Improved design and performance analysis of counterflow thrust vectoring technology under high subsonic

Abstract

With the development of aviation technology and the scramble for air supremacy is becoming increasingly fierce, people put forward higher requirements on the performance of the fighter. The thrust vector nozzle based on flow control has many advantages compared with the traditional mechanical control method, in the thrust vector technology, the thrust loss is low, it can also be applied in subsonic speed. Thrust vector technology has a wider application background. In this paper, the basic principle of counter current thrust vector technology is explained firstly, then the simplified derivation of the formula and the definition of related parameters are derived by the control body analysis. And fluent software is used to simulate the existing experimental model, the obtained numerical results are compared with the experimental data available in the literature, verification proves that the numerical method is feasible. Then change the Maher number of outflow size of vector analysis to effect change. Finally, for thrust vector effect is not obvious under the Maher problem, the design provides a method for vacuum reverse two secondary channel, and its feasibility by using the method of numerical analysis, the vacuum in the two channel is increased, and the thrust vector angle can reach to 18.1 degrees from 1.7 degrees, an increase of about 10 times.

Keywords

Thrust vector vector angle outflow Maher number suction pressure vacuum degree

1 Introduction

With the development of aviation technology and the scramble for air supremacy is becoming increasingly fierce, people put forward higher requirements on the performance of the fighter, which gave birth to the super maneuverability, stealth, super information superiority, supersonic cruise performance benchmark of fourth generation advanced fighter [1]. An important aspect of super maneuverability is the post stall maneuver, which means that the aircraft is still capable of maneuvering the aircraft after a stall angle of attack. In the new generation of advanced aircraft need to complete more complex maneuvering mission, harsh or bad flight conditions, the traditional control of the aerodynamic force/torque of the rudder is restricted, the control effect is reduced or even failure. At this point, we need to find new support outside the conventional control methods [2]. Thrust vectoring technology emerges as the times require and becomes one of the necessary technologies of the fourth generation fighter.

Thrust vector technology is a powerful thrust to make the appropriate adjustments and deflection. Thrust vector technology can not only provide thrust, but also can support aircraft pitch, yaw, backstepping direction force/torque individually or simultaneously, that is to vectorize the thrust, so as to achieve the purpose of. Trust vector technology to control the flight attitude the final is through the nozzle to achieve, therefore, has become the key to the development of vector nozzle thrust vector technology step. Vector nozzle can be divided into mechanical adjusting and airflow control type two [3]. Compared with vector nozzle flow control based on mechanical transmission parts, airflow control type has many advantages: save system, high sensitivity, fast response, and improve the thrust performance of infrared stealth performance, weight and cost reduction.

Flow adjustable thrust vectoring nozzle is introduced in the two lateral flow nozzle contraction, the pressure distribution of the nozzle surface is asymmetric, change the mainstream direction, so as to realize the thrust vector. The fluid control type of thrust vectoring technology mainly has four kinds: shock manipulation, throat offset, dual throat migration and counter current flow control [4]. Figure 1 counter flow thrust vector control is also called control for reflux, add a layer of coat outside the original nozzle, the nozzle of the outer tube and the original space is divided into upper and lower parts, need to control the mainstream, a part of space vacuum device using the suction, reverse the two times the flow in the outer sleeve pipe. Two reverse flow has the nozzle exit pressure distribution is uneven, the mainstream to the two flow direction [5], so as to achieve the purpose of vector control. Compared with other flow control of thrust vectoring technology, this control scheme of thrust loss and secondary flow are smaller, and the nozzle exit mainstream speed is effectively subsonic or supersonic [1].

Fig.1

Principle of counter current thrust vector.

