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Over-expanded separation transitions of single expansion ramp nozzle in the accelerating and decelerating processes
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Over-expanded separation transitions of single expansion ramp nozzle in the accelerating and decelerating processes
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Yang Yu
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School of Aeronautics, Chongqing Jiaotong University, 400074, Chongqing, China b Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power System, 210016, Nanjing, China
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Article history: Received 14 October 2019 Received in revised form 20 November 2019 Accepted 27 December 2019 Available online xxxx Keywords: Single expansion ramp nozzle Over-expanded separation External flow Separation pattern transition
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Flow separation is a basic fluid-dynamics phenomenon that occurs in supersonic nozzles at low pressure ratios. In the over-expanded flowfield of nozzles, the subsonic area is formed, such as separation bubble, recirculation zone, and flow downstream Mach reflection. In static ambient, the recirculation zone is opened with the environment. When the external flow is not still, it will interact with the recirculation zone. As a result, the external flow will make significant influences on the over-expanded separation flowfield. This paper aims to present a detailed description of separation patterns transitions caused by external Mach number variation, analyze the mechanism of separation transitions. Accelerating and decelerating processes of a long flap single expansion ramp nozzle (SERN) is investigated by numerical simulation. Separation transitions and the performance of SERN influenced by the separation transitions have been discussed. In the accelerating process, free shock separation (FSS) is a stable separation pattern and lasts for a long time. The decelerating process is not just the inverse process because a new over-expanded flowfield pattern appears in the decelerating process. Meanwhile, there is an apparent hysteresis between the accelerating and decelerating processes. © 2020 Elsevier Masson SAS. All rights reserved.
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1. Introduction
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Over-expanded status is a primary status in supersonic nozzles, which occurs to a lower pressure ratio than design condition. For the nozzles of widely worked combined cycle engines, seriously over-expanded operating condition is easily occurring because operating pressure ratio variegating for a wide range and a high pressure ratio chosen at the design condition [1–3]. Flow separation will result in shock formation and shock/turbulent-boundary layer interaction inside the nozzle [4–6]. In the propulsion system of scramjet, shock waves, shock wave interactions, and shock trains are common phenomena in the flow path [7–12]. Shock wave boundary layer interactions usually accompany unsteady effect and shock train movements [13–16]. For example, Li et al. [17] investigated the unstart/restart hysteresis characteristics analysis of an over-under TBCC inlet. As the inlet transfers from low-speed status to high-speed status with fixed backpressure, the shock train moves downstream. Shi et al. [18] investigated the path dependence characteristic of the shock train in the inlet and found that the existence of the separation bub-
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*
Correspondence to: School of Aeronautics, Chongqing Jiaotong University, 400074, Chongqing, China. E-mail address: [email protected]. https://doi.org/10.1016/j.ast.2019.105674 1270-9638/© 2020 Elsevier Masson SAS. All rights reserved.
ble intensifies the unsteadiness of shock train motion. Su et al. [19] explored the method of periodic air injection to suppress the pressure oscillation and to delay the hypersonic inlet unstart. Separation and shock train induced by backpressure is a prevalent phenomenon in scramjet combustor as well [20]. In scramjet combustors, separation shocks are oblique shocks, and the flow downstream oblique shock train remains supersonic. In general, the hysteresis exists in shock train mode transitions [21]. Compared with the inlet, the nozzle is a favorable pressure gradient part. Under the design condition, the air expands and accelerates in the nozzle. When the nozzle pressure ratio (NPR) of a supersonic nozzle is less than the design condition, ambient pressure is higher than the static pressure of flow at the nozzle exit, and nozzle works under over-expanded status [22,23]. Shock wave trains will be formed in the flowfield to match the pressure of jet and ambient. If operating NPR is low enough, the shock waves will move into the nozzle [24]. The strong adverse pressure gradient will cause boundary-layer separation, which interacts with shocks and gives rise to complex phenomena [25–27]. Papamoschou et al. found out the symmetric separation and asymmetric separation in over-expanded nozzle experiments and numerical simulation results, and confirmed the unsteady shock motion existed [28]. They pointed that shock motion unsteadiness contributed to the increased shear-layer instability, whereas the mixing enhance-
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ment was not due to the wave pattern [29]. Verma and Manisankar analyzed the origin of flow asymmetry in planar nozzles with separation [30]. Depending upon the local flow condition, the flow can experience either an early separation or a delayed separation resulting in either an FSS or an RSS. Verma et al. [31] analyzed the shock unsteadiness in a supersonic over-expanded planar nozzle. The study showed that the length of the intermittent region decreasing significantly as the boundary layer state transfers to the transitional regime. The asymmetric separation also exits in isolator and combustion. Separation transitions are found in the combustion cold flow experiment, and there is a lag between the boundary layer transformation and the separation transition [32]. The asymmetry separation also has been found in transonic channel flows by Bruce et al. [33], which was induced by the interaction of corner flow. In a single expansion ramp nozzle (SERN), the asymmetry separation and separation pattern transitions have been found in cold flow experiments [34]. Two separation patterns, RSS(ramp) and RSS(flap), have been observed in the experiments. In the RSS(ramp), the restricted separation bubble forms on the expansion ramp of the SERN, and the recirculation zone on the flap is filled by ambient air. The flow in the RSS(flap) separates from both the expansion ramp and the flap, and reattaches to the flap, forming a separation bubble. In the FSS, nozzle jet separates from both expansion ramp and flap but does not reattach to the wall. There is a transition from RSS(flap) to RSS(ramp) in the startup process, whereas the pattern transition from RSS(ramp) to RSS(flap) in the shutdown process. The separation transition process lasts less than 5 ms, and the hysteresis exists in startup and shutdown processes. Because of the flowfield alternation, the performance of the nozzle changes a lot in separation pattern transition [35]. Compare to the separation in isolator and combustion, normal shock occurs in the nozzle jet, and the separation zone will interact with external flow. As a result, the external flow will make significant influences on the over-expanded separation flowfield [36]. Mousavi et al. [37] found that the distances between Lambda shocks are different at two external flow Mach number. From the numerical simulation results, it could be found that external flow Mach number would affect the separation patterns of SERN [38]. Although external flow makes excellent influences on the overexpanded flowfield in SERN, few investigations have been conducted to analyze the phenomenon and the mechanism. This paper aims to present a detailed description of separation patterns transitions caused by external flow Mach number variation, analyze the mechanism of separation transitions. In the following sections, the accelerating and decelerating processes of a long flap SERN will be discussed.
