Abstract: A rotor of a fluid machine includes a wheel with a plurality of blades. Furthermore, the rotor includes an inter-blade area defined circumferentially between a first blade and a second blade of the plurality of blades with respect to the axis of rotation. Moreover, the rotor includes a balancing mark on the wheel and within the inter-blade area. The balancing mark is elongate and has a first end and a second end. The first end and the second end are stepped axially into the inter-blade area. The balancing mark extends arcuately between the first end and the second end. The balancing mark has a depth that varies as the balancing mark extends arcuately between the first end and the second end. The balancing mark has a width that varies as the balancing mark extends arcuately between the first end and the second end.

Abstract: A pump side part for use with a centrifugal slurry pump for pumping a fluid mixture containing particulate matter, the pump side part comprising a main body having a main axis, the main body including a side wall section which extends laterally with respect to the main axis and has opposite facing first and second sides, a plurality of formations on a surface of the second side including an inner formation and an outer formation in spaced relation to the inner formation, the formations being configured so that in use the formations generate a flow of the fluid mixture across the surface which detaches from the surface the particulate matter adjacent thereto.

Abstract: A electric motor assembly includes an electric motor and a fan assembly coupled to the electric motor and configured to rotate therewith about an axis. The fan assembly includes a hub including a core ring, a first inner ring circumscribing the core ring, and a first plurality of circumferentially-spaced ribs extending between the core ring and the first inner ring. The hub also includes a second inner ring circumscribing the first inner ring and a second plurality of circumferentially-spaced ribs extending between the first inner ring and the second inner ring, and a plurality of circumferentially-spaced blades coupled to an outer periphery of the hub.

Abstract: A rotor for an aircraft engine, has: a hub extending circumferentially about a central axis, the hub having a bore, a gaspath-facing surface located radially outwardly of the bore relative to the central axis, a first face extending from the bore to the gaspath-facing surface, and a second face opposite the first face and extending from the bore to the gaspath-facing surface; blades circumferentially distributed about the central axis, the blades protruding away from the gaspath-facing surface of the hub; and a crack mitigator located on the first face, the crack mitigator extending circumferentially relative to the central axis, the crack mitigator extending axially from a baseline surface of the first face.

Abstract: A refrigeration plant including: a first enclosure containing water in the liquid state at a temperature lower than or equal to the temperature of the triple point of water or higher than the temperature of the triple point of water by less than 10° C., and water in the gaseous state at a first pressure equal to the saturated vapor pressure of the water in equilibrium with the pressure of the water in the liquid state; a second enclosure at a second pressure strictly higher than the first pressure by a factor of at least two; a compression device connecting the first enclosure to the second enclosure; a condensing device adapted to condense the water in the gaseous state in the second enclosure into water in the liquid state; and a cold power extraction device for extracting cold power in the first enclosure.

Abstract: The invention concerns an inter-blade profile (14) for a turbine runner blade, said inter-blade profile (14) comprising a profile (16), and a plug (18), forming a basis of the profile (16) and intended for being inserted into a corresponding hole (21) made in a blade.

Abstract: The invention relates to a turbocompressor (1) comprising a compressor housing (2) and a compressor wheel (4) with blades (5). The compressor wheel (4) is rotatably mounted relative to the compressor housing (2) and is arranged such that the exposed upper edges of the blades (5) are spaced from a compressor housing (2) wall (3) facing the blade upper edges across a head gap (7), wherein both the upper edges of the blades (5) as well as the housing wall (3) have at least one recess (11, 13) and at least one elevation (10, 14) over the respective Meridian contour, said recess and elevation interacting locally such that the head gap (7) defines a Z-shaped course in the region of the recesses (11, 13) and the elevations (10, 14) when viewed on a Meridian plane.

Abstract: A rotating thrust-producing apparatus having a control system includes a rotatable foil having opposite first and second faces and a plurality of spaced apart fins occupying a periphery thereof. A pressure control assembly includes a first adjustable control surface disposed adjacent to a first face of the foil so as to be selectively movable over the fins of the foil. The pressure control assembly may include a second control surface disposed adjacent to the second face of the foil and which may be adjustable. As the foil is rotated, and the at least one adjustable control surface is moved over fins of the foil, a fluid pressure imbalance is created, causing a thrust in the direction of the pressure deficit.

