CN214247795U - Transonic compressor rotor blade with bulge and concave seam structure - Google Patents
Transonic compressor rotor blade with bulge and concave seam structure Download PDFInfo
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- CN214247795U CN214247795U CN202120138275.7U CN202120138275U CN214247795U CN 214247795 U CN214247795 U CN 214247795U CN 202120138275 U CN202120138275 U CN 202120138275U CN 214247795 U CN214247795 U CN 214247795U
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Abstract
The utility model provides a transonic compressor rotor blade with bulge and concave joint structure, which comprises a compressor movable blade, wherein the compressor movable blade comprises a blade top, a blade root, a suction surface and a pressure surface, and the suction surface is provided with a bulge; the suction surface is also provided with a concave seam which is arranged at the rear side of the bulge; 7 molding modes of the concave seam are provided; the bulges and the concave seams are changed along the continuity of the leaf height direction to respectively form a continuous full-leaf high bulge and a concave seam blade, a continuous partial-leaf high bulge and a concave seam blade, a discontinuous full-leaf high bulge and a concave seam blade, and a discontinuous partial-leaf high bulge and a concave seam blade. The utility model discloses an add swell and slot structure can control the shock wave and separate the flow loss that reduces strong shock wave loss and separation and arouse, and then improve the performance of transonic compressor.
Description
Technical Field
The utility model relates to an impeller machine technical field particularly, especially relates to a transonic speed compressor rotor blade with swell and slot structure.
Background
For a transonic compressor, shock losses and separation losses are one of the major sources of flow losses. The current flow control methods are classified into an active control method and a passive control method. Although an active control method, such as boundary layer suction, plasma excitation, synthetic jet flow, blade tip jet flow and the like, can well control shock waves and separation loss, an additional device and an energy source are required to be added, which not only increases the processing and manufacturing cost of the compressor, but also increases the difficulty in designing the compressor, while a passive control method, such as blade profile optimization, blade sweeping design, cavity and porous medium surfaces, casing treatment, vortex generators and the like, generally realizes the purpose of flow control by changing the design variables of rotor blades or runners of the compressor, and generally causes the blade profile or channel structure of the compressor to be greatly changed. The shock wave control bulge is a relatively new passive flow control technology, although the shock wave system structure in the transonic compressor can be effectively improved, the control effect on flow separation needs to be further improved, and the quality of the rotor blade of the compressor can be increased to a certain extent by adding the bulge.
SUMMERY OF THE UTILITY MODEL
According to the shock wave control bulge provided by the method, as a relatively new passive flow control technology, although the shock wave system structure in the transonic compressor can be effectively improved, the control effect on flow separation needs to be further improved, and the quality of the compressor rotor blade can be improved to a certain extent by adding the bulge, so that the transonic compressor rotor blade with the bulge and the concave seam structure is provided. The utility model mainly controls the shock wave and the separation by adding the bulge and the concave joint structure to reduce the strong shock wave loss and the flow loss caused by the separation, thereby improving the performance of the transonic compressor; the shock wave and the separation can be controlled without adding an auxiliary device; moreover, the design difficulty of redesigning a novel blade is saved by changing the modeling mode of the bulge and the concave seam on the basis of the existing blade profile; the mass of the blade is controlled by adjusting the length and the continuity of the bulge and the concave slot relative to the blade height direction, so that the total mass is unchanged or correspondingly reduced, and the blade has the advantages of flexible design, relatively low cost and the like.
The utility model discloses a technical means as follows:
a transonic speed compressor rotor blade with bulges and a concave seam structure comprises a compressor movable blade, wherein the compressor movable blade comprises a blade top, a blade root, a suction surface and a pressure surface, and bulges are arranged on the suction surface;
the suction surface is also provided with a concave seam which is arranged at the rear side of the bulge; 7 molding modes of the concave seam are provided;
the bulges and the concave seams are changed along the continuity of the leaf height direction to respectively form a continuous full-leaf high bulge and a concave seam blade, a continuous partial-leaf high bulge and a concave seam blade, a non-continuous full-leaf high bulge and a concave seam blade, and a non-continuous partial-leaf high bulge and a concave seam blade.
Further, according to different requirements, adjust the swell with the slot is for the position of blade chord direction, control the swell with the slot is for the length and the continuity of leaf height direction (leaf exhibition direction), through the difference the swell with the combination of the molding mode of slot realizes the influence of modification rotor blade to flow field structure and aerodynamic parameter, and constitutes continuity full leaf high swell and slot blade, continuity part leaf high swell and slot blade with length and position, continuity part leaf high swell and slot blade, discontinuity full leaf high swell and slot blade, discontinuity part leaf high swell and slot blade with length and position and discontinuity part leaf high swell and slot blade with position that differs respectively.
Further, the flow direction starting position and the flow direction ending position of the bulge are both tangent to the suction surface in a smooth flow direction; fitting smooth transition is carried out on the flow direction starting position and the flow direction ending position of the concave seam and the suction surface in the flow direction according to a modeling mode;
by controlling the starting positions of the bulge and the slot on the sections with different blade heights, the starting positions of the bulge and the slot in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
Further, the length and position of the bulge and the concave joint along the leaf height direction can be changed, and the full-leaf high bulge and concave joint blade, the partial-leaf high bulge and concave joint blade and the partial-leaf high bulge and concave joint blade are formed by changing the spanwise starting position and the spanwise ending position of the bulge and the spanwise starting position and the spanwise ending position of the concave joint, wherein the partial-leaf high bulge and concave joint blade comprises: the partial blade height bulges and the concave seam blades with the same length and position and the partial blade height bulges and the concave seam blades with different lengths and positions are specifically designed according to specific rotor blades.
Furthermore, 5 modeling modes in the 7 molding modes of the concave seam are the same as the modeling modes of the bulge, and are respectively a CST (Class function/Shape function Transformation) parameterization, a polynomial interpolation function, a B spline curve, a cubic C-Cardinal spline curve and a p-nary subdivision curve modeling mode;
the molding mode of the concave seam can also be constructed in an arc molding mode or a square molding mode;
the parameters involved in the shaping of the sipes include the depth H2 and the length L2 of the sipes, corresponding to the height H1 and the length L1 of the bulge, respectively.