where μ is the molecular viscosity, I is the unit tensor, and the second term on the right hand side is the effect of volume dilation. The turbulence model uses a mathematical technique known as “renormalization group” (RNG) methods, derived from the NavierStokes equations. The RNG k − ε model is similar to the standard k − ε model, but includes the refinements: improving the accuracy for rapidly strained flows, enhancing accuracy for swirling flows and providing an analytical formula for turbulent Prandtl numbers. Because of these features, RNG k − ε model are more accurate and reliable for a wider class of flows than the standard k − ε model. The transport equation of turbulent kinetic energy k can be written as follows:
∂ ∂ ∂ (ρ k ) + (ρ ku i ) = ∂t ∂ xi ∂xj The transport equation of
∂ ∂ ∂ (ρε ) + (ρε u i ) = ∂t ∂ xi ∂xj
∂k αk μeff ∂xj
ε is:
∂ε αε μeff ∂xj
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+ G k − ρε
(4)
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ε
ε2
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k
k (5)
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+ C 1ε G k − C 2ε ρ
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The term G k represents the production of turbulence kinetic energy. From the exact equation for the transport of k, this term may be defined as:
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∂u j G k = −ρ u i u j ∂ xi
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(6)
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To evaluate G k in a manner consistent with the Boussinesq hypothesis,
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G k = μt S 2
(7)
where S is the modulus of the mean rate-of-strain tensor, defined as
S=
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2S i j S i j
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μeff = μt = C μ ρ
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The effective viscosity is calculated by
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(9)
The model constants are derived using RNG theory and they are the default values for the RNG turbulent model in the software: C μ = 0.0845, αk = αe = 1.39, C 1ε = 1.42 and C 2ε = 1.68.
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3. Geometry, grid and validation
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2. Computational framework The computational modeling is based on time-averaged NavierStokes equations. Flow is governed by continuity and conservation of momentum equations, and the continuity equation can be written as follows:
∂ρ + ∇ · ρ v = 0 ∂t
(1)
Conservation of momentum can be described by
∂ ρ v + ∇ · ρ v v = −∇ p + ∇ · τ¯¯ ∂t
(2)
The stress tensor τ¯¯ is given by
τ¯¯ = μ
∇ v + ∇ v
T
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(3)
In this research, a straight expansion ramp SERN is considered for investigation, and geometry of the SERN is the same as Ref. [34]. The critical design parameters of straight ramp SERN are the height of the throat, the expansion area ratio, the length of the flap, and the angle of expansion ramp. The height of the throat determines the mass flow rate of the nozzle. The expansion area ratio is dependent on the design nozzle pressure ratio. The angle of expansion ramp influences the initial expansion angle of flow, as well as the length of the nozzle. The numerical method is validated by the experimental data reported in Ref. [34]. The experiments were conducted at the Internal Flow Research Center of Nanjing University of Aeronautics and Astronautics (NUAA). The facility utilizes a cold blow down wind tunnel. The geometry of SERN and the experimental SERN model is shown as Fig. 1. The expansion area ratio is 2.896, the angle of expansion ramp is 25◦ , and the height of the throat is 20 mm. The throat area was 1200 mm2 , and the flow path is 60 mm wide. The 2D numerical method could get well results of the flowfield at the symmetry plane.
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Fig. 1. Experimental model of the SERN in Ref. [34].
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Fig. 2. Grid regions of the SERN for numerical simulation.
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Fig. 4. Thrust variations with different time steps. Fig. 3. Numerical and experimental wall pressure distribution of test model.
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The geometry of the SERN has been meshed by ICEM with structured mesh. The grid is shown in Fig. 2. The node distributions in x and y directions of regions 1, 2, and 6 are 100×180, 140×180, and 140×80, respectively. The node distributions in regions 3, 4, and 5 are 70×140, 30×140, and 140×140. The node distributions in regions 7 and 8 are 70×80 and 180×80. The y + location in the simulation varies in the range of 10–50. In the over-expanded flowfield, the separation phenomena are involved. Separation and reattachment occur in SERN, and the flow speeds
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are quite different between the main jet and separation bubble. As a result, the y + location varies to a large degree. The grid case used above is defined as the medium grid case, and the node distributions in x and y directions are increased by a factor of 2, defined as the fine grid, and then decreased by a factor of 0.5, defined as the coarse grid. Commercial CFD software FLUENT is used. The results of the pressure contributions on expansion ramp and flap are shown in Fig. 3. The results of CFD and experiment fit well, and the medium grid is chosen for the simulation. The k-ε RNG model is also validated in Ref. [38].
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Fig. 5. Over-expanded separation flowfield of the long flap SERN in static ambient.
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Fig. 6. Steady simulation results of long flap SERN, increasing the external Mach number in steps, NPR=3.4.
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In the calculation, time steps 1×10−4 s, 5×10−5 s, and 2×10−5 s have been used to simulate the separation pattern transition in static ambient. The length of the nozzle is 52.9 mm, the maximum velocity in the nozzle is about 520 m/s, and therefore the timescale is about 1×10−4 s. Fig. 4 shows the results of thrust changes in the separation transition process with various time steps. It can be found from the figure that the thrust changes of different time steps are the same before and after the transition, and the transition pressure ratios of 5×10−5 s and 2×10−5 s are almost the same, so time step size 5×10−5 s has been chosen in the simulation.
4. Results and discussion
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4.1. Transition process of accelerating
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Limited by laboratory conditions, it is difficult for nozzle test wind tunnel to simulate external flowfield in general, and most nozzle test experiments are conducted in a static environment. However, the nozzle jet will interact with external flow under real flight conditions. When SERN works under design condition and under-expanded condition, flow downstream throat is supersonic, and therefore External flow cannot influence the flowfield inside
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Fig. 7. Performance variations of the long flap SERN in the accelerating process, NPR=3.4, Ma∞ = 0.1∼1.1.
