An interface flow field information generation method suitable for a ducted fan momentum source method

Abstract

This invention specifically relates to a method for generating interface flow field information applicable to the momentum source method of ducted fans, comprising the following steps: Step S1: The interface in front of the rotor blade is designated as the front interface, and the front interface is divided into the front hub boundary layer region, the front duct boundary layer region, the wing boundary layer region, the low-energy airflow region, the duct lip boundary layer region, the duct lip acceleration region, and the front uniform transition region; then, velocity distributions are generated according to the above-mentioned regions, and then assembled and merged to obtain the velocity distribution on the front interface; Step S2: The interface behind the stator blade is designated as the rear interface, and the rear interface is divided into the rear hub boundary layer region, the duct exponential distribution transition region, and the stator wake region; then, velocity distributions are generated according to the above-mentioned regions, and then assembled and merged to obtain the velocity distribution on the rear interface. This invention can eliminate the dependence on flow field calculations in multiple reference coordinate systems, and can also obtain accurate momentum source distribution characteristics, thus improving computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of distributed ducted fan aircraft design methods, specifically relating to a method for generating interface flow field information applicable to ducted fan momentum source methods. Background Technology

[0002] A ducted fan is a power unit that is electrically driven and housed within a duct. Compared to open-type electric propellers, it offers advantages such as a compact structure, low noise level, high safety, and ease of internal embedding. In recent years, the electrically driven distributed ducted fan-wing coupled layout has gradually become a key development direction for various research institutions. Conducting aerodynamic design research on such aircraft has significant engineering practical value and application value.

[0003] The characteristic of electrically driven distributed ducted fan aircraft is that multiple ducted fans are arranged on the wings, and there is a relatively close aerodynamic coupling effect between the fans, the wings, and the duct lips. Studies have shown that the flow field information at the front and rear interfaces has a significant impact on the aerodynamic performance of each component. The main influencing factors are the flow rate and velocity distribution characteristics. Therefore, accurately predicting the aerodynamic performance of an aircraft is a challenging task. Traditional multi-reference coordinate system methods are computationally expensive, while traditional momentum source methods suffer from large prediction errors in drag characteristics due to differences in flow rate and velocity distribution characteristics.

[0004] In the prior art, Chinese patent CN117371344A proposed a flow field simulation method for a distributed ducted fan-wing coupled layout. In this method, the flow field velocity information at the front and rear interfaces of the ducted fan is obtained by calculating the flow field in multiple reference coordinate systems to calculate the momentum source term. Although this method has certain advantages in terms of efficiency and accuracy, the acquisition of flow field velocity information depends on the flow field in multiple reference coordinate systems. The calculation of multiple reference systems is actually based on the RANS method to simulate the flow field. For the aerodynamic target evaluation method of aircraft design, this method still has the defect of low computational efficiency. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for generating interface flow field information applicable to the momentum source method of ducted fans. The method processes the front and rear interfaces separately. First, the average velocity at the fan under different incoming flow velocities and different thrusts is calculated using momentum theory. Then, the velocity distributions of the front and rear interfaces considering the influence of multiple components are generated. Finally, the obtained velocity distributions are assembled and merged to obtain the velocity distributions on the front and rear interfaces. This method can eliminate the dependence on flow field calculations in multiple reference coordinate systems, obtain accurate momentum source distribution characteristics, and improve computational efficiency.

[0006] This invention is achieved through the following technical solution:

[0007] A method for generating interface flow field information applicable to the momentum source method of ducted fans includes the following steps:

[0008] Step S1: The interface in front of the ducted fan blade is denoted as the front interface. The front interface is divided into the front hub boundary layer region, the front duct boundary layer region, the wing boundary layer region, the low-energy airflow region, the duct lip boundary layer region, the duct lip acceleration region, and the front uniform transition region. Then, the velocity distribution is generated according to the above-mentioned regions, and then assembled and merged to obtain the velocity distribution on the front interface.

[0009] Step S2: The interface behind the ducted fan stator blades is designated as the rear interface. The rear interface is divided into the rear hub boundary layer region, the ducted exponential distribution transition region, and the stator blade wake region. Then, velocity distributions are generated for each of the above-mentioned regions, and then assembled and merged to obtain the velocity distribution on the rear interface.

[0010] Furthermore, the method for obtaining the front and rear interfaces refers to the method for obtaining the front interface of the moving blade and the rear interface of the stationary blade in Chinese Patent CN117371344A.

[0011] Further, in step S1, the front hub boundary layer region refers to the annular region from the hub wall to the outer boundary of the hub boundary layer on the front interface; the front duct boundary layer region refers to the annular region from the inner wall of the duct to the outer boundary of the duct boundary layer on the front interface; the wing boundary layer region refers to the rectangular region from the upper surface of the wing to the outer boundary of the wing boundary layer; the low-energy airflow region refers to the region from the outer boundary of the wing boundary layer to the position of the average flow velocity at the interface; the duct lip boundary layer region refers to the region from the duct lip wall to the outer boundary of the duct lip boundary layer; the duct lip acceleration region refers to the region obtained by the intersection of the circumferential and radial action range regions, wherein the circumferential action range region is: respectively... Center angle, each center angle The range is defined as the circumferential range of action. The radial range of action is defined as follows: the radial center position is the point where each central angle ray intersects with the outer ring of the duct, and the radial range is defined as 1 / 10 to 1 / 5 of the duct radius around each radial center position; the front uniform transition zone is the remaining area on the front interface after removing the above-mentioned partitions.

[0012] Furthermore, step S1 includes the following sub-steps:

[0013] Step S11: Calculate the average velocity at the front interface under different incoming flow velocities and different thrust conditions based on momentum theory;

[0014] Momentum theory is a well-known method in this field. The specific process for calculating the average velocity at the front interface is as follows:

[0015] First, based on momentum theory, the fan thrust T is obtained. P The expression:

[0016]

[0017] In the formula, T P Let ρ represent the thrust of the fan, A1 be the air density, V0 be the free flow velocity, and V2 be the duct outlet velocity. From the above formula, the velocity at the duct outlet under different free flow velocities and thrust conditions can be obtained as follows:

[0018]

[0019] The average velocity V1 at the front interface is obtained by calculation based on the law of conservation of mass:

[0020]

[0021] In the formula, A2 is the cross-sectional area of ​​the culvert outlet;

[0022] Step S12: Based on the thickness formula of the laminar boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front hub boundary layer region; based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front duct boundary layer region; based on the thickness and two-dimensional velocity distribution of the front hub boundary layer region and the thickness and two-dimensional velocity distribution of the front duct boundary layer region, interpolate to calculate the two-dimensional velocity distribution of the front uniform transition region.

[0023] The thickness formulas and velocity power-law distribution assumptions for both laminar and turbulent boundary layers around a downstream flat plate are well-known techniques in the field. The specific process of this step is as follows:

[0024] ① The thickness of the front hub boundary layer region is calculated using the laminar boundary layer thickness calculation formula for a flat plate placed downstream. The specific expression is as follows:

[0025]

[0026] In the formula, δ f_hub x represents the front hub boundary layer thickness. hub Re is the chord length of the front cone of the propeller hub. x_f_hub The Reynolds number is calculated based on the chord length of the front cone of the propeller hub;

[0027] Based on the thickness δ of the front hub boundary layer region f_hub The velocity distribution within the front hub boundary layer region is obtained by calculating using a power function distribution, namely:

[0028]

[0029] In the formula, u f_hub Let z be the velocity at different normal positions within the front hub boundary layer region. f_hub V represents the coordinates of different normal positions inside the front hub boundary layer. f_hub The velocity at the outer edge of the front rotor hub boundary layer is calculated using the following formula:

[0030] V f_hub =ζV1

[0031] In the formula, ζ is the correction coefficient for the velocity at the outer edge of the front hub boundary layer, which characterizes the acceleration effect of the hub curvature on the airflow, and is taken between 1.05 and 1.1.

[0032] ② The thickness of the turbulent boundary layer region in the duct ahead is calculated using the formula for calculating the thickness of the turbulent boundary layer when a flat plate is placed downstream. The specific expression is as follows:

[0033]

[0034] In the formula, δ f_duct x represents the thickness of the boundary layer region of the duct. f_duct Re is the chord length of the duct. x_f_duct The Reynolds number is calculated based on the chord length of the duct.