The airflow control vector nozzle compared with the mechanical advantage of the counter flow thrust vectoring is subsonic and can be used in the mainstream, so in this paper, by comparing the results of numerical simulation and the university of Minnesota Buddha, shrinkage ratio provided by the university experimental model, counter flow thrust vector technique is proved the reliability of our numerical calculation method [3]. And through the analysis of the suction pressure is constant, the outflow of Maher number changes on thrust vector angle effect, we find the thrust vector angle effect is not obvious under large Maher number, we need a method of producing vacuum to solve this problem [5]. So we will analyze if flow valve control two channel flow can result vacuum which we need, and further study the micro the phenomenon of negative pressure and suction effect to solve the problem, for relevant personnel reference.

2 Methodology

2.1 Basic principle of countercurrent thrust vector

Figure 1 structure of counter flow thrust vectoring nozzle, the nozzle in the main external (two yuan only in the lower vector) with outer tube, two channel is formed between the outer tube and the main nozzle is arranged in the suction system. At the end of the tunnel can be started in accordance with the unilateral, mainstream required deflection angle, suction pressure difference. No production of soy sauces the presence of the outer tube, the main nozzle supersonic flow and quiescent air around to produce shear layer, through its thickness growth entrainment atmosphere. Because of the outer tube, to prevent air natural supplement, on two channel micro negative pressure, driven by gas two times and the atmospheric environment into the channel the region caused by air entrainment. Added at the nozzle exit to produce the same shear layer, resulting in the outer tube section of general shear layer. vector under the condition of open side suction system, reverse flow two times, and the interaction of the mainstream in counter flow shear layer. The counter flow thrust vectoring is mainly by using the shear layer characteristics and counter current attachment Tat (Coanda) effect [6].

2.2 Body analysis and parameter definition of countercurrent thrust vector control

The engine and the outer tube for controlling body is analyzed, and the following assumptions: (1) air stable parameters of engine inlet and outlet section; (2) the environment pressure is atmospheric pressure P_atm, flow rate of u₀; (3) vertical unit width, and ignore the three-dimensional effect; (4) and the mainstream the two stream flow parameter does not exist Y component; (5) neglecting the viscous resistance.

The structure shown in Fig. 1, the parameter is defined as: (1) R_x, R_y force on the engine of the aircraft, then the aircraft can be used to force the engine $R_{x}^{'}$ , $R_{x}^{'}$ said, because they are force and counterforce, meet the requirements of $R_{x} = - R_{x}^{'}$ and $R_{y} = - R_{y}^{'}$ ; (2) P_atm refers to the environmental pressure; (3) P_i, m_i, u_i, channel pressure, mass flow rate, respectively, 2, 3 respectively. The subscript 1 refers to the mainstream, the suction channel, cocurrent flow channel parameters; (4) F_x, F_y refers to the force of air flow in the role of the outer tube X and Y directions; (5) H, G. C L refers to the engine nozzle section height respectively, two flow channel height, height and length of outer tube. According to the theorem of momentum, available: ${\begin{matrix} R_{x} - F_{X} + (P_{atm} - P_{1}) H + (P_{atm} - P_{2}) G \\ + (P_{atm} - P_{3}) G + 2 P_{atm} C = m_{1} (u_{1} - u_{0}) \\ - m_{2} u_{2} + m_{3} u_{3} \\ R_{y} - F_{y} = 0 \end{matrix}$ (1)

Further simplify the analysis, and assume that:

the upper and lower walls of the outer casing of the force situation and the secondary channel pressure and ambient pressure, that is, $P_{up} = \frac{P_{2} + P_{atm}}{2}, P_{down} = (P_{3} + P_{atm}) / 2$ , Therefore: ${\begin{matrix} F_{x} = P_{up} C + P_{down} C = P_{atm} C \\ + (P_{2} + P_{3}) C / 2 \\ F_{y} = P_{down} L - P_{up} L = (P_{3} - P_{2}) L / 2 \end{matrix}$ (2)

the main stream has fully expanded in the nozzle: P₁ = P_atm;

the pressure of the same outlet is similar to atmospheric pressure at two times. P₃ = P_atm;

the two flow relative to the mainstream flow smaller, can be ignored. So finishing formula (1), available: ${\begin{matrix} R_{x} = ρ u_{1} H (u_{1} - u_{0}) - (P_{atm} - P_{2}) (\frac{c}{2} + G) \\ R_{y} = (P_{atm} - P_{2}) L / 2 \end{matrix}$ (3)

