Wide-area air inlet channel design method based on double-shoulder wave absorption flow field stable control

By adopting the three-stage external compression and first-stage internal compression in the intake channel of the suction hypersonic aircraft, combined with the principle of wave elimination on both shoulders, the geometric relationship of the intake channel is optimized, the problem of instability of flow field under low Mach numbers is solved, and efficient flow field stability control and performance improvement is achieved.

CN120145537APending Publication Date: 2025-06-13NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Patent Information

Application Number
CN202510069891.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-01-16
Publication Date
2025-06-13

AI Technical Summary

Technical Problem

The intake duct of the suction hypersonic aircraft is prone to instability in the flow field at low Mach numbers, resulting in the problems of separation flow and non-starting. The prior art relies on the suction groove for flow field stability control, but it leads to compressed airflow loss and additional aerodynamic resistance.

Method used

The three-stage external compression and first-stage internal compression are adopted to determine the profile scheme of the intake duct through theoretical oblique shock relationship, and the geometric relationship between the compression surface and the lip mask is optimized under the requirements of structural thermal protection, forming a wide-domain intake duct design with stable control of wave-elimination flow field on both shoulders.

Benefits of technology

Without the use of a suction groove, flow field stable control in the wide Mach number range of the intake channel is achieved, which improves the performance of the intake channel, reduces additional drag, and meets the needs of wide-domain flight.

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Abstract

According to the wide-area air inlet channel design method based on double-shoulder wave absorption flow field stable control, two shoulders corresponding to the high Mach number and the low Mach number of an air inlet channel are constructed, so that lip mask shock waves are located between the two shoulders all the time, expansion waves formed by the shoulders are used for greatly weakening the strength of the lip mask shock waves, the size of a separation area is restrained, and the stability of the separation area is improved. And stable control of the flow field of the wide-area air inlet channel is realized from the source of the wave system organization. Compared with an existing suction flow field stable control method, the method has the advantages that the actual flow of the engine is increased, the additional resistance of the suction groove is reduced, and the method is greatly beneficial to improving the performance of the wide-area air inlet channel.
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Description

Technical Field

[0001] The present invention relates to the field of air-breathing hypersonic vehicles, and particularly to a design method for a wide-range inlet based on dual-shoulder shock wave cancellation and flow field stability control. Background Art

[0002] Air-breathing hypersonic vehicles are continuously expanding their flight capabilities in a wide speed range and large airspace, requiring the engine to have the ability to operate in a wide range. The inlet is responsible for efficiently compressing the free incoming flow and providing the required air flow rate for the engine. It is an essential component of air-breathing ramjet-powered vehicles, and its flow field stability characteristics directly affect the aerodynamic force of the vehicle and the stable operating boundary of the engine. However, the free incoming flow is compressed step by step through the inlet, which is a reverse pressure gradient flow process. In particular, the anti-backpressure ability of the low Mach number incoming flow is poor, which easily leads to the instability of the inlet flow field, the emergence of a large flow separation zone, and the failure to start. Therefore, broadening the lower boundary of the operating Mach number of the hypersonic inlet is of great significance for the development of wide-range vehicles.

[0003] In fact, the interference between the shock wave and the boundary layer in the wide-range inlet is severe, especially the interference between the shock wave induced by the cowl and the boundary layer. Inevitably, separated flow occurs in the contraction section of the inlet. Once the suppression or control of this separation zone is improper, it will cause the instability of the inlet flow field. Under the action of the reverse pressure gradient, the separation zone continuously increases until it fails to start. In engineering, a large number of suction slots are designed in the interference region between the shock wave and the boundary layer to discharge the high-pressure boundary layer out of the engine flow channel, which has a good suppression and control effect on the separation zone. However, the suction slots cause losses of the compressed air flow and additional aerodynamic drag. If the interference intensity between the cowl shock wave and the boundary layer can be weakened from the wave system organization at the source, the separation zone can be eliminated or the size of the separation zone can be suppressed, and the flow field stability of the wide-range inlet at low Mach numbers can be improved, then the suction slots can be not used or the number of suction slots can be reduced, further improving the performance of the inlet. Therefore, it is necessary to develop a flow field stability control method for the wide-range inlet from the wave system organization. Summary of the Invention

[0004] Object of the Invention: To solve the above problems, the present invention provides a design method for a wide-range inlet with dual-shoulder shock wave cancellation and flow field stability control, which realizes the stable control of the inlet flow field in a wide Mach number range without using suction slots, improves the performance of the inlet, and meets the requirements of wide-range flight.

