PUMP FOR NUCLEAR APPLICATIONS

Abstract

The present invention describes an axial pump for pumping liquid metal, the axial pump comprising an inlet for receiving liquid, at least one rotor, the rotor comprising a rotor hub and a plurality of rotor blades positioned thereon, a stator, comprising a stator hub and a plurality of stator vanes, and an outlet for discharging the liquid metal, the pump being adapted for providing efficient pumping while reducing or avoiding erosion of the pump by the liquid metal.

Claims

1.-22. (canceled)

23. An axial pump for pumping liquid metal, the axial pump comprising: an inlet for receiving liquid, at least one rotor, the rotor comprising a rotor hub and a plurality of rotor blades positioned thereon, a stator, comprising a stator hub and a plurality of stator vanes, and an outlet for discharging the liquid metal, wherein the inlet is defined by two axially concentric walls, the concentric walls having curved edges such that the inlet walls define an inlet entrance area which normal vector is substantially perpendicular to the axis of the axial pump, and wherein the rotor blades have a tip being positioned closest to the wall opposing the rotor and whereby the ratio of the distance between the rotor axis and the rotor hub, being the rotor hub radius, to the distance between the rotor axis and the rotor blade tip, being the rotor tip radius, is larger than 0.87.

24. An axial pump according to claim 23, wherein said axial pump is adapted for pumping lead-bismuth eutectic mixtures.

25. An axial pump according to claim 23 wherein the inlet area of the pump is between 8.5 and 10.8 times larger than the area in front of the rotor.

26. An axial pump according to claim 23, wherein the longitudinal section of the walls comprise a monotonically decreasing curvature from the entrance of the inlet, the curvature being defined with respect to the axis of the pump.

27. An axial pump according to claim 23, wherein the length of the portion of the inlet before the rotor has a radius of curvature larger than 0.5 and is at least 1 meter long.

28. An axial pump according to claim 23, whereby the ratio of the distance between the rotor axis and the rotor hub, being the rotor hub radius, to the distance between the rotor axis and the rotor blade tip, being the rotor tip radius, is larger than 0.9, for example larger than 0.95.

29. An axial pump according to claim 23, wherein the rotor comprises at least 20 blades, advantageously at least 23 blades.

30. An axial pump according to claim 23, wherein the rotor blades comprising stainless steel.

31. An axial pump according to claim 23, wherein the rotor blades have a varying angle with respect to the axis of the pump, for different positions along a blade camber line of the rotor blade.

32. An axial pump according to claim 23, wherein the variation in the angle with respect to the axis of the pump is different for camber lines near the tip of the rotor blade compared to camber lines near the hub.

33. An axial pump according to claim 23, wherein the maximum rotor blade thickness is 11 mm at the hub and 10 mm in the tip.

34. An axial pump according to claim 23, wherein a cross section of the rotor blades is defined by intersecting double circular arcs or wherein a cross section of the rotor blades is defined by intersecting asymmetric double circular arcs.

35. An axial pump according to claim 23, wherein the outlet further comprises a diffuser, the diffuser having a length in between 1.39 and 1.64 times R.sub.HUB.

36. An axial pump as in claim 23, wherein the stator comprises at least one row of vanes.

37. An axial pump according to claim 30, wherein the vanes comprise a varying angle with respect to the axis of the pump along the vane camber line.

38. An axial pump according to claim 23, wherein at least one row of vanes comprises at least 25 axial vanes.

39. An axial pump according to claim 23, wherein the stator vane maximum thickness is between 10 mm and 11 mm.

40. A nuclear reactor cooled using a liquid coolant for cooling, the cooling system comprising an axial pump for pumping the liquid metal coolant according to claim 23.

41. A nuclear reactor according to claim 40, wherein the liquid coolant is a liquid metal coolant or wherein the liquid coolant is a lead-bismuth eutectic mixture.

42. Use of an axial pump according to claim 23 for pumping lead-bismuth eutectic mixtures for cooling of a nuclear reactor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] FIG. 1 illustrates a pump according to some embodiments of the present invention comprising a hub and a shroud.

