634000 cells. For both models refining the mesh within the possibilities of the computer strength render changes <<1%. The mesh has been checked for cell skewness and aspect ratio according to normal CFD standard. During the simulations all residuals were run down to < 5 10 5 - ⋅ . Using conductive heat flow through the water and the bedrock the model has been compared to an analytical exact model [START_REF]EED -Earth Energy Designer 2.0[END_REF] and the difference in result were <1%. The validation of the convective heat flow through the borehole water is presented for an annulus geometry in section 3. Figure 2 shows the mesh in a cross-section of the borehole and part of the bedrock.

In Fluent and for natural convection heat flows the Boussinesq approximation can be used to describe the fluid density as a function of temperature. The model treats density as a constant value in all solved equations, except for the buoyancy term in the momentum

equation. It is valid for ( ) 1 << -ref T T β
which is true for the temperature gradients in the borehole water. The buoyancy term in the momentum equation is then approximated to Eq.

(1).

( ) ( ) . g T T g ref ref ref - - ≈ - β ρ ρ ρ (1)
The densities versus temperature curve for water is non-linear (Fig. 3) with highest density value for a temperature level of approximately 4ºC [START_REF] Kell | Reanalysis of the density of liquid water in the range of 0-150ºC and 0-1 kbar[END_REF]. The non-linearity will affect the occurring density differences at a certain mean temperature level in the borehole water.

Lower mean temperature levels will result in smaller density differences for the same temperature gradient between pipe wall and borehole wall. If the mean temperature level in the borehole water is 10ºC, a temperature gradient of 1ºC will result in a density difference of 0.08 kg/m 3 . While at a mean temperature of 25ºC in the borehole water a temperature gradient of 1ºC result in 0.25 kg/m 3 in density difference. These differences in density will result in an increased velocity for the higher temperature level. Other parameter values for water (for instance kinematic viscosity) vary in the same direction and magnify the process. Thus there will be a decrease in borehole thermal resistance for increased borehole mean temperature.

Validation of numerical model

In 1983, Keyhani et al. [START_REF] Keyhani | Free convection in a vertical annulus with constant heat flux on the inner wall[END_REF] investigated free convection in a vertical annulus. They used an annulus-shaped experimental configuration with radius ratio R=4.33 and aspect ratio A=27.6, i.e. the effective heated length was 87.6 cm, the inner diameter was 1.91 cm and the outer diameter was 8.26 cm. The boundaries had constant heat fluxes over the inner radius and isothermal conditions on the outer radius. Two gases were used, air (Pr = 0.71 at 300 K) and helium (Pr = 0.68 at 300 K). The experimental results were fitted with a powerlaw dependence of aspect and radius ratios, and gave the following Nusselt number correlation, Eq. ( 2

⋅ ≤ ≤ ⋅ ⋅ = - Ra R A Ra Nu (2)
In 1986, Littlefield and Desai [START_REF] Littlefield | Buoyant laminar convection in a vertical cylindrical annulus[END_REF]

≤ ≤ ≤ ≤ ≤ ≤ Ra N A R hf (3)
An annulus model, M a , was assembled with measures according to Fig. 1a, giving the aspect ratio A=31.45 and radius ratio R=2.59. The inner surface was given a constant heat flux and the outer surface a constant temperature. The annulus was filled with water reaching a temperature of 281 K, giving a Prandtl number of 9.97. The model was built to match the conditions of Littlefield and Desai's numerical model and also the outer radius was chosen to be the same as the borehole radius in the U-pipe model (M u ), r bhw =0.0518 m.

Steady-state models require the same heat flow rate per meter in length (q') over both inner and outer surfaces, according to energy balance. The inner radius was chosen to satisfy the

condition 5 . 0 386 . 0 ≤ = hf N
, whereby r po =0.02 m.

Five different heat flow rates were used (25, 50, 75, 100 and 125 W/m) on the inner radius (r po ) in the simulations. At the outer boundary, temperatures were held constant at 280 K.

The estimated Nusselt number, Nu * , was calculated, Eq. ( 4), as a quota between the thermal resistance with pure conductive heat transfer in the borehole water (R w,c ) and the thermal resistances in the borehole water for the actual or total heat transfer including the convection (R w,t ) [START_REF] Hellström | Ground heat storage -Thermal Analyses of duct storage system, theory[END_REF].

t w c w R R Nu , , / = * (4)
The thermal resistance in the borehole water for conductive heat transfer (R w,c ) is calculated as conductive heat transfer in one dimension for an annulus, Eq. ( 5). (5)

14

The total resistance in the borehole water (R w.t ) is calculated from the simulation result, according to Eq. ( 6). The temperatures are calculated as surface mean values and the heat flow is given per meter of borehole length.

q T T R po bhw t w ′ - = , (6)
In Fig. 4, Nusselt number correlations according to Eq. ( 2), ( 3) and ( 4

Comparison with laboratory measurement on a U-pipe borehole

In 1999, Kjellsson and Hellström [START_REF] Hellström | Fluid-to-ground thermal resistance in duct ground heat storage[END_REF][START_REF] Kjellsson | Laboratory study of the heat transfer in a water-filled borehole with a c-pipe[END_REF] conducted a laboratory study of heat transfer in a water-filled borehole with different collector arrangements. The test equipment consisted of an outer 3 m high steel cylinder with a diameter of 0.4 m. A cryostat-controlled circulating fluid maintained the cylinder at a certain temperature (T brb ). An inner, concentric plastic pipe with an inner diameter of 0.1036 m represented the borehole wall. The annular ground region between the borehole and the steel cylinder was filled with a mixture of fine sand and a water-antifreeze fluid. Several collector types were tested. The tests were run at least three days and steady-state conditions were attained after about one day.

The single U-pipe DN40PN6 measurements from their experiment are here compared to the Fluent U-pipe model (M u ) described in Section 2 and Fig. 1b. The test was performed for different cryostat temperatures and heat injections rates. To minimize influence of heat losses to the surroundings, the injection rate for each measurement was calculated from the temperature gradient over the ground region assuming only conductive heat transfer and constant conductivity. Table 1 shows the cryostat temperature, here named T brb , and injection rate for each experimental measurement, named E1-E12.

Boundary conditions in the model were given as a constant temperature at the outer bedrock boundary (T brb ) and a constant temperature at the U-pipe outer wall (T po ). Water physical properties were taken from standard water parameter table [START_REF] Kell | Reanalysis of the density of liquid water in the range of 0-150ºC and 0-1 kbar[END_REF][START_REF] Incropera | Fundamentals of heat and mass transfer[END_REF] for the same temperature as the reference temperature (T ref ) in the Boussinesq equation. T ref was chosen to be a half degree less than the wall temperature (T po ) and thereby close to the mean borehole temperature. In Table 1, model boundary conditions and reference parameters are presented for the different simulations, named M u 1-M u 6.

Heat transfer through U-pipe wall and heat carrier fluid

The heat transfer through the collector pipes and the fluid inside must be added to the numerical model to be able to compare with the experimental results. The DN40PN6 Upipe has an outer radius of 0.02 m and an inner radius of 0.0177 m (Fig. 5).

The thermal conductivity for the pipe is assumed constant over the temperature interval, λ p = 0.42 W/m,K. The temperature on the inside of the pipe (T pi ) is calculated according to Eq. ( 7), where the temperature on the outside of the pipe wall (T po ) and the heat transfer rate (q') is received from the numerical simulation.

(

)

po p pi po pi T r r q T + ⋅ ′ = πλ 2 ln ( 7
)
To calculate the mean fluid temperature the heat transfer through the fluid has to be established. The convective heat transfer coefficient in the fluid is calculated by using Eq.

(8-11) [START_REF] Hellström | Ground heat storage -Thermal Analyses of duct storage system, theory[END_REF]. The volume flow rate is set to 0.97 l/s, the same as in the experiment [START_REF] Hellström | Fluid-to-ground thermal resistance in duct ground heat storage[END_REF][START_REF] Kjellsson | Laboratory study of the heat transfer in a water-filled borehole with a c-pipe[END_REF] ( ) ( )

) 1 (Pr 2 / f 7 . 12 1 Pr 1000 Re 2 / f 3 / 2 - ⋅ + ⋅ - ⋅ = f f D Nu ( 10
) pi f f r Nu h ⋅ ⋅ = 2 λ (11)
The mean fluid temperature (T f ) may now be calculated according to Eq. ( 12)

pi pi f f T r h q T + ⋅ ′ = π 2 ( 12
)
The borehole thermal resistance (R b ) is calculated as the temperature difference between mean fluid temperature (T f ) and borehole wall temperature (T bhw ) divided by the heat transfer rate (q') Eq. ( 13). Notice, in the experiment T f is the mean value of the ingoing and outgoing flow while for the model T f is calculated according to Eq. ( 12). The mean fluid temperature in the model is calculated from the mean value of the outer pipe temperature, T po . This may introduce some error in the comparison but for a three meter long borehole this ought to be insignificant.

q T T R bhw f b ′ - = (13)

Results

Borehole thermal resistances from experiment and the numerical model (Eq. 13) are shown in Fig. 6 as a function of fluid temperature. They show a decreased value for increased fluid temperatures, which is a result of a larger convective heat flow. The velocity flow is determined of the density differences in the borehole water. As discussed earlier, there will be an increased density difference for an increased mean temperature level (in the temperature interval of interest, 10-35ºC) due to the non-linearity of the densitytemperature curve. A larger density difference in the borehole water results in higher flow velocities and thus a more effective heat transfer. The model shows in general higher values, up to around 14 % higher compared to the experimental results.