[0005] Technical Solution: To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] Adopt the method of three - stage external compression and one - stage internal compression. First, artificially set the deflection angles of the first - stage and second - stage compression surfaces. Obtain the Mach numbers and their angles before and after each stage of compression shock from the theoretical oblique shock relationship. According to the geometric principle of sealing the compression shock and eliminating the shock at the shoulder of the cowl shock, determine the preliminary profile scheme of the inlet duct from the theoretical oblique shock relationship.

[0007] 1) Take the high Mach number at which the wide - range inlet duct operates as the design Mach number. Adopt the method of three - stage external compression and one - stage internal compression. Given the deflection angles of the first - stage and second - stage compression surfaces, obtain the Mach numbers and their angles before and after each stage of compression shock from the theoretical oblique shock relationship. Determine the preliminary profile scheme of the inlet duct according to the geometric relationship corresponding to the principle of sealing the compression shock and eliminating the shock at the shoulder of the cowl shock.

[0008] 2) Considering the need for structural thermal protection, round and blunt the leading edge and lip of the inlet duct. Based on the shock position under viscous passivation conditions obtained from numerical simulation, with the goals of sealing the compression shock and eliminating the shock at the shoulder of the cowl shock, optimize the lengths of the first - stage and second - stage compression surfaces, the flow - direction position of the cowl, and the position of the inlet - duct shoulder.

[0009] 3) Take the average Mach number M t at the throat outlet section to be about half of the high Mach number M h as the goal. Determine the throat height h t corresponding to the high Mach number through iteration, and form the basic profile scheme of the wide - range inlet duct.

[0010] 4) Take the intersection of the second - stage and third - stage compression surfaces as the rotation axis, use the third - stage compression surface as the rotation - adjustment surface, and adopt the throat - height adjustment scheme of a slider - driven parallel double - link mechanism to realize the adjustment of the internal contraction ratio of the wide - range inlet duct.

[0011] 5) Rotate the third - stage compression surface clockwise by an angle δ to increase the throat height, complete the numerical simulation of the low Mach number M l of the wide - range inlet duct, obtain the Mach number M t at the throat outlet and the position of the low - Mach - number cowl shock. Take the Mach number at the throat outlet to be about half of the low Mach number as the goal, and iteratively determine the throat height at the low Mach number and the corresponding position of the low - Mach - number cowl shock.

[0012] 6) According to the position of the low - Mach - number cowl shock, redesign the third - stage compression surface, add an inflection point to the original straight - line segment to construct the second inlet - duct shoulder, forming a three - stage compression surface with a shoulder. The inflection point is located on the low - Mach - number cowl shock, and the specific position can be determined according to the equality of the low - Mach - number shoulder expansion angle and the high - Mach - number shoulder expansion angle. Thus, a preliminary scheme of the wide - range inlet duct with stable control of the double - shoulder shock - elimination flow field is formed.

[0013] 7) For the preliminary design of a wide - range inlet for the stable control of the double - shoulder shock - attenuation flow field, numerical simulations at high and low Mach numbers are completed to obtain the shock position of the cowl under the double - shoulder profile and the Mach number at the throat exit section, and the position of the inflection point of the third - stage compression surface and the height of the throat are iteratively optimized;

[0014] 8) The cubic Bézier curve is used to enhance the expansion shock - attenuation effect of the second inlet shoulder. Taking the mid - points of the two straight - line segments of the third - stage compression surface as the tangent endpoints respectively, by changing the length coefficients of the Bézier curve endpoints and adjusting the Bézier curve, it can deflect rapidly at the low - Mach - number cowl shock.

[0015] Furthermore, the high Mach number generally takes the upper limit value of the working Mach number range, but should not exceed Mach number 7.0.