Abstract: An impeller associated with a compressor of a gas turbine engine includes a plurality of impeller blades. Each impeller blade of the plurality of impeller blades has a leading edge and a trailing edge opposite the leading edge in a streamwise direction. Each impeller blade of the plurality of impeller blades extends in a spanwise direction from a hub at 0% span to a tip at 100% span, and each impeller blade of the plurality of impeller blades has a plurality of mean camber lines that each extend from the leading edge to the trailing edge at a respective spanwise location. The leading edge includes a partially swept leading edge surface defined between 70% span to 100% span that extends in the streamwise direction between 3% to 15% of a mean camber line at 100% span.

Abstract: A washing machine appliance includes a wash basket rotatably mounted within a wash tub for receiving of a load of articles for washing. A motor assembly is operably coupled to the wash basket and an agitation element for selectively rotating the wash basket and the agitation element and includes a drive motor having a motor shaft defining an axial direction, a transmission assembly operably coupled to the wash basket for transmitting torque from the motor shaft to the wash basket and the agitation element and the agitation element, and a cooling fan mechanically coupled to the motor shaft for urging a flow of air as the drive motor rotates the motor shaft, the cooling fan comprising a plurality of blades, wherein the plurality of blades have a geometry that varies along the axial direction to follow a contour of an external surface of the drive motor.

Abstract: A blower wheel having a plurality of blower wheel blades arranged in a blade ring, which are connected to a disc covering the blower wheel blades, at least in sections, on at least one axial side, wherein a connection between the blower wheel blades and the disc determines a transition geometry, which has a rounded curve of a quadratic function when viewed in the cross-section, at least on one side of the blower wheel blades, particularly a side facing radially inward with respect to an axis of rotation of the blower wheel.

Abstract: A turbine rotor blade according to at least one embodiment to be connected to a rotational shaft so as to be rotatable around an axis includes a hub having a hub surface inclined with respect to the axis in a cross-section along the axis; and a plurality of rotor blades disposed on the hub surface. In a throat portion where a blade-to-blade distance between two adjacent rotor blades is smallest, a value (Lt/r) obtained by dividing the blade-to-blade Lt at a given radial position by a distance r from the axis to the radial position is maximum at a position where a dimensionless span length is in a range of 0.2 to 0.65, assuming that the dimensionless span length is 0 at a position of a root end portion on a hub side and is 1 at a position of a tip end portion opposite to the hub side.

Abstract: A curved surface processing method for an inlet edge of a cylindrical blade of a centrifugal pump impeller includes following steps. A center of an impeller is used as a center to draw circles having respective diameters. A first point having a first distance from the center is determined on a concave side curve at a top of the blade, and a second point having a second distance from the center is determined on a concave side curve at a bottom of the blade. By improving the shape of a blade in an impeller, the angle of an inlet edge at the top of the blade is more close to the tangent direction, and the inlet angle of the top blade is reduced. A twisted surface is formed between a first arc segment at the top and a second arc segment at the bottom.

Abstract: A system for cooling an engine is provided. The system uses a rim driven fan having an electric motor in a frame of the fan to move air through a radiator toward the outside of the vehicle. The electric motor may have the rotor and the stator axially or radially aligned. The plurality of fan blades extends radially inward of a support which is formed integral with or attached to the rotor. Rim driven fans are also provided.

Abstract: A centrifugal fan includes a motor, a support body, a rotating body, and a housing. The motor includes a rotor hub that rotates around a central axis extending up and down. The support body is fixed to the rotor hub and rotates together with the rotor hub. The rotating body is different from the support body in material. The rotating body is a continuous porous body. The housing accommodates the rotating body, the support body, and the motor. The housing includes an air inlet open in an axial direction and at least one air outlet open in a radial direction. A radially inner surface of the rotating body opposes a radially outer surface of the rotor hub with a gap interposed therebetween.

Abstract: A centrifugal compressor impeller comprises a gas inlet, a gas outlet, and a disc having a plurality of blades extending therefrom. Each blade has a leading edge at the impeller inlet and a trailing edge at the impeller outlet, a blade base extending along the disc between the leading edge and the trailing edge, a blade tip extending between the leading edge and the trailing edge opposite the disc, a pressure side and a suction side. Each blade has a three-dimensional curvature in at least a portion of the surface, adjacent the leading edge. The leading edge has a curved, non-linear profile in a meridian plane. The blade portion has a double-curvature. Each blade has a first metal angle distribution at the blade base, a second metal angle distribution at the blade tip and at least a third metal angle distribution between the blade base and the blade tip.