[0045] FIG. 2 illustrates a cross section of a pump according to some embodiments of the present invention.

[0046] FIG. 3 illustrates the inlet of a pump and its cross section, according to some embodiments of the present invention.

[0047] FIG. 4 illustrates a foil for a pump according to some embodiments of the present invention

[0048] FIG. 5 shows the change of camber line angle of a blade with respect to the axis of a pump according to some embodiments of the present invention.

[0049] FIG. 6 shows the thickness profile of a blade for a pump according to some embodiments of the present invention.

[0050] FIG. 7 shows the design choice of flow angles, for a given flow, related to the entry flow/exit flow ratio in a blade.

[0051] FIG. 8 illustrates the outlet of a pump and its cross section, according to some embodiments of the present invention.

[0052] FIG. 9 shows the outline of the cross section of an inlet as the radius of the walls as a function of the axis length, according to a particular embodiment of the present invention.

[0053] FIG. 10 shows the maximum (relative) flow along the camber line of a blade for given conditions of an embodiment of the present invention.

[0054] FIG. 11 shows the maximum (relative) flow along the camber line of a blade for given conditions of another embodiment of the present invention.

[0055] FIG. 12 shows the maximum flow along the camber line of a vane, as well as its flow angle variation, for given conditions of an embodiment of the present invention.

[0056] FIG. 13 shows the efficiency and total head rise as a function of the nominal flow rate, for six different speed regimes.

[0057] FIG. 14 shows the net positive suction head required and torque as a function of the nominal flow rate, for six different speed regimes.

[0058] FIG. 15 shows the total head rise as a function of the hydraulic efficiency, as well as the maximum (relative) flow as a function of hydraulic efficiency and a representative example of increase of maximum flow in the camber line of a blade with increase of efficiency.

[0059] FIG. 16 shows the total head loss of a pump at zero RPM (static rotor) as a function of nominal flow rate, for direct and inverse flow directions.

[0060] FIG. 17 shows the torque and total head as a function of nominal flow rate, for several speed regimes, for calculation of shutdown time (parabolic throttle line).

[0061] The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes.

[0062] Any reference signs in the claims shall not be construed as limiting the scope.

[0063] In the different drawings, the same reference signs refer to the same or analogous elements.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0064] The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not correspond to actual reductions to practice of the invention.

[0065] Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

[0066] Moreover, the terms top, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.

[0067] It is to be noticed that the term comprising, used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression a device comprising means A and B should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.

[0068] Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases in one embodiment or in an embodiment in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0069] Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.

[0070] Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0071] In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0072] The description of certain embodiments of the present invention will make reference to different parts of pumps. Some of these parts may not be present in all embodiments of the present invention. Pumps according to embodiments of the present invention comprise an inlet, which comprise walls such as an outer wall in a shroud and an inner wall, and an entrance defined by edges. In some embodiments of the present invention, the inner wall may define a hub supporting the rotor and stator. The inlet walls may serve to direct the pumped liquid towards a rotor and stator. Some embodiments of the present invention make reference to an outlet, which may comprise a diffusor. The outlet may direct the pumped liquid to the exit of the pump, such exit may be defined also by the shroud wall, or by the shroud and the hub wall.

[0073] Where in embodiments of the present invention reference is made to blade and vane, reference is made to a foil or plate, usually a metal or ceramic foil or plate, shaped and distributed for a particular function in the pump. A set of blades in a rotor may be known as a flow through cascade and a set of vanes in a stator may be known a ring vane.

[0074] Where in embodiments of the present invention reference is made to the camber line of a blade or vane, reference is made to the line formed by the points equidistant to the outer surfaces of the blade or vane, when viewing a cross-section of the blade or the vane.