In Fig. 6 for a mean fluid temperature of 23-24ºC there are two different borehole thermal resistances. The higher value is from simulation M u 2 with 55 W/m heat injection rate and the lower from M u 5 with 101 W/m. The almost twice as high heat injection rate in simulation M u 5 results in a decrease in borehole thermal resistance of 2.6%. The same may also be seen around 32-33ºC where the thermal resistances for M u 3 (50 W/m) and M u 6 (95 W/m) differs with 3%. The same percent is achieved between M u 2 and M u 3 where the heat injection rates are almost the same but the mean temperatures differ with 8ºC.

Due to the U-pipe configuration the heat flow close to the pipes will not be radial. After a short distance the heat flow will be more evenly distributed and a radial pattern will take form at a certain distance from the borehole. In Fig. 7a temperatures in and around the borehole are shown. The un-radial shape is clearly visible inside the borehole water, while a radial pattern is seen shortly after entering the bedrock. In Fig. 7b temperatures are shown along the borehole wall in the length direction. The highest temperatures are obtained in the x-direction where the U-pipe is close to the borehole wall and the lowest in the z-direction.

The borehole thermal resistance calculated from the model uses an area averaged mean value for all its parameters.

These differences in temperature at the borehole wall will affect the heat transfer in the bedrock close to the borehole. Figure 8 shows the temperature difference between the x and z-direction in the bedrock at the vertical level 1.5 m for simulations M u 5. The x and zdirections may be seen in Fig. 7a. The associated heat fluxes over the borehole wall vary from 275-375 W/m 2 with a surface mean average value of 310 W/m 2 . The differences are evened out quickly and a radial pattern may be seen at a distance of approximately 0.3 m.

The temperature gradient, when heat is injected, will result in an upward flow between the U-pipes and a downward flow at the borehole walls. Between these flows, regions with almost stagnant water will appear; see the blue areas in In Fig. 10a, temperature differences (∆T) in the borehole water are shown for different simulations over a line crossing the borehole between the two U-pipe legs in the middle of the borehole length. The temperature difference is calculated as the difference to the water temperature next to the borehole wall. It may be seen that M u 2 with slightly higher heat transfer rate result in an increased temperature difference. Figure 10b shows the vertical velocities over the same line. All of these simulations have a heat transfer rate of approximately 50 W/m. Due to the non-linearity of the density-temperature curve the lower mean temperature level of the water in M u 2 will result in smaller density differences (∆ρ), Table 2. Thus, M u 2 has lowest velocities of these three simulations and result in larger borehole thermal resistance.

In Fig. 11a temperature gradient in the borehole water is compared for simulations M u 2 and M u 5 and Fig. 11b shows the associated vertical velocities. Both these simulations have similar water temperatures in the borehole. Simulation M u 5 has twice the heat transfer rate though. The larger heat transfer rate result in an increased temperature gradient in the borehole water. The induced velocities are also higher due to a larger density difference.

Notice though that almost the same velocities are achieved in simulations M u 4 (Fig. 10b).

That simulation had instead a lower heat transfer rate but a larger mean temperature level.

The kinematic viscosity is also lower for M u 4 which result in that the influences between areas with high velocities and almost stagnant water decreases. This indicates that estimation of the borehole thermal resistance should be based on both the mean temperature level in the borehole water and the heat transfer rate.

The Nusselt number may be used to investigate how much the convective heat flow increase the heat transfer rate compared to stagnant water, i.e. with only conductive flow.

Figure 12 shows the estimated Nusselt number, Nu* (Eq. 4), as a function of mean borehole water temperature. The thermal resistance in the water for conductive heat flow (R w,c ) and for total heat transfer (including convective heat flow) (R w,t ) are calculated from the numerical result (Eq.6). For this geometry the convective flow make the heat transfer approximately 3 times as effective as for stagnant water.

Summary and conclusions

In In a groundwater-filled borehole heat exchanger, free convective flow will be induced due to the occurring temperature gradients and the resulting density differences. The convective flow will depend on both the mean temperature level in the groundwater and the heat transfer rate. A high injection rate may give similar borehole thermal resistance result as a lower injection rate if the water temperature is lower for the first case. Therefore, to determine the borehole thermal resistance both heat transfer rate and temperature level must be considered.

The U-pipe configuration result in an un-radial heat transfer pattern close to the borehole.

The heat transport will be 2D in the horizontal plane out to a certain radius where a uniform radial heat transport occurs. In simulation M u 5, with a heat flow of 101 W/m, the uniform heat transport is achieved at a radius of about 0.3 m. Borehole heat exchanger system usually operates with heat flows between 10-40 W/m and thermal response test rarely exceeds 100 W/m. It should therefore be possible to restrict numerical models to radius around 1 m if regional groundwater flow not is included. With no regional groundwater flow heat is only distributed by conduction in the bedrock and knowing the undisturbed ground temperature and the thermal influence radius an appropriate outer bedrock boundary temperature (T brb ) may be chosen.

By examine the Nusselt number it was determined that the heat transfer approximately increases three times compared to stagnant water in the temperature interval of 10-35ºC.

This makes water better than most commercial back-filling materials with regards to heat transfer capacity even though the thermal conductivity is lower for water. However, it should be noted that back-filling, or grouting, may be required when hydraulic sealing of the borehole is necessary or when the ground water level is low.

To disregard the convective flow in heat transfer calculation on groundwater filled borehole heat exchanger result in systems with over capacities. In these simulations giving the same boundary conditions the heat flow was in the range from 33-71 W/m with conductive heat transfer and increased to 47-101 W/m when convective heat flow were included. For a heat injection rate of 50 W/m using only conductive heat transfer result in a temperature difference between pipe wall and borehole wall of 7.7ºC while using convective heat transfer result in 1.1ºC difference. Thus in system design when considering the heat pumps temperature constraints and the buildings energy demands, calculations with only conductive heat flow will result in a larger required total borehole length.

An ordinary borehole heat exchanger is usually in the order of 50 to 200 meter. There may be other parameters affecting the heat transfer for a longer borehole than for the three meter long investigated in this paper. For example a longer hole will not be influenced of the top and bottom boundary as much as a shorter but the wall boundaries have a larger impact. In [START_REF] Gustafsson | Influence of natural convection in water-filled boreholes for GCHP[END_REF] result from thermal response tests is compared to simulations from the 3 m long CFD model. They shows similar thermal borehole resistance pattern as been presented in this

paper. An ordinary borehole may also interact with connecting fracture which may enlarge the convective flow. It is therefore recommended to perform thermal response test in order to determine the thermal borehole resistance for the specific borehole.

Further studies with this model will be investigations of model approximations such as geometrical approximations and boundary conditions. The goal is to construct a fast, simple model which may be used in TRT analysis and BHE design. It would also be desirable to be able to describe the convective flow when fractures connect to the BHE. Connecting fractures would result in a larger influence area where the convective flow also affects the heat transfer in the bedrock [START_REF] Gehlin | The influence of the thermosiphon effect on the thermal response test[END_REF]. Since every borehole has an unique set of fractures it is probably preferable to first perform multi-injection rate TRT [START_REF] Witte | Geothermal response test using controlled multipower level heating and cooling pulses (MPL-HCP): quantifying ground water effects on heat transport around a borehole heat exchanger[END_REF] and combine the result with a simple and fast design model to determine the convective influence in a water-filled BHE. 2), ( 3) and ( 4).

α

  Thermal diffusivity = λ / (ρ•c p ) (m 2 /s) β Thermal expansion coefficient (1/K) λ Thermal conductivity (W/m,K)ν Kinematic viscosity (m 2 /s)

  examined buoyant laminar convection in a vertical cylindrical annulus. The numerical model had a constant heat flux on the inner radius and either isothermal conditions or constant heat flux on the outer radius. The model was valid for Pr=10. They suggested the following relationship of Nusselt's number for isothermal boundary condition, Eq. (3).

  ) are shown as a function of the modified Rayleigh number. Ra* has been calculated with the material parameters for water for the actual mean temperature and with the heat transfer flux from the calculations. The agreement between the Fluent validation model and the reference Nusselt correlations is good, especially in relation to Littlefield and Desai's numerical model.

