A broadband pneumatic excitation suppression method and system based on turbine end wall design

Abstract

The present application belongs to the field of wideband vibration noise control of turbomachinery, and discloses a wideband pneumatic excitation suppression method and system based on turbine end wall design, so as to realize comprehensive regulation and control of end region secondary flow and suction surface separation flow, and further control wideband random pressure pulsation induced by blade surface turbulence. A full cycle trigonometric function type line is adopted to construct a circumferential control curve of the end wall, a Bézier curve is adopted to construct a circumferential control curve of the amplitude of the end wall, and a nonlinear variation process of the phase of the circumferential control curve function is adjusted according to the blade configuration. A non-axisymmetric end wall parameterized design configuration is obtained. The configuration of the present application considers comprehensive regulation and control of the blade suction surface separation flow, effectively suppresses the turbulence intensity in the turbine blade passage, and realizes effective control of the wideband random pneumatic excitation on the blade surface.

Description

Technical Field

[0001] This invention belongs to the field of broadband vibration and noise control of turbomachinery, and specifically relates to a broadband aerodynamic excitation suppression method and system based on turbine endwall design. Background Technology

[0002] Turbomachinery, as a core component of rotary propulsion systems, is used in aero engines, gas turbines, and steam turbines, and serves in surface ships, nuclear-powered submarines, aircraft, and other equipment. During operation, the unsteady, anisotropic, three-dimensional complex turbulent flow on the blade surface induces random pulsating pressure, exhibiting broadband characteristics. This broadband excitation causes random vibrations across a wide frequency band, exciting multimodal vibrations in the system structure and radiating noise. This radiated noise covers a wide frequency range, and effective control methods are lacking. On the one hand, it impacts the ecological environment; on the other hand, as a major component of mechanical noise, it directly determines the acoustic stealth performance of military equipment such as submarines, becoming a key issue restricting their combat capabilities and safety. Therefore, effective control of the broadband pulsating pressure on the blade surface, targeting the excitation source, is of great significance for the vibration reduction and noise reduction design of turbomachinery.

[0003] Broadband aerodynamic excitation on the blade surface is directly caused by random turbulent flow, making effective turbulence control crucial. The lateral and adverse pressure gradients within the blade passage induce complex end-zone secondary and separation flows, with various vortex structures significantly increasing turbulence intensity on the blade surface. Current control methods for unsteady flows within the blade passage include active control methods such as active boundary layer control and endwall boundary layer extraction, and passive control methods such as blade configuration design and endwall design. Active control methods require external energy, significantly increasing system complexity and imposing limitations. Passive control methods, on the other hand, require no external power source and offer advantages such as simplicity, low cost, high reliability, and low maintenance. Non-axisymmetric endwall design avoids adjustments to the blade configuration and is widely used in turbomachinery aerodynamic performance optimization, improving aerodynamic losses and stage efficiency by influencing the end-zone secondary flow within the blade passage. However, existing non-axisymmetric endwall design methods only focus on aerodynamic performance optimization without considering their impact on random turbulent excitation. However, there are still some drawbacks: existing endwall configurations mainly consider the impact on secondary flow in the end region, lacking control over the separation flow on the suction surface of the blades. In addition, too many design parameters complicate endwall design, and choosing inappropriate design parameters can worsen the internal flow field of the turbine, leading to negative effects. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a broadband aerodynamic excitation suppression method and system based on turbine endwall design, in order to regulate the secondary flow in the end region and the flow separation on the suction surface, thereby achieving broadband pulsating pressure control on the blade surface.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A broadband aerodynamic excitation suppression method based on turbine endwall design, the method comprising:

[0007] Within the blade passage, the circumferential control curve of the endwall is constructed using a full-cycle trigonometric function profile; the axial control curve of the endwall is constructed using a Bézier curve.

[0008] The amplitude of the circumferential control curve at different axial positions is controlled by the axial control curve. The phase of the circumferential control curve function is adjusted according to the axial position to generate a non-axisymmetric end wall.