[0016] Furthermore, the deflection angles of the first - stage compression surface and the second - stage compression surface should not be too large, generally within 6°.

[0017] Furthermore, the shock closure is that the first - stage compression shock and the second - stage compression shock hit the inlet lip position.

[0018] Furthermore, the shoulder shock - attenuation is that the high - Mach - number cowl shock hits the intersection of the third - stage compression surface and the throat profile.

[0019] Furthermore, the throat length is generally about 1 - 3 times the throat height h t of.

[0020] Furthermore, the low Mach number generally takes the lower limit value of the working Mach number range, but should not be lower than Mach number 2.5.

[0021] Furthermore, the low - Mach - number numerical simulation of the wide - range inlet is completed under the condition of having a suction slot. l is completed under the condition of having a suction slot.

[0022] Furthermore, the low - Mach - number shoulder expansion angle is the acute angle formed by the two straight - line segments of the third - stage compression surface with an inflection point, and generally should not be less than 6°.

[0023] Furthermore, the high - Mach - number shoulder expansion angle is the acute angle formed by the end of the third - stage compression surface with an inflection point and the throat, and generally should not be less than 6°.

[0024] Beneficial effects: Compared with the prior art, the present invention has the following remarkable effects: Double shoulders are constructed according to the upper and lower values of the working Mach number range, and the cowl shock wave is always located between the two shoulders. The expansion wave formed by the shoulders significantly weakens the intensity of the cowl shock wave, suppresses the size of the separation zone, and realizes the stable control of the flow field of the wide-range inlet. Compared with the existing suction flow field stable control method, the actual flow rate used for the engine is increased, the additional resistance of the suction slot is reduced, which is of great benefit to improving the performance of the wide-range inlet. Brief Description of the Drawings

[0025] Figure 1 It is a schematic diagram of the high Mach number profile of the wide-range inlet described in the present invention.

[0026] Figure 2 It is a schematic diagram of the principle of the adjustment scheme of the wide-range inlet described in the present invention.

[0027] Figure 3 It is a schematic diagram of the low Mach number profile of the wide-range inlet described in the present invention.

[0028] Figure 4 It is a schematic diagram of the double-shoulder design of the wide-range inlet described in the present invention.

[0029] Figure 5 It is a schematic diagram of the wide-range inlet based on the double-shoulder shock wave elimination flow field stability control described in the present invention.

[0030] Figure 6 It is a schematic diagram of the enhanced design of the shoulder expansion shock wave elimination effect. Detailed Embodiment

[0031] The present invention discloses a method for stabilizing the flow field of a wide-range inlet based on double-shoulder shock wave elimination. Please refer to Figures 1 to 5 As shown below, taking the wide-range two-dimensional inlet as an example, the detailed implementation steps of the design of the present invention will be described.

[0032] 1. As Figure 1 shown, taking the high Mach number at which the wide-range inlet operates as the design Mach number, adopting the method of three-stage external compression and one-stage internal compression, the deflection angles of the first-stage and second-stage compression surfaces are given empirically, and the Mach numbers and angles before and after each stage of compression shock wave are obtained according to the theoretical oblique shock wave relationship. According to the geometric relationship corresponding to the principle of compression shock wave sealing and cowl shock wave shoulder shock wave elimination, the preliminary profile scheme of the inlet is determined.

[0033] Generally, the upper limit value of the working Mach number range of the inlet is selected for the high Mach number, but it should not exceed Mach number 7.0.

[0034] The deflection angle θ 1 of the first-stage compression surface 1 and the deflection angle θ 2 of the second-stage compression surface 2 should not be too large, generally within 6°.

[0035] According to the theoretical oblique shock relations shown below, from the design Mach number M h , the deflection angle θ 1 of the first-stage compression surface 1, the angle β 1 of the first-stage compression shock 10 and the Mach number M 1 behind the wave can be calculated; further, from M 1 and θ 2 , the angle β 2 of the second-stage compression shock 9 and the Mach number M 2 behind the wave can be calculated; neglecting the influence of the third-stage compression shock 8, the deflection angle θ c of the air flow after being compressed by the lip cowl 6 is the sum of θ 1 and θ 2 , and combining with M 2 can calculate β c .

