Empirical formula blade generation system

Abstract

This paper discloses an empirical formula blade generation system for designing subsonic and transonic turbine stages. The values of the design variables used in the parameterized system are calculated by the relevant equations. Iteration is required to modify the design variables. The parameterized system then generates the geometries and blocks of the stator and rotor. Using these geometries and blocks, a mesh is automatically formed using an ICEM CFD script. The turbine stage performance is then evaluated using a CFD solver. The calculation results are analyzed to identify future improvements. The final blade design is obtained through multiple rounds of repeated training and residual iteration. Finally, a highly efficient subsonic and transonic turbine stage is produced.

Description

Technical Field

[0001] The present invention relates to the field of blade generation, and in particular to an empirical formula blade generation system. Background Art

[0002] Subsonic and transonic turbines are widely used in aero engines, gas turbines, ship propulsion and other fields. Among them, transonic blades are one of the important directions of current turbine design research due to their advantages such as high load, high power and small size. The existing blade designs of subsonic and transonic turbine stages are mainly generated based on repeated iterations of experimental results. The present invention proposes a simple and feasible turbine blade design method based on empirical evidence. The blade shapes of different speeds, different working conditions and different application scenarios that can be widely used can quickly generate turbine blade designs with better performance. The subsonic and transonic turbine stages generated by the current blade design have low efficiency. Summary of the Invention

[0003] The object of the present invention is to provide an empirical blade generation system that can produce high efficiency subsonic and transonic turbine stages through improved blade design.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is: an empirical formula blade generation system, which adopts a baseline mid-span blade profile design to design subsonic and transonic turbine stages, and the values of the design variables used in the parameterized system are calculated by related equations; iteration is required to modify the design variables to ensure that the baseline has reasonable aerodynamic performance; the geometric shapes and blocks of the stator and rotor are then generated by the parameterized system; by using the geometric shapes and blocks, a grid is automatically formed through the ICEM CFD script; the performance of the turbine stage is then evaluated through the CFD solver; the calculation results are analyzed and directions for future improvements are found; the final blade design is obtained through multiple rounds of repeated training and residual iterations.

[0005] Preferably, the blade axial chord length C among the 11 parameters of the mid-span blade section is ax , leading edge wedge angle ε LE , trailing edge wedge angle ε TE The velocity triangle is obtained based on prior experience; then the leading edge metal angle and trailing edge metal angle of the rotor and stator are derived from the velocity triangle with the specified flow coefficient, load factor and reaction force; finally, the stagger angle α is calculated stagger , pitch p, throat t, leading edge radius r LE , trailing edge radius r TE and unguided steering δ unguided .

[0006] Preferably, in a subsonic rotor, the flow coefficient φ, the load coefficient ψ and the reaction force R ηGenerate a velocity triangle where the stator metal angle is the angle of absolute velocity and the rotor metal angle is the angle of relative velocity.

[0007] Preferably, based on the leading edge metal angle β LE and trailing edge metal angle β TE Assignment of the value of stagger .

[0008] Preferably, the tangential lift coefficient C L Calculate the rotor pitch p rotor , as shown in formula (1), where F tan is the tangential clearance, A tan is the tangential leaf area, is the incompressible dynamic pressure head at the trailing edge:

[0009]

[0010] As shown in formula (2), is the mass flow rate in the rotor channel; w LE and w TE is the relative flow velocity, β LE and β TE It is the metal corner of the blade;

[0011]

[0012] By combining formula (1) and formula (2), formula (3) is derived to calculate the tangential lift coefficient C L , chord length C, leading edge metal angle β LE and trailing edge metal angle β TE and stagger angle α stagger Pitch p:

[0013]

[0014] The throat t can be TE , pitch p, throat Mach number M t , and the equivalent curvature radius r of the suction side curve of the blade downstream of the throat SS The correlation between them is calculated as shown in Equation 4:

[0015]

[0016] Preferably, the suction side curve downstream of the throat is a ninth-order Bezier curve, and the equivalent radius of the ninth-order Bezier curve is used to represent the rotation of the blade, and the equivalent curvature radius r SS Assumed to be r SS,1 and r SS,2 The average value of is shown in formula (5):

[0017]