  Fig. 9a. The figure shows the crosssectional area of the borehole at the vertical level 1.5 m for simulation M u 5. The lengths of the arrows in Fig. 9b indicate the rate of velocity. Towards the ends of the borehole, the speed is decelerated and the transition from inner to outer flow occurs.

  this paper, two different models are presented. An annulus model (M a ) is used in comparison with published results and is shown to be in good agreement with numerical study and experiments for an annulus. A U-pipe model (M u ) was used to investigate the heat transfer in the borehole water and how the convective heat flow influenced the borehole thermal resistance for different heat transfer rates and borehole water temperatures. Surrounding the BHE is solid bedrock with a constant temperature applied at the outer vertical boundary. At the U-pipe outer walls a constant temperature is set.The U-pipe model was also compared to a laboratory experiment of a three meter long Upipe borehole. The results show a similar pattern, although lower borehole thermal resistances are achieved in the laboratory experiment. As shown the temperature around the borehole wall differs due to the U-pipe configuration. The achieved difference of 0.35ºC for simulation M u 5 at the vertical level 1.5 m, will result in a 5% difference in calculated borehole thermal resistance. In the laboratory measurement the temperature were measured at 6 locations at the borehole wall (using 2 measurement points at 3 different levels; top, middle and bottom). A mean value based on six measured values compared to the model value calculated from 9000 cells may fail to incorporate temperature changes around the borehole. Included in the experiment geometry is also the u-pipe bend in the bottom, the plastic pipe representing the borehole wall and an outer boundary of the sand-filled ground region of 0.2 m. Other factors which may influence the result are the assumed pipe conductivity and the calculated thermal resistance in the fluid inside the pipe. There may also have been heat losses from the experimental equipment to the surrounding air. The temperature differences between the borehole wall and the mean fluid temperature in the model are between 0.5 to 0.8ºC higher than the measured temperature difference. In conclusion the model presented in this paper gives good result in comparison with the experiment.

Figure 4 .

 4 Figure 4. Nusselt number as a function of modified Rayleigh number for Eq. (2), (3) and

Figure 7 .

 7 Figure 7.a) Temperatures in and around the

Figure 8 . 5 Figure 9

 859 Figure 8. Temperature differences between the x and z direction in the bedrock at vertical

Figure 10 .

 10 Figure 10.a)Temperature gradient in the borehole b) Velocity profile in the vertical direction

Figure 11a )

 11a Figure 11a)Temperature gradients in the borehole b)Velocity profiles in the vertical direction

  ).

	291 . 0	( ) * 0 . 244	238 . 0	. 0	442	,	8 . 1	10	4	*	21 . 4	10	7	.

Table 1 .

 1 Boundary conditions for the laboratory measurement, E1-E12 and boundary conditions and reference parameters for the model calculations, M u 1-M u 6. -4 2.11•10 -4 2.95•10 -4 3.35•10 -4 1.98•10 -4 2.82•10 -4 ν [m 2 /s] 1.25•10 -6 9.95•10 -7 8.22•10 -7 7.44•10 -7 1.02•10 -6 8.48•10 -7

	Experiment E1	E2	E3	E4	E5	E6
	q' [W/m]	56.89	75.83	95.33	52.22	71.16	90.67
	T brb [ºC]	0.79	1.00	1.22	10.64	10.87	10.95
	Experiment E7	E8	E9	E10	E11	E12
	q' [W/m]	47.89	65.94	84.77	45.42	64.25	81.84
	T brb [ºC]	20.48	20.68	20.79	25.50	25.64	25.79
	Model	M u 1	M u 2	M u 3	M u 4	M u 5	M u 6
	q' [W/m]	59.49	55.05	49.54	46.74	101.16	95.18
	T brb [ºC]	0.79	10.64	20.48	25.51	1.22	10.95
	T ref [ºC]	11.43	20.23	28.97	33.45	19.05	27.52
	ρ ref [kg/m 3 ] 999.56	998.16	995.96	994.55	998.39	996.37
	β [1/K]	1.09•10

Table 2 :

 2 Detailed information for simulations M u 2-M u 5

		M u 2	M u 3	M u 4	M u 5
	Mean water temperature	20.01	28.87	33.40	18.34
	[ºC]
	∆T [ºC]	1.29	1.04	0.94	2.06
	∆ρ [kg/m 3 ]	0.26	0.30	0.31	0.38
	Max velocities [m/s]	9.92•10 -3	1.24•10 -2	1.17•10 -2	1.24•10 -2
	R b [m,K/W]	0.077	0.074	0.073	0.075

Figure 1. Outline of the model geometries, all dimensions are given in meter.

Figure 2. Numerical mesh in a cross-section of the borehole.

Figure 5. Top view of the U-pipe model, M u , with additional heat transfer geometry.

Figure 6. Borehole thermal resistance (R b ) from experiment and model calculations.

Figure 12. Nusselt number as a function of mean borehole water temperature.

Figure 3: Water density as a function of temperature


Boštjan Končar
email: bostjan.koncar@ijs.si

Prachai Norajitra

Klemen Oblak

Effect of nozzle sizes on jet impingement heat transfer in He-cooled divertor

Keywords: helium-cooled divertor, jet impingement, nozzle diameter, numerical analyses

The use of impinging jets for divertor cooling in the conceptual fusion power plant is attracting much attention due to its very high heat removal capability and moderate pumping power requirement. The latest and the most advanced divertor concept is based on modular design cooled by helium impinging jets. To reduce the thermal stresses, the plasma-facing side of the divertor is build up of numerous small cooling fingers cooled by an array of helium jets. In this study the influence of nozzle sizes on the heat transfer and flow characteristics of such cooling finger is investigated numerically. The main objective is to find an optimal size and distribution of nozzle diameters in the jet array in which the heat transfer would be the highest possible at an acceptable pressure drop through the cooling finger. Prior to nozzle diameters modification, the simulation results for the reference finger geometry were validated against high heat flux experiments. A good agreement was obtained. The nozzle diameters were then modified at two different mass flow rates (13.5 g/s and 6.8 g/s per cooling finger). The most critical design parameter of interest was the maximum thimble temperature, which is limited by the melting temperature of the filler material in the brazed finger joint. It has been found that an optimal jet arrangement should have equal nozzle diameters to reach the highest thimble temperature decrease, while keeping the pressure drop within reasonable limits.

Introduction

The divertor is one of the high-heat-flux components in a fusion reactor. Its main function is to remove the fusion reaction ash, unburned fuel, and eroded particles from the reactor first wall, which adversely affect the quality of the plasma. About 15 % of the total thermal power gained from the fusion reaction need to be removed by divertor, which results in an extremely high heat flux applied on a relatively small divertor target plate.

Different helium-cooled divertor concepts, described in [START_REF] Raffray | Optimizing the overall configuration of a He-cooled W-alloy divertor for a power plant[END_REF], have been proposed for a fusion power plant application. A modular helium-cooled divertor for post-ITER generation of fusion reactors has been developed at Forschungszentrum Karlsruhe (FZK) [START_REF]Conceptual design of a He-cooled divertor with integrated flow and heat transfer promoters[END_REF][START_REF] Norajitra | He-cooled Divertor for DEMO: Experimental Verification of the Conceptual Modular Design[END_REF]. Its main design requirement is to remove high heat flux loads of 10 to 15 MW/m 2 . Usage of helium as a coolant simplifies the balance of the power plant as the same coolant can be used for all internal components. Helium loop has also favorable safety characteristics, but is capable of efficient heat transfer only if operated at high pressure (10 MPa in the current design). It's comparatively low heat removal capability can be improved by heat transfer enhancement methods, such as jet impingement [START_REF] Baydar | An experimental and numerical investigation on a confined impinging air jet at high Reynolds numbers[END_REF]. Jet impingement heat transfer is a wellknown heat transfer enhancement technique that has found an extensive use in industrial application for aircraft engines, burners, gas turbine blades, cooling of electronic components, etc. When jets are used in arrays they are ideal for global cooling of the heated surface [START_REF] Whelan | Nozzle geometry effects in liquid jet array impingement[END_REF].

Impingent by multiple jets can be easily adapted also for cooling of the divertor target plate. The latest design of the helium cooled divertor uses small tungsten cooling fingers, cooled by high pressure helium impinging jets (Figure 1) [START_REF] Norajitra | He-cooled divertor development for DEMO[END_REF]. The design concept with multiple helium jets is denoted as HEMJ (Helium-cooled Multiple-Jet) design. To optimize the HEMJ design, the analyses with Computational Fluid Dynamics (CFD) programs are (4/33) necessary [START_REF] Ihli | An advanced He-cooled divertor concept: Design, cooling technology, and thermohydraulic analyses with CFD[END_REF]. By the help of the numerical analyses the local critical regions in the design can be identified and thus help to reduce the number of expensive experiments.

In this work the size and distribution of nozzles on the cartridge was optimized for the reference geometry of one cooling finger. The effect of nozzle diameters on the heat transfer and pressure drop characteristics was investigated. Diameters of the nozzles were varied at two different mass flow rates, 13.5 g/s and 6.8 g/s (characteristic for fusion reactor operating conditions). The heat removal ability and pressure drop is analyzed in detail for lower mass flow rate.

Divertor cooling finger -reference design and numerical model

The reference finger design denoted as J1-C [START_REF] Norajitra | He-cooled divertor development for DEMO[END_REF] was used as a basis for parametric analyses of nozzle diameters variation. The plasma-facing side of the divertor (target plate) is constructed of small hexagonal tungsten tiles. Each tile is brazed on the thimble, made of tungsten alloy W-1%La 2 O 3 (WL10). A steel cartridge with 25 nozzles on the top of it is inserted in the thimble. The helium jets under high pressure blow through these nozzles and cool the hot inner surface of the thimble. The geometry of the reference design is shown in Figure 1. The tile width is 17.8 mm, the thimble thickness is 1.03 mm and the outer diameter of the cartridge is 11.2 mm. The nozzles on the top of the cartridge have the diameter of 0.6 mm, except for the central nozzle with the diameter of 1.04 mm. The gap between the thimble and cartridge is 0.9 mm.