[0036]

[0037] Where: M 1 is the Mach number in front of the oblique shock; M 2 is the Mach number behind the oblique shock; β is the shock angle, θ is the deflection angle, and γ is the specific heat ratio of the gas, taking 1.4.

[0038] According to the first-stage compression shock 10 and the second-stage compression shock 9 being sealed (i.e., intersecting at the intake lip F point), the length of the first-stage compression surface 1 and the position of the lip cowl 6 can be determined by geometric relations.

[0039] The third-stage compression shock 8 can hit inside the lip cowl. First, arbitrarily specify the deflection angle of the third-stage compression surface 3, and its starting position C should be upstream of the intake entrance section.

[0040] The lip cowl 6 is designed according to the principle of minimum aerodynamic drag, that is, a flat lip cowl with first-stage internal compression is adopted. The induced shock 7 of the lip cowl intersects at the first intake shoulder D point (the intersection D of the third-stage compression surface 3 and the throat 4) of the intake, and the third-stage compression surface 3 can be determined by geometric relations.

[0041] The length of the throat 4 is generally 1 to 3 times the throat height h t , and the throat 4 and the end of the lip cowl 6 form the throat exit section 5.

[0042] 2. Considering the requirements of structural thermal protection, the leading edge A and the lip F of the intake are rounded and blunted. Based on the shock wave system position under the viscous blunting conditions obtained by numerical simulation, with the goal of sealing the compression shock and eliminating the wave at the lip cowl shock shoulder, optimize the lengths of the first-stage compression surface 1 and the second-stage compression surface 2, the flow direction position of the lip cowl 6, and the position of the first intake shoulder D.

[0043] Considering the real viscosity and blunting conditions, the compression shock angle slightly increases, and the cowl 6 moves upstream according to the position of the first-stage compression shock 10; according to the position of the optimized cowl 6 and the angle of the second-stage compression shock 9, the length of the first-stage compression surface 1 is shortened; according to the position of the cowl-induced shock 7, the length of the throat 4 is adjusted to ensure that the high Mach number cowl-induced shock 7 hits the point D on the shoulder of the first inlet.

[0044] 3. Taking the mass flow average Mach number M at the throat outlet section 5 t as about half of the high Mach number M h as the target, if the throat Mach number M t significantly exceeds half of the high Mach number M h , the height of the throat 4 is reduced; otherwise, the height of the throat 4 is increased until the deviation between the throat Mach number M t and the high Mach number M h is within ±0.2. The throat height h corresponding to the high Mach number is determined by iteration t to form the basic profile scheme of the wide-range inlet.

[0045] 4. As Figure 2 shown, taking the intersection point C of the second-stage compression surface 2 and the third-stage compression surface 3 as the rotation axis, using the throat height adjustment scheme of the slider 11 pushing the parallel double-link 12 to adjust the contraction ratio h 2 / h t in the wide-range inlet.

[0046] 5. Rotate the third-stage compression surface 3 clockwise by an angle δ to increase the height of the throat 4, complete the numerical simulation of the low Mach number M l in the wide-range inlet, obtain the mass flow average Mach number M at the throat outlet section 5 t and the position of the low Mach number cowl shock 13, and taking the throat outlet Mach number M t as about half of the low Mach number M l as the target, iteratively determine the height of the throat 4 at the low Mach number M l . If the throat Mach number M t significantly exceeds half of the low Mach number M l , the height of the throat 4 is reduced; otherwise, the height of the throat 4 is increased until the deviation between the throat Mach number M t and the low Mach number M l is within ±0.2.

[0047] The low Mach number M l is generally taken as the lower limit of the working Mach number range of the wide-range inlet, but should not be lower than Mach 2.5.

[0048] During the numerical calculation process, according to the oblique shock wave relationship, the approximate position where the low Mach number cowl shock wave 13 hits the third-stage compression surface 3 is estimated, and a bleed slot 14 is designed nearby to avoid the influence of inlet unstart on the determination of the low Mach number throat 4 height during the numerical calculation process.