[0035] Based on the thickness δ of the boundary layer region of the fore-culvert f_duct The velocity distribution within the boundary layer region of the duct is obtained by calculating using a power function distribution, namely:

[0036]

[0037] In the formula, u f_duct The velocity distribution at different normal positions within the boundary layer region of the duct is given by z. f_duct V represents the coordinates of different normal positions inside the boundary layer of the duct. f_duct The velocity at the outer edge of the boundary layer of the duct is calculated using the following formula:

[0038] V f_duct =ζ2V1

[0039] In the formula, ζ2 is the correction coefficient for the velocity at the outer edge of the duct boundary layer, which characterizes the acceleration effect of the duct curve on the airflow, and is taken as 1.2 to 1.3.

[0040] ③ Based on the calculated thickness and velocity distribution of the front hub boundary layer region and the front duct boundary layer region, the two-dimensional velocity distribution u of the front uniform transition region is calculated using a linear interpolation method. gd ;

[0041] Specifically, the outer edge coordinates of the front hub boundary layer and the front duct boundary layer are obtained by measuring their thicknesses. A linear interpolation function is then established between the outer edges of these two boundary layers to interpolate the velocity, ensuring a smooth transition between them and obtaining the two-dimensional velocity distribution u in the pre-uniform transition region. gd ;

[0042] Step S13: Assemble the two-dimensional velocity distribution in the front hub boundary layer region, the two-dimensional velocity distribution in the front uniform transition region, and the two-dimensional velocity distribution in the front duct boundary layer region obtained in step S12 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the front interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the front interface.

[0043] Step S14: The thickness and two-dimensional velocity distribution of the wing boundary layer region are calculated using the KAMAN-Bauhausen method. The thickness of the low-energy airflow region is calculated using xfoil. Based on the thickness and two-dimensional velocity distribution of the wing boundary layer region and the thickness of the low-energy airflow region, the two-dimensional velocity distribution of the low-energy airflow region is calculated using cubic spline distribution. The two-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region are assembled and spanwise extended to obtain the three-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region. The obtained three-dimensional velocity distribution is then "bow-shaped".

[0044] The KAMAN-Borghausen approximation method is a well-known method in the art, and xfoil is a well-known computational program in the art. The specific process of this step is as follows:

[0045] ① The thickness and velocity distribution of the wing boundary layer are calculated using the classic KAMAN-Borghausen approximation method. This method establishes the relationship between wall shear stress and velocity distribution by defining momentum thickness. Combining the no-slip condition in the wall normal and the far-field free flow velocity condition, the wing boundary layer thickness δ is obtained by iteratively solving the boundary layer integral equation. wing_bl and velocity distribution u wing_bl For details, refer to Chapter 5, Section 3 of "Viscous Fluid Mechanics" (written by Zhang Zixiong and Dong Zengnan); multiply the wing boundary layer velocity distribution obtained through the KAMAN-Bauhausen method by the ratio of the average velocity V1 at the front interface to the free flow velocity V0 to obtain the boundary layer velocity distribution considering the fan suction effect.

[0046] ② First, the momentum loss thickness of the low-energy airflow region is calculated using XFOIL. Then, the nominal boundary layer thickness of the low-energy airflow region is calculated based on the momentum loss thickness, and the thickness of the wing boundary layer is subtracted from this nominal thickness to obtain the low-energy airflow region thickness. Specifically:

[0047] The expression for calculating the momentum loss thickness δ2 in the low-energy airflow region is as follows:

[0048]

[0049] In the formula, δ is the nominal thickness of the boundary layer in the low-energy gas flow region, and Λ is a dimensionless quantity, expressed as:

[0050]

[0051] In the formula, υ is the kinematic viscosity coefficient. The velocity gradient along the wing surface;

[0052] From the above two equations, we get:

[0053]

[0054] Solving the above equation yields the nominal boundary layer thickness δ in the low-energy airflow region. Subtracting the wing boundary layer thickness δ from the calculated δ then... wing_bl That is, the thickness δ of the low-energy gas flow region is obtained. wing_lp ;

[0055] ③ Based on the obtained thickness of the wing boundary layer region, the coordinates of the outer edge of the wing boundary layer are obtained, based on the thickness δ of the low-energy airflow region. wing_lp The outer edge coordinates of the low-energy airflow region are obtained. The outer edge velocity value of the low-energy airflow region is set to be equal to the average velocity V1 of the front interface calculated in step S11. Then, based on the outer edge coordinates of the wing boundary layer, the outer edge coordinates of the low-energy airflow region, and the tangential constraint between the velocity distribution of the low-energy airflow region and the velocity distribution of the wing boundary layer and the velocity distribution of the front uniform transition region, the velocity distribution of the low-energy airflow region is calculated using cubic spline distribution.

[0056] ④ Combine the obtained velocity distribution in the low-energy airflow region with the velocity distribution in the wing boundary layer; obtain the two-dimensional velocity distribution in the wing boundary layer and the low-energy airflow region, and extend the two-dimensional velocity distribution along the spanwise direction to the outer edge of the duct to generate a three-dimensional rectangular velocity distribution;

[0057] ⑤ The obtained three-dimensional velocity distribution is then subjected to "bow-shaped" processing, the specific process of which is as follows:

[0058] The method for calculating the z-coordinate in the height direction of the bow-shaped curve is as follows:

[0059]

[0060] The coordinate system is defined as follows: the X-axis is along the direction of the free flow, the Y-axis is to the right from the pilot's perspective, and the Z-axis is perpendicular to the XY plane and upwards, satisfying a right-handed coordinate system; the calculation object is the velocity distribution points at different spanwise positions in a three-dimensional rectangular velocity distribution, where z j_i_moi z represents the corrected coordinates of the i-th point at the j-th spanwise position. j_i_orih represents the initial coordinates of the i-th point at the j-th spanwise position. j δ represents the z-axis height at the j-th spanwise position in the arc-shaped region. wing_lp The thickness of the low-energy airflow region;

[0061] Step S15: Assemble the velocity distribution of the wing boundary layer region and low-energy airflow region after the "bow-shaped" treatment obtained in step S14 with the three-dimensional velocity distribution "base" on the front interface obtained in step S13, and smooth the area where the wing boundary layer region and low-energy airflow region meet the "base" to obtain the velocity distribution of the front interface flow field considering the hub boundary layer, duct boundary layer, wing boundary layer and low-energy airflow region.

[0062] Step S16: Based on the velocity distribution of the front interface flow field obtained in step S15, the velocity distribution of the duct lip boundary layer region and the duct lip acceleration region is corrected by using a linear function scaling method to obtain the final velocity distribution of the front interface flow field.

[0063] Furthermore, the assembly method for obtaining the two-dimensional radial velocity distribution on the front interface in step S13 is to merge the two-dimensional matrices containing coordinate information and velocity information, as shown in the following equation:

[0064]

[0065] In the formula, z f_hub For the velocity distribution u in the front hub boundary layer region f_hub The corresponding position coordinates, z gd For the velocity distribution u in the previous uniform transition region gd The corresponding position coordinates, z f_duct To the velocity distribution u in the boundary layer region of the culvert f_duct Corresponding position coordinates; z 2D This represents the coordinate distribution of the assembled front hub boundary layer region, front uniform transition region, and front duct boundary layer region, u. 2D This indicates the velocity distribution after assembling the front hub boundary layer region, the front uniform transition region, and the front duct boundary layer region.

[0066] Furthermore, the specific process of assembling and smoothing the velocity distribution of the wing boundary layer region and low-energy airflow region after the "bow-shaped" treatment with the three-dimensional velocity distribution "base" on the front interface in step S15 is as follows:

[0067] The regions in the three-dimensional velocity distribution "base" that are lower than the top outer edge of the wing boundary layer region and the low-energy airflow region are deleted, and the velocity distributions of the wing boundary layer region and the low-energy airflow region after "bow-shaped" processing are used to replace them. For the velocity distribution step that occurs at the interface, the velocity step region is smoothed by linear interpolation, so as to obtain the velocity distribution of the front interface flow field that takes into account the hub boundary layer, duct boundary layer, wing boundary layer and low-energy airflow region.

[0068] Furthermore, the specific process of step S16 is as follows:

[0069] ① Establish a linear scaling factor function. The linear scaling function attenuation in the duct lip boundary layer region and the duct lip acceleration region mainly includes two parts: radial attenuation and circumferential attenuation, with the following formulas:

[0070] Radial scaling factor r factor :

[0071]

[0072] In the formula, r i The radius of the current grid point is represented by r, and the duct radius is represented by σ. r This parameter represents the set range for controlling radial scaling.

