CC BY
19
DC XXX.XXXX
F. FORGHANY1, A. ASDOLLAHI-GHOHIEH2, M. TAIEBI-RAHNI3
1 - Science and Research Branch, Islamic Azad University, Tehran, Iran 2 - Civil Aviation Technology College, Tehran, Iran 3 - Sharif University of Technology, Tehran, Iran
NUMERICAL INVESTIGATION OF THE FLUIDIC INJECTION ANGLE EFFECTS ON THRUST VECTORING
A computational investigation of the fluidic injection angle effects on fluidic thrust vectoring was conducted. Simulation of a two-dimensional convergent-divergent (2DCD) nozzle with shock-vector control method of fluidic injection for pitch vector control was performed with the computational fluid dynamics, using Spalart-Allmaras (S-A) one equation turbulence model. Nozzle design included fluidic variables and injection angle. The secondary flow was injected through a slot in the upper divergent wall. A nozzle pressure ratio (NPR) of 4.6.was assumed. Variable secondary pressure ratios (SPR) from 0.7 to 1.6 were investigated at Mw=0.05; which correspondeds to secondary mass flow rates of 4% to 10% of the primary mass flow rate. The effect of variable fluidic injection angle from 60° to 120° on pitch thrust vector angle and thrust vectoring efficiency were investigated. Computational results indicates that increasing SPR in all cases, increased pitch thrust vector angle and decreased thrust vectoring efficiency; also the greatest pitch thrust vector angle was achieved in the smaller fluidic injection angle.
Key words: Thrust Vectoring, Shock Vector Control, Optimize Fluidic Injection Angle.
Introduction
Thrust vectoring is a candidate technology for the next generation aircrafts that may help satisfy takeoff and landing requirements. Additionally, thrust vectoring could augment conventional controls for some control power to trim the aircraft and thus reduce cruise trim drag. Thrust vectoring can be a valuable control effector at low dynamic pressures, where traditional aerodynamic control technologies are less effective. There are two fundamental methods to accomplish thrust vectoring, namely mechanical and fluidic. Fluidic thrust vectoring offers the potential for structurally fixed nozzles, which have the potential for substantial weight reductions compared to mechanical thrust vectoring nozzles that require actuated hardware to force the exhaust flow off axis. Fluidic thrust vectoring is the control of the primary exhaust flow with use of a secondary air source, which typically bleeds air from the engine compressor or fan. Three primary mechanisms of fluidic thrust vectoring that have been studied over the last 15 years are: shock-vector control, throat shifting, and counterflow. These techniques can be used to vector the exhaust flow in the pitch and yaw directions. All thrust vectoring techniques are evaluated with some common parameters such as: thrust vector angle and thrust vectoring efficiency. Thrust vectoring efficiency () is an important parameter to evaluate and compare the ability of different configurations to vector the primary exhaust flow with a given amount of secondary fluidic injection [1-14].
The shock-vector control (SVC) method [2-9] uses supersonic flow turning through shocks created by fluidic injection in the divergent section of a convergent-divergent (CD) nozzle. Working best at off-design, over-expanded flow conditions, large thrust vector angles are generated with SVC techniques in expense of system thrust ratio as the flow is robustly turned and losses occur through shocks in the nozzle. Throat shifting (TS) methods [9-12] manipulate the subsonic flow upstream of the throat more efficiently. This technique shifts and skews the nozzle throat plane by fluidic injection in nozzle throat and typically achieves higher system thrust ratios than shock-vector control methods, but usually generates smaller thrust vector angles. Unlike the two previously described thrust-vectoring techniques, the counterflow method uses suction in a slot between a primary CD nozzle and an aft collar [13-14]. The counterflow technique can produce large thrust vector angles with little secondary suction flow requirements, but issues hysteresis effects such as suction supply source and airframe integration. The current investigation attempted to initiate a database of secondary flow injection angle effects on fluidic thrust vectoring. The nozzle under investigation was a two-dimensional, convergent-divergent (2DCD) rectangular nozzle with fluidic injection for pitch thrust vector control. The secondary air stream was injected through a slot in the upper divergent wall. Simulations were computed with nozzle pressure ratio (NPR) of 4.6, secondary pressure
© F. Forghany, A. Asdollahi-Ghohieh, M. Taiebi-Rahni, 2015
ISSN 1727-0219 Вестник двигателестроения № 2/2015
ratios (SPR) from 0.7 to 1.6 and with Mo>=0.05 to document the effect of the fluidic injection angle on vectoring effectiveness and thrust vectoring efficiency (corresponding to secondary mass flow rates of 4% to 10% of the primary mass flow rate, respectively) [15-17]. In addition, a comparison between computational and experimental results [15] was made to validate our computational method as a viable tool for predicting nozzle flows with injection streams. This study was meant to produce optimal configurations of secondary flow injection angle for fluidic thrust.
