Centrifugal impeller blade design method and system for reducing secondary flow loss

Abstract

The invention discloses a centrifugal impeller blade design method and system for reducing secondary flow loss. The method comprises the steps that the cutting line spacing is calculated at the front edge inlet position of a centrifugal impeller blade from the blade root to the blade top according to an equal residual height method; calculating a parameter spline curve family of the blade from the inlet to the outlet according to the cutting line spacing of the front edge inlet position; a novel centrifugal impeller blade control curve family for reducing secondary flow loss is obtained; obtaining a novel centrifugal impeller blade control point set; a novel impeller blade control curve family is obtained; a novel impeller blade control curve family, an arc line, an original blade root parameter line and an original blade top parameter line are reconstructed in a curved surface grid construction mode, and the novel centrifugal impeller blade capable of reducing secondary flow loss is obtained. The system comprises a calculation unit, a control curve family obtaining unit, a control point set obtaining unit and a novel centrifugal impeller blade design unit. The secondary flow loss of the centrifugal impeller is effectively improved, and the purpose of improving the performance of the impeller is achieved.

Description

Technical Field

[0001] The present invention relates to the field of machining, and particularly to a design method and system for centrifugal impeller blades to reduce secondary flow losses. Background Art

[0002] Centrifugal compressors are widely used in many industries such as aerospace, petrochemical, power, and refrigeration. They are responsible for compressing gases and vapors into higher pressures and are an essential part of modern industry. As a key energy conversion component of centrifugal compressors, the quality of the design and manufacture of centrifugal impellers directly affects the performance and efficiency of centrifugal compressors. Over the years, researchers have continuously optimized the shape of centrifugal impellers, selected high-quality materials, and adopted advanced manufacturing processes to meet the high requirements for the performance of centrifugal impellers in various industrial fields.

[0003] The invention patent with the Chinese patent number: CN113202789B discloses an impeller for a centrifugal compressor and a centrifugal compressor. By setting a small wing structure near the leading edge tip at the top of the blade body, this patent reduces or even eliminates the leakage vortex loss at the leading edge tip of high-speed centrifugal impellers, thereby achieving the purpose of improving the performance of centrifugal compressors. However, this method only improves the performance of centrifugal impellers by reducing the leakage vortex loss at the tip. In actual operation, in addition to the leakage vortex loss at the tip that easily affects the impeller performance, the secondary flow losses on the blade surface and at the tip clearance also have a significant impact on the impeller performance. Therefore, the present invention optimizes the surface structure of the centrifugal impeller blades to control the flow inside the impeller, thereby reducing the secondary flow losses and improving the overall performance of the centrifugal compressor. Summary of the Invention

[0004] The object of the present invention is to provide a design method and system for centrifugal impeller blades to reduce secondary flow loss. By arranging continuous arc-shaped convex structures on the blade surface along the flow direction from the inlet to the outlet, the present invention can better guide the airflow to the impeller outlet, thereby effectively improving the secondary flow loss of the centrifugal impeller in the background art and achieving the purpose of improving the impeller performance. This method first calculates the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blade according to the equal residual height method, and obtains a family of parametric spline curves of the blade from the inlet to the outlet based on the cutting row spacing at different inlet positions; secondly, the family of parametric spline curves is offset normally, and the normally offset family of parametric spline curves, the original blade root and blade tip parameter lines are discretized using the isoparametric method to obtain the control point set of the new centrifugal impeller blade; then, the control points of two adjacent new impeller blade parametric curves from the blade root to the blade tip are connected in sequence by an arc line; finally, the new impeller blade control curve family, the arc line and the original blade root and blade tip parameter lines are reconstructed by means of surface mesh construction to obtain the new centrifugal impeller blade with reduced secondary flow loss. The present invention combines the residual shape of the centrifugal impeller blade during the actual machining process, arranges continuous arc-shaped convex structures on the blade surface from the inlet to the outlet, reduces the secondary flow loss of the fluid leaking on the blade surface and at the blade tip gap, thereby improving the isentropic efficiency and total pressure ratio of the centrifugal impeller, and providing certain technical support for the structural design of the impeller blade and the field of modern mechanical manufacturing and processing.