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the nozzle. Under severely over-expanded conditions, some subsonic region, such as separation bubble, recirculation zone, and subsonic boundary layer, appears in SERN, shown as Fig. 5. Consequently, external flow will make significant influences on the subsonic region, for instance, the position of the separation and reattachment point, and the scale of the separation bubble and recirculation zone. Furthermore, movements of separation point and reattachment point, variations of separation bubble, and recirculation zone will affect the structures of shock waves in SERN directly, which might even cause separation pattern transitions. Accordingly, it is worth concerning the over-expanded flowfield variations and separation pattern transitions caused by external flow Mach number increasing and decreasing. The steady simulation results are shown by the contours of Mach number in Fig. 6. NPR is 3.4 and only Mach number of far-field boundary is altered in the simulation. At the Mach number of 0.1, the nozzle works as RSS(ramp) pattern. As the Mach number increases to 0.4, the separation bubble on expansion ramp alters to the recirculation zone, and the separation pattern changes from RSS(ramp) to FSS. Accordingly, a separation pattern transition, RSS(ramp) to FSS, will happen when the external flow Mach increases from 0.1 to 0.4. As the Mach number increase to 1.0, the recirculation zone on the flap disappears, and the recirculation zone on the expansion ramp becomes very small. From the above results, it could be found that external flow will affect the position of separation point and shape of the recirculation zone, which will affect the nozzle performance. In an accelerating flight, external Mach number increases continuously. In the simulation, total pressure at nozzle inlet and ambient pressure remain unchanged. NPR keeps 3.4, and then increases far-field Mach number 1.0/s. The process of external Mach number increasing from 0.1 to 1.1 has been simulated. Variations of thrust, lift, and moments in the accelerating process are shown in Fig. 7. The thrust, lift, and moments are nondimensionalized by the initial values at external Mach number 0.1. It could be observed obviously that the variations of thrust, lift, and moments can be divided into several stages. In stage (a), the SERN works as RSS(ramp), and the separation point moves downstream with external Mach number increasing, so thrust, lift, and moments all descend. The separation pattern transition from RSS(ramp) to FSS happens between stage (a) and (b). The process of RSS(ramp) to FSS transition is shown in Fig. 8. In the transition, the separation bubble becomes unclosed and transfers to the recirculation zone. At the beginning of stage (b), the reattachment point is near the tail of the expansion ramp, but the flow cannot always reattach to the
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expansion ramp. With the external Mach number increasing, the separation bubble transfers to the recirculation zone, and external air gets into the recirculation zone. In the long flap SERN, a large recirculation zone is formed on the flap as well. In the recirculation zone, flow speed and density are low, so the momentum is quite limited. Consequently, the shape of the recirculation zone can be changed easily by nozzle jet deflection, and the RSS(ramp) to FSS transition is evident in the long flap SERN. Fig. 9 shows the interaction between the nozzle jet and external flow at an expansion ramp tail. The flowfield is similar to a twostream flow convergence at a wedge. The stream on the upper side is subsonic, Ma1 < 1, which is external flow. The stream under the lower side is supersonic, Ma2 > 1, which is nozzle jet along the expansion ramp. The two streams converge at the tail of wedge, and then flow downstream along the same direction. Because the speeds of two streams are different, a slip line is formed in the flowfield. The control volume in the subsonic stream is shown as Fig. 9. The flow direction is vertical to the inlet section and outlet section. The flow direction is horizontal at the inlet section, but a vertical velocity component is formed at the outlet section. It can be known from the theorem of momentum that an upward force emerges on the slip line. When Ma1 increases, the momentum of the upper flow becomes higher, and the converged flow deflects downward. For the supersonic part, the flow downstream shock S 1 deflects downward, which will strengthen the shock S 1 and cause P 4 / P 2 rising. In the converged flow, P 4 is equal to P 3 , and P 3 changes little at low Mach number. As a result, P 2 must decrease to match the flowfield. For RSS(ramp) pattern, only the separation point and reattachment point moves downstream will cause the pressure drop at the exit. On another side, the upstream flow cannot be influenced by downstream flow in the supersonic flowfield. Under the design and under-expanded conditions, the external flow makes little influence on the flowfield in the nozzle. However, when the nozzle works under severely over-expanded conditions, subsonic separation zone is formed on the expansion ramp, and the subsonic boundary layer is thick downstream the reattachment point. Through the subsonic part in the nozzle, the influences of external flow could transmit to the internal flowfield. With external flow Mach number increasing, external flow and nozzle jet deflects downward. Meanwhile, the separation and reattachment point on expansion ramp moves downstream, and the pressure in the separation bubble dropped with external Mach number increasing. When the reattachment point moves to the tail of the expansion ramp, the external flow starts to get into the recirculation zone, and the separation pattern transfers from RSS(ramp) to FSS. In stage (b), the pressure in the recirculation zone is increasing gradually because the external flow gets into the recirculation zone. Besides, the separation point moves upstream, and the thrust, lift, moments are increasing. In early stage (b), the channel for external flow getting into the recirculation zone is narrow, so the pressure in the recirculation zone increases slowly. When the recirculation zone is fully developed, the separation point does not move upstream any longer. Then the separation point starts to move downstream with the external Mach number increasing, and stage (c) begins. In stage (c) (d) and (e), the separation point on expansion ramp moves downstream continuously. For the SERN, thrust only depends on the pressure distribution of the expansion ramp. For the certain NPR, closer separation point to the tail, worse thrust performance for the nozzle. Accordingly, the thrust decreases continuously with the separation point moving downstream continuously. As shown in Fig. 10, the external flow needs to deflect a greater angle to enter the recirculation zone, and a pair of vortex is formed between external flow and nozzle jet. One vortex is at the tail of the flap, and the other is in the recirculation zone. With the external Mach increasing, the nozzle jet
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Fig. 9. Scheme of the interaction between nozzle jet and external flow at expansion ramp tail.
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Fig. 10. Recirculation zone on the flap.
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deflects downward and compresses the recirculation zone on the flap, which caused more loss for external flow entering the recirculation zone. Consequently, the pressure in recirculation zone drops, and the thrust of the nozzle decreases fast in stage (d) and (e). Unlike thrust, lift, and moment depend on the pressure distributions of both expansion wall and flap, so the variation trend of lift and moment may be different from thrust. From the simulation results, lift and moment variation trend is similar. In stage (c), lift and moment increase slowly, but in stage (d), lift and moment decrease. In stage (e), when the external Mach number reaches about 0.95, the lift and moment increase again. It is because the local supersonic region is formed in external flow near the nozzle exit. The local supersonic region causes some disturbance to the pressure in the recirculation zone on the flap. When the supersonic region is fully developed, the flow returns to normal, and the lift and mo-
ment decrease gradually. With the separation point on flap moving downstream, the space of recirculation zones is compressed. At the same time, the channel between the nozzle jet and tail vortex becomes narrower. When nozzle jet and external tail vortex meet together, external flow cannot get into the recirculation zone any longer. As a result, the recirculation zone cannot keep on the flap, and the separation point on flap moves downstream rapidly until to tail. The shock wave formed on the flap transfers from the separation shock to the tail shock. Without the restriction of the separation shock on the flap, the separation shock on expansion ramp moves downstream as well, but the shock wave does not reach to tail, and there is still a small recirculation zone on expansion ramp. This recirculation zone is enclosed by expansion ramp, nozzle jet, and external flow. Therefore the external cannot get into
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Fig. 11. Transient simulation results of the accelerating process, the separation shock to tail shock transition on the flap, NPR=3.4.
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the recirculation zone. In this process, the flowfield changes a lot, which causes the performance of nozzle a step change. The process of shock wave transition from separation shock to tail shock is shown in Fig. 11. In this transition process, external flow and nozzle jet are both supersonic, but the space between nozzle jet and external flow forms subsonic recirculation zone. At the beginning of the transition, external flow can get into the recirculation zone, and the recirculation zone induces the separation shock. With external Mach number increasing, the separation shock moves downstream, and external air is difficult to enter the recirculation zone. When the recirculation zone on flap gets enclosed, the recirculation zone cannot maintain, and the separation shock moves downstream rapidly. In the transition, the reflection pattern of separation shock and tail shock transfers from regular reflection to Mach reflection (Fig. 11.b), and then transfers to regular reflection at the end (Fig. 11.c). After the transition, the recirculation zone on the expansion ramp is relatively stable, and the performance of the nozzle does not change suddenly anymore. From the simulation results and discussions above, it can be known that the separation pattern transitions in the accelerating process are mainly caused by interactions of the recirculation zone, external flow, and nozzle jet. Because the momentum of the recirculation zone is low, the nozzle jet can deflect easily, and the separation pattern transition completes in a short time. In addition, the reflection pattern of separation shocks transfers as well, so there may be hysteresis between accelerating and decelerating processes.
