Influences of nozzle pressure ratio on flow characteristics of serpentine multi-stream supersonic nozzle

The serpentine multi-stream supersonic nozzle (SMSN) is adopted for the multi-stream exhausted system of the Adaptive Cycle Engine to enhance the stealth performance of next-generation fighter. In this paper, the effects of the nozzle pressure ratio (NPR) on the flow characteristics of the SMSN were studied using the numerical simulation method validated by experimental data. The serpentine configuration leads to the nonuniform pressure distribution. At the mixing position, the expansion and shock waves are generated due to the pressure difference. As the NPR increases, the flow separation and shock wave in the mixing section gradually weaken and disappear. The thrust coefficient rises first and then drops. Due to the flow separation under the design condition, the thrust coefficient is the largest at MPR=6 and TPR=2.272. As the MPR increases at TPR=1.893, the compression effect of the main flow is enhanced on the upper third flow. The thrust coefficient rises first and then drops, and reaches the maximum at MPR=6. As the TPR increases at MPR=5, the compression effect of the main flow is weakened on the upper third flow. The thrust coefficient rises first and then drops, and reaches the maximum at TPR=2.272.


Introduction
With the rapid development of the modern aircraft technology, the higher requirements have been put forward for the propulsion system performance of the next-generation fighters [1].The Adaptive Cycle Engine (ACE) has the advantages of both turbojet and turbofan, which allow the propulsion system to fulfill the multi-mission requirements [2].Generally, the ACE adopts the multi-stream configuration, and the propulsive efficiency is markedly increased by the flow control and management of the streams [3].Air Force Research Laboratory presents the three-stream ACE configuration in the project of Adaptive Versatile Engine Technology whose the multi-stream supersonic nozzle has the multiple advantages over the conventional nozzle [4].The stealth performance heightens utilizing the serpentine configuration [5].The jet noise is signally reduced by shielding the high-speed main flow from the low-speed third flow [6].In addition, the rectangular nozzle exit has the unique advantages in the integration with aircraft, infrared suppression and thrust vector control [7].Therefore, the multi-stream supersonic nozzles are essential in the ACEs equipped on the next-generation fighters.
In recent years, the numerous studies have been carried out on the multi-stream supersonic nozzles.Magstadt et al. [8] designed the multi-stream single expansion ramp nozzle with the unilateral third flow, and studied the flow structures under the design condition according to the experimental schlieren photographs.The results showed that the complicated shock and expansion waves are generated at the trailing edge of the splitter plate.Kan et al. [9] investigated the interactions of the flow structures.Rusher et al. [10] studied the aeroacoustic characteristics under the design condition and the influence of the third pressure ratio (TPR).The results denoted that the noise reduction was optimized by adjusting the TPR without losing the thrust performance.Stack et al. [11] investigated the flow features and the influence of the main pressure ratio (MPR).The results showed that the MPR affected the flow features markedly.Tinney et al. [12] designed the planar multi-stream supersonic nozzle with the bilateral third flow, and investigated the influence of the MPR on the aeroacoustic characteristics.The results denoted that the MPR had a significant influence on the far-field noise by affecting the flow structures.Hromisin et al. [13] investigated the aeroacoustic characteristics of the multi-stream supersonic nozzles with the different configuration of the third flow.The results demonstrated that the multi-stream supersonic nozzles with the bilateral third flow were more advantageous to minify the mixing noise, and the unilateral third flow were able to eliminate the broadband shock noise completely.So far, the researches on the multi-stream supersonic nozzle are mainly aimed at the aeroacoustic characteristics and the influence of the flow features.Little attention has been paid to the aerodynamic performance of the multi-stream supersonic nozzle, and the multistream supersonic nozzle with serpentine configuration has not been considered.
With the advancement of the infrared and radar detectors, the super stealth feature has been essential for the next-generation fighters to complete the military missions [14].The engine exhaust system reflects the strongest infrared signature and main radar cross section in an aircraft [15].The serpentine nozzles have the unique advantages for reducing the infrared signature and radar cross section of the exhaust system.Therefore, it is indispensable to adopt the serpentine configuration on the multi-stream supersonic nozzles equipped on the next-generation aircrafts.Cheng et al [16] studied the influence of the shield ratio on the infrared signature of the serpentine nozzles.The results denoted that the infrared signature is minimum when the high-temperature components is completely shielded by the serpentine configuration, whereas the axial thrust reduced by 7.59% compared to the axisymmetric nozzle.Sun et al. [17] investigated the flow characteristics of the serpentine nozzles.The results showed that the aerodynamic parameter distributions in the serpentine nozzles were nonuniform.The above researches indicated that the serpentine configuration had a large impact on the flow features of the multi-stream supersonic nozzles, which were closely related to the aerodynamic performance.
In this paper, the effects of the nozzle pressure ratio (NPR) on the flow characteristics of the serpentine multi-stream supersonic nozzle (SMSN) were studied using the numerical simulation method validated by experimental data.First of all, The geometric model of the SMSN is described.Then, the numerical simulation method used in this study is introduced in brief and validated by the experimental data.At last, the effects of the NPR, MPR and TPR on the flow characteristics of the SMSN are investigated.