[0009] Preferably, the circumferential control curve of the end wall adopts a full-cycle sine function, with the expression:

[0010]

[0011] Where x is the normalized axial position within the blade passage, ranging from 0 to 1, where 0 represents the leading edge of the blade and 1 represents the trailing edge; t is the normalized circumferential position within the blade passage, ranging from 0 to 1, where 0 represents the pressure surface of the blade and 1 represents the suction surface; C r (t) represents the radial variation amplitude of the non-axisymmetric endwall relative to the initial endwall, C r (t)>0 indicates a bulge, C r (t)<0 indicates a depression; A m α(x) represents the design amplitude of the non-axisymmetric endwall, α(x) represents the amplitude coefficient for axial position control, and λ(x) represents the nonlinear phase coefficient for axial position control.

[0012] Preferably, the amplitude coefficient for axial position control is constructed using a Bézier curve, expressed as follows:

[0013]

[0014] Where B(z) is the amplitude of the constructed Bézier curve, and z is the path parameter of the Bézier curve, with a value ranging from 0 to 1; P i Let n be the curve control points, and n be the number of curve control points.

[0015] Preferably, the nonlinear phase coefficient for axial position control is determined by the following expression:

[0016]

[0017] Wherein, β is the relative airflow angle at the blade passage outlet, which enables the regulation of the phase change of the axial control curve within the passage with different blade configurations.

[0018] The present invention also provides a wideband aerodynamic excitation suppression system based on turbine endwall design, the system being used to implement any of the methods described above, the system comprising: a construction module and a generation module;

[0019] The construction module is used to construct the circumferential control curve of the endwall using a full-cycle trigonometric function profile within the blade passage; and to construct the axial control curve of the endwall using a Bézier curve.

[0020] The generation module is used to control the amplitude of the circumferential control curve at different axial positions using the axial control curve, and to adjust the phase of the circumferential control curve function according to the axial position to generate a non-axisymmetric end wall.

[0021] Preferably, the circumferential control curve of the end wall adopts a full-cycle sine function, with the expression:

[0022]

[0023] Where x is the normalized axial position within the blade passage, ranging from 0 to 1, where 0 represents the leading edge of the blade and 1 represents the trailing edge; t is the normalized circumferential position within the blade passage, ranging from 0 to 1, where 0 represents the pressure surface of the blade and 1 represents the suction surface; C r (t) represents the radial variation amplitude of the non-axisymmetric endwall relative to the initial endwall, C r (t)>0 indicates a bulge, C r (t)<0 indicates a depression; A m α(x) represents the design amplitude of the non-axisymmetric endwall, α(x) represents the amplitude coefficient for axial position control, and λ(x) represents the nonlinear phase coefficient for axial position control.

[0024] Preferably, the amplitude coefficient for axial position control is constructed using a Bézier curve, expressed as follows:

[0025]

[0026] Where B(z) is the amplitude of the constructed Bézier curve, and z is the path parameter of the Bézier curve, with a value ranging from 0 to 1; P i Let n be the curve control points, and n be the number of curve control points.

[0027] Preferably, the nonlinear phase coefficient for axial position control is determined by the following expression:

[0028]

[0029] Wherein, β is the relative airflow angle at the blade passage outlet, which enables the regulation of the phase change of the axial control curve within the passage with different blade configurations.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] This invention achieves parametric design of the non-axisymmetric endwall within the turbine blade passage. By using a small number of design parameters, combined with trigonometric functions and Bézier curves, a smooth transition of the endwall surface is achieved. Based on the blade design velocity triangle, the nonlinear phase variation of the endwall control curve within the passage is designed. This invention further optimizes the control effect of the non-axisymmetric endwall design on the turbulent flow within the turbine. On one hand, in the first half of the blade passage, the bulge on the pressure side accelerates the flow and reduces local static pressure, while the concave area on the suction side slows the flow and increases local static pressure, thereby weakening the lateral pressure gradient within the passage, suppressing the formation and development of secondary flow in the end region, and reducing turbulence intensity. On the other hand, in the second half of the blade passage, the nonlinear phase variation of the control curve causes a bulge on the endwall at the suction side of the blade, which accelerates the flow, suppresses flow separation, and reduces the turbulent kinetic energy on the suction side. This effectively suppresses random turbulent excitation on the blade surface.

