A quick judgment method for leakage instability flow in a tip region of a rotor blade of an impeller machine

Abstract

The application provides a quick judgment method for leakage unstable flow in a tip area of a rotor blade of an impeller machine, and the specific steps are as follows: step one: for a target rotor blade, a simulation model is established by using ICEM, autogrid or turbogrid modeling software; step two: vortex structures in a tip flow field are described by using a second invariant of a velocity gradient tensor and a dimensionless helicity; step three: the size of the tip vortex structure is calculated, and the size of a tip leakage vortex is quantified; and step four: after the size of the tip leakage vortex is obtained, the size is divided by a tip gap to obtain a dimensionless vortex size. The application does not need to carry out unsteady flow field calculation, and time cost is significantly saved. Compared with judging unstable flow phenomena by using a dimensionless tip gap, the consistency of the characteristic parameters obtained is obviously better, and the judgment accuracy of the dimensionless vortex size parameter given by the application is significantly improved compared with the dimensionless tip gap.

Description

Technical Field

[0001] This invention provides a method for rapid judgment of unstable flow with leakage in the tip region of turbomachinery rotor blades, which can realize the rapid judgment of unstable flow with leakage in the tip region of turbomachinery rotor blades, and belongs to the field of fluid machinery. Background Technology

[0002] Unstable flow phenomena such as tip leakage flow exist in turbomachinery. This unstable flow may narrow the compressor's stable operating margin, causing noise and even vibration problems, and in severe cases, even structural damage. Tip leakage flow, as an important flow phenomenon in turbomachinery flow fields, usually occurs under conditions of large tip clearance and small flow rate (left half of the characteristic curve).

[0003] Traditional methods for determining tip leakage in unstable flow rely heavily on simulations of unsteady flow fields, which are computationally intensive and time-consuming. Some researchers have used dimensionless tip clearance based on the tip chord length to determine the occurrence of unstable flow phenomena. While this has revealed tip leakage instability under large dimensionless tip clearances on the same model, it hasn't yielded a consistent dimensionless tip clearance for different models to determine unstable flow phenomena. In other words, the stability of tip leakage flow varies across different models under the same dimensionless tip clearance. The table below summarizes relevant data from some literature. It's understandable that dimensionless tip clearances cannot accurately determine unstable flow phenomena, as the parameters do not directly reflect relevant flow characteristics.

[0004] Table 1. Statistics on some domestic and international cases of unstable flow phenomena.

[0005]

[0006]

[0007] To address the above issues and accurately and quickly determine unsteady flow at the blade tip, the applicant has proposed a method for rapidly determining whether unsteady flow at the blade tip has occurred, based on the generation mechanism and motion characteristics of blade tip leakage flow. This method can provide criteria for unsteady flow phenomena based on steady flow field simulation, eliminating the need for unsteady flow field simulation and significantly saving time. Furthermore, because it considers both flow and structural influences, the consistency of the criteria given for different models is better than that for dimensionless blade tip clearance.

[0008] References

[0009] 1.Kielb,R.E.,Barter,J.W.,Thomas,J.P.,and Hall,K.C.,2003,“BladeExcitation by Aerodynamic Instabilities:A Compressor Blade Study,”ASME PaperNo.GT2003-38634.doi:10.1115 / GT2003-38634

[0010] 2.Mailach,R.,Lehmann,I.,and Vogeler,K.,2001,“Rotating Instabilitiesin an Axial Compressor Originating from the Fluctuating Blade Tip Vortex,”ASME J.Turbomach.,123(3),pp.453-463.doi:10.1115 / 1.1370160

[0011] 3.Maerz,J.,Hah,C.,and Neise,W.,2002,“An Experimental and NumericalInvestigation into the Mechanisms of Rotating Instabilities,”ASMEJ.Turbomach.,124(3),pp.367-375.doi:10.1115 / 1.1460915

[0012] 4.Du,J.,Lin,F.,Chen,J.,Nie,C.,and Biela,C.,2013,“Flow Structures inthe Tip Region for a Transonic Compressor Rotor,”ASME J.Turbomach.,135(3),p.031012.doi:10.1115 / 1.4006779

[0013] 5.Hah,C.,2017“Effects of Double-leakage Tip Clearance Flow on thePerformance of a Compressor Stage with a Large Rotor Tip Gap”ASMEJ.Turbomach.,139(6),p.061006.doi:10.1115 / 1.4035521