Geometric model description
As shown as in Figure 1, the SMSN is made of the main flow passage and the bilateral third flow passages.The main flow passage is a serpentine convergent-divergent nozzle, and the third flow is introduced in the divergent section.The ratio of the nozzle length (L) to the inlet diameter (D) is 2.5.The length ratio of the divergent section to the convergent section is 1.5.The mixing position is located at x/D=1.8.The origin coordinate is at the center of the main flow inlet.The main flow passage is constituted based on the serpentine centerline and a sequence of cross sections along the centerline.The centerline starts and ends on the x-axis, and the serpentine configuration is mainly embodied by the serpentine centerline structured on the basis of the Lee curve equations [18].The ratio of the offset distance to the inlet diameter is 0.4.The cross sections transition continuously from the circular inlet to the rectangular throat by the diverse parameters coupled method [17].The area ratio of the throat to the inlet is 0.413.The aspect ratio of the throat is 4. The crosssectional shape of the other sections are rectangular with the same width, and the Lee curve equations are also employed for the transition of the cross-sectional height.The area ratio of the exit to the throat is 1.346.The MPR is 5.0 at the perfectly expanded condition.
The bilateral third flow passages are convergent.The TPR is 1.893 at the design condition, which is the critical pressure ratio of the convergent nozzle.The cross sectional area of the third flow passage are such that the one-dimensional static pressure balance between the main and third flow is satisfied after the mixing position at the design condition.The area ratio of the third flow exit to the main flow throat is 0.3.

Numerical simulation method
The commercial software ANSYS Fluent is used to simulate the flowfield of the SMSN.The coupled pressure-based algorithm is used to solve the three-dimensional, steady compressible Reynoldsaveraged Navier-Stokes equations.The turbulence model selects the BSL k-ω turbulence model.The upwind second-order scheme is employed to solve the spatial discretization of the convection terms.The working fluid is an ideal gas.
The structured computational grids of the SMSN are generated using the commercial software ANSYS ICEM CFD, and the computational domain and boundary conditions are shown in Figure 2. Because the geometric model of the SMSN is bilateral symmetrical, the computational domain is half of the model for reducing the computational cost.The symmetry boundary condition is implemented on the symmetry plane.The dimensions of the external domain are 20D×10D×10D.The pressure farfield boundary condition is applied at the upstream and lateral surfaces of the external domain.The ambient pressure (P a ) is 101325Pa, and the ambient temperature is 288.15K.The Mach number of the external flow is 0.05.The pressure outlet boundary condition is specified on the downstream surface of the external domain.The back pressure is given as same as the ambient pressure.The pressure inlet boundary conditions are implemented on the main flow inlet and third flow inlets whose total pressure are confirmed according to the MPR and TPR.Moreover, the total temperature, turbulent intensity and turbulent viscosity ratio are 288.15K,5% and 10 respectively.The no-slip adiabatic wall boundary condition is applied at the wall surfaces, near which the first cell height is set as 0.005mm with the target y+=1 for satisfying the requirement of the BSL k-ω turbulent model.For validating the numerical simulation method, the computational data are compared with the experimental data of the planar multi-stream supersonic nozzle in the reference [12].The comparisons of the wall static pressure between the computational and experimental data are displayed in Figure 3.It can be seen that the computational wall static pressure agrees with the experimental data well, in particular the location of the shock wave and separation point.The maximum relative error in the wall static pressure is less than 2%.Therefore, the numerical simulation method is feasible to simulate the flow characteristics of the SMSN accurately.