[0032] This invention has the advantages of fewer design parameters, strong universality, and smooth surface. It also introduces control over the separated flow without affecting the flow outside the channel, and has good comprehensive control characteristics. With reasonable design, it can effectively improve the separation of secondary flow in the end region and blade suction surface, effectively reduce turbulence intensity, and thus suppress broadband random aerodynamic excitation on the blade surface. Attached Figure Description

[0033] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the blade channel parameters and the distribution area of ​​the non-axisymmetric endwall in an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the circumferential control curve of the non-axisymmetric end wall in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the phase change coefficient of the circumferential control curve in an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the amplitude control coefficient of the circumferential control curve in an embodiment of the present invention;

[0038] Figure 5 This is a contour map showing the radial amplitude offset of the non-axisymmetric end wall in an embodiment of the present invention.

[0039] Figure 6 This is a schematic diagram of a turbine blade passage with a non-axisymmetric endwall in an embodiment of the present invention;

[0040] Figure 7 This is a comparative schematic diagram of the spanwise distribution of turbulent kinetic energy at the blade channel outlet under a non-axisymmetric endwall configuration in an embodiment of the present invention;

[0041] Figure 8 This is a comparative schematic diagram of the spanwise distribution of the total pressure loss coefficient at the blade channel outlet under a non-axisymmetric endwall configuration in an embodiment of the present invention;

[0042] Figure 9 This is a schematic diagram comparing the power spectrum energy distribution of random pressure pulsations on the blade surface under a non-axisymmetric endwall configuration in an embodiment of the present invention;

[0043] Figure 10 This is a schematic diagram comparing the PSD logarithmic spectrum of broadband random pressure pulsations at the monitoring point of the blade suction surface under a non-axisymmetric endwall configuration in an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Example 1

[0047] The purpose of this invention is to provide a broadband aerodynamic excitation suppression method based on turbine endwall design, namely a parameterized design method for a novel non-axisymmetric endwall in turbine blade passage, to achieve comprehensive control of secondary flow and separation flow in the end region, thereby suppressing broadband random turbulent excitation on the blade surface.

[0048] To make the design process, advantages, and control performance of the present invention more apparent and understandable, the specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0049] The turbine is an axial-flow turbine, with blade passages between adjacent blades that are evenly distributed circumferentially. Non-axisymmetric endwalls are located within the blade passages. The side of the turbine blade surface with higher pressure is the pressure surface (PS), and the other side is the suction surface (SS), as shown below. Figure 1 As shown, the area within the dashed line represents the region where the endwall is not axisymmetric. x represents the normalized axial position within the blade passage, ranging from 0 to 1, where 0 represents the leading edge and 1 represents the trailing edge. t represents the normalized circumferential position within the blade passage, also ranging from 0 to 1, where 0 represents the pressure surface and 1 represents the suction surface. β represents the relative airflow angle at the blade passage exit.

[0050] Within the blade passage, a full-cycle trigonometric function profile is used to construct the circumferential control curve of the endwall to ensure a constant flow area within the blade passage. The expression is as follows:

[0051]

[0052] Non-axisymmetric endwalls accelerate flow and reduce local static pressure through convex configurations, and slow down flow and increase local static pressure through concave configurations, thereby weakening the lateral pressure gradient within the channel, suppressing the formation and development of secondary flows in the end region, and reducing turbulence intensity, such as... Figure 2 As shown.

[0053] Within the blade passage, from the leading edge to the trailing edge, the phase of the circumferential control curve changes nonlinearly with the normalized axial position. The expression for the phase coefficient λ(x) is as follows:

[0054]

[0055] Where β is the relative airflow angle at the blade passage exit, to achieve the control of the phase change of the axial control curve within the passage suitable for different blade configurations, such as... Figure 3 As shown.

[0056] Design amplitude A of non-axisymmetric end wall m Set to 3%~5% h 叶 ,h 叶 This represents the blade height.

[0057] Within the blade passage, from the leading edge to the trailing edge, the amplitude of the circumferential control curve is controlled by an amplitude control coefficient α(x) as the axial position changes. This amplitude control coefficient α(x) is constructed using a Bézier curve within the range [0,1]. The expression for the Bézier curve construction is as follows:

[0058]

[0059] Where B(z) is the amplitude of the constructed Bézier curve; z is the path parameter of the Bézier curve, ranging from 0 to 1; and n is the number of control points of the curve. P i The control points for the curve are set as shown in Table 1 below:

[0060] Table 1

[0061]

[0062] The Bézier curve, i.e., the curve showing the variation of the amplitude control coefficient α(x) within the blade passage, is obtained as follows: Figure 4 As shown.

[0063] This enabled the design of a non-axisymmetric endwall with nonlinear phase changes within the blade channel.