[0018] The beneficial effects of the empirical formula blade generation system of the present invention are as follows: in designing subsonic and transonic turbine stages, the values of the design variables used in the parameterized system are calculated by the relevant equations, and iteration is required to modify the design variables to ensure that the baseline has reasonable aerodynamic performance; the geometric shapes and blocks of the stator and rotor are then generated by the parameterized system; by using the geometric shapes and blocks, a grid is automatically formed using the ICEM CFD script; the performance of the turbine stage is then evaluated using a CFD solver; the calculation results are analyzed and directions for future improvements are sought; and the final blade design is obtained through multiple rounds of repeated training and residual iterations to produce highly efficient subsonic and transonic turbine stages. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Design processes for turbine stages;

[0020] Figure 2 is the velocity triangle of the baseline model;

[0021] Figure 3 is the correlation of the cross-section angle of a typical turbine blade, from Kacker and Okapuu;

[0022] Figure 4 is used to calculate the throat t and unguided turn δ unguided The equivalent curvature radius r SS and triangle ΔO r -pt3 up -pt3.O r -pt2 and O r -pt3, whose length is determined by their average value r SS Approximately, it is the normal of curve 2 at pt2 and pt3;

[0023] Figure 5 2D profiles of blades at different radial sections of the subsonic stage stator and rotor;

[0024] Figure 6 2D profiles of blades at different radial sections of the transonic stage stator and rotor;

[0025] Figure 7 Comparison of blade mid-span profiles in subsonic and transonic turbine stages;

[0026] Figure 8 is the computational domain of the subsonic turbine;

[0027] Figure 9 is the computational domain of the transonic turbine;

[0028] Figure 10a、 Figure 10b is the baseline model efficiency shown in the turbine Smith chart;

[0029] Figure 11 Figure 3 is the load diagram for the rotor blade at mid-span and 95% span in the subsonic and transonic stages. DETAILED DESCRIPTION

[0030] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solutions of the present invention, but the present invention is not limited to these embodiments.

[0031] Combined with attachment Figure 1-11 As shown, a blade in this embodiment

[0032] 1Baseline mid-span blade profile design

[0033] Through the parametric system (parametric design system is carried out in a 2D-3D manner: first generate 2D blade profiles along the radial direction and then generate 3D blades along the stacking line), this embodiment designs subsonic and transonic turbine stages. The general procedure of stage design is as follows: Figure 1 As shown in the figure. To ensure a reasonable turbine design from the outset, the values of the design variables used in the parameterized system are calculated by the relevant equations. Iterations are required to modify the design variables to ensure that the baseline has reasonable aerodynamic performance. The geometry and blocks of the stator and rotor are then generated by the parameterized system. By using the geometry and blocks, the mesh is automatically formed using the ICEM CFD script. Afterwards, the performance of the turbine stage is evaluated using the CFD solver. The calculation results are analyzed and directions for future improvements are found. The final blade design is obtained through multiple rounds of repeated training and residual iterations. Finally, high-efficiency subsonic and transonic turbine stages are produced. Since the procedures for the subsonic and transonic stages are similar, only the design practice of the subsonic stage is shown here.

[0034] Among the 11 parameters of the mid-span blade section (the 11 parameters include the axial chord length C ax , pitch p, stagger angle α stagger , throat t, unguided steering δ unguided , blade leading edge radius r LE , trailing edge radius r TE , leading edge wedge angle ε LE , trailing edge wedge angle ε TE , leading edge metal angle β LE , trailing edge metal angle β TE ), blade axial chord length C ax , leading edge wedge angle ε LE , trailing edge wedge angle ε TEThe velocity triangle is obtained a priori. Then, the leading and trailing metal angles of the rotor and stator are derived from the velocity triangle with the specified flow coefficient, load factor, and reaction force. Finally, the stagger angle α is calculated. stagger , pitch p, throat t, leading edge radius r LE , trailing edge radius r TE and unguided steering δ unguided In this case, the tip gap is a constant equal to 0.8% of the span.

