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Numerical investigation of improving the performance of a single expansion ramp nozzle at off-design conditions by secondary injection
Acta Astronautica 133 (2017) 233–243
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Research paper
Numerical investigation of improving the performance of a single expansion ramp nozzle at off-design conditions by secondary injection
MARK
⁎
Zheng Lva, Jinglei Xua, , Jianwei Mob a b
College of Energy & Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, People's Republic of China Xi’an Aerospace Propulsion Institute, Xi’an, Shanxi 710100, People's Republic of China
A R T I C L E I N F O
A BS T RAC T
Keywords: Single expansion ramp nozzle Poor performance Over-expanded condition Improve Secondary injection
The performance of a single expansion ramp nozzle (SERN) is poor due to over-expansion at off-design conditions. The present study focuses on improving the SERN performance by secondary injection on the cowl and is carried out by using the k − ε RNG turbulence model. The incidence shock wave resulting from the secondary injection impinges on the expansion ramp, resulting in separation and the increase of the pressure distribution along the ramp. The performance of the SERN can be improved significantly, and the augmentation of the thrust coefficient, lift and pitch moment can be as high as 3.16%, 29.43% and 41.67%, respectively, when the nozzle pressure ratio (NPR) is 10. The location of the injection has a considerable effect on the lift and pitching moment, and the direction of the pitch moment can be changed from nose-up to nose-down when the injection is on the tail of the cowl. The effect of the injection on the axial thrust coefficient is much more apparent, if the operation NPR is far from the design point, and however, the results for the lift and pitching moment are opposite. The increases of injection total pressure and injection width have positive impacts on the SERN performance. And if the parameter φ maintains constant, the axial thrust coefficient would increase when the injection total pressure decreases, so low energy flow can also be used as the secondary injection without decreasing the lift and pitching moment. The mass flow rate of the injection can be decreased by applying the higher total temperature flow without reducing the performance of the SERN.
1. Introduction With the development of hypersonic flight and propulsion technologies, the vehicle that can take off horizontally and fly up to a top speed of Mach 5+ will become a reality. As the most promising propulsion systems for hypersonic flight vehicles，the airbreathing engine does not need to carry any oxidizer on board, so it can provide a significant specific impulse, compared to the conventional transportation system such as rockets. One common feature of the propulsion system is that it should operate over a wide range of the flight Mach numbers [1]. Thus, the single expansion ramp nozzle (SERN) integrated with the after-body airframe, which is the indispensable component of the airbreathing propulsion system, also undergoes the Mach numbers from subsonic to hypersonic, so the nozzle pressure ratio (NPR, i.e., the ratio of internal total pressure at the nozzle entrance to the ambient static pressure) of the SERN ranges from 2 to 600 or even higher at hypersonic speeds depending on the inlet recovery [2]. In addition, the SERN acts as the major thrust producing part of the engine and it produces 70% of the net thrust in the entire propulsion system, when
⁎
the flight Mach number is great than six [3], so the performance of the SERN has a significant influence on the efficiency of the whole propulsion system and the SERN is always expected to obtain the optimal performance over the wide flight trajectory. Unfortunately, it is designed on the certain operation point, usually at the cruise condition [4,5], resulting in the great in the expansion area ratio. As a result, when operating at the off-design conditions, the SERN would be strongly over-expanded, which leads to the low pressure acting on the expansion ramp [6]. The sub-ambient pressure distribution along the ramp tends to increase drag and reduce performance with low thrust and strong nose-up pitching moment, which seriously affects the acceleration and stability of the vehicle [12,25]. In order to avoid detrimental over-expansion losses and improve the performance of the SERN under a highly over-expanded condition, previous studies have put forward to some approaches such as variable geometry [7,8], external burning [13,14], passive cavity concept [15,16] and secondary air injection [9–11]. The expansion area ratio can match fairly well with the NPR by means of variable geometry over the wide flight Mach numbers, and as shown in Fig. 1 [8], a rotatable
Corresponding author. E-mail address: [email protected] (J. Xu).
http://dx.doi.org/10.1016/j.actaastro.2017.01.013 Received 21 September 2016; Received in revised form 4 January 2017; Accepted 9 January 2017 Available online 14 January 2017 0094-5765/ © 2017 IAA. Published by Elsevier Ltd. All rights reserved.
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ṁ Ma∞ → n P Pb Pt R Rx Fig. 1. Schematic of variable geometry [8].
Tt → V Vx X x ΔX
Nomenclature NPR RANS SERN
Nozzle pressure ratio Reynolds-averaged Navier-stokes Single expansion ramp nozzle
α ρ θ γ φ
Variables
A b Cfx Fx Fs He Ht hs L LC LR LSec M
Area of nozzle entrance or exit Width of secondary injection Axial thrust coefficient Axial thrust Ideal thrust Height of nozzle exit Height of nozzle throat Height of the injection-plume terminal shock Lift Length of cowl Length of ramp Distance from secondary injection to nozzle throat Pitching moment
Mass flow rate Flight Mach number Direction of the nozzle entrance or exit plane Static pressure Back pressure of the secondary injection Total pressure Gas constant Axial force by integrating the relative pressure on the nozzle internal wall Total temperature Velocity Axial velocity Nozzle performance parameters include Cfx ，L and M Streamwise coordinate Augmentation of nozzle performance include ΔCfx ,ΔL and ΔM Angle of secondary injection Gas density Slope angle of the nozzle exit Specific heat ratio Non-dimensional parameter defined as NPRSec b Ht
Subscript
amb AB CD no P Sec with
Ambient Nozzle entrance plane Nozzle exit plane Without secondary injection Nozzle primary flow Secondary injection With secondary injection
is the main reason for the poor performance of the nozzle at off-design flight conditions. One possible solution to raise the pressure distribution along the ramp is to induce the separation of the over-expanded flow. Consequently, Gamble et al. [10,17] introduced an oblique shock generated by the interaction between primary flow and sonic injection on the lower cowl (Fig. 3) to separate the over-expanded flow on the ramp. Compared to the injection on the ramp, this method requires only simple adjustment mechanism without changing the contour of the expansion ramp. The interaction between a sonic jet and a supersonic cross flow has been the subject of interest in aerospace engineering [18–20], and it is mostly employed to the thrust vectoring nozzle in prior investigation [21,22], and the studies of its application on over-expanded nozzle are very few [10,17]. In Ref. [10], a performance analysis based on the turbojet cycle resulted in a net thrust increase of 3% and thrust specific fuel consumption improvement of 1% with the fluidic injection, validating the feasibility of the design. Reference [17] studied the effects of the injection pressure and flow on the performance of the over-expanded nozzle, but the resulting performance decreased as flow
cowl is applied to change the nozzle exit area for different operations. Even though the nozzle performance can be improved considerably, the adjustment mechanism is complicated with unacceptable weight, limiting its application in highly integrated propulsion system. Youngster et al. [13] studied the effects of the external burning on the performance of the SERN operating at transonic speeds. The fuel was injected into the external flow and was subsequently mixed and burned, and then increased static pressure acts on the entire expansion ramp and cowl trailing edge, as shown in Fig. 2. The results indicated that external burning can be superior to other forms of thrust augmentation methods at transonic speeds. However, a large base drag created by the external burning can offset the augmentation of the nozzle thrust and much more fuel should be carried on board. Reference [15,16] investigated a passive cavity concept for improving the off-design performance of fixed-geometry exhaust nozzles. The passive cavity added the ability to control the off-design nozzle by either encouraging or alleviating the separation appearing in it. Encouraging stable separation offered significant improvements at low NPRs by improving off-design thrust efficiency as much as 2.8%, while separation alleviation had the potential to reduce off-design static thrust efficiency as much as 3.2% at forward flight speeds. Therefore, the passive cavity may have completely opposite effects on the nozzle performance at different flight Mach numbers. In reference [9], a secondary injection on the expansion ramp that filled out the large after-body exit area was employed to avoid the non-matched nozzle state, giving rise to favorable gross thrust angles and improve thrust efficiency in the flight direction. Nevertheless, the complicated adjustment mechanism was also required to turn the injection flap upwards to close the injection air duct. At the same time, the optimal expansion ramp contour might be changed, which was unfavorable to the performance at the cruise condition. As mentioned earlier, the sub-ambient pressure acting on the ramp
Fig. 2. Schematic of external burning [13].