4.2. Transition process of decelerating
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As the accelerating process, the steady simulation results should be cognized firstly. The steady simulation results are shown by the contours of Mach number in Fig. 12. The NPR is 3.4 and the simulation only alters the Mach number of far-field boundary. Only a small recirculation zone is formed on the expansion ramp at Ma∞ = 1.1. As the Mach number decreases to 0.93, the recirculation zone on the expansion ramp becomes more extensive, and external flow re-enters the recirculation zone. At this time, the jet does not separate from the flap, and the tail shock is formed. Significantly, this separation pattern does not appear in the accelerating process. Then the decelerating process of external Mach number decreasing from 1.1 to 0.2 has been simulated. In the simulation, the inlet total pressure and ambient pressure is unchanged, and the NPR remains 3.4. Then, decrease the Mach number of the far-field 1.0/s to simulate the decelerating process. Variations of thrust, lift, and moments in the decelerating process are shown as Fig. 13. It could be observed that the variations of thrust, lift, and moments have several stages. In stage (a), only a small recirculation zone is formed on expansion ramp, and the recirculation zone is relatively stable, so the separation point on expansion ramp moves slowly with the external Mach number decreasing. As a result, the performance of SERN degrades slowly. When the external flow and the jet cannot enclose the recirculation zone, external flow starts to enter into the recirculation zone, and the stage (b) begins.
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Fig. 12. Steady simulation results of the long flap SERN, decreasing the external Mach number in steps, NPR=3.4.
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Fig. 13. Performance variations in the decelerating process, NPR=3.4, Ma∞ = 1.1∼0.2.
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In stage (b), the recirculation zone on expansion ramp transforms from enclosed by external flow and nozzle jet, shown as Fig. 14(a), to opened with ambient, and shown as Fig. 14(c). At the beginning of the transition, the reflection of separation shock on expansion ramp and tail shock on flap transfers from regular reflection to Mach reflection. When the Mach stem fully develops, the external flow starts to enter into the recirculation zone, and the separation point moves upstream rapidly, which causes the nozzle performance improvement suddenly. The process of recirculation zone transition is shown in Fig. 14. After the transition,
the jet and the nozzle performance oscillates for a short time. In stage (c), the thrust, lift, and moments increase smoothly with the external Mach number decreasing. In stage (b) and (c), the shock wave on the flap is still at the tail, but the flap tail shock cannot remain with the external Mach number decreasing and the separation shock wave on expansion ramp moving upstream. When the tail shock on flap starts to move upward and transfers to separation shock, stage (d) begins, and the over-expanded flowfield transfers from the only recirculation zone on expansion ramp to both the recirculation zones on expansion ramp and flap. The process of transition is shown as Fig. 15. With the external Mach number decreasing, the separation point and the separation shock on expansion ramp moves upstream. The interaction point of separation shock and tail shock gets closer to the nozzle, which makes the length of tail shock shorter. Besides, the type of shock wave reflection transfers from regular reflection to Mach reflection. When the strength of tail shock cannot maintain the Mach reflection, the separation shock on flap moves upstream rapidly and the tail shock transfers to separation shock. After the transition, it is the typical FSS pattern flowfield in which both recirculation zones are on expansion ramp and flap. In this transition, a separation shock is formed on the flap, and nozzle jet deflects upward. As a result, the space of the recirculation zone on the expansion ramp is compressed, but it has little influence on the pressure in the recirculation zone. The separation point on expansion ramp moves downwards a little, and the performance degrades a little. However, the pressure distribution on flap changes a lot caused by the recirculation zone formed after the transition. The static pressure in the recirculation zone is much higher than
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the overexpansion part, so the lift and the moments of the nozzle have a sharp decline. In the whole decelerating process, the FSS pattern is a relatively stable over-expanded flowfield pattern, and it lasts for a long time. The FSS-RSS(ramp) transition, stage(e), happens at a low external Mach number, and the process of the transition is shown in Fig. 16. Before the transition, the nozzle jet deflects upwards with the external Mach number decreasing. The recirculation zone on the expansion ramp is compressed, which caused the difficulties for external flow entering into the recirculation zone. As a result, the pressure in recirculation zone decline, the separation point on expansion ramp moves downstream, and the performance of nozzle degrades. Finally, the FSS-RSS(ramp) transition happens, which caused the recirculation zone getting closed and transferring to the separation bubble. Compared to the accelerating process, the decelerating process is not just the inverse process. The new over-expanded flowfield pattern appears in decelerating process. Meanwhile, there is an apparent hysteresis between accelerating and decelerating processes. Table 1 shows the differences between the accelerating and decelerating processes in transition A and B marked in Fig. 7 and Fig. 13. It could be found that the external Mach number of transition A and B is quite different, especially the transition A, although the performances of the nozzle are similar. In the separation pattern transition, the types of shock waves and shock reflections are changed at the same time. The conditions which cause the shock waves and the reflection alternation are different between acceler-
ating and decelerating processes. As a result, there is a hysteresis between the accelerating and decelerating processes.
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5. Conclusions
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In this article, the processes of over-expanded SERN accelerating and decelerating have been studied by numerical simulation. The separation pattern transitions caused by external flow variation have been described in detail. The mechanisms of the separation transitions and the performance of SERN influenced by separation transitions have been discussed. From the results, the following conclusions can be drawn:
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(1) Compared to the over-expanded flowfield in SERN without external flow, free shock separation (FSS) is a stable separation pattern and lasts for a long time in accelerating and decelerating processes. (2) In the accelerating process, the transition from RSS(flap) to FSS occurs firstly, and then the FSS transfers to tail shock pattern. (3) In the decelerating process, a new kind of separation transition occurs, and the transition of tail shock pattern to FSS has been decomposed into two steps. Firstly, the flowfield transfers from tail shock pattern to only tail shock on flap and recirculation zone on the expansion ramp. Secondly, the flowfield transfers to typical FSS with both recirculation zones on expansion ramp and flap. (4) There is hysteresis between accelerating and decelerating processes. The external Mach numbers of the transition have con-
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Table 1 Comparison of thrust and external Mach Number of the separation transitions in the accelerating and decelerating processes.
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Transition A
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Accelerating Decelerating
siderable differences, but the nozzle performance at the transition point is similar.
Ma
Fx
Ma
Fx
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100% 99.22%
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100% 99.35%
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Declaration of competing interest
Transition B
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Acknowledgements
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This work is supported by the National Natural Science Foundation of China under Grant No. 11802124 and China Postdoctoral Science Foundation under Grant No. 2018M632306.
