- School of Aeronautics, Northwestern Polytechnical University, Xi’an, China

Blowing air at the end of the airport runway can accelerate the decay of the near-ground aircraft wake vortex, thereby reducing the negative impact of the vortex on the following aircraft. However, the benefits of accelerating wake dissipation vary for different blowing parameters, so it is necessary to set appropriate parameters in order to obtain better acceleration results. Because of the high cost of traditional optimization methods, this research uses a Kriging surrogate model to optimize the blowing parameters. The results show that the current optimization algorithm can deal with the global optimization problem well. After obtaining 205 sample points, the response surface model of the blowing parameters and blowing yield was accurately established. A relatively optimal parameter setting range was given, and numerical simulation shows that the current parameter setting can obtain improved benefits from accelerated vortex dissipation. In addition, since the optimization process is partially dimensionless, the above optimization results can be used to achieve multi-objective design, that is, the same set of blowing devices can efficiently accelerate the dissipative process of the tail vortices of different aircraft types, thus improving the engineering feasibility of the current blowing method.

## Introduction

### Wake Vortex Hazards

The lift of an aircraft originates from the interaction between the aircraft and the air. While the aircraft gains lift, the air will flow along the wing spanwise and form high-intensity aircraft wake vortices at the wingtips, which may lead to sudden lift loss or uncontrollable rolling for the trailing aircraft, with fatal effects. Due to the presence of the ground, the primary vortex induces secondary vortices, which have the opposite sign of vorticity and may drive the primary vortex rebound to the flight altitude [1]. Although the near-ground aircraft wake vortex pair will gradually move away from the flight path due to the induction of the mirror vortex, a crosswind with specific strength (e.g., when the height of the wake vortex is 1

In order to ensure the flight safety of civil aircraft, the existing measure is to control the flight distance between two adjacent approaching aircrafts. For instance, the International Civil Aviation Organization (ICAO) regulations ensure that when the preceding and following aircraft are heavy or medium types, the wake separation of the aircrafts should be 9.3 km [4], which corresponds to a time interval of more than 2 min. This method is certainly effective, but it also greatly restricts the growth of airport traffic, and when there are extremely unfavourable meteorological conditions for wake vortex dissipation, the current regulations still cannot guarantee the safety of the following aircraft.

### Methods on Wake Alleviation

Researchers have proposed three methods for wake vortex control. The first method, Low-Vorticity-Vortex (LVV), reduces the induced roll moment on the following aircraft by redistributing the load of the preceding aircraft [5, 6]. The second method, the Quickly-Decaying-Vortex (QDV), seeks to trigger stronger instability for the vortex pair by exerting perturbations [7, 8] or by constructing a multi-vortex system [9–11]. Numerical simulations and wind tunnel experiments have proved such improvements effective, at least within ten times the wingspan of the aft fuselage [6]. However, both of these methods require modifications on aircrafts themselves, which might negatively affect the flight performance.

The third method hopes to accelerate vortex pair dissipation by applying perturbations to the wake vortices after their roll-up process. Cho et al. proposed to configure the relative positions of the preceding and following aircraft so that their wake vortices would interact and dissipate into harmless turbulence more quickly [12]. Nevertheless, this method is only suitable for vortices at a relatively high altitude and requires a precise prediction of the position of the preceding wake vortex. The acceleration of aircraft wake dissipation by ground-based equipment was first proposed by Kohl. His wind-tunnel experiments confirmed the effectiveness of these methods [13]. Stephan et al. quantitatively investigated the ground obstacles effects on in-ground-effect (IGE) wake vortex, with Large Eddy Simulation (LES) and towing tank experiments. They found that the hairpin vortices generated by ground obstacles entangle the primary and secondary vortices together, which ultimately advance the rapid decay to a large extent [14]. In addition, numerical simulations and field measurements have demonstrated that impressive acceleration results can still be obtained after simplifying the columnar obstacle into a flat plate array [15, 16]. In 2020, field experiments at Vienna International Airport further confirmed the effectiveness of this approach: the use of flat plate arrays reduced the wake vortex lifespan by 21%–35% [17]. But as the obstacles placed near the runway are large in size (