Effects of the NPR on the flow characteristics
The MPRs and TPRs at the different NPRs are listed in Table 4.The ratio of the MPR to the TPR is always the same as that under the design condition.The MPR and TPR are 5 and 1.893 under the design condition, respectively.The MPR and TPR are 3 and 1.136 at NPR=3.The MPR and TPR are 4 and 1514 at NPR=4.The MPR and TPR are 6 and 2.272 at NPR=6.The MPR and TPR are 7 and 2.65 at NPR=7.The MPR and TPR are 8 and 3.029 at NPR=8.The Mach number and static pressure distributions on the symmetry plane of the SMSN at the different NPRs are shown in Figure 4 and Figure 5, respectly.Since the third flow mixes with the supersonic main flow in the divergent section, the third flow does not affect the main flow upstream.The Mach number distributions of the main flow are similar before the mixing section.Because the centripetal force is provided by the pressure difference to deflect the streamline in the SMSN, the airflow accelerates at the inner side of turnings, and decelerates at the outer side of turnings.The static pressure decreases at the inner side of turnings, and increases at the inner side of turnings.

Effects of the MPR on the flow characteristics
The value of TPR is fixed at 1.893, consistent with the design condition.The MPR ranges from 4 to7.The Mach number and static pressure distributions on the symmetry plane of the SMSN at the different MPRs are shown in Figure 10 and Figure 11, respectly.Since the third flow mixes with the supersonic main flow in the divergent section, the third flow does not affect the main flow upstream.The Mach number distributions of the main flow are similar before the mixing section.At MPR=3, the static pressure of the upper third flow is higher than that of the main flow at the mixing section.The discharge coefficients of main and third flow at the different MPRs are shown in Figure 14.As the MPR increases, the flow features of the main flow remains unchanged before the mixing section.The discharge coefficient of the main flow is basically constant.The discharge coefficient of the third flow is determined by the discharge coefficients of the upper and lower third flow together.Because the discharge coefficient of the upper third flow drops, and the discharge coefficient of the lower third flow is basically constant.Therefore, the discharge coefficient of the third flow drops.The discharge coefficient is reduced by 66%.The thrust coefficients of the SMSN at the different MPRs are shown in Figure 15.As the MPR increases to 5, the flow losses are reduced since the shock waves and flow separation inside the SMSN weaken.The thrust coefficient of the SMSN rises.At MPR=5, the static presssure at the nozzle exit is partially lower than the ambient pressure.As the MPR increases to 6, the static presssure at the nozzle exit rises.The static presssure difference between the nozzle exit and the ambiente decreases.The over-expanded extent weakens.The thrust coefficient continues to rises.As the MPR increases further, the flow losses increase.The pressure energy of the airflow cannot be fully converted into kinetic energy.The thrust coefficient of the SMSN drops.As the NPR increases, the thrust coefficient first increases and then decreases.The thrust coefficient is the largest at MPR=6.