Further, the fact that the depth H2 and the length L2 of the concave seam correspond to the height H1 and the length L1 of the bump, respectively, means that in the involved formula, when the height of the bump is m, the depth of the concave seam is also m, but in the opposite direction, m > 0; if the length of the bulge is n, the length of the concave seam is also n, the direction is the same, and n is greater than 0.
Further, the arc-shaped concave seam is constructed by adopting an arc modeling mode, the arc diameter D of the arc-shaped concave seam is used for controlling the length L2 and the depth H2, the length L2 is 0.05 b-0.2 b, b is the chord length of the blade, and the depth H2 is not more than 50% of the thickness of the blade at the position where the arc-shaped concave seam is located;
the curvature and the shape of the concave seam are controlled by changing the diameter of the arc, the length of the concave seam and the depth of the concave seam, so that the arc-shaped concave seam with different characteristics is realized.
Furthermore, a rectangular concave seam is constructed by adopting a square modeling mode, the length L2 of the rectangular concave seam is 0.05 b-0.2 b, b is the chord length of the blade, and the depth H2 is not more than 50% of the thickness of the blade at the position;
the size of a flow direction vortex generated by the concave slot is controlled by changing the length-depth ratio of the concave slot, so that the flow loss of the suction surface is restrained; meanwhile, the bottom of the concave seam can be machined and manufactured by using an arc chamfer or a straight chamfer according to the requirement of the machining process of a specific rotor.
Further, the expression of the CST parameterized shape function s (x) satisfies the following formula:
in the formula (I), the compound is shown in the specification,
is a Bernstein polynomial (Bernstein polynomial) and i is
N is
The order of (a);
is the number of combinations; biIs the weight factor introduced, i ═ 0,1, …, n; x is X/b, b is the chord length of the blade, and X is the coordinate of the X axis;
the polynomial interpolation function y satisfies the following formula:
y＝f(x)(1-x)0.5x0.5±g(x)(1-x)1.5x0.5
wherein f (x), g (x) are polynomial interpolation functions,
x is a node vector; a. thei、BiThe coefficient is a polynomial coefficient and can be obtained by fitting original blade data through a least square method; changing the coefficient and order of the polynomial in f (x) can change the bending degree of the arc curve, and further change the bending degree of the bulge; the thickness of the bump and the like can be changed by changing the coefficients and the order of the polynomial in g (x);
the B-spline curve is a curve defined by control vertexes, the B-spline base function is a base function which can describe a complex shape and has global particularity, and a curve equation P (u) meets the following formula:
in the formula (d)jTo control the vertices, j ═ N (i-k, i-k +1, …, i), Ni,k(u) is a k-degree canonical B-spline basis function, i represents the serial number, i is 0,1,2,3 … n, k is the number of basis functions, u represents a parameter, and the interval is [ ui,ui+k+1](ii) a The basis function of the B spline curve is a polynomial spline, and is related to the times and the node interval where the parameter is located, so that the flexibility and diversity of the B spline regulation curve are improved;
the mathematical definition formula of the cubic C-Cardinal spline curve satisfies the following formula:
0≤t≤α，i＝0,1,2,…,n-3
in the formula, point biFor a given shape point, i is 0,1,2,3 … n, j is 0-3, bi+jIs contained in biMiddle, omegaj,a(t) is a spline basis function, t is a node value, the value size determines the precision of the drawn curve in the drawing of the spline curve, a parameter alpha can be used for fine adjustment of the spline curve without influencing the continuity of the curve, the parameter alpha is also called a fine adjustment factor, alpha is larger than 0, and a curve segment P is formedi(t) the curve P (t) consisting is called cubic C-Cardinal spline curve;
the p-nary subdivision curve satisfies the following formula:
given an initial ordered set of control vertices
J0A finite set of subscripts that are initial ordered control vertices; is provided with
For the ordered set of control vertices after the kth subdivision, JkAre a corresponding finite set of subscripts; wherein α ═ { α ═ αjThe real coefficient sequence has only a limited number of components which are not zero, called mask, and are shape parameters; the modeling mode of the uniformly stable p-nary subdivision curve actually comprises p subdivision rules for defining new ordered control points under the curve condition:
in the formula (I), the compound is shown in the specification,
represents the jth ordered control vertex after the K +1 subdivision, Pi kRepresenting the ith ordered control vertex after the Kth subdivision, Z representing an integer collection, i representing an integer, artificially giving that i is smaller than j, j being an initial given value, alphaj-piRepresents j-pi real coefficient parameters, p represents integer times of subdivision, and p is more than or equal to 1; β ═ j-i, β is greater than 0;
if p is 1, the subdivision rule is:
if p is 2, the subdivision rule is:
if p is 3, the subdivision rule is 3, and so on.
Compared with the prior art, the utility model has the advantages of it is following:
1. the utility model provides a transonic compressor rotor blade with swell and slot structure can control the flow loss that reduces strong shock wave loss and separation and arouse through adding swell and slot structure to shock wave and separation, and then improves transonic compressor's performance.
2. The transonic compressor rotor blade with the bulge and the concave seam structure can realize control of shock waves and separation under the condition that an auxiliary device is not required to be added; and the design difficulty of redesigning the novel blade is saved by changing the modeling mode of the bulge and the concave seam on the basis of the existing blade profile.
3. The utility model provides a transonic speed compressor rotor blade with swell and slot structure can be according to different work condition, adjusts the length and the continuity of swell and the relative leaf height direction of slot respectively, and the swell and the slot of the full leaf height of continuity and the partial leaf height of continuity, the swell and the slot of the full leaf height of discontinuity and the partial leaf height of discontinuity promptly make the more accurate control shock wave of swell and slot and the separation condition.
4. The utility model provides a transonic compressor rotor blade with bulge and concave joint structure, through adjusting the length and continuity of the bulge and the concave joint relative to the blade height direction, the quality of the blade is controlled, so that the total mass is not changed or correspondingly reduced; and has the advantages of flexible design, relatively low cost and the like.