PLACE FIGURE 1 HERE.

This geometry was found as a result of previous studies [START_REF] Norajitra | He-cooled divertor development for DEMO[END_REF], where base geometrical parameters (geometry of the tile and the thimble, the gap size, the number and arrangement of nozzles on the cartridge) were determined to accommodate for a heat flux of at least 10 (5/33) MW/m 2 . The heat transfer and flow characteristics of the reference design were also experimentally tested and numerically validated in an air flow loop under a wide range of Reynolds numbers but at much lower heat fluxes (up to 1 MW/m 2 ) [START_REF] Weathers | Development of modular helium-cooled divertor for DEMO based on the multi-jet impingement (HEMJ) concept: Experimental validation of thermal performance[END_REF]. The main goal of optimization studies is to cool down the divertor structures as much as possible and at the same time limit the pressure drop to reasonable values to save pumping power. One of the most critical design limits is the maximum allowable temperature of the thimble dictated by the re-cristallization temperature of the WL10 material (currently assumed at 1300°C under irradiated condition). In this respect the geometry should be further optimized to enhance the heat transfer and, hence, to enlarge the safety margin. In this work, the design modification is focused on optimization of the size and distribution of nozzle diameters on the cartridge.

Heat transfer performance of different cartridge design variants are analyzed numerically using the code ANSYS-CFX 11.0 [START_REF]ANSYS CFX, Release11.0, ANSYS CFX-Solver Theory Guide[END_REF]. Taking into account the symmetry of the cooling finger, a 30 o periodic segment of the finger is being simulated. Numerical domain consists of 3 solid domains (tile, thimble, cartridge) and of one fluid domain. Heat transfer equations through solid and fluid are solved simultaneously. The transport processes are assumed to be at steady-state. In the fluid domain, the helium is modeled as an ideal gas. The following transport equations are solved in the fluid domain:

continuity equation 0 ) ( = ⋅ ∇ v r ρ , (1)
momentum equation

v g p v v t v v v v 2 ) ( ) ( ∇ + + + -∇ = ∇ ⋅ µ µ , (2)
and energy equation

(6/33) 0 ) ( ) ( = ⋅ ∇ + ∇ ⋅ ∇ - ∇ ⋅ v p T U v v v λ ρ , (3)
where ρ , v v , U, p, µ , t µ , g v , λ ,T are helium density, velocity, internal energy, pressure, dynamic viscosity, turbulent viscosity, gravity force density, thermal heat conductivity of the helium and temperature, respectively. Shear stress transport (SST) two-equation turbulence model [START_REF] Menter | Multiscale model for turbulent flows, 24th Fluid Dynamics Conference[END_REF] has been used to resolve turbulence and heat transfer scales in the helium flow. The SST formulation combines k-ω model to resolve near-wall turbulence and k-ε model for the bulk flow. In the solid domain the heat conduction equation for steadystate conditions is solved:

0 ) ( = ∇ ⋅ ∇ s s T λ , ( 4
)
where ρ s , c s , T s and λ s are the density, specific heat capacity and thermal conductivity of the solid, respectively. The material properties of the tile and the thimble are modeled as temperature-dependent according to the ITER Material Properties Handbook [START_REF]ITER Material Properties Handbook[END_REF]. Due to low temperature gradients in the steel cartridge, its material properties are taken at constant temperature. Constant heat flux is applied at the upper surface of the tile and adiabatic boundary conditions are assumed at the outer walls. Helium flow enters the cartridge at the constant mass flow rate.

The flow field and the structures are meshed by hexagonal mesh with about 400,000 cells, as shown in Figure 2. The mesh refinement is applied especially in near-wall region at the helium-thimble interface, where the highest velocity and temperature gradients occur.

Our previous analyses [START_REF] Končar | Numerical Investigation of Multiple-Jet Cooling Concept for Helium Cooled Divertor[END_REF] have shown that this mesh is sufficient to obtain mesh independent results. Hexagonal mesh was constructed in ANSYS Multiphysics program package [START_REF] Kohonke | Ansys Inc., Theory Reference[END_REF] in a parametrical way that enables automatic mesh generation based on (7/33) predefined geometry dimensions and mesh refinement parameters. Such parametrization enabled fast mesh generation for different design changes used in this study.

PLACE FIGURE 2 HERE.

Validation against experimental data

To have confidence in CFD results, the numerical simulations were first verified against the experimental data. The high heat flux experiments with the reference cooling finger mock-up were performed at the experimental facility located at the Efremov Institute, St. Petersburg, Russia [START_REF] Ovchinnikov | Experimental study of DEMO helium cooled divertor target mock-ups to estimate their thermal and pumping efficiencies[END_REF]. The facility consists of the electron beam (60 kW at 27 keV beam energy) and of the helium loop (see Figure 3). Powerful electron beam gun enables testing of mock-ups at high heat fluxes up to 15 MW/m 2 .

The data for validation of numerical results were extracted from the first test series, performed in 2006 [START_REF] Giniytulin | Manufacturing and testing the He-cooled target module mockups for DEMO fusion reactor divertor[END_REF]. During the tests thermo-cyclic loading was applied to the tile upper surface aiming to test the integrity of divertor materials. Thermo-cycles were simulated by switching the beam on and off. For the selected test case the thermo-cyclic loading was applied at five heat flux levels. At each heat flux level, 10 cycles were performed. The helium mass flow rate was kept approximately constant at about 13.5 g/s.

To validate steady-state CFD simulations, the data were extracted at different heat flux levels, during the time intervals, when the laser beam was switched on. In the first set of modifications, the diameter of the central nozzle was varied from 0.6 mm up to 1.3 mm whereas in the second set (case1 to case4) also the other nozzles were modified (see Table 2). For cases 1 to 4, the total jets cross section area was kept constant, which resulted in a very small change of the pressure drop. For all cases the minimum (10/33) nozzle diameter was limited to 0.6 mm to avoid potential danger of a blockage. Nozzles are arranged in four circular rows around the central nozzle as shown in Figure 5.

PLACE FIGURE 5 HERE.

In Table 2 For constant jets cross-section, the change in the pressure drop is much lower (3.8 to 12.8 kPa) than for the first set of design changes (-42.8 to 82 kPa). In Figure 6 To evaluate and classify the heat removal ability versus the helium flow resistance for different designs, the "divertor efficiency" is given as the ratio between the HTC in the centre and the overall pressure drop. The divertor efficiency versus the central nozzle diameter is shown in Figure 11 (right). The highest efficiency was achieved for Case3 design (equal nozzle diameters at constant jets cross section). At central nozzle diameter changes, the best result is achieved for 0.6 mm nozzle (also in this case all nozzle diameters are the same). This is also the most attractive solution from the point of view of reaching the highest thimble temperature reduction of around 30 o C, while keeping the pressure drop within reasonable limits. The decrease of thimble temperature for this case is more than 27 o C and the pressure drop is still acceptable at 130 kPa. (see Table 3).

PLACE FIGURE 10 HERE.

Conclusions

CFD analyses were used to optimize the nozzle diameters on the cartridge of the reference divertor cooling finger. To gain confidence in simulation results, they were first verified against the high heat flux experiments. The calculated and measured values of the tile surface temperature show good agreement. The cartridge design optimization was focused on variation of nozzle diameters at two different mass flow rates, 13.5 g/s and 6.8 g/s (the lower value is characteristic for fusion power plant operating conditions). The most critical design parameter of interest was the maximum thimble temperature. The heat transfer characteristics and pressure drop have been analyzed in detail at a lower mass flow rate. The main findings of this analysis can be summarized as follows:

(15/33)

• By increasing the diameter of the central nozzle, the maximum thimble temperature increases linearly, whereas the pressure loss trend shows linear decrease.

• In the second series of design changes, all nozzle diameters were varied, while keeping the jets cross section area constant. For this type of design changes, the pressure drop change was considerably lower or even negligible for a lower mass flow rate.

• Maximum thimble temperature decrease per pressure drop is much higher at the lower mass flow rate. At the lower mass flow rate conditions, the thimble temperature is very sensitive even to a very small change of nozzle diameter (in the range of manufacturing accuracy). The effect of the design change on the pressure drop is more important at higher mass flow rates.

• Analysis of local flow conditions in the jet array shows that the smaller central nozzle diameter contributes to higher central jet velocity and consequently to reduction of the maximum temperature of the thimble material.

• Local heat transfer coefficient in the centre and overall pressure drop through the finger appear to be the most appropriate parameters to characterize the design from the heat removal and thermohydraulic point of view. To evaluate the performance of different design changes, the "divertor efficiency" was introduced as the ratio between heat transfer coefficient in the centre and overall pressure drop.

• The highest divertor efficiency was achieved for the design with equal nozzle diameters at constant jets cross section (Case3).