[0073] Circumferential scaling factor θ factor :

[0074]

[0075] In the formula, θ i -θ center σ represents the circumferential angle difference between the current grid point and the center of the boundary layer at the duct lip. θ This parameter represents the set range for controlling circumferential scaling.

[0076] ② Multiply the velocity distribution of the front interface obtained in step S15 by the corresponding scaling function to obtain the corrected velocity distribution of the front interface after adjusting for the boundary layer region and acceleration region of the duct lip; specifically:

[0077] For the duct lip boundary layer region, which is a region of decreasing velocity, the product of the circumferential and radial scaling factors is used as the total scaling factor sc for the duct lip boundary layer region. factor_bl :

[0078] sc factor_bl =r factor ·θ factor

[0079] Based on the total scaling factor of the duct lip boundary layer region, the velocity at the front interface is first scaled and corrected using the following expression:

[0080] u isc1 =u i ·(1-sc factor_bl )

[0081] Expanded to:

[0082]

[0083] In the formula, u i Let u be the flow velocity at each point on the interface. isc1 The flow field velocity at each point on the front interface after the first scaling correction of the velocity on the front interface;

[0084] For the duct lip acceleration region, which is the area where the velocity increases, the following expression is used as the total scaling factor sc for the duct lip acceleration region. factor_ac :

[0085] sc factor_ac =1+(ms-1)·r factor ·θ factor

[0086] In the formula, ms is the maximum value of velocity scaling. The curve at the maximum curvature of the duct lip can be used as the leading edge. After completing the airfoil, the potential flow method is used to obtain the airflow velocity ratio at the relative position of the leading interface. The empirical value is taken as 1.2 to 1.4.

[0087] Based on the total scaling factor of the acceleration zone at the duct lip, the velocity at the front interface is corrected for a second scaling using the following expression:

[0088] u isc2 =u isc1 ·sc factor_ac

[0089] Expanded to:

[0090]

[0091] In the formula, u isc2 The velocity distribution at each point on the front interface after the second scaling correction of the velocity on the front interface is the final velocity distribution of the front interface.

[0092] Furthermore, in step S2, the aft hub boundary layer region refers to the annular region on the aft interface from the hub wall to the outer boundary of the hub boundary layer; the stator wake region refers to the central outline of the stator wake region obtained by projecting the stator trailing edge shape onto the aft interface, and then extending the central outline of the stator wake region circumferentially. The area within the angular range; the duct index distribution transition zone refers to the remaining area on the rear interface after removing the aforementioned partitions.

[0093] Furthermore, step S2 includes the following sub-steps:

[0094] Step S21: Calculate the average velocity V at the rear interface under different incoming flow velocities and different thrust conditions based on momentum theory. b1 ;

[0095] Momentum theory is a well-known method in this field. The specific process of calculating the average velocity at the rear interface is the same as that of calculating the average velocity at the front interface.

[0096] Step S22: Based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power distribution assumption of velocity, calculate the thickness and two-dimensional velocity distribution of the rear hub boundary layer region, and calculate the two-dimensional velocity distribution of the duct exponential distribution transition region based on the velocity distribution law assumption in the circular pipe.

[0097] The formulas for the thickness of the turbulent boundary layer around a downstream flat plate and the assumptions for the power-law velocity distribution, as well as the assumptions for the velocity distribution law inside a circular pipe, are all well-known techniques in this field. The specific process of this step is as follows:

[0098] ① The thickness of the hub boundary layer region was calculated using the formula for calculating the thickness of the turbulent boundary layer on a flat plate:

[0099]

[0100] In the formula, l S Re represents the length of the stator blade domain in a single-duct fan-airfoil coupled configuration. b_hub For l S The Reynolds number, calculated from the characteristic length, is given by the following formula:

[0101]

[0102] In the formula, μ is the dynamic viscosity coefficient, and V b1 The average velocity at the interface after the intersection;

[0103] Based on the thickness δ of the rear hub boundary layer region b_hub The velocity distribution within the rear hub boundary layer region was obtained by calculating using a power function distribution, namely:

[0104]

[0105] In the formula, u b_hub z represents the velocity at different normal positions within the rear hub boundary layer region. b_hub V represents the coordinates of different normal positions inside the rear hub boundary layer. b_max The maximum velocity in the two-dimensional radial velocity distribution at the rear interface is taken as the outer edge velocity of the rear hub boundary layer, V. b_maxThe flow velocity distribution law inside a circular pipe is used for calculation, and the specific expression is as follows:

[0106]

[0107] In the formula, the constant n is taken as 7, and V b1 The average velocity at the interface after the intersection;

[0108] The coordinate point information z of the rear hub boundary layer region b_hub and speed information u b_hub The velocity information matrix of the rear hub boundary layer region is obtained:

[0109] V b_hub =[z b_hub ,u b_hub ]

[0110] ② The velocity distribution in the duct's exponential distribution transition zone is calculated using the exponential formula for velocity distribution within a circular pipe, i.e.:

[0111]

[0112] In the formula, u b_duct r-δ represents the velocity at different normal positions within the transition region of the duct exponent distribution. b_hub z is the length from the outer ring to the outer edge of the rear hub boundary layer. b_duct The coordinates of different normal positions within the transition zone of the duct index distribution are given, with the constant m taking the value of 10.

[0113] The coordinate point information z of the transition zone of the duct index distribution b_duct and speed information u b_duct The velocity information matrix of the duct exponential distribution transition region is obtained:

[0114] V b_duct =[z b_duct ,u b_duct ]

[0115] Step S23: Assemble the two-dimensional velocity distribution in the rear hub boundary layer region and the two-dimensional velocity distribution in the duct index distribution transition region obtained in step S22 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the rear interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the rear interface.

[0116] Step S24: Based on the shape of the stator blade trailing edge, generate the central contour of the stator blade wake region. Specifically, obtain the stator blade wake centerline by projecting the stator blade trailing edge shape onto the aft interface. Extend both ends of the stator blade wake centerline to the rotor hub and the duct at the aft interface, respectively, to form the central contour of the stator blade wake region. Based on the central contour of the stator blade wake region, obtain the circumferential angle θ of the central contour of the stator blade wake region. center ;

[0117] Step S25: Based on the three-dimensional velocity distribution "baseline" on the back interface obtained in step S23 and the central contour of the stator blade wake region obtained in step S24, the velocity distribution of the duct exponential distribution transition region is corrected by using a linear function scaling method to obtain the final velocity distribution of the back interface flow field.

[0118] Furthermore, the assembly method for obtaining the two-dimensional radial velocity distribution on the interface in step S23 involves merging two-dimensional matrices containing coordinate and velocity information, as shown in the following equation:

[0119]

[0120] In the formula, z b_2D This represents the coordinate distribution after assembling the aft hub boundary layer region and the duct index distribution transition region, u b_2D This indicates the velocity distribution after assembling the rear hub boundary layer region and the duct index distribution transition region.

[0121] Furthermore, the specific process of step S25 is as follows:

[0122] Circumferential scaling factor θ of the wake wj_factor for:

[0123]

[0124] In the formula, θ i -θ center σ represents the circumferential angle difference between the current grid point and the central contour of the still leaf wake region. θ This parameter represents the set range for controlling circumferential scaling.

[0125] Based on the circumferential scaling factor θ of the wake wj_factor The following expression is used to scale and correct the velocity on the subsequent interface:

[0126] u isc_b =u i_b ·(1-θ wj_factor )

[0127] In the formula, u i_b For the flow field velocity at each grid point on the "base" distribution of the post-interface, u isc_bThe velocity distribution at each grid point of the back interface after scaling and correcting the velocity on the back interface is the final velocity distribution of the back interface flow field.