To sum up, use the technical scheme of the utility model shock wave control swell among the prior art can be solved as a relatively newer passive flow control technique, though can effectual improvement transonic compressor inside shock wave system structure, but still remain further improvement to the control effect of flow separation, the problem of the quality of the gas compressor rotor blade also can be increased to a certain extent to the addition of swell simultaneously.
Based on the reason, the utility model discloses can extensively promote in impeller machinery fields such as transonic compressor.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required to be used in the description of the embodiments or the prior art are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive labor.
Fig. 1 is a schematic view of a transonic compressor rotor with continuous full-blade high bulge and groove of the present invention.
Fig. 2 is a schematic view of a transonic compressor rotor blade with a continuous full-blade high bulge and a groove of the present invention.
Fig. 3 is a schematic view of a transonic compressor rotor blade with a part of the lobe height bulge and the groove having the same length and position in the continuity of the invention.
Fig. 4 is a schematic view of a transonic compressor rotor with a part of a blade height bump and a groove having the same length and position in the continuity of the invention.
Fig. 5 is a schematic view of a transonic compressor rotor blade with a portion of the lobe height bulge and groove of different lengths and positions in continuity according to the present invention.
Fig. 6 is a schematic view of a transonic compressor rotor with portions of lobes and grooves of different lengths and positions in continuity according to the present invention.
In the figure: 1. moving blade blades of the compressor; 2. a hub; 3. a wheel disc; 4. a suction surface; 5. a flow direction starting position; 6. bulging; 7. a flow direction end position; 8. a flow direction starting position; 9. concave gaps; 10. a flow direction end position; 11. a spanwise starting position; 12. a spanwise starting position; 13. a deployment-to-deployment ending position; 14. a deployment-to-deployment ending position; 15. leaf tops; 16. a blade root; 17. a blade leading edge; 18. a trailing edge of the blade; 19. a pressure surface.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by a person skilled in the art without creative work belong to the protection scope of the present invention.
In order to continuously improve the pressure ratio and efficiency of the compressor, the flow condition in the compressor needs to be deeply understood, and various flow control technologies need to be developed and applied. For a transonic compressor, a compressor passage has a supersonic speed area, so that a strong shock wave can be generated, and the loss caused by the shock wave mainly comprises the following two aspects: firstly, the loss caused by the shock wave itself; and secondly, the shock wave can induce boundary layer separation, so that the boundary layer separation loss is increased. In order to improve the performance of the transonic compressor, the method is an effective method for reasonably controlling the shock wave loss and the separation loss.
The utility model provides a transonic speed compressor rotor blade with swell and slot structure, through the molding mode of adjustment swell and slot, arrange position and cooperation mode and obtain the compressor rotor blade who has swell and slot to can adjust the length and the continuity of swell along the leaf height direction, adapt to different operating modes, thereby improve the inside shock wave system structure of compressor and realize weakening shock wave intensity, reduce the separation loss, improve the purpose of compressor aerodynamic performance.
As shown in the figure, the transonic compressor rotor blade with the bulge and the concave seam structure comprises a compressor movable blade 1, wherein the compressor movable blade 1 comprises a blade top 15, a blade root 16, a suction surface 4 and a pressure surface 19, and the suction surface 4 is provided with a bulge 6.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The bulges 6 and the concave seams 9 are changed along the continuity of the leaf height direction to respectively form a continuous full-leaf high bulge and a concave seam blade, a continuous partial-leaf high bulge and a concave seam blade, a non-continuous full-leaf high bulge and a concave seam blade, and a non-continuous partial-leaf high bulge and a concave seam blade.
Preferably, according to different requirements, adjust swell 6 with the slot 9 is for the position of blade chord direction, control swell 6 with the slot 9 is for the length and the continuity of leaf height direction (leaf exhibition direction), through the difference swell 6 with the combination of slot 9's molding mode realizes the influence of modification rotor blade to flow field structure and aerodynamic parameter, and constitutes continuity full leaf high bulge and slot blade, continuity part leaf high bulge and slot blade with same length and position, the part leaf high bulge and slot blade that the continuity differs length and position, discontinuity full leaf high bulge and slot blade, discontinuity with same length and position part leaf high bulge and slot blade and discontinuity differ length and position part leaf high bulge and slot blade respectively.
Preferably, the flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both tangent to the suction surface 4 in a smooth flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode;
by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
Preferably, the length and position of the bulge 6 and the concave seam 9 in the leaf height direction can be changed, and the full-leaf bulge and concave seam blade and the partial-leaf bulge and concave seam blade are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulge 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave seam 9, and the partial-leaf bulge and concave seam blade comprises: the partial blade height bulges and the concave seam blades with the same length and position and the partial blade height bulges and the concave seam blades with different lengths and positions are specifically designed according to specific rotor blades.
Preferably, 5 of the 7 modeling modes of the concave seam 9 are the same as the modeling mode of the bulge 6, and are respectively a CST (Class function/Shape function Transformation) parameterization, a polynomial interpolation function, a B spline curve, a cubic C-Cardinal spline curve and a p-nary subdivision curve modeling mode;
the molding mode of the concave seam 9 can also be constructed in an arc molding mode or a square molding mode;
the parameters involved in the shaping of the recess 9 include the depth H2 and the length L2 of the recess 9, corresponding to the height H1 and the length L1, respectively, of the bulge 6.
Preferably, the depth H2 and the length L2 of the concave seam correspond to the height H1 and the length L1 of the bump respectively, which means that in the formula concerned, when the height of the bump is m, the depth of the concave seam is m, but in the opposite direction, m is greater than 0; if the length of the bulge is n, the length of the concave seam is also n, the direction is the same, and n is greater than 0.
Preferably, the arc-shaped concave slot is constructed by adopting an arc modeling mode, the arc diameter D of the arc-shaped concave slot is used for controlling the length L2 and the depth H2, the length L2 is 0.05 b-0.2 b, b is the chord length of the blade, and the depth H2 is not more than 50% of the thickness of the blade at the position where the arc-shaped concave slot is located;
the curvature and the shape of the concave joint 9 are controlled by changing the diameter of the circular arc, the length of the concave joint and the depth of the concave joint, so that the circular arc-shaped concave joint with different characteristics is realized.