[0075] Where in embodiments of the present invention reference is made to hub radius, or R.sub.HUB, reference is made to the distance between the axis of the pump and the hub wall. For example, the rotor hub radius (or R.sub.HUB) is the part of rotor blade closest (e.g. attached) to the hub. On the other hand, foil tip radius or R.sub.TIP refers to the distance between the axis of the pump and the part of the rotor most far away from the axis of the pump, assuming the rotor is positioned on the inner wall of the pump. Depending of the type of blade, there shall be references to the blade (hub or tip) radius, R.sub.BHUB and R.sub.BTIP as well as vane (hub or tip) radius, R.sub.VHUB and R.sub.VTIP. The difference R.sub.TIPR.sub.HUB determines the height of the blade or vane, which in particular embodiments of the present invention may be close to the distance between the hub and the shroud at that region of the rotor.

[0076] In a first aspect, the present invention relates to an axial pump for pumping liquid, specifically to an axial pump suitable for pumping liquid metal, such as for example a lead alloy such as liquid bismuth eutectic (LBE) mixture. LBE melts at around 125 C., hence it is a very suitable liquid metal coolant for nuclear reactors.

[0077] In embodiments of the present invention, an axial pump comprises an inlet for receiving liquid, at least one rotor, a stator, and an outlet for discharging the liquid. The rotor comprises a rotor hub and a plurality of rotor blades positioned thereon. The stator, comprising a stator hub and a plurality of stator vanes. According to embodiments of the present invention the inlet is defined by two axially concentric walls, the concentric walls having curved edges such that the inlet walls define an inlet entrance area which normal vector is substantially perpendicular to the axis of the axial pump.

[0078] One or both of the walls may have substantially cylindrical or conical parts (e.g. both walls having a circular cross-section). The walls may comprise at least a portion with a certain curvature and/or curved slope with respect of the pump axis. The walls may be bell-shaped walls, e.g. a cylinder or a cone with curved rims. The entrance of the inlet may be defined by curved rims of the outer surface and the inner surface walls, and the entrance may define an area (e.g. the lateral wall of a cylinder) whose normal may be perpendicular to the axis of the pump. The flow may not be unidirectional, reducing stresses in the hub. In some embodiments of the present invention, the axial pump comprises an outer surface and an inner surface defining a hub defining part of the rotor and the stator. The outer surface and the inner surface may have axial symmetry and be concentric with respect to the pump axis. Hence, the inlet may be defined by the walls of the outer and inner surfaces, which are concentric with respect to the pump axis, allowing a symmetrical flow, which is advantageous for a smooth rotation and reduction of erosion risk.

[0079] According to embodiments of the present invention, the rotor blades have a tip being positioned closest to the wall opposing the rotor and the ratio of the distance between the rotor axis and the rotor hub, being the rotor hub radius, to the distance between the rotor axis and the rotor blade tip, being the rotor tip radius, is larger than 0.87.

[0080] As shown in FIG. 1, an embodiment of the axial pump 100 may comprise an inlet 101 defined by an inner wall 102 defining a hub 110 and a wall 103 of an outer portion 120. Both walls are shown as bell-shaped (although the present invention is not limited thereto). The ensemble of both walls may define an inlet entrance area 104 for liquid metal to enter in the pump. The entrance may be defined by the curved edges of the walls. The inner wall 102 and the outer wall 103 of the pump may both have an edge, outwardly curved with respect to the axis. The entrance 104 may have the shape of the lateral area of a cylinder, advantageously allowing the flow to enter in the pump and producing an axially symmetrical flow. The present invention is not limited thereto and other shapes for the inlet entrance 104 may be also used, e.g. elliptic cylinder. The hub 110 may form the basis of a rotor which may comprise a flow-through cascade 111 formed by, for example, one ring of rotor blades. The hub 110 also may form a stator which may comprise one ring 112 of vanes. The present invention may not be limited thereto, and the rotor may comprise several rotor blade rings, and the stator may comprise several stator vane rings or even no vanes. The axial pump 100 may comprise an outlet 105 further comprising an exit area 106, for allowing discharge of pumped liquids. In some embodiments of the present invention, the outlet may comprise other structures and features, for example a diffuser 107.