The R_x, R_y as the force and control force, based on the formula one, will affect the size of the outflow velocity of thrust, but had no effect on control; improve the suction pressure, thrust decreases, control force increased; the outer tube length, control force increased; and the two flow passage height and the outer tube height increases. It will reduce the thrust. The definition of thrust vector angle: $δ = arctan \frac{R_{y}^{'}}{R_{x}^{'}} = arctan \frac{R_{y}}{R_{x}}$ (4)

This is an important parameter for evaluating vectoring performance of counter flow thrust vectoring nozzle, which will be further deduced and simplified.

2.3 Introduction of numerical simulation method of counter current thrust vector

In this paper, fluent software is used to numerically solve the counter flow thrust vectoring nozzle model. The following control equations and turbulence models are introduced briefly. This is control equation:

Fluid flow and heat transfer are subject to mass, momentum, and energy conservation. $\frac{\partial (ρ φ)}{\partial t} + \frac{\partial (ρ u_{i} φ)}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} (Γ_{φ} \frac{\partial φ}{\partial x_{i}}) + S_{φ}$ (5)

Formula (5), from left to right are time items, convection terms, diffusion terms and source terms. For continuity equation, φ = 1, S_φ = 0; For the N-S equation, φ = u_j, Γ_φ = μ, $S_{φ} = ρ f_{j} - \frac{\partial P}{\partial x_{j}}$ ; For the energy equation, φ = T, Γ_φ = λ/C_υ, S_φ = ρ (q + φ)/C_V.

2.4 Turbulence model

$\frac{\partial (ρ u_{i})}{\partial (x_{i})} = 0$ (6) $\begin{matrix} \frac{\partial (ρ U_{i})}{\partial t} + \frac{\partial (ρ U_{i} U_{j})}{\partial x_{j}} \\ = ρ f_{i} - \frac{\partial P}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} (μ \frac{\partial U_{i}}{\partial x_{j}}) + [- \frac{\partial (ρ \bar{U_{i}^{'} U_{j}^{'}})}{\partial x_{j}}] \end{matrix}$ (7)

Only the control equations composed of (6) and (7) time averaged motions are not closed and contain Reynolds stress terms, so some assumptions on Reynolds stress are needed to construct the turbulence model.

(1) turbulence viscosity model

Introducing turbulent viscosity, the Reynolds stress is expressed as a function of turbulent viscosity: $- ρ \bar{u_{i}^{'} u_{j}^{'}} = μ_{t} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) - \frac{2}{3} (ρ κ + μ \frac{\partial u_{i}}{\partial x_{i}}) δ_{ij}$ (8)

Formula (8), μ_t refers to the turbulent viscosity, the κ refers to the turbulent kinetic energy, defined as $κ = \bar{u_{i}^{'} u_{j}^{'}} / 2$ , The μ_t and the turbulent mean link, using the κ - ɛ model, κ defined type, ɛ represents a turbulent dissipation rate, defined as $ɛ = \frac{μ}{ρ} \bar{(\frac{\partial u_{i}^{'}}{\partial x_{k}}) (\frac{\partial u_{i}^{'}}{\partial x_{k}})}$ . μ_t is expressed as a function of the epsilon κ and ɛ, $μ_{t} = ρ C_{μ} \frac{κ^{2}}{ɛ}$ , C_μ is empirical constant.

About the κ - ɛ transport equations for: $\begin{matrix} \frac{\partial (ρ κ)}{\partial t} + \frac{\partial (ρ κ u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{κ}}) \frac{\partial κ}{\partial x_{j}}] \\ + G_{κ} + G_{b} - ρ ɛ - Y_{m} + S_{κ} \end{matrix}$ (9) $\begin{matrix} \frac{\partial (ρ ɛ)}{\partial t} + \frac{\partial (ρ ɛ u_{i})}{\partial x_{i}} = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ɛ}}) \frac{\partial ɛ}{\partial x_{j}}] \\ + C_{1 ɛ} \frac{ɛ}{κ} (G_{κ} + C_{3 ɛ} G_{b}) - C_{2 ɛ} ρ \frac{ɛ^{2}}{κ} + S_{ɛ} \end{matrix}$ (10)

Significance and value of related parameters in (9) and (10) refer to reference [7].