Abstract: A method for preventing corrosion of an impeller-shaft assembly of a turbomachine comprises the steps of assembling an impeller on a shaft in order to define an impeller-shaft assembly; plating the assembly by inserting the assembly into a plating bath; and coating at least a first predefined surface on the impeller and a second predefined surface on the shaft wherein the coating step is performed by spraying the predefined surfaces.

Abstract: Modular flow control systems include several differently-shaped structures to achieve desired flow characteristics in fluid flow. Systems include one or many plates held in desired positions by a retainer within the flow. The plates are uniquely shaped based on their position, or vice versa, to shape flow in a desired manner. The plates may fill an entire flow area or may extend partially throughout the area. Plates can take on any shape and are useable in systems installed in any type of flow conduit. When used in a PCCS upper manifold in a nuclear reactor, a chevron plate directly below the inlet divides flow along the entire upper manifold. Perforated plates allow flow to pass at ends of the PCCS upper manifold. The plates can be installed along a grooved edge during an access period and held in static position by filling the length of the PCCS upper manifold.

Abstract: An impeller and rotor structure for a magnetically levitated pump define a smooth primary flow path and U-shaped secondary flow path, which extends around an annular magnetic rotor. The u-shaped secondary flow path is defined by a large outer side gap along an outer surface of the rotor, a large bottom gap along a bottom surface of the rotor and a large inner gap along an inner surface of the rotor. Shroudless impeller blades are purely radial and overhung from a thin peripheral ring attached to the annular magnetic rotor. A center post having a low aspect ratio extends through the annular rotor. The low aspect ratio is configured to prevent flow in the primary flow path from colliding directly with flow in the secondary flow path at the inner radial gap.

Abstract: A fan for generating an air current includes a body having an air inlet, and a nozzle connected to the body. The nozzle includes an interior passage and an air outlet from which the air flow is emitted from the fan. The interior passage extends about an opening or bore through which air from outside the nozzle is drawn by air emitted from the air outlet. The body includes a duct having a first end defining an air inlet of the duct and a second end located opposite to the first end and defining an air outlet of the duct, an impeller located within the duct for drawing the air flow through the duct, and a motor for driving the impeller. The second end of the duct protrudes from the body into the interior passage of the nozzle.

Abstract: A compressor wheel of a charging device may include a hub, a plurality of blades and a wheel back. The wheel back may have an undulating profile which extends from the hub in a radial direction. The undulating profile may include a plurality of regions. The plurality of regions may adjoin one another and may include a first concave region, a second convex region, a third concave region, and a fourth convex region. The second convex region may adjoin the first concave region. The third concave region may adjoin the second convex region. The fourth convex region may adjoin the third concave region.

Abstract: An air conditioner includes a scroll body comprising an inlet through which air is introduced, an outlet through which the air is discharged, and an air passage between the inlet and the outlet, a sirocco fan rotatably disposed in the scroll body, the sirocco fan configured to allow the air to be sucked through the inlet and to be discharged through the outlet when the sirocco fan rotates, and a bell mouth formed around the inlet of the scroll body, wherein the scroll body and the sirocco fan satisfy a following formula: 0.76?H/D?0.8, where H (mm) is a height of the scroll body, and D (mm) is an outer diameter of the sirocco fan.

Abstract: A runner device (1) for a hydraulic fluid flow machine is described, the runner (1) including a runner hub (2) and a number of vanes (4) distributed around the center axis (S) of the runner (1), the vanes (4) being releasably connected to the runner (1) by means of bases (41) that complementarily fit grooves (21) in the runner hub (2), characterized by the grooves (21) in the runner hub (2) extending, at least at one of the outer edge portion (23) or the inner edge portion (25) of the runner hub, respectively all the way out to or all the way in to the edge portion (23, 25), whereby the bases (41) may extend radially out to or in to at least one of the outer edge portion (23) or the inner edge portion (25), respectively, of the runner hub (2). A method of providing a runner (1) for a hydraulic fluid flow machine is described as well.

