Effect of U-shaped notches on nozzle performance and jet flow structures

In nacelle design, optimization of nozzle shape is crucial for flow control. To understand the effect of nozzle shape on its aerodynamic performance and jet flow structures, the numerical experiment is performed using the dual separate flow reference (DSFR) nozzle released by the Aero Systems Engineering (ASE) FluidDyne Laboratory. A pair of U-shaped notches are made on the nozzle. The results show that the discharge coefficient and thrust angle increase with the size of the notches in all the simulated operating conditions. The notches induce a pair of streamwise vortices, which enhance turbulent mixing and decrease turbulent kinetic energy in the mixing layer.


Introduction
Research on the impact of nozzle shape on jet flow structures can be traced back to the 1950s.Initially, the main focus of researchers was on the nozzles with "tabs", which are square-shaped protrusions.The tabs can effectively reduce jet screeching noise in supersonic conditions [1,2].The tabs induce streamwise vortices, which increase the turbulent mixing rate, reduce the jet centerline velocity, and decrease the length of the potential core [3][4][5][6][7].Subsequently, researchers found that the triangular cuts (chevrons) have more significant effects on jet noise reduction because they lead to stronger turbulent mixing effects and cause less drag [8,9].After extensive research, the nozzles with chevrons finally stepped into the engineering application stage [10,11].Nowadays, nozzles with chevrons are used on many civil aircraft models.
In recent years, the nozzles with two U-shaped notches have been employed on a new civil aircraft model.The notches follow a non-axisymmetric placement to the nozzle centerline, which leads to a certain flow-control function.To the author's knowledge, there are few studies focusing on this new type of nozzle.To further improve nozzle efficiency, research on this type of nozzle is urgent.Hence, a numerical experiment is performed in this study to explore the effect of the notched nozzle on its aerodynamic performance and jet flow structures.

Methodology
In this paper, numerical simulations are conducted to evaluate the aerodynamic performance of the DSFR nozzle.Its performance is compared with the results from the ASE Laboratory to verify the reliability of our numerical method.Besides, numerical simulations are performed on the nozzle with different notches to investigate their impact on the nozzle performance and jet flow structures.

Nozzle geometry
The DSFR nozzle used in this paper is released by the Dual Flow Reference Nozzle Working Group affiliated with the ASE FluiDyne Laboratory [12].Its aim is to provide aircraft/engine manufacturers and researchers with a benchmark for equipment testing and CFD comparison.As shown in Figure 1, the conical nozzle has separate fan flow and core flow from its inner and outer ducts with a bypass ratio between 10 and 12.The area of the fan flow exit is about 193.6  , while the area of the core flow exit is around 38.7  .The convergence angles of its core cowl and plug are 13° and 17°, respectively Besides, a pylon is installed on the nozzle, which results in the upper and lower bifurcators in the fan flow duct.Additionally, the simulations of the nozzle with three sets of notches are performed.The diagram of the notches and the coordinate system settings are shown in Figure 2. The geometric parameters of the notches are shown in Table 1.

Computational grids
In the numerical simulation, the full model of the DSFR nozzle is used to generate the unstructured grids (Figure 3(a)).The far field of the computational domain is rectangular, and the distance between two far-field boundaries in the X direction is 50 D (D is the diameter of the fan flow nozzle at the exit).The distance between the far field boundary in the ±Y or ±Z direction and the nozzle centerline is 12.5 D. The near-wall grids are hexahedral and prism, and the growth rate is 1.1 in the wall-normal direction. 3 The first layer of the near-wall grids is located at y 1.The girds far away from the wall are tetrahedral.In order to ensure minimal distinctions between the grids in our simulations, a subdomain in the flow field is set up near the nozzle exit (Figure 3