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through a comparison against experimental data in reference [23], in which a secondary injection is applied in a convergent-divergent nozzle for thrust vectoring, and the flowfield is similar to the study in this paper. The configuration and mesh of the model in the experiment [23] is shown in Fig. 5, and the location of the injection is on the divergent contour. The flowfield structure of numerical simulation and experiment is compared in Fig. 6. Detailed comparison of wall pressure between experimental and computational results is presented in Fig. 7. It can be seen that the numerical method could clearly resolve the detail flowfield, and the Mach number contour is highly consistent with experimental shadowgraph. Besides, the calculated wall static pressure agrees with the experimental data very well, in particular the location of the separation point. Therefore, the RNG k−ε turbulence model with standard wall function can be applied in the current study.
Fig. 3. Schematic diagram of the transverse jet in supersonic cross flows.
was injected. From the two studies above, it is found that the detailed theoretical analysis about the flow mechanism is insufficient, and the results of the secondary injection on the over-expanded SERN performance are uncertain. What's more, the effects of many parameters such as the location, width, total pressure, temperature of the injection, which may affect the nozzle performance greatly, are very complicated and also need to be studied further. Therefore, it is necessary to investigate the effects of the secondary injection on the over-expanded SERN systematically. In this paper, the improvement of the SERN performance by the secondary injection on the cowl has been studied thoroughly by numerical simulations. Firstly, the turbulence model applied in the study is validated with experiment data; then the theoretical analysis that verifies the feasibility of improving the performance of the overexpanded nozzle by secondary injection is presented; at last, the effects of the geometric and aerodynamic parameters of the secondary injection are investigated.
2.3. Computational mesh Structured and unstructured hybrid grids are generated for the computation domain of the SERN with secondary injection using Gambit, as shown in Fig. 8. The grid covers the computation domain of 1.4 m by 1.2 m, corresponding to about 7 times the nozzle length and 12 times the height of nozzle exit, which is sufficient to avoid the influence from the far field boundaries. The meshes that are close to the secondary injection and nozzle walls have been refined by structured grids, and the unstructured grids are employed in the nozzle domain. The displacement of the first layer thickness of the wall is set as 0.02 mm, which ensures the y+ to be between 30 and 60 and meet the requirement of the standard wall function. For the entrance of the secondary injection, the boundary condition is defined as pressure-inlet for the case with injection and wall for the case without injection. A mesh independent study is performed with the following three meshes: 54,600 (coarse), 114,800 (medium), 209,000 (fine). The pressure distributions on the upper wall along the flow direction obtained for different meshes are shown in Fig. 9. It can be found that the medium mesh case and the fine mesh case provide very similar pressure distribution, while the coarse case reveals a different pressure distribution with an upstream separation point. Therefore, the mesh of 114,800 cells is adopted for the further numerical analysis, which can reveal the real flowfield with reasonable calculation expanse.
2. Numerical simulation model 2.1. Computation model The model simulated in this paper is a two-dimensional SERN with secondary injection on the cowl, as displayed in Fig. 4. The cruise Mach number is 4.0 and the expansion area ratio is 5. The ideal NPR is designed to be 47.6, when the specific heat ratio is 1.4. Ht ,He indicate the height of the throat and exit, and LC , LR represent the length of the cowl and ramp, respectively. LSec , b and α are the three main parameters of the secondary injection, which correspond to the distance from secondary injection to throat, the width and angle of the secondary injection, respectively. To obtain an optimal performance, the injection angle is set as 90° relative to the cowl inner surface [17]. For better comparison, the model without injection is also analyzed.
3. Theory analysis In order to quantify the nozzle performance, the parameters such as the axial thrust coefficient, lift, pitching moment, are defined. 3.1. Axial thrust coefficient The thrust of the nozzle is defined as the sum of flow moment and the gauge pressure force at the nozzle exit plane. As shown in Fig. 4, the exit plane of the nozzle is the plane CD, and the thrust could be decomposed into the axial force and the normal force. The axial thrust is the x direction component, and can be calculated as
2.2. Turbulence model To achieve a better understanding of the over-expanded nozzle flowfield with and without secondary injection, FLUENT software is used to simulate the flowfield. The two-dimensional, compressible Reynolds-averaged Navier-stokes (RANS) equations are utilized to solve this problem. The governing equations, which include the conservation equations for mass, momentum, and energy, along with the equation of state for the ideal gas, are written in generalized coordinates and in conservative form. The density based solver, 2D space, and steady formulation are adopted in the simulation. The second order upwind method is selected for discretization, and a nonslip, adiabatic condition is imposed on the wall. Due to the limitation of computing power and to accelerate the computation convergence, the RNG k−ε turbulence model is chosen for closure of the RANS equations under the premise of ensuring the precision and accuracy of the calculation results. The effectiveness of the turbulence model is verified
Fig. 4. Configuration of the nozzle with secondary injection.
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Fig. 5. Configuration and mesh of the model in reference [23].
Fx =
Fig. 7. Comparison of experimental and computational wall pressure.
→
∫CD ρVx (V ∙→n ) dA + ∫CD (PCD − Pamb) dA sin θ
(1)
where θ is the slope angle of the plane CD, PCD is the absolute pressure on it, and Pamb is the ambient pressure. The ideal thrust Fs is used to calculate the axial thrust coefficient, which can be expressed as γ −1 2γ P RTt [1 − ( amb ) γ ] γ−1 Pt
∙
Fs = m
(2)
∙
where m , Tt are the mass flow rate and the total temperature, respectively. For the case without secondary injection, the thrust coefficient can be defined as
Cfx, no =
Fx, no Fs, P
(3)
where Fs, P is the ideal thrust of the nozzle primary flow. The axial thrust coefficient for the case with secondary injection is defined as
Cfx, with =
Fx, with Fs, P + Fs, Sec
Fig. 8. Computation mesh for the domain.
3.2. Lift and pitching moment (4) The lift of the nozzle, signed as L, is the y direction force by integrating the relative pressure on the nozzle internal wall. Pitching moment is denoted as M, and its reference point is the center of the nozzle entrance. In this paper,NPRP and NPRSec are the nozzle pressure ratios of the
where Fs, Sec is the ideal thrust of the secondary injection. The secondary injection flow must be included in the performance calculation since this flow may provide additional thrust if it is not injected into the nozzle.
Fig. 6. Flowfield structure comparison between the numerical simulation and experimental results. (a) Experiment shadowgraph image [23] (b) Mach number contour of simulation.
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Fig. 9. Pressure distributions of different meshes on the upper-wall.
Fig. 11. Zoomed flow feature for the case with injection.
Fig. 10. Mach number contour for the two cases: (a) without injection (b) with injection.
Fig. 12. Pressure distribution of ramp and cowl for the two cases.
primary flow and secondary injection, which can be calculated as
NPRP =
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Pt , P Pamb
(5)
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where Pt , P and Pt , Sec are the total pressure of the primary flow and the secondary injection, respectively. To quantify the augmentation of the nozzle performance, the parameter ΔX is defined as
Table 1 Performance of the nozzle with and without injection.
No Injection Injection
Cfx
L (N)
M (N ∙m )
ΔCfx
ΔL
ΔM
0.8287 0.8549
−350 −247
−48 −28
3.16%
29.43%
41.67%
Xwith − Xno × 100% Xno
ΔX =
(7)
where X is the performance parameters of the nozzle defined above, including the axial thrust coefficient Cfx , lift L and pitching moment M. Table 2 Parameters of the secondary injection.
3.3. Theory analysis NPRSec
Tt , Sec
LSec /Ht
b /Ht
10
300k
2.5
0.1
According to the law of conservation of moment, the axial thrust can also be expressed as
Fx =
Table 3 Cases for investigating the influence of the location.
Case A Case B Case C
NPRSec
Ma∞
NPRP
NPRSec
LSec /Ht
1.6 2.0 2.5
10 15 20
10 15 20
1.25、1.50、1.75、2.00、2.25、2.50
Pt , Sec = Pamb
→
∫AB ρVx (V ∙→n ) dA + ∫AB (PAB − Pamb) dA − Rx
(8)
where AB is the entrance of the nozzle (Fig. 4), Rx is the x direction force by integrating the relative pressure on the nozzle internal wall. Therefore, the axial thrusts for the cases with and without injection can be calculated as
Fx, with = Fx, no =
(6)
→
∫AB ρVx (V ∙→n ) dA + ∫AB (PAB − Pamb) dA − Rx,with ∫AB
→ ρVx ( V ∙→ n ) dA +
∫AB (PAB − Pamb) dA − Rx,no
(9) (10)
Compared with the axial thrusts of the two cases, it can be found
Fig. 13. Zoomed Mach contour of the secondary injection for different injection locations: (a)LSec /Ht = 1.25 (b)LSec /Ht = 2.00 (c)LSec /Ht = 2.50 .
