CN103569373B

CN103569373B - The method of calculating of whirlpool oar aircraft under static state tail jet velocity field

Info

Publication number: CN103569373B
Application number: CN201310566578.9A
Authority: CN
Inventors: 吴宇; 钟剑龙
Original assignee: Xian Aircraft Design and Research Institute of AVIC
Current assignee: Xian Aircraft Design and Research Institute of AVIC
Priority date: 2013-11-13
Filing date: 2013-11-13
Publication date: 2016-03-09
Anticipated expiration: 2033-11-13
Also published as: CN103569373A

Abstract

The invention belongs to the calculation technology of jet flow velocity field of aircraft, and relates to a method for calculating velocity field of jet jet flow of a turboprop aircraft in a static state. It is characterized in that the steps of calculating the jet velocity field of the turboprop jet are as follows: establish a coordinate system; define; calculate the characteristic angle α; determine the boundary line equation of the core area of the jet flow; calculate the characteristic angle β; determine the boundary line equation of the slip stream mainstream area; Calculate the characteristic angle γ; determine the boundary line equation of the slipstream transition zone; determine the characteristic angle θ; determine the boundary line equation of the slipstream zone; determine the boundary line equation of the jet deceleration zone; calculate any coordinate point (x _a ,y _a ) speed. The invention simplifies the calculation process and shortens the calculation cycle.

Description

Calculation method of jet flow velocity field of turboprop aircraft in stationary state

技术领域technical field

本发明属于飞机尾喷流速度场计算技术，涉及一种涡桨飞机在静止状态下尾喷速度场计算的方法。The invention belongs to the calculation technology of jet flow velocity field of aircraft, and relates to a method for calculating velocity field of jet jet flow of a turboprop aircraft in a static state.

背景技术Background technique

飞机设计阶段，如何较为准确地预测飞机尾喷流场分布，为其它系统提供设计输入参数，是飞机设计过程的一个重点。涡喷发动机的尾喷流场计算的方法参见“XX型发动机尾喷口射流参数的计算”,《成发科技》，段春红,2003,5(1)，P.40-44。涡轮螺旋桨飞机不同于涡轮喷气动力飞机，其向前的力主要源于螺旋桨的拉力，产生的螺旋桨滑流，对涡桨飞机的尾喷流场影响较大，因此，适用于涡喷发动机的喷流计算公式，不再适用于涡桨飞机的尾喷流计算。目前，针对涡桨飞机在静止状态下尾喷速度场计算的问题，采用计算流体力学方法解决，参见“螺旋桨滑流与机翼气动干扰的非定常数值模拟”,《航空学报》，夏贞锋，杨永，2011，32(7)，P.1195-1201。其缺点是：由于用计算流体力学方法计算涡桨飞机尾喷流场过于复杂，计算周期长，不适宜于快速工程计算。In the aircraft design stage, how to accurately predict the jet flow field distribution of the aircraft and provide design input parameters for other systems is a key point in the aircraft design process. For the calculation method of the tail jet flow field of the turbojet engine, please refer to "Calculation of Jet Flow Parameters of Type XX Engine Tail Nozzle", "Chengfa Technology", Duan Chunhong, 2003, 5(1), P.40-44. The turboprop aircraft is different from the turbojet powered aircraft, its forward force mainly comes from the pulling force of the propeller, and the generated propeller slipstream has a great influence on the tail jet flow field of the turboprop aircraft. The flow calculation formula is no longer applicable to the wake jet flow calculation of turboprop aircraft. At present, computational fluid dynamics is used to solve the problem of calculating the tail jet velocity field of a turboprop aircraft in a static state. Yong, 2011, 32(7), P.1195-1201. Its disadvantages are: the computational fluid dynamics method is too complex to calculate the tail jet flow field of a turboprop aircraft, and the calculation period is long, which is not suitable for rapid engineering calculations.

发明内容Contents of the invention

本发明的目的是：提出一种快速计算涡桨飞机在静止状态下尾喷速度场计算的方法，以便简化计算过程，缩短计算周期。The purpose of the present invention is: to propose a kind of fast calculation method of tail jet velocity field calculation of turboprop aircraft in static state, so that the calculation process is simplified and the calculation cycle is shortened.

本发明的技术解决方案是：涡桨飞机在静止状态下尾喷流速度场的计算方法，发动机尾喷管的轴线与螺旋桨旋转轴线同轴，计算中不考虑环境风速的影响，基于以下已知参数：螺旋桨直径D_f、飞机发动机尾喷口半径R₀、发动机短舱长度L，指发动机进气道唇口前缘点与飞机发动机尾喷口平面的距离；还基于飞机所处大气环境压力和温度参数以及发动机尾喷口排气速度V₀和螺旋桨下游出口面气流平均速度V_f，螺旋桨下游出口面1是指：螺旋桨旋转面在一个特定平面上的投影，该特定平面是过发动机进气道唇口前缘点且垂直于发动机轴线的平面；其特征在于，计算涡桨飞机尾喷速度场的步骤如下：The technical solution of the present invention is: the calculation method of the tail jet flow velocity field of the turboprop aircraft in a static state, the axis of the engine tail nozzle is coaxial with the rotation axis of the propeller, and the influence of the ambient wind speed is not considered in the calculation, based on the following known Parameters: propeller diameter D _f , aircraft engine exhaust nozzle radius R ₀ , engine nacelle length L, refers to the distance between the leading edge point of the engine inlet lip and the plane of the aircraft engine exhaust nozzle; it is also based on the atmospheric pressure and temperature of the aircraft Parameters, as well as the exhaust velocity V ₀ of the engine tail nozzle and the average airflow velocity V _f of the outlet surface downstream of the propeller. The plane at the point of the leading edge of the mouth and perpendicular to the axis of the engine; it is characterized in that the steps for calculating the jet velocity field of the turboprop jet are as follows:

1、建立坐标系：将发动机尾喷流场视为三维轴对称模型，取垂直于水平面并过发动机轴线的平面为二维坐标平面；以发动机轴线为X轴，尾喷流方向为正方向，以发动机尾喷口平面与发动机轴线的交点为原点O，垂直于X轴并过原点O的直线为Y轴，正方向向上；1. Establish a coordinate system: regard the engine tail jet flow field as a three-dimensional axisymmetric model, take the plane perpendicular to the horizontal plane and passing the engine axis as the two-dimensional coordinate plane; take the engine axis as the X axis, and the tail jet flow direction as the positive direction, Take the intersection point of the engine tail nozzle plane and the engine axis as the origin O, the straight line perpendicular to the X axis and passing the origin O is the Y axis, and the positive direction is upward;

2、定义：2. Definition:

2.1、喷流核心区定义为:尾喷流速度V＝V₀的区域，为圆锥状区域；2.1, the jet flow core area is defined as: the area of the tail jet flow velocity V=V ₀ , which is a conical area;

2.2、滑流主流区定义为:处于螺旋桨的下游，且尾喷流速度V＝V_f的区域；2.2, the slip stream mainstream area is defined as: be in the downstream of propeller, and the area of tail jet velocity V=V _f ;

2.3、喷流减速区定义为：处于喷流核心区和滑流主流区下游，并且尾喷流速度V≥V_f,且V＜V₀的区域；2.3. The jet deceleration area is defined as: the area located downstream of the jet core area and the slip stream mainstream area, and the tail jet velocity V≥V _f , and V<V ₀ ;

2.4、滑流衰减区定义为：尾喷流速度V＜V_f，且V＞0的区域；2.4. The slip flow attenuation area is defined as: the area where the tail jet velocity V<V _f and V>0;

2.5、喷流核心区边界线10为发动机喷流核心区边界锥面与二维坐标平面的交线；2.5. The boundary line 10 of the jet flow core area is the intersection line between the boundary cone surface of the engine jet flow core area and the two-dimensional coordinate plane;

2.6、滑流主流区边界线8定义为：滑流主流区的圆锥面与二维坐标平面的交线，该交线邻接喷流减速区；2.6. The boundary line 8 of the slipstream mainstream area is defined as: the intersection line between the conical surface of the slipstream mainstream area and the two-dimensional coordinate plane, which is adjacent to the jet flow deceleration area;

2.7、喷流减速区边界线7定义为：滑流衰减区和喷流减速区的分界线；2.7. The boundary line 7 of the jet deceleration zone is defined as: the boundary line between the slip stream attenuation zone and the jet deceleration zone;

2.8、滑流衰减区边界线4定义为：滑流主流区的圆锥面与二维坐标平面的交线，该交线邻接滑流衰减区；2.8. The boundary line 4 of the slipstream attenuation zone is defined as: the intersection line between the conical surface of the slipstream mainstream zone and the two-dimensional coordinate plane, which is adjacent to the slipstream attenuation zone;

2.9、滑流区边界线5定义为：滑流衰减区的外围边界锥面与二维坐标平面的交线；2.9. The boundary line 5 of the slipstream area is defined as: the intersection line of the peripheral boundary cone surface of the slipstream attenuation zone and the two-dimensional coordinate plane;

2.10、喷流核心区边界线10与X轴线的夹角为特征角α；2.10. The angle between the boundary line 10 of the jet core area and the X-axis is the characteristic angle α;

2.11、滑流主流区边界线8与X轴线的夹角为特征角β；2.11. The angle between the boundary line 8 of the slipstream mainstream area and the X-axis is the characteristic angle β;

2.12、滑流衰减区边界线4与X轴线的夹角为特征角γ；2.12. The angle between the boundary line 4 of the slipstream attenuation zone and the X-axis is the characteristic angle γ;

2.13、滑流区边界线5与X轴线的夹角为特征角θ；2.13. The angle between the boundary line 5 of the slipstream area and the X-axis is the characteristic angle θ;

3、计算特征角α：将R₀、V₀、V_f带入下式，计算得到α；3. Calculate the characteristic angle α: put R ₀ , V ₀ , and V _f into the following formula to calculate α;

$tan the tan α α = = \frac{{R R}_{00}}{{x x}_{00}} = = 2.33 2.33 \cdot &Center Dot; \frac{{V V}_{00}}{c c} \cdot &Center Dot; \frac{11}{{V V}_{f f}^{0.75 0.75}} + + 0.149 0.149 \cdot &Center Dot; \frac{11}{{V V}_{00} - - {V V}_{f f}} - - 0.007 0.007 . . . . . . . . . . . . [[11]]$

式中，c为当地声速，取340m/s；x₀为喷流核心区边界线与X轴交点的X坐标值；In the formula, c is the local sound velocity, which is taken as 340m/s; x ₀ is the X coordinate value of the intersection point of the boundary line of the jet core area and the X axis;

式[1]有效的条件是：c＞V_f≥25m/s，c＞V₀≥10m/s且V₀≠V_f；The valid condition of formula [1] is: c>V _f ≥25m/s, c>V ₀ ≥10m/s and V ₀ ≠V _f ;

4、确定喷流核心区边界线方程：喷流核心区边界线方程为：4. Determine the boundary line equation of the jet core area: the boundary line equation of the jet core area is:

y＝-tanα·x+R₀…………………………………………………[2]y＝-tanα x+R ₀ …………………………………………[2]

式中，x≥0,且x≤x₀；In the formula, x≥0, and x≤x ₀ ;

5、计算特征角β：将V₀、V_f带入下式，计算得到特征角β；5. Calculate the characteristic angle β: Put V ₀ and V _f into the following formula to calculate the characteristic angle β;

$tan the tan β β = = 0.204 0.204 \cdot &Center Dot; \sqrt{{V V}_{00} / / c c} - - 0.235 0.235 \cdot &Center Dot; \sqrt{{V V}_{f f} / / c c} - - 0.006 0.006 . . . . . . . . . . . . [[33]]$

式[3]有效的条件是：c＞V_f≥25m/s，c＞V₀≥10m/s；The valid condition of formula [3] is: c>V _f ≥25m/s, c>V ₀ ≥10m/s;

6、计算特征角γ：将V₀、V_f带入下式，计算得到特征角γ；6. Calculate the characteristic angle γ: Put V ₀ and V _f into the following formula to calculate the characteristic angle γ;

