A method for designing a nozzle of an injector

Through the design of the injector ring cavity and the optimization of the injection nozzle, the problem of incomplete injection nozzle design in the existing technology is solved, the stability and reliability of the injector are improved, the development cycle is shortened, the cost is reduced, and it is suitable for injectors of various combustion media.

CN116227050BActive Publication Date: 2025-10-10XIAN AEROSPACE PROPULSION TESTING TECHN INST
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Patent Information

Application Number
CN202211610112.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-14
Publication Date
2025-10-10
Estimated Expiration
2042-12-14

AI Technical Summary

Technical Problem

The existing injector nozzle design method does not take all factors into consideration, resulting in poor steam generator working stability, long development cycle and high cost, and easily having adverse effects on liquid rocket engines.

Method used

An injector annular cavity design is adopted, including an oxidizer annular cavity and a fuel annular cavity. By calculating the momentum density and mixing ratio of the injector, the flow rate of each annular cavity is allocated, and the number and diameter of the injectors are set to ensure that the mixing ratio of the main combustion zone and the side zone meets the chemical equivalence deviation requirements, and optimize the injector arrangement density and impact angle.

Benefits of technology

The stability and reliability of the injector are improved, the development cycle is shortened, the cost is reduced, and the injector is suitable for injectors of different combustion media.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application relates to a design method of a spray port of an injector, and solves the problems that the existing design method of the spray port of the injector is not comprehensive in consideration factors, thereby causing poor working stability of a steam generator, long development period, high development cost, and easy adverse effects on the steam generator and a liquid rocket engine. The design method of the spray port of the injector comprises the following steps: S1: determining the number N of ring cavities according to the total flow and pressure drop of oxidant or fuel, wherein N is an integer greater than or equal to 2; S2: calculating the momentum density and mixing ratio of the injector, and distributing the flow of each ring cavity; S3: setting the number of spray ports at the bottom of the ring groove according to the ring cavity flow obtained in step S2; S4: calculating the flow of a single spray port according to the ring cavity flow in step S2 and the number of spray ports in step S3; and S5: calculating the diameter of the spray port, and completing the design of the spray port of the injector.
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Description

Technical Field

[0001] The present invention relates to a method for designing an injection port of an injector. Background Art

[0002] During high-altitude simulation testing of an engine, the engine is installed in a vacuum chamber, and the chamber is evacuated using a vacuum unit, air jets, or steam jets. Steam jets, with their high jetting capacity, are suitable for high-altitude simulation testing of high-thrust engines. However, steam jets require high-temperature, high-pressure steam as a power source. For example, a high-altitude simulation test bench requires steam at a pressure of 1.3 MPa, a temperature of 190°C, and a flow rate of 80 t / h. This steam can be generated using boilers or steam generators. Using boilers to produce steam is expensive, and boiler equipment can only be used during testing, resulting in low utilization. Therefore, steam generation devices (such as liquid oxygen-alcohol steam generators and liquid oxygen-methane steam generators) are often used to generate steam at the required pressure, temperature, and flow rate. This steam drives a steam jet vacuum pump to create the vacuum environment within the chamber.

[0003] The mainstream injector nozzle design method in the existing technology is to calculate the flow density in each partition, control the distribution of flow density in the radial direction, and distribute the flow to each partition. However, the calculation of flow density only takes into account the distribution of medium flow in the radial direction. In fact, the factor affecting combustion instability is the product of flow rate and velocity, that is, momentum. Due to the differences in medium density, pressure drop of different component media and cross-sectional area of ​​the injection hole, there is often a large difference between the momentum density and flow density of each partition. Simply using flow density as the principle of flow distribution cannot take into account the impact of velocity on liquid partitions, resulting in unreasonable flow distribution. Unreasonable flow distribution has an adverse effect on the stability of the generator and even the liquid rocket engine. At the same time, as a key device for combustion organization, the injector currently does not have a standardized and streamlined design process, which is not conducive to the rapid and accurate completion of injector design work.