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Fig. 14. Mach number contour of the nozzles for Case A.
and external flow. The jet plume interacts with freestream flow at the trailing edge of the SERN, leading to the shock waves in the nozzle. In addition to the internal shock waves, the shear layers, which are formed by the difference in velocity between the exhaust jet and external flow and emanating from the trailing edge of the cowl and ramp, are well captured.(Fig. 11) Since the nozzle operates at the off-design condition, the flow through the nozzle is over-expanded and the sub-ambient pressure acts on the expansion ramp, as shown in Fig. 12. Because the operational NPR deviates far from the design point, flow separation exists on the rear part of the ramp. The performance of the nozzle without secondary injection is given in Table 1, which shows a poor performance with low thrust coefficient and strong nose-up pitching moment, both of which have negative impacts on the acceleration and trimming of the vehicle.
that the sums of the axial component of the flow moment and the absolute pressure force at the nozzle entrance plane for the two cases are identical, for the secondary injection can’t affect the flowfield in the convergent section. The difference between Eq. (9) and Eq. (10) is the term Rx , and for the case with secondary injection, the increased pressure acting on the expansion ramp gives rise to the decrease of the x direction force of the entire nozzle internal wall, so
Rx, with < Rx, no
(11)
And the relation of the axial thrusts for the two cases is
Fx, with > Fx, no
(12)
However, the increase of the axial thrust for the case with injection does not imply the increase of the axial thrust coefficient, for the ideal thrust includes the effect of secondary injection, as shown in Eq. (4). From the relation Cfx, with > Cfx, no , it can be obtained
Rx, no − Rx, with > Cfx, no Fs, Sec
4.1.2. Flowfield of the SERN with secondary injection Compared to the nozzle flowfield without secondary injection, the nozzle flowfield with secondary injection is much complex, as shown in Fig. 10(b). The parameters of the secondary injection are shown in Table 2. Except the aforementioned internal shock waves and the shear layers, the shock wave/boundary layer interaction and the interaction of transverse sonic jet with supersonic flow are also illustrated in the Mach number contour. The incidence shock wave generated by the interaction between secondary injection and nozzle primary flow impinges on the expansion ramp, causing the separation on the ramp. Then the shock wave induced by the separation and the reflected shock wave are emerged (Fig. 11(b)). Fig. 11(a) presents the enlarged flowfield near the secondary injection, which clearly shows the secondary injection induces separation on both upstream and downstream. The separation shown in Fig. 11(b) causes an increased pressure to act on the ramp, which can be seen in Fig. 12, and the pressure on the ramp increases abruptly at x / Ht = 2.7. When x / Ht > 5.5, the subambient pressure acts on the ramp again due to the expansion flow along it. Moreover, the nozzle exit area decreases as a result of the
(13)
So the requirement of improving the axial thrust coefficient via the secondary injection can be satisfied by that the reducing of the x direction force on the nozzle internal wall resulting from the secondary injection can be greater than the value of the term Cfx, no Fs, Sec . As stated above, it has been proven that it is feasible to improve the performance of an over-expanded nozzle by secondary injection. 4. Result and analysis 4.1. Flow features 4.1.1. Flowfield of the SERN without secondary injection The Mach number contour of the SERN operating at an off-design condition is shown in Fig. 10(a). The NPR is 10 and the flight Mach number is 1.6. The shock waves, expansion waves, viscous shear layers and other flow feature are all clearly revealed in the Mach number contour, which is a typical problem of the interaction between exhaust 239
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Fig. 15. Augmentation of the nozzle performance: (a) ΔCfx (b) ΔL (c) ΔM .
width of the injection have positive effects on the injection-plume terminal shock height and the injection back pressure has the opposite effect. Except for the total pressure and width of the injection, other important parameters of secondary injection, such as the injection location and the total temperature are also studied in this study.
secondary injection, both of which are beneficial for improving the performance of the nozzle. The performance of the nozzle with secondary injection and the augmentation of the performance are also given in Table 1. It can be seen that the performance can be improved considerably through the secondary injection, especially the lift and pitching moment, which is in favor of the acceleration and balance of the vehicle.
4.2.1. Location of the injection The cases used to study the influence of the injection location are listed in Table 3; the varied NPRs of the SERN can provide the different over-expanded flowfields and the location of the injection changes from 1.25 to 2.50 for every case. With the increase of LSec / Ht , the back pressure of the injection decreases, which leads to the increase of the height of injection-plume terminal shock as presented in Fig. 13. Even though the increased height of injection-plume terminal shock benefits the intensity of the incidence shock wave, the expansion flow in the nozzle can dissipate the intensity of the shock wave near the separation bubble, so the angle of the incidence shock wave reduces and the separation bubble on the ramp almost remain unchanged, as shown in Fig. 14. Fig. 15 shows the augmentation of the performance for the different injection locations. In Fig. 15(a), the variations in LSec / Ht from 1.25 to 2.5, ΔCfx increases at first and then decreases slightly, which denotes the injection location has little effects on the thrust coefficient for all
4.2. Influences of parameters on the nozzle performance Since the incidence shock wave can induce the separation on the ramp and increase the pressure acting on the ramp for the overexpanded nozzle, it has a considerable effect on the performance of the nozzle. Reference [24] investigated the two-dimensional interaction between sonic jet and supersonic cross flow, and the incidence shock wave was determined by the height of the injection-plume terminal shock, which could be calculated as
hs = 0.52
Pt , Sec b Pb
(14)
where Pb is the back pressure of the secondary injection, and it can be determined by the location of the secondary injection on the nozzle cowl. From the Eq. (14), it can be found that the total pressure and the 240
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Fig. 16. Mach number contour of the nozzles: (a) varied injection total pressure (b) varied injection width. Table 4 Augmentation of the nozzle performance for different injection total pressure.
NPRP
NPRSec
ΔCfx
ΔL
ΔM
10
5 8 10
1.25% 2.63% 2.94%
15.14% 24.00% 29.43%
20.83% 35.42% 41.67%
Table 5 Augmentation of the nozzle performance for the different injection widths.
NPRP
b /Ht
ΔCfx
ΔL
ΔM
10
0.05 0.10 0.15
1.56% 2.94% 4.01%
16.00% 29.43% 42.86%
25.00% 41.67% 56.25%
the three cases. From Fig. 15(b), with the increase of LSec / Ht , the trend of ΔL is the same as ΔCfx , and when LSec / Ht < 2.0 , ΔL changes considerably, and then decreases a little. The increase of LSec / Ht results in that the separation bubble moves downstream (Fig. 14) and the arm of the force by integrating the raised pressure behind the separation bubble increases, so the pitching moment increases greatly as the increase of LSec / Ht , as shown in Fig. 13(c); particularly the direction of the pitching moment can change from nose-up to nose-down for the NPRP =20, which is a good match with the strong nose-up pitching moment generated by the compression fore-body and is very essential to the stability of the vehicle. Moreover, the NPRP has a significant impact on the augmentation of the nozzle performance, and if the nozzle operates at a greater NPR, the lift and pitching moment can be improved more considerably by secondary injection, which is contrary to the thrust coefficient. Since the location of the secondary injection has little effect on the
Fig. 17. Mach number contour of the nozzles corresponding to φ = 1.
thrust coefficient and the gained pitching moment can be greater with the larger LSec / Ht , the proper location of the secondary injection may be the tail of the cowl.