• The reference design (central nozzle diameter of 1.04 mm) showed the lowest efficiency amongst all proposed design changes.

(16/33)

Figure 4 . 1

 41 The critical quantity of interest is the maximum thimble temperature. Two critical values should be considered.The first one is the re-cristallization temperature of the thimble material WL10 (1300 o C) and the other limitation is the melting temperature of the brazing filler material. Tile and thimble are brazed together with STEMET 1311 ® , which has a melting temperature at about 1050 o C. The helium mass flow rate was rather high (~13.5 g/s) to keep the temperature at the tile/thimble brazed joint below 1050 o C. As shown in Figure4(right), a reasonable agreement between the measured and calculated tile surface temperature has been obtained. The experimental heat flux in Table1was re-calculated from the measured helium temperature difference (the removed heat is absorbed in helium) to exclude the errors due to beam reflection and due to heat losses through the flange, where the mock-up is fixed (the real boundary condition in the experiment is not completely adiabatic). The calculated thimble temperature exceeds the allowable temperature of 1050 o C for the highest heat flux value 12.62 MW/m 2 . The post-test metallographic examination of the mock-up confirmed tile detachment, which indicates that the tile-thimble brazing temperature was exceeded also in the experiment[START_REF] Giniytulin | Manufacturing and testing the He-cooled target module mockups for DEMO fusion reactor divertor[END_REF].PLACE FIGURE 4 HERE. Parametric analysis of nozzle diameters at high mass flow rate of 13.5 g/sThe main objective is to reduce the maximum thimble temperature by changing the nozzle diameters on the cartridge. At the same time the increase of the pressure drop should be as low as possible. Various experimental and numerical investigations have shown that optimized nozzle geometric parameters may improve the heat transfer and flow characteristics of impinging jets[START_REF] Baydar | An experimental and numerical investigation on a confined impinging air jet at high Reynolds numbers[END_REF][START_REF] Whelan | Nozzle geometry effects in liquid jet array impingement[END_REF][START_REF] Luo | Effects of geometric parameters on confined impinging jet heat transfer[END_REF][START_REF] Brignoni | Effects of nozzle-inlet chamfering on pressure drop and heat transfer in confined air jet impingement[END_REF]. The reference geometry of the cooling finger (see Figure1) was used as a basis to perform parametric analysis of cartridge design changes. Diameters of the nozzles were varied, whereas other geometry parameters remained unchanged. The hexagonal mesh as shown in Figure2was used for all cartridge designs. Modified cartridge geometries require minor mesh adaptation perpendicular to the jet flow. Mesh accommodation itself has no significant effect on the results. Parametric calculations were performed for the reference scenario without internal heating (similar to Efremov experiments). The following boundary conditions were adopted:• He mass flow rate: 13.5 g/s • He inlet temperature: 540 °C • He inlet pressure: 10.0 MPa • Heat flux: 11.6 MW/m 2

4 . 2 Figure 9 .Figure 9 ,

 4299 Figure 9. To compare heat transfer coefficients, the distribution of local HTC values along

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 2 Figure 3 Figure 4

 12345678910234 Figure 1 Divertor cooling finger Figure 2 Numerical mesh of the 30 o segment of the cooling finger

Figure 7 Figure 8 Figure 9

 789 Figure 7 Maximum thimble temperature vs. pressure drop due to changed nozzle diameters

  , the comparison of pressure drop and maximum tile and thimble temperatures are presented. The values of maximum thimble temperature change and pressure drop change are calculated with regard to the reference cartridge design (gray column). The lowest thimble temperature decrease of approximately 20 o C was achieved at the smallest central nozzle diameter, but in that case the pressure drop increased by 82 kPa.

PLACE TABLE 2 HERE.

•

  The highest thimble temperature reduction of around 27 o C was achieved for the cartridge design with equal nozzle diameters of 0.6 mm.

	TABLES
	Table 1 Measured parameters during thermo-mechanical tests of HEMJ#J1-C [16]
	q (dT He)	m &	He	p (He inlet)	∆p	T (He inlet)	∆T He	T Tile-surf. max
	[MW/m 2 ]	[g/s]	[MPa]	[kPa]	[ o C]	[ o C]	[ o C]
	4.01	13.06 9.61	326.7	523.6	15.3	941
	6.28	13.7	9.79	321.2	536.9	22.8	1153
	9.69	13.73 9.69	326.6	555.4	35.1	1424
	11.63	13.7	9.84	327.4	558.9	42.2	1597
	12.62	13.28 9.72	313.3	567.8	47.2	1788
	(19/33) (20/33)

Table 2

 2 Variation of nozzle diameters at mass flow rate 13.5 g/s

		Reference 0.6	0.8	1.3	Case 1	Case 2	Case 3	Case 4
	D centr. jet [mm]	1.04	0.6	0.8	1.3	0.6	0.75	0.6236	0.7
	D 1. row [mm]	0.6	0.6	0.6	0.6	0.69	0.65	0.6236	0.65
	D 2. row [mm]	0.6	0.6	0.6	0.6	0.6035	0.62	0.6236	0.63
	D 3. row [mm]	0.6	0.6	0.6	0.6	0.6	0.6	0.6236	0.6
	D 4. row [mm]	0.6	0.6	0.6	0.6	0.6	0.6	0.6236	0.6
	T max, Tile [oC]	1,670.85	1,656.5	1,661.6	1,679.6	1,667.8	1,670.2	1,668.6	1,670.3
	T max, Thim. [oC]	1,016.85	997.5	1,004.1	1,029.2	1,008.8	1,012.2	1,010.7	1,011.9
	T He,out [oC]	584.85	584.7	584.2	584.7	584.2	584.4	584.3	584.0
	∆p [kPa]	430.00	512.0	472.9	387.2	442.8	435.0	437.3	433.8
	d∆p [kPa]	/	82.0	42.9	-42.8	12.8	5.0	7.3	3.8
	dT max,Thim. [oC]	/	-19.4	-12.7	12.4	-8.0	-4.6	-6.1	-4.9
	A jets [mm 2 ]	7.64	7.07	7.29	8.11	7.64	7.64	7.64	7.64

Table 3

 3 Variation of nozzle diameters at mass flow rate 6.8 g/s

		Reference 0.6	0.8	1.3	Case 1	Case 2	Case 3	Case 4
	D centr. jet [mm]	1.04	0.6	0.8	1.3	0.6	0.75	0.6236	0.7
	D 1. row [mm]	0.6	0.6	0.6	0.6	0.69	0.65	0.6236	0.65
	D 2. row [mm]	0.6	0.6	0.6	0.6	0.6035	0.62	0.6236	0.63
	D 3. row [mm]	0.6	0.6	0.6	0.6	0.6	0.6	0.6236	0.6
	D 4. row [mm]	0.6	0.6	0.6	0.6	0.6	0.6	0.6236	0.6
	T max, Tile [oC]	1,874.2	1,849.9	1,859.1	1,890.6	1,873.6	1,873.3	1,869.9	1,868.9
	T max, Thim. [oC]	1,202.3	1,175.1	1,185.3	1,223.2	1,199.0	1,198.0	1,196.2	1,193.7
	T He,out [oC]	625.2	624.3	624.9	626.4	624.6	625.0	624.0	625.0
	∆p [kPa]	112.8	130.4	122.5	100.7	113.2	113.1	113.0	114.5
	d∆p [kPa]	/	17.6	9.6	-12.1	0.4	0.3	0.2	1.6
	dT max,Thim. [oC]	/	-27.2	-17.0	21.0	-3.2	-4.2	-6.0	-8.6
	HTC center	28,490	35,236	31,521	25,821	34,209	31,753	33,950	32,338
	[W/m 2 K]
	HTC/∆p	252.55	270.20	257.40	256.49	298.91	280.43	300.36	285.85
	[W/m 2 KkPa]

  Figure 11 HTC above the central jet (left) and thermalhydraulic performance (right) of design changes at mass flow rate 6.8 g/s -variation of central nozzle diameter (blue ticks)vs. variation of all nozzle diameters at constant jets cross section (red ticks)

		36000.00				1.04		310.00
						0.6
		34000.00				0.8		300.00	Case 3
	HTC (W/m 2 K)	24000.00 26000.00 28000.00 30000.00 32000.00				1.3 Case 1 Case 2 Case 3 Case 4	KkPa) 2 HTC/∆p (W/m	270.00 280.00 290.00	Case 1 Case 4 Case 2	1.04 0.6 case3 Central hole change Constant A total
		22000.00						260.00
		20000.00						250.00
		100.00	110.00	120.00	130.00	140.00		0.5	0.7	0.9	1.1	1.3	1.5
			pressure drop (kPa)					Central hole diameter (mm)
								Central	1. row	2. row	3. row	4. row
	Figure 10 Nozzle Reynolds numbers (left) and average nozzle velocities (right) affected by
					different designs at mass flow rate 6.8 g/s
		(33/33)

ACKNOWLWDGEMENTS

This work, supported by the European Commission and the Slovenian Research Agency was carried out within the framework of European Fusion Development Agreement (EFDA).