$tan the tan γ γ = = 0.092 0.092 \cdot &Center Dot; \frac{{V V}_{f f}}{{V V}_{00}} + + 0.012 0.012 \cdot &Center Dot; {[[{V V}_{00} (({V V}_{00} - - {V V}_{f f}))]]}^{0.2 0.2} - - 0.056 0.056 . . . . . . . . . . . . [[44]]$

式[4]有效的条件是：c＞V_f≥25m/s，c＞V₀≥10m/s且V₀≠V_f；The valid condition of formula [4] is: c>V _f ≥25m/s, c>V ₀ ≥10m/s and V ₀ ≠V _f ;

7、确定滑流主流区边界线方程：滑流主流区边界线方程为：7. Determine the boundary line equation of the slipstream mainstream area: the boundary line equation of the slipstream mainstream area is:

y＝tanβ·x+R₀……………………………………………………[5]y=tanβ·x+R ₀ ……………………………………………[5]

式中，x≥0,且 In the formula, x≥0, and

根据下式计算： Calculate according to the following formula:

8、确定滑流过渡区边界线方程：滑流过渡区边界线方程为：8. Determine the boundary line equation of the slipstream transition zone: the boundary line equation of the slipstream transition zone is:

y＝-tanγ·(x+L)+0.5·D_f…………………………………………[7]y＝-tanγ·(x+L)+0.5·D _f ……………………………………[7]

式中，x≥-L,且 In the formula, x≥-L, and

9、确定特征角θ：取θ＝2°～5°；9. Determine the characteristic angle θ: take θ=2°～5°;

10、确定滑流区边界线方程：滑流区边界线方程为：10. Determine the boundary line equation of the slipstream area: the boundary line equation of the slipstream area is:

y＝tanθ·(x+L)+0.5·D_f…………………………………………[8]y＝tanθ·(x+L)+0.5·D _f …………………………………[8]

式中，x≥-L,且x≤10·D_f；In the formula, x≥-L, and x≤10·D _f ;

11、确定喷流减速区边界线方程：喷流减速区边界线方程为：11. Determine the boundary line equation of the jet deceleration zone: the boundary line equation of the jet deceleration zone is:

式中，且x≤10·D_f；In the formula, And x≤10·D _f ;

式中通过将带入式[5]计算得到；In the formula by putting into formula [5] to calculate;

12、计算涡桨飞机尾喷流区域任意坐标点(x_a,y_a)的速度V_a：根据坐标点(x_a,y_a)的具体位置，分为以下几种情况：12. Calculate the velocity V _a of any coordinate point (x _a , y _a ) in the tail jet area of the turboprop aircraft: According to the specific position of the coordinate point (x _a , y _a ), it can be divided into the following situations:

12.1、坐标点(x_a,y_a)处于喷流核心区时，V_a＝V₀；12.1. When the coordinate point (x _a , y _a ) is in the jet core area, V _a =V ₀ ;

12.2、坐标点(x_a,y_a)处于喷流核心区边界线上时，V_a＝V₀；12.2. When the coordinate point (x _a , y _a ) is on the boundary line of the jet core area, V _a = V ₀ ;

12.3、坐标点(x_a,y_a)处于喷流减速区边界线上时，V_a＝V_f；12.3. When the coordinate point (x _a , y _a ) is on the boundary line of the jet deceleration zone, V _a = V _f ;

12.4、坐标点(x_a,y_a)处于滑流主流区边界线上时，V_a＝V_f；12.4. When the coordinate point (x _a , y _a ) is on the boundary line of the slipstream mainstream area, V _a = V _f ;

12.5、坐标点(x_a,y_a)处于滑流区边界线上时，V_a＝0；12.5. When the coordinate point (x _a , y _a ) is on the boundary line of the slipstream area, V _a =0;

12.6、坐标点(x_a,y_a)处于滑流主流区时，V_a＝V_f；12.6. When the coordinate point (x _a , y _a ) is in the slipstream mainstream area, V _a = V _f ;

12.7、坐标点(x_a,y_a)处于对称中心轴线上，且处于喷流减速区时，12.7. When the coordinate point (x _a , y _a ) is on the central axis of symmetry and in the jet deceleration zone,

${V V}_{a a} = = {V V}_{axis axis} = = \frac{{V V}_{00}}{\sqrt{0.001 0.001 \cdot &Center Dot; {V V}_{00} \cdot &Center Dot; ((x x - - {x x}_{00})) + + 11}} - - \frac{{V V}_{f f}}{{V V}_{00}} ((x x - - {x x}_{00})) . . . . . . . . . . . . [[1010]]$

式[10]有效的条件是：V₀≥10m/s,10·D_f≥x＞x₀；The effective condition of formula [10] is: V ₀ ≥ 10m/s, 10·D _f ≥ x > x ₀ ;

12.8、坐标点(x_a,y_a)处于喷流减速区时，V_a的计算采用沿Y轴方向线性插值方法获取，分两种情况：12.8. When the coordinate point (x _a , y _a ) is in the jet deceleration zone, the calculation of V _a is obtained by linear interpolation along the Y-axis direction, and there are two cases:

12.8.1、当时，分三种情况：12.8.1 When , there are three situations:

12.8.1.1、若坐标点(x_a,y_a)处于喷流核心区边界线和滑流主流区边界线之间，直线x＝x_a，与喷流核心区边界线的交点为B(x_a,y_b)，与滑流主流区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为：12.8.1.1, if The coordinate point (x _a , y _a ) is between the boundary line of the core area of the jet flow and the boundary line of the main flow area of the slipstream, the straight line x=x _a , and the intersection point with the boundary line of the core area of the jet flow is B(x _a , y _b ) , the intersection point with the boundary line of the slipstream mainstream area is C(x _a , y _c ), and the velocity of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{00} + + \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} (({V V}_{f f} - - {V V}_{00})) . . . . . . . . . . . . [[1111]]$

12.8.1.2、若坐标点(x_a,y_a)处于喷流核心区边界线和喷流减速区边界线之间，直线x＝x_a，与喷流核心区边界线的交点为B(x_a,y_b)，与喷流减速区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为:12.8.1.2, if The coordinate point (x _a , y _a ) is between the boundary line of the jet flow core area and the jet flow deceleration area boundary line, the straight line x=x _a , and the intersection point with the jet flow core area boundary line is B(x _a , y _b ) , the intersection point with the boundary line of the jet deceleration zone is C(x _a , y _c ), and the velocity of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{00} + + \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} (({V V}_{f f} - - {V V}_{00})) . . . . . . . . . . . . [[1212]]$