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strong. The results of the nozzle performance affected by the injection total pressure and width are given in Tables 4, 5. The increase of the injection total pressure and width are of great benefit to the augmentation of the nozzle performance, which is corresponding to the change of the nozzle flowfield in Fig. 16. The greater separation bubble causes more beneficial pressure distribution along the ramp, which is advantageous to the nozzle performance. However, only the sufficient mass flow rate can provide the increase of the injection total pressure and width, the possibility of increasing the mass flow rate to improve the nozzle performance should be a compromise in practical application. From Eq. (14), it can be found that the height of the injectionplume terminal shock is changeless, if the product of the injection total pressure and the injection width is constant. So a non-dimensional parameter φ can be defined as
φ= Fig. 18. Pressure distribution of the ramp corresponding to φ = 1.
b /Ht
ΔCfx
ΔL
ΔM
20 10 20/3
0.05 0.10 0.15
2.26% 2.94% 3.29%
30.00% 29.43% 28.86%
41.67% 41.67% 39.58%
4.2.3. Total temperature of the injection From the Fig. 19, it can be found that the injection total temperature has no influence on the pressure distribution on the ramp, which implies that the incidence shock waves don’t change for different total temperature. On the other hand, the injection total temperature can’t determine the height of the injection-plume terminal shock (Eq. (14)), so the flowfields are identical for the three cases, which is the same as the performance of the nozzle in Table 7. Even the mass flow rate of the injection decreases as the total temperature increases, the ideal thrust of the injection is identical, so the axial thrust coefficient changes only a little. Because the secondary injection total temperature can’t affect the improvement of the nozzle performance, the gas with higher total temperature can be used for the secondary injection, which can reduce the mass flow rate of the injection. However, the higher total temperature through the secondary injection flowpath will give rise to the problems like the setup of the mechanical structure. The superalloy should be applied to make sure that the structure can bear the high temperature and the cooling of the structure should be taken into account for the setup of the secondary injection, such as film cooling [26]. Furthermore, an experiment that the secondary injection was employed to control thrust vectoring has been conducted in a gas turbine engine [27], so the use of the secondary injection with higher temperature gas in this current study is feasible.
Fig. 19. Pressure distribution of the ramp for different injection total temperature.
Table 7 Augmentation of the nozzle performance for different injection total temperature.
NPRP
Tt , Sec (k)
ΔCfx
ΔL
ΔM
10
300 900 1800
2.94% 3.03% 3.31%
29.43% 29.14% 29.14%
41.67% 41.67% 41.67%
(15)
Based on the analysis above, when the parameter φ is constant, the flowfields in the nozzles are identical, which can be demonstrated in Figs. 17 and 18. The angles and the impinging points of the incidence shock waves are the same for the three cases, so the pressure distribution on the ramp does not change (Fig. 18), which indicates that the augmentations of the lift and pitching moment are almost the same, as shown in Table 6. Due to the identical pressure distributions on the ramp, the axial thrusts of the nozzles for the three cases are the same, but the decrease of the injection total pressure leads to the decrease of the ideal thrust Fs, Sec in Eq. (4), so the thrust coefficient increases gradually, as shown in Table 6. In the practical application, since the injection has no effect on the pressure distribution on the ramp when the parameter φ is constant, the low energy flow such as the flow from the fore-body boundary layer or the inlet bleed air rather than the primary flow in the engine can be employed as the secondary injection with the suitable injection width, which can reduce spillage drag and increase the augmentation of the axial thrust coefficient at the same time.
Table 6 Augmentation of the nozzle performance corresponding to φ = 1.
NPRSec
NPRSec b Ht
4.2.2. Total pressure and width of the injection As the important parameters, the total pressure and width of the injection have significant effects on the height of the injection-plume terminal shock as presented in Eq. (14). Hence, the total pressure and width of the injection can affect the flow field of the over-expanded nozzle considerably, which can be seen from Fig. 16. As the increase of the total pressure and width, the angle of the incidence shock wave increases and the separation bubble on the ramp becomes large gradually, both of which denote that the incidence shock wave becomes
5. Conclusions As the important component of the air-breathing propulsion system operating over a wide range of the flight Mach numbers, the SERN is 242
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highly over-expanded at the low flight Mach number, which is resulting from the large expansion area ratio designed at the cruise Mach number. In order to improve the performance of the over-expanded nozzle, the SERN with secondary injection on the cowl has been studied. The k − ε RNG turbulence model is used to simulate the flowfield of the nozzle with a secondary injection, and it can capture the flow features very well. The main conclusions are as followings:
(1) (2004) 27–58. [2] C. Snyder, J. Maldonado, The Design and Performance Estimates for the Propulsion Module for the Booster of a TSTO Vehicle, AIAA Paper, 1991, pp. 91– 3136. [3] C.L.W. Edwards, W.J. Small, J.P. Weidner, P.J. Jonhston, Studies of Scramjet/ airframe Integration Techniques for Hypersonic Aircraft, AIAA Paper, 1975, pp. 1975–58. [4] J.W. Mo, J.L. Xu, L.H. Zhang, Design and experiment study of an Over-Under TBCC exhaust System, ASME J. Eng. Gas. Turbines Power 136 (2014) 0145011–014501-8. [5] J.W. Mo, J.L. Xu, R. Gu, Z.P. Fan, Design and validation of an asymmetric scramjet nozzle with circular to rectangular shape transition, J. Propuls. Power 30 (3) (2014) 812–819. [6] W.W.Hinz, J.M.King, Aeropropulsion Design Challenges for Mach 7 Reusable Combined-Cycle Flight Demonstrator, Technology Review Journal, Fall/Winter 1428, 2006. [7] R. Lederer, Testing the Actively Cooled, Fully Variable Hypersonic Demonstrator Nozzle, AIAA Paper, 1996, pp. 96–4550. [8] L.H. Zhang, J.L. Xu, J.W. Mo, Experimental study of 2D adjustable asymmetric nozzles, Acta Aeronaut. Et. Astronaut. Sin. 34 (4) (2013) 772–778. [9] T. Gronland, T. Berens, Nozzle/Afterbody Integration for Hypersonic Vehicle by Means of Secondary Air Injection, AIAA Paper, 1995, pp. 95–6050. [10] E.J. Gamble, D. Haid, Improving off-design Nozzle Performance using Fluidic Injection, AIAA Paper, 2004, pp. 2004–1206. [11] D.X. Hao, Z.X. Wang, The design and flow field simulation of single expansion ramp nozzle with variable flaps, Mach. Des. Manuf. 12 (2009) 8–10 (in Chinese). [12] Y. Yu, J.L. Xu, J.W. Mo, M.T. Wang, Principal parameters in flow separation patterns of over-expanded single expansion RAMP nozzle, Eng. Appl. Comput. Fluid Mech. 8 (2) (2014) 274–288. [13] S. Youngster, C.J. Trefny, Computational Study of Single-Expansion-Ramp Nozzles with External Burning, AIAA Paper, 1994, pp. 94–0024. [14] H.T. Lai, Computation of H2/Air Reacting Flowfields in Drag-Reduction External Combustion, AIAA Paper, 1992, pp. 92–3672. [15] S.C. Asbury, C.L. Gunther, C.A. Hunter, A passive cavity concept for improving the off-design performance of fixed geometry nozzles, AIAA Paper, 1996, pp. 96–2541. [16] L. Zhou, H. Xiao, Z.X. Wang, Z.W. Liu, Effects of passive cavity on high pressure ratio single expansion ramp nozzle, J. Aerosp. Power 8 (2015) 1811–1817. [17] E.J. Gamble, R. DeFrancesco, D. Haid, D. Buckwalter, Fluidic Nozzle to Improve Transonic Pitch and Thrust Performance of Hypersonic Vehicle, AIAA Paper, 2005, pp. 2005–3501. [18] S. Ravichandra, D.W.B. Rodney, Simulation of transverse gaseous injection through ports into supersonic freestream, J. Propuls. Power 23 (4) (2007) 772–782. [19] L. Yan, W. Huang, T.T. Zhang, H. Li, X.T. Yan, Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species, Acta Astronaut. 105 (2014) 17–23. [20] W. Huang, Transverse jet in supersonic crossflows, Aerosp. Sci. Technol. 50 (2016) 183–193. [21] K.A. Deere, B.L. Berrier, J.D. Flamm, S.K. Johnson, Computation study of fluidic thrust vectoring using separation control in a nozzle, AIAA Paper, 2003, pp. 2003– 3803. [22] J.D. Flamn, K.A. Deere, M.L. Mason, B.L. Berrier, S.K. Johnson, Experimental study of an axisymmetric dual throat fluidic thrust vectoring nozzle for supersonic aircraft application, AIAA Paper, 2007, pp. 2007–5084. [23] A.W. Kenrick, A.D. Karen, Experimental and Computation Investigation of Multiple Injection Ports in a Convergent-divergent Nozzle for Fluidic Thrust Vectoring, AIAA Paper, 2003, pp. 2003–3802. [24] M.J. Werle, R.T. Driftmyer, D.G. Shaffer, Jet-interaction-induced separation of supersonic turbulent boundary layers - The Two-dimension Problem, AIAA Paper, 1970, pp. 70–765. [25] D.W. Lam, Use of the PARC code to estimate the off-design transonic performance of an over/under turbo-ramjet nozzle, AIAA Paper, 1995, pp. 95–2616. [26] B. Aupoix, A. Mignosi, S. Viala, F. Bouvier, R. Gillard, Experimental and numerical study of supersonic film cooling, AIAA J. 36 (6) (1998) 915–923. [27] D. Dores, M. Madruga Santos, A. Krothapalli, L. Lourenco, E. Collins Jr, F. Alvi, P. Strykowski, Characterization of a Counterflow Thrust Vectoring Scheme on Gas Turbine Engine Exhaust Jet, AIAA Paper, 2006, pp. 2006–3516.