[0049] 6. As Figure 3 shown, according to the position of the low Mach number cowl shock wave 13, the third-stage compression surface 3 is redesigned, and an inflection point G is added in the middle of the straight line segment CD to construct the second shoulder of the inlet, forming a three-stage compression surface 15 with a shoulder. The G point of the second inlet shoulder is located on the low Mach number cowl shock wave 13. Thus, a preliminary scheme of a wide-range inlet with a double-shoulder shock wave elimination flow field stable control is formed.

[0050] As Figure 4 shown, the included angle between the line segment CF and the line segment FD is the low Mach number shoulder expansion angle θ l ; the three-stage compression surface 15 with a shoulder is rotated counterclockwise by δ degrees to restore the height of the high Mach number throat 4. At this time, the included angle between the line segment FD and the throat 4 is the high Mach number shoulder expansion angle θ h . Moving the G point of the second inlet shoulder along the low Mach number cowl shock wave 13 can simultaneously change the shoulder expansion angles θ l and θ h corresponding to high and low Mach numbers. The position of the G point of the second inlet shoulder can be determined according to the equality of the high and low Mach number shoulder expansion angles, that is, θ l = θ h , generally not less than 6°.

[0051] 7. As Figure 5 shown, for the preliminary scheme of the wide-range inlet with a double-shoulder shock wave elimination flow field stable control, numerical simulations of high Mach number M h and low Mach number M l are completed to obtain the position of the low Mach number cowl shock wave 13 and the Mach number of the throat outlet section 5 under the double-shoulder profile. Taking the high Mach number cowl shock wave 7 hitting exactly at the D point of the first inlet shoulder and the low Mach number cowl shock wave 13 hitting exactly at the G point of the second inlet shoulder as the goal, the position of the inflection point G of the third-stage compression surface 15 and the height of the throat 4 are iteratively optimized.

[0052] 8. As Figure 6 shown, when the structural implementation allows, a cubic Bézier curve 16 can be used to enhance the expansion shock wave elimination effect of the G point of the second inlet shoulder. Taking the midpoints H and I of the line segments CF and DE as the tangent endpoints respectively, by changing the length coefficients n 1 and n 2 of the Bézier curve endpoints, the Bézier curve is adjusted to make it deflect rapidly at the low Mach number cowl shock wave 13.