12.8.1.3、若x_a＞x₀，坐标点(x_a,y_a)处于对称中心轴线和喷流减速区边界线之间，直线x＝x_a，与对称中心轴线的交点为B(x_a,0)，与喷流减速区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为:12.8.1.3. If x _a > x ₀ , the coordinate point (x _a , y _a ) is between the central axis of symmetry and the boundary line of the jet deceleration area, and the intersection point of the straight line x=x _a with the central axis of symmetry is B(x _a ,0), the intersection point with the boundary line of the jet deceleration zone is C(x _a ,y _c ), and the velocity of the coordinate point (x _a ,y _a ) is:

${V V}_{a a} = = {V V}_{axis axis} + + \frac{{y the y}_{a a}}{{y the y}_{c c}} (({V V}_{f f} - - {V V}_{axis axis})) . . . . . . . . . . . . [[1313]]$

上式中，V_axis通过将x_a带入式[10]计算得到；In the above formula, V _axis is calculated by bringing x _a into formula [10];

12.8.2、当时,分三种情况：12.8.2, when , there are three situations:

12.8.2.1、若x_a≤x₀，坐标点(x_a,y_a)处于喷流核心区边界线和滑流主流区边界线之间，直线x＝x_a，与喷流核心区边界线的交点为B(x_a,y_b)，与滑流主流区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为：12.8.2.1. If x _a ≤ x ₀ , the coordinate point (x _a , y _a ) is between the boundary line of the core area of the jet flow and the boundary line of the main flow area of the slip stream, and the straight line x=x _a is in line with the boundary line of the core area of the jet flow The intersection point of is B(x _a , y _b ), the intersection point with the boundary line of the slipstream mainstream area is C(x _a , y _c ), and the velocity of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{00} + + \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} (({V V}_{f f} - - {V V}_{00})) . . . . . . . . . . . . [[1414]]$

12.8.2.2、若坐标点(x_a,y_a)处于对称中心轴线和滑流主流区边界线之间，直线x＝x_a，与对称中心轴线的交点为B(x_a,0)，与滑流主流区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为：12.8.2.2, if The coordinate point (x _a , y _a ) is between the central axis of symmetry and the boundary line of the slipstream mainstream area, the straight line x = x _a , the intersection with the symmetry central axis is B(x _a , 0), and the boundary of the slipstream mainstream area The intersection point of the lines is C(x _a , y _c ), and the speed of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{axis axis} + + \frac{{y the y}_{a a}}{{y the y}_{c c}} (({V V}_{f f} - - {V V}_{axis axis})) . . . . . . . . . . . . [[1515]]$

12.8.2.3、若坐标点(x_a,y_a)处于对称中心轴线和喷流减速区边界线之间，直线x＝x_a，与对称中心轴线的交点为B(x_a,0)，与喷流减速区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为:12.8.2.3, if The coordinate point (x _a , y _a ) is between the central axis of symmetry and the boundary line of the jet deceleration zone, the straight line x=x _a , the intersection point with the central axis of symmetry is B(x _a ,0), and the boundary of the jet deceleration zone The intersection point of the lines is C(x _a , y _c ), and the speed of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{axis axis} + + \frac{{y the y}_{a a}}{{y the y}_{c c}} (({V V}_{f f} - - {V V}_{axis axis})) . . . . . . . . . . . . [[1616]]$

12.9、坐标点(x_a,y_a)处于滑流衰减区时，V_a的计算采用沿Y轴方向线性插值方法获取，分两种情况：12.9. When the coordinate point (x _a , y _a ) is in the slipstream attenuation zone, the calculation of V _a is obtained by linear interpolation along the Y-axis direction, and there are two cases:

12.9.1、若坐标点(x_a,y_a)处于滑流区边界线和滑流衰减区边界线之间，直线x＝x_a，与滑流衰减区边界线的交点为B(x_a,y_b)，与滑流区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为：12.9.1, if The coordinate point (x _a , y _a ) is between the boundary line of the slipstream area and the boundary line of the slipstream attenuation area, the straight line x=x _a , and the intersection point with the boundary line of the slipstream attenuation area is B(x _a , y _b ), The point of intersection with the boundary line of the slipstream area is C(x _a , y _c ), and the velocity of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{f f} - - \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} \cdot &Center Dot; {V V}_{f f} . . . . . . . . . . . . [[1717]]$

12.9.2、若坐标点(x_a,y_a)处于滑流区边界线和喷流减速区边界线之间，直线x＝x_a，与喷流减速区边界线的交点为B(x_a,y_b)，与滑流区边界线的交点为C(x_a,y_c),坐标点(x_a,y_a)的速度为：12.9.2, if The coordinate point (x _a , y _a ) is between the boundary line of the slipstream zone and the boundary line of the jet deceleration zone, the straight line x=x _a , and the intersection point with the boundary line of the jet deceleration zone is B(x _a , y _b ), The point of intersection with the boundary line of the slipstream area is C(x _a , y _c ), and the velocity of the coordinate point (x _a , y _a ) is:

${V V}_{a a} = = {V V}_{f f} - - \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} \cdot &Center Dot; {V V}_{f f} . . . . . . . . . . . . [[1818]]$

至此，完成涡桨飞机尾喷流速度场的计算。So far, the calculation of the velocity field of the turboprop tail jet has been completed.

本发明的优点是：提出了一种快速计算涡桨飞机在静止状态下尾喷速度场计算的方法，简化了计算过程，缩短了计算周期。本发明的一个实施例，经计算验证，所用的计算时间仅为目前方法的10％以内。The invention has the advantages of proposing a method for quickly calculating the tail jet velocity field of a turboprop aircraft in a static state, which simplifies the calculation process and shortens the calculation cycle. In one embodiment of the present invention, it is verified by calculation that the calculation time used is only within 10% of the current method.

附图说明Description of drawings

图1是本发明的计算原理示意图。Fig. 1 is a schematic diagram of the calculation principle of the present invention.