(1) According to the result of the theoretical analysis, the relation of Rx, no − Rx, with > Cfx, no Fs, Sec is the requirement for increasing the thrust coefficient by secondary injection on the cowl. (2) Compared to the flowfield without secondary injection, the flowfield of the over-expanded nozzle with secondary injection is much more complex. The interaction between the primary and the secondary injection generates an incidence shock wave which impinges on the ramp, and then a shock wave induced by the separation and a reflected shock wave penetrates the primary flow. The separation on the ramp resulting from the incidence shock wave leads to the increase of pressure on the ramp. Therefore, the performance of the nozzle can be improved significantly, and the augmentation of the thrust coefficient, lift and pitching moment can be as high as 3.16%, 29.43% and 41.67%, respectively, when NPRP is 10. (3) The location of the injection has a significant effect on the lift and pitching moment, and the direction of the pitching moment can be changed from nose-up to nose-down when the injection is on the tail of the cowl. If the nozzle operates a greater NPR, the effects of the injection on the lift and pitching moment are much more apparent, which is contrary to the thrust coefficient. (4) As the increases of the injection total pressure and width, all the nozzle performances will be improved. And if the parameter φ maintains constant, the axial thrust coefficient would increase when the injection total pressure decreases, so low energy flow can also be used as the secondary injection without decreasing the lift and pitching moment. (5) The total temperature of the secondary injection has no effects on the pressure distribution along the ramp, so the higher total temperature gas can be employed to decrease the mass flow rate of the injection without reducing the performance of the nozzle. Acknowledgements We would like to acknowledge the support of NSFC (Natural Science Fund of China) on the contract numbers of 90916023, 11672346, and the help of our friend Depeng Wang from State University of New York. The authors are grateful to the anonymous reviewers. References [1] R.S. Fry, A century of ramjet propulsion technology evolution, J. Propuls. Power 20
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Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Research paper
Numerical investigation of improving the performance of a single expansion ramp nozzle at off-design conditions by secondary injection
MARK
⁎
Zheng Lva, Jinglei Xua, , Jianwei Mob a b
College of Energy & Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, People's Republic of China Xi’an Aerospace Propulsion Institute, Xi’an, Shanxi 710100, People's Republic of China
A R T I C L E I N F O
A BS T RAC T
Keywords: Single expansion ramp nozzle Poor performance Over-expanded condition Improve Secondary injection
The performance of a single expansion ramp nozzle (SERN) is poor due to over-expansion at off-design conditions. The present study focuses on improving the SERN performance by secondary injection on the cowl and is carried out by using the k − ε RNG turbulence model. The incidence shock wave resulting from the secondary injection impinges on the expansion ramp, resulting in separation and the increase of the pressure distribution along the ramp. The performance of the SERN can be improved significantly, and the augmentation of the thrust coefficient, lift and pitch moment can be as high as 3.16%, 29.43% and 41.67%, respectively, when the nozzle pressure ratio (NPR) is 10. The location of the injection has a considerable effect on the lift and pitching moment, and the direction of the pitch moment can be changed from nose-up to nose-down when the injection is on the tail of the cowl. The effect of the injection on the axial thrust coefficient is much more apparent, if the operation NPR is far from the design point, and however, the results for the lift and pitching moment are opposite. The increases of injection total pressure and injection width have positive impacts on the SERN performance. And if the parameter φ maintains constant, the axial thrust coefficient would increase when the injection total pressure decreases, so low energy flow can also be used as the secondary injection without decreasing the lift and pitching moment. The mass flow rate of the injection can be decreased by applying the higher total temperature flow without reducing the performance of the SERN.
1. Introduction With the development of hypersonic flight and propulsion technologies, the vehicle that can take off horizontally and fly up to a top speed of Mach 5+ will become a reality. As the most promising propulsion systems for hypersonic flight vehicles，the airbreathing engine does not need to carry any oxidizer on board, so it can provide a significant specific impulse, compared to the conventional transportation system such as rockets. One common feature of the propulsion system is that it should operate over a wide range of the flight Mach numbers [1]. Thus, the single expansion ramp nozzle (SERN) integrated with the after-body airframe, which is the indispensable component of the airbreathing propulsion system, also undergoes the Mach numbers from subsonic to hypersonic, so the nozzle pressure ratio (NPR, i.e., the ratio of internal total pressure at the nozzle entrance to the ambient static pressure) of the SERN ranges from 2 to 600 or even higher at hypersonic speeds depending on the inlet recovery [2]. In addition, the SERN acts as the major thrust producing part of the engine and it produces 70% of the net thrust in the entire propulsion system, when
⁎
the flight Mach number is great than six [3], so the performance of the SERN has a significant influence on the efficiency of the whole propulsion system and the SERN is always expected to obtain the optimal performance over the wide flight trajectory. Unfortunately, it is designed on the certain operation point, usually at the cruise condition [4,5], resulting in the great in the expansion area ratio. As a result, when operating at the off-design conditions, the SERN would be strongly over-expanded, which leads to the low pressure acting on the expansion ramp [6]. The sub-ambient pressure distribution along the ramp tends to increase drag and reduce performance with low thrust and strong nose-up pitching moment, which seriously affects the acceleration and stability of the vehicle [12,25]. In order to avoid detrimental over-expansion losses and improve the performance of the SERN under a highly over-expanded condition, previous studies have put forward to some approaches such as variable geometry [7,8], external burning [13,14], passive cavity concept [15,16] and secondary air injection [9–11]. The expansion area ratio can match fairly well with the NPR by means of variable geometry over the wide flight Mach numbers, and as shown in Fig. 1 [8], a rotatable
Corresponding author. E-mail address: [email protected] (J. Xu).
http://dx.doi.org/10.1016/j.actaastro.2017.01.013 Received 21 September 2016; Received in revised form 4 January 2017; Accepted 9 January 2017 Available online 14 January 2017 0094-5765/ © 2017 IAA. Published by Elsevier Ltd. All rights reserved.
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ṁ Ma∞ → n P Pb Pt R Rx Fig. 1. Schematic of variable geometry [8].