When the strain rate is larger for the case, the standard κ - ɛ model may lead to stress is negative. In order to make the flow in accordance with the laws of physics of turbulence, the turbulent viscosity coefficient in the calculation of C_μ type should be associated with the strain rate, resulting in a Realizable κ - ɛ model. Compared with the standard κ - ɛ model, turbulent viscosity formula with rotation and curvature related content; ɛ transport formula no longer contains the generated G_κ of κ, and the right end of third does not have singularities (κ values are very small or 0, the denominator is not 0).

(2) Reynolds stress model

His model constructs represent supplementary equation of Reynolds stress, when the simultaneous motion control equations. As with the κ - ɛ turbulence model, Reynolds stress model (RSM) also belongs to the high Reynolds number turbulence model, a wide range of applications, in the calculation of sudden expansion flow separation zone and turbulent transport flow strong anisotropy when the performance is better, in the near wall region of the flow, the Reynolds number is low, to introduce the use of the turbulence model to calculate, you must use special treatment, the most commonly used is the wall function method. The solution procedure is not sticky bottom layer and transition layer for turbulence equations, but with a set of semi empirical formula will be linked to the corresponding physical quantity of physical quantity on the surface and turbulence in the core area, does not require encryption in the near wall region, only need to put the nodes within a first set up in the logarithmic layer region, i.e. turbulent fully developed region Domain [8].

2.5 Numerical verification of countercurrent thrust vector

This paper uses the literature of the prototype, the first model and the division of the grid, parameters are briefly introduced. Then by changing the suction pressure, wall pressure and thrust vector angle, and compared with the experimental and numerical results. Finally, change the outflow of Maher number under different size the Maher number and the thrust vector angle, wall pressure. The model used in this chapter is the scaled experimental model provided by University of Minnesota and University of Florida [9]. Geometric dimensions of scaled experimental models: the experimental nozzle is a rectangular nozzle with two elements. Width: W = 52 mm, High = 13 mm, throat area: A₈ = 400 mm², The expansion ratio of A₉/A₈ = 1.69, the design of pressure drop ratio NPR_D = 7.824. Jacket is a section of circular arc, axial length L/H = 6.9, curvature radius of R/H = 15.7, the two flow channel height G/H = 0.73, two-dimensional model in Fig. 2. Then computing grid: With ICEM structured grid, the external flow range of the nozzle before taking 10 H, nozzle after 40 H, up and down each 30 H, the total number of 153760 grid, in the wall of encryption processing. Mesh quality is better, as Figs. 3 and 4 initial/boundary value setting: The main entrance: the entrance boundary pressure, total pressure and total temperature P₀ = 7.824 atm, T₀ = 300 K; the same to the two flow boundary pressure entrance, pressure P₃ = P_atm = 1 atm, temperature T₃ = 300 K; boundary two suction pressure outlet, suction pressure of P₂ between 0.6 atm∼1.0 atm, total temperature T₂ = 300 K; outflow boundary: outlet pressure, total pressure P_∞ = P_atm = 1 atm the total temperature, T_∞ = 300 K; the outflow entrance and the upper and lower boundaries of the far field pressure: P_∞ = P_atm = 1 atm, total pressure, total temperature T_∞ = 300 K, the flow Maher number MA in 0∼0.8. Other parameters with default values. With the entrance into the mainstream boundary conditions of initialization. Other setting: The ambient pressure is 0 MPa, using Realizable κ - ɛ model, near the wall with the standard wall function method. The pressure solver based on the iteration number more than ten thousand times, in the 10^-3 Order.

Fig.2

Dimension model of counterflow thrust vector.