[0005] To achieve the above object, the present invention adopts the following technical solutions: A design method for centrifugal impeller blades to reduce secondary flow loss. The centrifugal impeller includes a hub and blades, and is a semi-open centrifugal impeller. Among them, the blades can be defined as a bi-parametric spline surface. The method includes the following steps: 1) Calculate the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blade according to the equal residual height method; 2) Calculate a family of parametric spline curves of the blade from the inlet to the outlet according to the cutting row spacing at the leading edge inlet position; 3) Offset the family of parametric spline curves normally to obtain a family of control curves of the new centrifugal impeller blade with reduced secondary flow loss; 4) Discretize the family of control curves of the new centrifugal impeller blade and the original blade root and blade tip parameter lines using the isoparametric method to obtain the control point set of the new centrifugal impeller blade; 5) Connect the control points of two adjacent new centrifugal impeller blades from the blade root to the blade tip in sequence by an arc line to obtain a family of control curves of the new impeller blade; 6) Reconstruct the family of control curves of the new impeller blade, the arc line and the original blade root and blade tip parameter lines by means of surface mesh construction to obtain the new centrifugal impeller blade with reduced secondary flow loss.

[0006] A further improvement of the present invention lies in that the specific implementation method of step 1) is as follows: Define the blade double-parameter spline surface with the parameter direction from the inlet to the outlet and the parameter direction from the blade root to the blade tip; u The blade double-parameter spline surface equation expression is v , where are the control vertices of the surface, are the basis functions of the spline curves in the parameter direction and parameter directions of the parametric surface respectively, and the parameters u , v have a variable range of [0, 1], u , v are the curve degrees in the k and l directions of the surface respectively; u , v The calculation of the cutting feed pitch needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface, and the expressions are respectively: S , , , , where h is the residual height, R is the tool radius, r is the curvature radius; the curvature radius r and its concavity and convexity are judged by the Gaussian curvature method, and the curvature radius calculation expression is , where E, F, G, L, M, N are the correlation coefficients of the first fundamental form of the surface and the second fundamental form of the surface respectively; the correlation coefficients of the first fundamental form and the second fundamental form of the surface are obtained by calculating the partial derivatives of the surface parametric equation , as shown in the following formula:

[0007] .

[0008] A further improvement of the present invention lies in that the calculation of the cutting feed pitch at the leading edge inlet position needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface, and the curvature radius and its concavity and convexity are judged by the Gaussian curvature method: the curvature radius r > 0 is a convex surface, r < 0 is a concave surface, r = 0 is a plane.

[0009] A further improvement of the present invention lies in that the residual height value h in the equal residual height method is determined according to the standard of the blade surface roughness.

[0010] A further improvement of the present invention lies in that the specific implementation method of step 2) is as follows: First, according to the blade root C root ( u ) and the blade tip C tip ( u ) parameter curve equations, calculate the curve length at the blade inlet position L ; then, from the cutting row spacing at different positions at the blade inlet S 0, S 1… S m , calculate the corresponding parameter values v from the blade root to the blade tip at the blade inlet v 0, v 1… v m , where v 0 = S 0 / L , v 1 = ( S 0 + S 1) / L … v m = ([[]] S 0 + S 1 + … + S m ) / L ; finally, fix the parameters in the blade double - parameter spline surface equation v , that is, the parameter values v 0, v 1… v m obtained above, and the parameter spline curve family equations u from the blade inlet to the blade outlet C ( u v0 ), C ( u v1 )… C ( u vm ) can be obtained.

[0011] A further improvement of the present invention lies in that the specific implementation method of step 3) is as follows: Normally offset the parameter spline curve family equations u from the blade inlet to the blade outlet C ( u v0 ), C ( u v1)… C ( u vm ) to obtain the equation of the new impeller blade control curve family C´ ( u v0 )、 C´ ( u v1 )… C´ ( u vm ) with the expression: 、 … , where, h is the residual height, is the normal vector, is obtained by solving the partial derivatives of the blade two-parameter spline surface u in the v direction and S u 、 S v , and the cross product of the two is obtained, with the expressions being 、 、 .