### Present Study

To overcome the limitations of above methods, we investigated the effect of ground blowing on wake vortex dissipation. As an active flow control method, this strategy is able to reduce the lifespan of the IGE wake vortex without affecting flight safety. Numerical simulations indicated that although the direct effect of the blowing airflow on the vortices is limited, the starting vortex produced by the blowing air can develop into a hairpin vortex, inducing the interference between the primary and secondary vortices, and thus accelerating the wake dissipation [18]. Further, we have also investigated the blowing effect in crosswind conditions and screened for optimal blowing parameters [19].

Although increasing the blowing zone area and blowing velocity improves the blowing effect, maintaining a large flow rate consumes a huge amount of energy. With restrictions to the blowing flux and blowing zone area, a better choice—and the aim of this study—is to find a set of blowing zone parameters that can best enhance the wake decay through the blowing process. Since there is no analytical function between the blowing parameters and blowing effect, it is difficult to find an explicit optimal solution. On this basis, a surrogate model was adopted to approximate the relationship between blowing parameters and blowing effect. Different blowing aspect ratios and positions were tested. A rich number of sample points were used to establish the response surface, so that the optimal design of the blowing parameters could be estimated.

The structure of this paper is as follows: the first section introduces the research background; the second section introduces the numerical method adopted, the third section introduces and validates the surrogate optimization method; the fourth section demonstrates the optimization results; the fifth section presents the optimization settings for different aircraft types, and the final section is the summary.

## Numerical Backgrounds

### Turbulence Modelling

The numerical simulation in this paper was conducted by solving the incompressible Navier-Stokes equation. The finite volume method was used for spatial discretization. In order to capture the eddies in the flow, the Large Eddy Simulation (LES) method was used for turbulence modelling. The filtered incompressible Navier-Stokes equation can be written as Equations 1, 2:

where

The SIMPLE algorithm was used in the calculations to handle the pressure-velocity coupling, with both convective and diffusive terms discretized using the second-order central difference scheme. The unsteady term was advanced using the second-order implicit scheme.

### Boundary and Initial Conditions

In this study, the wake vortices of two types aircraft were considered, and the parameters are listed in Table 1. The characteristic time and time were obtained by

Figure 1 shows the computational domain of the LES simulations (

The height of the first layer of the mesh near the ground is 0.1 m (

The wake vortex pairs were initialised using the Lamb-Oseen model, which describes the velocity field as Equation 3:

*Optimization for Enhanced Wake Vortex Decay* section.

### Methods Validation

To validate the numerical methods, a numerical simulation was performed and the result was compared with the water-tank experiment data [14]. In the validation, the wake vortex of A340 was employed and the initial vortex height was reduced to *Boundary and Initial Conditions* section.

To evaluate the vortex strength decay history, the vortex centre was tracked by considering the local minimum pressure and the extreme vorticity values first. After that, the vortex circulation on a specify axial plane was obtained by Equation 4:

where

Figure 2 shows the comparison between the CFD result and the experimental data. Before

## Optimization Method

### Kriging Surrogate Model

Surrogate models, also known as response surface models, are approximate mathematical tools used as an alternative to complex numerical analysis, which reduce the difficulty of the optimization process. By learning from the sample data, the computer trains and fits a function mapping the relationship between the design parameters and the corresponding objective values that satisfy a certain accuracy range [21, 22]. The upper and lower bounds of the design variables

In the Kriging surrogate model, the actual function

The superscript

and

### Infill-Sampling Criteria

A parallel infill-sampling criteria combing two criteria was used to better approximate the real function. The first criterion, minimizing surrogate prediction (MSP), selects the minimum of the objective function obtained by the current surrogate model as the new sample point [23, 24]. The MSP sub-optimization problem with constraints can be written as Equation 11

The second infill-sampling criteria, expected improvement (EI), is also known as the efficient global optimization algorithm [25]. The standard EI function can be written as Equation 12:

In this study, the gradient optimization is combined with the Kriging surrogate model to conduct the optimization process. To be specific, the optimization process consists of the following steps:

1) initial sample points are chosen with the Latin hypercube sampling method and the functional responses are evaluated by CFD solver;

2) initial surrogate models for the objective and constraint functions are constructed based on the current samples;

3) parallel infill-sampling criteria combing the EI and MSP criterion is conducted to obtain new sample points, and the corresponding response values are obtained using CFD;

4) the surrogate model is updated, and the sub-optimization process is performed based on it;

5) steps 3 and 4 are repeated until the termination condition is satisfied.

### Benchmark Analytical Test Cases

To validate the above-mentioned optimization framework, three analytical test cases were used.

#### Rosenbrock Test Case

The Rosenbrock function has a minimum that lies in a “flat valley” (Figure 3C), around which the gradient value is small [24]. Thus, this case assessed the local optimization capability of the algorithm. The Rosenbrock function is expressed as Equation 13:

**FIGURE 3**. Rosenbrock function and the convergence history. **(A)** Convergence histories of 6 optimizations, **(B)** Average convergence histories of 30 optimizations, **(C)** Schematic of Rosenbrock function.

The optimization was performed 30 times and Figure 3 shows the convergence histories. In all calculations, when the number of the function evaluations (NFE) reaches 100, the predicted minimum of the function drops to the order of

#### Rastrigin Test Case

Rastrigin function is written as [22] Equation 14:

The optimal solution of the Rastrigin function is

**FIGURE 4**. Rastrigin function and the convergence history. **(A)** Convergence histories of 6 optimizations, **(B)** Average convergence histories of 30 optimizations, **(C)** Schematic of Rastrigin function.

#### Constraint Handling Test Case

In this case, two constraints are applied. As shown in Figure 5C, the feasible region is a narrow interval between the constraints, and the minimum of the objective function lies approximately in the middle of the feasible region. The optimization problem is described as [25] Equation 15:

**FIGURE 5**. Function of test case 3 and the convergence history. **(A)** Convergence histories of 6 optimizations, **(B)** Average convergence histories of 30 optimizations, **(C)** Schematic of the objective function.

Before optimizing, it was checked to ensure that all the initial sample points lie within the feasible region. When using the logarithmic barrier method, the optimization problem can be rewritten as Equation 16:

where

In summary, the current algorithm combing the Kriging surrogate model and the gradient optimization method is able to deal with both constrained and unconstrainted problems, and will be used for the subsequent study.

## Optimization for Enhanced Wake Vortex Decay

Before the optimization, the enhancement of wake vortex decay by active flow control method will be introduced briefly. Two rectangular blowing zones were equipped symmetrically about the runway central line, at the end of the runway. When air flows (blowing) vertically from the blowing zones, starting vortices are generated at the edges of the rectangular zones. At the same time, secondary vortices are induced and roll up inhomogeneously, due to the presence of the blowing air. Naturally, these vortical structures interact and develop into a hairpin like vortex (*AR* = *length/width*, where *width* = *area/length*. It was found that the blowing effect is improved by an increasing blowing velocity and blowing zone area [18]. Therefore, it is believed that the optimization on blowing velocity and zone area is not necessary. In this study, the blowing zone area was fixed at

The wake vortex of A340 is considered in this section, the detailed vortex parameters are listed in Table 1, and the initial vortex altitude is *AR*, determined by the blowing zone length) and blowing zone position (*P*). Thus, our aim in this section is to find the optimum selection of *AR* and *P* and obtain the best enhancement effect.