[0014] 6.Inoue,M.,Kuromaru,M.,Yoshida,S.,Minami,T.,Yamada,K.,and Furukawa,M.,2004,“Effects of Tip Clearance on Stall Evolution Process in a Low-SpeedAxial Compressor Stage,”ASME Paper No.GT2004-5335.doi:10.1115 / GT2004-53354

[0015] 7.Young,A.M.,Day,I.J.,and Pullan,G.,2013,“Stall Warning by BladePressure Signature Analysis,”ASME J.Turbomach.,135(1),p.011033.doi:10.1115 / 1.4006426

[0016] 8.Brandstetter,C.,Juengst,M.,and Schiffer,H.P.,2018,“Measurements ofRadial Vortices,Spill Forward,and Vortex Breakdown in a TransonicCompressor,”ASME J.Turbomach.,140(6),p.061004.doi:10.1115 / 1.4039053

[0017] 9. Du, J., Lin, F., Zhang, H., and Chen, J., 2010, "Numerical Investigation on the Self-induced Unsteadiness in Tip Leakage Flow for a Transonic Fan Rotor," ASME J. Turbomach., 132(2), p.021017.doi:10.1115 / 1.3145103 Summary of the Invention

[0018] The purpose of this invention is to provide a rapid method for judging unstable flow with leakage in the tip region of turbomachinery rotor blades. This method enables rapid judgment of unstable flow with leakage in the tip region of turbomachinery rotor blades. Based on engineering requirements, flow field results are obtained through steady flow field simulation. The method provided in this invention is then used to obtain criteria for unstable flow, thereby determining whether unstable flow phenomena will occur. This method can improve design evaluation efficiency and reduce computational resources.

[0019] This invention proposes a method for rapidly determining unstable flow with leakage in the tip region of impeller rotor blades, the specific steps of which are as follows:

[0020] Step 1: Establish a simulation model for the target rotor blade using modeling software such as ICEM, Autogrid, and Turbogrid. During modeling, it is recommended to ensure that the blade leading edge is 0.5 to 1.5 times the axial chord length from the computational domain inlet and the blade trailing edge is 1.5 to 3 times the axial chord length from the computational domain outlet. Considering the accuracy requirements for tip flow field identification, refine the mesh in the tip region, typically ensuring that the mesh scale in the mainstream region is no larger than 0.1 times the scale of the vortex of interest. Conduct steady flow field simulations, using numerical simulation to discretize and solve the Reynolds-averaged Navier-Stokes equations. Given inlet conditions, obtain the flow field characteristics under target speed and flow rate conditions by adjusting the outlet pressure conditions.

[0021] Step 2: Characterize the vortex structure in the tip flow field using the second-order invariant of the velocity gradient tensor (Equation 1) and the dimensionless helicity (Equation 2). Utilize the relationship between the vortex structure and the mainstream flow direction reflected by the dimensionless helicity to determine whether radial vortices exist in the flow field. A vortex structure refers to the rotation of the fluid around a point (vortex center), and is represented by the directional partial derivative of the velocity field function.

[0022]

[0023]

[0024] in,

[0025]

[0026] In Equation 1, U x U y and U z This represents the relative velocity component in the Cartesian coordinate system. Since the invariant Q does not change with the choice of coordinate system, the velocity component in the absolute coordinate system can also be chosen here. Furthermore, a dimensionless helicity is defined to characterize the relationship between the vortex direction and the direction of motion, thereby determining the vortex's rotation direction. In Equation 2, It is the gradient operator. and These represent the vortex vector and the relative velocity vector, respectively. The dimensionless helicity represents the cosine value of both. Therefore, Hn = 0 indicates that the vortex direction is perpendicular to the airflow direction; while |Hn| = 1 indicates that the tip leakage vortex direction is consistent with the velocity direction, and the position of |Hn| = 1 corresponds to the vortex center position. Viewed along the streamline direction, Hn = 1 and -1 represent the tip leakage vortices rotating clockwise and counterclockwise, respectively.

[0027] If radial vortices are absent, unstable flow phenomena such as tip leakage will not occur. If radial vortices are present, proceed with the following steps for further assessment.