1. Computational Method
The CFD code PMB3D (Parallel Multi-Block, three-dimensional) was developed and used to predict thrust vectoring efficiency, internal nozzle performance, and fluidic thrust vectoring by convergent-divergent rectangular nozzle concept. PMB3D requires a structured-mesh computational domain and a multi-block feature to allow the domain to be partitioned into different sections, which is critical for modeling complex configurations (like the 2DCD and for efficiently, running the parallel version). Our Explicit, finite-volume flow solver represents the three-dimensional (3D), unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The URANS equations were solved together with the Spalart-Allmaras (S-A) one equation turbulence model for closure of the URANS equations. AUSM+ flux splitting scheme and 4th order Runge-Kutta scheme for time integration were all implemented in each block. MUSCL interpolation was used to provide high order accuracy with the Van Albada limiter to prevent spurious oscillations across shock waves [18-25].
A first order extrapolation outflow condition was used at downstream far field boundary. The stagnation conditions were specified in nozzle inlet and the injection port with total pressure boundary condition and a fixed total temperature. A no-slip adiabatic wall boundary conditions was implemented on nozzle surfaces to obtain viscous solutions.
The nozzle used in this study was an axisymmetric, rectangular, two-dimensional CD nozzle from NASA Langley Research Center [15]. The length of the nozzle was 115.57 mm, while the nozzle width was 101.346 mm. In addition, the throat area of the nozzle was 2785.19 mm2, half height of the throat was 13.741 mm, and 57.785 mm from throat to inlet. The area ratio of the nozzle outlet to the throat (expansion ratio) was 1.796 and nozzle divergence angle was 11.01°. The nozzle inlet center was set to be the origin of coordinates, the secondary inlet located at 104.14 mm and the length of slot was 2.032 mm (Fig's. 1-2).
The computational mesh was three-dimensional with 8 blocks defining the internal nozzle, 1 block representing the injection plenum, and 10 blocks representing the external freestream domain. The injection plenum (Fig. 3) had one-to-one grid matching with the nozzle divergent section mesh. The far field was located 2 nozzle lengths upstream and 8 nozzle lengths downstream of the nozzle exit. The upper and lower lateral far field was located 6 body lengths above and below the nozzle. The first grid height in the boundary layer was defined for y+<1.5 on the fine mesh spacing for adequate modeling of the boundary layer flow and its interaction with secondary flow injection.
2. Results
A computational investigation of the aerodynamic effects on fluidic thrust vectoring has been conducted. Simulation of a two-dimensional, convergent-divergent (2DCD) nozzle with shock-vector control method of fluidic injection for pitch vector control were performed using URANS approach and Spalart-Allmaras one equation turbulence model. Nozzle design included a variable fluidic injection angle. Simulations were conducted for nozzle pressure ratio (NPR) of 4.6 and variable secondary pressure ratios (SPR) from 0.7 to 1.6 and with M¥=0.05, corresponding to secondary mass flow rates of 4% to 10% of the primary mass flow rate. The effect of variable fluidic injection angle (from 60° to 120°) on pitch thrust vector angle and thrust vectoring efficiency were investigated (Fig. 4). The performance of fluidic thrust vectoring (FTV) was evaluated by thrust vector angle and thrust vectoring efficiency in the nozzle exit. The effect of fluidic thrust vectoring parameters, such as NPR, SPR, and fluidic injection angle on FTV performance were studied.
2.1. Code Validation
Our computational results were compared with experimental data of Ref. [15]. The centerline pressure at, SPR=0.7 (4% of primary mass flow rate) is shown in Fig. 1. Our PMB3D results for pitch thrust vector angle and static pressures along the upper and lower nozzle surfaces correlated well with experimental data (with a few correlate well with experimental data (with a few notable exceptional points near shock). The shock location, at the upper surface was predicted to be x/xt=1.56 (xt is axial location of throat), while it was 1.53 in the experiment. Our results at the lower surface gave x/xt=1.91, compared to 1.89 found by the above experimental (Fig. 5).