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References
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Over-expanded separation transitions of single expansion ramp nozzle in the accelerating and decelerating processes
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Yang Yu
a,b,∗
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a
School of Aeronautics, Chongqing Jiaotong University, 400074, Chongqing, China b Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power System, 210016, Nanjing, China
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Article history: Received 14 October 2019 Received in revised form 20 November 2019 Accepted 27 December 2019 Available online xxxx Keywords: Single expansion ramp nozzle Over-expanded separation External flow Separation pattern transition
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a b s t r a c t
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Flow separation is a basic fluid-dynamics phenomenon that occurs in supersonic nozzles at low pressure ratios. In the over-expanded flowfield of nozzles, the subsonic area is formed, such as separation bubble, recirculation zone, and flow downstream Mach reflection. In static ambient, the recirculation zone is opened with the environment. When the external flow is not still, it will interact with the recirculation zone. As a result, the external flow will make significant influences on the over-expanded separation flowfield. This paper aims to present a detailed description of separation patterns transitions caused by external Mach number variation, analyze the mechanism of separation transitions. Accelerating and decelerating processes of a long flap single expansion ramp nozzle (SERN) is investigated by numerical simulation. Separation transitions and the performance of SERN influenced by the separation transitions have been discussed. In the accelerating process, free shock separation (FSS) is a stable separation pattern and lasts for a long time. The decelerating process is not just the inverse process because a new over-expanded flowfield pattern appears in the decelerating process. Meanwhile, there is an apparent hysteresis between the accelerating and decelerating processes. © 2020 Elsevier Masson SAS. All rights reserved.
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1. Introduction
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Over-expanded status is a primary status in supersonic nozzles, which occurs to a lower pressure ratio than design condition. For the nozzles of widely worked combined cycle engines, seriously over-expanded operating condition is easily occurring because operating pressure ratio variegating for a wide range and a high pressure ratio chosen at the design condition [1–3]. Flow separation will result in shock formation and shock/turbulent-boundary layer interaction inside the nozzle [4–6]. In the propulsion system of scramjet, shock waves, shock wave interactions, and shock trains are common phenomena in the flow path [7–12]. Shock wave boundary layer interactions usually accompany unsteady effect and shock train movements [13–16]. For example, Li et al. [17] investigated the unstart/restart hysteresis characteristics analysis of an over-under TBCC inlet. As the inlet transfers from low-speed status to high-speed status with fixed backpressure, the shock train moves downstream. Shi et al. [18] investigated the path dependence characteristic of the shock train in the inlet and found that the existence of the separation bub-
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*
Correspondence to: School of Aeronautics, Chongqing Jiaotong University, 400074, Chongqing, China. E-mail address: [email protected]. https://doi.org/10.1016/j.ast.2019.105674 1270-9638/© 2020 Elsevier Masson SAS. All rights reserved.
ble intensifies the unsteadiness of shock train motion. Su et al. [19] explored the method of periodic air injection to suppress the pressure oscillation and to delay the hypersonic inlet unstart. Separation and shock train induced by backpressure is a prevalent phenomenon in scramjet combustor as well [20]. In scramjet combustors, separation shocks are oblique shocks, and the flow downstream oblique shock train remains supersonic. In general, the hysteresis exists in shock train mode transitions [21]. Compared with the inlet, the nozzle is a favorable pressure gradient part. Under the design condition, the air expands and accelerates in the nozzle. When the nozzle pressure ratio (NPR) of a supersonic nozzle is less than the design condition, ambient pressure is higher than the static pressure of flow at the nozzle exit, and nozzle works under over-expanded status [22,23]. Shock wave trains will be formed in the flowfield to match the pressure of jet and ambient. If operating NPR is low enough, the shock waves will move into the nozzle [24]. The strong adverse pressure gradient will cause boundary-layer separation, which interacts with shocks and gives rise to complex phenomena [25–27]. Papamoschou et al. found out the symmetric separation and asymmetric separation in over-expanded nozzle experiments and numerical simulation results, and confirmed the unsteady shock motion existed [28]. They pointed that shock motion unsteadiness contributed to the increased shear-layer instability, whereas the mixing enhance-
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ment was not due to the wave pattern [29]. Verma and Manisankar analyzed the origin of flow asymmetry in planar nozzles with separation [30]. Depending upon the local flow condition, the flow can experience either an early separation or a delayed separation resulting in either an FSS or an RSS. Verma et al. [31] analyzed the shock unsteadiness in a supersonic over-expanded planar nozzle. The study showed that the length of the intermittent region decreasing significantly as the boundary layer state transfers to the transitional regime. The asymmetric separation also exits in isolator and combustion. Separation transitions are found in the combustion cold flow experiment, and there is a lag between the boundary layer transformation and the separation transition [32]. The asymmetry separation also has been found in transonic channel flows by Bruce et al. [33], which was induced by the interaction of corner flow. In a single expansion ramp nozzle (SERN), the asymmetry separation and separation pattern transitions have been found in cold flow experiments [34]. Two separation patterns, RSS(ramp) and RSS(flap), have been observed in the experiments. In the RSS(ramp), the restricted separation bubble forms on the expansion ramp of the SERN, and the recirculation zone on the flap is filled by ambient air. The flow in the RSS(flap) separates from both the expansion ramp and the flap, and reattaches to the flap, forming a separation bubble. In the FSS, nozzle jet separates from both expansion ramp and flap but does not reattach to the wall. There is a transition from RSS(flap) to RSS(ramp) in the startup process, whereas the pattern transition from RSS(ramp) to RSS(flap) in the shutdown process. The separation transition process lasts less than 5 ms, and the hysteresis exists in startup and shutdown processes. Because of the flowfield alternation, the performance of the nozzle changes a lot in separation pattern transition [35]. Compare to the separation in isolator and combustion, normal shock occurs in the nozzle jet, and the separation zone will interact with external flow. As a result, the external flow will make significant influences on the over-expanded separation flowfield [36]. Mousavi et al. [37] found that the distances between Lambda shocks are different at two external flow Mach number. From the numerical simulation results, it could be found that external flow Mach number would affect the separation patterns of SERN [38]. Although external flow makes excellent influences on the overexpanded flowfield in SERN, few investigations have been conducted to analyze the phenomenon and the mechanism. This paper aims to present a detailed description of separation patterns transitions caused by external flow Mach number variation, analyze the mechanism of separation transitions. In the following sections, the accelerating and decelerating processes of a long flap SERN will be discussed.
