A method for fast prediction and dynamic regulation of compressor flow field quality under low reynolds number

Abstract

This invention discloses a method for rapid prediction and dynamic control of compressor flow field quality at low Reynolds numbers. The method first obtains the pressure gradient parameters at the laminar separation point of the blade suction surface at different Reynolds numbers through high-precision performance testing / numerical calculation. K s Then establish them in sequence. K s With the incoming Reynolds number Re, the momentum-thickness Re at the separation point θs An empirical predictive model for blade surface separation scale and boundary layer development characteristics quantifies the impact of low Reynolds number effects on the separated bubble structure and boundary layer growth rate, thereby rapidly predicting the degree of compressor performance degradation at low Reynolds numbers. Based on the above model, parameters such as the excitation frequency of the blade leading-edge deformable surface are optimized to induce periodic pressure disturbance waves, achieving dynamic control of large-scale separated flow at low Reynolds numbers. This invention improves the prediction speed of compressor performance variations at low Reynolds numbers, providing support for the aerodynamic design and performance control of high-altitude compressors.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic thermodynamics of aero-engine compressors, and relates to large-scale separation and transition flow inside compressors at low Reynolds numbers. Specifically, it relates to a method for rapid prediction and dynamic control of compressor flow field quality at low Reynolds numbers, which is used to quickly assess the degree of change in compressor flow field quality at low Reynolds numbers, quantify the impact of low Reynolds number effects on compressor performance degradation, and provide a basis for compressor flow field control and performance improvement at low Reynolds numbers. Background Technology

[0002] Lightweight turbofan engines are the primary power source for high-altitude unmanned aerial vehicles (UAVs). To achieve higher thrust-to-weight ratios and propulsion efficiency, turbofan engines are increasingly employing larger bypass ratios, more compact core structures, smaller blade sizes, and rapidly decreasing compressor blade chord length and Reynolds number. Especially under the high altitude conditions of UAVs, the compressor inlet Reynolds number is further reduced to 10. 5 At high altitudes, the Reynolds number is approximately 1-2 orders of magnitude lower than on the ground. In this state, the low Reynolds number effect leads to a decrease in compressor pressure ratio, a decline in efficiency, and a sharp degradation in stability margin, which in turn severely impacts engine fuel consumption and operational stability. Therefore, to ensure stable engine operation during high-altitude cruise, it is crucial to clarify the internal flow variation mechanism of the compressor at low Reynolds numbers, establish a rapid prediction method for flow field quality, and subsequently develop efficient dynamic control strategies.

[0003] When the Reynolds number decreases to the critical value (10) 5 Near the Reynolds number, the laminar region on the compressor blades and their endwall surfaces expands rapidly. Under the influence of the adverse pressure gradient, the laminar boundary layer typically transitions to a turbulent state in the form of a separated bubble. When this separation transition occurs, local turbulent fluctuations accelerate, losses increase sharply, the boundary layer thickens rapidly, and significant three-dimensional turbulent mixing and blockage directly affect compressor efficiency and stable operating boundaries. Therefore, the separation transition process is the essential factor inducing the low Reynolds number effect in compressors. However, at low Reynolds numbers, the separation transition leads to more significant turbulent nonequilibrium / anisotropy in the local flow field. Traditional numerical calculations based on the Reynolds-averaged framework struggle to accurately predict the degree of performance variation at low Reynolds numbers. While high-precision calculation methods based on large eddy simulation or direct numerical simulation can provide relatively accurate predictions, their computational costs are extremely high, making large-scale batch calculations difficult and unable to meet the iterative flow field calculation requirements of the aerodynamic design phase. Furthermore, experimental measurements also suffer from problems such as long processing time and high cost. Moreover, the degree of compressor performance variation at low Reynolds numbers is highly sensitive to external disturbances; even minor errors during the experiment can cause the flow field to deviate significantly from the preset state, severely interfering with the quantification of compressor performance variation at low Reynolds numbers. Therefore, how to improve the timeliness of flow field prediction for low Reynolds number compressors while ensuring computational accuracy is one of the urgent technical challenges to be solved.

[0004] In terms of flow field control, conventional passive control methods (such as blade leading edge modification, load distribution optimization, and endwall non-axisymmetric design) have limited effectiveness in large-scale separated flows at low Reynolds numbers and cannot accommodate different operating conditions. While conventional active control technologies (such as synthetic jets and plasma excitation) have good potential for controlling large-scale separated flows, they generally suffer from inherent drawbacks such as complex auxiliary structures and high energy consumption, failing to meet the urgent need for compressor loss reduction and efficiency improvement at low Reynolds numbers.

[0005] Chinese invention patent application 202410458038.7 discloses a method for analyzing engine performance at high altitudes and low Reynolds numbers. This method, based on a zero-dimensional engine model and a three-dimensional simulation model, combined with design point information, performs parameter calculations and iterative updates for multiple rotating components (including axial compressors, turbines, etc.) to achieve engine performance evaluation under high-altitude, low Reynolds number conditions. However, this method mainly focuses on the overall engine performance evaluation and does not address laminar separation, transition processes, and turbulent non-equilibrium effects at low Reynolds numbers. Therefore, it is difficult to accurately reflect the underlying physical mechanisms of compressor performance degradation at low Reynolds numbers, and its practical application value is relatively limited.