Abstract: A rotating machine includes a hub portion, wherein the hub portion comprises a forward face and an aft face. The rotating machine further includes a cooling channel formed on either the forward face or the aft face and configured to direct cooling air to a location on the rotating machine, wherein the cooling channel extends from a radially inner location along the face to a radially outer location along the face, and wherein the cooling channel is configured as a recess formed into an outer surface of the face.

Abstract: Ventilation device including a turbine mounted inside a radially volute-shaped casing, the peripheral wall of the casing moving progressively away from the periphery of the turbine from a volute tongue to a distal end (E2) of the volute, the radial expansion of the volute being defined by an angle of expansion (ai), characterised by the fact that the initial angle of expansion (a1) in the vicinity of the volute tongue is 1.5 times to 3 times greater than the final angle of expansion (a2) in the vicinity of the distal end (E2) of the volute, so that the peripheral wall of the casing moves away from the blades more rapidly at the start of the volute minimising the turbulences generated at the volute tongue.

Abstract: A blade of an impeller has a blade surface made up of line elements. The line elements forming the blade surface are not parallel to each other. A relationship between a twist angle of the line elements and a distance between the origin and an intersection of a central line of the impeller and an extension line of a Z-axis projection line obtained by projecting each of the line elements onto a Z-axis projection plane is represented by a curve.

Abstract: An impeller which is applied to a fan includes a hub, a plurality of first centrifugal blade and a plurality of second centrifugal blades. The hub is disposed in an accommodating space of the fan. The first centrifugal blades and the second centrifugal blades are connected to the hub. The first centrifugal blades have first ends away from the hub. The second centrifugal blades have second ends away from the hub. A distance between the second end and a center of the hub is larger than that between the first end and the hub center, and the first centrifugal blades and the second centrifugal blades are arranged periodically. Thus, an airflow noise in a constant frequency generated by the impeller can be avoided, and noises in inconstant frequency would not accumulate or generate annoying noise peak.

Abstract: A fan for generating an air current includes a body having an air inlet, and a nozzle connected to the body. The nozzle includes an interior passage for receiving an air flow from the body and an air outlet from which the air flow is emitted from the fan. The interior passage extends about an opening or bore through which air from outside the nozzle is drawn by air emitted from the air outlet. The body includes a duct having an air inlet and an air outlet, an impeller located within the duct for drawing the air flow through the duct, and a motor for driving the impeller. An annular guide member extends about the duct for guiding air from the air inlet of the body to the air inlet of the duct. The guide member defines with the duct an annular noise suppression cavity.

Abstract: A fan for generating an air current includes a body having an air inlet, and a nozzle connected to the body. The nozzle includes an interior passage for receiving an air flow from the body and an air outlet from which the air flow is emitted from the fan. The interior passage extends about an opening or bore through which air from outside the nozzle is drawn by air emitted from the air outlet. The body includes a duct having an air inlet and an air outlet, an impeller located within the duct for drawing the air flow through the duct, and a motor for driving the impeller. A noise suppression cavity is located beneath the air inlet of the duct. The cavity has an inlet which is located beneath, and is preferably concentric with, the air inlet of the duct.

Abstract: A method is provided for extending the service life of a used metallic compressor wheel having a damaged surface. The method generally comprises the steps of inspecting the used compressor wheel for material discontinuities such as fatigue cracks and, if fatigue cracks exceeding a predetermined length are not present, renewing the used compressor wheel such as by peening. The inspection process comprises conducting a non-destructive examination of the used compressor wheel to detect cracks larger than those which would fall generally within the compressive stress zone that is generated by peening.

Abstract: A turbine rotor of a turbine includes a hub that serves as an axis of rotation, and a plurality of turbine blades. The turbine blades each have a line extending along a shroud-side edge of the turbine blade from the inlet to the outlet as a shroud line. The shroud line includes an entrance-side shroud line La that makes a small change from the inlet toward the outlet in a blade angle with respect to the axis of rotation, a center shroud line Lb that extends from the outlet side of the entrance-side shroud line La and makes a greater change than that of the entrance-side shroud line La, and an exit-side shroud line Lc that extends from the outlet side of the center shroud line Lb to the outlet and makes a smaller change than that of the center shroud line Lb.

Abstract: A hybrid radial gas turbine engine component comprises an inner hub portion joined to an outer ring portion. The inner hub portion is a first alloy and operates at temperatures less than 1200° F. The outer ring portion is a second alloy and is designed to withstand extended periods at temperatures greater than 1200° F.