where μ is the molecular viscosity, I is the unit tensor, and the second term on the right hand side is the effect of volume dilation. The turbulence model uses a mathematical technique known as “renormalization group” (RNG) methods, derived from the NavierStokes equations. The RNG k − ε model is similar to the standard k − ε model, but includes the refinements: improving the accuracy for rapidly strained flows, enhancing accuracy for swirling flows and providing an analytical formula for turbulent Prandtl numbers. Because of these features, RNG k − ε model are more accurate and reliable for a wider class of flows than the standard k − ε model. The transport equation of turbulent kinetic energy k can be written as follows:
∂ ∂ ∂ (ρ k ) + (ρ ku i ) = ∂t ∂ xi ∂xj The transport equation of
∂ ∂ ∂ (ρε ) + (ρε u i ) = ∂t ∂ xi ∂xj
∂k αk μeff ∂xj
ε is:
∂ε αε μeff ∂xj
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+ G k − ρε
(4)
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The term G k represents the production of turbulence kinetic energy. From the exact equation for the transport of k, this term may be defined as:
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(6)
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To evaluate G k in a manner consistent with the Boussinesq hypothesis,
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G k = μt S 2
(7)
where S is the modulus of the mean rate-of-strain tensor, defined as
S=
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2S i j S i j
(8)
μeff = μt = C μ ρ
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ε
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The effective viscosity is calculated by
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(9)
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3. Geometry, grid and validation
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2. Computational framework The computational modeling is based on time-averaged NavierStokes equations. Flow is governed by continuity and conservation of momentum equations, and the continuity equation can be written as follows:
∂ρ + ∇ · ρ v = 0 ∂t
(1)
Conservation of momentum can be described by
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(2)
The stress tensor τ¯¯ is given by
τ¯¯ = μ
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(3)
In this research, a straight expansion ramp SERN is considered for investigation, and geometry of the SERN is the same as Ref. [34]. The critical design parameters of straight ramp SERN are the height of the throat, the expansion area ratio, the length of the flap, and the angle of expansion ramp. The height of the throat determines the mass flow rate of the nozzle. The expansion area ratio is dependent on the design nozzle pressure ratio. The angle of expansion ramp influences the initial expansion angle of flow, as well as the length of the nozzle. The numerical method is validated by the experimental data reported in Ref. [34]. The experiments were conducted at the Internal Flow Research Center of Nanjing University of Aeronautics and Astronautics (NUAA). The facility utilizes a cold blow down wind tunnel. The geometry of SERN and the experimental SERN model is shown as Fig. 1. The expansion area ratio is 2.896, the angle of expansion ramp is 25◦ , and the height of the throat is 20 mm. The throat area was 1200 mm2 , and the flow path is 60 mm wide. The 2D numerical method could get well results of the flowfield at the symmetry plane.
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.3 (1-11)
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Fig. 1. Experimental model of the SERN in Ref. [34].
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Fig. 2. Grid regions of the SERN for numerical simulation.
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Fig. 4. Thrust variations with different time steps. Fig. 3. Numerical and experimental wall pressure distribution of test model.
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The geometry of the SERN has been meshed by ICEM with structured mesh. The grid is shown in Fig. 2. The node distributions in x and y directions of regions 1, 2, and 6 are 100×180, 140×180, and 140×80, respectively. The node distributions in regions 3, 4, and 5 are 70×140, 30×140, and 140×140. The node distributions in regions 7 and 8 are 70×80 and 180×80. The y + location in the simulation varies in the range of 10–50. In the over-expanded flowfield, the separation phenomena are involved. Separation and reattachment occur in SERN, and the flow speeds
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are quite different between the main jet and separation bubble. As a result, the y + location varies to a large degree. The grid case used above is defined as the medium grid case, and the node distributions in x and y directions are increased by a factor of 2, defined as the fine grid, and then decreased by a factor of 0.5, defined as the coarse grid. Commercial CFD software FLUENT is used. The results of the pressure contributions on expansion ramp and flap are shown in Fig. 3. The results of CFD and experiment fit well, and the medium grid is chosen for the simulation. The k-ε RNG model is also validated in Ref. [38].
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.4 (1-11)
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Fig. 5. Over-expanded separation flowfield of the long flap SERN in static ambient.
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Fig. 6. Steady simulation results of long flap SERN, increasing the external Mach number in steps, NPR=3.4.
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In the calculation, time steps 1×10−4 s, 5×10−5 s, and 2×10−5 s have been used to simulate the separation pattern transition in static ambient. The length of the nozzle is 52.9 mm, the maximum velocity in the nozzle is about 520 m/s, and therefore the timescale is about 1×10−4 s. Fig. 4 shows the results of thrust changes in the separation transition process with various time steps. It can be found from the figure that the thrust changes of different time steps are the same before and after the transition, and the transition pressure ratios of 5×10−5 s and 2×10−5 s are almost the same, so time step size 5×10−5 s has been chosen in the simulation.
4. Results and discussion
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4.1. Transition process of accelerating
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Limited by laboratory conditions, it is difficult for nozzle test wind tunnel to simulate external flowfield in general, and most nozzle test experiments are conducted in a static environment. However, the nozzle jet will interact with external flow under real flight conditions. When SERN works under design condition and under-expanded condition, flow downstream throat is supersonic, and therefore External flow cannot influence the flowfield inside
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.5 (1-11)
Y. Yu / Aerospace Science and Technology ••• (••••) ••••••
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Fig. 7. Performance variations of the long flap SERN in the accelerating process, NPR=3.4, Ma∞ = 0.1∼1.1.
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the nozzle. Under severely over-expanded conditions, some subsonic region, such as separation bubble, recirculation zone, and subsonic boundary layer, appears in SERN, shown as Fig. 5. Consequently, external flow will make significant influences on the subsonic region, for instance, the position of the separation and reattachment point, and the scale of the separation bubble and recirculation zone. Furthermore, movements of separation point and reattachment point, variations of separation bubble, and recirculation zone will affect the structures of shock waves in SERN directly, which might even cause separation pattern transitions. Accordingly, it is worth concerning the over-expanded flowfield variations and separation pattern transitions caused by external flow Mach number increasing and decreasing. The steady simulation results are shown by the contours of Mach number in Fig. 6. NPR is 3.4 and only Mach number of far-field boundary is altered in the simulation. At the Mach number of 0.1, the nozzle works as RSS(ramp) pattern. As the Mach number increases to 0.4, the separation bubble on expansion ramp alters to the recirculation zone, and the separation pattern changes from RSS(ramp) to FSS. Accordingly, a separation pattern transition, RSS(ramp) to FSS, will happen when the external flow Mach increases from 0.1 to 0.4. As the Mach number increase to 1.0, the recirculation zone on the flap disappears, and the recirculation zone on the expansion ramp becomes very small. From the above results, it could be found that external flow will affect the position of separation point and shape of the recirculation zone, which will affect the nozzle performance. In an accelerating flight, external Mach number increases continuously. In the simulation, total pressure at nozzle inlet and ambient pressure remain unchanged. NPR keeps 3.4, and then increases far-field Mach number 1.0/s. The process of external Mach number increasing from 0.1 to 1.1 has been simulated. Variations of thrust, lift, and moments in the accelerating process are shown in Fig. 7. The thrust, lift, and moments are nondimensionalized by the initial values at external Mach number 0.1. It could be observed obviously that the variations of thrust, lift, and moments can be divided into several stages. In stage (a), the SERN works as RSS(ramp), and the separation point moves downstream with external Mach number increasing, so thrust, lift, and moments all descend. The separation pattern transition from RSS(ramp) to FSS happens between stage (a) and (b). The process of RSS(ramp) to FSS transition is shown in Fig. 8. In the transition, the separation bubble becomes unclosed and transfers to the recirculation zone. At the beginning of stage (b), the reattachment point is near the tail of the expansion ramp, but the flow cannot always reattach to the