[0006] In summary, the low Reynolds number effect has a significant impact on compressor performance. However, existing numerical simulation and measurement methods are unable to accurately predict complex flow phenomena such as separation and transition at low Reynolds numbers, and cannot accurately quantify the degree of compressor performance degradation at low Reynolds numbers. Traditional flow control methods generally suffer from problems such as complex structure, high energy consumption, and difficulty in balancing multiple operating conditions. Therefore, how to quickly predict the degree of change in compressor flow field quality at high altitudes and low Reynolds numbers, and on this basis, develop efficient dynamic control strategies, is a technical problem that urgently needs to be solved in the design of high-altitude light aero-engine compression systems. Summary of the Invention

[0007] (a) Purpose of the invention

[0008] To address the challenges of compressor performance prediction and efficient control at low Reynolds numbers, this invention focuses on the separation flow transition flow, a fundamental factor inducing low Reynolds number effects in compressors, and proposes a method based on the pressure gradient parameter at the laminar separation point. Ks The flow field quality prediction method with the core of the method enables rapid quantification of the performance degradation of the compressor at low Reynolds numbers. Based on the prediction results of the separation scale, key parameters such as the excitation frequency of the leading edge deformable surface are determined, forming a three-dimensional flow field dynamic control scheme for the compressor at low Reynolds numbers, which provides support for improving the aerodynamic characteristics of the compressor at high altitudes and low Reynolds numbers.

[0009] (II) Technical Solution

[0010] The purpose of this invention is to propose a rapid prediction method for compressor flow field quality at low Reynolds numbers. Based on this method, a control strategy based on the leading-edge deformable surface is developed to achieve efficient organization and performance improvement of the internal flow field of the compressor at low Reynolds numbers. The key to this invention lies in establishing a method based on the pressure gradient parameter at the laminar separation point. K s The core of this study is a separation scale prediction model and a leading-edge deformation surface control scheme. The main steps are as follows:

[0011] SS1. Acquisition of low Reynolds number flow field characteristic data:

[0012] Based on high-precision performance testing or numerical calculations, obtain flow field characteristic data of the compressor blade surface at different Reynolds numbers, including at least the pressure gradient parameters at the laminar separation point. K s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs Distance from the laminar flow separation point to the leading edge of the blade S sep Separation bubble length L bs Maximum thickness of the separation bubble Boundary layer displacement thickness at laminar separation point turbulent reattachment boundary layer momentum thickness i r and the boundary layer momentum thickness at the trailing edge of the blade i T ;

[0013] SS2. Establishing the Reynolds Number Re and K s Association model:

[0014] The least squares method was used to fit the results at different Reynolds numbers Re. K s Data, to establish a relationship model between the two. K s = f (Re) quantitatively describes the effect of Reynolds number variation on the pressure gradient at the laminar separation point;

[0015] SS3. Establish the boundary layer momentum thickness Reynolds number Re θs and K s Association model:

[0016] Based on the boundary layer momentum thickness and Reynolds number at the laminar separation point θs With pressure gradient parameters K s Empirical Relationship Establish Re at different Reynolds numbers θs andK s The association model, in which l θ These are the Polhausen parameters, and their specific values ​​are determined by least squares fitting.

[0017] SS4. Establish the geometric scale of the separated bubble and K s Association model:

[0018] Based on the length of the separated bubble L bs With boundary layer momentum thickness Reynolds number θs Empirical relationship between , and Re θs and K s Empirical relationship between Establish the separation bubble length respectively L bs Maximum thickness of the separation bubble and K s Association model:

[0019]

[0020] Among them, parameters C , D , a , b , A 1. B 1 and C The value of 1 was determined by least squares fitting;

[0021] SS5. Establish boundary layer development characteristics and Association model:

[0022] With the maximum thickness of the separation bubble The momentum thickness of the turbulent reattached boundary layer is established as the main characterizing variable. i r Boundary layer momentum thickness at the trailing edge of the blade i T With the maximum thickness of the separation bubble The correlation model is used to quantify the impact of blade surface separation scale on the growth rate and loss level of turbulent boundary layer:

[0023]

[0024]

[0025] in, C axFor the axial chord length of the blade, parameters A 2. B 2. C 2. A 3 and B 3 is an empirical coefficient, determined by least squares fitting;

[0026] SS6. Prediction of flow field quality changes and performance degradation at low Reynolds numbers:

[0027] Based on the correlation models established in steps SS2 to SS5, the Reynolds number Re of the operating condition to be predicted is input, and the pressure gradient parameters at the laminar separation point are calculated sequentially. K s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs Separation bubble length L bs and maximum thickness turbulent reattachment boundary layer momentum thickness i r Boundary layer momentum thickness at the trailing edge of the blade i T This enables rapid quantitative prediction of the separation scale and performance degradation of the blade surface.