Governing equations and boundary conditions
In the numerical simulations, the governing equations are the three-dimensional Reynolds-Averaged Navier•Stocks (RANS) equations.In the Cartesian coordinate system, the equations are as follows: Where U is the velocity vector.F and G are the convection term and diffusion term, respectively.S is the source term.
In the present study, the numerical simulations use the CFX solver, and the finite volume method is employed to solve the integral form of the RANS equations.The spatial discretization uses the secondorder upwind scheme, and the time advancement scheme is fully implicit.The turbulence model used in the simulation is the k-ω SST model.
In the simulations, the inlet boundary condition is applied to the far field in the -X direction, the inlet of the fan flow, and the inlet of the core flow.The open boundary condition is applied to the far fields in the ±Y and ±Z directions.The outlet boundary condition is applied to the far field in the X direction.Besides, a no-slip boundary condition is implemented on the walls.The diagram of the boundary condition settings is shown in Figure 4.

Simulated operating conditions and evaluation of nozzle performance
The ASE Laboratory conducted wind tunnel tests and numerical simulations on the DSFR nozzle under seven operating conditions [12].The conditions are listed in Table 2, in which P , and P , are the total pressures at the inlets of the fan flow and core flow, respectively.P is the ambient pressure, which is equivalent to one standard atmosphere pressure.Under each operating condition (OC), the total pressure ratio (P , /P , ) is maintained at 1.2., the thrust coefficient C and the thrust vector angle  of each nozzle.The evaluation method of each parameter is introduced in the paper by the ASE Laboratory [12]./ , respectively.The N0-3 legends represent the CFD results of each nozzle, while the ASE_Exp and ASE_CFD legends represent the experimental results and CFD results from the ASE Laboratory [12].It can be seen from the figure that C , , C , , and C of the N0 nozzle follow the same trend as ASE Laboratory's results.Compared with ASE Laboratory's results of the N0 nozzle, the largest deviation of C , is reached at P , / 2.8, which is about 0.6%.The largest deviation of C , occurs at P , / 1.833 (corresponding to P , / 2.2), which is about 1.6%.The largest deviation of C is about 0.6%, while the largest deviation of θ occurs at P , / 1.4, which is about 0.09° (5.6%).The comparison shows that the present CFD results of the N0 nozzle are in good agreement with ASE Laboratory's results, which confirms the reliability of the numerical method used in this study.

Results of the nozzle performance evaluation
Since only the fan-flow nozzles are notched, it has a significant impact on C , (Figure 5(a)).Under each operating condition, C , of the notched nozzles is increased compared with the N0 nozzle, and the increase is proportional to the resection area.The notch leads to a higher fan-flow exit area, resulting in a higher discharge rate.Besides, the C , curves of N1-N3 nozzles show a trend of overall translation relative to the N0 curve, illustrating that changing the notch size can increase the discharge rate of the fan flow in a wide range of operating pressure.In Figure 5(b), a good uniformity of C , of N0-N3 nozzles is observed at P , / 1.833, indicating a minor impact of the notches on the core flow.Since Mach rings appears at P , / 1.833, the C , curves of N0-N3 nozzles tend to deviate from each other.As the thrust coefficient represents the efficiency of thrust generation, it can be seen that the N0 nozzle has the highest thrust efficiency under various operating conditions (Figure 5(c)).The nozzle notch affects the distribution of shear stress near the nozzle exit and results in an earlier expansion of the local jet flow.Hence, the local jet flow has higher momentum in the radial direction, which decreases the thrust coefficient.Besides, the notch has a significant effect on the thrust vector angle (Figure 5(d)).This effect is caused by the pair of notches located at one side of the X-Y plane.The N0 nozzle also leads to a certain thrust angle, but it results from the pylon, which decreases the speed of local flow.Taking the  curve of N0 as a benchmark, it can be seen that the effect of the notches on  is more evident at higher flow rates.In contrast, the jets from N1-N3 nozzles start to expand earlier, resulting in additional radial force.The Z-direction component of the radial force causes the thrust vector angle to increase while the notch area grows.As shown in Figures 6(a) and 7(a), the Mach number distributions of both nozzles are basically symmetrical, indicating good convergence of the simulations is achieved.However, the Mach number shown in Figure 7(a) is generally lower, which may be caused by the influence of the notch.Figure 6(b) shows the asymmetric Mach number distribution caused by the pylon.The pylon shortens the highspeed region out of the fan-flow nozzle and affects the direction of local jet flow.Taking the distribution in Figure 7 (a) as a benchmark and comparing it to Figure 7(b), it can be seen that the high-speed jet flow tends to persist longer, but the high-speed region is still shorter than the flow far from the pylon at this cross-section.In addition, the radial flow expansion is observed in the high-speed region behind the notch.The radial expansion is more evidently shown in the Y-Z cross-sectional view.The notch causes a radial protrusion in the Mach number distribution at X=0.5 D (Figure 7(c)).The local high-speed flow mixes with the nearby flow while it develops downstream and finally forms a ∇-shaped distribution (Figure 7(f)).For the N0 nozzle, the Mach number distributions at all Y-Z cross-sections are symmetric.However, there are high-speed regions at X=0.5 D due to the influence of the pylon, while high-speed flow develops downstream and mixes, it eventually forms a circular and symmetric Mach number distribution at D=5.5 D (Figure 6