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expansion ramp. With the external Mach number increasing, the separation bubble transfers to the recirculation zone, and external air gets into the recirculation zone. In the long flap SERN, a large recirculation zone is formed on the flap as well. In the recirculation zone, flow speed and density are low, so the momentum is quite limited. Consequently, the shape of the recirculation zone can be changed easily by nozzle jet deflection, and the RSS(ramp) to FSS transition is evident in the long flap SERN. Fig. 9 shows the interaction between the nozzle jet and external flow at an expansion ramp tail. The flowfield is similar to a twostream flow convergence at a wedge. The stream on the upper side is subsonic, Ma1 < 1, which is external flow. The stream under the lower side is supersonic, Ma2 > 1, which is nozzle jet along the expansion ramp. The two streams converge at the tail of wedge, and then flow downstream along the same direction. Because the speeds of two streams are different, a slip line is formed in the flowfield. The control volume in the subsonic stream is shown as Fig. 9. The flow direction is vertical to the inlet section and outlet section. The flow direction is horizontal at the inlet section, but a vertical velocity component is formed at the outlet section. It can be known from the theorem of momentum that an upward force emerges on the slip line. When Ma1 increases, the momentum of the upper flow becomes higher, and the converged flow deflects downward. For the supersonic part, the flow downstream shock S 1 deflects downward, which will strengthen the shock S 1 and cause P 4 / P 2 rising. In the converged flow, P 4 is equal to P 3 , and P 3 changes little at low Mach number. As a result, P 2 must decrease to match the flowfield. For RSS(ramp) pattern, only the separation point and reattachment point moves downstream will cause the pressure drop at the exit. On another side, the upstream flow cannot be influenced by downstream flow in the supersonic flowfield. Under the design and under-expanded conditions, the external flow makes little influence on the flowfield in the nozzle. However, when the nozzle works under severely over-expanded conditions, subsonic separation zone is formed on the expansion ramp, and the subsonic boundary layer is thick downstream the reattachment point. Through the subsonic part in the nozzle, the influences of external flow could transmit to the internal flowfield. With external flow Mach number increasing, external flow and nozzle jet deflects downward. Meanwhile, the separation and reattachment point on expansion ramp moves downstream, and the pressure in the separation bubble dropped with external Mach number increasing. When the reattachment point moves to the tail of the expansion ramp, the external flow starts to get into the recirculation zone, and the separation pattern transfers from RSS(ramp) to FSS. In stage (b), the pressure in the recirculation zone is increasing gradually because the external flow gets into the recirculation zone. Besides, the separation point moves upstream, and the thrust, lift, moments are increasing. In early stage (b), the channel for external flow getting into the recirculation zone is narrow, so the pressure in the recirculation zone increases slowly. When the recirculation zone is fully developed, the separation point does not move upstream any longer. Then the separation point starts to move downstream with the external Mach number increasing, and stage (c) begins. In stage (c) (d) and (e), the separation point on expansion ramp moves downstream continuously. For the SERN, thrust only depends on the pressure distribution of the expansion ramp. For the certain NPR, closer separation point to the tail, worse thrust performance for the nozzle. Accordingly, the thrust decreases continuously with the separation point moving downstream continuously. As shown in Fig. 10, the external flow needs to deflect a greater angle to enter the recirculation zone, and a pair of vortex is formed between external flow and nozzle jet. One vortex is at the tail of the flap, and the other is in the recirculation zone. With the external Mach increasing, the nozzle jet
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.6 (1-11)
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Fig. 9. Scheme of the interaction between nozzle jet and external flow at expansion ramp tail.
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Fig. 10. Recirculation zone on the flap.
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deflects downward and compresses the recirculation zone on the flap, which caused more loss for external flow entering the recirculation zone. Consequently, the pressure in recirculation zone drops, and the thrust of the nozzle decreases fast in stage (d) and (e). Unlike thrust, lift, and moment depend on the pressure distributions of both expansion wall and flap, so the variation trend of lift and moment may be different from thrust. From the simulation results, lift and moment variation trend is similar. In stage (c), lift and moment increase slowly, but in stage (d), lift and moment decrease. In stage (e), when the external Mach number reaches about 0.95, the lift and moment increase again. It is because the local supersonic region is formed in external flow near the nozzle exit. The local supersonic region causes some disturbance to the pressure in the recirculation zone on the flap. When the supersonic region is fully developed, the flow returns to normal, and the lift and mo-
ment decrease gradually. With the separation point on flap moving downstream, the space of recirculation zones is compressed. At the same time, the channel between the nozzle jet and tail vortex becomes narrower. When nozzle jet and external tail vortex meet together, external flow cannot get into the recirculation zone any longer. As a result, the recirculation zone cannot keep on the flap, and the separation point on flap moves downstream rapidly until to tail. The shock wave formed on the flap transfers from the separation shock to the tail shock. Without the restriction of the separation shock on the flap, the separation shock on expansion ramp moves downstream as well, but the shock wave does not reach to tail, and there is still a small recirculation zone on expansion ramp. This recirculation zone is enclosed by expansion ramp, nozzle jet, and external flow. Therefore the external cannot get into
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.7 (1-11)
Y. Yu / Aerospace Science and Technology ••• (••••) ••••••
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Fig. 11. Transient simulation results of the accelerating process, the separation shock to tail shock transition on the flap, NPR=3.4.
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the recirculation zone. In this process, the flowfield changes a lot, which causes the performance of nozzle a step change. The process of shock wave transition from separation shock to tail shock is shown in Fig. 11. In this transition process, external flow and nozzle jet are both supersonic, but the space between nozzle jet and external flow forms subsonic recirculation zone. At the beginning of the transition, external flow can get into the recirculation zone, and the recirculation zone induces the separation shock. With external Mach number increasing, the separation shock moves downstream, and external air is difficult to enter the recirculation zone. When the recirculation zone on flap gets enclosed, the recirculation zone cannot maintain, and the separation shock moves downstream rapidly. In the transition, the reflection pattern of separation shock and tail shock transfers from regular reflection to Mach reflection (Fig. 11.b), and then transfers to regular reflection at the end (Fig. 11.c). After the transition, the recirculation zone on the expansion ramp is relatively stable, and the performance of the nozzle does not change suddenly anymore. From the simulation results and discussions above, it can be known that the separation pattern transitions in the accelerating process are mainly caused by interactions of the recirculation zone, external flow, and nozzle jet. Because the momentum of the recirculation zone is low, the nozzle jet can deflect easily, and the separation pattern transition completes in a short time. In addition, the reflection pattern of separation shocks transfers as well, so there may be hysteresis between accelerating and decelerating processes.