[0028] Step 3: Calculate the dimensions of the blade tip vortex structure and quantify the size of the blade tip leakage vortex. The specific method is as follows:

[0029] During the fully developed stage of the tip leakage flow, a cross section perpendicular to the flow direction is taken (usually located at 30% to 35% of the chord length); the vortex core position is located by the dimensionless helicity characteristics or the local minimum values ​​of density and pressure; then, a local coordinate system is established based on the velocity conditions at the vortex core (Equation 3), and the velocity distribution relative to the vortex core within the cross section is given; from the velocity distribution characteristics of the vortex, it is known that the maximum value of the velocity of the vortex core outward along the radius represents the vortex size (the size accuracy here is directly related to the previous mesh resolution), and the tip leakage vortex size can be obtained through the velocity distribution.

[0030]

[0031] in,

[0032]

[0033]

[0034] in, and Let x′ and y′ be the basis vectors of the local coordinate system. and Directional coordinates It is the velocity vector in the rotating coordinate system, U tip It is the tangential velocity at the leaf tip, U′x and U′ y They are in the local coordinate system and Velocity in a certain direction.

[0035] The size of the tip leakage vortex corresponds to the location of the maximum tangential velocity.

[0036] R = R(U′) t，max (4)

[0037] Step 4: After obtaining the tip leakage vortex size, divide it by the tip clearance to obtain the dimensionless vortex size D. * Its expression is as follows:

[0038] D * =D / τ (4)

[0039] In the formula, D is the tip leakage vortex size, representing the flow field characteristics that cause tip leakage unsteady flow; is the tip clearance size; and τ represents the structural characteristics that cause tip leakage unsteady flow. This represents D. * The relationship between the above-mentioned flow field characteristics and structural characteristics. Dimensionless parameter D for different transonic compressor models. * After approximately less than 3, unstable flow phenomena begin to appear, using D... * The above-mentioned normalized characteristics of the parameters are used to determine the occurrence of tip leakage unsteady flow phenomena: if the obtained D * If the value is less than 3, then unstable flow is considered to occur; if the obtained D * If the value is greater than 3, it is considered that unstable flow will not occur.

[0040] Through the above steps, we can finally obtain the characteristic parameters of unsteady flow through steady simulation, and obtain consistent critical parameters on different models, thereby determining whether tip leakage unsteady flow phenomenon occurs.

[0041] The advantages of this invention are: it eliminates the need for unsteady flow field calculations, significantly saving time and costs. Compared to using dimensionless tip clearance as a parameter to determine unsteady flow phenomena, the consistency of the obtained characteristic parameters is significantly better, and the accuracy of the dimensionless vortex size parameter provided by this invention is significantly improved compared to dimensionless tip clearance. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method described in this invention.

[0043] Figure 2a The blade is shown as a three-dimensional geometric model in the embodiment.

[0044] Figure 2b The geometric model of the blade meridional plane is shown in the embodiment.

[0045] Figure 2c The blade mesh model is shown in the embodiment.

[0046] Figure 3a The pressure ratio characteristics of the blades in this example are shown.

[0047] Figure 3b The efficiency characteristics of the blades are shown in the example.

[0048] Figure 4a The present invention provides a method for characterizing the blade tip flow field structure.

[0049] Figure 4b This refers to the situation of fluid fluctuations.

[0050] Figure 5a The relationship between the cross-sectional position and the tip leakage vortex position is described for the vortex size.

[0051] Figure 5b The position of the local coordinate system at the leaf tip is established.

[0052] Figure 5c This represents the relative velocity distribution within the local coordinate system.

[0053] Figure 5d The size of the tip leakage vortex.

[0054] Figure 6 This invention presents the relationship between the dimensionless vortex size and the intensity of unsteady flow at the blade tip leakage.

[0055] The serial numbers, symbols, and codes in the diagram are explained as follows:

[0056] Hn represents the dimensionless helicity, C p U represents the pressure coefficient, U represents the velocity, and D represents the vortex size. * This represents the dimensionless vortex size. Detailed Implementation

[0057] The present invention will now be described in further detail with reference to the accompanying drawings and examples. The purpose of this invention is to provide a method for rapidly determining unstable flow leakage in the tip region of turbomachinery rotor blades. Based on engineering requirements, flow field results are obtained through steady flow field simulation. The method provided in this invention is then used to obtain criteria for unstable flow, thereby determining whether unstable flow phenomena will occur. This method can improve design evaluation efficiency and reduce computational resources.