[0035] In a subsonic rotor, the flow coefficient φ, load coefficient ψ, and reaction force R η are 0.70, 2.33 and 0.44 respectively, thus generating Figure 2 The velocity triangle is shown in Figure 1. Stations 1, 2, and 3 represent the stator inlet, stator outlet (or rotor inlet), and rotor outlet. The rotational speed is U, the absolute speed is u, and the relative speed is w. The stator metal angle is the angle of absolute speed, while the rotor metal angle is the angle of relative speed. The mid-span blade profiles of the stator and rotor are shown on the left. According to the velocity triangle, the metal angle β TE,stator ,β LE,rotor and β TE,rotor It can be calculated as 68°, 46° and -67°. Assuming the inlet flow is along the axial direction, the stator inlet metal angle β LE,stator is 0°. The axial chord length of the rotor is C ax , leading edge wedge angle ε LE , trailing edge wedge angle ε TE They are designated as 26mm, 30° and 5° respectively. For the stator, the axial chord length is 1.4 times the axial chord length of the rotor; the leading edge wedge angle ε LE and trailing edge wedge angles ε TE 40° and 5°.

[0036] Based on the leading edge metal angle β LE and trailing edge metal angle β TE The assignment can be obtained from Figure 3 The correlation diagram shown in the figure derives the stagger angle α stagger As can be seen from the figure, the stator and rotor stagger angles are 51° and 30° respectively. Figure 3 The values obtained in are an initial guess for the blade profile. Further iterations are needed to vary these parameters and improve efficiency. Therefore, the stagger angle used in the stator is Figure 3 The values shown vary slightly.

[0037] The tangential lift coefficient C can then be calculated L Calculate the rotor pitch p rotor , which is defined as the normalized tangential load acting on the blade surface. As shown in formula (1), where F tan is the tangential clearance, Atan is the tangential leaf area, It is the incompressible dynamic pressure head at the trailing edge.

[0038]

[0039] The tangential load is F tan It is calculated by applying Newton's law to the deflection of the fluid passing through the blade. As shown in formula (2), where is the mass flow rate in the rotor channel; w LE and w TE is the relative flow velocity, β LE and β TE It is the metal corner of the blade.

[0040]

[0041] By combining formula (1) and formula (2), formula (3) is derived to calculate the tangential lift coefficient C L , chord length C, leading edge metal angle β LE and trailing edge metal angle β TE and stagger angle α stagger In current design practice, C L The range of variation is 0.9 to 1.2, and in the present invention, the value is 0.9. Therefore, the rotor pitch p is obtained. rotor The ratio of the number of blades between the stator and the rotor is 1:2. stator For p rotor twice, that is 44mm.

[0042]

[0043] The throat t, can be TE , pitch p, throat Mach number M t , and the equivalent curvature radius r of curve 2 (suction side of the blade downstream of the throat) SS , the correlation between them is calculated as shown in Equation 4.

[0044]

[0045] Although the curve on the suction side downstream of the throat (curve 2) is a ninth-order Bezier curve in this study, the equivalent radius of the curve is used to represent the rotation of the blade, e.g. Figure 4 As shown, the two normals perpendicular to the tangent of curv2 at points pt2 and pt3 are at point O. r Intersect at. r and the length between pt2 and O r The lengths between pt3 and r are SS,1 and rSS,2 . Equivalent curvature radius r SS Assumed to be r SS,1 and r SS,2 The average value of is shown in formula (5). In current design practice, the pitch p and r SS The ratio is between 0.25 and 0.625. In high subsonic turbines, the throat Mach number is between 0.5 and 1. Therefore, the throat value can be obtained by the third equation in the equation group 4.

[0046]

[0047] Figure 4 In, due to O r -pt2 and O r -pt3 is perpendicular to curve 2 at pt2 and pt3, so their intersection angle is equal to the unguided turning angle δ unguided Therefore, using r SS To approximate the length r SS,1 and r SS,2 , we can solve the triangle ΔO by the cosine law r -pt3 up -pt3 to calculate the unguided turning angle δ unguided , as shown in formula (6).

[0048]

[0049] According to the design guide, the leading edge radius r LE The ratio of the pitch p is between 0.05 and 0.10. In this study, it is taken as 0.08 for the stator and 0.03 for the rotor. TE The ratio of the stator to the chord length C is between 0.015 and 0.050, with the stator taking 0.015 and the rotor taking 0.017. Therefore, the stator r can be calculated. LE and the rotor's r TE The value can be calculated.