[0012] A further improvement of the present invention lies in that the specific implementation method of step 4) is as follows: Using the isoparametric method to discretize the new centrifugal impeller blade control curve family C´ ( u v0 )、 C´ ( u v1 )… C´ ( u vm ) and the original root and tip parameter lines of the blade C root ( u )、 C tip ( u ) to obtain the control point sets of the new centrifugal impeller blade { j uv0,0 、 j uv0,1 … j uv0,n}, { j uv1,0 、 j uv1,1 … j uv1,n}…{ j uvm,0 、 j uvm,1 … juvm,n}, { j root,0 、 j root,1 … j root,n}, { j tip,0 、 j tip,1 … j tip,n}, where the value ranges of parameters such as are [0.01, 0.1].

[0013] A further improvement of the present invention lies in that the specific implementation method of step 5) is as follows: Successively connect the control point sets of the parameter curves of two adjacent new impeller blades from the blade root to the blade tip with an arc line, that is, { v root,0 、 j uv0,0 、 j uv1,0 … j uvm,0 、j tip,0 j root,1}, { j uv0,1 、 j uv1,1 、 j uvm,1 … 、j tip,1 j root,n}, { j uv0,n 、 j uv1,n 、 j uvm,n … j tip,n 、 v root}, and the arc connection adopts the three - point method, and the starting and ending points are v the control point sets in pairs, and the mid - point is tangent to the original blade surface.

[0014] A centrifugal impeller blade design system for reducing secondary flow loss. The centrifugal impeller includes a hub and blades, and is a semi - open centrifugal impeller. Among them, the blades can be defined as a bi - parameter spline surface. The system includes: The first calculation unit calculates the cutting row spacing from the blade root to the blade tip at the leading - edge inlet position of the centrifugal impeller blade according to the equal residual height method; The second calculation unit calculates the parameter spline curve family of the blade from the inlet to the outlet according to the cutting row spacing at the leading - edge inlet position; The first control curve family obtaining unit, the normal offset parameter spline curve family, obtains a new type of centrifugal impeller blade control curve family that reduces secondary flow loss; The control point set obtaining unit uses the isoparametric method to discretize the new type of centrifugal impeller blade control curve family and the original blade root and blade tip parameter lines, and obtains the control point set of the new type of centrifugal impeller blade; The second control curve family obtaining unit uses circular arcs to sequentially connect two adjacent control point sets of the new type of centrifugal impeller blade from the blade root to the blade tip, and obtains the new type of impeller blade control curve family; The new type of centrifugal impeller blade design unit reconstructs the new type of impeller blade control curve family, circular arcs, and the original blade root and blade tip parameter lines through the method of surface grid construction, and obtains a new type of centrifugal impeller blade that reduces secondary flow loss.

[0015] A further improvement of the present invention is that in the first calculation unit, the cutting row spacing is calculated from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blade according to the equal residual height method, including: Define that the blade double-parameter spline surface is the parameter u direction from the inlet to the outlet, and the parameter v direction from the blade root to the blade tip; the expression of the blade double-parameter spline surface equation is , where is the control vertex of the surface, are the basis functions of the spline curves in the u direction and v direction of the parametric surface respectively, and the parameters u , v have a variable range of [0,1], k , l are the curve degrees of the surface in the u direction and v direction respectively; The calculation of the cutting row spacing S needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface, and the expressions are respectively: , , , where h is the residual height, R is the tool radius, r is the radius of curvature. The radius of curvature r and its concavity and convexity are judged by the Gaussian curvature method, and the calculation expression of the radius of curvature is , where E, F, G, L, M, N are the relevant coefficients of the first fundamental form and the second fundamental form of the surface in sequence. The relevant coefficients of the first fundamental form and the second fundamental form of the surface are obtained by differentiating the parametric equation of the surface Obtained by calculating partial derivatives, as shown in the following formula:

[0016]

[0017] Compared with the prior art, the present invention has at least the following beneficial technical effects: A centrifugal impeller blade design method and system for reducing secondary flow loss provided by the present invention focus on the secondary flow loss on the blade surface and the tip clearance during the actual working process of the centrifugal impeller. Combining the residual shape in actual processing of the blade, an innovative centrifugal impeller blade design method for reducing secondary flow loss is proposed. First, at the leading edge inlet position of the centrifugal impeller blade, the cutting row spacing is calculated from the blade root to the blade tip according to the equal residual height method, and a family of parametric spline curves of the blade from the inlet to the outlet is obtained from the cutting row spacing at different inlet positions; secondly, the family of parametric spline curves is offset normally, and the normally offset family of parametric spline curves and the original blade root and tip parametric lines are discretized using the isoparametric method to obtain a control point set of the new centrifugal impeller blade; then, the control point sets of the two adjacent new impeller blade parametric curves from the blade root to the blade tip are connected in sequence by circular arcs; finally, the new impeller blade control curve family, circular arcs and the original blade root and tip parametric lines are reconstructed by means of surface mesh construction, and a new centrifugal impeller blade with reduced secondary flow loss can be obtained. By arranging a continuous arc-shaped convex structure from the inlet to the outlet of the prototype impeller blade, the present invention can better guide the air flow to the impeller outlet, effectively reducing the secondary flow loss of the fluid on the blade surface and the tip clearance, thereby improving the isentropic efficiency and total pressure ratio of the centrifugal impeller; and it has good engineering practicability, providing certain technical support for the structural design of impeller blades and the field of modern mechanical manufacturing and processing. Description of the Drawings

[0018] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 It is a schematic diagram of the prototype centrifugal impeller model; Figure 2 It is a schematic diagram for calculating the cutting row spacing, where Figure 2 (a) is a plane, Figure 2 (b) is a convex surface, Figure 2 (c) is a concave surface; Figure 3 It is a schematic diagram for generating the new centrifugal impeller blade; Figure 4 It is a schematic diagram of the complete model of a new centrifugal impeller and the enlarged view of a local position. Among them, Figure 4 (a) is the complete model of the new centrifugal impeller, Figure 4 (b) is the enlarged comparison schematic diagram of the prototype impeller and the new impeller at the local position; Figure 5 It is a comparison diagram of the streamline distributions of the prototype impeller and the new centrifugal impeller at the blade outlet position. Among them, Figure 5 (a) is the prototype impeller, Figure 5 (b) is the new impeller; Figure 6 It is a comparison diagram of the performance curves of the prototype impeller and the new centrifugal impeller. Among them, Figure 6 (a) is the isentropic efficiency, Figure 6 (b) is the total pressure ratio; Figure 7 It is the structural block diagram of a centrifugal impeller blade design system for reducing secondary flow loss according to the present invention. Detailed implementation manners

[0020] In the following, only some exemplary embodiments are simply described. As those skilled in the art can recognize, the described embodiments can be modified in various different ways without departing from the spirit or scope of the present invention. Therefore, the drawings and the description are considered to be exemplary in nature rather than restrictive.

[0021] It should be understood that when used in this specification and the appended claims, the terms "comprises" and "comprising" indicate the presence of the described features, wholes, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0022] It should also be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms.

[0023] It should be further understood that the term " / and" used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0024] Schematic diagrams of various structures according to the disclosed embodiments of the present invention are shown in the accompanying drawings. These drawings are not drawn to scale, where certain details are enlarged for the purpose of clear expression, and some details may be omitted. The shapes of various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary. In practice, there may be deviations due to manufacturing tolerances or technical limitations, and those skilled in the art can design regions / layers with different shapes, sizes, and relative positions according to actual requirements.