[0128] Beneficial effects

[0129] This invention provides a method for generating interface flow field information applicable to the momentum source method of ducted fans. The method processes the front and rear interfaces separately. First, the average velocity at the fan under different incoming flow velocities and different thrusts is calculated using momentum theory. Then, the velocity distributions of the front and rear interfaces considering the influence of multiple components are generated. Finally, the obtained velocity distributions are assembled and merged to obtain the velocity distributions on the front and rear interfaces. This method can eliminate the dependence on flow field calculations in multiple reference coordinate systems, obtain more accurate momentum source distribution characteristics, and improve computational efficiency. Attached Figure Description

[0130] Figure 1 This is a flowchart of an embodiment of the present invention;

[0131] Figure 2 This is a single-ducted fan-wing section coupled configuration with a ducted fan according to an embodiment of the present invention;

[0132] Figure 3 This is a single-duct fan-wing section coupled configuration calculated using a momentum source in an embodiment of the present invention;

[0133] Figure 4 This is a schematic diagram of the front interface partitioning according to an embodiment of the present invention;

[0134] Figure 5 This is a schematic diagram of the post-interface partitioning in an embodiment of the present invention;

[0135] Figure 6 This is a schematic diagram of the velocity distribution and partitioning at the central section of the front interface according to an embodiment of the present invention;

[0136] Figure 7 This is a schematic diagram of the velocity distribution and partitioning at the center section below the front interface according to an embodiment of the present invention;

[0137] Figure 8 This is a schematic diagram of the velocity distribution and partitioning at the center section of the post-intersection interface according to an embodiment of the present invention;

[0138] Figure 9 This is the two-dimensional radial velocity distribution at the front interface in an embodiment of the present invention;

[0139] Figure 10 This is the "base" generated based on the two-dimensional radial velocity distribution at the front interface in this embodiment of the invention;

[0140] Figure 11 The velocity distribution of the wing boundary layer and low-energy airflow region in this embodiment of the invention;

[0141] Figure 12 This illustrates the "bow-shaped" operation effect in an embodiment of the present invention.

[0142] Figure 13 In this embodiment of the invention, the "bow-shaped" region is assembled with the "substrate";

[0143] Figure 14 A comparison is made between the velocity distribution at the front interface generated by the method of the present invention and the momentum source distribution calculated from the velocity distribution at the front interface extracted from the MRF flow field.

[0144] in, Figure 14 (a) is the momentum source distribution calculated based on the velocity distribution of the front interface generated by the method of the present invention. Figure 14 (b) shows the momentum source distribution calculated from the velocity distribution at the front interface extracted by the MRF flow field.

[0145] Figure 15 This is the two-dimensional radial velocity distribution at the interface in an embodiment of the present invention;

[0146] Figure 16 This is the "base" generated based on the two-dimensional radial velocity distribution at the post-interface in this embodiment of the invention;

[0147] Figure 17 The central contour of the rear interface wake in this embodiment of the invention;

[0148] Figure 18 A comparison is made between the velocity distribution at the post-interface generated by the method of the present invention and the momentum source distribution calculated from the velocity distribution at the post-interface extracted from the MRF flow field;

[0149] in, Figure 18 (a) is the momentum source distribution calculated based on the velocity distribution of the front interface generated by the method of the present invention. Figure 18 (b) shows the momentum source distribution calculated from the velocity distribution at the front interface extracted by the MRF flow field.

[0150] Figure 19 The relative errors of the lift coefficient, drag coefficient, and drag coefficient calculated by the method of this invention under different incoming flow velocities compared with the MRF method;

[0151] Figure 20 The relative errors of the lift coefficient, drag coefficient, and drag coefficient calculated by the method of this invention at different fan speeds compared to the MRF method are:

[0152] In the diagram: 1-Duct shell; 2-Rotating blade; 3-Buzzer hub; 4-Duct lip; 5-Exhaust duct; 6-Stationary blade; 7-Wing; 8-Forward interface; 9-Rear interface; 11-Duct lip boundary layer region; 12-Duct lip acceleration region; 13-Wing boundary layer region; 14-Low-energy airflow region; 15-Forward hub boundary layer region; 16-Forward uniform transition region; 17-Forward duct boundary layer region; 21-Rear hub boundary layer; 22-Stationary blade wake region; 23-Duct exponential distribution transition region. Detailed Implementation

[0153] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer and to enable those skilled in the art to better understand the invention, the invention will be further described in detail and in full below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0154] This embodiment employs an interface flow field information generation method for ducted fan momentum source methods provided by the present invention. Taking a wing section with a ducted fan on the trailing edge of the upper surface as an example, it verifies the effectiveness and practicality of the method. The wing section model with a ducted fan on the trailing edge of the upper surface is shown below. Figure 2 As shown, the wing segment model with leading and trailing interfaces on the trailing edge of the upper surface of the wing calculated using the momentum source method is as follows: Figure 3 As shown.

[0155] like Figure 1 As shown in the figure, a method for generating interface flow field information applicable to the momentum source method of ducted fans in this embodiment includes the following steps:

[0156] Step S1: Denote the interface in front of the ducted fan blades as the front interface. Divide the front interface into the front hub boundary layer region, the front duct boundary layer region, the wing boundary layer region, the low-energy airflow region, the duct lip boundary layer region, the duct lip acceleration region, and the front uniform transition region, as follows: Figure 4 As shown; then generate velocity distributions according to the above-described regions, and then assemble and merge them to obtain the velocity distribution on the front interface;

[0157] The forward hub boundary layer region refers to the annular region from the hub wall to the outer boundary of the hub boundary layer on the forward interface; the forward duct boundary layer region refers to the annular region from the inner wall of the duct to the outer boundary of the duct boundary layer on the forward interface; the wing boundary layer region refers to the rectangular region from the upper surface of the wing to the outer boundary of the wing boundary layer; the low-energy airflow region refers to the region from the outer boundary of the wing boundary layer to the position of the average flow velocity at the interface; the duct lip boundary layer region refers to the region from the duct lip wall to the outer boundary of the duct lip boundary layer; the duct lip acceleration region refers to the region obtained by the intersection of the circumferential and radial action range regions, wherein the circumferential action range region is defined as follows: Center angle, each center angle The range is defined as the circumferential range of action. The radial range of action is defined as follows: the radial center position is the point where each central angle ray intersects with the outer ring of the duct, and the radial range is defined as 1 / 10 to 1 / 5 of the duct radius around each radial center position; the front uniform transition zone is the remaining area on the front interface after removing the above-mentioned partitions.

[0158] Step S2: Denote the interface behind the stator blades of the ducted fan as the rear interface. Divide the rear interface into the rear hub boundary layer region, the duct index distribution transition region, and the stator wake region, as follows: Figure 5 As shown; then generate velocity distributions according to the above-described regions, and then assemble and merge them to obtain the velocity distribution on the interface.

[0159] The aft hub boundary layer region refers to the annular area on the aft interface from the hub wall to the outer boundary of the hub boundary layer; the stator wake region refers to the central outline of the stator wake region obtained by projecting the stator trailing edge shape onto the aft interface, and then extending the central outline of the stator wake region circumferentially. The area within the angular range; the duct index distribution transition zone refers to the remaining area on the rear interface after removing the aforementioned partitions;

[0160] In this embodiment, the method for obtaining the front and rear interfaces refers to the method for obtaining the front interface of the moving blade and the rear interface of the stationary blade in Chinese Patent CN117371344A.

[0161] In this embodiment, step S1 includes the following sub-steps:

[0162] Step S11: Calculate the average velocity at the front interface under different incoming flow velocities and different thrust conditions based on momentum theory;

[0163] Momentum theory is a well-known method in this field. The specific process for calculating the average velocity at the front interface is as follows:

[0164] First, based on momentum theory, the fan thrust T is obtained. P The expression:

[0165]

[0166] In the formula, T P Let ρ represent the thrust of the fan, A1 be the air density, V0 be the free flow velocity, and V2 be the duct outlet velocity. From the above formula, the velocity at the duct outlet under different free flow velocities and thrust conditions can be obtained as follows:

[0167]

[0168] The average velocity V1 at the front interface is obtained by calculation based on the law of conservation of mass:

[0169]

[0170] In the formula, A2 is the cross-sectional area of ​​the culvert outlet;

[0171] In this embodiment, the fan duct diameter is 0.15m, the rotor hub diameter is 0.06m, and the fan thrust T P The atmospheric density is 1.11166 kg / m³, with a value of 10.06 N. 3 The flow channel area A1 at the front interface is 0.014844 m². 2 The free-flow velocity V0 is 41.667 m / s, and the culvert outlet area A2 is 0.0158 m². 2 Therefore, the average velocity V1 at the front interface is 57.85 m / s.

[0172] Step S12: Based on the thickness formula of the laminar boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front hub boundary layer region; based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front duct boundary layer region; based on the thickness and two-dimensional velocity distribution of the front hub boundary layer region and the thickness and two-dimensional velocity distribution of the front duct boundary layer region, interpolate to calculate the two-dimensional velocity distribution of the front uniform transition region.