[0004] In summary, the existing injector nozzle design method has incomplete considerations, resulting in poor generator working stability. The injector design needs to be completed through an iterative process of ignition verification, multiple improvements to the flow distribution results, and then re-ignition. The development cycle is long and the development cost is high. Summary of the Invention

[0005] The object of the present application is to provide a design method for the injection port of an injector, so as to realize the stability and reliability of the injector, in view of the fact that the existing design method for the injection port of an injector does not take into account all factors, thus resulting in poor stability of the steam generator, long development cycle and high development cost, and easily causing adverse effects on the steam generator and liquid rocket engine.

[0006] To solve the above technical problems, the technical scheme adopted by the present application is as follows:

[0007] A design method for the injection port of an injector, wherein the annular cavity of the injector comprises an oxidant annular cavity and a fuel annular cavity which are coaxially and spaced apart from the injection disc, and the fuel annular cavity is arranged close to the center of the injection disc.

[0008] The special features are as follows:

[0009] S1: determining the number N of annular cavities according to the total flow rate and pressure drop of the oxidant or fuel, wherein N is an integer greater than or equal to 2;

[0010] S2: calculating the momentum density and mixing ratio of the injector, and distributing the flow rate of each annular cavity;

[0011] 2.1) calculating the momentum density of the injector by the following formula:

[0012]

[0013] In the formula, I si is the momentum density in the partition of the injection surface i, with the unit of kg / (s 2 ·m), i=2,3, …, M, and M is the number of partitions on the injection surface;

[0014] q i is the flow rate of the oxidant or fuel in the partition of the injection surface i, with the unit of kg / s;

[0015] v i is the flow velocity of the oxidant or fuel in the partition of the injection surface i along the axial direction of the injector, with the unit of m / s;

[0016] A i is the partition area in the partition of the injection surface i, with the unit of m 2 ;

[0017] 2.2) calculating the mixing ratio of the injector by the following formula:

[0018] k i = q io / q if

[0019] In the formula, k i is the mixing ratio in the partition i of the injection surface;

[0020] q io is the oxidant flow rate in the i-th zone of the injection surface, in kg / s;

[0021] q if is the fuel flow rate in the i-th zone of the injection surface, in kg / s;

[0022] 2.3) Distribute the flow rate of each annular cavity according to the momentum density obtained in step 2.1) and the mixing ratio obtained in step 2.2);

[0023] S3: Set the number of injection ports at the bottom of the annular groove according to the flow rate of the annular cavity obtained in step S2;

[0024] S4: Calculate the flow rate of a single injection port according to the flow rate of the annular cavity in step S2 and the number of injection ports in step S3;

[0025] S5: Calculate the diameter of the injection port, and complete the design of the injection port of the injector.

[0026] Further, the pressure drop in step S1 is calculated by the following formula:

[0027] 1.1) The injection port pressure drop of the oxidant on the injection surface is calculated as:

[0028] Δp ho = p o - p c

[0029] wherein: p o is the oxidant annular cavity pressure;

[0030] p c is the combustion chamber pressure;

[0031] 1.2) The injection port pressure drop of the fuel on the injection surface is calculated as:

[0032] Δp hf = p f - p c

[0033] wherein: p f is the fuel annular cavity pressure.

[0034] Further, step S3 is specifically:

[0035] According to the flow rate of the annular cavity obtained in step 2.3), set the number of injection ports in each zone on the injection surface, so that the arrangement density of the injection ports in each zone is in the range of 0.2-1.2 / cm 2 . 2

[0036] Further, step S4 is specifically: ​

[0037] Based on the annular cavity flow rate in step 2.3) and the number of injection ports in step S3, calculate the flow rate of a single injection port:

[0038] qd i =q i* / n i

[0039] Where: qd i is the flow rate of a single injection port in zone i, in kg / s;

[0040] q i* is the oxidant flow rate or fuel flow rate in zone i, in kg / s, * represents o or f, o represents oxidant, and f represents fuel;

[0041] n i is the number of injection ports in partition i.

[0042] Furthermore, step S5 is specifically as follows:

[0043] Based on the oxidant injection port pressure drop obtained in step 1.1) or the fuel injection port pressure drop obtained in step 1.2) and the flow rate of a single injection port obtained in step S4, the injection port diameter is calculated using the following formula:

[0044]

[0045] Where: c d is the flow coefficient of the injection port, ranging from 0.6 to 0.85;

[0046] d h is the diameter of the injection port, in mm;

[0047] △p h* is the injection port pressure drop, in MPa;

[0048] ρ is the oxidizer density or fuel density, in kg / m 3 .