[0025] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0026] Embodiment 1 Figure 1 It is a schematic diagram of the model of the prototype centrifugal impeller according to the embodiment of the present invention. The centrifugal impeller includes a hub 1 and blades 2. Among them, the blades include a leading-edge inlet 3, a trailing-edge outlet 4, a blade root 5, and a blade tip 6. The specific implementation is as follows: 1. Calculate the cutting feed distance from the blade root to the blade tip at the leading-edge inlet position of the centrifugal impeller blade according to the equal residual height method. The blade is defined as a bi-parametric spline surface, and the equation expression is: , where are the control vertices of the surface, are the basis functions of the parametric curves in the u direction and the v direction of the parametric surface respectively, k , l are the curve degrees in the u direction and the v direction of the surface respectively. It is defined that the parameter u from the inlet to the outlet of the blade is in the v direction, and the parameter from the blade root to the blade tip is in the k direction. The surface type in this embodiment is a bi-parametric cubic uniform B-spline surface, so l = S = 3. The calculation of the cutting feed distance , , needs to be determined according to the corresponding surface form. The surface forms are divided into three types: plane, convex surface, and concave surface. The specific expressions are: h , where R is the residual height, r is the tool radius, Figure 2 is the radius of curvature. Figure 2 (a) is a plane, Figure 2 (b) is a convex surface, Figure 2 (c) is a concave surface. The radius of curvature r and its concavity and convexity are determined by calculating through the Gaussian curvature method. The calculation expression is: , where E, F, G, L, M, N are the coefficients related to the first fundamental form of the surface and the second fundamental form of the surface respectively. The coefficients related to the first and second fundamental forms of the surface are obtained by calculating partial derivatives of the parametric equation of the surface as shown in the following formula:

[0027]

[0028] The convexity and concavity of the surface are judged by the following criteria: the radius of curvature r >0 indicates a convex surface, r <0 indicates a concave surface, r =0 indicates a plane. At the same time, the residual height h should be determined according to the standard of the surface roughness of the blade body. The value of the residual height on the surface of the blade in this embodiment h = is 0.1 mm.

[0029] 2. Calculate the parametric spline curve family of the blade from the inlet to the outlet according to the cutting row spacing at the leading edge inlet position. The specific steps for calculating the parametric spline curve family are as follows: First, according to the blade root C root ( u ), the tip C tip ( u ) parametric curve equations, calculate the curve length L at the inlet position of the blade; Then, from the different cutting row spacings S 0, S 1... S m , calculate v the corresponding parameter values v 0, v 1... v m , where v 0 = S 0 / L , v 1 = ( S 0 + S 1) / L ... v m = ( S 0 + S 1 +... + S m ) / L ; Finally, fix the parameter in the double parametric spline surface equation of the blade v , that is, the obtained parameter valuesv 0, v 1… v m to obtain the blade u the parametric spline curve family equations in the normal direction C ( u v0 ) C ( u v1 )… C ( u vm ) Figure 3 It is a schematic diagram for generating the blades of a new type of centrifugal impeller.

[0030] 3. The parametric spline curve family equations for normal offset of the original blade C ( u v0 ) C ( u v1 )… C ( u vm ) to obtain the control curve family of the new type of centrifugal impeller blades for reducing secondary flow losses C´ ( u v0 ) C´ ( u v1 )… C´ ( u vm ) The expression is: , … where h is the residual height, is the normal vector, By solving the partial derivatives of the blade's two-parameter spline surface u in the v direction and S u , S v The two are obtained by cross multiplication, and the expressions are respectively , ,

[0031] 4. Using the isoparametric method to transform the control curve family of the new type of centrifugal impeller blades C´ ( u v0 ) C´ ( u v1 )… C´ ( u vm ) and the original root and tip parameter line equationsC root ( u )、 C tip ( u ) are discretized to obtain a new set of control points for the centrifugal impeller blade { j uv0,0 、 j uv0,1 … j uv0,n}, { j uv1,0 、 j uv1,1 … j uv1,n}…{ j uvm,0 、 j uvm,1 … j uvm,n}, { j root,0 、 j root,1 … j root,n}, { j tip,0 、 j tip,1 … j tip,n}., where the equation of the new impeller blade curve family C´ ( u v0 )、 C´ ( u v1 )… C´ ( u vm ) and the parametric line equations of the blade root and blade tip C root ( u )、 C tip ( u ) should be discretized with the same parameter values, and the value range is [0.01, 0.1]. The equal parameter value used in this embodiment is 0.05.