2.2. Effect of SPR
In all cases, increasing SPR, increases pitch thrust vector angle and decreases thrust vectoring
efficiency. The effect of the oblique shock or oblique expansion waves becomes strong by increasing the mass flow rate of the fluidic injection (increasing 2% of mass flow rate per increasing 0.3 of SPR). Increasing secondary injection flow rate decreases the effective minimum area in the nozzle, which substantially decreases thrust vectoring efficiency by total pressure losses due to shocks and separated flow. Fig. 6, shows the Mach number shadowgraph along the nozzle for NPR=4.6 and variable SPR. As shown in this figure, the thrust vector angle increases with percent injection, although the thrust vectoring efficiency is much higher in lower injection rates. Pressure distribution along the nozzle, NPR=4.6, SPR=0.7 (4% of primary mass flow rate), are shown in Fig. 7. Similar trends are witnessed for SPR=1.0 (6% of primary mass flow rate), SPR=1.3 (8% of primary mass flow rate), and SPR=1.6 (10% of primary mass flow rate). Increasing SPR increases the strength of the oblique shock and moves the shock upstream, as shown in upper surface (Fig. 8). The pressure distributions by increasing SPR shown in Fig. 8 helps to explain improvement to pitch thrust vector angle. The shock and flow separation from the upper wall moves
further upstream, then, reattaches the upper wall near, as injection total pressure increases.
The effect of increasing total pressure of the secondary injection stream has positive impact on thrust vector angle and negative impact on thrust vectoring efficiency. The increased pressure differential along the upper and lower wall, results in improved pitch vector angle. Finally, the effect of increasing total pressure of the secondary injection stream has positive impact on thrust vector angle and negative impact on thrust vectoring efficiency.
2.3. Effect of Fluidic Injection Angle
The highest thrust vector angle in variable SPR (which is achieved from 10.32° to 19.27° by the fluidic injection angles) was varied from 110° to 85° with improvement from 36.3% to 8.31%. In addition, the greatest pitch thrust vector angle with increasing SPR is achieved in the smaller fluidic injection angle. The best thrust vectoring efficiency, which was achieved from 3.446°/%- injection to 1.958°/%-injection by the fluidic injection angles is varied from 120° to 85° with improvement from 44.1% to 9.03%, (Table 1 & Fig. 9).
Table 1
Effect of fluidic injection angles on internal performance improvement
Case 1 Fluidic injection angle (optimize) Fluidic injection angle (normal to boundary) Improvement
NPR SPR <P (deg| 6p (deg) I") |deg/%inj| <P (deg] ôp (deg) Г) (deg/%inj) 6p% Г)%
4. Б 0.05 0.7 110 10.329 3.099 78,99 7.578 2.151 36.3 44.1
1 110 14 274 2.925 78.99 11.167 1.965 27.8 48.8
1.3 100 17.626 2,555 78,99 14.391 1.961 22.4 30.2
1.6 85 19 279 2,135 78,99 17.799 1.958 8.31 9.03
Fig. 1. Sketch of the geometric design for 2DCD rectangular
Point Coord in at
X, mm У, mm
A 0 О
Б 0 -15.595
С 0 35.204
D 23.291 29.541
E 50.495 15.519
F 57.785 13.741
G 60.807 14.046
H 57.785 29.616
1 115.57 24.688
All positions measured from centerline of nozzle
fluidic thrust vectoring nozzle (x-y plane)
Fig. 2. Sketch of the design injection slot for 2DCD rectangular fluidic thrust vectoring nozzle (x-z plane)
Fig. 3. The computational domain representing the 2DCD nozzle with ainjection plenum (the injecton plenum has one-to-one
grid matching with the primary nozzle grid)
Fig. 4. Diagram of fluidic injecton angle in two-dimensions (x-y plane)
Fig. 5.
Experimental and comptational centerline pressures along internal nozzle upper wall, NPR=4.6, SPR=0.7, static
freestream conditions
c d
Fig. 6. Mach number shadowgraph inside and outside the nozzle at NPR=4.6 and (a) SPR=0.7, (b) SPR=1.0,
(c) SPR=1.3, (d) SPR=1.6
Fig. 7. Pressure distribution along the nozzle at NPR = 4.6 and SPR = 0.7
Fig. 8. Pressure distribution of upper surface along the nozzle at NPR = 4.6
Fig. 8. Pressure distribution of upper surface along the nozzle at NPR = 4.6
80 90 100
cp, deg
110 120
4 35
о
aj 3
2 5 2 1.5 1
cn a> тз
50
60
70
80 90 100 110 120
cp, deg
80 90 100
cp, deg
d
b
c
f
e
Conclusion
A computational investigation of the aerodynamic effects on fluidic thrust vectoring has been conducted. The effect of variable fluidic injection angle (from 60° to 120°) on pitch thrust vector angle and on thrust vectoring efficiency were investigated. The performance of fluidic thrust vectoring (FTV) was evaluated by studying thrust vector angle and thrust vectoring efficiency in nozzle exit. The effects of fluidic thrust vectoring parameters, such as NPR, SPR, and fluidic injection angle on FTV performance were studied. The data from the current computational investigation indicate that:
1. In all cases, increasing SPR, increases pitch thrust vector angle and decreases thrust vectoring efficiency (the effect of the oblique shock or oblique expansion waves become strong by increasing the mass flow rate of the fluidic injection; increasing 2% of mass flow rate per increasing 0.3 of SPR). Increasing secondary injection flow rate decreases the effective minimum area in the nozzle, which substantially increased pitch thrust vector angle and decreases thrust vectoring efficiency. The effect of increasing total pressure of the secondary injection stream has positive impact on thrust vector angle and negative impact on thrust vectoring efficiency,
2. The highest thrust vector angle in variable SPR (which is achieved from 10.32° to 19.27° by the fluidic injection angles) is varied from 110° to 85° with improvement from 36.3% to 8.31%. Also, the greatest pitch thrust vector angle with increasing SPR is achieved in the smaller fluidic injection angle, and
3. The best thrust vectoring efficiency is achieved from 3.446°/%- injection to 2.135°/%-injection by the fluidic injection angles varied from 120° to 85° with improvement from 44.1% to 9.03%.