[0064] To provide a more intuitive understanding of the design method of this invention, a specific turbine example will be used as an example below.

[0065] The annular blade of a high-pressure turbine was selected as the design object. The configuration design was carried out according to the above-mentioned non-axisymmetric endwall design process. The control mechanism of the blade on the unsteady turbulent characteristics inside the turbine and the broadband random pressure fluctuation induced by turbulence on the blade surface was studied through numerical simulation.

[0066] The turbine blade height is h. 叶 =55mm, the relative airflow angle at the blade passage outlet is β=150°. Therefore, the design amplitude of the non-axisymmetric endwall is selected as A. m =2.5mm, phase change coefficient rate set to Generate a radial magnitude offset contour plot of the non-axisymmetric endwall (relative to the initial endwall) as follows: Figure 5 As shown.

[0067] like Figure 6 As shown, numerical simulations were performed on turbine blade passages with both initial and non-axisymmetric endwall configurations. The turbulent kinetic energy distribution and total pressure loss coefficient distribution at the blade passage exit section were compared to verify the effectiveness of the endwall design in controlling turbulent flow within the blade passage, while also considering its impact on turbine aerodynamic performance.

[0068] The circumferential distribution of turbulent kinetic energy at the blade passage exit section was calculated and compared as follows: Figure 7 As shown. Under the designed non-axisymmetric endwall configuration, at 40% h 叶 Below, the turbulent kinetic energy within the blade passage is effectively reduced. At 30% h 叶 At this location, the relative reduction rate of turbulent kinetic energy is up to about 20%. This indicates that the non-axisymmetric endwall configuration has a significant inhibitory effect on secondary flow and turbulent kinetic energy induced by flow separation over a large area within the channel.

[0069] The total pressure loss coefficient is used to reflect the aerodynamic performance of the turbine blade passage. The total pressure loss coefficient is defined as follows:

[0070]

[0071] in, P is the average total pressure at the blade passage inlet. * For the local total pressure, P is the average total pressure at the channel outlet. out The average static pressure at the blade channel outlet is given. The circumferential distribution of the total pressure loss coefficient at the blade channel outlet section is compared as follows: Figure 8 As shown. With the designed non-axisymmetric endwall configuration, at 25%–35% h 叶 Within the range, the total pressure loss coefficient is effectively reduced, with a relative reduction rate of up to about 5%, reflecting that this endwall configuration also has good optimization performance for turbine aerodynamic performance.

[0072] Furthermore, numerical calculations verified the control performance of this design for broadband random aerodynamic excitation induced by turbulence on the blade surface. By extracting the time-domain signal of the fluctuating pressure on the blade surface, the power spectral density (Φ) of the broadband random excitation was calculated. pp The power spectral density (PSD) of the extracted blade surface pulsating pressure is used to calculate the power spectral distribution over a wide frequency range. The expression is as follows:

[0073] PS=∫PSD df

[0074] The calculated power spectrum energy distribution of random pressure pulsations on the blade surface in the frequency range of 0–4 kHz is as follows: Figure 9 As shown. The PSD logarithmic spectrum of pressure pulsations at a point near the leaf root on the suction surface of the leaf is extracted, for example... Figure 10 As shown in the figure. The results show that the broadband random aerodynamic excitation induced by turbulence on the blade surface is significantly suppressed, and this non-axisymmetric endwall design achieves control of random pressure fluctuations over a large area and a wide frequency range on the blade surface.

[0075] Example 2

[0076] The present invention also provides a wideband aerodynamic excitation suppression system based on turbine endwall design, the system being used to implement any of the methods described above, the system comprising: a construction module and a generation module;

[0077] The construction module is used to construct the circumferential control curve of the endwall using a full-cycle trigonometric function profile within the blade passage; and to construct the axial control curve of the endwall using a Bézier curve.

[0078] The generation module is used to control the amplitude of the circumferential control curve at different axial positions using the axial control curve, and to adjust the phase of the circumferential control curve function according to the axial position to generate a non-axisymmetric end wall.