[0049] Furthermore, in step 1.1), the injection surface includes a main combustion area and a non-main combustion area;

[0050] The non-main combustion area includes a side area;

[0051] The edge area is an interval extending inward from the outer edge of the injection surface to 5% to 10% of the radius of the injection surface.

[0052] Furthermore, the momentum density of the main combustion zone presents a steep hump distribution along the radial direction.

[0053] Furthermore, in step 1.1), the working medium of the edge zone is set to fuel, and the fuel flow rate of the edge zone is not less than 15% of the total flow rate of the oxidant and the fuel;

[0054] The density of the nozzles in the edge area is not less than 0.25 / cm 2 .

[0055] Furthermore, the deviation between the mixing ratio of the main combustion zone and the chemical equivalent is less than or equal to 30%;

[0056] The deviation between the mixing ratio of the edge region and the chemical equivalent is greater than or equal to 30%.

[0057] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0058] (1) The nozzle design method of the injector of the present invention can adjust the working condition of the injector in the generator, and perform working condition adjustment calculations on the injector according to the use requirements, so that the oxidant flow rate and fuel flow rate entering the combustion chamber change, thereby controlling the water vapor flow rate and pressure generated by the injector to meet the working condition requirements.

[0059] (2) The injector nozzle design method of the present invention uses momentum density as a key control factor for stability design. Thermal ignition data shows that controlling the distribution of momentum density significantly improves stability, accuracy, and reliability.

[0060] (3) The injection port design method of the injector of the present invention distributes the flow rate of each annular cavity according to the following distribution principle: the momentum density in the radial direction presents a steep hump distribution; the mixing ratio of each partition is calculated based on the flow rate distributed in the annular cavity. Since the deviation between the mixing ratio of the main combustion zone and the chemical equivalence ratio is ensured to be no more than ±30% (i.e., high mixing ratio) and the deviation between the mixing ratio of the side zone and the chemical equivalence ratio is no less than ±30% (i.e., low mixing ratio), the combustion stability of the injector is effectively improved while ensuring the high performance of the injector.

[0061] (4) The injection port design method of the injector of the present invention is not only applicable to the liquid collecting cavity of the annular cavity structure, but also to the DC impact (DC self-impact or DC mutual impact) of the radial liquid inlet structure. It is not only applicable to liquid oxygen and alcohol injectors, but also to injectors of other combustion media, and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a structural diagram of a three-bottom structure injector.

[0063] Figure 1 The reference numerals in the figures are: 01 - outsole, 02 - nozzle, 03 - midsole, 04 - insole, 05 - first brazing seam, 06 - second brazing seam.

[0064] Figure 2 This is a schematic diagram of the structure of the radial channel liquid injection nozzle.

[0065] Figure 2 The reference numerals in the figure are: 001-injection disk, 002-flange, 003-cover plate, 004-direct current nozzle;

[0066] Figure 3 Schematic diagram of the injection nozzle. DETAILED DESCRIPTION

[0067] Figure 1 It is a three-bottom structure injector. Figure 2 It is a radial channel liquid inlet injector. The present invention is not only applicable to the liquid collecting cavity of the annular cavity structure, but also applicable to the DC impact (DC self-impact or DC mutual impact) of the radial liquid inlet structure. The general working process of the injector is: the ignition channel is ignited by the ignition device on the top of the injector. An oxidizer annular cavity and a fuel annular cavity are respectively formed between the injection disk and the cover plate. The oxidizer and fuel enter the oxidizer annular cavity and the fuel annular cavity through the oxidizer inlet channel and the fuel inlet channel respectively, and then pass through the injection port set on the injection surface, such as Figure 3 As shown, the fuel enters the combustion chamber from the injection port, is atomized, mixed, and burned, and produces the pressurized fuel gas required at the rear end.

[0068] The present invention provides a method for designing an injection port of an injector, wherein the injector annulus includes an oxidizer annulus and a fuel annulus coaxially spaced apart from each other with an injection disk, and the fuel annulus is disposed near the center of the injection disk; the method comprises the following steps:

[0069] S1: Determine the number of annular cavities N of the injector based on the given total flow rate and pressure drop of the oxidant and fuel, where N is an integer greater than or equal to 2; wherein the annular cavities include an oxidant annular cavity and a fuel annular cavity coaxially spaced apart from the injection disk, and the annular cavity close to the center of the injection disk is the fuel annular cavity.