Enrico Di Stasio

Federica Romitelli

Stefano Lancellotti

Alessandro Arcovito

Bruno Giardina

Raimondo De Cristofaro
email: rdecristofaro@rm.unicatt.it

Di Stasio

Romitelli Federica

Lancellotti Stefano

Arcovito Alessandro

Giardina Bruno

Cristofaro De

Raimondo

Kinetic study of von willebrand factor self-aggregation induced by ristocetin

Keywords: Protein aggregation, ristocetin, vonWillebrand Factor, light scattering, primary haemostasis, allostery

Von Willebrand factor (VWF) is a multimeric glycoprotein present in circulating blood and in secretory granules of endothelial cells and platelets. VWF is sensitive to hydrodynamic shear stress that promotes conformational changes, rendering it able to interact with subendothelial proteins and platelets, thus promoting primary haemostasis. Likewise, the binding of the glycopeptide antibiotic ristocetin to VWF triggers hemostatically relevant conformational transitions. These changes reveal both the interaction site for platelet receptor GpIbα and the Tyr1605-Met1606 peptide bond, which is cleaved by the regulatory metalloprotease ADAMTS-13.

In this study we investigated by a combined approach of light scattering spectroscopy and turbidimetry the ability of VWF to self-associate in solution in the presence of ristocetin and in the absence of any protein adsorbing surface. Micro-and macro-aggregates induced by ristocetin, have been characterized under static conditions in the early stage of formation and on a longer time scale (up to 10 hr). These findings show that VWF multimers form supramolecular structures favoring platelet trapping not only under high shear stress or interaction with external surfaces, but also in solution under static conditions when the conformational state of the protein is changed only by chemical potential of allosteric effectors.

A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T

INTRODUCTION

Vascular damage is followed rapidly by adhesion and firm attachment of platelets at the site of endothelial injury. At sites of high blood flow, von Willebrand factor (VWF) plays a central role in this process [START_REF] Sakariassen | Human blood platelet adhesion to artery subendothelium is mediated by factor VIII-Von Willebrand factor bound to the[END_REF][START_REF] Sadler | Biochemistry and genetics of von Willebrand factor[END_REF], as it primarily modulates platelet-subendothelium interaction by linking the platelet receptor GpIb/IX/V to the extracellular matrix [START_REF] Savage | Mechanisms of platelet aggregation[END_REF][START_REF] Moroi | A mechanism to safeguard platelet adhesion under high shear flow: von Willebrand factor-glycoprotein Ib and integrin alphabeta-collagen interactions make complementary, collagen-type-specific contributions to adhesion[END_REF]. In fact, when immobilized on subendothelial matrix, VWF forms a reactive surface capable of capturing platelets from flowing blood [START_REF] Singh | Solution structure of human von Willebrand factor studied using small angle neutron scattering[END_REF][START_REF] Sadler | Update on the pathophysiology and classification of von Willebrand disease: a report of the Subcommittee on von Willebrand Factor[END_REF]. High shear stress causes micro-and macro-conformational changes of VWF from a globular state to a stretched chain [START_REF] Siedlecki | Shear-dependent changes in the three-dimensional structure of human von factor[END_REF]. VWF derives from a complex gene (180 kb, 52 exons), and is synthesized as pre-pro-VWF, including a 22-residue signal peptide and a 741-residue propeptide.

VWF undergoes extensive post-translational processing, glycosylation, and assembly in the endoplasmic reticulum, Golgi and post-Golgi and consists of ∼250 kDa monomeric subunits, which form disulfide-linked multimers of 500 to 20000 kDa. Each VWF subunit contains 2050 amino acids made up of conserved modular domains in the order D8-D3-A1-A2-A3-D4-B1-B2-B3-C1-C2

( [START_REF] Sadler | Biochemistry and genetics of von Willebrand factor[END_REF]). Interaction of the platelet GpIbα receptor with the A1-domain of immobilized VWF [START_REF] Miura | Interaction of von Willebrand factor domain A1 with platelet glycoprotein Ibalpha-(1-289). Slow intrinsic binding kinetics mediate rapid platelet adhesion[END_REF] results in an initial adhesion, characterized by a continuous surface translocation of the platelets [START_REF] Savage | Initiation of platelet adhesion by arrest onto fibrinogen or translocation on von Willebrand factor[END_REF].

This process ultimately leads to a stable platelet adhesion through interaction with the platelet collagen receptors GpVI and GpIa/2A [START_REF] Nieswandt | Platelet-collagen interaction: is GPVI the central receptor?[END_REF], activation of the platelet Gp2B/I2A receptor complex [START_REF] Savage | Mechanisms of platelet aggregation[END_REF] and finally to platelet aggregation.

The interaction between VWF and GpIbα does not occur under static conditions and needs a pre-activation of soluble VWF. This process consists of a conformational change of VWF molecules, that expose within the A1 domain the binding site for GpIbα. This mechanism is triggered either by mechanical forces, such as high shear rate (>5000 sec -1 ) found in the arterial circulation, or by chemical potential generated by interaction with external surfaces and chemicals/snake venoms [START_REF] Singh | Solution structure of human von Willebrand factor studied using small angle neutron scattering[END_REF][START_REF] Savage | Functional self-association of von Willebrand factor during platelet adhesion under flow[END_REF][START_REF] Ulrichts | The von Willebrand factor self-association is modulated by a multiple domain interaction[END_REF][START_REF] Barg | Soluble plasma-derived von Willebrand factor assembles to a haemostatically active filamentous network[END_REF][START_REF] Matsushita | Localization of von willebrand factor-binding sites for platelet glycoprotein Ib and botrocetin by charged-to-alanine scanning mutagenesis[END_REF][START_REF] Matsui | Structure and function of snake venom toxins interacting with human von Willebrand factor[END_REF]. Finally, natural mutations causing type 2B von Willebrand disease (VWD 2B) such as the Arg1306Trp or Arg1341Trp [START_REF] Sadler | Update on the pathophysiology and classification of von Willebrand disease: a report of the Subcommittee on von Willebrand Factor[END_REF], are also able to stabilize a

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conformational state that is prone to the interaction with the platelet receptor even under very low shear conditions and causes platelet clumping in the systemic circulation [START_REF] Sadler | Update on the pathophysiology and classification of von Willebrand disease: a report of the Subcommittee on von Willebrand Factor[END_REF][START_REF] Groot | The presence of active von Willebrand factor under various pathological conditions[END_REF].

Recently, it has been demonstrated that VWF multimers undergo a dramatic shape change as a function of shear rate [START_REF] Barg | Soluble plasma-derived von Willebrand factor assembles to a haemostatically active filamentous network[END_REF][START_REF] De Luca | Structure and function of the von Willebrand factor A1 domain: analysis with monoclonal antibodies reveals distinct binding sites involved in recognition of the platelet membrane glycoprotein Ib-IX-V complex and ristocetin-dependent activation[END_REF], which is responsible for the formation of VWF fibers, that are organized as a spider-web like structures. This network may represent an ideal anchor to capture flowing platelets during the process of primary haemostasis [START_REF] Barg | Soluble plasma-derived von Willebrand factor assembles to a haemostatically active filamentous network[END_REF]. Notably, that VWF could self associate and aggregate under high shear stress was known from previous studies. For instance, a shear-dependent self-association of VWF in suspension was demonstrated in a cone-plate viscometer [START_REF] Singh | Solution structure of human von Willebrand factor studied using small angle neutron scattering[END_REF]. These studies showed that in all cases the aggregation and web-formation process is essentially linked to the mechanical force generated by shear. In this study, we investigated the formation of VWF macro-aggregates induced by ristocetin. The latter is a polyphenol glycopeptide synthesized by the actinomycete Nocardia lurida, that was shown to have potent antibacterial activity. The introduction of this antibiotic in clinical practice, caused frequent drug-induced thrombocytopenia, which was demonstrated to be associated with extensive intravascular platelet agglutination [START_REF] Gangarosa | Ristocetin-induced thrombocytopenia: site and mechanism of action[END_REF][START_REF] Gangarosa | Hematologic complications arising during ristocetin therapy; relation between dose and toxicity[END_REF]. Later on in vitro studies discovered that this molecule is able to specifically bind to the A1-domain of VWF, eliciting a conformational change responsible for VWF binding to platelet GpIbα [START_REF] De Luca | Structure and function of the von Willebrand factor A1 domain: analysis with monoclonal antibodies reveals distinct binding sites involved in recognition of the platelet membrane glycoprotein Ib-IX-V complex and ristocetin-dependent activation[END_REF]. This property is currently used in the clinical diagnostics of VWD, to detect both defective (type 2A and 2M) and hyper-reactive (type 2B) VWF mutants. The investigation is aimed at assessing the ability of VWF to undergo a self association process induced by chemical potential of this allosteric effector, even in the absence of hydrodynamic shear stress and any protein adsorbing surface.