Preferably, the rectangular concave slot is constructed by adopting a square modeling mode, the length L2 of the rectangular concave slot is 0.05 b-0.2 b, b is the chord length of the blade, and the depth H2 is not more than 50% of the thickness of the blade at the position;
the size of a flow direction vortex generated by the concave slot is controlled by changing the length-depth ratio of the concave slot, so that the flow loss of the suction surface is restrained; meanwhile, the bottom of the concave seam can be machined and manufactured by using an arc chamfer or a straight chamfer according to the requirement of the machining process of a specific rotor.
Preferably, the expression of the CST parameterized shape function s (x) satisfies the following formula:
in the formula (I), the compound is shown in the specification,
is a Bernstein polynomial (Bernstein polynomial) and i is
N is
The order of (a);
is the number of combinations; biIs the weight factor introduced, i ═ 0,1, …, n; x is X/b, and b is blade chordLength, X is the X-axis coordinate;
the polynomial interpolation function y satisfies the following formula:
y＝f(x)(1-x)0.5x0.5±g(x)(1-x)1.5x0.5
wherein f (x), g (x) are polynomial interpolation functions,
x is a node vector; a. thei、BiThe coefficient is a polynomial coefficient and can be obtained by fitting original blade data through a least square method; changing the coefficient and order of the polynomial in f (x) can change the bending degree of the arc curve, and further change the bending degree of the bulge; the thickness of the bump and the like can be changed by changing the coefficients and the order of the polynomial in g (x);
the B-spline curve is a curve defined by control vertexes, the B-spline base function is a base function which can describe a complex shape and has global particularity, and a curve equation P (u) meets the following formula:
in the formula (d)jTo control the vertices, j ═ N (i-k, i-k + 1, …, i), Ni,k(u) is a k-degree canonical B-spline basis function, i represents the serial number, i is 0,1,2,3 … n, k is the number of basis functions, u represents a parameter, and the interval is [ ui,ui+k+1](ii) a The basis function of the B spline curve is a polynomial spline, and is related to the times and the node interval where the parameter is located, so that the flexibility and diversity of the B spline regulation curve are improved;
the mathematical definition formula of the cubic C-Cardinal spline curve satisfies the following formula:
0≤t≤α，i＝0,1,2,…,n-3
in the formula, point biFor given purposeI is 0,1,2,3 … n, j is 0-3, bi+jIs contained in biMiddle, omegaj,a(t) is a spline basis function, t is a node value, the value size determines the precision of the drawn curve in the drawing of the spline curve, a parameter alpha can be used for fine adjustment of the spline curve without influencing the continuity of the curve, the parameter alpha is also called a fine adjustment factor, alpha is larger than 0, and a curve segment P is formedi(t) the curve P (t) consisting is called cubic C-Cardinal spline curve;
the p-nary subdivision curve satisfies the following formula:
given an initial ordered set of control vertices
J0A finite set of subscripts that are initial ordered control vertices; is provided with
For the ordered set of control vertices after the kth subdivision, JkAre a corresponding finite set of subscripts; wherein α ═ { α ═ αjThe real coefficient sequence has only a limited number of components which are not zero, called mask, and are shape parameters; the modeling mode of the uniformly stable p-nary subdivision curve actually comprises p subdivision rules for defining new ordered control points under the curve condition:
in the formula (I), the compound is shown in the specification,
represents the jth ordered control vertex after the K +1 subdivision, Pi kRepresenting the ith ordered control vertex after the Kth subdivision, Z representing an integer collection, i representing an integer, artificially giving that i is smaller than j, j being an initial given value, alphaj-piRepresenting j-pi real coefficient parameters, p representing integer sub-divisionsNumber, p is greater than or equal to 1; β is j-i, β is greater than 0.
If p is 1, the subdivision rule is:
if p is 2, the subdivision rule is:
if p is 3, the subdivision rule is 3, and so on.
The utility model provides a transonic speed compressor rotor blade with swell and slot structure has combined swell and slot structure advantage in the aspect of flow control, not only can the effective control shock wave intensity, reduce the shock wave loss, but also can restrain the flow separation, reduce the flow separation loss, can also make the total mass of blade not change basically simultaneously.
Example 1
As shown in fig. 1-2, a transonic compressor rotor blade with a bulge and a concave seam structure comprises a compressor moving blade 1, wherein the compressor moving blade 1 is a transonic compressor rotor blade with a continuous full-blade high bulge and a groove structure and is installed on a transonic compressor rotor. The wheel disc 3 arranged on the transonic compressor rotor is a base of the compressor movable blade blades 1, the outer edge of the wheel disc 3 is provided with a hub 2, and the compressor movable blade blades 1 are sequentially arranged at intervals along the circumferential direction of the hub 2.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a continuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a continuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The length and position of the bulge 6 and the concave slot 9 along the blade height direction can be changed, and the full-blade high bulge and the concave slot blade are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulge 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave slot 9, and are specifically designed according to specific rotor blades.
The continuity of the bulges 6 and the concave seams 9 along the blade height direction is changed to form a continuous full-blade-height bulge and a concave seam blade.
According to different requirements, the positions of the bulges 6 and the concave seams 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave seams 9 relative to the height direction (the spanwise direction) of the blade are controlled, the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave seams 9, and a continuous full-blade high bulge and a concave seam blade are formed.
In this embodiment, the forming manner of the concave seam 9 is constructed by adopting an arc forming manner, the parameters related to the forming of the concave seam 9 include a depth H2 and a length L2 of the concave seam 9, which correspond to a height H1 and a length L1 of the bulge 6, respectively, specifically, when the height of the bulge 6 is m, the depth of the concave seam 9 is m, but the direction is opposite, and m is greater than 0; if the length of the bulge 6 is n, the length of the concave seam 9 is also n, the direction is the same, and n > 0. The arc-shaped concave seam is constructed by adopting an arc modeling mode, the arc diameter D of the arc-shaped concave seam is used for controlling the length L2 and the depth H2, the length L2 is 2-8mm, and the depth H2 is not more than 1 mm; the curvature and the shape of the concave joint 9 are controlled by changing the diameter of the circular arc, the length of the concave joint and the depth of the concave joint, so that the circular arc-shaped concave joint with different characteristics is realized.