Fig.3

Computational grid.

Fig.4

Grid quality report.

3 Results and discussion

3.1 Comparison and analysis of numerical results

When we change suction pressure, other conditions remain unchanged: changing the suction pressure, numerical simulation is carried out from 0.6 atm to 0.95 atm every 0.05 atm. Figure 5 shows the pressure in the suction under different outer tube, under the wall static pressure distribution. As can be seen from Fig. 5, with the decrease of suction pressure, on the wall static pressure also declined, and in the same direction the outer side of the casing wall surface pressure is equal to atmospheric pressure, the pressure difference between the upper and lower wall lateral thrust, the thrust vector [10]. At the same suction pressure, wall static pressure along the flow direction is on the rise, approximately equal to the suction pressure at the nozzle exit, approximately equal to the atmospheric pressure outside the casing exit. It cannot give a direct comparison of the data in the literature, but the simulation results and other parameters in the literature from other literature in the numerical experiment results show that the two have the same pressure change trend. Figure 6 is in the suction pressure is equal to 0.8 atm, compared with literature [11], experimental data and calculated data can be seen, the calculated results accord well with the experimental values, it proves the rationality of numerical simulation method and the corresponding parameter settings.

Fig.5

Upper and lower wall pressure under different suction pressure.

Fig.6

Pressure of upper wall when suction pressure is 0.8 atm.

When we change the outflow parameters, we analyze the influence of the outflow velocity to thrust vector angle, the Maher number range from 0 to 0.8. What is expected: with the increase of Maher number of outflow, the thrust vector angle is reduced. Because with the increase of the Maher number, the outflow of static pressure lowering, upper wall pressure decreases small, and the lower wall pressure is reduced to a similar the external static pressure, lateral pressure decreases differently, so the thrust vector angle decrease. Although the thrust will be reduced, but the decrease is much smaller compared to the lateral force [12].

Figure 7 the outer tube on the lower wall surface of the pressure distribution, with setting is the suction pressure at 0.8 atm, the outflow of Maher numbers changes from 0.1 to 0.8. It can be seen that with the increase of the Maher number, the following changes: (1) upper wall static pressure in 0.7 atm to 0.8 atm, with the increase of the outflow of Maher number, wall the pressure decreased slightly, while increased along the flow direction of static pressure decreases, the wall pressure value tends to be the same. This is due to the outflow of the environment with the Maher number, the static pressure decreases [13]. (2) on the outer tube at the outlet of the pressure drop point after the first move, and then disappear. Combine the following flow line can be seen in Fig. 8 this is due to the increase of the outflow of Maher number, the tip of the outer tube of the separation vortex is reduced, and then from the wall to the outside the basin [14]. (3) lower wall static pressure decreases with the increase of the Maher number. This is in line with the outflow is expected, because the outflow in the environment with Maher increase the number of static pressure decreases, so that The whole wall under hydrostatic pressure is decreased. (4) lower wall gradually pressures minimum at 0.08 m. Combined with streamline Fig. 8 shows, as the mainstream and the double volume outflow suction effect and with two times to flow along the wall flow increases the distance according to the Tat theorem, there is a transverse wall flow pressure difference so, in these locations (near 0.08 m) static pressure decreases, which is the minimum value [15].

Fig.7

Variation of upper and lower wall pressure with Maher number at suction pressure of 0.8 atm.

Fig.8

Streamline chart with different Maher numbers.

