Novel parallel double-throat thrust vectoring nozzle and design method thereof

By designing a parallel double throat system in the thrust vector nozzle, and using the rectifier and deflection control plate to achieve airflow deflection, the problem of low vector control efficiency at high down pressure ratio of existing nozzles is solved, and structural simplification and efficient vector control are achieved.

CN119686868AActive Publication Date: 2025-03-25NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Patent Information

Application Number
CN202411621508.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-14
Publication Date
2025-03-25
Estimated Expiration
2044-11-14

AI Technical Summary

Technical Problem

The existing thrust vector nozzle has low vector control efficiency under high down pressure ratio conditions, and is complex in structure, heavy in weight, and has high maintenance difficulty.

Method used

A new type of parallel double throat thrust vector nozzle is designed. By setting a rectifier and a deflection control plate on the nozzle, a parallel double throat system is formed, and the deflection and vector control of the airflow is achieved by linear action of the deflection control plate.

Benefits of technology

Linear vector control under high down pressure ratio conditions is realized, structural design is simplified, and weight and maintenance difficulty is reduced.

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Abstract

The invention discloses a novel parallel double-throat thrust vectoring nozzle and a design method thereof. The novel parallel double-throat thrust vectoring nozzle comprises a nozzle main wall, a nozzle side wall and a control device, an internal space formed by the spray pipe main wall and the spray pipe side wall forms a flow channel, and the section of the flow channel is rectangular; the spray pipe main wall is composed of a spray pipe equal straight section, a spray pipe contraction section and a spray pipe expansion section which are integrally designed, and molded surfaces are smoothly connected; one side of the nozzle straight section is an inlet section of the nozzle, and one side of the nozzle expansion section is an outlet section of the nozzle; the control device comprises a rectification piece and a deflection control piece, and the rectification piece is fixed in a groove formed in the side wall of the spray pipe; and the deflection control sheet is fixed on the side wall of the spray pipe through a rotating shaft. The parallel double-throat thrust vectoring nozzle is simple in structure, and establishment of a flow field is guaranteed; the rectifying piece can guarantee that upstream airflow is stable, linear vector control over wake flow can be achieved through linear deflection of the deflection control piece, and the vector control effect cannot be attenuated under the high drop pressure ratio.
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Description

Technical Field

[0001] The present invention belongs to the technical field of supersonic thrust vectoring nozzles, and in particular relates to a novel parallel double-throat thrust vectoring nozzle and a design method thereof. Background Art

[0002] With the rapid development of aircraft, thrust vector control will become a standard configuration of aircraft in the future. As the core of thrust vector control technology, thrust vector nozzle can greatly improve the overall performance of aircraft and expand the flight envelope; give full play to the potential of aircraft, such as maneuverability and agility in over-stall conditions such as high angle of attack flight; reduce the size of rudders or even replace horizontal tail and vertical tail, enhance the stealth performance of aircraft, and reduce the weight of aircraft; greatly shorten the take-off and landing distance of aircraft, such as vertical take-off and landing.

[0003] At present, thrust vectoring nozzles are mainly divided into two types: mechanical and pneumatic. Traditional mechanical thrust vectoring nozzles are complex in structure, heavy in weight, and difficult to maintain; the vector control effect of most pneumatic thrust vectoring nozzles is nonlinear, often accompanied by hysteresis, and the vector control efficiency is low under high pressure drop ratio (NPR>10) conditions. Therefore, it is urgent to propose a new type of thrust vectoring nozzle that can be linearly controlled, has a simple structure, and can still achieve normal control effects under high NPR conditions. Summary of the invention

[0004] In view of the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a novel parallel dual-throat thrust vector nozzle and a design method thereof. Based on the Laval nozzle profile, a deflection control plate arranged at a special position is obtained through transformation. The control plate and the upper and lower walls of the nozzle respectively form a parallel dual-throat system. The mainstream is disturbed by the linear actuation of the control plate to achieve deflection of the airflow, thereby achieving linear vector control; the needs of the aircraft for thrust vector control can be met.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A novel parallel double-throat thrust vector nozzle of the present invention comprises: a nozzle main wall, a nozzle side wall and a control device; the internal space formed by the nozzle main wall and the nozzle side wall forms a flow channel, and the cross section of the flow channel is rectangular;