[0070] 1.1) Calculate the pressure drop of the oxidant injection port on the injection surface as follows:

[0071] Δp ho =p o -p c

[0072] Where: p o is the oxidant annular cavity pressure;

[0073] p c is the combustion chamber pressure;

[0074] 1.2) Calculate the injection port pressure drop of the fuel on the injection surface as:

[0075] Δp hf =p f -p c

[0076] Where: p f is the fuel annulus pressure.

[0077] S2: Calculate the momentum density and mixing ratio of the injector and distribute the flow rate to each annular cavity;

[0078] 2.1) Calculate the momentum density of the injector using the following formula:

[0079]

[0080] Where: I si is the momentum density in the injection area i, in kg / (s 2 m), i is an integer greater than or equal to 2;

[0081] q i is the oxidant flow rate or fuel flow rate in the injection surface i zone, unit is kg / s;

[0082] v i is the flow velocity of the oxidant or fuel along the injector axis in the injection surface zone i, in m / s;

[0083] A i is the area of ​​the injection surface within the i-th zone, in m 2 ;

[0084] 2.2) Calculate the mixing ratio of the injector by the following formula:

[0085] k i =q io / q if

[0086] Where: k i is the mixing ratio within the i-th zone of the injection surface;

[0087] q io is the oxidant flow rate in the i-th zone of the injection surface, in kg / s;

[0088] q if is the fuel flow rate in the i-th zone of the injection surface, in kg / s;

[0089] 2.3) allocating the flow rate to each annular cavity according to the momentum density obtained in step 2.1) and the mixing ratio obtained in step 2.2);

[0090] S3: according to the annular cavity flow rate obtained in step S2, the number of injection ports at the bottom of the annular groove is set;

[0091] According to the annular cavity flow rate obtained in step 2.3), the number of injection ports in each partition on the injection surface is set so that the density of the injection ports in each partition is 0.2 / cm 2~1.2 pieces / cm 2 within the scope;

[0092] S4: Calculate the flow rate of a single injection port according to the annular cavity flow rate in step S2 and the number of injection ports in step S3;

[0093] S4: Calculate the flow rate of a single injection port according to the annular cavity flow rate in step S2 and the number of injection ports in step S3;

[0094] According to the annular cavity flow rate in step 2.3) and the number of injection ports in step S3, calculate the flow rate of a single injection port:

[0095] qd i =q i* / n i

[0096] Where: qd i is the flow rate of a single injection port in zone i, in kg / s;

[0097] q i* is the oxidant flow rate or fuel flow rate in zone i, in kg / s, * represents o or f, o represents oxidant, and f represents fuel;

[0098] n i is the number of injection ports in partition i.

[0099] S5: Based on the oxidant injection port pressure drop obtained in step 1.1) or the fuel injection port pressure drop obtained in step 1.2) and the flow rate of a single injection port obtained in step S4, the injection port diameter is calculated using the following formula to complete the injection port design of the injector;

[0100]

[0101] Where: c d is the flow coefficient of the injection port, ranging from 0.6 to 0.85;

[0102] d h is the diameter of the injection port, in mm;

[0103] △p h is the injection port pressure drop, in MPa;

[0104] ρ is the oxidizer density or fuel density, in kg / m 3 .

[0105] In this embodiment, the injection surface of the injection disk includes a main combustion zone and a non-main combustion zone; the non-main combustion zone includes a side zone; the side zone is the area extending inward from the outer edge of the injection disk to 5% to 10% of the injection disk radius; the deviation between the mixing ratio of the main combustion zone and the chemical equivalent is less than or equal to 30%; the deviation between the mixing ratio of the side zone and the chemical equivalent is greater than or equal to 30%. The working medium in the side zone is set to fuel, and the fuel flow rate in the side zone is not less than 15% of the total flow rate of liquid oxygen and alcohol; the density of the injection nozzles in the side zone is not less than 0.25 / cm 2 . Reduce backflow by setting the nozzle impact angle and nozzle layout.