Figure 8 is the outflow of Maher numbers from 0.1 to 0.8 changes, the outer tube river flow diagram [16]. Obviously, the main deflection angle decreased with the increase of the outflow of the Maher number. In addition, the outflow of Maher number is greater than 0.4, the two part is the mainstream of reverse flow entrainment away; Maher number is greater than 0.6, the reverse two flow fully into the same flow, and the counter current shear layer to the outside move, the outer tube vortex structure in different scales [17], the effect is reduced. The outflow of vector Maher number is not 0, the thrust vector angle is simplified: $\begin{matrix} δ = {tan}^{- 1} \frac{F_{y}}{F_{x} + m_{1} (u_{1} - u_{0}) + m_{2} u_{2} + m_{3} u_{3} + (P_{2} + P_{3} - 2 P_{atm}) G - P_{{atm}^{2 C}}} \end{matrix}$

The calculation of thrust vector angle under different flow Maher number, the results in Fig. 9. From the general trend with the Mach number increases, the thrust vector angle is reduced, the result is consistent with the prediction [19]. When the outflow of Maher number is less than 0.3, the vector angle decreased slowly, the Maher number is greater than 0.4, increasing the vector angle the decreasing trend, and in the Maher number is greater than 0.7. Almost no vector effect speculate that this is due in the suction pressure is equal to 0.8 atm, the outflow of Maher number around 0.4, and the separation bubble counter flow shear layer from outer tube, and the outflow pressure is close to the suction pressure, pressure difference is reduced, thereby sharply reduce the vector angle.

Fig.9

Variation of thrust vector angle with outflow Maher number.

In conclusion, we verify the numerical calculation method which deduced in this paper, it proves the theory is reliable. On this basis, we use the control variable method. When the suction pressure is constant and the Maher number of outflow is changed, the effect on thrust vector angle was calculated. When the suction pressure is 0.8 atm, the Maher numbers of outflow change from 0.1 to 0.8, the general trend is increases with the Mach number, the thrust vector angle decreases. When the Maher number is less than the outflow 0.3, the vector angle decreased slowly, basically stable at around 12 degrees; when the Maher number is greater than 0.4, the increasing vector angle decreased; while Maher number is greater than 0.7 there is almost no vector effect. Analysis shows that this is due to when the suction pressure is 0.8 atm and the outflow of Maher number around 0.4, separation bubble and counter flow shear layer exit outer tube, and the outflow of static pressure is close to the suction pressure, pressure difference is reduced, thus the vector angle is drastically reduced.

3.2 Vacuum program

Whether the counter flow thrust vectoring technology can make the practical progress, vacuum suction scheme is an urgent need to address the problem of. we will conduct a simple inquiry [20]. And because the Maher number is greater than 0.7 almost no effect for really empty vector. The scheme is used in the engine will meet some design requirements: it should achieve a certain degree of vacuum and remained stable, and do not have a greater impact on the mainstream, weight, cost and try to optimize the easy control system. Considering the turbojet engine in general, because the mainstream speed greatly, it produced strong entrainment, and because of the outer tube prevent the natural atmosphere added, it will form a micro negative pressure in the mainstream. Both sides might try to produce a certain vacuum using micro negative pressure here [21].

Therefore, we can make the same side to maintain communication with the external environment, the upstream side also communicated with the external environment. When the valve fully open at the exit into the control valve is same to the two mainstream flow, Air flow into the mainstream of entrainment makes the outside world, we get no current, no vector effect; When the valve is half open or all closed, the outer tube is slightly negative, while in the reverse side air passage two times of incomplete or no supplement, it will be two times in the reverse flow channel is formed in a certain vacuum. So we discuss the method of vacuum, the valve control of the two channel flow, when the valve is fully closed, the analysis of the causes of the vector angle and thrust vector, simulation results in different outflow Maher number. The results show that it is a vacuum method to provide effective especially at high Maher number flow [22].

The calculation model is same, we consider the valve fully closed, even if the two channel outlet for suction wall conditions, the outflow of Maher number 0 the outer tube wall pressure values in Fig. 10. It can be seen through regulating valve, compared with the suction pressure of 0.8 atm, it is similar to the lower wall surface of the pressure distribution. While upper wall and lower wall does exist pressure. We can see Fig. 11 flow, due to entrainment in the reverse channel in the formation of a certain degree of vacuum and reverse flow, so we get the counter current shear layer.

Fig.10

Upper and lower wall pressure of suction scheme and the entrainment scheme.

Fig.11

Flow diagram of entrainment scheme.