Tt → V Vx X x ΔX
Nomenclature NPR RANS SERN
Nozzle pressure ratio Reynolds-averaged Navier-stokes Single expansion ramp nozzle
α ρ θ γ φ
Variables
A b Cfx Fx Fs He Ht hs L LC LR LSec M
Area of nozzle entrance or exit Width of secondary injection Axial thrust coefficient Axial thrust Ideal thrust Height of nozzle exit Height of nozzle throat Height of the injection-plume terminal shock Lift Length of cowl Length of ramp Distance from secondary injection to nozzle throat Pitching moment
Mass flow rate Flight Mach number Direction of the nozzle entrance or exit plane Static pressure Back pressure of the secondary injection Total pressure Gas constant Axial force by integrating the relative pressure on the nozzle internal wall Total temperature Velocity Axial velocity Nozzle performance parameters include Cfx ，L and M Streamwise coordinate Augmentation of nozzle performance include ΔCfx ,ΔL and ΔM Angle of secondary injection Gas density Slope angle of the nozzle exit Specific heat ratio Non-dimensional parameter defined as NPRSec b Ht
Subscript
amb AB CD no P Sec with
Ambient Nozzle entrance plane Nozzle exit plane Without secondary injection Nozzle primary flow Secondary injection With secondary injection
is the main reason for the poor performance of the nozzle at off-design flight conditions. One possible solution to raise the pressure distribution along the ramp is to induce the separation of the over-expanded flow. Consequently, Gamble et al. [10,17] introduced an oblique shock generated by the interaction between primary flow and sonic injection on the lower cowl (Fig. 3) to separate the over-expanded flow on the ramp. Compared to the injection on the ramp, this method requires only simple adjustment mechanism without changing the contour of the expansion ramp. The interaction between a sonic jet and a supersonic cross flow has been the subject of interest in aerospace engineering [18–20], and it is mostly employed to the thrust vectoring nozzle in prior investigation [21,22], and the studies of its application on over-expanded nozzle are very few [10,17]. In Ref. [10], a performance analysis based on the turbojet cycle resulted in a net thrust increase of 3% and thrust specific fuel consumption improvement of 1% with the fluidic injection, validating the feasibility of the design. Reference [17] studied the effects of the injection pressure and flow on the performance of the over-expanded nozzle, but the resulting performance decreased as flow
cowl is applied to change the nozzle exit area for different operations. Even though the nozzle performance can be improved considerably, the adjustment mechanism is complicated with unacceptable weight, limiting its application in highly integrated propulsion system. Youngster et al. [13] studied the effects of the external burning on the performance of the SERN operating at transonic speeds. The fuel was injected into the external flow and was subsequently mixed and burned, and then increased static pressure acts on the entire expansion ramp and cowl trailing edge, as shown in Fig. 2. The results indicated that external burning can be superior to other forms of thrust augmentation methods at transonic speeds. However, a large base drag created by the external burning can offset the augmentation of the nozzle thrust and much more fuel should be carried on board. Reference [15,16] investigated a passive cavity concept for improving the off-design performance of fixed-geometry exhaust nozzles. The passive cavity added the ability to control the off-design nozzle by either encouraging or alleviating the separation appearing in it. Encouraging stable separation offered significant improvements at low NPRs by improving off-design thrust efficiency as much as 2.8%, while separation alleviation had the potential to reduce off-design static thrust efficiency as much as 3.2% at forward flight speeds. Therefore, the passive cavity may have completely opposite effects on the nozzle performance at different flight Mach numbers. In reference [9], a secondary injection on the expansion ramp that filled out the large after-body exit area was employed to avoid the non-matched nozzle state, giving rise to favorable gross thrust angles and improve thrust efficiency in the flight direction. Nevertheless, the complicated adjustment mechanism was also required to turn the injection flap upwards to close the injection air duct. At the same time, the optimal expansion ramp contour might be changed, which was unfavorable to the performance at the cruise condition. As mentioned earlier, the sub-ambient pressure acting on the ramp
Fig. 2. Schematic of external burning [13].
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through a comparison against experimental data in reference [23], in which a secondary injection is applied in a convergent-divergent nozzle for thrust vectoring, and the flowfield is similar to the study in this paper. The configuration and mesh of the model in the experiment [23] is shown in Fig. 5, and the location of the injection is on the divergent contour. The flowfield structure of numerical simulation and experiment is compared in Fig. 6. Detailed comparison of wall pressure between experimental and computational results is presented in Fig. 7. It can be seen that the numerical method could clearly resolve the detail flowfield, and the Mach number contour is highly consistent with experimental shadowgraph. Besides, the calculated wall static pressure agrees with the experimental data very well, in particular the location of the separation point. Therefore, the RNG k−ε turbulence model with standard wall function can be applied in the current study.
Fig. 3. Schematic diagram of the transverse jet in supersonic cross flows.
was injected. From the two studies above, it is found that the detailed theoretical analysis about the flow mechanism is insufficient, and the results of the secondary injection on the over-expanded SERN performance are uncertain. What's more, the effects of many parameters such as the location, width, total pressure, temperature of the injection, which may affect the nozzle performance greatly, are very complicated and also need to be studied further. Therefore, it is necessary to investigate the effects of the secondary injection on the over-expanded SERN systematically. In this paper, the improvement of the SERN performance by the secondary injection on the cowl has been studied thoroughly by numerical simulations. Firstly, the turbulence model applied in the study is validated with experiment data; then the theoretical analysis that verifies the feasibility of improving the performance of the overexpanded nozzle by secondary injection is presented; at last, the effects of the geometric and aerodynamic parameters of the secondary injection are investigated.
2.3. Computational mesh Structured and unstructured hybrid grids are generated for the computation domain of the SERN with secondary injection using Gambit, as shown in Fig. 8. The grid covers the computation domain of 1.4 m by 1.2 m, corresponding to about 7 times the nozzle length and 12 times the height of nozzle exit, which is sufficient to avoid the influence from the far field boundaries. The meshes that are close to the secondary injection and nozzle walls have been refined by structured grids, and the unstructured grids are employed in the nozzle domain. The displacement of the first layer thickness of the wall is set as 0.02 mm, which ensures the y+ to be between 30 and 60 and meet the requirement of the standard wall function. For the entrance of the secondary injection, the boundary condition is defined as pressure-inlet for the case with injection and wall for the case without injection. A mesh independent study is performed with the following three meshes: 54,600 (coarse), 114,800 (medium), 209,000 (fine). The pressure distributions on the upper wall along the flow direction obtained for different meshes are shown in Fig. 9. It can be found that the medium mesh case and the fine mesh case provide very similar pressure distribution, while the coarse case reveals a different pressure distribution with an upstream separation point. Therefore, the mesh of 114,800 cells is adopted for the further numerical analysis, which can reveal the real flowfield with reasonable calculation expanse.
2. Numerical simulation model 2.1. Computation model The model simulated in this paper is a two-dimensional SERN with secondary injection on the cowl, as displayed in Fig. 4. The cruise Mach number is 4.0 and the expansion area ratio is 5. The ideal NPR is designed to be 47.6, when the specific heat ratio is 1.4. Ht ,He indicate the height of the throat and exit, and LC , LR represent the length of the cowl and ramp, respectively. LSec , b and α are the three main parameters of the secondary injection, which correspond to the distance from secondary injection to throat, the width and angle of the secondary injection, respectively. To obtain an optimal performance, the injection angle is set as 90° relative to the cowl inner surface [17]. For better comparison, the model without injection is also analyzed.
3. Theory analysis In order to quantify the nozzle performance, the parameters such as the axial thrust coefficient, lift, pitching moment, are defined. 3.1. Axial thrust coefficient The thrust of the nozzle is defined as the sum of flow moment and the gauge pressure force at the nozzle exit plane. As shown in Fig. 4, the exit plane of the nozzle is the plane CD, and the thrust could be decomposed into the axial force and the normal force. The axial thrust is the x direction component, and can be calculated as
2.2. Turbulence model To achieve a better understanding of the over-expanded nozzle flowfield with and without secondary injection, FLUENT software is used to simulate the flowfield. The two-dimensional, compressible Reynolds-averaged Navier-stokes (RANS) equations are utilized to solve this problem. The governing equations, which include the conservation equations for mass, momentum, and energy, along with the equation of state for the ideal gas, are written in generalized coordinates and in conservative form. The density based solver, 2D space, and steady formulation are adopted in the simulation. The second order upwind method is selected for discretization, and a nonslip, adiabatic condition is imposed on the wall. Due to the limitation of computing power and to accelerate the computation convergence, the RNG k−ε turbulence model is chosen for closure of the RANS equations under the premise of ensuring the precision and accuracy of the calculation results. The effectiveness of the turbulence model is verified
Fig. 4. Configuration of the nozzle with secondary injection.
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Fig. 5. Configuration and mesh of the model in reference [23].
Fx =
Fig. 7. Comparison of experimental and computational wall pressure.
→
∫CD ρVx (V ∙→n ) dA + ∫CD (PCD − Pamb) dA sin θ
(1)
where θ is the slope angle of the plane CD, PCD is the absolute pressure on it, and Pamb is the ambient pressure. The ideal thrust Fs is used to calculate the axial thrust coefficient, which can be expressed as γ −1 2γ P RTt [1 − ( amb ) γ ] γ−1 Pt
∙
Fs = m
(2)
∙
where m , Tt are the mass flow rate and the total temperature, respectively. For the case without secondary injection, the thrust coefficient can be defined as
Cfx, no =
Fx, no Fs, P
(3)
where Fs, P is the ideal thrust of the nozzle primary flow. The axial thrust coefficient for the case with secondary injection is defined as
Cfx, with =
Fx, with Fs, P + Fs, Sec
Fig. 8. Computation mesh for the domain.