Vortex circulation at an axial position is generally used to evaluate the vortex strength. However, instantaneous circulation is affected by many random factors and is unrepresentative for the entire wake decay process. Therefore, the vortex strengths at

Taking the case 1 in reference [19] as an example, as shown in Figure 6, the shadow area

**FIGURE 6**. Circulation history of case 1 in reference [19].

During the simulation, the flow field data is logged at 4s interval, and thus, the objective function can be simplified as Equation 18:

where

It must be noted that the response value for every new sample point is evaluated by CFD, which may consume more than 20 h when using a 64 cores server. The automated process is as follows (Figure 8):

1) for a new sample point, the batch file is generated according to the input design parameters; then, the structured mesh is generated using the batch files in ICEM CFD;

2) the CFD simulation is conducted using ANSYS FLUENT, in which the .*jou* file controls the CFD simulation details such as timestep and turbulence modelling etc.;

3) the flow field information is extracted and post-processed using an in-house code to get the objective function value;

4) the new sample point parameter and corresponding objective function value is transferred to update the surrogate model;

5) another round of sample infilling is conducted if necessary.

Considering the high cost of the CFD, two termination conditions are employed:

1) the total number of samples exceeds 210 (

2) the error of the adjacent two iterations is smaller than

As shown in Figure 9A, the optimal design of the current problem is found at the 20th sample point, while none of the subsequent sample points show a significant decrease in the objective function value. The better designs are concentrated around *obj*. = 11. Nevertheless, as the number of sample points increases, the surrogate model gradually stabilizes, and the adjacent error of the optimal value found by the surrogate model exhibits an overall decreasing trend. At the end of the optimization, the adjacent decreases to the order of

**FIGURE 9**. Convergence history of blowing zone optimization. **(A)** Convergence history, **(B)** Adjacent error.

Figure 10 illustrates the modelling when the error of the optimal value decreases to the order of *obj*. value is observed in the middle of the design space. It is observed that in most of the region of *obj*. is smaller than 11. When

**FIGURE 10**. Response surface and EI contour. **(A)** **(B)** **(C)** **(D)** **(E)** **(F)**

Figures 11–17 exhibit the vortex structures of two initial sample cases, four infilled sample cases, and the best performing sample case during the optimization. All the relative positions in the design space are shown in Figure 18, the design parameters are shown in Table 2, and the circulation decay histories are exhibited in Figure 19.

**FIGURE 11**. Structures of initial sample 1. **(A)** **(B)** **(C)** **(D)**

**FIGURE 12**. Structures of initial sample 2. **(A)** **(B)** **(C)** **(D)**

**FIGURE 13**. Structures of sample 70. **(A)** **(B)** **(C)** **(D)**

**FIGURE 14**. Structures of sample 73. **(A)** **(B)** **(C)** **(D)**

**FIGURE 15**. Structures of sample 76. **(A)** **(B)** **(C)** **(D)**

**FIGURE 16**. Structures of sample 150. **(A)** **(B)** **(C)** **(D)**

**FIGURE 17**. Structures of the optimal sample. **(A)** **(B)** **(C**) **(D)**

**FIGURE 19**. Circulation history at different axial positions (seven cases). **(A)** average, **(B)** **(C)** **(D)**

Take sample cases *76* and *150* as examples. The *Sample 73* has already had contact with the primary vortex at *Sample 150* sets off later than that in *Sample 73*. It is noted that the slope of the circulation curves at *Sample 150* are steeper than those in *Sample 73*. This is because the blowing zone in *Sample 150* has a smaller length (*Sample 70* is an exception of the above cases. Since the blowing zone is far from the centre line (*Sample 76* sets off late. Figure 15B shows that the *Sample 76* is only better than that of *Sample 70*.

The vortex structures in the two initial sample cases and the best performing case are similar. Considering the induced lateral movement of the IGE vortex, a large value of *Initial 2* experienced a rebound between *Initial 2* sets off later than those in other two cases, which is also the consequence of the weak starting vortex. The helical vortex in *Initial 2*, developed from the starting vortex, extends slower and affects the wake vortex to a limited extension. Compared with *Initial 1*, the design parameters and vortex decay history in *Opt.* is similar. It is noticed that, although the starting vortex in *Opt.* is relatively weak, due to the influence of the blowing zone position, the circulation in *Opt.* is lower after the rapid decay phase.