[0081] Other elements and structural features may be present in the pump. For example, in FIG. 2 a scheme of the pump is represented comprising, as before, an inlet 101, a hub 110 forming a rotor 201 (comprising the flow-through cascade 111), and a stator 202 (which may comprise the vane ring 112). FIG. 2 further shows also the axis 204 of the axial pump, and also indicates the curvature of the surfaces at the edges: the curvature 205 of the outer surface edge and the curvature 206 of the inner surface edge.

[0082] The outer surface 120, also referred to as the shroud, may comprise two pieces: a first piece 211 forming part of the inlet 101 and a second piece 212 forming part of the outlet 105. Embodiments of the present invention are not limited thereto, and the outer surface may be one block. The inner surface forming the hub in particular embodiments of the present invention may comprise a rotatable beam 207 which may power the rotor, hence the flow through cascade 111 of rotor blades can be attached to the hub in these embodiments. Other alternative embodiments may comprise rotor blades attached to a rotor comprised in the outer surface.

[0083] The vane ring 112 may be attached to the stator in the hub, and be immobile. Some embodiments of the present invention may have the vane ring attached to the second piece 212 of the shroud 120.

[0084] Other features may be present, or some features may have more than one function. For example, in the particular embodiment represented in FIG. 2, one or more fins 203 may serve as structural support between the hub 110 and shroud 120. They may also serve as exit vanes for reducing whirl component of the liquid at the exit of the pump.

[0085] FIG. 3 represents an isolated inlet 101, as well as its cross section 300, of a pump according to some embodiments of the present invention. The cross section corresponds to the line 301 in the shroud wall 103 and the line 302 in the inner wall 102. In some embodiments of the present invention, the inlet entrance 104 is defined by the rim 205 of shroud wall 103 and the rim 206 of hub wall 102. The vector 303 normal to the entrance area may be perpendicular to the axis 204 of the pump. Several parameters are shown in the cross section 300, which can be optimized by design according to the desired flow, head rise, pressure, etc. while simultaneously reducing or avoiding erosion of the pump parts.

[0086] For example, with reference to the figure, the size of the entrance is given by H.sub.IN. Its value may be chosen according to the distance between the hub and the shroud at the rotor region, its ratio to the hub radius between 0.88 and 1.14. This way, the pumping may be sufficiently efficient with no need for high speed of liquid at the entrance area. The length L.sub.1 may have values between 0.50 and 0.63 times the hub radius R.sub.HUB, and the length L.sub.2 between 0.63 and 1.0 times the hub radius R.sub.HUB. The curvature of the inner surface edge may be defined by the length L.sub.3 and the angle .sub.HUB (alpha hub), which may have values between 0.38 and 0.44 times the hub radius R.sub.HUB and 25 to 35 respectively. The longitudinal section of the walls may also comprise a monotonically decreasing curvature 304 towards the flow through cascade 111 of the rotor, the curvature being defined with respect to the axis of the pump 204. It is an advantage of embodiments of the present invention that the flow (and liquid speed) may gradually increase towards the rotor, further avoiding corners, hence reducing erosion, reducing flow blockages or instabilities. Formation of erosion zones is also reduced, thereby reducing cavitation in the inlet. The curvature 304 in the hub wall 102 may be defined by the length L.sub.4, and it may have values between 0.38 and 0.63 times the hub radius RHUB. The lengths L.sub.5 and L.sub.10 may be in between 0.25 and 0.45 time R.sub.HUB. These lengths define the part of the inlet closest to the rotor region, and in some embodiments may be a square toroid of height L.sub.5=L.sub.10. The length L.sub.6 may have the values of 0.25 to 0.30 times RHUB, and it may define the necking towards the rotor, which contributes in the increase of liquid pressure towards the rotor region. The length L.sub.7 and L.sub.8, together with the angle .sub.SHROUD may define the curvature of the shroud rim 205. The values may be between 0.38 to 0.63 times RHUB, 0.19 to 0.29 times R.sub.HUB and 20 to 30 respectively. The length L.sub.9 may be linked to the monotonic curvature 305 in the shroud wall 103 towards the rotor region, and it may have values between 0.25 and 0.43 times RHUB.