3.2. Lift and pitching moment (4) The lift of the nozzle, signed as L, is the y direction force by integrating the relative pressure on the nozzle internal wall. Pitching moment is denoted as M, and its reference point is the center of the nozzle entrance. In this paper,NPRP and NPRSec are the nozzle pressure ratios of the
where Fs, Sec is the ideal thrust of the secondary injection. The secondary injection flow must be included in the performance calculation since this flow may provide additional thrust if it is not injected into the nozzle.
Fig. 6. Flowfield structure comparison between the numerical simulation and experimental results. (a) Experiment shadowgraph image [23] (b) Mach number contour of simulation.
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Fig. 9. Pressure distributions of different meshes on the upper-wall.
Fig. 11. Zoomed flow feature for the case with injection.
Fig. 10. Mach number contour for the two cases: (a) without injection (b) with injection.
Fig. 12. Pressure distribution of ramp and cowl for the two cases.
primary flow and secondary injection, which can be calculated as
NPRP =
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Pt , P Pamb
(5)
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where Pt , P and Pt , Sec are the total pressure of the primary flow and the secondary injection, respectively. To quantify the augmentation of the nozzle performance, the parameter ΔX is defined as
Table 1 Performance of the nozzle with and without injection.
No Injection Injection
Cfx
L (N)
M (N ∙m )
ΔCfx
ΔL
ΔM
0.8287 0.8549
−350 −247
−48 −28
3.16%
29.43%
41.67%
Xwith − Xno × 100% Xno
ΔX =
(7)
where X is the performance parameters of the nozzle defined above, including the axial thrust coefficient Cfx , lift L and pitching moment M. Table 2 Parameters of the secondary injection.
3.3. Theory analysis NPRSec
Tt , Sec
LSec /Ht
b /Ht
10
300k
2.5
0.1
According to the law of conservation of moment, the axial thrust can also be expressed as
Fx =
Table 3 Cases for investigating the influence of the location.
Case A Case B Case C
NPRSec
Ma∞
NPRP
NPRSec
LSec /Ht
1.6 2.0 2.5
10 15 20
10 15 20
1.25、1.50、1.75、2.00、2.25、2.50
Pt , Sec = Pamb
→
∫AB ρVx (V ∙→n ) dA + ∫AB (PAB − Pamb) dA − Rx
(8)
where AB is the entrance of the nozzle (Fig. 4), Rx is the x direction force by integrating the relative pressure on the nozzle internal wall. Therefore, the axial thrusts for the cases with and without injection can be calculated as
Fx, with = Fx, no =
(6)
→
∫AB ρVx (V ∙→n ) dA + ∫AB (PAB − Pamb) dA − Rx,with ∫AB
→ ρVx ( V ∙→ n ) dA +
∫AB (PAB − Pamb) dA − Rx,no
(9) (10)
Compared with the axial thrusts of the two cases, it can be found
Fig. 13. Zoomed Mach contour of the secondary injection for different injection locations: (a)LSec /Ht = 1.25 (b)LSec /Ht = 2.00 (c)LSec /Ht = 2.50 .
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Fig. 14. Mach number contour of the nozzles for Case A.
and external flow. The jet plume interacts with freestream flow at the trailing edge of the SERN, leading to the shock waves in the nozzle. In addition to the internal shock waves, the shear layers, which are formed by the difference in velocity between the exhaust jet and external flow and emanating from the trailing edge of the cowl and ramp, are well captured.(Fig. 11) Since the nozzle operates at the off-design condition, the flow through the nozzle is over-expanded and the sub-ambient pressure acts on the expansion ramp, as shown in Fig. 12. Because the operational NPR deviates far from the design point, flow separation exists on the rear part of the ramp. The performance of the nozzle without secondary injection is given in Table 1, which shows a poor performance with low thrust coefficient and strong nose-up pitching moment, both of which have negative impacts on the acceleration and trimming of the vehicle.
that the sums of the axial component of the flow moment and the absolute pressure force at the nozzle entrance plane for the two cases are identical, for the secondary injection can’t affect the flowfield in the convergent section. The difference between Eq. (9) and Eq. (10) is the term Rx , and for the case with secondary injection, the increased pressure acting on the expansion ramp gives rise to the decrease of the x direction force of the entire nozzle internal wall, so
Rx, with < Rx, no
(11)
And the relation of the axial thrusts for the two cases is
Fx, with > Fx, no
(12)
However, the increase of the axial thrust for the case with injection does not imply the increase of the axial thrust coefficient, for the ideal thrust includes the effect of secondary injection, as shown in Eq. (4). From the relation Cfx, with > Cfx, no , it can be obtained
Rx, no − Rx, with > Cfx, no Fs, Sec
4.1.2. Flowfield of the SERN with secondary injection Compared to the nozzle flowfield without secondary injection, the nozzle flowfield with secondary injection is much complex, as shown in Fig. 10(b). The parameters of the secondary injection are shown in Table 2. Except the aforementioned internal shock waves and the shear layers, the shock wave/boundary layer interaction and the interaction of transverse sonic jet with supersonic flow are also illustrated in the Mach number contour. The incidence shock wave generated by the interaction between secondary injection and nozzle primary flow impinges on the expansion ramp, causing the separation on the ramp. Then the shock wave induced by the separation and the reflected shock wave are emerged (Fig. 11(b)). Fig. 11(a) presents the enlarged flowfield near the secondary injection, which clearly shows the secondary injection induces separation on both upstream and downstream. The separation shown in Fig. 11(b) causes an increased pressure to act on the ramp, which can be seen in Fig. 12, and the pressure on the ramp increases abruptly at x / Ht = 2.7. When x / Ht > 5.5, the subambient pressure acts on the ramp again due to the expansion flow along it. Moreover, the nozzle exit area decreases as a result of the
(13)
So the requirement of improving the axial thrust coefficient via the secondary injection can be satisfied by that the reducing of the x direction force on the nozzle internal wall resulting from the secondary injection can be greater than the value of the term Cfx, no Fs, Sec . As stated above, it has been proven that it is feasible to improve the performance of an over-expanded nozzle by secondary injection. 4. Result and analysis 4.1. Flow features 4.1.1. Flowfield of the SERN without secondary injection The Mach number contour of the SERN operating at an off-design condition is shown in Fig. 10(a). The NPR is 10 and the flight Mach number is 1.6. The shock waves, expansion waves, viscous shear layers and other flow feature are all clearly revealed in the Mach number contour, which is a typical problem of the interaction between exhaust 239
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Fig. 15. Augmentation of the nozzle performance: (a) ΔCfx (b) ΔL (c) ΔM .
width of the injection have positive effects on the injection-plume terminal shock height and the injection back pressure has the opposite effect. Except for the total pressure and width of the injection, other important parameters of secondary injection, such as the injection location and the total temperature are also studied in this study.
secondary injection, both of which are beneficial for improving the performance of the nozzle. The performance of the nozzle with secondary injection and the augmentation of the performance are also given in Table 1. It can be seen that the performance can be improved considerably through the secondary injection, especially the lift and pitching moment, which is in favor of the acceleration and balance of the vehicle.
4.2.1. Location of the injection The cases used to study the influence of the injection location are listed in Table 3; the varied NPRs of the SERN can provide the different over-expanded flowfields and the location of the injection changes from 1.25 to 2.50 for every case. With the increase of LSec / Ht , the back pressure of the injection decreases, which leads to the increase of the height of injection-plume terminal shock as presented in Fig. 13. Even though the increased height of injection-plume terminal shock benefits the intensity of the incidence shock wave, the expansion flow in the nozzle can dissipate the intensity of the shock wave near the separation bubble, so the angle of the incidence shock wave reduces and the separation bubble on the ramp almost remain unchanged, as shown in Fig. 14. Fig. 15 shows the augmentation of the performance for the different injection locations. In Fig. 15(a), the variations in LSec / Ht from 1.25 to 2.5, ΔCfx increases at first and then decreases slightly, which denotes the injection location has little effects on the thrust coefficient for all
4.2. Influences of parameters on the nozzle performance Since the incidence shock wave can induce the separation on the ramp and increase the pressure acting on the ramp for the overexpanded nozzle, it has a considerable effect on the performance of the nozzle. Reference [24] investigated the two-dimensional interaction between sonic jet and supersonic cross flow, and the incidence shock wave was determined by the height of the injection-plume terminal shock, which could be calculated as
hs = 0.52
Pt , Sec b Pb
(14)
where Pb is the back pressure of the secondary injection, and it can be determined by the location of the secondary injection on the nozzle cowl. From the Eq. (14), it can be found that the total pressure and the 240
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Fig. 16. Mach number contour of the nozzles: (a) varied injection total pressure (b) varied injection width. Table 4 Augmentation of the nozzle performance for different injection total pressure.