具体实施方式detailed description

下面对本发明作进一步详细说明。参见图1，涡桨飞机在静止状态下尾喷流速度场的计算方法，发动机尾喷管的轴线与螺旋桨旋转轴线同轴，计算中不考虑环境风速的影响，基于以下已知参数：螺旋桨直径D_f、飞机发动机尾喷口半径R₀、发动机短舱长度L，指发动机进气道唇口前缘点与飞机发动机尾喷口平面的距离；还基于飞机所处大气环境压力和温度参数以及发动机尾喷口排气速度V₀和螺旋桨下游出口面气流平均速度V_f，螺旋桨下游出口面1是指：螺旋桨旋转面在一个特定平面上的投影，该特定平面是过发动机进气道唇口前缘点且垂直于发动机轴线的平面；其特征在于，计算涡桨飞机尾喷速度场的步骤如下：The present invention will be described in further detail below. See Figure 1, the calculation method of the tail jet flow velocity field of a turboprop aircraft in a static state, the axis of the engine tail nozzle is coaxial with the rotation axis of the propeller, and the influence of the ambient wind speed is not considered in the calculation, based on the following known parameters: propeller diameter D _f , aircraft engine tail nozzle radius R ₀ , and engine nacelle length L refer to the distance between the leading edge point of the engine inlet lip and the aircraft engine tail nozzle plane; it is also based on the atmospheric environment pressure and temperature parameters of the aircraft and the engine tail The nozzle exhaust velocity V ₀ and the average velocity V _f of the airflow at the downstream outlet surface of the propeller, the downstream outlet surface 1 of the propeller refers to the projection of the rotating surface of the propeller on a specific plane, which is the leading edge point of the engine inlet lip And perpendicular to the plane of the engine axis; it is characterized in that the steps of calculating the turboprop jet velocity field are as follows:

2、定义：2. Definition:

$tan the tan α α = = \frac{{R R}_{00}}{{x x}_{00}} = = 2.33 2.33 \cdot &Center Dot; \frac{{V V}_{00}}{c c} \cdot \cdot \frac{11}{{V V}_{f f}^{0.75 0.75}} + + 0.149 0.149 \cdot \cdot \frac{11}{{V V}_{00} - - {V V}_{f f}} - - 0.007 0.007 . . . . . . . . . . . . [[11]]$

式中，x≥0,且x≤x₀；In the formula, x≥0, and x≤x ₀ ;

式中，x≥0,且 In the formula, x≥0, and

根据下式计算： Calculate according to the following formula:

式中，x≥-L,且 In the formula, x≥-L, and

式中，x≥-L,且x≤10·D_f；In the formula, x≥-L, and x≤10·D _f ;

式中，且x≤10·D_f；In the formula, And x≤10·D _f ;

12.8.1、当时，分三种情况：12.8.1 When , there are three situations:

12.8.2、当时,分三种情况：12.8.2, when , there are three situations:

${V V}_{a a} = = {V V}_{f f} - - \frac{{y the y}_{a a} - - {y the y}_{b b}}{{y the y}_{c c} - - {y the y}_{b b}} \cdot \cdot {V V}_{f f} . . . . . . . . . . . . [[1818]]$

实施例Example

本发明一种涡桨飞机在静止状态下尾喷速度场计算的方法，计算某飞机处于海平面高度、标准大气环境，飞机静止，环境风速为0，发动机最大功率状态，螺旋桨直径D_f＝4.0m，发动机尾喷口半径R₀＝0.32m,短舱长度L＝3.6m，发动机尾喷口气流速度V₀＝135m/s，螺旋桨下游出口面气流平均速度V_f＝50m/s；具体实施步骤如下：The present invention is a method for calculating the tail jet velocity field of a turboprop aircraft in a static state, calculating that an aircraft is at sea level and in a standard atmospheric environment, the aircraft is stationary, the ambient wind speed is 0, the engine is in the maximum power state, and the propeller diameter D _f =4.0 m, engine tail nozzle radius R ₀ =0.32m, nacelle length L=3.6m, engine tail nozzle airflow velocity V ₀ =135m/s, propeller downstream outlet surface airflow average _{velocity Vf} =50m/s; specific implementation steps are as follows :

1.建立坐标系：将发动机尾喷流场视为三维轴对称模型，取垂直于水平面并过发动机轴线的平面为二维坐标平面；以发动机轴线为X轴，尾喷流方向为正方向，以发动机尾喷口平面与发动机轴线的交点为原点O，垂直于X轴并过原点O的直线为Y轴，正方向向上；1. Establish a coordinate system: regard the engine tail jet flow field as a three-dimensional axisymmetric model, take the plane perpendicular to the horizontal plane and passing the engine axis as the two-dimensional coordinate plane; take the engine axis as the X axis, and the tail jet flow direction as the positive direction, Take the intersection of the plane of the engine tail nozzle and the engine axis as the origin O, the line perpendicular to the X axis and passing through the origin O is the Y axis, and the positive direction is upward;

2、定义；2. Definition;

3、计算特征角α：将R₀、V₀、V_f带入下式；3. Calculate the characteristic angle α: put R ₀ , V ₀ , and V _f into the following formula;

$tan the tan α α = = \frac{{R R}_{00}}{{x x}_{00}} = = 2.33 2.33 \cdot \cdot \frac{{V V}_{00}}{c c} \cdot &Center Dot; \frac{11}{{V V}_{f f}^{0.75 0.75}} + + 0.149 0.149 \cdot &Center Dot; \frac{11}{{V V}_{00} - - {V V}_{f f}} - - 0.007 0.007 . . . . . . . . . . . . [[11]]$

计算得x₀＝7.27m，tanα＝0.044；It is calculated that x ₀ =7.27m, tanα=0.044;

4、确定喷流核心区边界线方程：将tanα、R₀代入下式；4. Determine the boundary line equation of the jet core area: Substitute tanα and R ₀ into the following formula;

喷流核心区边界线方程为:The boundary line equation of the jet core area is:

y＝-0.044·x+0.32…………………………………………………[3]式中，x≥0,且x≤7.27；y＝-0.044 x+0.32……………………………………………………[3] In the formula, x≥0, and x≤7.27;