[0087] The distance between the inlet and the rotor region may also be chosen to be in the range 1.5 to 3 times RHUB, for a good and smooth increase of liquid flow velocity.

[0088] In some embodiments of the present invention, the distance between the shroud and the hub walls is smallest in the rotor area, in some embodiments the area being at least 8 to 10 times smaller than the inlet area. The blades may extend from the hub to the shroud, leaving just enough space to avoid contact of the blades with the shroud during operation. With reference to the dimensions of the pump, the hub radius is small compared to the tip radius. For example, the hub radius/tip radius ratio for the blade may be between 0.87 and 1, for example being at least 0.87, e.g. at least 0.9, e.g. at least 0; 95, hence R.sub.HUB may be 0.9 R.sub.TIP. Similar values can be provided for the stator vane, but the present invention is not limited thereto, and the hub/tip ratio may be different in the vane.

[0089] Additionally, all these values may be optimized for any desired value of head rise, pressure, flow, etc.

[0090] The shape of the blades may also be optimized to ensure a determined reduction of the maximum flow velocity, thus reducing the erosion risk, which is very high in case of pumps of liquid metal. For example, in some embodiments of the present invention, the rotor cross-section is defined by for example intersecting double-circular arcs. Vanes may also present characteristics similar to the rotor blades. FIG. 4 shows an exemplary rotor blade 400 and its section 410. The distance between the axis and the part of the blade closest (e.g. attached) to the hub is the R.sub.HUB, while the distance between the axis and the foil tip is R.sub.TIP. The section 410 of the foil 400 according to the dashed line 401 can be seen in the rightmost schematic representation of the foil section 410, together with the flow angles .sub.1, .sub.2 (beta 1 and 2) of the flow direction W with respect to the pump axis 204. In the particular case of blades, the flow (and the flow direction determined by the beta angles) changes along the blade due to its curved shape, hence the flow is W.sub.1 at the entrance of the blade, and W.sub.2 at the exit.

[0091] Moreover, the flow angles shown in the diagram 410 of FIG. 4 may change with the height (R.sub.TIPR.sub.HUB) of the foil. The diagram in FIG. 5 shows the angle variation along the normalized length (S/S.sub.0) of the camber line of, e.g., a blade. The characterizing camber angle of the blade tip 501 of the camber line may differ from the camber angle of the blade near the hub 502. For example, the angle at the flow entry may be 70 in the tip and 68 at the hub, while at the flow exit may be 55 in the tip and near 45 in the hub. This results in a twisted blade. The angles may be optimized according to desired parameters, as before.

[0092] The shape of the blade surfaces may be symmetrical or asymmetrical. In some embodiments, it may be asymmetrical as shown in the diagram of FIG. 6 showing the profile of an exemplary blade with a bulge close to the flow entry side, for example at one third of the length. The thickness of the blade may also be variable along its height (R.sub.BTIPR.sub.BHUB). For example, it may be thinner in the tip, and the profile of the tip 601 (represented by a dashed line) may have a maximum thickness of a value of 10 mm (shown is the half thickness value), for example 4.8 mm, while the thickness at the hub 602 (represented by a full line) may have a maximum thickness of a value of 10.4 mm. As indicated above, in embodiments of the present invention the thickness can be larger than the above indicated values.

[0093] An appropriate shape and thickness may not only prolong the lifetime of the blades and increase their effectivity, but also blade erosion and pitting may be reduced by a proper choice of shape and thickness.