[0173] The thickness formulas and velocity power-law distribution assumptions for both laminar and turbulent boundary layers around a downstream flat plate are well-known techniques in the field. The specific process of this step is as follows:

[0174] ① The thickness of the front hub boundary layer region is calculated using the laminar boundary layer thickness calculation formula for a flat plate placed downstream. The specific expression is as follows:

[0175]

[0176] In the formula, δ f_hub x represents the front hub boundary layer thickness. hub Re is the chord length of the front cone of the propeller hub. x_f_hub The Reynolds number is calculated based on the chord length of the front cone of the propeller hub;

[0177] In this embodiment, the chord length of the front cone of the propeller hub is 0.04m, and the Reynolds number calculated from the chord length of the front cone of the propeller hub is 1.4484 × 10⁻⁶. 5 The front hub boundary layer thickness is 5.2552 × 10⁻⁶. -4 m.

[0178] Based on the thickness δ of the front hub boundary layer region f_hubThe velocity distribution within the front hub boundary layer region is obtained by calculating using a power function distribution, namely:

[0179]

[0180] In the formula, u f_hub Let z be the velocity at different normal positions within the front hub boundary layer region. f_hub V represents the coordinates of different normal positions inside the front hub boundary layer. f_hub The velocity at the outer edge of the front rotor hub boundary layer is calculated using the following formula:

[0181] V f_hub =ζV1

[0182] In the formula, ζ1 is the correction coefficient for the velocity at the outer edge of the front hub boundary layer, which characterizes the acceleration effect of the hub surface on the airflow, and is taken as 1.08.

[0183] ② The thickness of the turbulent boundary layer region in the duct ahead is calculated using the formula for calculating the thickness of the turbulent boundary layer when a flat plate is placed downstream. The specific expression is as follows:

[0184]

[0185] In the formula, δ f_duct x represents the thickness of the boundary layer region of the duct. f_duct Re is the chord length of the duct. x_f_duct The Reynolds number is calculated based on the chord length of the duct.

[0186] In this embodiment, the duct chord length is 0.02m, and the Reynolds number calculated from the duct chord length is 7.2418 × 10⁻⁶. 4 The front hub boundary layer thickness is 7.076 × 10⁻⁶. -4 m.

[0187] Based on the thickness δ of the boundary layer region of the fore-culvert f_duct The velocity distribution within the boundary layer region of the duct is obtained by calculating using a power function distribution, namely:

[0188]

[0189] In the formula, u f_duct The velocity distribution at different normal positions within the boundary layer region of the duct is given by z. f_duct V represents the coordinates of different normal positions inside the boundary layer of the duct. f_duct The velocity at the outer edge of the boundary layer of the duct is calculated using the following formula:

[0190] V f_duct =ζ2V1

[0191] In the formula, ζ2 is the correction coefficient for the velocity at the outer edge of the duct boundary layer, which characterizes the acceleration effect of the duct curve on the airflow, and is taken as 1.24;

[0192] ③ Based on the calculated thickness and velocity distribution of the front hub boundary layer region and the front duct boundary layer region, the two-dimensional velocity distribution u of the front uniform transition region is calculated using a linear interpolation method. gd ;

[0193] Specifically, the outer edge coordinates of the front hub boundary layer and the front duct boundary layer are obtained by measuring their thicknesses. A linear interpolation function is then established between the outer edges of these two boundary layers to interpolate the velocity, ensuring a smooth transition between them and obtaining the two-dimensional velocity distribution u in the pre-uniform transition region. gd ;

[0194] Step S13: Assemble the two-dimensional velocity distribution in the front hub boundary layer region, the two-dimensional velocity distribution in the front uniform transition region, and the two-dimensional velocity distribution in the front duct boundary layer region obtained in step S12 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the front interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the front interface.

[0195] The assembly method for obtaining the two-dimensional radial velocity distribution on the interface is to merge two-dimensional matrices containing coordinate and velocity information, as shown in the following equation:

[0196]

[0197] In the formula, z gd For the velocity distribution u in the previous uniform transition region gd The corresponding position coordinates, z 2D This represents the coordinate distribution of the assembled front hub boundary layer region, front uniform transition region, and front duct boundary layer region, u. 2D This represents the velocity distribution after assembling the front hub boundary layer region, the front uniform transition region, and the front duct boundary layer region, such as... Figure 9 As shown; the generated three-dimensional velocity distribution "baseline" on the front interface is as follows Figure 10 As shown;

[0198] Step S14: The thickness and two-dimensional velocity distribution of the wing boundary layer region are calculated using the KAMAN-Bauhausen method. The thickness of the low-energy airflow region is calculated using xfoil. Based on the thickness and two-dimensional velocity distribution of the wing boundary layer region and the thickness of the low-energy airflow region, the two-dimensional velocity distribution of the low-energy airflow region is calculated using cubic spline distribution. The two-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region are assembled and spanwise extended to obtain the three-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region. The obtained three-dimensional velocity distribution is then "bow-shaped".

[0199] The KAMON-BUHAUSEN approximation method is a well-known method in the art, and xfoil is a well-known computational program in the art. The specific process of this step is as follows:

[0200] ① The thickness and velocity distribution of the wing boundary layer are calculated using the classic KAMAN-Borghausen approximation method. This method establishes the relationship between wall shear stress and velocity distribution by defining momentum thickness. Combining the no-slip condition in the wall normal and the far-field free flow velocity condition, the wing boundary layer thickness δ is obtained by iteratively solving the boundary layer integral equation. wing_bl and velocity distribution u wing_bl For details, refer to Chapter 5, Section 3 of "Viscous Fluid Mechanics" (by Zhang Zixiong and Dong Zengnan); multiply the wing boundary layer velocity distribution obtained through the KAMAN-Bauhausen method by the ratio of the average velocity V1 at the interface to the free flow velocity V0 to obtain the boundary layer velocity distribution considering the fan suction effect; in this embodiment, the wing boundary layer thickness δ wing_bl It is 7.84×10 -4 m;

[0201] ② First, the momentum loss thickness of the low-energy airflow region is calculated using XFOIL. Then, the nominal boundary layer thickness of the low-energy airflow region is calculated based on the momentum loss thickness, and the thickness of the wing boundary layer is subtracted from this nominal boundary layer thickness to obtain the final low-energy airflow region thickness. Specifically:

[0202] The expression for calculating the momentum loss thickness δ2 in the low-energy airflow region is as follows:

[0203]

[0204] In the formula, δ is the nominal thickness of the boundary layer in the low-energy gas flow region, and Λ is a dimensionless quantity, expressed as:

[0205]

[0206] In the formula, υ is the kinematic viscosity coefficient. The velocity gradient along the wing surface;

[0207] From the above two equations, we get:

[0208]

[0209] Solving the above equation yields the nominal boundary layer thickness δ in the low-energy airflow region. Subtracting the wing boundary layer thickness δ from the calculated δ then... wing_bl That is, the thickness δ of the low-energy gas flow region is obtained. wing_lp In this embodiment, the nominal thickness of the boundary layer is 0.0203 m, and the thickness δ of the low-energy gas flow region is... wing_lp It is 0.019516m;

[0210] ③ Based on the obtained thickness of the wing boundary layer region, the coordinates of the outer edge of the wing boundary layer are obtained, based on the thickness δ of the low-energy airflow region. wing_lp The outer edge coordinates of the low-energy airflow region are obtained. The outer edge velocity value of the low-energy airflow region is set to be equal to the average velocity V1 of the front interface calculated in step S11. Then, based on the outer edge coordinates of the wing boundary layer, the outer edge coordinates of the low-energy airflow region, and the tangential constraint between the velocity distribution of the low-energy airflow region and the velocity distribution of the wing boundary layer and the velocity distribution of the front uniform transition region, the velocity distribution of the low-energy airflow region is calculated using cubic spline distribution.

[0211] ④ Combine the obtained velocity distribution in the low-energy airflow region with the velocity distribution in the wing boundary layer; obtain the two-dimensional velocity distribution in the wing boundary layer and the low-energy airflow region, such as... Figure 11 As shown, the two-dimensional velocity distribution is extended along the spanwise direction to the outer edge of the duct. In this embodiment, the length of the extension along the spanwise direction is 0.10262m, generating a three-dimensional rectangular velocity distribution.