Abstract: A centrifugal fan includes an impeller, a motor and a case. The impeller includes a hub and multiple blades. The hub has a center. The blades are connected to the hub and have all respective outmost edges collectively define a circle with the center and a radius R. Each blade has at least one concave cutout. Each concave cutout is equipped with a depth of greater than 0.5 millimeters and an obtuse angle of less than 170 degrees, wherein the obtuse angle is an included angle between an inner edge of the concave cutout and an outer edge of the blade. The motor is secured to the huh and drives the impeller to rotate. The case houses the impeller and the motor.

Abstract: Embodiments of the invention include instant food systems and methods regarding the same. In an embodiment, the invention includes a method for preparing a hot instant food product. The method can include adding a heated liquid to a container, adding a substantially dry food product mixture to the container, wherein the volume of the dry food product mixture is equal to at least 20% of the volume of heated liquid, placing a mixing head into the container, and rotating the mixing head for a period of less than sixty seconds in order to form a fully hydrated frothed food product. In an embodiment, an instant food preparation machine is included. In an embodiment, a mixing head is included. In an embodiment, an instant food preparation kit is included. Other embodiments are also included herein.

Abstract: A turbine rotor of a turbine includes a hub that serves as an axis of rotation, and a plurality of turbine blades. The turbine blades each have a line extending along a shroud-side edge of the turbine blade from the inlet to the outlet as a shroud line. The shroud line includes an entrance-side shroud line La that makes a small change from the inlet toward the outlet in a blade angle with respect to the axis of rotation, a center shroud line Lb that extends from the outlet side of the entrance-side shroud line La and makes a greater change than that of the entrance-side shroud line La, and an exit-side shroud line Lc that extends from the outlet side of the center shroud line Lb to the outlet and makes a smaller change than that of the center shroud line Lb.

Abstract: Provided is an impeller in which a through hole is provided in a center of a base member of the impeller and a plurality of recessed parts are formed on a bottom surface of the base member. Meanwhile, a jig using in a cutting work of the impeller includes a seating part having a seating surface, a shaft part is erected from a central part of the seating part and is engageable with the through hole of the impeller, and protruded parts are formed on the seating surface and are engageable with the recessed parts provided on the base-member bottom surface of the impeller.

Abstract: The present document describes a centrifugal ceiling fan. The fan comprises a casing, a motor and a centrifugal propeller. The casing comprises an upper surface comprising an air inlet and a lower surface comprising an air outlet. In an embodiment, the lower surface has a round bowl-like shape including a plurality of openings defining the air outlet. The propeller comprises a shaft and a plurality of blades provided around the shaft. The blades may be curved to push the air in all directions between a first direction substantially perpendicular to the rotation shaft and a second direction substantially parallel to the rotation shaft in order to evenly ventilate the room. The fan may include a heating element for heating the air as it exits from the fan.

Abstract: Turbocharger turbine wheels are designed to accelerate rapidly and to rotate at very high RPM. A turbine wheel is provided with improved low cycle fatigue resistance. The wheel can be balanced by conventional methods.

Abstract: An impeller includes a top shroud, a bottom shroud, and a plurality of vanes extending from the top shroud to the bottom shroud. The top and bottom shrouds are generally planar, and a lower edge of each vane tapers from an outer edge of the bottom shroud to a transverse tip edge thereof.

Abstract: An impeller for a turbo-machine and is provided. The impeller includes a metallic base having a central hole, a back surface and a front surface opposite to the back surface; at least one blade extending on the front surface of the metallic base; a composite shroud attached to the at least one blade such that plural closed paths or vanes are formed by the front surface of the metallic base, the at least one blade and the composite shroud; and a connector configured to attach the composite shroud to the metallic base or the at least one blade.

Abstract: A heat-dissipation fan including a base and an impeller disposed at the base, wherein the impeller includes a plurality of first blades, a plurality of second blades and a plurality of connection ribs. Each of the first blades and each of the second blades are arranged alternately. Each of the connection ribs comprises a first edge, a second edge and a third edge. The first edge is connected with the first blade, the second edge is connected with the second blade, the third edge is connected with the first edge and the second edge, and the third edge and the second blade are spaced apart to form a first vent. The first edge comprises a first length, the second edge comprises a second length, and the first length is larger than the second length.