The modeling mode of the bulge 6 is a CST parameterized modeling mode.
The expression of the CST parameterized shape function s (x) satisfies the following formula:
in the formula (I), the compound is shown in the specification,
is a Bernstein polynomial (Bernstein polynomial) and i is
N is
The order of (a);
is the number of combinations; biIs the weight factor introduced, i ═ 0,1, …, n; and X is X/b, b is the chord length of the blade, and X is an X-axis coordinate.
Example 2
As shown in fig. 3-4, unlike embodiment 1, in this embodiment, a transonic compressor rotor blade with a bulge and a concave seam structure includes a compressor moving blade 1, and the compressor moving blade 1 is a transonic compressor rotor blade with a part of high bulge and a concave seam structure having the same length and position in continuity, and is mounted on a transonic compressor rotor.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a continuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a continuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The length and the position of the bulge 6 and the concave slot 9 along the blade height direction can be changed, and partial blade height bulges and concave slot blades with the same length and position are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulge 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave slot 9, and are specifically designed according to specific rotor blades.
The continuity of the bulges 6 and the concave seams 9 along the blade height direction is changed to form a continuous part of blade height bulges and concave seam blades.
According to different requirements, the positions of the bulges 6 and the concave gaps 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave gaps 9 relative to the height direction (the spanwise direction) of the blade are controlled, and the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave gaps 9, so that part of the height bulges and the concave gaps with the same continuity and length and position are formed.
In this embodiment, the concave seam 9 is formed in a square shape; the parameters involved in the shaping of the recess 9 include the depth H2 and the length L2 of the recess 9, corresponding to the height H1 and the length L1, respectively, of the bulge 6. The rectangular concave seam is constructed by adopting a square modeling mode, the length L2 of the rectangular concave seam is 2-8mm, and the depth H2 is less than or equal to 1 mm; the size of a flow direction vortex generated by the concave slot is controlled by changing the length-depth ratio of the concave slot, so that the flow loss of the suction surface is restrained; meanwhile, the bottom of the concave seam can be machined and manufactured by using an arc chamfer or a straight chamfer according to the requirement of the machining process of a specific rotor.
The modeling mode of the bulge 6 is a polynomial interpolation function modeling mode.
The polynomial interpolation function y satisfies the following formula:
y＝f(x)(1-x)0.5x0.5±g(x)(1-x)1.5x0.5
wherein f (x), g (x) are polynomial interpolation functions,
x is a node vector; a. thei、BiThe coefficient is a polynomial coefficient and can be obtained by fitting original blade data through a least square method; changing the coefficient and order of the polynomial in f (x) can change the bending degree of the arc curve, and further change the bending degree of the bulge; the thickness of the bulge and the like can be changed by changing the coefficients and the order of the polynomial in g (x).
Example 3
As shown in fig. 5-6, unlike embodiment 1, in this embodiment, a transonic compressor rotor blade with a bulge and a concave seam structure includes a compressor movable blade 1, and the compressor movable blade 1 is a transonic compressor rotor blade with a partial high bulge and a concave seam structure having different lengths and positions in continuity, and is mounted on a transonic compressor rotor.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a continuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a continuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The lengths and positions of the bulges 6 and the concave gaps 9 along the blade height direction can be changed, and partial blade height bulges and concave gap blades with different lengths and positions are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulges 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave gaps 9, and are specifically designed according to specific rotor blades.
The continuity of the bulges 6 and the concave seams 9 along the blade height direction is changed to form a continuous part of blade height bulges and concave seam blades.
According to different requirements, the positions of the bulges 6 and the concave seams 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave seams 9 relative to the height direction (the spanwise direction) of the blade are controlled, and the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave seams 9, so that part of the height bulges and the concave seams blades with different lengths and positions in continuity are formed.
The 7 modeling modes of the concave seam 9 include 5 modeling modes which are the same as the modeling mode of the bulge 6 and respectively refer to CST (Class function/Shape function Transformation) parameterization, polynomial interpolation function, B spline curve, cubic C-Cardinal spline curve and p-nary subdivision curve modeling modes. In this embodiment, the molding mode of the concave seam 9 is a CST parameterized molding mode.
The expression of the CST parameterized shape function s (x) satisfies the following formula:
in the formula (I), the compound is shown in the specification,
is a Bernstein polynomial (Bernstein polynomial) and i is
N is
The order of (a);
is the number of combinations; biIs the weight factor introduced, i ═ 0,1, …, n; and X is X/b, b is the chord length of the blade, and X is an X-axis coordinate.
The bulge 6 is shaped in a B-spline curve mode.
The B-spline curve is a curve defined by control vertexes, the B-spline base function is a base function which can describe a complex shape and has global particularity, and a curve equation P (u) meets the following formula:
in the formula (d)jTo control the vertices, j ═ N (i-k, i-k + 1, …, i), Ni,k(u) is a k-degree canonical B-spline basis function, i represents the serial number, i is 0,1,2,3 … n, k is the number of basis functions, u represents a parameter, and the interval is [ ui,ui+k+1](ii) a The basis function of the B spline curve is a polynomial spline, and is not only related to the degree, but also related to the node interval where the parameter is located, so that the flexibility and diversity of the B spline control curve are improved.
Example 4
Different from the embodiment 1, in the embodiment, the transonic compressor rotor blade with the bulge and the concave seam structure comprises a compressor movable blade 1, wherein the compressor movable blade 1 is a transonic compressor rotor blade with a non-continuous full-blade high bulge and a concave seam structure and is installed on a transonic compressor rotor.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a discontinuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a discontinuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The length and position of the bulge 6 and the concave slot 9 along the blade height direction can be changed, and the full-blade high bulge and the concave slot blade are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulge 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave slot 9, and are specifically designed according to specific rotor blades.
The bulges 6 and the concave gaps 9 are changed along the continuity of the leaf height direction to form non-continuous full-leaf high bulges and concave gap blades.