[0032] 5. Use an arc line to sequentially connect the control point sets of two adjacent new impeller blade parametric curves from the blade root to the blade tip, that is, { j root,0 、 j uv0,0 、 j uv1,0 … j uvm,0 、j tip,0}, {j root,1 , j uv0,1 , j uv1,1 … j uvm,1 、j tip,1}…{ j root,n , j uv0,n , j uv1,n … j uvm,n , j tip,n}, the arc connection method adopts the three - point method, and the starting and ending points are v the control point sets in pairs, and the mid - point is tangent to the original blade surface.

[0033] 6. Using the surface grid method to reconstruct the u - direction new - type centrifugal impeller blade control curve family, the v - direction arc line and the original blade root and blade tip parameter lines, then the new - type centrifugal impeller can be obtained, as shown in Figure 4 (a), Figure 4 (b) is Figure 4 (a) The partial enlarged schematic comparison diagram of the new - type centrifugal impeller and the prototype impeller at the outlet position 7. Among them, 8 is the prototype impeller, and 9 is the new - type centrifugal impeller. Figure 5 is the streamline distribution comparison diagram of the prototype impeller and the new - type impeller at the outlet position 7. Among them, Figure 5 (a) is the prototype impeller, Figure 5 (b) is the new - type impeller. It can be seen from the figure that there is a secondary flow from the disk side to the shroud side on the blade surface of the prototype impeller. At the same time, due to the tip clearance between the blade and the shroud, the secondary flow flowing to the shroud side further develops into the leakage secondary flow of the tip clearance; compared with the prototype impeller, the new - type centrifugal impeller effectively reduces the secondary flow loss from the disk side to the shroud side on the blade surface, thereby also reducing the leakage secondary flow loss of the tip clearance. Figure 6 is the performance curve comparison diagram of the prototype impeller and the new - type centrifugal impeller. Among them, Figure 6 (a) is the isentropic efficiency, Figure 6 (b) is the total pressure ratio. It can be seen from the figure that the isentropic efficiency and the total pressure ratio of the present invention are both improved compared with the prototype centrifugal impeller. Thus, it can be obtained that by arranging a continuous arc - shaped convex structure on the blades of the prototype impeller from the inlet to the outlet, the present invention achieves the purpose of reducing the secondary flow loss and improving the performance of the centrifugal impeller, thereby providing certain technical support for the field of modern mechanical manufacturing and processing, and having certain popularization and application value.

[0034] Embodiment 2 As Figure 7 shown, a centrifugal impeller blade design system for reducing secondary flow loss provided by the present invention. The centrifugal impeller includes a hub and blades, and is a semi-open centrifugal impeller. Among them, the blades can be defined as a bi-parametric spline surface. The system includes: A first calculation unit that calculates the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blade according to the equal residual height method; A first calculation unit that calculates a family of parametric spline curves of the blade from the inlet to the outlet according to the cutting row spacing at the leading edge inlet position; A first control curve family obtaining unit that normally offsets the family of parametric spline curves to obtain a new type of centrifugal impeller blade control curve family for reducing secondary flow loss; A control point set obtaining unit that discretizes the new type of centrifugal impeller blade control curve family and the original blade root and blade tip parameter lines by using the isoparametric method to obtain a new type of centrifugal impeller blade control point set; A second control curve family obtaining unit that sequentially connects two adjacent new type of centrifugal impeller blade control point sets from the blade root to the blade tip by using circular arcs to obtain a new type of impeller blade control curve family; A new type of centrifugal impeller blade design unit that reconstructs the new type of impeller blade control curve family, circular arcs, and the original blade root and blade tip parameter lines through the method of surface mesh construction to obtain a new type of centrifugal impeller blade for reducing secondary flow loss.