[0007] The main wall of the nozzle is composed of a straight section, a nozzle contraction section and a nozzle expansion section, and the three are designed as an integrated whole and connected with smooth surfaces; one side of the straight section is the inlet section of the nozzle, and one side of the nozzle expansion section is the outlet section of the nozzle;

[0008] The control device comprises a straightening piece and a deflection control piece. The straightening piece is fixed in a groove provided on the side wall of the nozzle; the deflection control piece is fixed on the side wall of the nozzle through a rotating shaft.

[0009] Furthermore, the straightening piece gradually becomes wider, and the nozzle contraction section and the straightening piece form a gradual contraction trend of the flow channels on both sides of the control device; the deflection control piece gradually becomes narrower, and the nozzle expansion section and the deflection control piece form a gradual expansion trend of the flow channels on both sides of the control device, thereby the control device is combined with the nozzle contraction section and the nozzle expansion section to form a contraction-expansion nozzle, and the flow channels on both sides of the control device are respectively provided with a throat to form a parallel double throat.

[0010] Furthermore, the throat indicates the narrowest position of the flow channel.

[0011] Furthermore, the upper and lower surfaces of the rectifying piece and the deflection control piece are both smooth curved surfaces.

[0012] Furthermore, the windward end of the rectifying piece is a sharp angle, and the leeward end is an arc.

[0013] Furthermore, the windward end of the deflection control piece is an arc, the leeward end is a sharp angle, and the windward end is completely fitted with the leeward end of the rectifying piece.

[0014] Furthermore, the nozzle expansion section has two expansions along the airflow direction, the first expansion part is called the basic section; the second expansion part is called the re-expansion section; and the intermediate transition part between the first expansion and the second expansion is called the connecting section.

[0015] Furthermore, the nozzle expansion section is composed of a base section, a connecting section and a re-expansion section, and the three sections are smoothly connected.

[0016] Furthermore, the deflection control plate and the rotating shaft are integrally formed.

[0017] In the present invention, the airflow enters the flow channel from the inlet section of the nozzle, and is divided into two airflows through the straightening plate. The two airflows are gradually accelerated in the contraction flow channel formed by the nozzle contraction section and the straightening plate, respectively, reaching the speed of sound at the throat position, and gradually accelerated to the supersonic speed in the expansion flow channel formed by the nozzle expansion section and the deflection control plate; the two airflows are formed into one after passing through the deflection control plate, and the rotation of the rotating shaft drives the deflection control plate to deflect, thereby realizing the deflection of the outflowing airflow.

[0018] The present invention provides a design method for a novel parallel double-throat thrust vectoring nozzle, the steps of which are as follows:

[0019] Step 1): Determine the original throat height H of the nozzle that first contracts and then expands according to the design requirements. th , exit height, overall expansion length of the nozzle, and the required vector deflection angle α;

[0020] Step 2): Determine the overall profile of the control device according to the vector deflection angle α: make a straight line with an angle α with the horizontal position tangent to the expansion part of the original first contraction-then expansion nozzle selected in step 1), the straight line intersects the contraction part of the original first contraction-then expansion nozzle at a point, intercept the original first contraction-then expansion nozzle profile between the tangent point and the intersection point, and symmetric along the straight line;

[0021] Step 3): Set the minimum distance h between the nozzle expansion section and the control device: Denote point A on the control device, point B on the nozzle expansion section, and the distance between AB is h;

[0022] Step 4): replace the profile near point A on the control device in step 3) with a small arc to ensure that the minimum distance h of the control device remains unchanged when performing vector control around the rotation axis. Specifically, a circle is drawn with the rotation axis as the center and the distance from the center to point A as the radius, and is smoothly connected to the profile of the control device;

[0023] Step 5): cutting the profile obtained in step 2) into two parts along the circle made in step 4), wherein the part close to the nozzle inlet section is a straightening piece, and the other part close to the nozzle outlet section is a deflection control piece, so as to ensure that the upstream airflow is stable when the control device performs vector control around the rotation axis;