According to different requirements, the positions of the bulges 6 and the concave seams 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave seams 9 relative to the height direction (the spanwise direction) of the blade are controlled, and the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave seams 9, so that the non-continuous full-blade high-bulge and concave seam blade is formed.
The 7 modeling modes of the concave seam 9 include 5 modeling modes which are the same as the modeling mode of the bulge 6 and respectively refer to CST (Class function/Shape function Transformation) parameterization, polynomial interpolation function, B spline curve, cubic C-Cardinal spline curve and p-nary subdivision curve modeling modes. In this embodiment, the modeling mode of the concave seam 9 is a polynomial interpolation function modeling mode.
The polynomial interpolation function y satisfies the following formula:
y＝f(x)(1-x)0.5x0.5±g(x)(1-x)1.5x0.5
wherein f (x), g (x) are polynomial interpolation functions,
x is a node vector; a. thei、BiThe coefficient is a polynomial coefficient and can be obtained by fitting original blade data through a least square method; changing the coefficient and order of the polynomial in f (x) can change the bending degree of the arc curve, and further change the bending degree of the bulge; the thickness of the bulge and the like can be changed by changing the coefficients and the order of the polynomial in g (x).
The modeling mode of the bulge 6 is a cubic C-Cardinal spline curve.
The mathematical definition formula of the cubic C-Cardinal spline curve satisfies the following formula:
0≤t≤α，i＝0,1,2,…,n-3
in the formula, point biFor a given shape point, i is 0,1,2,3 … n, j is 0-3, bi+jIs contained in biMiddle, omegaj,a(t) is a spline basis function, t is a node value, the value size determines the precision of the drawn curve in the drawing of the spline curve, a parameter alpha can be used for fine adjustment of the spline curve without influencing the continuity of the curve, the parameter alpha is also called a fine adjustment factor, alpha is larger than 0, and a curve segment P is formedi(t) the curve P (t) composed is called cubic C-Cardinal spline curve.
Example 5
Different from the embodiment 1, in the embodiment, the transonic compressor rotor blade with the bulge and the concave seam structure comprises a compressor movable blade 1, wherein the compressor movable blade 1 is a transonic compressor rotor blade with a discontinuous blade height bulge and a concave seam structure at the same length and position and is installed on a transonic compressor rotor.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a discontinuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a discontinuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The length and the position of the bulge 6 and the concave slot 9 along the blade height direction can be changed, and partial blade height bulges and concave slot blades with the same length and position are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulge 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave slot 9, and are specifically designed according to specific rotor blades.
The continuity of the bulges 6 and the concave seams 9 along the blade height direction is changed to form discontinuous part blade height bulges and concave seam blades.
According to different requirements, the positions of the bulges 6 and the concave seams 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave seams 9 relative to the height direction (the spanwise direction) of the blade are controlled, and the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave seams 9, so that the partial high bulges and the concave seams blades with the same length and positions are formed.
The 7 modeling modes of the concave seam 9 comprise 5 modeling modes which are the same as the modeling modes of the bulge 6 and respectively comprise CST (Class function/Shape function Transformation) parameterization, polynomial interpolation functions, B spline curves, cubic C-Cardinal spline curves and p-nary subdivision curve modeling modes; in this embodiment, the shaping mode of the concave seam 9 is a B-spline curve shaping mode.
The B-spline curve is a curve defined by control vertexes, the B-spline base function is a base function which can describe a complex shape and has global particularity, and a curve equation P (u) meets the following formula:
in the formula (d)jTo control the vertices, j ═ N (i-k, i-k + 1, …, i), Ni,k(u) is a k-degree canonical B-spline basis function, i represents the serial number, i is 0,1,2,3 … n, k is the number of basis functions, u represents a parameter, and the interval is [ ui,ui+k+1](ii) a The basis function of the B spline curve is a polynomial spline, and is not only related to the degree, but also related to the node interval where the parameter is located, so that the flexibility and diversity of the B spline control curve are improved.
The modeling mode of the bulge 6 is a p-nary subdivision curve modeling mode.
The p-nary subdivision curve satisfies the following formula:
given an initial ordered set of control vertices
J0For initial ordered control of verticesPerforming standard set; is provided with
For the ordered set of control vertices after the kth subdivision, JkAre a corresponding finite set of subscripts; wherein α ═ { α ═ αjThe real coefficient sequence has only a limited number of components which are not zero, called mask, and are shape parameters; the modeling mode of the uniformly stable p-nary subdivision curve actually comprises p subdivision rules for defining new ordered control points under the curve condition:
in the formula (I), the compound is shown in the specification,
represents the jth ordered control vertex after the K +1 subdivision, Pi kRepresenting the ith ordered control vertex after the Kth subdivision, Z representing an integer collection, i representing an integer, artificially giving that i is smaller than j, j being an initial given value, alphaj-piRepresents j-pi real coefficient parameters, p represents integer times of subdivision, and p is more than or equal to 1; β is j-i, β is greater than 0.
If p is 1, the subdivision rule is:
if p is 2, the subdivision rule is:
if p is 3, the subdivision rule is 3, and so on.
Example 6
Different from the embodiment 1, in the embodiment, the transonic compressor rotor blade with the bulge and the concave seam structure comprises a compressor movable blade 1, wherein the compressor movable blade 1 is a transonic compressor rotor blade with discontinuous blade height bulge and concave seam structures with different lengths and positions and is installed on a transonic compressor rotor.
The compressor moving blade 1 comprises a blade top 15, a blade root 16, a blade front edge 17, a blade tail edge 18, a suction surface 4 and a pressure surface 19, wherein a bulge 6 is arranged on the suction surface 4, and the bulge 6 is a discontinuous bulge.
The suction surface 4 is also provided with a concave seam 9, and the concave seam 9 is a discontinuous concave seam and is arranged at the rear side of the bulge 6; 7 molding modes of the concave seam 9 are provided.