[0094] The choice of geometry of the blade (flow angles, camber angles, thickness, etc.) has an influence on the flow at the entrance and exit of the blade. Additionally, the flow at the tip may be different from the flow at the hub. FIG. 7 shows the ratio 701 between exit flow and the entry flow in a blade, as well as the flow turning 702 in degrees between rotor inlet and outlet at the hub (=maximum turning) as function of the inlet flow speed near the tip (=maximum velocity). The selected design corresponds to a flow angle difference 703 of approximately 7 and an entry flow at the blade tip of 10.5 to 11 m/s results in a flow ratio 704 of approximately 0.74. The flow ratio of 0.74 relates to the diffusion effort of the cascade, i.e. it results in a slow down of the flow to generate head. When a low diffusion ratio is used, this results in a high peak velocity on the suction side.

[0095] As before, this type of profile may be present in blade and/or vane. Vanes may have for example a relative high thickness, to still deal with erosion if erosion would occur anyway.

[0096] The present invention is not be limited thereto, and the pump may comprise other type of foils, or mix a type of blade with a different type of vane.

[0097] Some embodiments of a pump according to the present invention may comprise an outlet. FIG. 8 represents an isolated outlet 105 for a pump, as well as its cross section 800 (showing flow-through cascade 111 and vane ring 112), according to some embodiments of the present invention. The outlet may be defined by a wall 102 of the hub 110 and a wall 103 of the shroud, for example the wall 102 belonging to the stator 202 and the wall 103 belonging to a second piece 212 of the shroud. The exit 106 of the pump may be defined in the outlet 105. Several parameters are shown in the cross section 800, which can be optimized by design according to the desired flow, head rise, pressure, etc. while simultaneously reducing or avoiding erosion of the pump parts. With reference to FIG. 8, the outlet may comprise a diffuser 107, for reducing the kinetic energy in the flow and hence increase the pressure. The length L.sub.Diffuser defines the total length of the diffuser from the vane to the exit. The distance between the flow through cascade and the vane ring is S. The distance L.sub.1 defined in the shroud from the vane ring 112 may have a value between 0.4 to 0.55 times RHUB. The vane ring helps decreasing the whirl component of the liquid, further increasing the pressure. The length L.sub.2, defined from the exit 106 towards the stator, and the angle .sub.SHROUD (alpha shroud), may be all related to the curvature of the diffuser 107, and may have a value between 0.45 to 0.60 times RHUB for L.sub.2 and 0 to 7.5 for the angle. The length L.sub.3 defined in the hub from the vane ring 112 may have a value between 0.25 to 0.50 times RHUB. Together with L.sub.3, the length L.sub.4 defined from the exit 106 and the angle .sub.HUB (alpha hub) may define the curvature of the hub in the diffuser 107, and may have a value of 0.25 to 0.50 times RHUB, 0.45 to 0.60 times RHUB, and 0 to 10 respectively. The flow escapes from the pump in an area defined by H.sub.EXIT and R.sub.SHROUD. For example, in the case of axially symmetrical pumps, the exit 106 will form a ring with inner and outer radii R.sub.SHROUD and H.sub.EXIT.

[0098] In some embodiments of the present invention, the distance between the shroud and the hub is smallest in the rotor and it increases towards the exit (hence R.sub.VTIPR.sub.VHUB<<H.sub.EXIT), and the walls may comprise an increasing curvature from the stator towards the exit. The curvature of the diffuser walls may be smaller in the shroud than in the hub wall. Optimization of the diffuser dimensions is also possible.