[0058] This invention provides a method for rapidly identifying unstable flow with leakage in the tip region of impeller rotor blades, the process of which is as follows: Figure 1 As shown, the specific steps are as follows:

[0059] Step 1: Taking a transonic compressor rotor blade and the NASA Rotor 67 rotor blade as the research objects, a simulation model is established using modeling software such as ICEM, Autogrid, and Turbogrid. Figure 2a As shown, during the modeling process, the distance from the leading edge of the blade to the inlet of the computational domain is approximately 1.5 times the axial chord length, and the distance from the trailing edge of the blade to the outlet of the computational domain is approximately 2.5 times the axial chord length. Figure 2b To meet the accuracy requirements for blade tip flow field identification, the mesh in the blade tip region is refined. In this embodiment, the radial mesh size within the area affected by blade tip leakage flow is guaranteed to be no greater than 0.1 mm. The total number of meshes is approximately 2 million. Figure 2c Steady flow field calculations were performed under the desired rotational speed conditions by solving the Reynolds-averaged Navier-Stokes equations. The inlet was given total temperature, total pressure, and velocity direction conditions. The desired flow rate conditions were further obtained by adjusting the outlet back pressure. The residual was less than 10... -6 Alternatively, the calculation is considered convergent after parameters such as flow rate, pressure ratio, and pressure at the efficiency monitoring point stabilize. At this point, the flow field under the target speed and flow rate conditions is obtained, and the characteristics of the transonic compressor rotor blades are as follows: Figure 3a and Figure 3b As shown, OP1 to 8 are the working conditions of interest.

[0060] Step 2: Characterizing the vortex structure in the tip flow field using the second-order invariant of the velocity gradient tensor (Equation 1) and the dimensionless helicity (Equation 2). The vortex structure refers to the rotation of the fluid around a point (vortex center), represented by the directional partial derivative of the velocity field function. In Equation 1, the typical value of Q is between 0.05 and 0.2; in this embodiment, Q is set to 0.12 to achieve better display results. The results are as follows... Figure 4a and Figure 4b As shown, when there is no radial vortex in the flow field that starts from the tip leakage vortex and ends at the casing wall, it is assumed that the tip leakage flow will not be unstable; when there is a radial vortex in the flow field that starts from the tip leakage vortex and ends at the casing wall, i.e. in the region near Hn=0, step three is continued.

[0061] Step 3: As Figures 5a-5d As shown, the dimensions of the leakage vortex structure in the blade tip region are quantified. The specific method is as follows:

[0062] First, during the fully developed stage of the tip leakage flow, a cross-section perpendicular to the flow direction is selected (usually located at 30% to 35% of the chord length). In this embodiment, the cross-section is located at 35% of the chord length. Figure 5a );

[0063] Then, in this embodiment, the position of the vortex center is initially determined by the minimum density in the local area of ​​the blade tip, and then the accurate position of the vortex center is further determined by Hn = ±1. Figure 5b );

[0064] Next, a local coordinate system is established based on the velocity conditions at the vortex center (Equation 3), and the velocity distribution relative to the vortex center within the cross section is given. Figure 5c );

[0065] Finally, based on the velocity distribution characteristics of the vortex, the maximum velocity outward from the vortex center along the radius represents the vortex size. The tip leakage vortex size can be obtained through the velocity distribution. Figure 5d Considering the vortex structure deformation caused by the blades and casing wall, the vortex size is represented by twice the vortex radius in the negative y direction of the figure.

[0066] Step 4: From Equation 4, after obtaining the tip leakage vortex size D, divide it by the tip clearance τ to obtain the dimensionless vortex size D. * This represents the relationship between flow field characteristics and structural characteristics that cause unstable flow at the blade tip leakage. For example... Figure 6 As shown, in the two models of this invention, the dimensionless tip leakage vortex size with good consistency can be used to determine the occurrence of tip leakage unstable flow phenomenon: when the dimensionless tip leakage vortex size is less than 3, the tip leakage flow unstable flow phenomenon begins to appear, and the smaller the parameter, the more severe the tip leakage flow unstable flow.