The flow direction starting position 5 and the flow direction ending position 7 of the bulge 6 are both smoothly tangent to the suction surface 4 in the flow direction; the flow direction starting position 8 and the flow direction ending position 10 of the concave seam 9 are both fitted with the suction surface 4 in a smooth transition mode in the flow direction according to the modeling mode; by controlling the starting positions of the bulge 6 and the concave slot 9 on the sections with different blade heights, the starting positions of the bulge 6 and the concave slot 9 in the blade height direction relative to the chord length percentage are kept the same or different, and the rotor blade is specifically designed according to a specific rotor blade.
The lengths and positions of the bulges 6 and the concave gaps 9 along the blade height direction can be changed, and partial blade height bulges and concave gap blades with different lengths and positions are formed by changing the spanwise starting position 11 and the spanwise ending position 13 of the bulges 6 and the spanwise starting position 12 and the spanwise ending position 14 of the concave gaps 9, and are specifically designed according to specific rotor blades.
The continuity of the bulges 6 and the concave seams 9 along the blade height direction is changed to form discontinuous part blade height bulges and concave seam blades.
According to different requirements, the positions of the bulges 6 and the concave seams 9 relative to the chord direction of the blade are adjusted, the lengths and the continuity of the bulges 6 and the concave seams 9 relative to the blade height direction (the blade unfolding direction) are controlled, and the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges 6 and the concave seams 9, so that partial blade height bulges and concave seam blades with different lengths and positions in the non-continuity mode are formed.
The 7 modeling modes of the concave seam 9 include 5 modeling modes which are the same as the modeling mode of the bulge 6 and respectively refer to CST (Class function/Shape function Transformation) parameterization, polynomial interpolation function, B spline curve, cubic C-Cardinal spline curve and p-nary subdivision curve modeling modes. In this embodiment, the concave seam 9 and the bulge 6 have the same modeling mode, and are both cubic C-Cardinal spline curves or p-nary subdivision curves.
The mathematical definition formula of the cubic C-Cardinal spline curve satisfies the following formula:
0≤t≤α，i＝0,1,2,…,n-3
in the formula, point biFor a given shape point, i is 0,1,2,3 … n, j is 0-3, bi+jIs contained in biMiddle, omegaj,a(t) is a spline basis function, t is a node value, the value size determines the precision of the drawn curve in the drawing of the spline curve, a parameter alpha can be used for fine adjustment of the spline curve without influencing the continuity of the curve, the parameter alpha is also called a fine adjustment factor, alpha is larger than 0, and a curve segment P is formedi(t) the curve P (t) composed is called cubic C-Cardinal spline curve.
The p-nary subdivision curve satisfies the following formula:
given an initial ordered set of control vertices
J0A finite set of subscripts that are initial ordered control vertices; is provided with
Is the k timeSet of ordered control vertices after subdivision, JkAre a corresponding finite set of subscripts; wherein α ═ { α ═ αjThe real coefficient sequence has only a limited number of components which are not zero, called mask, and are shape parameters; the modeling mode of the uniformly stable p-nary subdivision curve actually comprises p subdivision rules for defining new ordered control points under the curve condition:
in the formula (I), the compound is shown in the specification,
represents the jth ordered control vertex after the K +1 subdivision, Pi kRepresenting the ith ordered control vertex after the Kth subdivision, Z representing an integer collection, i representing an integer, artificially giving that i is smaller than j, j being an initial given value, alphaj-piRepresents j-pi real coefficient parameters, p represents integer times of subdivision, and p is more than or equal to 1; β is j-i, β is greater than 0.
If p is 1, the subdivision rule is:
if p is 2, the subdivision rule is:
if p is 3, the subdivision rule is 3, and so on.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention.
Claims (9)
1. A transonic speed compressor rotor blade with bulges and a concave seam structure comprises a compressor movable blade (1), wherein the compressor movable blade (1) comprises a blade top (15), a blade root (16), a suction surface (4) and a pressure surface (19), and the suction surface (4) is provided with bulges (6);
the suction surface (4) is also provided with a concave seam (9), and the concave seam (9) is arranged at the rear side of the bulge (6); 7 modeling modes of the concave seam (9) are provided;
the bulges (6) and the concave seams (9) are changed along the continuity of the leaf height direction to respectively form a continuous full-leaf high bulge and a concave seam blade, a continuous partial-leaf high bulge and a concave seam blade, a non-continuous full-leaf high bulge and a concave seam blade, and a non-continuous partial-leaf high bulge and a concave seam blade.
2. The transonic compressor rotor blade with a bulge and fillet configuration of claim 1, characterized in that the positions of the bulges (6) and the concave gaps (9) relative to the chord direction of the blade are adjusted according to different requirements, the lengths and the continuity of the bulges (6) and the concave gaps (9) relative to the blade height direction are controlled, the influence of the modified rotor blade on the flow field structure and the aerodynamic parameters is realized through the combination of different modeling modes of the bulges (6) and the concave seams (9), and respectively form a continuous full-leaf high bulge and a concave seam blade, a partial-leaf high bulge and a concave seam blade with the same length and position in continuity, a partial-leaf high bulge and a concave seam blade with different lengths and positions in continuity, a non-continuous full-leaf high bulge and a concave seam blade, a partial-leaf high bulge and a concave seam blade with the same length and position in non-continuity, and a partial-leaf high bulge and a concave seam blade with different lengths and positions in non-continuity.
3. The transonic compressor rotor blade with a bulge and a fillet structure according to claim 1 or 2, characterized in that the flow direction starting position (5) and the flow direction ending position (7) of the bulge (6) are both smoothly tangential to the suction surface (4) in the flow direction; the flow direction starting position (8) and the flow direction ending position (10) of the concave joint (9) are smoothly and transitionally fitted with the suction surface (4) in the flow direction according to the modeling mode;
by controlling the starting positions of the bulges (6) and the concave gaps (9) on different blade height sections, the starting positions of the bulges (6) and the concave gaps (9) in the blade height direction are kept the same or different relative to the chord length percentage.