5、计算特征角β：将V₀、V_f带入下式；5. Calculate the characteristic angle β: put V ₀ and V _f into the following formula;

$tan the tan β β = = 0.204 0.204 \cdot &Center Dot; \sqrt{{V V}_{00} / / c c} - - 0.235 0.235 \cdot &Center Dot; \sqrt{{V V}_{f f} / / c c} - - 0.006 0.006 . . . . . . . . . . . . [[44]]$

计算得tanβ＝0.0324；Calculated tanβ=0.0324;

6、计算特征角γ：将V₀、V_f带入下式；6. Calculate the characteristic angle γ: put V ₀ and V _f into the following formula;

$tan the tan γ γ = = 0.092 0.092 \cdot &Center Dot; \frac{{V V}_{f f}}{{V V}_{00}} + + 0.012 0.012 \cdot \cdot {[[{V V}_{00} (({V V}_{00} - - {V V}_{f f}))]]}^{0.2 0.2} - - 0.056 0.056 . . . . . . . . . . . . [[55]]$

计算得到tanγ＝0.0558；Calculated to get tanγ=0.0558;

7、确定滑流主流区边界线方程：将tanβ、R₀代入下式；7. Determine the boundary line equation of the slipstream mainstream area: Substitute tanβ and R ₀ into the following formula;

y＝tanβ·x+R₀……………………………………………………[6]将tanβ、tanγ、D_f、R₀、L带入[7]式，y=tanβ·x+R ₀ ……………………………………………………………………………………………………………………[6] put tanβ, tanγ, D _f , R ₀ , L into formula [7],

计算得 calculated

滑流主流区边界线方程为：The boundary line equation of the slip flow mainstream area is:

y＝0.0324·x+0.32…………………………………………………[8]式中，16.77≥x≥0；y＝0.0324 x+0.32……………………………………………………[8] where, 16.77≥x≥0;

8、确定滑流衰减区边界线方程：将tanγ、R₀、L、D_f代入下式；y＝-tanγ·(x+L)+0.5·D_f…………………………………………[9]8. Determine the boundary line equation of the slipstream attenuation zone: Substitute tanγ, R ₀ , L, and D _f into the following formula; y=-tanγ·(x+L)+0.5·D _f …………………… ………………[9]

滑流衰减区边界线方程为：The boundary line equation of the slipstream attenuation zone is:

y＝-0.0558·(x+3.6)+2.0…………………………………………[10]式中，16.77＞x＞-3.6；y＝-0.0558·(x+3.6)+2.0…………………………………………[10] In the formula, 16.77＞x＞-3.6;

9、确定特征角θ：取θ＝4.2°；9. Determine the characteristic angle θ: take θ=4.2°;

10、确定滑流区边界线方程：将θ、L、D_f代入下式；10. Determine the boundary line equation of the slipstream area: Substitute θ, L, D _f into the following formula;

y＝tanθ·(x+L)+0.5·D_f………………………………………[11]y＝tanθ·(x+L)+0.5·D _f …………………………………[11]

滑流区边界线方程为：The boundary line equation of the slipstream region is:

y＝0.0734·(x+3.6)+2.0…………………………………………[12]y＝0.0734·(x+3.6)+2.0…………………………………[12]

式中，40.0＞x≥-3.6；In the formula, 40.0>x≥-3.6;

11、确定喷流减速区边界线方程：11. Determine the boundary line equation of the jet deceleration zone:

将带入[8]式，计算得 Will Putting it into the formula [8], we can get

将β、γ、代入下式；Put β, γ, Substitute into the following formula;

喷流减速区边界线方程为： The boundary line equation of the jet deceleration zone is:

y＝-0.0232·(x-16.77)+0.863………………………………………[14]y＝-0.0232·(x-16.77)+0.863…………………………………[14]

式中，40.0≥x＞16.77；In the formula, 40.0≥x＞16.77;

12、计算涡桨飞机尾喷流区域任意坐标点(x_a,y_a)的速度V_a：12. Calculate the velocity V _a of any coordinate point (x _a , y _a ) in the wake area of the turboprop aircraft:

12.1、取x_a＝10.0，y_a＝0.56,经判断，坐标点(x_a,y_a)处于喷流减速区，且点(x_a,y_a)处于对称中心轴线和滑流主流区边界线之间，直线x＝10.0，与对称中心轴线的交点为B(10.0,0)，与滑流主流区边界线的交点为C(10.0,y_c),将x_a代入[8]式，求得y_c＝0.644；12.1. Take x _a = 10.0, y _a = 0.56. After judging, the coordinate point (x _a , y _a ) is in the jet deceleration zone, and The point (x _a , y _a ) is between the central axis of symmetry and the boundary line of the slipstream mainstream area, the straight line x=10.0, the intersection point with the symmetry central axis is B(10.0,0), and the intersection point with the slipstream mainstream area boundary line is C(10.0, y _c ), substitute x _a into formula [8], and obtain y _c =0.644;

将x＝x_a＝10.0、x₀＝7.27、V₀＝135、V_f＝50带入式[15]：Put x=x _a =10.0, x ₀ =7.27, V ₀ =135, V _f =50 into formula [15]:

${V V}_{axis axis} = = \frac{{V V}_{00}}{\sqrt{0.001 0.001 \cdot &Center Dot; {V V}_{00} \cdot &Center Dot; ((x x - - {x x}_{00})) + + 11}} - - \frac{{V V}_{f f}}{{V V}_{00}} ((x x - - {x x}_{00})) . . . . . . . . . . . . [[1515]]$

计算得V_axis＝114.4m/s；Calculate V _axis = 114.4m/s;

将V_axis＝114.4m/s、V_f＝50、y_a＝0.56、y_c＝0.644带入式[16]：Put V _axis =114.4m/s, V _f =50, y _a =0.56, y _c =0.644 into formula [16]:

计算得坐标点(10.0,0.56)的速度V_a＝58.4m/s。该点的试验值为63m/s,误差小于10％，计算耗时8分钟。The velocity V _a of the coordinate point (10.0,0.56) is calculated to be 58.4m/s. The test value of this point is 63m/s, the error is less than 10%, and the calculation takes 8 minutes.