[0024] Step 6): The expansion angle β of the basic section of the nozzle expansion section and the vector deflection angle α are set to have the following relationship: β=α+13°, the expansion angle γ of the re-expansion section and the vector deflection angle α are set to have the following relationship: γ=β+20°, the basic section and the re-expansion section are smoothly connected by the connecting section, and the three sections are combined to obtain the nozzle expansion section;

[0025] Step 7): Set the height of the nozzle inlet section and the height of the nozzle straight section to be greater than the original height H of the nozzle throat that first contracts and then expands in step 1). th , and obtain straight sections such as the nozzle;

[0026] Step 8): The nozzle contraction section is set to reach the contraction limit at the throat position, and the nozzle contraction section is smoothly connected with the nozzle straight section and the nozzle expansion section respectively;

[0027] Step 9): the straight section of the nozzle obtained in step 7), the nozzle contraction section set in step 8), and the nozzle expansion section obtained in step 6) are combined to form a new first contraction-then expansion nozzle as the nozzle main wall;

[0028] Step 10): Setting the length of the nozzle side wall to be greater than or equal to the distance from the nozzle inlet section to the nozzle outlet section to obtain the nozzle side wall;

[0029] Step 11): The nozzle side wall obtained in step 10), the nozzle main wall obtained in step 9), and the rectifying piece and the deflection control piece obtained in step 5) are combined to form a complete vector nozzle.

[0030] Beneficial effects of the present invention:

[0031] The parallel double-throat vector nozzle of the present invention has a simple structure, and the main wall of the nozzle is of the type of first contraction and then expansion, which ensures the establishment of the flow field; the control device is composed of two parts: a straightening plate and a deflection control plate. The straightening plate can ensure the stability of the upstream airflow, and the linear vector control of the wake can be achieved through the linear deflection of the deflection control plate. Moreover, under a high pressure drop ratio (NPR>10), the vector control effect will not decay. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the three-dimensional structure of the vector nozzle of the present invention;

[0033] Figure 2 It is a two-dimensional structural schematic diagram of the deflection control plate in the vector nozzle of the present invention in the undeflected state;

[0034] Figure 3 It is a two-dimensional structural schematic diagram of the deflection state of the deflection control plate in the vector nozzle of the present invention;

[0035] Figure 4 It is a partial schematic diagram of the vector nozzle of the present invention;

[0036] Figure 5 This is a simulation diagram of the vector control effect of the vector nozzle of the present invention. DETAILED DESCRIPTION

[0037] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0038] Reference Figures 1 to 3 As shown, a novel parallel double-throat thrust vector nozzle of the present invention comprises: a nozzle main wall, a nozzle side wall and a control device; the internal space formed by the nozzle main wall and the nozzle side wall forms a flow channel, and the cross section of the flow channel is rectangular;

[0039] The main wall of the nozzle is composed of a nozzle straight section 2, a nozzle contraction section 3 and a nozzle expansion section 7, and the three are designed as an integrated whole and connected with smooth surfaces; one side of the nozzle straight section 2 is an inlet section 1 of the nozzle, and one side of the nozzle expansion section 7 is an outlet section 8 of the nozzle;

[0040] The control device comprises a straightening piece 4 and a deflection control piece 6. The straightening piece 4 is fixed in a groove provided on the side wall of the nozzle; the deflection control piece 6 is fixed on the side wall of the nozzle through a rotating shaft 5.

[0041] Among them, the straightening piece 4 gradually becomes wider, and the nozzle contraction section 3 and the straightening piece 4 form a gradual contraction trend of the flow channels on both sides of the control device; the deflection control piece 6 gradually becomes narrower, and the nozzle expansion section 7 and the deflection control piece 6 form a gradual expansion trend of the flow channels on both sides of the control device, thereby the control device and the nozzle contraction section 3 and the nozzle expansion section 7 are combined to form a contraction-expansion nozzle, and the flow channels on both sides of the control device are respectively provided with a throat 9 to form a parallel double throat.