[0050] 2-base blade stack

[0051] In order to maintain the radial balance of the 3D blade, a free vortex design is used to generate the blade section from the hub to the tip. Starting from the velocity triangle at the mid-diameter position, the axial velocity u at the ith section can be calculated. ax,i and the peripheral speed u θ,i Then from the velocity triangle at each section, the metal angles at the leading and trailing edges of the blade at the ith section can be calculated. Assuming the stagger angle α stagger,i and pitch ratio p / r SS is a constant, then the pitch p is calculated in sequence by formula (3) and formula (4) iThroat i . Unguided turning angle δ unguided,i , can be calculated by formula (6). Finally, assuming the axial chord length C ax,i , leading edge wedge angle ε LE,i , trailing edge wedge angle ε TE,i , leading edge radius r LE,i and the trailing edge radius are both r TE,i is a constant, then 11 parameters of each radial section can be obtained.

[0052] In the stator, three radial sections, hub, midspan, and casing, are used to generate the 3D blades. In the rotor, five sections are used, including hub, midspan, blade tip groove bottom plate, tip, and casing. The profiles of these sections are as follows: Figure 5 It is worth noting that with the increase of the cross-sectional radius, due to the increase of the rotational speed, in the rotor, the absolute value of the blade metal angle decreases at the leading edge and increases at the trailing edge to comply with the free vortex design.

[0053] 3. Benchmark transonic blade design

[0054] Similar design techniques are implemented in the transonic stage blade design. The cross-sections of the transonic stage at different radial sections are as follows: Figure 6 shown.

[0055] Figure 7 A comparison of the mid-span profiles of blades in subsonic and transonic turbine stages is shown. The blade profiles are referenced by the axial stator chord length (x) and the circumferential stator pitch (y). It is noteworthy that the transonic blades, both stator and rotor, are thinner than those in the subsonic stage, and the leading edge of the transonic rotor is blunter and less curved.

[0056] 4CFD Verification

[0057] The computational domains of the subsonic stage and transonic stage are as follows: Figure 8 and Figure 9 They represent 1 / 32 of a hypothetical turbine stage with 32 stators and 64 rotors. ax,stator , and C ax,rotor are the axial chord lengths of the stator and rotor respectively. span is the rotor span. The stage inlet, rotor-stator interface, and outlet are labeled stations 1, 2, and 3. The rotors of both stages rotate at 9500 rpm. The tip clearance between the casing and the tip is 0.8% of the span. For the baseline case, a flat tip is used. The interface between the stator and rotor is approximated using a mixed plane. Periodic boundary conditions are used for the blade channel boundaries. Adiabatic wall boundary conditions are used for the walls in the CFD model. The boundary conditions are shown in Table 1. The inlet boundary conditions for both stages are shown in the table, and the rotational speed is the same.

[0058] Table 1 Boundary conditions of subsonic and transonic turbine stages

[0059]

[0060]

[0061] 5 Baseline results analysis

[0062] From the CFD simulation, the exit Mach numbers of the subsonic and transonic stages are 0.7 and 1.1 respectively. The Reynolds numbers of the subsonic and transonic turbine stages are matched. The Reynolds numbers of the subsonic and transonic stages are 8.9×10 5 and 8.8×10 5 .

[0063] The explanation for the different Mach numbers of the subsonic and transonic stages but the similar Reynolds numbers is as follows: at the inlet, the total temperature and total pressure of the two stages are the same, so the total density at the inlet is the same, which means that the difference in speed is compensated by the difference in density. At the exit, the relative Mach numbers of the subsonic and transonic stages are 0.7 and 1.1 respectively, while their densities are 2.2 kg / m 3 and 1.5kg / m 3 Therefore, the reduced speed in the subsonic case is mainly compensated by the increased density. Since the axial chord lengths of the two stages are similar, their Reynolds numbers are similar.

[0064] Based on this definition, the aerodynamic efficiency of subsonic and transonic stages can be calculated and compared with traditional knowledge such as the "Smith Chart." The turbine Smith Chart is a contour plot of stage efficiency versus flow coefficient and stage load factor. The data points on the chart were obtained from 70 Rolls-Royce aircraft gas turbines before 1965, such as Avon, Dart, Spey, Conway, etc., and it represents the optimal efficiency of a specific machine within a certain pressure ratio range. Due to the limitations of the experimental equipment, the test is based on the following assumptions:

[0065] 1) The turbine inlet temperature is only 100°C to 200°C, while the actual inlet temperature is on the order of 1000°C;

[0066] 2) No auxiliary airflow;

[0067] 3) Corrected to zero tip leakage turbine efficiency.