[0035] The above shows and describes the basic principles, main features, and advantages of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

[0036] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only includes an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only to illustrate the technical idea of the present invention, and cannot be used to limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A design method for centrifugal impeller blades to reduce secondary flow losses, characterized in that, The centrifugal impeller includes a hub and blades, and is a semi-open centrifugal impeller. Among them, the blades can be defined as a bi-parametric spline surface. The method includes the following steps: 1) Calculate the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blades according to the equal residual height method; 2) Calculate the family of parametric spline curves of the blades from the inlet to the outlet according to the cutting row spacing at the leading edge inlet position; 3) Normally offset the family of parametric spline curves to obtain a new family of centrifugal impeller blade control curves that reduce secondary flow losses; 4) Use the isoparametric method to discretize the new family of centrifugal impeller blade control curves and the original blade root and blade tip parameter lines to obtain a set of control points for the new centrifugal impeller blades; 5) Sequentially connect two adjacent sets of control points of the new centrifugal impeller blades from the blade root to the blade tip with circular arcs to obtain a new family of impeller blade control curves; 6) Reconstruct the new family of impeller blade control curves, circular arcs, and the original blade root and blade tip parameter lines by means of surface mesh construction to obtain new centrifugal impeller blades that reduce secondary flow losses.

2. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 1, characterized in that, The specific implementation method of step 1) is as follows: Define the blade double - parameter spline surface with the parameter direction from the inlet to the outlet and from the blade root to the blade tip u ; the blade double - parameter spline surface equation expression is v , where ; are the control vertices of the surface, are the basis functions of the spline curves in the parameter surface u direction and v direction respectively. The parameter u , v variable ranges are [0, 1], k , l are the curve degrees of the surface u direction and v direction respectively; Cutting feed pitch S The calculation needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface. The expressions are as follows: , , , where h is the residual height, R is the tool radius, r is the radius of curvature; the radius of curvature r and its concavity and convexity judgment are obtained by calculating through the Gaussian curvature method. The calculation expression of the radius of curvature , where E, F, G, L, M, N are the relevant coefficients of the first fundamental form and the second fundamental form of the surface in turn; the relevant coefficients of the first fundamental form and the second fundamental form of the surface are obtained by calculating the partial derivatives of the surface parametric equation as shown in the following formula: 。 3. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 2, characterized in that The calculation of the cutting row spacing at the leading edge inlet position needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface. The curvature radius and its concavity and convexity are judged by calculating through the Gaussian curvature method: the curvature radius r >0 is a convex surface, r <0 is a concave surface, r =0 is a plane.

4. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 2, characterized in that Residual height value in the equal residual height method h Determined according to the standard of blade surface roughness.

5. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 2, characterized in that, The specific implementation method of step 2) is as follows: First, according to the blade root C root ( u ), the blade tip C tip ( u ), calculate the curve length at the blade inlet position L ; Then, from the cutting row spacing at different positions at the blade inlet S 0, S 1… S m , calculate the corresponding parameter values from the blade root to the blade tip at the blade inlet v 0, v 1… v 1… v m , where v 0 = S 0 / L , v 1 = ( S 0 + S 1) / L … v m = ([[]] S 0 + S 1 + … + S m ) / L ; Finally, fix the parameters in the bivariate spline surface equation of the blade v , that is, the parameter values obtained from the above solution v 0, v 1… v m , then the parametric spline curve family equations in the direction from the blade inlet to the blade outlet can be obtained u ( C ( u v0 ), C ( u v1 )… C ( u vm ).

6. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 5, characterized in that, The specific implementation method of step 3) is as follows: The parametric spline curve family equations of the normal offset blades from the inlet to the outlet u are C ( u v0 ), C ( u v1 )… C ( u vm ) to obtain the control curve family equations of the new impeller blades C´ ( u v0 ), C´ ( u v1 )… C´ ( u vm ) with the expressions as follows: , … , where h is the residual height, is the normal vector, is obtained by solving the partial derivatives of the blade two-parameter spline surface u in the v direction and S u , S v . Their cross product is obtained, and the expressions are respectively , , .

7. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 6, characterized in that The specific implementation method of step 4) is as follows: The control curve families of the new centrifugal impeller blades are parameterized C´ ( u v0 )、 C´ ( u v1 )… C´ ( u vm ) and the original root and tip parameter lines C root ( u )、 C tip ( u ) are discretized to obtain the control point sets of the new centrifugal impeller blades { j uv0,0 、 j uv0,1 … j uv0,n}, { j uv1,0 、 j uv1,1 … j uv1,n}…{ j uvm,0 、 j uvm,1 … j uvm,n}, { j root,0 、 j root,1 … j root,n}, { j tip,0 、 j tip,1 … j tip,n}, where the range of the isoparametric values is [0.01, 0.1].

8. A design method for centrifugal impeller blades to reduce secondary flow losses according to claim 7, characterized in that The specific implementation method of step 5) is as follows: Connect from the blade root to the blade tip in turn with an arc line v to the control point sets of the parameter curves of two adjacent new impeller blades, namely { j root,0 , j uv0,0 , j uv1,0 … j uvm,0 、j tip,0}, { j root,1 , j uv0,1 , j uv1,1 … j uvm,1 、j tip,1}… { j root,n , j uv0,n , j uv1,n … j uvm,n , j tip,n}, and the arc connection adopts the three-point method, with the starting and ending points being v the control point sets in pairs, and the midpoint is tangent to the original blade surface.

9. A centrifugal impeller blade design system for reducing secondary flow losses, characterized in that, The centrifugal impeller includes a hub and blades, and is a semi-open centrifugal impeller. Among them, the blades can be defined as a bi-parametric spline surface. The system includes: A first calculation unit that calculates the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blades according to the equal residual height method; A second calculation unit that calculates the family of parametric spline curves of the blades from the inlet to the outlet according to the cutting row spacing at the leading edge inlet position; A first control curve family obtaining unit that normally offsets the family of parametric spline curves to obtain a new family of centrifugal impeller blade control curves that reduce secondary flow losses; A control point set obtaining unit that uses the isoparametric method to discretize the new family of centrifugal impeller blade control curves and the original blade root and blade tip parameter lines to obtain a set of control points for the new centrifugal impeller blades; A second control curve family obtaining unit that sequentially connects two adjacent sets of control points of the new centrifugal impeller blades from the blade root to the blade tip with circular arcs to obtain a new family of impeller blade control curves; A new centrifugal impeller blade design unit that reconstructs the new family of impeller blade control curves, circular arcs, and the original blade root and blade tip parameter lines by means of surface mesh construction to obtain new centrifugal impeller blades that reduce secondary flow losses.

10. A centrifugal impeller blade design system for reducing secondary flow losses according to claim 9, characterized in that, In the first calculation unit, calculating the cutting row spacing from the blade root to the blade tip at the leading edge inlet position of the centrifugal impeller blades according to the equal residual height method includes: Define the blade double - parameter spline surface with the parameter direction from the inlet to the outlet and from the blade root to the blade tip u direction, and from the blade root to the blade tip as the parameter v direction; The expression of the blade double - parameter spline surface equation is , where are the control vertices of the surface, are the basis functions of the spline curves in the parameter surface u direction and v direction respectively. The parameter u , v variable ranges are [0, 1], k , l are the curve degrees of the surface u direction and v direction respectively; Cutting feed pitch S The calculation needs to be determined according to the corresponding surface form, which is divided into three types: plane, convex surface, and concave surface. The expressions are as follows: , , , where h is the residual height, R is the tool radius, r is the radius of curvature. The radius of curvature r and its convexity and concavity judgment are obtained by calculating through the Gaussian curvature method. The calculation expression of the radius of curvature , where E, F, G, L, M, N are the relevant coefficients of the first fundamental form and the second fundamental form of the surface in turn. The relevant coefficients of the first fundamental form and the second fundamental form of the surface are obtained by calculating the partial derivatives of the surface parametric equation as shown in the following formula: 。

Images