Concluding remarks
This study investigates the effect of notches on nozzle performance and flow structures.The main conclusions are as follows: 1) The notch can increase the jet rate and net thrust at all simulated operating conditions, but it reduces the thrust coefficient of the nozzle.The notch has a significant impact on the thrust angle, which is caused by the radial expansion of the jet near the notch.2) The notch extends the high-speed region in the jet flow.Hence, the Mach number distributions in the view of the streamwise direction develop from a circular shape with two protrusions to a ∇ shape.
3) The notch significantly reduces the TKE in the shear layer.
4) The notch induces a pair of vortices into the jet flow, which enhances the turbulent mixing.

Figure 2 .
Figure 2. Geometry of the notch and coordinate system.

Figure 5
compares the performances of N0-3 nozzles with the experimental data from the ASE Laboratory.Figures5(a)-5(d)show the variations of C , , C , , C and θ with P , / or P ,

Figure 5 . 4 . 4 .
Figure 5. N0-N3 nozzles performance.4. Effect of the notches on the jet flow field Figures 6 and 7 show the Mach number distributions at different cross-sections of N0 and N1 jets at the operating condition P , / 2.4.The cross-section in Figure 6(a) is the X-Y plane, and the crosssection in Figure 6(b) is 45° to the X-Y plane in the circumferential direction.The upper half of Figure 6(b) shows the region far from the pylon, where the local flow is less affected.The flow in the lower half of Figure 6(b) is close to the pylon and at the center of the notch on the N1 nozzle, where the local jet flow is affected by the notch and pylon.Figures 6(c), 6(d), 6(e), and 6(f) show the distributions at X=0.5 D, 2.5 D, 4.5 D, and 5.5 D, respectively.As shown in Figures6(a) and 7(a), the Mach number distributions of both nozzles are basically symmetrical, indicating good convergence of the simulations is achieved.However, the Mach number shown in Figure7(a) is generally lower, which may be caused by the influence of the notch.Figure6(b)shows the asymmetric Mach number distribution caused by the pylon.The pylon shortens the highspeed region out of the fan-flow nozzle and affects the direction of local jet flow.Taking the distribution in Figure7(a) as a benchmark and comparing it to Figure7(b), it can be seen that the high-speed jet flow tends to persist longer, but the high-speed region is still shorter than the flow far from the pylon at this cross-section.In addition, the radial flow expansion is observed in the high-speed region behind the notch.The radial expansion is more evidently shown in the Y-Z cross-sectional view.The notch causes

Table 2 .
Nozzle operating conditions.The present study evaluates the discharge coefficient of the fan flow C , , the discharge coefficient of the core flow C ,