12.2、取x_a＝6.0，y_a＝1.7,经判断，坐标点(x_a,y_a)处于滑流衰减区，且点(x_a,y_a)处于滑流区边界线和滑流衰减区边界线之间，直线x＝6.0，与滑流衰减区边界线的交点为B(6.0,y_b)，与滑流区边界线的交点为C(6.0,y_c)。将x_a分别代入[10]、[12]式，求得y_b＝1.464、y_c＝2.705；12.2. Take x _a = 6.0, y _a = 1.7. After judging, the coordinate point (x _a , y _a ) is in the slipstream attenuation zone, and The point (x _a , y _a ) is between the boundary line of the slipstream area and the boundary line of the slipstream attenuation area, the straight line x=6.0, and the intersection point with the boundary line of the slipstream attenuation area is B(6.0, y _b ), and the intersection with the slipstream attenuation area The intersection point of the district boundary lines is C(6.0,y _c ). Substitute x _a into formulas [10] and [12] to obtain y _b = 1.464, y _c = 2.705;

将y_a、y_b、y_c、V_f带入式[17]；Put y _a , y _b , y _c , V _f into formula [17];

计算得坐标点(6.0,1.7)的速度V_a＝40.5m/s,该点的试验值为39m/s,误差小于10％，计算耗时2分钟。The calculated velocity V _a of the coordinate point (6.0,1.7) is 40.5m/s, the test value of this point is 39m/s, the error is less than 10%, and the calculation takes 2 minutes.

Claims

1. the method for calculating of whirlpool oar aircraft under static state tail jet velocity field, the axis of nozzle is coaxial with propeller rotational axis, does not consider the impact of ambient wind velocity in calculating, based on following known parameters: diameter of propeller D _f, aero-engine nozzle radius R ₀, engine nacelle length L, refer to the distance of engine inlets lip leading edge point and aero-engine nozzle plane; Also based on atmospheric environmental pressure residing for aircraft and temperature parameter and engine tail nozzle exhaust velocity V ₀with screw propeller lower exit face air-flow average velociity V _f, screw propeller lower exit face (1) refers to: the projection of propellerpiston on a specific plane, and this specific plane was engine inlets lip leading edge point and perpendicular to the plane of engine axis; It is characterized in that, the step calculating whirlpool oar airplane tail spray velocity field is as follows:

1.1, set up system of axes: engines tail jet flow field is considered as Three-dimensional Axisymmetric model, getting perpendicular to horizontal surface and crossing the plane of engine axis is two-dimensional coordinate plane; Take engine axis as X-axis, tail jet direction is positive dirction, and with the intersection point of engine tail nozzle plane and engine axis for initial point O, perpendicular to X-axis and the straight line crossing initial point O is Y-axis, positive dirction upwards;

1.2, define:

1.2.1, jet flow core space is defined as: tail jet speed V=V ₀region, be coniform region;

1.2.2, slip-stream main flow area is defined as: the downstream being in screw propeller, and tail jet speed V=V _fregion;

1.2.3, jet flow deceleration area is defined as: be in jet flow core space and slip-stream main flow area downstream, and tail jet speed V>=V _f, and V < V ₀region;

1.2.4, slip-stream decay area is defined as: tail jet speed V < V _f, and the region of V > 0;

1.2.5, jet flow core space boundary line (10) intersection that is the jet cutting car flow core space border conical surface and two-dimensional coordinate plane;

1.2.6, slip-stream main flow area boundary line (8) is defined as: the circular conical surface of slip-stream main flow area and the intersection of two-dimensional coordinate plane, and this intersection adjoins jet flow deceleration area;

1.2.7, boundary line, jet flow deceleration area (7) are defined as: the demarcation line of slip-stream decay area and jet flow deceleration area;

1.2.8, boundary line, slip-stream decay area (4) is defined as: the circular conical surface of slip-stream main flow area and the intersection of two-dimensional coordinate plane, and this intersection adjoins slip-stream decay area;

1.2.9, boundary line, slipstream (5) are defined as: the peripheral boundary conical surface of slip-stream decay area and the intersection of two-dimensional coordinate plane;

1.2.10, jet flow core space boundary line (10) are characteristic angle α with the angle of X-axis line;

1.2.11, slip-stream main flow area boundary line (8) are characteristic angle β with the angle of X-axis line;

1.2.12, boundary line, slip-stream decay area (4) are characteristic angle γ with the angle of X-axis line;

1.2.13, boundary line, slipstream (5) are characteristic angle θ with the angle of X-axis line;

1.3, calculated characteristics angle α: by R ₀, V ₀, V _fbring following formula into, calculate α;

t a n α = \frac{R_{0}}{x_{0}} = 2.33 \cdot \frac{V_{0}}{c} \cdot \frac{1}{V_{f}^{0.75}} + 0.149 \cdot \frac{1}{V_{0} - V_{f}} - 0.007 ... [1]

In formula, c is local velocity of sound, gets 340m/s; x ₀for the X-coordinate value of jet flow core space boundary line and X-axis intersection point;

Formula [1] actv. condition is: c > V _f>=25m/s, c > V ₀>=10m/s and V ₀≠ V _f;

1.4, jet flow core space boundary line equation is determined: jet flow core space boundary line equation is:

y＝-tanα·x+R ₀…………………………………………………[2]

In formula, x>=0, and x≤x ₀;

1.5, calculated characteristics angle β: by V ₀, V _fbring following formula into, calculate characteristic angle β;

t a n β = 0.204 \cdot \sqrt{V_{0} / c} - 0.235 \cdot \sqrt{V_{f} / c} - 0.006 ... [3]

Formula [3] actv. condition is: c > V _f>=25m/s, c > V ₀>=10m/s;

1.6, calculated characteristics angle γ: by V ₀, V _fbring following formula into, calculate characteristic angle γ;

t a n γ = 0.092 \cdot \frac{V_{f}}{V_{0}} + 0.012 \cdot {[V_{0} (V_{0} - V_{f})]}^{0.2} - 0.056 ... [4]

Formula [4] actv. condition is: c > V _f>=25m/s, c > V ₀>=10m/s and V ₀≠ V _f;

1.7, slip-stream main flow area boundary line equation is determined: slip-stream main flow area boundary line equation is:

y＝tanβ·x+R ₀……………………………………………………[5]