[0079] In this embodiment, the circumferential control curve of the end wall adopts a full-cycle sine function, the expression of which is:

[0080]

[0081] Where x is the normalized axial position within the blade passage, ranging from 0 to 1, where 0 represents the leading edge of the blade and 1 represents the trailing edge; t is the normalized circumferential position within the blade passage, ranging from 0 to 1, where 0 represents the pressure surface of the blade and 1 represents the suction surface; C r (t) represents the radial variation amplitude of the non-axisymmetric endwall relative to the initial endwall, C r (t)>0 indicates a bulge, C r (t)<0 indicates a depression; A m α(x) represents the design amplitude of the non-axisymmetric endwall, α(x) represents the amplitude coefficient for axial position control, and λ(x) represents the nonlinear phase coefficient for axial position control.

[0082] In this embodiment, the amplitude coefficient for axial position control is constructed using a Bézier curve, and its expression is:

[0083]

[0084] Where B(z) is the amplitude of the constructed Bézier curve, and z is the path parameter of the Bézier curve, with a value ranging from 0 to 1; P i Let n be the curve control points, and n be the number of curve control points.

[0085] In this embodiment, the nonlinear phase coefficient for axial position control is determined by the following expression:

[0086]

[0087] Wherein, β is the relative airflow angle at the blade passage outlet, which enables the regulation of the phase change of the axial control curve within the passage with different blade configurations.

[0088] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A broadband aero- excitation suppression method based on turbine endwall design, characterized in that, The method comprises: Within the blade passage, a full-period triangular function type line is used to construct a circumferential control curve of the end wall; a Bézier curve is used to construct an axial control curve of the end wall; An axial control curve is used to control the amplitude of the circumferential control curve at different axial positions, and the phase of the circumferential control curve function is adjusted according to the axial position, to generate a non-axially symmetric end wall; The circumferential control curve of the end wall adopts a full-period sine function, and the expression is: ； wherein, is the normalized axial position in the blade passage, with a value ranging from 0 to 1, 0 representing the leading edge of the blade and 1 representing the trailing edge of the blade; is the normalized circumferential position in the blade passage, with a value ranging from 0 to 1, 0 representing the pressure side of the blade and 1 representing the suction side of the blade; is the radial variation amplitude of the non-axisymmetric endwall with respect to the initial endwall, denotes a protrusion, denotes a recess; is the design amplitude of the non-axisymmetric endwall, is the amplitude coefficient of the axial position control; is the non-linear variation phase coefficient of the axial position control; The amplitude coefficient controlled by the axial position adopts a Bézier curve to construct, and the expression is: ； wherein, is the constructed Bézier curve amplitude, is the path parameter of the Bézier curve, and the value range is 0~1; is the curve control point, n is the number of curve control points; The determination of the nonlinearly changing phase coefficient controlled by the axial position is: ； wherein, is the relative flow angle at the outlet of the vane passage, enabling the adjustment of the phase of the axial control profile within the passage for different vane configurations.

2. A broadband aero- excitation suppression system based on a turbine endwall design, said system for implementing the method of claim 1, characterized in that, The system comprises a construction module and a generation module; The construction module is used to, within the blade passage, a full-period triangular function type line is used to construct a circumferential control curve of the end wall; a Bézier curve is used to construct an axial control curve of the end wall; The generation module is used to, an axial control curve is used to control the amplitude of the circumferential control curve at different axial positions, and the phase of the circumferential control curve function is adjusted according to the axial position, to generate a non-axially symmetric end wall; The circumferential control curve of the end wall adopts a full-period sine function, and the expression is: ； wherein, is the normalized axial position in the blade passage, with a value ranging from 0 to 1, 0 representing the leading edge of the blade and 1 representing the trailing edge of the blade; is the normalized circumferential position in the blade passage, with a value ranging from 0 to 1, 0 representing the pressure side of the blade and 1 representing the suction side of the blade; is the radial variation amplitude of the non-axisymmetric endwall with respect to the initial endwall, denotes a protrusion, denotes a recess; is the design amplitude of the non-axisymmetric endwall, is the amplitude coefficient of the axial position control; is the non-linear variation phase coefficient of the axial position control; The amplitude coefficient controlled by the axial position adopts a Bézier curve to construct, and the expression is: ； wherein, is the constructed Bézier curve amplitude, is the path parameter of the Bézier curve, and the value range is 0~1; is the curve control point, n is the number of curve control points; The determination of the nonlinearly changing phase coefficient controlled by the axial position is: ； wherein is the relative flow angle at the outlet of the vane passage, enabling the adjustment of the phase of the axial control profile within the passage for different vane configurations.

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