[0028] The second objective of this invention is to provide a dynamic control method for large-scale separated flow on the surface of a compressor blade at low Reynolds numbers. This method involves setting a periodically vibrating deformable surface near the leading edge of the compressor blade. The periodic vibration of this deformable surface induces pressure disturbance waves to influence the downstream boundary layer velocity profile distribution, thereby achieving dynamic control of the separated flow characteristics on the surface of the compressor blade at low Reynolds numbers. The dynamic control method, when implemented, includes at least the following steps:

[0029] SS1. Design and Layout of Deformable Surfaces

[0030] A deformable surface is provided near the leading edge of the compressor blade. This deformable surface undergoes sinusoidal periodic vibration along the normal direction of the wall surface, and its vibration amplitude... A The excitation frequency is on the same order of magnitude as the local boundary layer thickness. f Based on the length of the separated bubble L bs and the propagation speed of leading edge disturbances V 1. It should be determined that, at least at any given time, there should be a pressure disturbance wave induced by the deformation surface inside the separated shear layer in order to achieve the best control effect;

[0031] SS2. Dynamic optimization of excitation frequency of deformable surface

[0032] Based on the rapid prediction method for compressor flow field quality at low Reynolds numbers described above in this invention, the distance from the laminar separation point to the leading edge of the blade under the current operating condition is obtained. Ssep and separation bubble length L bs Combined with the propagation speed of the leading edge disturbance V 1 and induced vortex transport velocity in large-scale separation regions V 2 Dynamically optimize the excitation frequency of the deformable surface f satisfy:

[0033]

[0034] This allows pressure disturbance waves to continuously act on the separating shear layer, thereby suppressing large-scale separation flow;

[0035] SS3. Performance Feedback and Adjustment of Dynamic Control Effects

[0036] Based on the aforementioned method for rapid prediction of compressor flow field quality at low Reynolds numbers, the flow field characteristics on the compressor blade surface can be rapidly predicted, including at least the distance from the laminar separation point to the blade leading edge. S sep Separation bubble length L bs Maximum thickness of the separation bubble turbulent reattachment boundary layer momentum thickness i r and the boundary layer momentum thickness at the trailing edge of the blade i T The effect of real-time feedback on the vibration parameter adjustment of the deformable surface: when the separation bubble length L bs When the frequency is increased, the excitation frequency is increased. f To accelerate the propagation of disturbances; when the separation bubble reaches its maximum thickness When the amplitude increases, the amplitude increases. A To enhance the disturbance intensity; by dynamically adjusting the excitation frequency f and amplitude A To optimize the intensity of pressure disturbance waves, and ultimately achieve continuous and efficient suppression of large-scale separation flow under extreme conditions.

[0037] (III) Technical Effects

[0038] Compared with the prior art, the method for rapid prediction and dynamic control of compressor flow field quality at low Reynolds numbers of the present invention has the following beneficial and significant technical effects:

[0039] (1) The rapid prediction method for compressor flow field quality at low Reynolds numbers proposed in this invention has clear physical meaning and can quickly guide the design of control schemes. Pressure gradient parameters at the laminar separation point. K sIt is the fundamental factor determining the separation bubble structure, boundary layer growth rate, and overall loss / performance variation. Based on the above physical essence, this invention constructs a system... K s Establish a separate scaling prediction model for the core variables. K s With the incoming Reynolds number Re, the momentum-thickness Re at the separation point θs The quantitative relationship between blade surface separation scale and boundary layer development characteristics enables rapid quantification of the degree of compressor performance degradation at low Reynolds numbers, providing a direct theoretical basis for flow field control at low Reynolds numbers.

[0040] (2) Starting from the separation scale prediction model under low Reynolds number, this invention proposes an efficient flow field control method based on a dynamic deformation surface at the leading edge. By establishing a minimum excitation frequency criterion, it ensures that pressure disturbance waves can continuously act on the separation shear layer. The periodic vibration of the deformation surface along the local normal generates pressure disturbance waves, making the boundary layer velocity profile fuller and significantly enhancing the resistance to adverse pressure gradients, thereby suppressing large-scale separation. In addition, the deformation surface can also take into account the control effects under different operating conditions, and has significant advantages in reducing flow field loss and improving efficiency in a wide spatial range. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the implementation of the rapid prediction method for compressor flow field quality at low Reynolds numbers according to the present invention.

[0042] Figure 2 A schematic diagram of the relationship between momentum-thickness Reynolds number and pressure gradient parameters at the laminar separation point;

[0043] Figure 3 A schematic diagram of the correlation model between the separation bubble length and the pressure gradient parameter at the laminar separation point;

[0044] Figure 4 This is a schematic diagram of the correlation model between the separation bubble thickness and the pressure gradient parameter at the laminar separation point;

[0045] Figure 5 The trailing boundary layer momentum thickness i T With the maximum thickness of the separation bubble d B Schematic diagram of the association model;

[0046] Figure 6 This is a schematic diagram of the leading edge dynamic deformation surface control of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are some, but not all, embodiments of this invention, and are exemplary and intended to explain the invention, not to limit it. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0048] Example 1: Fast Prediction Method

[0049] To address the challenges of compressor performance prediction and efficient control at low Reynolds numbers, this invention focuses on the separation flow transition flow, a fundamental factor inducing low Reynolds number effects in compressors, and proposes a method based on the pressure gradient parameter at the laminar separation point. Ks The flow field quality prediction method with the core of the method enables rapid quantification of the performance degradation of the compressor at low Reynolds numbers. Based on the prediction results of the separation scale, key parameters such as the excitation frequency of the leading edge deformable surface are determined, forming a three-dimensional flow field dynamic control scheme for the compressor at low Reynolds numbers, which provides support for improving the aerodynamic characteristics of the compressor at high altitudes and low Reynolds numbers.