NPRP
NPRSec
ΔCfx
ΔL
ΔM
10
5 8 10
1.25% 2.63% 2.94%
15.14% 24.00% 29.43%
20.83% 35.42% 41.67%
Table 5 Augmentation of the nozzle performance for the different injection widths.
NPRP
b /Ht
ΔCfx
ΔL
ΔM
10
0.05 0.10 0.15
1.56% 2.94% 4.01%
16.00% 29.43% 42.86%
25.00% 41.67% 56.25%
the three cases. From Fig. 15(b), with the increase of LSec / Ht , the trend of ΔL is the same as ΔCfx , and when LSec / Ht < 2.0 , ΔL changes considerably, and then decreases a little. The increase of LSec / Ht results in that the separation bubble moves downstream (Fig. 14) and the arm of the force by integrating the raised pressure behind the separation bubble increases, so the pitching moment increases greatly as the increase of LSec / Ht , as shown in Fig. 13(c); particularly the direction of the pitching moment can change from nose-up to nose-down for the NPRP =20, which is a good match with the strong nose-up pitching moment generated by the compression fore-body and is very essential to the stability of the vehicle. Moreover, the NPRP has a significant impact on the augmentation of the nozzle performance, and if the nozzle operates at a greater NPR, the lift and pitching moment can be improved more considerably by secondary injection, which is contrary to the thrust coefficient. Since the location of the secondary injection has little effect on the
Fig. 17. Mach number contour of the nozzles corresponding to φ = 1.
thrust coefficient and the gained pitching moment can be greater with the larger LSec / Ht , the proper location of the secondary injection may be the tail of the cowl.
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strong. The results of the nozzle performance affected by the injection total pressure and width are given in Tables 4, 5. The increase of the injection total pressure and width are of great benefit to the augmentation of the nozzle performance, which is corresponding to the change of the nozzle flowfield in Fig. 16. The greater separation bubble causes more beneficial pressure distribution along the ramp, which is advantageous to the nozzle performance. However, only the sufficient mass flow rate can provide the increase of the injection total pressure and width, the possibility of increasing the mass flow rate to improve the nozzle performance should be a compromise in practical application. From Eq. (14), it can be found that the height of the injectionplume terminal shock is changeless, if the product of the injection total pressure and the injection width is constant. So a non-dimensional parameter φ can be defined as
φ= Fig. 18. Pressure distribution of the ramp corresponding to φ = 1.
b /Ht
ΔCfx
ΔL
ΔM
20 10 20/3
0.05 0.10 0.15
2.26% 2.94% 3.29%
30.00% 29.43% 28.86%
41.67% 41.67% 39.58%
4.2.3. Total temperature of the injection From the Fig. 19, it can be found that the injection total temperature has no influence on the pressure distribution on the ramp, which implies that the incidence shock waves don’t change for different total temperature. On the other hand, the injection total temperature can’t determine the height of the injection-plume terminal shock (Eq. (14)), so the flowfields are identical for the three cases, which is the same as the performance of the nozzle in Table 7. Even the mass flow rate of the injection decreases as the total temperature increases, the ideal thrust of the injection is identical, so the axial thrust coefficient changes only a little. Because the secondary injection total temperature can’t affect the improvement of the nozzle performance, the gas with higher total temperature can be used for the secondary injection, which can reduce the mass flow rate of the injection. However, the higher total temperature through the secondary injection flowpath will give rise to the problems like the setup of the mechanical structure. The superalloy should be applied to make sure that the structure can bear the high temperature and the cooling of the structure should be taken into account for the setup of the secondary injection, such as film cooling [26]. Furthermore, an experiment that the secondary injection was employed to control thrust vectoring has been conducted in a gas turbine engine [27], so the use of the secondary injection with higher temperature gas in this current study is feasible.
Fig. 19. Pressure distribution of the ramp for different injection total temperature.
Table 7 Augmentation of the nozzle performance for different injection total temperature.
NPRP
Tt , Sec (k)
ΔCfx
ΔL
ΔM
10
300 900 1800
2.94% 3.03% 3.31%
29.43% 29.14% 29.14%
41.67% 41.67% 41.67%
(15)
Based on the analysis above, when the parameter φ is constant, the flowfields in the nozzles are identical, which can be demonstrated in Figs. 17 and 18. The angles and the impinging points of the incidence shock waves are the same for the three cases, so the pressure distribution on the ramp does not change (Fig. 18), which indicates that the augmentations of the lift and pitching moment are almost the same, as shown in Table 6. Due to the identical pressure distributions on the ramp, the axial thrusts of the nozzles for the three cases are the same, but the decrease of the injection total pressure leads to the decrease of the ideal thrust Fs, Sec in Eq. (4), so the thrust coefficient increases gradually, as shown in Table 6. In the practical application, since the injection has no effect on the pressure distribution on the ramp when the parameter φ is constant, the low energy flow such as the flow from the fore-body boundary layer or the inlet bleed air rather than the primary flow in the engine can be employed as the secondary injection with the suitable injection width, which can reduce spillage drag and increase the augmentation of the axial thrust coefficient at the same time.
Table 6 Augmentation of the nozzle performance corresponding to φ = 1.
NPRSec
NPRSec b Ht
4.2.2. Total pressure and width of the injection As the important parameters, the total pressure and width of the injection have significant effects on the height of the injection-plume terminal shock as presented in Eq. (14). Hence, the total pressure and width of the injection can affect the flow field of the over-expanded nozzle considerably, which can be seen from Fig. 16. As the increase of the total pressure and width, the angle of the incidence shock wave increases and the separation bubble on the ramp becomes large gradually, both of which denote that the incidence shock wave becomes
5. Conclusions As the important component of the air-breathing propulsion system operating over a wide range of the flight Mach numbers, the SERN is 242
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highly over-expanded at the low flight Mach number, which is resulting from the large expansion area ratio designed at the cruise Mach number. In order to improve the performance of the over-expanded nozzle, the SERN with secondary injection on the cowl has been studied. The k − ε RNG turbulence model is used to simulate the flowfield of the nozzle with a secondary injection, and it can capture the flow features very well. The main conclusions are as followings:
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(1) According to the result of the theoretical analysis, the relation of Rx, no − Rx, with > Cfx, no Fs, Sec is the requirement for increasing the thrust coefficient by secondary injection on the cowl. (2) Compared to the flowfield without secondary injection, the flowfield of the over-expanded nozzle with secondary injection is much more complex. The interaction between the primary and the secondary injection generates an incidence shock wave which impinges on the ramp, and then a shock wave induced by the separation and a reflected shock wave penetrates the primary flow. The separation on the ramp resulting from the incidence shock wave leads to the increase of pressure on the ramp. Therefore, the performance of the nozzle can be improved significantly, and the augmentation of the thrust coefficient, lift and pitching moment can be as high as 3.16%, 29.43% and 41.67%, respectively, when NPRP is 10. (3) The location of the injection has a significant effect on the lift and pitching moment, and the direction of the pitching moment can be changed from nose-up to nose-down when the injection is on the tail of the cowl. If the nozzle operates a greater NPR, the effects of the injection on the lift and pitching moment are much more apparent, which is contrary to the thrust coefficient. (4) As the increases of the injection total pressure and width, all the nozzle performances will be improved. And if the parameter φ maintains constant, the axial thrust coefficient would increase when the injection total pressure decreases, so low energy flow can also be used as the secondary injection without decreasing the lift and pitching moment. (5) The total temperature of the secondary injection has no effects on the pressure distribution along the ramp, so the higher total temperature gas can be employed to decrease the mass flow rate of the injection without reducing the performance of the nozzle. Acknowledgements We would like to acknowledge the support of NSFC (Natural Science Fund of China) on the contract numbers of 90916023, 11672346, and the help of our friend Depeng Wang from State University of New York. The authors are grateful to the anonymous reviewers. References [1] R.S. Fry, A century of ramjet propulsion technology evolution, J. Propuls. Power 20
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