[0042] Specifically, the throat 9 indicates the narrowest position of the flow channel.

[0043] Specifically, the upper and lower surfaces of the rectifying piece 4 and the deflection control piece 6 are both smooth curved surfaces.

[0044] Specifically, the windward end (front end) of the straightening piece 4 is a sharp angle, and the leeward end (rear end) is an arc.

[0045] Specifically, the windward end of the deflection control piece 6 is an arc, the leeward end is a sharp angle, and the windward end is completely in contact with the leeward end of the rectifying piece 4 .

[0046] Specifically, the nozzle expansion section 7 expands twice along the airflow direction, the first expansion section is called the basic section; the second expansion section is called the re-expansion section; and the intermediate transition section between the first expansion and the second expansion is called the connecting section.

[0047] Specifically, the nozzle expansion section 7 is composed of a base section, a connecting section and a re-expansion section, and the three sections are smoothly connected.

[0048] Specifically, the deflection control sheet 6 and the rotating shaft 5 are formed in one piece.

[0049] In the present invention, the airflow enters the flow channel from the inlet section 1 of the nozzle, and is divided into two airflows through the straightening piece 4. The two airflows are gradually accelerated in the contraction flow channel formed by the nozzle contraction section 3 and the straightening piece 4, respectively, and reach the speed of sound at the throat 9, and are gradually accelerated to the supersonic speed in the expansion flow channel formed by the nozzle expansion section 7 and the deflection control piece 6; the two airflows are formed into one after passing through the deflection control piece 6, and the rotation of the rotating shaft 5 drives the deflection control piece 6 to deflect, thereby realizing the deflection of the outflowing airflow.

[0050] The present invention provides a design method for a novel parallel double-throat thrust vectoring nozzle, the steps of which are as follows:

[0051] Step 1): Determine the original throat height H of the nozzle that first contracts and then expands according to the design requirements. th , exit height, overall expansion length of the nozzle, and the required vector deflection angle α;

[0052] Step 2): Determine the overall profile of the control device according to the vector deflection angle α: make a straight line with an angle α with the horizontal position tangent to the expansion part of the original first contraction-then expansion nozzle selected in step 1), the straight line intersects the contraction part of the original first contraction-then expansion nozzle at a point, intercept the original first contraction-then expansion nozzle profile between the tangent point and the intersection point, and symmetric along the straight line;

[0053] Step 3): Set the minimum distance h between the nozzle expansion section and the control device: Denote point A on the control device, point B on the nozzle expansion section, and the distance between AB is h;

[0054] Step 4): replace the profile near point A on the control device in step 3) with a small arc to ensure that the minimum distance h of the control device remains unchanged when performing vector control around the rotation axis. Specifically, a circle is drawn with the rotation axis as the center and the distance from the center to point A as the radius, and is smoothly connected to the profile of the control device;

[0055] Step 5): cutting the profile obtained in step 2) into two parts along the circle made in step 4), wherein the part close to the nozzle inlet section is a straightening piece, and the other part close to the nozzle outlet section is a deflection control piece, so as to ensure that the upstream airflow is stable when the control device performs vector control around the rotation axis;

[0056] Step 6): The expansion angle β of the basic section of the nozzle expansion section and the vector deflection angle α are set to have the following relationship: β=α+13°, the expansion angle γ of the re-expansion section and the vector deflection angle α are set to have the following relationship: γ=β+20°, the basic section and the re-expansion section are smoothly connected by the connecting section, and the three sections are combined to obtain the nozzle expansion section;

[0057] Step 7): Set the height of the nozzle inlet section and the height of the nozzle straight section to be greater than the original height H of the nozzle throat that first contracts and then expands in step 1). th , and obtain straight sections such as the nozzle;

[0058] Step 8): The nozzle contraction section is set to reach the contraction limit at the throat position, and the nozzle contraction section is smoothly connected with the nozzle straight section and the nozzle expansion section respectively;

[0059] Step 9): the straight section of the nozzle obtained in step 7), the nozzle contraction section set in step 8), and the nozzle expansion section obtained in step 6) are combined to form a new first contraction-then expansion nozzle as the nozzle main wall;

[0060] Step 10): Setting the length of the nozzle side wall to be greater than or equal to the distance from the nozzle inlet section to the nozzle outlet section to obtain the nozzle side wall;

[0061] Step 11): The nozzle side wall obtained in step 10), the nozzle main wall obtained in step 9), and the rectifying piece and the deflection control piece obtained in step 5) are combined to form a complete vector nozzle.