[0050] The present invention proposes a rapid prediction method for compressor flow field quality at low Reynolds numbers. This method is used to rapidly predict compressor flow field quality under low Reynolds number conditions, quantify the impact of low Reynolds number effects on compressor performance degradation, and provide a theoretical basis for the dynamic control of the compressor. Figure 1 As shown, the main steps are as follows:

[0051] SS1. Acquisition of low Reynolds number flow field characteristic data:

[0052] Based on high-precision performance testing or numerical calculations, obtain flow field characteristic data of the compressor blade surface at different Reynolds numbers, including at least the pressure gradient parameters at the laminar separation point. K s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs Distance from the laminar separation point to the leading edge of the blade S sep Separation bubble length L bs Maximum thickness of the separation bubble Boundary layer displacement thickness at laminar separation point turbulent reattachment boundary layer momentum thickness i r and the boundary layer momentum thickness at the trailing edge of the blade i T wait.

[0053] As a preferred option, high-precision performance testing can be performed by measuring the load distribution and boundary layer velocity profile on the compressor blade surface through wall static pressure holes, hot-wire anemometers, laser Doppler velocimeters, or particle image velocimeters to obtain the pressure gradient parameters and boundary layer integral parameters at the laminar separation point on the compressor blade surface.

[0054] Numerical calculations can be performed using Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS) methods. By setting different inlet and outlet conditions to change the incoming Reynolds number, high-precision numerical analysis of the compressor flow field can be conducted, with the near-wall mesh scale satisfying the following requirements. y + <1, the time step advance satisfies the CFL number being less than 1, in order to capture highly unsteady flow characteristics such as separation and transition under low Reynolds number conditions, and obtain pressure gradient parameters, boundary layer parameters and separation bubble structure information at the laminar separation point on the compressor blade surface.

[0055] In this embodiment of the invention, the pressure gradient parameter at the laminar flow separation point K s The strength of the pressure gradient at the separation point is used to characterize the perturbation amplification rate and transition trigger position in the separation shear layer, thus affecting the separation scale and loss level. The algorithm formula is as follows: ,in v The coefficient of kinematic viscosity, U The flow velocity on the blade surface. x The coordinates represent the flow direction of the blades. dU / dx The flow velocity gradient on the blade surface; by obtaining the flow velocity distribution on the blade surface. U ( x ), using numerical difference method to calculate K s .

[0056] In this embodiment of the invention, the boundary layer momentum thickness Reynolds number Re θs The acquisition and calculation include: obtaining the boundary layer velocity profile at the laminar separation point on the compressor blade surface through high-precision performance testing or numerical calculation, based on algorithm formulas. Integral calculation of boundary layer momentum thickness θs ,in U The flow velocity on the blade surface. The mainstream velocity at the laminar flow separation point. As the mainstream density, d For boundary layer thickness, n The coordinates are the wall normal coordinates; then, based on the obtained boundary layer momentum thickness... θs Calculate the momentum thickness Reynolds number .

[0057] SS2. Establish Reynolds number Re andK s Association model:

[0058] Based on the obtained pressure gradient parameters at the laminar separation point on the blade surface under different Reynolds numbers Re K s Data, using the least squares method to establish different Reynolds numbers K s Correlation model with Reynolds number K s = f (Re).

[0059] As a preferred option, pressure gradient parameters are established. K s Relationship model with Reynolds number Re K s = f (Re) includes: First, sequentially obtaining the pressure gradient parameters at the laminar separation point under different Reynolds numbers Re. K s Then, a nonlinear least squares regression method was used to fit the data. K s The functional relationship between Re and the model is determined, and cross-validation is used during the fitting process to evaluate the model's generalization ability and optimize the fitting parameters.

[0060] SS3. Establish the boundary layer momentum thickness Reynolds number Re θs and K s Association model:

[0061] Based on Polhausen parameters l θ ,Establish K s The boundary layer momentum thickness Re at the laminar separation point θs The empirical formula is then used. Similarly, the least squares method is employed to determine... l θ Specific numerical values.

[0062]

[0063] Specifically, based on the boundary layer momentum thickness Reynolds number at the laminar separation point... θs With pressure gradient parameters K s Empirical Relationship Establish Re at different Reynolds numbers θs and K s The association model, in which l θThese are the Polhausen parameters, and their specific values ​​are determined by least squares fitting.

[0064] As a preferred option l θ The specific values ​​are determined through the following steps: First, obtain the boundary layer momentum thickness and Reynolds number Re at the laminar separation point under different Reynolds numbers. θs and pressure gradient parameters K s Then, the Polhausen parameters under different Reynolds numbers were determined using the least squares method. Thus, Re is obtained. θs and K s The relationship model between K s = f (Re θs ).