Abstract: A system, in certain embodiments, includes an impeller having a plurality of impeller blades coupled to an impeller hub body, wherein each impeller blade is sculpted having a nonlinear profile extending from a hub intersect surface of the impeller blade to a shroud intersect surface of the impeller blade.

Abstract: An inner combustion chamber casing of a turbomachine, which is intended to be placed downstream of a centrifugal compressor, is provided. The casing has the shape of a disc, pierced by a central circle, and includes on its disc at least one guide vane of the drawn-off air. The guide vane extends longitudinally over the disc between the periphery of the disc and the central circle and spreads out axially from the disc so as to form with the downstream face of the centrifugal compressor a guide channel for the air which is drawn off upon exit from the said compressor. The guide vane has a curved shape orienting in a radial direction at the level of its most central end.

Abstract: A turbine wheel is disposed about an axis and has a back having a separator disposed thereon, an inner undercut disposed between the separator and the axis, and an outer undercut disposed between the separator and an outer periphery of the back face. The inner undercut is defined by a first radius blending toward the axis and into a first flat section, and further defined by a second radius blending into the first flat section and into the separator.

Abstract: A fan wheel (1) is designed as a radial or diagonal fan, comprising a top plate (2) with an inlet port (4), a base plate (6) and a plurality of fan blades (8) distributed around the inlet port (4) and around an axis of rotation (Z). Blade ducts extend (10) respectively between the adjacent fan blades (8). The blade ducts lead radially or diagonally outward from the area of the inlet port (4) and form blow-out ports in the outer region. The blade ducts (10) are designed, with respect to their effective flow cross-section, as large enough that during operation, a turbulent flow with a Reynolds number markedly greater than 2300 is achieved. The top plate (2) or the base plate (6) or both feature a rotationally asymmetrical geometry with a continuous profile, at least in angular sections encompassing the fan blades (8).

Abstract: A washing machine having a centrifugal fan which may increase a discharge flow rate. The washing machine includes a centrifugal fan adapted to cool a motor, wherein the centrifugal fan comprises a circular plate connected to a shaft of the motor, and a plurality of blades radially arranged around a center of the circular plate, each of the blade includes an inlet portion extending to form an inlet for external air passing therethrough, and a guide bent and inclined from the inlet portion, and an outlet portion bent from the guide to form an outlet for the external air.

Abstract: A centrifugal compressor wheel including a hub, a web extending radially from the hub, and a plurality of blades carried by the wheel. The web includes an erosion indicator of the wheel.

Abstract: A hub is supported rotatably about an axis of rotation, and the diameter thereof increases from upstream to downstream sides along a fluid flow. A plurality of impeller blades extend radially outward from an outer circumferential surface of the hub. A shroud is formed in a cylindrical shape whose diameter increases from the upstream to downstream sides along the fluid flow and joins outer circumferential ends of the plurality of impeller blades. The impeller blades are composed of upstream blade segments and downstream blade segments bonded at a bonding surface extending in a direction substantially perpendicular to the axis of rotation. The upstream blade segments are integral with at least a portion of the shroud, and the downstream blade segments are integral with at least a portion of the hub. This improves the reliability and performance of an impeller and a compressor.

Abstract: According to one embodiment, a molten metal impeller is provided. It includes a generally cylindrical graphite body having a plurality of passages extending from a top surface to a side wall. A hub is formed in the center of the graphite body. A ceramic cap member is secured to the top surface of the graphite body. The cap member is comprised of a ring forming a central passage shaped cooperatively to overlap the hub and a plurality of vanes extending radially from the ring to an outer rim. The rim has a height between adjacent vanes which increases in the direction of intended impeller rotation. The rim further has a height which decreases from its radially outer most edge to an inner most edge.

Abstract: A radial turbine includes a radial turbine wheel provided with a main pathway in which blade height progressively increases while curving toward an axial direction from a radial direction. A sub-let is formed on a shroud side of the radial turbine wheel at a position separated from the main inlet in the radial direction and the axial direction. Also, a blade shape that forms the sub-inlet is such that, in a plane orthogonal to the axial line of the radial turbine wheel, a center line of the blade is inclined at a predetermined angle toward the rotation direction with respect to the radial direction.