4. The transonic compressor rotor blade with bump and fillet configuration as in claim 1 or 2, characterized in that the length and position of the bump (6) and the fillet (9) in the direction of the blade height can be varied, constituting full-lobe and fillet blades and partial-lobe and fillet blades by varying the spanwise starting position (11) and the spanwise ending position (13) of the bump (6) and the spanwise starting position (12) and the spanwise ending position (14) of the fillet (9), said partial-lobe and fillet blades comprising: the partial blade height bulges and the concave seam blades with the same length and position and the partial blade height bulges and the concave seam blades with different lengths and positions.
5. The transonic compressor rotor blade with bulge and fillet structure according to claim 1, wherein 5 of the 7 types of fillet (9) are the same as the bulge (6), namely CST parameterization, polynomial interpolation function, B-spline curve, cubic C-Cardinal spline curve and p-nary subdivision curve modeling;
the molding mode of the concave seam (9) can also be constructed in an arc molding mode or a square molding mode;
the parameters involved in the shaping of the sipes (9) include the depth H2 and the length L2 of the sipes (9), corresponding to the height H1 and the length L1, respectively, of the bulge (6).
6. The transonic compressor rotor blade with bump and fillet configuration as in claim 5, characterized in that the depth H2 and length L2 of the fillet (9) correspond to the height H1 and length L1, respectively, of the bump (6) in such a way that in the formula involved, when the height of the bump (6) is m, the depth of the fillet (9) is m, in the opposite direction, m > 0; when the length of the bulge (6) is n, the length of the concave seam (9) is also n, the direction is the same, and n is larger than 0.
7. The transonic compressor rotor blade with bulge and groove structure as claimed in claim 5, wherein the arc-shaped groove is constructed by arc modeling, the arc diameter D of the arc-shaped groove is used for controlling the length L2 and the depth H2, the length L2 is 0.05 b-0.2 b, b is the chord length of the blade, and the depth H2 is not more than 50% of the thickness of the blade at the position;
the curvature and the shape of the concave joint (9) are controlled by changing the diameter of the circular arc, the length of the concave joint and the depth of the concave joint, so that the circular arc-shaped concave joint with different characteristics is realized.
8. The transonic compressor rotor blade with a bump and fillet configuration as in claim 5, wherein the rectangular fillet is constructed in a square shape with a length L2 of 0.05 b-0.2 b, b being the chord length of the blade, and a depth H2 of no more than 50% of the thickness of the blade at the location;
the size of a flow direction vortex generated by the concave slot is controlled by changing the length-depth ratio of the concave slot, so that the flow loss of the suction surface is restrained; meanwhile, the bottom of the concave seam can be machined and manufactured by using an arc chamfer or a straight chamfer according to the requirement of the machining process of a specific rotor.
9. The transonic compressor rotor blade with bump and fillet configuration of claim 5 wherein said CST parameterized shape function S (x) has an expression satisfying the following formula:
in the formula (I), the compound is shown in the specification,
is a Bernstein polynomial, i is
N is
The order of (a);
is the number of combinations; biIs the weight factor introduced, i ═ 0,1, …, n; x is X/b, b is the chord length of the blade, and X is the coordinate of the X axis;
the polynomial interpolation function y satisfies the following formula:
y＝f(x)(1-x)0.5x0.5±g(x)(1-x)1.5x0.5
wherein f (x), g (x) are polynomial interpolation functions,
x is a node vector; a. thei、BiThe coefficient is a polynomial coefficient and can be obtained by fitting original blade data through a least square method; changing the coefficient and order of the polynomial in f (x) can change the bending degree of the arc curve, and further change the bending degree of the bulge; changing the coefficients and orders of the polynomials in g (x), changing the thickness of the bump;
the B-spline curve is a curve defined by control vertexes, the B-spline base function is a base function which can describe a complex shape and has global particularity, and a curve equation P (u) meets the following formula:
in the formula (d)jTo control the vertices, j ═ N (i-k, i-k +1, …, i), Ni,k(u) is a k-degree canonical B-spline basis function, i represents the serial number, i is 0,1,2,3 … n, k is the number of basis functions, u represents a parameter, and the interval is [ ui,ui+k+1](ii) a The basis function of the B spline curve is a polynomial spline, and is related to the times and the node interval where the parameter is located, so that the flexibility and diversity of the B spline regulation curve are improved;
the mathematical definition formula of the cubic C-Cardinal spline curve satisfies the following formula:
0≤t≤α，i＝0,1,2,…,n-3
in the formula, point biFor a given shape point, i is 0,1,2,3 … n, j is 0-3, bi+jIs contained in biMiddle, omegaj,a(t) is a spline basis function, t is a node value, the value size determines the precision of the drawn curve in the drawing of the spline curve, a parameter alpha can be used for fine adjustment of the spline curve without influencing the continuity of the curve, the parameter alpha is also called a fine adjustment factor, alpha is larger than 0, and a curve segment P is formedi(t) the curve P (t) consisting is called cubic C-Cardinal spline curve;
the p-nary subdivision curve satisfies the following formula:
given an initial ordered set of control vertices
J0A finite set of subscripts that are initial ordered control vertices; is provided with
For the ordered set of control vertices after the kth subdivision, JkAre a corresponding finite set of subscripts; wherein α ═ { α ═ αjThe real coefficient sequence has only a limited number of components which are not zero, called mask, and are shape parameters; the modeling mode of the uniformly stable p-nary subdivision curve actually comprises p subdivision rules for defining new ordered control points under the curve condition:
in the formula (I), the compound is shown in the specification,
represents the jth ordered control vertex after the K +1 th subdivision,
representing the ith ordered control vertex after the Kth subdivision, Z representing an integer collection, i representing an integer, given that i is less than j, j being an initial given value, alphaj-piRepresents j-pi real coefficient parameters, p represents integer times of subdivision, and p is more than or equal to 1; β ═ j-i, β is greater than 0;
if p is 1, the subdivision rule is:
if p is 2, the subdivision rule is:
if p is 3, the subdivision rule is 3, and so on.
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| CN112648235A (en) * | 2021-01-19 | 2021-04-13 | 大连海事大学 | Transonic compressor rotor blade with bulge and concave seam structure |
| CN112648235B (en) * | 2021-01-19 | 2024-05-07 | 大连海事大学 | Transonic compressor rotor blade with bulge and concave seam structure |
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