[0065] SS4. Establish the geometric scale of the separated bubble and K s Association model:

[0066] The structure of the separated bubble (length and thickness) has a decisive influence on the boundary layer growth rate and loss level at low Reynolds numbers, and is also a direct representation of the degree of performance variation / degradation at low Reynolds numbers. Separated bubble length L bs With Re θs The following empirical relation is satisfied:

[0067]

[0068] In the above formula, S sep This represents the distance from the leading edge of the blade to the laminar separation point. Parameters are determined using the least squares method. C , D Then, further deductions were made. L bs and K s The association model is, in other words:

[0069]

[0070] by L bs / S sep Using this as an intermediate variable, the maximum relative thickness of the separation bubble can be obtained. and K s The association model. Among them, The boundary layer displacement thickness at the laminar separation point.

[0071]

[0072]

[0073] By following the steps above, a mathematical model of the separation scale (separation bubble length + thickness) on the blade surface can be completed at different Reynolds numbers.

[0074] As a preferred option, the geometric scale of the separation bubble and K s The parameters in the correlation model are determined through the following steps: First, obtain the pressure gradient parameters at the laminar separation point under different low Reynolds number conditions. K s Boundary layer momentum thickness Reynolds number θs Distance from the laminar separation point to the leading edge of the blade S sep Separation bubble length L bs Maximum thickness of the separation bubble Boundary layer displacement thickness Secondly, based on the algorithm formula , , The parameters were determined by fitting the data using the least squares method. C , D , a , b , A 1. B 1 and C The specific value of 1.

[0075] SS5. Establish boundary layer development characteristics and Association model:

[0076] To characterize the impact of blade surface separation scale on loss / performance, the momentum thickness of the turbulent reattachment boundary layer is then established. i r and boundary layer momentum thickness at the trailing edge i T With the maximum thickness of the separation bubble The empirical prediction model is as follows:

[0077]

[0078]

[0079] Maximum thickness of separation bubble It directly determines the growth rate of the turbulent boundary layer. The larger the bubble, the faster the turbulent boundary layer grows downstream of the separation bubble. i r and i T Rapidly increasing momentum induces severe flow blockage and wake mixing, deteriorating blade aerodynamic performance. Preferably, the boundary layer momentum thickness at the turbulent reattachment point... i r Boundary layer momentum thickness at the trailing edge of the blade i T With the maximum thickness of the separation bubble In the correlation model, the empirical coefficients are determined through the following steps: First, the momentum thickness of the turbulent reattachment boundary layer under different low Reynolds number conditions is obtained. i r Boundary layer momentum thickness at the trailing edge of the blade i T Maximum thickness of the separation bubble Secondly, empirical coefficients are determined by fitting the data using the least squares method. A 2. B 2. C 2. A 3 and B The specific value of 3.

[0080] SS6. Prediction of flow field quality changes and performance degradation at low Reynolds numbers:

[0081] Based on the correlation models established in steps SS2 to SS5, the Reynolds number Re of the operating condition to be predicted is input, and the pressure gradient parameters at the laminar separation point are calculated sequentially. K s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs Separation bubble length L bs and maximum thickness turbulent reattachment boundary layer momentum thickness i r Boundary layer momentum thickness at the trailing edge of the blade i T This enables rapid quantitative prediction of the separation scale and performance degradation of the blade surface.

[0082] As a preferred option, the separation bubble length at different Reynolds numbers obtained based on the correlation model... L bs and maximum thickness Quantifying the variability of internal flow blockage in compressors at low Reynolds numbers; obtaining the turbulent reattachment boundary layer momentum thickness based on a correlation model. i r Boundary layer momentum thickness at the trailing edge of the blade i TThis study quantifies the variability of three-dimensional mixing losses in compressors at low Reynolds numbers, thereby assessing the impact of low Reynolds number effects on compressor efficiency and stability boundaries, and providing theoretical support for compressor flow control and performance improvement at low Reynolds numbers.

[0083] Example 2: Dynamic Control Method

[0084] As described in Embodiment 1 above, the present invention is based on the pressure gradient parameter at the laminar separation point. K s A rapid prediction method for compressor flow field quality at low Reynolds numbers was constructed, enabling quantitative characterization of the separated bubble structure and boundary layer growth rate, and quantifying the impact of low Reynolds number effects on compressor performance degradation. Building upon this, to further improve the aerodynamic performance of compressors at low Reynolds numbers, Example 2 proposes a dynamic control method based on a leading-edge deformable surface. By setting a periodically vibrating deformable surface at the blade leading edge, pressure disturbance waves are induced to influence the downstream boundary layer velocity profile distribution, enhancing the ability to resist adverse pressure gradients. This effectively eliminates large-scale flow separation within the compressor at low Reynolds numbers, achieving reduced losses and increased efficiency.

[0085] Specifically, since the separation scale determines the loss level at low Reynolds numbers, it is also the main target and objective of flow control. Introducing a periodically vibrating deformable surface near the leading edge, which induces pressure disturbance waves to influence the velocity profile distribution of the downstream boundary layer, is expected to improve the separation scale and loss level. For the deformable surface, the excitation frequency is a key factor affecting the separation control effect. Under ideal control conditions, pressure disturbance waves must be continuously felt in the separated shear layer at any given time. Therefore, the excitation frequency of the leading edge deformable surface should satisfy:

[0086]

[0087] in, V 1 and V 2 These are the leading-edge disturbance propagation velocity and the induced vortex transport velocity in the large-scale separation region, respectively. Generally speaking, The aforementioned separation scale prediction model can quickly determine the excitation frequency of the deformable surface, the most critical parameter in the dynamic control scheme of the flow field, providing fundamental support for achieving efficient flow field organization and loss reduction and efficiency improvement at low Reynolds numbers.