[0099] Examples of particular embodiments will be discussed in the following, illustrating the results of pump simulation experiments for optimizing pump design. An inlet for a pump according to an exemplary embodiment of the present invention may comprise a shroud and a hub with bell-shaped walls, and may be concentric with respect to a common pump axis. The inlet entrance area may be defined by the curvature of the edge of each wall. The particular geometry and dimensions of the inlet, outlet and foils may be optimized according to, for instance, the maximum flow expected, the maximum head rise, the desired flow, the desired angular speed, etc. The outline of the cross section of an inlet is shown in FIG. 9 as the radius (distance from the axis) of the walls as a function of the axis length. The size H.sub.IN of the inlet entrance 104 may be, in this exemplary embodiment of the present invention, 40 cm, while the distance between the walls at the flow through cascade 111 may be 5 cm or less. In order to reduce cavitation, the flow of the liquid metal into the rotor area may be done smoothly, avoiding corners. For example, the shroud and hub walls may be curved. The shroud rim may have a curvature 901 (shown as a dashed circle) of a 10 cm radius, and the hub rim may be defined by one quadrant of a dashed ellipse 902 of 40 cm semi-major axis and 30 cm semi-minor axis. The present invention may not be limited to said shapes and dimensions, and the rim may be parabolic or have an irregular curvature. The distance D between the center of the inlet entrance and the flow-through cascade 111 may be 80 cm. These geometric characteristics help in reducing erosion and damages, as well as increasing flow. For example, one of the parameters determining the maximum relative velocity (which in embodiments of the present invention may be 11 m/s) is the distance D.

[0100] It has also been found that, for embodiments of the present invention with such geometric characteristics, the optimal rotor hub radius should be only slightly smaller than the foil tip radius in order to obtain good flow, obtaining low cavitation and increasing head rise. For instance, R.sub.HUB=0.9 R.sub.TIP. It may have other values depending on the particular application.

[0101] The camber line angle (blade angle) may also be optimized. In one exemplary embodiment in which the pump comprises 27 blades, the blade angle would change from 67 to 45 degrees in the hub and from 72 to 54 degrees in the shroud. The maximum flow (W/W.sub.0) is indicated in the graph 1000 of FIG. 10, corresponding to a head rise of 2.25 m, 454.92 liters per second, 113.45 kW of power and efficiency (ratio of real vs ideal head rise) of 0.88.

[0102] For a flow through cascade comprising 24 blades, on the other hand, the optimal camber line angle would have 65 to 40 degrees in the hub and 67 to 50 degrees in the shroud. The maximum flow is reduced as indicated in the graph 1100 of FIG. 11, corresponding to a head rise of 3.07 m, 455.47 liters per second, 149.31 kW of power and efficiency of 0.92.

[0103] In embodiments of the present invention comprising a vane ring, the same can be applied to vane design. As it can be seen in FIG. 12, for embodiments comprising 25 vanes, the optimal camber line angle should be between 40 and 15 degrees in the hub and 49 and 19 degrees in the shroud as shown in the graph 1200 on the right of FIG. 12. Nevertheless also designs having a different outlet angle, e.g. an outlet angle equal to 0, also are envisaged in embodiments of the present invention. The graph 1210 on the left of FIG. 12 corresponds to the reduction of maximum flow for the optimized values. It corresponds to a head rise of 2.98 m, 454.66 liters per second, 142.57 kW. The speed of discharge is 1.89 m/s. It is to be noticed that the above values are obtained for an optimized geometry. More particularly, the Hub/tip radius ratio is 0.88, rtip was 0.45 m and the rotational speed was 223.67 rpm.

[0104] The corresponding pump characteristics of the optimized pump can be seen in the diagrams of FIG. 13 and FIG. 14.

[0105] The diagram 1300 of FIG. 13 shows the efficiency with respect to the nominal flow rate, while the diagram 1310 of FIG. 13 shows the total head rise, for several regimes of angular speeds with respect to the maximum speed (from 50% to 110% of the maximum speed, in RPM). The chosen design efficiency, at maximum speed (100%), gives an efficiency 1301 close to 0.9 and a total head rise 1311 of slightly more than 3 m, for a nominal flow rate of 1.

[0106] Analogously, the diagram 1400 of FIG. 14 shows the net positive suction head required (NPSH, minimum pressure required at the suction port of a pump for avoiding cavitation) with respect to the nominal flow rate, while the diagram 1410 of FIG. 14 shows the total torque, for the same regimes of angular speeds as in FIG. 13. The chosen design efficiency, at maximum speed (100%), gives an NPSH 1401 of 2 m and a torque 1411 of slightly more than 6500 Nm, for a nominal flow rate of 1.