Overall, the vortex evolutions in most cases are similar: a) the starting vortex generated by blowing air is raised by the blowing air and primary vortex induction b) the starting vortex evolves into a hairpin vortex (*x* direction. The main difference between different cases is the timing and intensity of the above processes. From Figure 10E, the surrogate model shows that the best performing setting for A340 wake decay enhancement is

## Multi-Objective Design

The optimum blowing zone for an A340 wake vortex pair may not be enough to destroy the wake of a heavier aircraft, such as an A380, within a short period. Therefore, a better design could be obtained by overlapping the design space of two blowing zone types, which are for different aircraft wake decay enhancements, respectively. Taking the above optimization result as an example, Figure 10E can be dimensionalized using A340 and A380 parameters (Table 3). It is highlighted that the optimization process in the previous section is partially dimensionless. Since the initial vortex altitude of

1) for A380 (aircraft with larger span), the dimensionless initial altitude is less than that used in the optimization;

2) for A340 (aircraft with shorter span), the dimensionless blowing area is larger than that used in the optimization.

These two facts ensure that the simulated blowing effect is not worse than that predicted by the surrogate model.

The design space is divided by the contour lines of the response surface (objective function), the value of the objective function inside the contour lines is smaller than that of the objective function on the contour lines. Figure 20 shows the contour lines on which the objective function equals 11.5. When the design parameters inside the blue contour line (

Two simulations are performed to validate the optimization results. For A340 and A380 wake vortex simulations, the same non-dimensional computation domain (

Figure 21 and Figure 22 show the wake vortex structures of A340 and A380 under the blowing effect. Due to the large initial circulation of the A380 wake vortex, the starting vortex experiences high induced velocity and is raised quickly. Figure 22B shows that a vortex loop is evolved from the *x* direction and forms helical vortices, which destruct the wake vortex structures rapidly. It is noted that at

**FIGURE 21**. Structures of A340 wake vortex (coloured by *y* vorticity 1/s). **(A)** **(B)** **(C)** **(D)**

**FIGURE 22**. Structures of A380 wake vortex (coloured by *y* vorticity 1/s). **(A)** **(B)** **(C)** **(D)**

Figure 23 shows the decay history of the A340 and A380 wake vortex with optimized blowing zones. Due to the interference of the starting vortex, the rapid decay of the A340 wake vortex is brought approximately 1.5

**FIGURE 23**. Averaged circulation histories for different aircraft wakes with optimized blowing zones. **(A)** A340, **(B)** A380.

## Conclusion

In this paper, the Kriging surrogate model is used to help obtain a better design of the blowing zone for enhancement of wake vortex decay. By overlapping and comparing the design spaces for different wake vortices, a multi-objective design is realized, which improves the engineering feasibility of the current blowing method. The main findings are as follows:

1. The current optimization algorithm combing Kriging surrogate model and gradient optimization algorithm deal with the global optimization problems and constrained problems well;

2. The blowing effect is non-linearly related to the blowing zone aspect ratio and position. The blowing zone should not be too close to the centre of the computational domain and the blowing zone aspect ratio should be close to 1;

3. For the A340 wake vortex with an initial altitude of

4. By overlapping the design spaces, an optimized blowing zone, which enhances the decay of A340 and A380 wake vortex, is founded. Numerical simulation proves this blowing zone effective and reduces the objective function to 11.12 and 10.19 for the different wake vortices, respectively.

## Data Availability Statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

## Author Contributions

ZX (the first author) was responsible for numerical simulations, data processing and manuscript writing. DL (the second author) was responsible for the conceptual design of the study, funding support and the manuscript review. All authors contributed to the article and approved the submitted version.

## Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Keywords: active flow control, aircraft wake vortex, multi-objective design, Kriging, CFD

Citation: Xu Z and Li D (2024) Numerical Optimization on Aircraft Wake Vortex Decay Enhancement. *Aerosp. Res. Commun.* 2:12444. doi: 10.3389/arc.2024.12444

Received: 19 November 2023; Accepted: 05 January 2024;

Published: 24 January 2024.

Copyright © 2024 Xu and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Dong Li, ldgh@nwpu.edu.cn