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MATERIAL AND METHODS

VWF purification and characterization

VWF was purified from fresh frozen plasma of type A-or B-specific blood group of healthy volunteers by glycine salt precipitation [START_REF] Ramasamy | Biological activity von Willebrand factor during the manufacture of therapeutic factor VIII concentrates as determined by the collagen-binding assay[END_REF]. It was gel filtered on a Sephacryl-S500 3x100 column equilibrated with Hepes 10 mM, NaCl 150 mM, pH 7.5 connected to an FPLC apparatus (Pharmacia) operating at a flow rate of 1 ml/min. Eluate was collected in 5 ml-fractions, following the procedure described elsewhere [START_REF] Tsai | Physiologic cleavage of von Willebrand factor by a plasma protease is dependent on its conformation requires calcium ion[END_REF]. Electrophoresis and immunoblotting of VWF in 1-5% agarose gels containing sodium dodecyl sulfate (SDS-agarose) was performed as previously described [22]. Final protein concentration was determined by UV absorbance at 280 nm on a double beam Varian model Cary 2200 spectrophotometer (PaloAlto, CA), using an extinction coefficients ε (0.1%) = 0.846, calculated on the basis of the amino acid composition of the VWF monomer. In addition, VWF concentration was also measured by an immunoturbidometric method, using an automatic coagulometer (Top, Instrumentation Laboratory, Milano, Italy) and a commercially available assay (Hemosyl VWF antigen, Instrumentation Laboratory, Milano, Italy), which show that a concentration of 10 µg/ml VWF, measured by spectrophotometric method, correspond to about 1 U/ml. A modification of the standard protocol for sodium dodecyl sulfate (SDS-agarose) gel was used [22]. After the electrophoresis and immunoblotting of VWF in 1.5% agarose gels, the detection was performed using a chemiluminescence procedure (Amersham Life Science). A sheet of Kodak BioMax MR film (Eastman Kodak Company, New Haven, CT, USA) was placed over the membrane and exposed for times varying from 10 seconds to 2 minutes.

Ristocetin (Helena Laboratories Corp., Beaumont, TX) standard solution (16 mg/ml) was prepared and freed of sulphate ions, as previously detailed [START_REF] De Cristofaro | Role of chloride ions in modulation of the interaction between von Willebrand factor and ADAMTS-13[END_REF]. The molarity of the ristocetin solution was calculated using a molecular mass value of 2166 Da and an ε value (0.1%, w/v) at 280 nm equal to 4.41. This solution was added to the sample according to the experimental condition under investigation.

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VWF aggregation kinetics induced by ristocetin

Light Scattering Theory

The outlines of the theory related to light scattering techniques is described in biophysics textbooks [START_REF] Schmitz | An introduction to Dynamic Light Scattering by Macromolecules[END_REF]. We shall only briefly describe some basic aspects.

Back Scattering measurements

Dynamic Light Scattering (DLS) measurements on protein solutions were carried out with a Zetasizer Nano S (Malvern Instruments, Malvern, U.K.) equipped with a 4 mW He-Ne laser (633 nm). Measurements were performed at 25°C, at an angle of 173° from the incident beam. Peak intensity analyses were used to determine the average hydrodynamic diameters (Z-average diameter) of the scattering particles. Polydispersity index was obtained by a cumulant analysis of the intensity autocorrelation function using version 5.0 of the Nano software [START_REF] Koppel | Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulant[END_REF]. In each measurement the sample was placed in a 45 µl quartz Suprasil cuvette of 10 mm light path (Hellma Italia, Milan, Italy). After the sample was allowed to equilibrate to 25°C, ristocetin was added and the aggregate formation and evolution was monitored for 24 h. Each measurement was the average of a different number of subruns automatically determined, each being averaged for 10 s. Control measurements were made on solvent and on different ristocetin or VWF concentrations (ranging from 0.01 and 4 mg/ml and 0.01 and 0.9 µM, respectively). Kinetics of the self-aggregation mechanism induced by ristocetin was studied monitoring the Z-average diameter and scattered intensity as a function of time. Time zero was defined as a VWF solution in the measurement cell before ristocetin was added.

Both scattered intensity and Z-average diameter vs time plots showed a multiphase process.

Scattered intensity rapidly increases, reaches a plateau and finally decays (i.e. an asymmetrical bellshaped curve). On the other hand, the Z-average diameter time-dependent profile shows, after an exponential increase (phase 1), a sigmoidal shape. Finally, the asymptote is reached, but significant fluctuation in the Z-average diameter values are observed. The process is well described by the

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following phenomenological equation, that has been used to fit the experimental data according to the least square minimization procedure, by means of Microsoft Excel software.

:

              + ∆ +         - × ∆ + = - C t i H t B R e R R t f 1 ) ( 1 ) ( 2 1
τ Where: R i H (nm) is the VWF hydrodynamic radius just before the Ristocetin addition and ∆R 1 , ∆R 2 , B, C and τ are fitting parameters. Moreover, R r H (nm) = R i H + ∆R 1 is the mean VWF hydrodynamic radius at the end of phase 1, just after Ristocetin addition; and R n H (nm) = R i H + ∆R 1 + ∆R 2 is the mean VWF hydrodynamic radius after phase 2. From the analytic function is possible to derive the further following parameters:

1) v i (nm/min) = the initial rate of the process (i.e. the derivatives at time 0)

2) t p (min) = the turning point (i.e. the phase 2 starting time -measured by the derivatives sign change)

3) v m (nm/min) = the maximal rate of phase 2 (i.e. the maximal derivatives) 4) t m (min) = the v m corresponding time All the derivatives were calculated using a mathematical subroutine of Microsoft Excel Software.

Turbidimetric measurements

Turbidimetric measurements were performed using DU Series 700 UV/Vis scanning spectrophotometer (Beckman Coulter, Fullerton, CA) selecting the Kinetic/Time mode option.

Absorbance at fixed wavelength (350 nm) or spectra (320-700 nm), for a total time of 24 h and reading interval of 1-5 min were recorded. Temperature was set at 25°C and the sample (prepared as previously described) was transferred in a 45 µl quartz Suprasil cuvette of 10 mm light path (Hellma Italia, Milan, Italy). The kinetics run started immediately after ristocetin was added to the sample. The turbidity of a solution is a measure of the intensity decrease of transmitted light due to

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scattering and can be calculated simply by integration of the scattered intensity over all possible directions. Several authors [START_REF] Camerini-Otero | Molecular weights, dispersion of refractive index increments, and dimensions from transmittance spectrophotometry. Bacteriophages R17, T7, and PM2, and tobacco mosaic virus[END_REF][START_REF] Carr | Size and density of fibrin fibers from turbidity[END_REF] have developed theoretical models to determine the size, molecular weight, mass-length ratio of biological macromolecules and systems. Such models were able to describe a reasonable molecular structure when applied to soluble VWF molecules, but completely failed in the analysis of the aggregated system.

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RESULTS

In figure 1 the aggregation process following the kinetic rate constant observed in the corresponding Z-average diameter variation. Finally, the significant fluctuation of the asymptotic Z-average diameter term at the end of the second phase is indicative of an increase in the heterogeneity of the sample; this condition could be due to the building up of a supra-molecular structure associated with a sol-gel phase transition or the presence of a non-specific protein precipitate. The visual inspection of samples at higher VWF concentrations showed an evident physical phase transition in the absence of any macroscopic precipitate or aggregate thus supporting the first hypothesis.

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On the other hand, the absorbance variation reported in figure 3 seems to increase following the Z-average diameter plot profile until the end of phase 1, then reaches a stable plateau and does not change further during the remainder of the experiment. This behaviour could be related to the cluster dimension (>300 nm) that is reached at the end of the first phase with respect to the incident wavelength (350 nm), that could make it insensitive to further variation.

The effect of ristocetin and VWF concentration on the kinetic process has been further investigated by means of DLS and results are shown in fig. 5a andb. Addition of ristocetin to VWF solution (0.9 µM) at a final concentration ranging from 0.1 to 1.0 mg/ml is able to quickly increase the R H to 100-200 nm. However, the Z-average diameter vs time profile is limited to phase 1 within 24h of observation (data not shown). For final ristocetin concentration ≥ 1.5 mg/ml the previously described two-phase process takes place. An asymptotic R H of about 400 nm after 3500-4000 min and 800 nm after 1500-2000 min is reached for ristocetin concentration of 1.5 and 2.0 mg/ml, respectively; at higher concentration the apparent final R H raises to 2000-4000 nm (fig. 5a). Finally, at a fixed ristocetin concentration of 3 mg/ml, the characteristic multi-steps profile kinetic occurs with each of the single phase being dependent on VWF concentration (range 0.1-0.9 µM -fig. 5b).

As soon as the final plateau is reached for the Z-average diameter, its value is insensitive to five fold dilution with a buffer solution containing the same final ristocetin concentration, or to the same dilution with a buffer solution alone (data not shown). This fact demonstrates that the aggregation process is irreversible.

Alternatively, the polymerization-aggregation process can be followed by means of changes of the wavelength (λ) dependence of turbidity (τ) over time. Different theoretical models were described for simple molecule shapes (spheres, rods, random coils [START_REF] Schmitz | An introduction to Dynamic Light Scattering by Macromolecules[END_REF]). In case of rod-like particles (expected for VWF multimers) with diameters that are small compared with the wavelength, τ should vary as -3 and should go to zero as → ∞ [START_REF] Casassa | Light scattering from very long rod-like particles and an application to polymerized fibrinogen[END_REF]. When the fiber diameter grows relative to λ, the plot is no longer linear, but the quantity cτ -1 λ -3 , where c is the concentration,

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changes linearly with λ -2 , and the intercept of the plot gives the mass-length ratio of the fibers [START_REF] Carr | Size and density of fibrin fibers from turbidity[END_REF].