[0088] More specifically, the dynamic control method for large-scale separated flow on the surface of compressor blades at low Reynolds numbers provided in this embodiment includes at least the following steps in its implementation:

[0089] SS1. Design and Layout of Deformable Surfaces

[0090] A deformable surface is provided near the leading edge of the compressor blade. This deformable surface undergoes sinusoidal periodic vibration along the normal direction of the wall surface, and its vibration amplitude... A The excitation frequency is on the same order of magnitude as the local boundary layer thickness. f Based on the length of the separated bubble L bs and the propagation speed of leading edge disturbances V 1. It should be determined that, at least at any given time, there should be a pressure disturbance wave induced by the deformation surface inside the separated shear layer in order to achieve the best control effect;

[0091] SS2. Dynamic optimization of excitation frequency of deformable surface

[0092] Based on the rapid prediction method for compressor flow field quality at low Reynolds numbers described above in this invention, the distance from the laminar separation point to the leading edge of the blade under the current operating condition is obtained. S sep and separation bubble length L bs Combined with the propagation speed of the leading edge disturbance V 1 and induced vortex transport velocity in large-scale separation regions V 2 Dynamically optimize the excitation frequency of the deformable surface f satisfy:

[0093]

[0094] This allows pressure disturbance waves to continuously act on the separating shear layer, thereby suppressing large-scale separation flow;

[0095] SS3. Performance Feedback and Adjustment of Dynamic Control Effects

[0096] Based on the above-described rapid prediction method for compressor flow field quality at low Reynolds numbers according to the present invention, the flow field characteristics on the compressor blade surface can be rapidly predicted, including at least the distance from the laminar separation point to the leading edge of the blade. S sep Separation bubble length L bs Maximum thickness of the separation bubble turbulent reattachment boundary layer momentum thickness i r and the boundary layer momentum thickness at the trailing edge of the blade i T The effect of real-time feedback on the vibration parameter adjustment of the deformable surface: when the separation bubble length L bs When the frequency is increased, the excitation frequency is increased. f To accelerate the propagation of disturbances; when the separation bubble reaches its maximum thickness When the amplitude increases, the amplitude increases. A To enhance the disturbance intensity; by dynamically adjusting the excitation frequencyf and amplitude A To optimize the intensity of pressure disturbance waves, and ultimately achieve continuous and efficient suppression of large-scale separation flow under extreme conditions.

[0097] Example 3: Application Case

[0098] Taking a high-subsonic compressor blade as an example, at a low Reynolds number of 1.5 × 10⁻⁶... 5 ~4.5×10 5 Separation scale prediction and efficient regulation can be carried out within the specified range. Figure 2 The momentum thickness and Reynolds number at the laminar separation point of the blade suction surface are given under different operating conditions. With pressure gradient parameters K s The correlation model. At this point, the Polhausen parameters... Take -0.093. When the Reynolds number is 4.5 × 10⁻⁶... 5 Reduced to 1.5×10 5 hour, K s The absolute value increased by 2.1 times.

[0099] Figure 3-Figure 4 The separation scale (separation bubble length) of the blade surface is given under different Reynolds number conditions. L bs and maximum thickness )and K s The association model was determined based on the least squares method. Model parameters a =13972.6, b =0.716. Compared to a Reynolds number of 4.5 × 10⁻⁶. 5 Operating condition, Reynolds number 1.5 × 10⁻⁶ 5 The separation bubble length increased by 122%, and the maximum thickness increased by 147%. These results indicate that the laminar separation point does not change significantly with decreasing Reynolds number. S sep Approximately 30% of the axial chord length), but the adverse pressure gradient is enhanced at the laminar separation point ( K s The increase in absolute value leads to a sharp increase in both the length and maximum thickness of the separation bubble.

[0100] As the Reynolds number decreases, the separation bubble on the blade surface grows rapidly, and the eddy dynamics and turbulent mixing in the separation shear layer are enhanced, which has a more significant impact on the boundary layer growth rate and loss level. Figure 5 The momentum thickness of the trailing boundary layer on the suction surface of the blade is given under different operating conditions. With the maximum thickness of the separation bubble The association model. As can be seen, Almost Linear growth. When the Reynolds number increases from 4.5 × 10⁻⁶. 5 Reduced to 1.5×10 5 hour, An increase of 185% corresponds to a 241% increase in airfoil loss, resulting in a sharp performance decline. Therefore, the size of the separation bubble (length and maximum thickness) can serve as a direct representation of the degree of performance variation / degradation at low Reynolds numbers. The above process quantifies the impact of low Reynolds number effects on the separation bubble structure and boundary layer growth rate, enabling rapid prediction of the degree of compressor performance degradation at low Reynolds numbers.