[0107] An example of design optimization is seen in FIG. 15, showing two graphs illustrating the optimization values of total head rise with respect to the hydraulic efficiency. While the highest hydraulic efficiency and a high head rise may be desirable, the optimization of the experimental design shows that maximum flow increases dramatically for efficiencies over 0.92, following the arrow 1512. The sub-diagram 1520 shows the unacceptable increase of the maximum flow for such high efficiencies, increasing erosion risk.

[0108] The total head loss can be obtained with the rotor stopped (zero RPM), as a function of the nominal flow rate. This is shown in FIG. 16 for a pump according to some embodiments of the present invention. In the figure, the flow direction is indicated by arrows in the cross sections 1610, 1620: the forward flow direction 1601, in which liquid enters the pump through the inlet and exits through the outlet, and reverse flow direction 1602, in which liquid enters the pump through the outlet and exits through the inlet. The present invention reduces the dynamic head loss by reducing the number of corners and elbows in the pipe system, as well as providing a symmetrical flow.

[0109] The pump shutdown time of a pump according to embodiments of the present invention can be calculated according to Nourbakhsh, A., Joumotte, A., Hirsch, Ch., Parizi, H. B. Turbopumps and Pumping Systems, Springer, 2008:

[00001]$t_{\mathrm{SHUT}}=\frac{.Math..Math.J}{30}.Math..Math.\frac{.Math..Math.n_i}{T_i}$

[0110] Assuming a parabolic throttle line, and assuming friction forces and inertia of the LBE and walls are negligible, the torques for different angular speed regimes (0-110%) are shown in FIG. 17 (upper diagram), together with the total head (lower diagram) as a function of the nominal flow rate for a parabolic throttle line. These values (except for the value at 110% RPM) are also shown in the Table 1.

TABLE-US-00001 TABLE 1 Torque for different RPM regimes i n [%] n [1/min] n Torque T [Nm] 0 0 1 50% 111.8 111.8 1630 2 60% 134.2 22.4 2344 3 75% 167.8 33.6 3670 4 90% 201.3 33.5 5280 5 100% 223.67 22.4 6521

[0111] For the values of Table 1 of speed regimes and torque, the shutdown time has been calculated for three different moments of inertia, as shown in Table 2.

TABLE-US-00002 TABLE 2 Shutdown time in seconds Moment of Inertia J [Kg m.sup.2] Shutdown time t [s] 600 6.1 1600 16.3 2600 26.4

[0112] The knowledge and control of the shutdown time of a pump may be a critical parameter in nuclear applications. The pump according to embodiments of the present invention, thanks to optimization, allows a high level of control over its parameters and characteristics, which are oriented to the minimization of cavitation, erosion, etc of the pump.

[0113] However, mechanical stresses play a particularly important role in the continuous performance of pumps. In particular embodiments of the present invention, a blade at 60% of its thickness may sustain von Mises stresses of 50-60 MPa on the suction side, due to centrifugal forces at 223.67 RPM and pressure loading. At 100% of blade thickness, the von Mises stresses may be 20-40 MPa. Due to these high mechanical stresses, in some embodiments of the present invention, the flow through cascade may advantageously comprise blades comprising stainless steel, for example 316L stainless steel of a Young modulus of at least 190 GPa and yield strength of at least 290 MPa. Vanes may comprise the same materials. Steel is particularly advantageous because of its versatility and inexpensive production, but other types of material, such different alloys or even ceramics, may be within the scope of the present invention. Blades/Vanes may be attached onto the rotor and the stator individually, for example by fitting a root of a blade or vane in a slot and soldering. Other techniques for attaching the blades/vanes to the rotor/stator may be suitable, or alternatively the blades/vanes may be integrally machined.

[0114] Other added elements and features, such as pre-vanes, may be within the scope of the present invention.

[0115] In one aspect, the present invention also relates to a nuclear reactor comprising a pump as described in the first aspect. Furthermore, the present invention also relates to the use of a pump as described in the first aspect, for pumping lead-bismuth eutectic mixtures in a nuclear reactor.