References
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Thrust Vectoring for Fixed-Exit Exhaust Nozzles. AIAA 97-3148, July 1997.
3. Abeyounis W.K., and Bennett B.D.: Static Internal Performance of an Overexpanded, Fixed-Geometry, Nonaxisymmetric Nozzle with Fluidic Pitch-Thrust-Vectoring Capability, NASA TP-3645, October 1997.
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Submitted to the editorship 01.06.2015
Р. Ро^Иапу, А. А8(1о11аЫ-С1юЫс11, М. Та1еЫ-КаЬш. Чисельш дос.пджсння впливу кута вдуву струменя на вщхилення вектора тяги
Проведено чисельш досл1дження впливу кута вдуву вторинного струменя на в^дхилення вектора тяги. Моделювання двовим^рного сопла з1 звуженням-розширенням було виконано з використанням методу контролю стрибка ущтьнення I керування вдувом струменя для ке-рування вектором тангажа 1з застосуванням методов обчислювальног газодинамики I з використанням однопараметричног модели турбулентности Спаларта-Аллмараса. Розрахунков1 параметри сопла в якост1 змтних включали параметри потоку I кут вдуву вторинного струменя. Вдув вторинного потоку здшснювався через вузький отв1р у верхнш стти,1, що розширюеться. Прийнято ступть тдвищення тиску газу в сопл1 р1вною 4,6. Ступть тдвищення тиску вторинного потоку, що змтюеться, у межах 0,7 - 1,6 досл1джувалася при Мк> = 0,05, що в1дпов1дае масовш витрат1 вторинного потоку равному в1д 4 до 10% масовог витрати первинного потоку. Проведено досл^дження впливу кута вдуву струменя, змтюваного в1д 60 до 120°, на векторний кут тангажа I ккд вектора тяги, що в^дхиляе. Результати розрахунк1в показують, що у вах випадках збтьшений ступть тдвищення тиску вторинного потоку приводить до збтьшення кута вектора тяги, що в^дхиляеться, I ккд вектора тяги, що в^дхиляеться, а також максимальний кут вектора тяги, що в^дхиляеться, було отримано при меншому кут1 вдуву струменя.
Ключов1 слова: в^дхилення вектора тяги, контроль напрямку стрибка, оптим^защя кута вдуву струменя.
Р. Ро^Иапу, А. А8((о11аЫ-С1юЫе11, М. Та1еЫ-КаЬп1. Численные исследования влияния угла вдува струи на отклонение вектора тяги
Проведены численные исследования влияния угла вдува вторичной струи на отклонение вектора тяги. Моделирование двумерного сопла с сужением-расширением было выполнено с использованием метода контроля скачка уплотнения и управления вдувом струи для управления вектором тангажа с применением методов вычислительной газодинамики и с использованием однопараметрической модели турбулентности Спаларта-Аллмараса. Расчетные параметры сопла в качестве переменных включали параметры потока и угол вдува вторичной струи. Вдув вторичного потока осуществлялся через узкое отверстие в верхней расширяющейся стенке. Принята степень повышения давления газа в сопле равная 4,6. Степень повышения давления изменяющегося вторичного потока в пределах 0,7 — 1,6 исследовалась при М<х> = 0,05, что соответствует массовому расходу вторичного потока равному от 4 до 10% массового расхода первичного потока. Проведено исследование влияния угла вдува струи, изменяемого от 60 до 120°, на векторный угол тангажа и кпд отклоняемого вектора тяги. Результаты расчетов показывают, что во всех случаях увеличенная степень повышения давления вторичного потока приводит к увеличению угла отклоняемого вектора тяги и кпд отклоняемого вектора тяги, а также максимальный угол отклоняемого вектора тяги были получены при меньшем угле вдува струи.
Ключевые слова: отклонение вектора тяги, контроль направления скачка, оптими-заиия угла вдува струи.