4.2. Transition process of decelerating
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As the accelerating process, the steady simulation results should be cognized firstly. The steady simulation results are shown by the contours of Mach number in Fig. 12. The NPR is 3.4 and the simulation only alters the Mach number of far-field boundary. Only a small recirculation zone is formed on the expansion ramp at Ma∞ = 1.1. As the Mach number decreases to 0.93, the recirculation zone on the expansion ramp becomes more extensive, and external flow re-enters the recirculation zone. At this time, the jet does not separate from the flap, and the tail shock is formed. Significantly, this separation pattern does not appear in the accelerating process. Then the decelerating process of external Mach number decreasing from 1.1 to 0.2 has been simulated. In the simulation, the inlet total pressure and ambient pressure is unchanged, and the NPR remains 3.4. Then, decrease the Mach number of the far-field 1.0/s to simulate the decelerating process. Variations of thrust, lift, and moments in the decelerating process are shown as Fig. 13. It could be observed that the variations of thrust, lift, and moments have several stages. In stage (a), only a small recirculation zone is formed on expansion ramp, and the recirculation zone is relatively stable, so the separation point on expansion ramp moves slowly with the external Mach number decreasing. As a result, the performance of SERN degrades slowly. When the external flow and the jet cannot enclose the recirculation zone, external flow starts to enter into the recirculation zone, and the stage (b) begins.
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.8 (1-11)
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Fig. 12. Steady simulation results of the long flap SERN, decreasing the external Mach number in steps, NPR=3.4.
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Fig. 13. Performance variations in the decelerating process, NPR=3.4, Ma∞ = 1.1∼0.2.
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In stage (b), the recirculation zone on expansion ramp transforms from enclosed by external flow and nozzle jet, shown as Fig. 14(a), to opened with ambient, and shown as Fig. 14(c). At the beginning of the transition, the reflection of separation shock on expansion ramp and tail shock on flap transfers from regular reflection to Mach reflection. When the Mach stem fully develops, the external flow starts to enter into the recirculation zone, and the separation point moves upstream rapidly, which causes the nozzle performance improvement suddenly. The process of recirculation zone transition is shown in Fig. 14. After the transition,
the jet and the nozzle performance oscillates for a short time. In stage (c), the thrust, lift, and moments increase smoothly with the external Mach number decreasing. In stage (b) and (c), the shock wave on the flap is still at the tail, but the flap tail shock cannot remain with the external Mach number decreasing and the separation shock wave on expansion ramp moving upstream. When the tail shock on flap starts to move upward and transfers to separation shock, stage (d) begins, and the over-expanded flowfield transfers from the only recirculation zone on expansion ramp to both the recirculation zones on expansion ramp and flap. The process of transition is shown as Fig. 15. With the external Mach number decreasing, the separation point and the separation shock on expansion ramp moves upstream. The interaction point of separation shock and tail shock gets closer to the nozzle, which makes the length of tail shock shorter. Besides, the type of shock wave reflection transfers from regular reflection to Mach reflection. When the strength of tail shock cannot maintain the Mach reflection, the separation shock on flap moves upstream rapidly and the tail shock transfers to separation shock. After the transition, it is the typical FSS pattern flowfield in which both recirculation zones are on expansion ramp and flap. In this transition, a separation shock is formed on the flap, and nozzle jet deflects upward. As a result, the space of the recirculation zone on the expansion ramp is compressed, but it has little influence on the pressure in the recirculation zone. The separation point on expansion ramp moves downwards a little, and the performance degrades a little. However, the pressure distribution on flap changes a lot caused by the recirculation zone formed after the transition. The static pressure in the recirculation zone is much higher than
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.9 (1-11)
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the overexpansion part, so the lift and the moments of the nozzle have a sharp decline. In the whole decelerating process, the FSS pattern is a relatively stable over-expanded flowfield pattern, and it lasts for a long time. The FSS-RSS(ramp) transition, stage(e), happens at a low external Mach number, and the process of the transition is shown in Fig. 16. Before the transition, the nozzle jet deflects upwards with the external Mach number decreasing. The recirculation zone on the expansion ramp is compressed, which caused the difficulties for external flow entering into the recirculation zone. As a result, the pressure in recirculation zone decline, the separation point on expansion ramp moves downstream, and the performance of nozzle degrades. Finally, the FSS-RSS(ramp) transition happens, which caused the recirculation zone getting closed and transferring to the separation bubble. Compared to the accelerating process, the decelerating process is not just the inverse process. The new over-expanded flowfield pattern appears in decelerating process. Meanwhile, there is an apparent hysteresis between accelerating and decelerating processes. Table 1 shows the differences between the accelerating and decelerating processes in transition A and B marked in Fig. 7 and Fig. 13. It could be found that the external Mach number of transition A and B is quite different, especially the transition A, although the performances of the nozzle are similar. In the separation pattern transition, the types of shock waves and shock reflections are changed at the same time. The conditions which cause the shock waves and the reflection alternation are different between acceler-
ating and decelerating processes. As a result, there is a hysteresis between the accelerating and decelerating processes.
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5. Conclusions
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In this article, the processes of over-expanded SERN accelerating and decelerating have been studied by numerical simulation. The separation pattern transitions caused by external flow variation have been described in detail. The mechanisms of the separation transitions and the performance of SERN influenced by separation transitions have been discussed. From the results, the following conclusions can be drawn:
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(1) Compared to the over-expanded flowfield in SERN without external flow, free shock separation (FSS) is a stable separation pattern and lasts for a long time in accelerating and decelerating processes. (2) In the accelerating process, the transition from RSS(flap) to FSS occurs firstly, and then the FSS transfers to tail shock pattern. (3) In the decelerating process, a new kind of separation transition occurs, and the transition of tail shock pattern to FSS has been decomposed into two steps. Firstly, the flowfield transfers from tail shock pattern to only tail shock on flap and recirculation zone on the expansion ramp. Secondly, the flowfield transfers to typical FSS with both recirculation zones on expansion ramp and flap. (4) There is hysteresis between accelerating and decelerating processes. The external Mach numbers of the transition have con-
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[m5G; v1.261; Prn:8/01/2020; 16:22] P.10 (1-11)
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114
49
115
50
116
51
117
52
118
53
119
54
120
55
121 122
56
Fig. 16. Transient simulation results of the decelerating process, the FSS-RSS(ramp) transition, NPR=3.4.
57 59 60 61
Table 1 Comparison of thrust and external Mach Number of the separation transitions in the accelerating and decelerating processes.
62
Transition A
63 64 65 66
123 124
58
Accelerating Decelerating
siderable differences, but the nozzle performance at the transition point is similar.
Ma
Fx
Ma
Fx
1.029 0.938
100% 99.22%
0.197 0.184
100% 99.35%
126 127
Declaration of competing interest
Transition B
125
128 129
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
130 131 132
JID:AESCTE AID:105674 /FLA
[m5G; v1.261; Prn:8/01/2020; 16:22] P.11 (1-11)
Y. Yu / Aerospace Science and Technology ••• (••••) ••••••
1
Acknowledgements
2 3 4 5
This work is supported by the National Natural Science Foundation of China under Grant No. 11802124 and China Postdoctoral Science Foundation under Grant No. 2018M632306.
6 7
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