[0212] ⑤ The obtained three-dimensional velocity distribution is then subjected to "bow-shaped" processing, the specific process of which is as follows:

[0213] The method for calculating the z-coordinate in the height direction of the bow-shaped curve is as follows:

[0214]

[0215] The coordinate system is defined as follows: the X-axis is along the direction of the free flow, the Y-axis is to the right from the pilot's perspective, and the Z-axis is perpendicular to the XY plane and upwards, satisfying a right-handed coordinate system; the calculation object is the velocity distribution points at different spanwise positions in a three-dimensional rectangular velocity distribution, where z j_i_moi z represents the corrected coordinates of the i-th point at the j-th spanwise position. j_i_ori h represents the initial coordinates of the i-th point at the j-th spanwise position. j δ represents the z-axis height at the j-th spanwise position in the arc-shaped region. wing_lp The thickness of the low-energy airflow region, such as Figure 12 As shown;

[0216] Step S15: Assemble the velocity distribution of the wing boundary layer region and low-energy airflow region after the "bow-shaped" treatment obtained in step S14 with the three-dimensional velocity distribution "base" on the front interface obtained in step S13, and smooth the area where the wing boundary layer region and low-energy airflow region meet the "base" to obtain the velocity distribution of the front interface flow field considering the hub boundary layer, duct boundary layer, wing boundary layer and low-energy airflow region.

[0217] The specific process is as follows:

[0218] The regions in the three-dimensional velocity distribution "baseline" whose height is lower than the top outer edge of the wing boundary layer region and the low-energy airflow region are deleted, and replaced with the velocity distributions of the wing boundary layer region and the low-energy airflow region after "bow-shaped" processing. For velocity distribution steps that occur at the interface, linear interpolation is used to smooth the velocity step regions, resulting in the velocity distribution of the front interface flow field that considers the hub boundary layer, duct boundary layer, wing boundary layer, and low-energy airflow region. Figure 13 As shown,

[0219] Step S16: Based on the velocity distribution of the front interface flow field obtained in step S15, the velocity distribution of the duct lip boundary layer region and the duct lip acceleration region is corrected by using a linear function scaling method to obtain the final velocity distribution of the front interface flow field.

[0220] The specific process is as follows:

[0221] ① Establish a linear scaling factor function. The linear scaling function attenuation in the duct lip boundary layer region and the duct lip acceleration region mainly includes two parts: radial attenuation and circumferential attenuation, with the following formulas:

[0222] Radial scaling factor r factor :

[0223]

[0224] In the formula, r i The radius of the current grid point is represented by r, and the duct radius is represented by σ. r This parameter represents the set range for controlling radial scaling.

[0225] Circumferential scaling factor θ factor :

[0226]

[0227] In the formula, θ i -θ center σ represents the circumferential angle difference between the current grid point and the center of the boundary layer at the duct lip. θ This parameter represents the set range for controlling circumferential scaling.

[0228] ② Multiply the velocity distribution of the front interface obtained in step S15 by the corresponding scaling function to obtain the corrected velocity distribution of the front interface after adjusting for the boundary layer region and acceleration region of the duct lip; specifically:

[0229] For the duct lip boundary layer region, which is a region of decreasing velocity, the product of the circumferential and radial scaling factors is used as the total scaling factor sc for the duct lip boundary layer region. factor_bl :

[0230] sc factor_bl =r factor ·θ factor

[0231] Based on the total scaling factor of the duct lip boundary layer region, the velocity at the front interface is first scaled and corrected using the following expression:

[0232] u isc1 =u i ·(1-sc factor_bl )

[0233] Expanded to:

[0234]

[0235] In the formula, u i Let u be the flow velocity at each point on the interface. isc1 The flow field velocity at each point on the front interface after the first scaling correction of the velocity on the front interface;

[0236] For the duct lip acceleration region, which is the area where the velocity increases, the following expression is used as the total scaling factor sc for the duct lip acceleration region. factor_ac :

[0237] sc factor_ac =1+(ms-1)·r factor ·θ factor

[0238] In the formula, ms is the maximum value of velocity scaling. The curve at the maximum curvature of the duct lip can be used as the leading edge. After completing the airfoil, the potential flow method is used to obtain the airflow velocity ratio at the relative position of the leading interface. The empirical value is taken as 1.3.

[0239] Based on the total scaling factor of the acceleration zone at the duct lip, the velocity at the front interface is corrected for a second scaling using the following expression:

[0240] u isc2 =u isc1 ·sc factor_ac

[0241] Expanded to:

[0242]

[0243] In the formula, u isc2 The flow field velocity at each point on the front interface after a second scaling correction is obtained, which is the final flow field velocity distribution at the front interface. In this embodiment, the momentum source distribution at the front interface generated based on the velocity distribution at the front interface obtained by the method of the present invention is compared with the result calculated by MRF. Figure 14 As shown.

[0244] In this embodiment, step S2 includes the following sub-steps:

[0245] Step S21: Calculate the average velocity V at the rear interface under different incoming flow velocities and different thrust conditions based on momentum theory. b1 ;

[0246] Momentum theory is a well-known method in the field. The specific process for calculating the average velocity at the rear interface is the same as that for calculating the average velocity at the front interface. In this embodiment, since the flow channel areas at the front and rear interfaces are the same, therefore, V b1 =V1;

[0247] Step S22: Based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power distribution assumption of velocity, calculate the thickness and two-dimensional velocity distribution of the rear hub boundary layer region, and calculate the two-dimensional velocity distribution of the duct exponential distribution transition region based on the velocity distribution law assumption in the circular pipe.

[0248] The formulas for the thickness of the turbulent boundary layer around a downstream flat plate and the assumptions for the power-law velocity distribution, as well as the assumptions for the velocity distribution law inside a circular pipe, are all well-known techniques in this field. The specific process of this step is as follows:

[0249] ① The thickness of the hub boundary layer region was calculated using the formula for calculating the thickness of the turbulent boundary layer on a flat plate:

[0250]

[0251] In the formula, l S Re represents the length of the stator blade domain in a single-duct fan-airfoil coupled configuration. b_hub For l S The Reynolds number, calculated from the characteristic length, is given by the following formula:

[0252]

[0253] In the formula, μ is the dynamic viscosity coefficient, and V b1 The average velocity at the interface is δ; in this embodiment, δ b_hub =0.0023

[0254] Based on the thickness δ of the rear hub boundary layer region b_hub The velocity distribution within the rear hub boundary layer region was obtained by calculating using a power function distribution, namely:

[0255]

[0256] In the formula, u b_hub z represents the velocity at different normal positions within the rear hub boundary layer region. b_hub V represents the coordinates of different normal positions inside the rear hub boundary layer. b_max The maximum velocity in the two-dimensional radial velocity distribution at the rear interface is taken as the outer edge velocity of the rear hub boundary layer, V. b_max The flow velocity distribution law inside a circular pipe is used for calculation, and the specific expression is as follows:

[0257]

[0258] In the formula, the constant n is taken as 7, and V b1 V represents the average velocity at the interface after the intersection. In this embodiment, V b_max It is 66.133 m / s;

[0259] The coordinate point information z of the rear hub boundary layer region b_hub and speed information u b_hub The velocity information matrix of the rear hub boundary layer region is obtained:

[0260] V b_hub =[z b_hub ,u b_hub ]

[0261] ② The velocity distribution in the duct's exponential distribution transition zone is calculated using the exponential formula for velocity distribution within a circular pipe, i.e.:

[0262]

[0263] In the formula, u b_duct r-δ represents the velocity at different normal positions within the transition region of the duct exponent distribution. b_hub z is the length from the outer ring to the outer edge of the rear hub boundary layer. b_duct The coordinates of different normal positions within the transition zone of the duct index distribution are given, with the constant m taking the value of 10.

[0264] The coordinate point information z of the transition zone of the duct index distribution b_duct and speed information u b_duct The velocity information matrix of the duct exponential distribution transition region is obtained:

[0265] V b_duct =[z b_duct ,u b_duct ]

[0266] Step S23: Assemble the two-dimensional velocity distribution in the rear hub boundary layer region and the two-dimensional velocity distribution in the duct index distribution transition region obtained in step S22 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the rear interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the rear interface.