[0106] The idea of ​​the injection port design method of the injector in the present invention is as follows:

[0107] First, determine the overall injector design, including the number of liquid collection annular cavities and the type of medium supplied to each cavity. Generally, the bicomponent mediums are arranged in a staggered pattern, with the fuel medium arranged in the outermost and innermost annular cavities, i.e., a "fuel-oxidizer-fuel-oxidizer...fuel" layout from the inside out. Also, determine the liquid inlet method for each annular cavity, with options including capillary tubes, double-layer cover plates, and secondary liquid collection. Determine the injector material and pretreatment requirements. Finally, determine the connection and sealing method between the injector's key components, such as welding, threaded connections, or O-rings.

[0108] Second, the nozzle arrangement design

[0109] When designing the nozzle arrangement, the primary consideration is ensuring a certain atomization quality. For DC self-impact nozzles, the primary factors influencing atomization quality are nozzle density and the angle of the impinging jet. For a given flow density, nozzle density is inversely proportional to nozzle aperture. Properly increasing the density can improve the impulse efficiency of the combustion chamber.

[0110] The impact jet angle also has a significant impact on atomization quality. The larger the impact angle, the better the atomization effect. After the liquid (i.e., liquid oxygen and alcohol) flows out of the nozzle and impacts, the atomized droplets will splash in all directions, inevitably splashing toward the injection surface of the injector. After the oxidizer is atomized through the nozzle, if a large number of droplets splash onto the injection surface, it will cause the injection surface to partially turn blue or even burn through. When designing the generator head, in order to reduce the splash of the atomized oxidizer droplets onto the injection surface, a small angle impact method should be adopted to form a large distance between the impact point of the oxidizer and the injection surface.

[0111] To ensure optimal mixing between the two components, the atomizer cone formed by the impact of one component should be enclosed by the atomizer cone of the other component, resulting in good mixing. Furthermore, the nozzle arrangement must ensure an appropriate mixing ratio distribution. The vast majority (over 80%) of the total flow of liquid oxygen and alcohol should have (or approach) the optimal mixing ratio and pass through the radial center area of ​​the injection surface.

[0112] Third, combustion stability design

[0113] Correctly select the type and arrangement of injection nozzles. Experiments show that the type of injection nozzle has a great influence on high-frequency unstable combustion. The high-frequency stability of DC self-impact injection nozzles is better than that of mutual-impact injection nozzles.

[0114] Correctly organize the radial momentum density distribution. A uniform distribution of momentum density along the radius results in the worst stability. However, two different sloped distributions eliminate the tangential and radial mixing instabilities that occur with a uniform distribution, leaving only the first vibration mode of radial high-frequency instability. A moderate hump has little effect on improving stability, while a steep hump-shaped distribution is most effective. Therefore, when distributing injector flow, the momentum density should be arranged to form a steep hump shape along the radius.

[0115] Liquid phase partitioning can also be used to prevent the occurrence of high-frequency unstable combustion, but due to the existence of partitioned injection ports, the flow density and mixing ratio are unevenly distributed, thereby reducing the engine specific impulse (injector efficiency).

[0116] Fourth, arrange and calculate the nozzle diameter

[0117] 1) Flow distribution of each annular cavity is carried out according to the principle that the momentum density in the radial direction presents a steep hump distribution;

[0118] According to the flow rate distributed in the annular cavity, the mixing ratio of each partition is calculated to ensure a high mixing ratio in the main combustion zone and a low mixing ratio in the side zone.

[0119] 2) Based on the annular cavity dimensions, preliminarily determine the number of annular cavity impactors and the nozzle pressure drop, and then calculate the nozzle diameter. The calculated nozzle diameter should generally not be too small, with a minimum of no less than 0.4mm, to avoid increased processing difficulty.

[0120] 3) Arrange as many impact pairs as possible while ensuring the processability of small hole drilling.