Conclusions
The paper investigated the effects of the nozzle pressure ratio (NPR) on the flow characteristics of the serpentine multi-stream supersonic nozzle (SMSN).the effects of the NPR, MPR and TPR on the flow characteristics of the SMSN are investigated using the numerical simulation method validated by experimental data.The main conclusions are as follows: (1) The flow features are similar under the different NPRs when the ratio of the main pressure ratio (MPR) to the third pressure ratio (TPR) is always consistent with those under the design condition.The serpentine configuration leads to the nonuniform pressure distribution.At the mixing position, the expansion and shock waves are generated due to the pressure difference.The upper third flow is compressed by the main flow, and its passage is convergent, while the the lower third flow passage is divergent.
(2) The discharge coefficient of the upper third flow is always lower than that of the lower.As the NPR increases, the flow separation and shock wave in the mixing section gradually weaken and disappear.The discharge coefficients of the main and third flow are basically constant when the NPR is higher than 5.The thrust coefficient rises first and then drops.Due to the flow separation under the design condition, the thrust coefficient is the largest at MPR=6 and TPR=2.272.
(3) As the MPR increases at TPR=1.893, the compression effect of the main flow is enhanced on the upper third flow.The discharge coefficient is reduced by 66%.The flow separation of the lower third flow is gradually weakened and disappeared.The thrust coefficient rises first and then drops, and reaches the maximum at MPR=6.
(4) As the TPR increases at MPR=5, the compression effect of the main flow is weakened on the upper third flow.The discharge coefficient of the upper third flow rises by 112%.The thrust coefficient rises first and then drops, and reaches the maximum at TPR=2.272.

Figure 1
Figure 1 Geometric model of SMSN.

Figure 2
Figure 2 Computational domain and boundary conditions.

Figure 3
Figure 3 Comparisons of wall static pressure between computational and experimental data.

Figure 4
Figure 4 Mach number distributions on symmetry plane of SMSN at different NPRs.

Figure 5
Figure 5 Static pressure distributions on symmetry plane of SMSN at different NPRs.The total pressure recovery coefficients (δ P ) of the SMSN at the different NPRs are shown in Figure 6.As the NPR increases to 6, the flow losses are reduced since the shock waves and flow separation inside the SMSN weaken.The total pressure recovery coefficient of the SMSN rises.As the NPR increases further, the flow features inside the SMSN remain unchanged.The total pressure recovery coefficient of SMSN is basically constant.The discharge coefficients (C D ) of upper and lower third flow at the different NPRs are shown in Figure 7.At NPR=3, the upper third flow passage is blocked by the flow separation.The discharge coefficient is so low.The lower third flow passage is divergent.The exit area is bigger than the designated exit area.The discharge coefficient is bigger than 1.As the NPR increases to 5, the upper third flow passage expands, and the lower is compressed by the main flow.The exit area of the upper third flow increases, and the exit area of the lower third flow decreases.The discharge coefficient of the upper third flow rises, and that of the lower drops.As the NPR increases further, The exit area of the upper and lower third flow remains unchanged.The discharge coefficients of upper and lower third flow are basically constant.Because the exit area of the upper third flow is less than that of the lower.The discharge coefficient of the upper third flow is lower than that of the lower at the different NPRs.The lower third flow accelerates to supersonic speed through the convergent-divergent passage.

Figure 6
Figure 6 Total pressure recovery coefficients of SMSN at different NPRs.