Claims

1. A wide-range air intake design method based on double-shoulder wave-breaking flow field stability control, characterized in that: The following steps are involved: 1) Taking the high Mach number of the wide-band inlet as the design Mach number, adopting the method of three-stage external compression and one-stage internal compression, given the deflection angles of the first-stage and second-stage compression surfaces, the Mach number and angle before and after each stage of compression shock wave are obtained from the theoretical oblique shock wave relationship, and the preliminary profile scheme of the inlet is determined according to the geometric relationship corresponding to the compression shock wave sealing and lip cover shock wave shoulder wave elimination principle; The three-stage external compression method comprises a first-stage compression surface (1), a second-stage compression surface (2) and a third-stage compression surface (3) extending from front to rear, and the third-stage compression surface (3) extends into the inner channel of the air inlet duct; the one-stage internal compression method adopts a flat lip mask of the one-stage internal compression; 2) The leading edge and lip of the inlet are rounded, and the shock wave system position under the viscous passivation condition obtained by numerical simulation is optimized with the compression shock wave sealing and the lip cover shock wave shoulder wave elimination as the goal, and the length of the first-stage compression surface (1) and the second-stage compression surface (2), the flow direction position of the lip cover (6), and the position of the first inlet shoulder (D) are optimized; 3) The average Mach number M of the mass flow rate at the throat outlet section (5) t For high Mach number M h The target is about half of the throat Mach number M. t Significantly exceeds the high Mach number M h half of the height h of the throat (4). t Otherwise, the height h of the throat (4) is increased. t , until the throat Mach number M t With high Mach number M h The deviation between them is within the preset deviation, forming the basic profile scheme of the wide-range air intake; 4) The intersection of the second-stage compression surface (2) and the third-stage compression surface (3) is used as a rotation axis, and the third-stage compression surface (3) is used as a rotation adjustment surface. The back surface of the third-stage compression surface (3) is hinged to one end of a parallel double connecting rod (12), and a slider (11) is hinged to the other end of the parallel double connecting rod (12). The slider (11) pushes the parallel double connecting rod (12) to make the third-stage compression surface (3) close to or away from the lip mask, so that the height of the throat (4) is adjusted, thereby realizing the adjustment of the contraction ratio in the wide range of the air intake duct; 5) Rotate the third stage compression surface (3) clockwise by an angle δ to increase the height of the throat (4) to achieve a wide range inlet with low Mach number M l The numerical simulation of the throat outlet section (5) is used to obtain the average Mach number M of the mass flow rate. t and the position of the low Mach number lip shock wave (13), and the throat exit Mach number M t For low Mach number M l The target is about half of the throat exit Mach number M. t Significantly exceeds the low Mach number M l If the Mach number at the throat exit is half of that at the throat exit, the height of the throat (4) is reduced; otherwise, the height of the throat (4) is increased until the Mach number M at the throat exit is t With low Mach number M l The deviation between them is within the preset deviation; 6) According to the position of the low Mach number lip shock wave (13), the third-stage compression surface (3) is redesigned, and an inflection point is added in the middle of the compression surface to construct the second air inlet shoulder (G), so as to form a third-stage compression surface with a shoulder (15). The second air inlet shoulder (G) is located on the low Mach number lip shock wave (13), and the specific position is determined according to the equal expansion angle of the low Mach number shoulder and the high Mach number shoulder. Thus, a preliminary scheme of a wide-range air inlet with double shoulder wave-breaking flow field stability control is formed; 7) A preliminary scheme for a wide-range inlet with stable control of the double-shoulder wave-breaking flow field is developed. The numerical simulations of high and low Mach numbers are completed to obtain the position of the lip shroud shock wave under the double-shoulder profile and the Mach number of the throat outlet section (5). The position of the inflection point of the third-stage compression surface (15) and the height of the throat (4) are adjusted with the goal that the high-Mach-number lip shroud shock wave (7) hits the first inlet shoulder (D) and the low-Mach-number lip shroud shock wave (13) hits the second inlet shoulder (G); 8) A cubic Bezier curve (16) is used to enhance the expansion and wave-breaking effect of the shoulder (G) of the second inlet duct, and the midpoints (H, I) of two straight line segments of the third stage compression surface (15) are used as tangent endpoints. By changing the length coefficient of the Bezier curve endpoints and adjusting the Bezier curve, the Bezier curve is rapidly deflected at the low Mach number lip shroud shock wave (13).

2. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The high Mach number is an upper limit of the working Mach number range, but does not exceed Mach number 7.

0.

3. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The deflection angles of the first-stage compression surface and the second-stage compression surface are within 6°.

4. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The compression shock wave sealing principle is to design the first-stage compression shock wave (10) and the second-stage compression shock wave (9) to hit the lip position of the air inlet under the Mach number.

5. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The lip shroud shock wave shoulder wave elimination principle is that the high Mach number lip shroud shock wave (7) hits the intersection of the third stage compression surface (3) and the throat (4) profile.

6. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The throat length is the throat height h t 1 to 3 times of.

7. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The low Mach number is the lower limit of the working Mach number range, but is not lower than Mach number 2.

5.

8. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The low Mach number M of the wide inlet l The numerical simulation is completed under the condition that the approximate position of the low Mach number lip shroud shock wave (13) hitting the third stage compression surface (3) is determined based on the oblique shock wave relationship and the suction groove (14) is designed.

9. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 1 is characterized in that: The low Mach number shoulder expansion angle is an acute angle formed by two straight line segments of the third-stage compression surface with an inflection point, which is not less than 6°; the high Mach number shoulder expansion angle is an acute angle formed by the tail end of the third-stage compression surface with an inflection point and the throat, which is not less than 6°.

10. The wide-range air intake design method based on double-shoulder wave-breaking flow field stability control according to claim 9 is characterized in that: In step (6), moving the shoulder (G) point of the second inlet duct along the low Mach number lip shock wave (13) can simultaneously change the shoulder expansion angle θ corresponding to high and low Mach numbers. l and θ h , according to the high and low Mach number shoulder expansion angles are equal to determine the position of the second inlet shoulder (G), that is, θ l =θ h .

Citation Information

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