[0068] Comparison between CFD results and Smith chart prediction efficiency Figure 10a-Figure 10bAs shown in the figure, the x-axis and y-axis represent the flow coefficient and load factor, respectively. The circled numbers represent the efficiency of the performance profile. The baseline model points are shown as red dots. At the subsonic stage midspan, the flow coefficient and load factor are 0.7 and 2.33, respectively; the calculated efficiency is 91.80%. At the transonic stage midspan, the flow coefficient and load factor are 0.7 and 1.94, respectively; the calculated efficiency is 91.63%. In the Smith chart, the predicted efficiencies are 89.5% and 91.7%, respectively. The agreement between the correlation predicted efficiency and the calculated results indicates that the baseline model is a reasonably well-designed and representative turbine performance.

[0069] The load diagrams for mid-span and 95% span are as follows Figure 11 The load is evaluated by the ratio between the isentropic Mach number and the exit Mach number. isen Calculation as public

[0070] As shown in formula 7:

[0071]

[0072] Where P is the pressure on the blade surface; γ is the specific heat ratio; P t,rel is the relative stagnation pressure at the rotor inlet. At each span section, the maximum static pressure is taken as P t,rel .

[0073] Transonic blades have higher loading at the front and lower loading at the center. The relative loading on the blades should not be equal. This is because as the Mach number of the operating flow increases, the blades tend to become thinner to minimize interference with the high-speed flow. Therefore, even if the blade loading (pressure difference) can be matched, the pressure gradient at the tip clearance is unlikely to be the same.

[0074] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. An empirical formula blade generation system, characterized by: Design of subsonic and transonic turbine stages. The values of the design variables used in the parametric system are calculated by the relevant equations. Iterations are required to modify the design variables. The geometries and blocks of the stator and rotor are then generated by the parametric system. By using the geometries and blocks, the mesh is automatically formed in the ICEM CFD script. The turbine stage performance is then evaluated using a CFD solver. The results are analyzed to identify areas for future improvements. The final blade design is obtained through multiple rounds of repeated training and residual iterations. The blade axial chord length C among the 11 parameters of the mid-span blade section ax , leading edge wedge angle ε LE , trailing edge wedge angle ε TE The velocity triangle is obtained based on prior experience; then the leading edge metal angle and trailing edge metal angle of the rotor and stator are derived from the velocity triangle with the specified flow coefficient, load factor and reaction force; finally, the stagger angle α is calculated stagger , pitch p, throat t, leading edge radius r LE , trailing edge radius r TE and unguided steering δ unguided ; In a subsonic rotor, the known flow coefficient φ, load coefficient ψ and reaction force R η Generate a velocity triangle where the stator metal angle is the angle of absolute velocity and the rotor metal angle is the angle of relative velocity; Based on the leading edge metal angle β LE and trailing edge metal angle β TE Assignment of the value of stagger ; Through the tangential lift coefficient C L Calculate the rotor pitch p rotor , as shown in formula (1), where F tan is the tangential clearance, A tan is the tangential leaf area, is the incompressible dynamic pressure head at the trailing edge: As shown in formula (2), is the mass flow rate in the rotor channel; w LE and w TE is the relative flow velocity, β LE and β TE It is the metal corner of the blade; By combining formula (1) and formula (2), formula (3) is derived to calculate the tangential lift coefficient C L , chord length C, leading edge metal angle β LE and trailing edge metal angle β TE and stagger angle α stagger Pitch p: The throat t can be TE , pitch p, throat Mach number M t , and the equivalent curvature radius r of the suction side curve of the blade downstream of the throat SS The correlation between them is calculated as shown in Equation 4:

2. The empirical formula blade generation system according to claim 1, characterized in that: The suction side curve downstream of the throat is a ninth-order Bezier curve. The equivalent radius of the ninth-order Bezier curve is used to represent the rotation of the blade. The equivalent curvature radius r SS Assumed to be r SS,1 and r SS,2 The average value of is shown in formula (5):

Images