The calculation formula of the thrust vector angle can get δ = 5.36 degrees, we roughly equivalent to using suction, suction pressure on the thrust vector is between 0.9 atm ∼0.95 atm angle, so this scheme can generate vector effect. Due to the verification scheme in the outflow of the vector’s performance, so Maher is equal to the number of selected 0.7 cases are analyzed. In high velocity outflow, as shown in Fig. 12 and the suction pressure is 0.8 atm, the same parameters outflow comparison, it can be seen lower wall pressure distribution and wall surface approximation. With the method of suction valve control, the pressure is small, so lateral pressure difference is bigger. We can see from the flow Fig. 13, counter flow shear layer entered the outer tube, there is speculation that is due to the counter current flow, the double volume outflow and mainstream suction effect, so the vacuum reverse two times within the channel to further increase thrust Vector effect increases.

Fig.12

Upper and lower wall pressure of suction scheme and the entrainment scheme ma = 0.7.

Fig.13

Flow chart of suction scheme in outflow ma = 0.7.

Calculate its thrust vector angle:

$δ = {tan}^{- 1} \frac{F_{y}}{F_{x} + m_{1} (u_{1} - u_{0}) + m_{2} u_{2} + m_{3} u_{3} + (P_{2} + P_{3} - 2 P_{atm}) G - P_{atm} 2 C} = 18 . 1^{\circ}$ (11)

The thrust vector angle than in the absence of Maher when the number of large outflows of nearly two times, while using old suction, when the outflow of Maher number reached 0.7, the thrust vector angle has been reduced to a very low level, is 1.7 degrees. The results indicated that when the mainstream and high Maher number flows away from the outer tube inside and outside, its production the entrainment effect is stronger, the reverse flow two times lower negative pressure inside the channel, even lower than the suction vacuum produced, so that the outer tube lateral pressure is greater, the greater thrust vector angle.

Shown in Fig. 14, with the increase of the outflow of Maher number, the thrust vector angle increased. The Maher number is less than 0.5, the thrust vector angle is unchanged, and in the same direction and the reverse of two channel pressure is essentially the same; the Maher number is greater than 0.5, lower wall pressure drop is small, upper wall pressure continued to decline, the thrust vector angle increases. Thus, this scheme in the high speed environment can get the thrust vector effect. If you want to reduce the thrust vector angle, you can control the valve, to make it slightly open, the reverse channel is in the state of insufficient suction volume. Therefore, in the actual condition it is an effective reverse flow scheme.

Fig.14

Relationship between Maher number and thrust vector angle.

4 Conclusions

This paper introduces the basic principle of counter flow thrust vectoring and simplifies consolidation calculation formula, we got the simplified formula of thrust force and lateral force. And we define dynamic parameters such as vector angle of corresponding gas, then compare the calculation results of this paper and the prototype results which provided by the University of Minnesota and University of Florida. We verify the numerical calculation method which deduced in this paper, it proves the theory is reliable.

The above calculation shows the thrust vector angle effect is bad under large Maher number, so we further explore the method to improve the vacuum so as to changing the vector effect. A scheme is put forward which is the valve control of the two channel flow to improve the feasibility of vector effect. The results of the study can be concluded: under the two control valve channel program, the thrust vector angle is increase along with the increase of Maher number of the outflow. When the Maher number is less than 0.5, because of two channel pressure is essentially the same, the thrust vector angle does not change; When the Maher number is greater than 0.5, the lower wall pressure drop just a little, but the upper wall the pressure continued to decline, so the thrust vector angle began accelerated increasing. And if we do not use the valve control scheme, when the Maher number is greater than 0.4, the thrust vector angle began to accelerated decline. When the outflow rate was 0.7 and the Maher number with the suction pressure is 0.8 atm, the thrust vector angle is only 1.7 degrees. And the scheme is adopted due to outflow and mainstream dual entrainment, reverse two channels in the vacuum increases further, the thrust vector angle can reach 18.1 degrees.

The results show that the proposed scheme can significantly improve the thrust vector effect in the environment of high Maher number.

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