[0267] The assembly method for obtaining the two-dimensional radial velocity distribution on the interface is to merge two-dimensional matrices containing coordinate and velocity information, as shown in the following equation:

[0268]

[0269] In the formula, z b_2D This represents the coordinate distribution after assembling the aft hub boundary layer region and the duct index distribution transition region, u b_2D This represents the velocity distribution after assembling the aft hub boundary layer region and the duct index distribution transition region, such as... Figure 15 As shown; the generated three-dimensional velocity distribution "baseline" on the post-interface is as follows Figure 16 As shown;

[0270] Step S24: Based on the shape of the stator blade trailing edge, generate the central contour of the stator blade wake region. Specifically, obtain the stator blade wake centerline by projecting the stator blade trailing edge shape onto the aft interface. Extend both ends of the stator blade wake centerline to the rotor hub and the duct at the aft interface, respectively, as the central contour of the stator blade wake region. Figure 17 As shown; based on the central contour of the stator blade wake region, the circumferential angle θ of the central contour of the stator blade wake region is obtained. center ;

[0271] Step S25: Based on the three-dimensional velocity distribution "baseline" on the back interface obtained in step S23 and the central contour of the stator blade wake region obtained in step S24, the velocity distribution of the duct exponential distribution transition region is corrected by using a linear function scaling method to obtain the final velocity distribution of the back interface flow field.

[0272] The specific process is as follows:

[0273] Circumferential scaling factor θ of the wake wj_factor for:

[0274]

[0275] In the formula, θ i -θ center σ represents the circumferential angle difference between the current grid point and the central contour of the still leaf wake region. θ This parameter represents the set range for controlling circumferential scaling.

[0276] Based on the circumferential scaling factor θ of the wakewj_factor The following expression is used to scale and correct the velocity on the subsequent interface:

[0277] u isc_b =u i_b ·(1-θ wj_factor )

[0278] In the formula, u i_b For the flow field velocity at each grid point on the "base" distribution of the post-interface, u isc_b The velocity distribution at each grid point of the post-interface is the final velocity distribution of the post-interface flow field after scaling and correction of the velocity at the post-interface. In this embodiment, the momentum source distribution of the post-interface generated based on the velocity distribution of the post-interface obtained by the method of the present invention is compared with the result of MRF calculation. Figure 18 As shown.

[0279] based on Figure 3 The bladeless grid configuration of the single-duct fan-wing section fusion configuration shown verifies the momentum source generation method developed in this patent. The flight conditions and model geometric parameters are shown in Table 1.

[0280] Table 1 Calculation conditions and geometric parameters for the single-ducted fan-wing section blended configuration

[0281]

[0282]

[0283] Based on the Latin hypercube method, 25 sample points were randomly selected within a design space ranging from 35 m / s to 60 m / s, covering the speed range from climb to cruise. First, the flow field of the single-ducted fan-wing section blended configuration at a 4° angle of attack was calculated using the MRF method under different incoming flow velocities, obtaining aerodynamic performance such as thrust and lift-drag coefficients. Then, based on the incoming flow velocity and thrust at each sample point, the momentum source distribution at the front and rear interfaces was calculated using the velocity distribution at the front and rear interfaces obtained by the method of this invention. The lift-drag coefficients were calculated using a flow field simulation method for a distributed ducted fan-wing coupled layout as described in Chinese Patent CN117371344A, and the results were compared with those obtained using the MRF method.

[0284] like Figure 19As shown, within the study scope, under different incoming flow velocities, the average relative error of the lift coefficient was 2.61%, with an error range of 1.13% to 3.72% and a standard deviation of 0.77% for 25 sample points; the average relative error of the drag coefficient was 2.44%, with an error range of 0.75% to 3.94% and a standard deviation of 0.87%; and the average relative error of the pitch moment coefficient was 1.01%, with an error range within 2.88% and a standard deviation of 0.7%. Data analysis indicates that the method used in this invention to calculate the momentum source distribution at the front and rear interface using the velocity distribution at the front and rear interfaces still exhibits high calculation accuracy under different incoming flow velocity conditions.

[0285] Based on the Latin hypercube method, 25 sample points were randomly selected within the design space of 9000RPM≤ω≤12000RPM. The MRF method was used to calculate the flow field of a single ducted fan-wing section blended configuration at a 4° angle of attack under different fan speeds, obtaining aerodynamic performance such as thrust and lift-drag coefficients. Then, based on the incoming flow velocity and thrust of each sample point, the momentum source distribution of the front and rear interfaces was calculated using the velocity distribution of the front and rear interfaces obtained by the method of this invention. The lift-drag coefficient was calculated using a flow field simulation method for distributed ducted fan-wing coupled layout in Chinese Patent CN117371344A, and the results were compared with those of the MRF method.

[0286] like Figure 20 As shown, within the study scope, at different fan speeds, the average relative error of the lift coefficient was 2.93%, with an error range of 1.71% to 4.06% and a standard deviation of 0.63% for 25 sample points; the average relative error of the drag coefficient was 1.9%, with an error range of 1.6% to 2.2% and a standard deviation of 1.15%; and the average relative error of the pitch moment coefficient was 0.72%, with an error range within 1.52% and a standard deviation of 0.41%. Data analysis indicates that the method used in this invention to calculate the momentum source distribution at the front and rear interfaces using the velocity distribution at the front and rear interfaces still exhibits high calculation accuracy under different fan speed conditions.

[0287] In summary, to overcome the problem of decreased computational efficiency caused by the reliance on MRF flow field information in novel momentum source methods, this invention proposes an interface flow field information generation method suitable for ducted fan momentum source methods. This method can improve the aerodynamic performance prediction efficiency of distributed ducted fan-wing blended configurations. After verification under different incoming flow velocities and different fan speeds, the method of this invention improves the aerodynamic performance prediction efficiency while ensuring high computational accuracy.

[0288] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An interface flow field information generation method suitable for a bypass fan momentum source method, characterized by: Includes the following steps: Step S1: Denote the interface in front of the ducted fan blades as the front interface. Divide the front interface into the front hub boundary layer region, the front duct boundary layer region, the wing boundary layer region, the low-energy airflow region, the duct lip boundary layer region, the duct lip acceleration region, and the front uniform transition region. Then, generate velocity distributions for each of the above-described regions, and then assemble and merge them to obtain the velocity distribution on the front interface. The front hub boundary layer region refers to the annular region from the hub wall to the outer boundary of the hub boundary layer on the front interface. The front duct boundary layer region refers to the front hub boundary layer region. The annular region from the inner wall of the duct to the outer boundary of the duct boundary layer; the wing boundary layer region refers to the rectangular region from the upper surface of the wing to the outer boundary of the wing boundary layer; the low-energy airflow region refers to the region from the outer boundary of the wing boundary layer to the position of the average flow velocity at the interface; the duct lip boundary layer region refers to the region from the duct lip wall to the outer boundary of the duct lip boundary layer; the duct lip acceleration region refers to the region obtained by the intersection of the circumferential and radial action range regions, wherein the circumferential action range region is defined as follows: , , , For the center angle, the ± of each center angle The circumferential range is defined as the circumferential range of action. The radial range of action is defined as follows: the radial center position is the point where each central angle ray intersects with the outer ring of the duct, and the radial range around each radial center position is 1 / 10 to 1 / 5 of the duct radius. The pre-uniform transition zone is the remaining area on the pre-intersection interface after removing the above-mentioned partitions. Step S1 includes the following sub-steps: Step S11: Calculate the average velocity at the front interface under different incoming flow velocities and different thrust conditions based on momentum theory; Step S12: Based on the thickness formula of the laminar boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front hub boundary layer region; based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power-law velocity distribution assumption, calculate the thickness and two-dimensional velocity distribution of the front duct boundary layer region; based on the thickness and two-dimensional velocity distribution of the front hub boundary layer region and the thickness and two-dimensional velocity distribution of the front duct boundary layer region, interpolate to calculate the two-dimensional velocity distribution of the front uniform transition region. Step S13: Assemble the two-dimensional velocity distribution in the front hub boundary layer region, the two-dimensional velocity distribution in the front uniform transition region, and the two-dimensional velocity distribution in the front duct boundary layer region obtained in step S12 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the front interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the front interface. Step S14: The thickness and two-dimensional velocity distribution of the wing boundary layer region are calculated using the KAMAN-Bauhausen method. The thickness of the low-energy airflow region is calculated using xfoil. Based on the thickness and two-dimensional velocity distribution of the wing boundary layer region and the thickness of the low-energy airflow region, the two-dimensional velocity distribution of the low-energy airflow region is calculated using cubic spline distribution. The two-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region are assembled and spanwise extended to obtain the three-dimensional velocity distributions of the wing boundary layer region and the low-energy airflow region. The obtained three-dimensional velocity distribution is then "bow-shaped". The specific process of "bow-shaped" processing of the obtained three-dimensional velocity distribution is as follows: Bow-shaped height direction The method for calculating coordinates is as follows: The coordinate system is defined as follows: The axis is along the direction of free flow. The axis is to the right from the pilot's perspective. Direction perpendicular to The plane is upward, satisfying a right-handed system; the calculation object is the velocity distribution scatter points at different spanwise positions in a three-dimensional rectangular velocity distribution, where, Indicates the first The first exhibition position Corrected coordinates of each point Indicates the first The first exhibition position The initial coordinates of the points Indicates the first in the arc-shaped region Individual exhibition location Towards altitude, The thickness of the low-energy airflow region; Step S15: Assemble the velocity distribution of the wing boundary layer region and low-energy airflow region after the "bow-shaped" treatment obtained in step S14 with the three-dimensional velocity distribution "base" on the front interface obtained in step S13, and smooth the area where the wing boundary layer region and low-energy airflow region meet the "base" to obtain the velocity distribution of the front interface flow field considering the hub boundary layer, duct boundary layer, wing boundary layer and low-energy airflow region. Step S16: Based on the velocity distribution of the front interface flow field obtained in step S15, the velocity distribution of the duct lip boundary layer region and the duct lip acceleration region is corrected by using a linear function scaling method to obtain the final velocity distribution of the front interface flow field. Step S2: The interface behind the ducted fan stator blades is designated as the rear interface. The rear interface is divided into the rear hub boundary layer region, the ducted exponential distribution transition region, and the stator blade wake region. Then, velocity distributions are generated for each of the above-mentioned regions, and then assembled and merged to obtain the velocity distribution on the rear interface.

2. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 1, characterized in that: The assembly method for obtaining the two-dimensional radial velocity distribution on the front interface in step S13 is to merge the two-dimensional matrices containing coordinate information and velocity information, as shown in the following formula: In the formula, For the velocity distribution in the front hub boundary layer region Corresponding position coordinates For the uniform transition region velocity distribution Corresponding position coordinates For the velocity distribution in the boundary layer region of the culvert Corresponding position coordinates; This represents the coordinate distribution after assembling the front hub boundary layer region, the front uniform transition region, and the front duct boundary layer region. This indicates the velocity distribution after assembling the front hub boundary layer region, the front uniform transition region, and the front duct boundary layer region.

3. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 1, characterized in that: The specific process of assembling and smoothing the velocity distribution of the wing boundary layer region and low-energy airflow region after the "bow-shaped" treatment with the three-dimensional velocity distribution "base" on the front interface in step S15 is as follows: The regions in the three-dimensional velocity distribution "base" that are lower than the top outer edge of the wing boundary layer region and the low-energy airflow region are deleted, and the velocity distributions of the wing boundary layer region and the low-energy airflow region after "bow-shaped" processing are used to replace them. For the velocity distribution step that occurs at the interface, the velocity step region is smoothed by linear interpolation, so as to obtain the velocity distribution of the front interface flow field that takes into account the hub boundary layer, duct boundary layer, wing boundary layer and low-energy airflow region.

4. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 1, characterized in that: The specific process of step S16 is as follows: ① Establish a linear scaling factor function. The linear scaling function attenuation in the duct lip boundary layer region and the duct lip acceleration region mainly includes two parts: radial attenuation and circumferential attenuation, with the following formulas: Radial scaling factor : In the formula, Indicates the radius of the current grid point. Indicates the duct radius. This parameter represents the set range for controlling radial scaling. Circumferential scaling factor : In the formula, This represents the circumferential angle difference between the current grid point and the center of the boundary layer at the duct lip. This parameter represents the set range for controlling circumferential scaling. ② Multiply the velocity distribution of the front interface obtained in step S15 by the corresponding scaling function to obtain the corrected velocity distribution of the front interface after adjusting for the boundary layer region and acceleration region of the duct lip; specifically: For the duct lip boundary layer region, which is a region of decreasing velocity, the product of the circumferential and radial scaling factors is used as the total scaling factor for the duct lip boundary layer region. : Based on the total scaling factor of the duct lip boundary layer region, the velocity at the front interface is first scaled and corrected using the following expression: Expanded to: In the formula, Let the flow field velocity be the velocity at each point on the interface. The flow field velocity at each point on the front interface after the first scaling correction of the velocity on the front interface; For the duct lip acceleration region, which is the area where the velocity increases, the following expression is used as the total scaling factor for the duct lip acceleration region. : In the formula, To obtain the maximum value of the velocity scaling, the curve at the maximum curvature of the duct lip can be used as the leading edge. After completing the airfoil, the potential flow method can be used to obtain the airflow velocity ratio at the relative positions of the leading interface. The empirical value is taken as 1.2~1.

4. Based on the total scaling factor of the acceleration zone at the duct lip, the velocity at the front interface is corrected for a second scaling using the following expression: Expanded to: ； In the formula, The velocity distribution at each point on the front interface after the second scaling correction of the velocity on the front interface is the final velocity distribution of the front interface.

5. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 1, characterized in that: In step S2, the aft hub boundary layer region refers to the annular region on the aft interface from the hub wall to the outer boundary of the hub boundary layer; the stator wake region refers to the central outline of the stator wake region obtained by projecting the stator trailing edge shape onto the aft interface, and then expanding the central outline of the stator wake region circumferentially. The area within the angular range; the duct index distribution transition zone refers to the remaining area on the rear interface after removing the aforementioned partitions.

6. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 1, characterized in that: Step S2 includes the following sub-steps: Step S21: Calculate the average velocity at the rear interface under different incoming flow velocities and different thrust conditions based on momentum theory; Step S22: Based on the thickness formula of the turbulent boundary layer around the downstream flat plate and the power distribution assumption of velocity, calculate the thickness and two-dimensional velocity distribution of the rear hub boundary layer region, and calculate the two-dimensional velocity distribution of the duct exponential distribution transition region based on the velocity distribution law assumption in the circular pipe. Step S23: Assemble the two-dimensional velocity distribution in the rear hub boundary layer region and the two-dimensional velocity distribution in the duct index distribution transition region obtained in step S22 according to their spatial positions to obtain the two-dimensional radial velocity distribution on the rear interface. Rotate the obtained two-dimensional radial velocity distribution around the fan axis in the circumferential direction to generate the three-dimensional velocity distribution "base" on the rear interface. Step S24: Based on the shape of the stator blade trailing edge, generate the central contour of the stator blade wake region. Specifically, obtain the stator blade wake centerline by projecting the stator blade trailing edge shape onto the aft interface. Extend both ends of the stator blade wake centerline to the rotor hub and the duct at the aft interface, respectively, to form the central contour of the stator blade wake region. Based on the central contour of the stator blade wake region, obtain the circumferential angle of the central contour of the stator blade wake region. ; Step S25: Based on the three-dimensional velocity distribution "baseline" on the back interface obtained in step S23 and the central contour of the stator blade wake region obtained in step S24, the velocity distribution of the duct exponential distribution transition region is corrected by using a linear function scaling method to obtain the final velocity distribution of the back interface flow field.

7. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 6, characterized in that: The assembly method for obtaining the two-dimensional radial velocity distribution on the interface in step S23 is to merge the two-dimensional matrices containing coordinate and velocity information, as shown in the following formula: In the formula, This represents the coordinate distribution after assembling the aft hub boundary layer region and the duct index distribution transition region. This represents the velocity distribution after assembling the aft hub boundary layer region and the duct index distribution transition region. This indicates the coordinates of different normal positions inside the rear hub boundary layer. The velocity at different normal positions within the rear hub boundary layer region. These represent the coordinates of different normal positions within the transition zone of the duct index distribution. This represents the velocity at different normal positions within the transition zone of the duct index distribution.

8. The method for generating interface flow field information applicable to the momentum source method of ducted fans according to claim 6, characterized in that: The specific process of step S25 is as follows: Circumferential scaling factor of the wake for: In the formula, This represents the circumferential angle difference between the current grid point and the central contour of the still leaf wake region. This parameter represents the set range for controlling circumferential scaling. Based on the circumferential scaling factor of the wake The following expression is used to scale and correct the velocity on the subsequent interface: In the formula, The flow field velocity at each grid point on the "base" distribution of the post-interface interface. The velocity distribution at each grid point of the back interface after scaling and correcting the velocity on the back interface is the final velocity distribution of the back interface flow field.

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