Claims

1. A method for designing an injection port of an injector, wherein the injector annulus comprises an oxidizer annulus and a fuel annulus coaxially spaced apart from each other with the injection disk, and the fuel annulus is disposed near the center of the injection disk; characterized in that: The following steps are involved: S1: Determine the number of annular cavities N according to the total flow rate and pressure drop of the oxidant or fuel, where N is an integer greater than or equal to 2; S2: Calculate the momentum density and mixing ratio of the injector and distribute the flow rate to each annular cavity; 2.1) Calculate the momentum density of the injector using the following formula: Where: I si is the momentum density in the injection area i, in kg / (s 2 m), i = 2, 3, ... M, M is the number of partitions on the injection surface; q i is the oxidant flow rate or fuel flow rate in the injection surface i zone, unit is kg / s; v i is the flow velocity of the oxidant or fuel along the injector axis in the injection surface zone i, in m / s; A i is the area of ​​the injection surface within the i-th zone, in m 2 ; 2.2) Calculate the mixing ratio of the injector by the following formula: k i =q io / q if Where: k i is the mixing ratio within the i-th zone of the injection surface; q io is the oxidant flow rate in the i-th zone of the injection surface, in kg / s; q if is the fuel flow rate in the i-th zone of the injection surface, in kg / s; 2.3) allocating the flow rate to each annular cavity according to the momentum density obtained in step 2.1) and the mixing ratio obtained in step 2.2); S3: according to the annular cavity flow rate obtained in step S2, the number of injection ports at the bottom of the annular groove is set; S4: Calculate the flow rate of a single injection port according to the annular cavity flow rate in step S2 and the number of injection ports in step S3; S5: Calculate the nozzle diameter and complete the nozzle design of the injector.

2. The method for designing an injection nozzle of an injector according to claim 1, wherein: The pressure drop in step S1 is specifically calculated by the following formula: 1.1) Calculate the pressure drop of the oxidant injection port on the injection surface as follows: Δp ho =p o -p c Where: p o is the oxidant annular cavity pressure; p c is the combustion chamber pressure; 1.2) Calculate the injection port pressure drop of the fuel on the injection surface as: Δp hf =p f -p c Where: p f is the fuel annulus pressure.

3. The method for designing an injection nozzle of an injector according to claim 2, wherein: Step S3 is specifically as follows: According to the annular cavity flow rate obtained in step 2.3), the number of injection ports in each partition on the injection surface is set so that the density of the injection ports in each partition is 0.2 / cm 2 ~1.2 pieces / cm 2 within the range.

4. The method for designing an injection nozzle of an injector according to claim 3, wherein: Step S4 is specifically as follows: Based on the annular cavity flow rate in step 2.3) and the number of injection ports in step S3, calculate the flow rate of a single injection port: qd i =q i* / n i Where: qd i is the flow rate of a single injection port in zone i, in kg / s; q i* is the oxidant flow rate or fuel flow rate in zone i, in kg / s, * represents o or f, o represents oxidant, and f represents fuel; n i is the number of injection ports in partition i.

5. The method for designing an injection nozzle of an injector according to claim 4, characterized in that: Step S5 is specifically as follows: Based on the oxidant injection port pressure drop obtained in step 1.1) or the fuel injection port pressure drop obtained in step 1.2) and the flow rate of a single injection port obtained in step S4, the injection port diameter is calculated using the following formula: Where: c d is the flow coefficient of the injection port, ranging from 0.6 to 0.85; d h is the diameter of the injection port, in mm; △p h* is the injection port pressure drop, in MPa; ρ is the oxidizer density or fuel density, in kg / m 3 .

6. The method for designing an injection port of an injector according to claim 5, wherein: In step 1.1), the injection surface includes a main combustion area and a non-main combustion area; The non-main combustion area includes a side area; The edge area is an interval extending inward from the outer edge of the injection surface to 5% to 10% of the radius of the injection surface.

7. The method for designing an injection port of an injector according to claim 6, wherein: The momentum density of the main combustion zone is distributed in a steep hump shape along the radial direction.

8. The method for designing an injection port of an injector according to claim 7, wherein: In step 1.1), the working medium of the edge zone is set to fuel, and the fuel flow rate of the edge zone is not less than 15% of the total flow rate of the oxidant and fuel; The density of the nozzles in the edge area is not less than 0.25 / cm 2 .

9. The method for designing an injection port of an injector according to claim 8, wherein: The deviation between the mixing ratio of the main combustion zone and the chemical equivalent is less than or equal to 30%; The deviation between the mixing ratio of the edge region and the chemical equivalent is greater than or equal to 30%.

Citation Information

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