[0062] In this example, for a certain requirement, the designed vector nozzle can achieve a vector deflection angle of ±15°, refer to Figure 4 As shown, the specific steps are as follows:

[0063] 1) Select the Ma2.5 "contract first and then expand" nozzle profile. t =22.19mm, the nozzle outlet height is 150mm;

[0064] 2) A straight line with an angle of 15° to the horizontal direction is tangent to the Ma2.5 nozzle expansion section profile at point X, and the straight line intersects with the Ma2.5 nozzle contraction section profile at point Y. The profile curve XY is the single-sided profile of the control device. The complete profile formed by symmetry along the straight line XY is the two-dimensional cross-section of the control device.

[0065] 3) Draw a perpendicular line XY from point A of the two-dimensional cross section of the control device obtained in step 2), the intersection of which is the location of the rotating shaft 5, and draw an arc with the intersection as the center and the distance from the intersection to point A as the radius, to divide the combined two-dimensional cross section into a rectifier piece and a deflection control piece;

[0066] 4) The arc obtained in step 3) is used to replace the surface near point A and the other side of the symmetry, and is smoothly connected with the surface of the rear section of the deflection control plate;

[0067] 5) According to the formula Determine the location of the larynx;

[0068] 6) According to the formula β=α+13°=25°, γ=β+20°=48°, the profile positions of the base section and the re-expansion section in the nozzle expansion section are determined, and the base section and the re-expansion section are smoothly connected by the connecting section to obtain the nozzle expansion section;

[0069] 7) Set the nozzle inlet height and the nozzle straight section height to 40 mm to obtain the nozzle straight section;

[0070] 8) The nozzle contraction section is set to gradually contract to the throat position, and the nozzle contraction section is smoothly connected with the straight section of the nozzle and the nozzle expansion section;

[0071] 9) combining the straight section of the nozzle obtained in step 7), the nozzle contraction section set in step 8), and the nozzle expansion section obtained in step 6) to obtain the nozzle main wall;

[0072] 10) Setting the length of the nozzle side wall to 200 mm, and obtaining the nozzle side wall;

[0073] 11) The nozzle main wall obtained in step 9), the nozzle side wall obtained in step 9), and the straightening piece and the deflection control piece obtained in step 3) are combined to form a complete vector nozzle.

[0074] Figure 5 The linear deflection effect of the deflection control plate on the wake flow when the nozzle pressure ratio is 15 is explained, and the feasibility of the vector control technology of the present invention is confirmed.

[0075] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A new type of parallel double-throat thrust vectoring nozzle, characterized in that: include: Nozzle main wall, nozzle side wall and control device; The internal space formed by the nozzle main wall and the nozzle side wall forms a flow channel, and the cross section of the flow channel is rectangular; The main wall of the nozzle is composed of a nozzle straight section (2), a nozzle contraction section (3) and a nozzle expansion section (7), and the three are designed as an integrated whole and are smoothly connected; one side of the nozzle straight section (2) is the nozzle inlet section (1), and one side of the nozzle expansion section (7) is the nozzle outlet section (8); The control device comprises a straightening plate (4) and a deflection control plate (6), wherein the straightening plate (4) is fixed in a groove provided on the side wall of the nozzle; and the deflection control plate (6) is fixed on the side wall of the nozzle via a rotating shaft (5).

2. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The straightening piece (4) gradually widens, and the nozzle contraction section (3) and the straightening piece (4) form a gradually contracting state of the flow channels on both sides of the control device; the deflection control piece (6) gradually narrows, and the nozzle expansion section (7) and the deflection control piece (6) form a gradually expanding state of the flow channels on both sides of the control device, thereby the control device is combined with the nozzle contraction section (3) and the nozzle expansion section (7) to form a contraction-expansion nozzle, and the flow channels on both sides of the control device are respectively provided with a throat (9) to form a parallel double throat.

3. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The throat (9) represents the narrowest position of the flow channel.

4. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The upper and lower surfaces of the rectifying piece (4) and the deflection control piece (6) are both smooth curved surfaces.

5. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The windward end of the rectifying piece (4) is a sharp angle, and the leeward end is an arc.

6. The novel parallel double-throat thrust vectoring nozzle according to claim 5 is characterized in that: The windward end of the deflection control piece (6) is an arc, the leeward end is a sharp angle, and the windward end is completely fitted with the leeward end of the rectifying piece (4).

7. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The nozzle expansion section (7) expands twice along the airflow direction, the first expansion section is called the basic section; the second expansion section is called the re-expansion section; and the transition section between the first expansion and the second expansion is called the connecting section.

8. The novel parallel double-throat thrust vectoring nozzle according to claim 7 is characterized in that: The nozzle expansion section (7) is composed of a base section, a connection section and a re-expansion section, and the three sections are smoothly connected.

9. The novel parallel double-throat thrust vectoring nozzle according to claim 1 is characterized in that: The deflection control plate (6) and the rotating shaft (5) are integrally formed.

10. A design method for a novel parallel double-throat thrust vectoring nozzle, characterized in that: Here are the steps: Step 1): Determine the original throat height H of the nozzle that first contracts and then expands according to the design requirements. th , exit height, overall expansion length of the nozzle, and the required vector deflection angle α; Step 2): Determine the overall profile of the control device according to the vector deflection angle α: make a straight line with an angle α with the horizontal position tangent to the expansion part of the original first contraction-then expansion nozzle selected in step 1), the straight line intersects the contraction part of the original first contraction-then expansion nozzle at a point, intercept the original first contraction-then expansion nozzle profile between the tangent point and the intersection point, and symmetric along the straight line; Step 3): Set the minimum distance h between the nozzle expansion section and the control device: Denote point A on the control device, point B on the nozzle expansion section, and the distance between AB is h; Step 4): replace the profile near point A on the control device in step 3) with a small arc to ensure that the minimum distance h of the control device remains unchanged when performing vector control around the rotation axis. Specifically, a circle is drawn with the rotation axis as the center and the distance from the center to point A as the radius, and is smoothly connected to the profile of the control device; Step 5): cutting the profile obtained in step 2) into two parts along the circle made in step 4), wherein the part close to the nozzle inlet section is a straightening piece, and the other part close to the nozzle outlet section is a deflection control piece, so as to ensure that the upstream airflow is stable when the control device performs vector control around the rotation axis; Step 6): The expansion angle β of the basic section of the nozzle expansion section and the vector deflection angle α are set to have the following relationship: β=α+13°, the expansion angle γ of the re-expansion section and the vector deflection angle α are set to have the following relationship: γ=β+20°, the basic section and the re-expansion section are smoothly connected by the connecting section, and the three sections are combined to obtain the nozzle expansion section; Step 7): Set the height of the nozzle inlet section and the height of the nozzle straight section to be greater than the original height H of the nozzle throat that first contracts and then expands in step 1). th , and obtain straight sections such as the nozzle; Step 8): The nozzle contraction section is set to reach the contraction limit at the throat position, and the nozzle contraction section is smoothly connected with the nozzle straight section and the nozzle expansion section respectively; Step 9): the straight section of the nozzle obtained in step 7), the nozzle contraction section set in step 8), and the nozzle expansion section obtained in step 6) are combined to form a new first contraction-then expansion nozzle as the nozzle main wall; Step 10): Setting the length of the nozzle side wall to be greater than or equal to the distance from the nozzle inlet section to the nozzle outlet section to obtain the nozzle side wall; Step 11): The nozzle side wall obtained in step 10), the nozzle main wall obtained in step 9), and the rectifying piece and the deflection control piece obtained in step 5) are combined to form a complete vector nozzle.

Citation Information

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