Figure 7
Figure 7 Discharge coefficients of upper and lower third flow at different NPRs.The discharge coefficients of main and third flow at the different NPRs are shown in Figure 8.As the NPR increases, the flow features of the main flow remains unchanged before the mixing section.The discharge coefficient of the main flow is basically constant.The discharge coefficient of the third flow is determined by the discharge coefficients of the upper and lower third flow together.At NPR=3, the upper third flow passage is blocked by the flow separation.The discharge coefficient of the third flow is mainly determined by the discharge coefficient of the upper third flow, and so low.As the NPR increases to 5, the discharge coefficient of the upper third flow rises, and the discharge coefficient of the lower third flow drops.The discharge coefficient of the third flow rises first and then drops.As the NPR increases further, the discharge coefficient of the third flow is basically constant.The thrust coefficients (C F ) of the SMSN at the different NPRs are shown in Figure 8.As the NPR increases to 6, the flow losses are reduced since the shock waves and flow separation inside the SMSN weaken.The thrust coefficient of the SMSN rises.As the NPR increases further, the pressure energy of the airflow cannot be fully converted into kinetic energy.The thrust coefficient of the SMSN drops.As the NPR increases, the thrust coefficient first rises and then drops.Due to the flow separation under the design condition, the thrust coefficient is the largest at MPR=6 and TPR=2.272.

Figure 8
Figure 8 Discharge coefficients of main and third flow at different NPRs.
The shock wave originates from the lip of the upper wall at the mixing position.The lower third flow passage is divergent.The main flow is compressed by the lower third flow at the mixing position.The shock wave originates from the lip of the lower wall at the mixing position.Because the static pressure of the lower third flow is lower than the ambient pressure, the flow separation and shock wave are induced by the adverse pressure gradient.As the MPR increases, the static pressure of the main flow raises.The third flow is compressed by the main flow.The upper third flow decelerates.The static pressure of the lower third flow raises.The flow separation weakens and disappears as the adverse pressure gradient weakens.The shock wave from the lip of the lower wall is replaced by the expansion wave at MPR=5.The shock wave from the lip of the upper wall disappears at MPR=6, and is replaced by the expansion wave at MPR=7.

Figure 10 Figure 11
Figure 10 Mach number distributions on symmetry plane of SMSN at different MPRs.

Figure 12
Figure 12 Total pressure recovery coefficients of SMSN at different MPRs.

Figure 13
Figure 13 Discharge coefficients of upper and lower third flow at different MPRs.

Figure 14
Figure 14 Discharge coefficients of main and third flow at different MPRs.

Figure 15 4 . 3 .Figure 16 Figure 17
Figure 15 Thrust coefficients of SMSN at different MPRs.4.3.Effects of the TPR on the flow characteristics The value of MPR is fixed at 5, consistent with the design condition.The TPR ranges from 1.514 to 2.65.The Mach number and static pressure distributions on the symmetry plane of the SMSN at the different TPRs are shown in Figure 16 and Figure 17, respectly.Since the third flow mixes with the supersonic main flow in the divergent section, the third flow does not affect the main flow upstream.The Mach number distributions of the main flow are similar before the mixing section.At MPR=3, the upper third flow passage is convergent, while the lower third flow passage is divergent.The lower third flow accelerates to supersonic speed.Because the static pressure of the lower third flow is lower than the ambient pressure, the flow separation and shock wave are induced by the adverse pressure gradient.As the TPR increases, the static pressure of the third flow raises.The third flow passages expand.The upper third flow accelerates.The static pressure of the lower third flow raises.The flow separation weakens and disappears as the adverse pressure gradient weakens.The shock waves at the mixing position are enhanced.The flow separation disappears at TPR=2.272.

Figure 18
Figure 18 Total pressure recovery coefficients of SMSN at different TPRs.

Figure 19
Figure 19 Discharge coefficients of upper and lower third flow at different TPRs.The discharge coefficients of main and third flow at the different TPRs are shown in Figure 20.As the TPR increases, the flow features of the main flow remains unchanged before the mixing section.The discharge coefficient of the main flow is basically constant.The discharge coefficient of the third flow is determined by the discharge coefficients of the upper and lower third flow together.Therefore, the discharge coefficient of the third flow rises by 112%.The thrust coefficients of the SMSN at the

Figure 20
Figure 20 Discharge coefficients of main and third flow at different TPRs.

Table 1
MPRs and TPRs at different NPRs.