Claims

1. A method for rapid judgment of unstable flow leakage in the tip region of impeller rotor blades, characterized in that: The specific steps are as follows: Step 1: For the target rotor blade, establish a simulation model using ICEM, AutoGrid, or TurboGrid modeling software. Step 2: Characterize the vortex structure in the tip flow field using the second-order invariant of the velocity gradient tensor and the dimensionless helicity; Step 3: Calculate the dimensions of the tip vortex structure and quantify the dimensions of the tip leakage vortex; Step 4: After obtaining the tip leakage vortex size, divide it by the tip clearance to obtain the dimensionless vortex size; In step three, the tip leakage vortex velocity distribution is as follows: (3) in, ； ； in, and These are the basis vectors of the local coordinate system. and In the local coordinate system and Directional coordinates It is the velocity vector in the rotating coordinate system. U tip It is the leaf tip tangential velocity. and They are in the local coordinate system and velocity in the direction; The size of the tip leakage vortex is: (4) In step four, the dimensionless vortex size is obtained by dividing the tip leakage vortex size by the tip clearance. The expression is as follows: ； In the formula, D is the tip leakage vortex size, representing the flow field characteristics that cause unstable flow at the tip leakage; is the tip clearance size. τ This indicates the structural features that cause unstable flow at the blade tip leakage; it represents The relationship between the above-mentioned flow field characteristics and structural characteristics.

2. The method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade according to claim 1, characterized in that: In step one, during the modeling process, ensure that the distance between the leading edge of the blade and the inlet of the computational domain is not less than 0.5 times the axial chord length, and the distance between the trailing edge of the blade and the outlet of the computational domain is not less than 1.5 times the axial chord length.

3. A method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade according to claim 1 or 2, characterized in that: In step one, the mesh in the tip region is refined to ensure that the mesh scale in the mainstream region is no greater than 0.1 times the scale of the vortex of interest. Steady flow field simulation is carried out, and the Reynolds-averaged Navier-Stokes equations are solved discretely using numerical simulation. Given the inlet conditions, the flow field characteristics under the target speed and flow rate conditions are obtained by adjusting the outlet pressure conditions.

4. The method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade according to claim 1, characterized in that: In step two, the relationship between the vortex structure and the mainstream flow direction reflected by the dimensionless helicity is used to determine whether radial vortices exist in the flow field; the vortex structure refers to the rotation of the fluid around a certain point, which is represented by the directional partial derivative of the velocity field function; (1) (2) in, ； In Equation 1, U x , U y and U z This represents the relative velocity components in the Cartesian coordinate system; a dimensionless helicity is defined to characterize the relationship between the vortex direction and the direction of motion, thereby determining the vortex's rotation direction; in Equation 2, It is the gradient operator. and These represent the vortex vector and the relative velocity vector, respectively, and the dimensionless helicity represents the cosine value of both.

5. A method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade as described in claim 1 or 4, characterized in that: In step two, Hn =0 indicates that the vortex direction is perpendicular to the airflow direction; while | Hn |=1 indicates that the direction of the tip leakage vortex is the same as the velocity direction. Hn The position where |=1 corresponds to the vortex center; looking along the streamline direction... Hn =1 and -1 represent tip leakage vortices rotating clockwise and counterclockwise, respectively; if there are no radial vortices, the unstable flow phenomenon of tip leakage will not occur; if there are radial vortices, further judgment is required.

6. The method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade according to claim 1, characterized in that: In step three, a cross section perpendicular to the flow direction is taken during the fully developed stage of the tip leakage flow. The vortex core position is located by the dimensionless helicity characteristics or the local minimum values ​​of density and pressure. Subsequently, a local coordinate system is established based on the velocity conditions at the vortex core to give the velocity distribution relative to the vortex core within the cross section. From the velocity distribution characteristics of the vortex, it is known that the maximum value of the velocity of the vortex core outward along the radius represents the vortex size. The tip leakage vortex size is obtained through the velocity distribution.

7. The method for rapid judgment of unstable flow leakage in the tip region of a turbomachinery rotor blade according to claim 1, characterized in that: In step four, the dimensionless parameters of different transonic compressor models When the value is less than 3, unstable flow phenomena begin to appear. The above-mentioned normalized characteristics of the parameters are used to determine the occurrence of tip leakage unsteady flow phenomena: if the obtained If the value is less than 3, it is considered that an unstable flow phenomenon will occur; if the obtained value is less than 3, it is considered that an unstable flow phenomenon will occur. If the value is greater than 3, it is considered that unstable flow will not occur.

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