[0101] Figure 6 A schematic diagram of the dynamic deformation surface control at the leading edge under low Reynolds numbers is presented. Near the leading edge, the deformation surface undergoes sinusoidal periodic vibration along the wall normal. A The amplitude is typically on the same order of magnitude as the local boundary layer thickness. f The vibration frequency is given. By combining this with the proposed separation zone scale prediction model, the excitation frequency of the leading-edge dynamic deformation surface can be obtained, thus completing the design of the control scheme. Within one vibration cycle, when the surface bulges, the airflow accelerates, forming a transient low-pressure zone; when the surface contracts, the airflow decelerates, resulting in a transient high-pressure zone. Therefore, pressure disturbance waves are periodically generated downstream of the dynamic deformation surface. These pressure disturbance waves travel at a velocity... V 1. Propagation downstream makes the local boundary layer velocity profile more complete, significantly enhancing its ability to resist adverse pressure gradients, thereby achieving efficient control of large-scale separated flows. Furthermore, it should be noted that when the excitation source on the deformable surface is removed, the flow field automatically transitions to an uncontrolled state. Therefore, this dynamic control scheme can take into account the control effects under different operating conditions, demonstrating significant advantages in reducing flow loss and improving efficiency over a wide spatial range.

[0102] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. A method for rapid prediction of compressor flow field quality at low Reynolds numbers, characterized in that, include: SS1. Based on high-precision performance testing or numerical calculation, obtain flow field characteristic data of the compressor blade surface at different Reynolds numbers, including at least the pressure gradient parameter K at the laminar separation point. s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs The distance S from the laminar flow separation point to the leading edge of the blade sep Separation bubble length L bs Maximum thickness of the separation bubble Boundary layer displacement thickness at laminar separation point Turbulent reattachment boundary layer momentum thickness θ r and the boundary layer momentum thickness θ at the trailing edge of the blade T ; SS2. Fitting K under different Reynolds numbers Re using the least squares method. s Data, establish a correlation model K between the two s =f(Re), which quantitatively describes the effect of Reynolds number variation on the pressure gradient at the laminar separation point; SS3. Based on the boundary layer momentum thickness and Reynolds number at the laminar separation point θs With pressure gradient parameter K s Empirical Relationship Establish Re at different Reynolds numbers θs With K s The association model, where λ θ These are the Polhausen parameters, and their specific values ​​are determined by least squares fitting. SS4. Based on the separation bubble length L bs With boundary layer momentum thickness Reynolds number θs Empirical relationship between and Re θs With K s Empirical relationship between Establish the separation bubble length L respectively bs Maximum thickness of the separation bubble With K s Association model: The values ​​of parameters C, D, a, b, A1, B1, and C1 are determined by least squares fitting. SS5. Based on the maximum thickness of the separated bubble Using θ as the primary characterization variable, the momentum thickness θ of the turbulent reattached boundary layer is established. r and the boundary layer momentum thickness θ at the trailing edge of the blade T and Association model: Among them, C ax The axial chord length of the blade is given by parameters A2, B2, C2, A3, and B3, which are empirical coefficients and determined by least squares fitting. SS6. Based on the correlation models established in steps SS2 to SS5, input the Reynolds number Re for the operating condition to be predicted, and calculate the pressure gradient parameter K at the laminar separation point in sequence. s Boundary layer momentum thickness and Reynolds number at the laminar separation point θs Separation bubble length L bs and maximum thickness Turbulent reattachment boundary layer momentum thickness θ r and the boundary layer momentum thickness θ at the trailing edge of the blade T This enables rapid quantitative prediction of the surface separation scale and performance degradation of compressor blades.

2. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS1 above, the high-precision performance test measures the load distribution and boundary layer velocity profile on the compressor blade surface using a wall static pressure hole, hot-wire anemometer, laser Doppler velocimeter, or particle image velocimetry to obtain the pressure gradient parameters and boundary layer integral parameters at the laminar separation point on the compressor blade surface. The numerical calculation employs large eddy simulation or direct numerical simulation methods, changing the incoming Reynolds number by setting different inlet and outlet conditions to perform high-precision numerical analysis of the compressor flow field. The near-wall mesh scale satisfies y + <1, the time step advance satisfies the CFL number being less than 1, in order to capture the unsteady flow characteristics of separation and transition height under low Reynolds number conditions, and obtain the pressure gradient parameters, boundary layer parameters and separation bubble structure information at the laminar separation point on the compressor blade surface.

3. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS1 above, the pressure gradient parameter K at the laminar separation point... s The algorithm formula is used to characterize the strength of the flow-direction pressure gradient at that location. Where v is the kinematic viscosity coefficient, U is the flow velocity on the blade surface, x is the flow coordinate position of the blade, and dU / dx is the flow velocity gradient on the blade surface; by obtaining the flow velocity distribution U(x) on the blade surface, the pressure gradient parameter K is calculated using the numerical difference method. s .

4. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 3, characterized in that, In step SS1 above, the boundary layer momentum thickness Reynolds number Re θs The acquisition and calculation include: firstly, obtaining the boundary layer velocity profile at the laminar separation point on the compressor blade surface through high-precision performance testing or numerical calculation, based on the algorithm formula. Integral calculation of boundary layer momentum thickness θ s Where U is the flow velocity on the blade surface, U ∞ ρ is the mainstream velocity at the laminar separation point. ∞ The mainstream density is given by δ, the boundary layer thickness is given by δ, and the normal coordinate of the wall is given by n. Then, the momentum-thickness Reynolds number is calculated based on the obtained boundary layer momentum thickness θs.

5. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS2 above, the pressure gradient parameter K is established. s K-related model with Reynolds number Re s When f(Re) is equal to the value of Re, the following steps are taken: First, the pressure gradient parameter K at the laminar separation point is obtained sequentially under different Reynolds numbers Re. s Then, a nonlinear least squares regression method was used to fit K. s The functional relationship between Re and the model is determined, and cross-validation is used during the fitting process to evaluate the model's generalization ability and optimize the fitting parameters.

6. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS3 above, the Polhausen parameter λ θ The specific values ​​are determined through the following steps: First, obtain the boundary layer momentum thickness and Reynolds number Re at the laminar separation point under different Reynolds numbers. θs and pressure gradient parameter K s Then, the Polhausen parameters under different Reynolds numbers were determined using the least squares method. Therefore, Re is obtained. θs and K s The correlation model K between them s =f(Re θs ).

7. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS4 above, the separation bubble geometry and K s The parameters in the correlation model are determined through the following steps: First, obtain the pressure gradient parameter K at the laminar separation point under different Reynolds number conditions. s Boundary layer momentum thickness Reynolds number θs The distance S from the laminar flow separation point to the leading edge of the blade sep Separation bubble length L bs Maximum thickness of the separation bubble Boundary layer displacement thickness Secondly, based on algorithm formula The specific values ​​of parameters C, D, a, b, A1, B1, and C1 are determined by fitting the data using the least squares method.

8. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS5 above, the turbulent reattachment point boundary layer momentum thickness θ r and the boundary layer momentum thickness θ at the trailing edge of the blade T With the maximum thickness of the separation bubble In the correlation model, the empirical coefficients are determined through the following steps: First, obtain the momentum thickness θ of the turbulent reattachment boundary layer under different Reynolds number conditions. r θ, the boundary layer momentum thickness at the trailing edge of the blade T Maximum thickness of the separation bubble Secondly, the specific values ​​of the empirical coefficients A2, B2, C2, A3 and B3 are determined by fitting the data using the least squares method.

9. The method for rapid prediction of compressor flow field quality at low Reynolds numbers according to claim 1, characterized in that, In step SS6 above, the separation bubble length L at different Reynolds numbers is obtained based on the correlation model. bs and maximum thickness Quantifying the degree of variability in internal flow blockage of compressors at low Reynolds numbers; The turbulent reattached boundary layer momentum thickness θ is obtained based on the correlation model. r and the boundary layer momentum thickness θ at the trailing edge of the blade T This study quantifies the variability of three-dimensional mixing losses in compressors at low Reynolds numbers, thereby assessing the impact of low Reynolds number effects on compressor efficiency and stability boundaries, and providing theoretical support for compressor flow control and performance improvement at low Reynolds numbers.

10. A dynamic control method for large-scale separated flow on the surface of a compressor blade at low Reynolds numbers, characterized in that, The dynamic control method, when implemented, includes at least the following steps: SS1. Design and Layout of Deformable Surfaces A deformable surface is provided near the leading edge of the compressor blade. This deformable surface undergoes sinusoidal periodic vibration along the normal direction of the wall surface. The vibration amplitude A is on the same order of magnitude as the local boundary layer thickness, and the excitation frequency f is based on the separation bubble length L. bs Given the propagation velocity V1 of the leading edge disturbance, it should be ensured that there is a pressure disturbance wave induced by the deformation surface inside the separated shear layer at any time to achieve the best control effect. SS2. Dynamic optimization of excitation frequency of deformable surface Based on the rapid prediction method for compressor flow field quality at low Reynolds numbers as described in any one of claims 1 to 9, the distance S from the laminar separation point to the leading edge of the blade under the current operating condition is obtained. sep and separation bubble length L bs Combining the leading-edge disturbance propagation velocity V1 and the induced vortex transport velocity V2 in the large-scale separation region, the excitation frequency f is dynamically optimized to satisfy: This allows pressure disturbance waves to continuously act on the separating shear layer, thereby suppressing large-scale separation flow; SS3. Performance Feedback and Adjustment of Dynamic Control Effects Based on the rapid prediction method for compressor flow field quality at low Reynolds numbers according to any one of claims 1 to 9, the flow field characteristics on the compressor blade surface are rapidly predicted, including at least the distance S from the laminar separation point to the leading edge of the blade. sep Separation bubble length L bs Maximum thickness of the separation bubble Turbulent reattachment boundary layer momentum thickness θ r and the boundary layer momentum thickness θ at the trailing edge of the blade T The effect of real-time feedback on the adjustment of vibration parameters of the deformable surface: when the separation bubble length L bs When the mass increases, the excitation frequency f is increased to accelerate the propagation of the disturbance; when the separation bubble reaches its maximum thickness... When the amplitude A is increased, the disturbance intensity is enhanced; the intensity of the pressure disturbance wave is optimized by dynamically adjusting the excitation frequency f and amplitude A, until continuous and efficient suppression of large-scale separation flow under extreme conditions is achieved.

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