In formula, x>=0, and

calculate according to following formula:

1.8, boundary line, slip-stream decay area equation is determined: boundary line, slip-stream decay area equation is:

y＝-tanγ·(x+L)+0.5·D _f…………………………………………[7]

In formula, x>=-L, and

1.9, characteristic angle θ is determined: get θ=2 ° ~ 5 °;

1.10, determine boundary line, slipstream equation: boundary line, slipstream equation is:

y＝tanθ·(x+L)+0.5·D _f…………………………………………[8]

In formula, x>=-L, and x≤10D _f;

1.11, boundary line, jet flow deceleration area equation is determined: boundary line, jet flow deceleration area equation is:

In formula, and x≤10D _f;

In formula by inciting somebody to action bring formula [5] into calculate;

1.12, oar Fighter Plane Plume region, whirlpool arbitrary coordinate point (x is calculated _a, y _a) speed V _a: according to coordinate points (x _a, y _a) particular location, be divided into following several situation:

1.12.1, coordinate points (x _a, y _a) when being in jet flow core space, V _a=V ₀;

1.12.2, coordinate points (x _a, y _a) when being on jet flow core space boundary line, V _a=V ₀;

1.12.3, coordinate points (x _a, y _a) when being on boundary line, jet flow deceleration area, V _a=V _f;

1.12.4, coordinate points (x _a, y _a) when being on slip-stream main flow area boundary line, V _a=V _f;

1.12.5, coordinate points (x _a, y _a) when being on boundary line, slipstream, V _a=0;

1.12.6, coordinate points (x _a, y _a) when being in slip-stream main flow area, V _a=V _f;

1.12.7, coordinate points (x _a, y _a) be on center axis of symmetry, and when being in jet flow deceleration area,

V_{a} = V_{a x i s} = \frac{V_{0}}{\sqrt{0.001 \cdot V_{0} \cdot (x - x_{0}) + 1}} - \frac{V_{f}}{V_{0}} (x - x_{0}) ... [10]

Formula [10] actv. condition is: V ₀>=10m/s, 10D _f>=x > x ₀;

1.12.8, coordinate points (x _a, y _a) when being in jet flow deceleration area, V _acalculating adopt along Y direction linear interpolation method obtain, in two kinds of situation:

1.12.8.1, when time, point three kinds of situations:

If 1.12.8.1.1 coordinate points (x _a, y _a) be between jet flow core space boundary line and slip-stream main flow area boundary line, straight line x=x _a, be B (x with the intersection point of jet flow core space boundary line _a, y _b), be C (x with the intersection point of slip-stream main flow area boundary line _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{0} + \frac{y_{a} - y_{b}}{y_{c} - y_{b}} (V_{f} - V_{0}) ... [11]

If 1.12.8.1.2 coordinate points (x _a, y _a) be between jet flow core space boundary line and boundary line, jet flow deceleration area, straight line x=x _a, be B (x with the intersection point of jet flow core space boundary line _a, y _b), be C (x with the intersection point of boundary line, jet flow deceleration area _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{0} + \frac{y_{a} - y_{b}}{y_{c} - y_{b}} (V_{f} - V_{0}) ... [12]

If 1.12.8.1.3 x _a> x ₀, coordinate points (x _a, y _a) be between center axis of symmetry and boundary line, jet flow deceleration area, straight line x=x _a, be B (x with the intersection point of center axis of symmetry _a, 0), be C (x with the intersection point of boundary line, jet flow deceleration area _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{a x i s} + \frac{y_{a}}{y_{c}} (V_{f} - V_{a x i s}) ... [13]

In above formula, V _axisby by x _abring formula [10] into calculate;

1.12.8.2, when time, point three kinds of situations:

If 1.12.8.2.1 x _a≤ x ₀, coordinate points (x _a, y _a) be between jet flow core space boundary line and slip-stream main flow area boundary line, straight line x=x _a, be B (x with the intersection point of jet flow core space boundary line _a, y _b), be C (x with the intersection point of slip-stream main flow area boundary line _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{0} + \frac{y_{a} - y_{b}}{y_{c} - y_{b}} (V_{f} - V_{0}) ... [14]

If 1.12.8.2.2 coordinate points (x _a, y _a) be between center axis of symmetry and slip-stream main flow area boundary line, straight line x=x _a, be B (x with the intersection point of center axis of symmetry _a, 0), be C (x with the intersection point of slip-stream main flow area boundary line _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{a x i s} + \frac{y_{a}}{y_{c}} (V_{f} - V_{a x i s}) ... [15]

In above formula, V _axisby by x _abring formula [10] into calculate;

If 1.12.8.2.3 coordinate points (x _a, y _a) be between center axis of symmetry and boundary line, jet flow deceleration area, straight line x=x _a, be B (x with the intersection point of center axis of symmetry _a, 0), be C (x with the intersection point of boundary line, jet flow deceleration area _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{a x i s} + \frac{y_{a}}{y_{c}} (V_{f} - V_{a x i s}) ... [16]

In above formula, V _axisby by x _abring formula [10] into calculate;

1.12.9, coordinate points (x _a, y _a) when being in slip-stream decay area, V _acalculating adopt along Y direction linear interpolation method obtain, in two kinds of situation:

If 1.12.9.1 coordinate points (x _a, y _a) be between boundary line, slipstream and boundary line, slip-stream decay area, straight line x=x _a, be B (x with the intersection point of boundary line, slip-stream decay area _a, y _b), be C (x with the intersection point of boundary line, slipstream _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{f} - \frac{y_{a} - y_{b}}{y_{c} - y_{b}} \cdot V_{f} ... [17]

If 1.12.9.2 coordinate points (x _a, y _a) be between boundary line, slipstream and boundary line, jet flow deceleration area, straight line x=x _a, be B (x with the intersection point of boundary line, jet flow deceleration area _a, y _b), be C (x with the intersection point of boundary line, slipstream _a, y _c), coordinate points (x _a, y _a) speed be:

V_{a} = V_{f} - \frac{y_{a} - y_{b}}{y_{c} - y_{b}} \cdot V_{f} ... [18]

So far, the calculating of whirlpool oar Fighter Plane Plume velocity field is completed.