This behaviour can be partially observed with soluble VWF molecules (R H ranging from 35 to190 nm, see fig. 2c). In the 700-600 nm interval τ/τ max vs λ -3 plot is linear (see figure 6 -closed circle) but does not extrapolate to the origin (probably due to the presence of particles of different shape arising from the intrinsic multimeric pattern of the protein); for λ ranging from 320 to 600 nm the plot is no longer linear. After addition of ristocetin, the plot completely deviates from the theoretical model and evolves over time progressively deviating from the initial shape, so that the interference at lower wavelength can be only partially ascribed to ristocetin spectroscopic properties. In figure 6 we have reported representative curves at intermediate time (t=54 min, open squares) and the time corresponding to the end of the aggregation process (t=550 min, open circles). Finally, the peculiar profile of the plot, not captured by any simple molecular structure model, supports the previously stated hypothesis of a sol-gel phase transition occurring in the sample.

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DISCUSSION

VWF does not normally interact with platelets in the bloodstream, but exposed vascular subendothelium enables VWF to interact with the platelet glycoprotein Ib-IX-V complex (GP Ib-IX-V). Ristocetin is a poly-phenol molecule, which interacts with the A1 domain of VWF and also promotes interaction of VWF with GPIb-IX-V, thus providing a model for changes in VWF conformation that may occur in vivo. The molecular mapping of the ristocetin binding site in the A1 domain of VWF is not known in detail, although site-directed mutagenesis showed some of the residues directly or indirectly involved in binding of the antibiotic (Lys534, Arg571, Lys572, Glu596, Glu613, Arg616, Glu626, and Lys642 of the A1 domain, (numbering based on the A1 primary sequence) [START_REF] Matsushita | Localization of von willebrand factor-binding sites for platelet glycoprotein Ib and botrocetin by charged-to-alanine scanning mutagenesis[END_REF]). Likewise, the mechanism responsible for the induced conformational changes is not known. Recent X-ray diffraction studies of the GpIb-A1 crystal complex revealed that the α1-β2 loop of A1 serves as a conformational switch. In fact, both an open α1-β2 isomer, which allows faster dissociation of GpIbα-A1, and an extended isomer, which favours tight association, were observed in the complex containing A1 with a wild-type and type 2B von Willebrand Disease (VWD) mutation, respectively [START_REF] Dumas | Crystal structure of the wild-type von Willebrand factor A1-glycoprotein Ibalpha complex reveals conformation differences with a complex bearing von Willebrand disease mutations[END_REF]. Binding of ristocetin to VWF A1 domain, inducing the interaction of the protein with the N-terminal domain of platelet GpIb, supports the process of primary haemostasis. The latter arises also from the VWF ability to interact with subendothelial matrix proteins, such as collagen. Previous studies showed that the transformation of multimeric plasma-derived VWF into a widespread immobilized network depends on several physical and biochemical factors as a critical protein concentration, induced shear stress, and an appropriate anchoring surface, mainly represented in vivo by matrix proteins [START_REF] Barg | Soluble plasma-derived von Willebrand factor assembles to a haemostatically active filamentous network[END_REF].

In the present study, a multiphase process of VWF conformational transitions after interaction with ristocetin is described for the first time and the kinetic aspect of the reaction are shown. The molecular transition induced in vivo by shear stress or promoted in vitro by ristocetin is a part of a more complex process composed by different steps. The rapid interaction with ristocetin "activates" VWF molecules triggering an increase in the their apparent dimension, as detectable by This process reflects an initial formation of activated clusters of VWF multimers. The second part of the kinetics is characterized by a slower rate constant and by a non exponential time dependence of the increase in the size of the cluster, thus suggesting the occurrence of a reaction-limited regime, culminating with a physical phase transition that is detectable by eye-inspection. We were able to find highly reproducible experimental conditions so that each step of the process can be described.

The observed multiphase scattering signal is strongly dominated by the aggregating VWF molecules, even if ristocetin is likely to dimerize at the concentration used in the present study [START_REF] Scott | Dimeric ristocetin flocculates proteins, binds to platelets, and mediates von Willebrand factor-dependent agglutination of platelets[END_REF].

Ristocetin was previously reported to trigger flocculation of several proteins, included fibrinogen and VWF [START_REF] Scott | Dimeric ristocetin flocculates proteins, binds to platelets, and mediates von Willebrand factor-dependent agglutination of platelets[END_REF]. However this process is a non-specific aggregation following a simple linear kinetic. Moreover, in a previous study, the amount of flocculated proteins was evaluated after centrifugation (i.e. after disrupting possible growing supramolecular structures) [START_REF] Scott | Dimeric ristocetin flocculates proteins, binds to platelets, and mediates von Willebrand factor-dependent agglutination of platelets[END_REF]. We were able to confirm, by light scattering measures, that human fibrinogen flocculation occurs also at low ristocetin concentration (<1 mg/ml -data not shown). On the other hand, the complex kinetic profile observed with VWF, triggered only at high (>1 mg/ml) ristocetin concentration, suggests for a specific binding of molecules and an ordered polymerization process. Finally, the peculiar behaviour of scattered intensity and turbidity could be attributed to destructive interferences by large particles or physical state sol-gel transition as also evident by visual inspection of samples at higher VWF concentrations.

Self-aggregation of VWF was already observed using high hydrodynamic shear stress (>30 dyn/cm 2 ); in this case the "physical" stretching triggers the molecular activation thus leading to conformational changes promoting the potential adhesion of the protein. Beside inducing the binding to GpIb or to collagen surface, "activated" VWF was demonstrated to self-aggregate [START_REF] Barg | Soluble plasma-derived von Willebrand factor assembles to a haemostatically active filamentous network[END_REF][START_REF] Schneider | Shear-induced unfolding triggers adhesion of von Willebrand factor fibers[END_REF]. However, the data on molecular dimensions of VWF were obtained on the protein studied as a function of shear rate (up to >5000 sec -1 ) in a viscometer and successively transferred in a light

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scattering apparatus, thus disrupting growing supra-molecular structures. Likewise, a previous study using biotinylated VWF, immobilized on a plastic surface, showed that VWF is able to reversibly self-agregate under static condition [START_REF] Ulrichts | The von Willebrand factor self-association is modulated by a multiple domain interaction[END_REF]. Both the regions 1-1365 and 1366-2050 are able to inhibit this VWF-VWF interaction [START_REF] Ulrichts | The von Willebrand factor self-association is modulated by a multiple domain interaction[END_REF]. However it must be emphasized that this self-aggregation was obtained under static condition but linked to VWF adhesion to synthetic surface that elicits VWF conformational changes. The present study demonstrates, for the first time, the ability of chemical potential (i.e. binding) to induce in solution under static conditions VWF self-aggregation and network development in suspension, likely mimicking the physiological mechanism, triggered by physical forces, involved in controlling platelet adhesion rates in circulation.

On the basis of the present findings, we propose that the conformational changes induced by ristocetin binding disrupts the multiple domain interactions present in the native VWF structure.

Hence, upon stabilization of the extended conformation, the swapped domains of a VWF multimer can interact with another domain of a different multimer. In other words, the non-covalent intramolecular interaction between domains in the same VWF multimer chain, may be broken and restored between different multimer chains by identical intermolecular contacts [START_REF] Liu | 3D domain swapping: as domains continue to swap[END_REF]. This process can contribute to progressive aggregation culminating in a phase transition with the formation of the micro-gel network.

This mechanism, in vivo, should optimize the formation of a spider-web like network, which anchors circulating platelets through binding of the GpIb-IX-V membrane complex. Moreover, we can hypothesize that the dimensions of VWF multimers affect the efficiency and thus the rate of this network's formation. The proposed mechanism may play a relevant role in all the clinical conditions characterized by particular abundance of ultra-large VWF multimers such as thrombotic microangiopathies; in fact, a pathological deposition of these VWF aggregates in microcirculation, may contribute to the thrombo-hemorrhagic syndromes occurring in these clinical settings.

A C C E P T E D M A N U S C R I P T TABLE and FIGURES

  figure 3 as a result of two experimental techniques: DLS and turbidimetry. The Z-average diameter

A

  C C E P T E D M A N U S C R I P T light scattering measurements. The time course of the first part of the aggregation curve suggests for a diffusion limited process as the maximum aggregate size increases exponentially with time[START_REF] Schmitz | An introduction to Dynamic Light Scattering by Macromolecules[END_REF].

Figure 1

 1 Figure 1

Figure 2

 2 Figure 2 Panel a) scattered intensities of ristocetin (3 mg/ml -○) and VWF (0.4 µM -) normalized by the

Figure 3 AFigure 5

 35 Figure 3

Figure 6 Figure 3 .

 63 Figure 6

ACKNOWLEDGEMENTS

Financial support by the Italian Ministry of University and Research [Linea D1 "ex-60%" 2007-2008 Università Cattolica Sacro Cuore] and PRIN-2007 [RDC and EDS] are gratefully acknowledged.