Modeling and simulation of ventilation and cooling of aircraft piston engine based on genetic algorithm

Abstract

With the gradual orderly opening of low-altitude areas and the increasing number of private aircraft, the general aviation industry has ushered in new opportunities for development. Ventilation and cooling optimization of the piston aeroengine has become a very important field in general aviation enterprises. The traditional aircraft engine design method and control system do not consider the coupling between aircraft and engine, which can not meet the needs of development. Therefore, an optimization method for the ventilation and cooling of aircraft piston engines based on a genetic algorithm is proposed. Firstly, the engine cooling model is constructed, the ventilation and cooling principles of aircraft piston engines are analyzed, and then the genetic algorithm is used to optimize the ventilation and cooling program of the aircraft piston engine. The results show that the method can effectively optimize the ventilation and cooling scheme of the aero piston engine. During the optimization process, the average convergence value is always greater than 95.00%. Under different working conditions, the maximum failure rate of the optimized ventilation and cooling scheme is 0.03. The maximum failure rate is lower than that of similar methods.

Keywords:

• Genetic algorithm
• aircraft
• piston
• engine
• ventilation
• cooling
• modeling

1. Introduction

With the continuous improvement of aircraft performance requirements, the independent design of traditional aircraft control systems and engine control systems has been unable to meet needs. The rapid development of modern modeling and control and prediction technology and the rapid increase of computer operation speed make the integrated control of flight propulsion system an inevitable trend. Aeroengine performance optimization control is the key technology of the integrated control of flight propulsion systems (Xue et al., 2013). The traditional independent design of aircraft and engine control systems has been unable to meet the needs of development. The reason is that the independent design method does not consider the coupling between aircraft and engine. In order to ensure engine safety, engine performance is usually not fully developed (Faizollahzadeh Ardabili et al., 2018). For example, in order to ensure that the engine does not surge under all conditions, the traditional design method is to design the engine with sufficient surge margin in the worst conditions, while in other conditions the surge margin of the engine appears very large (Liu et al., 2002). This means achieving engine stability at the expense of engine performance (Ghalandari et al., 2019). Engine performance optimization control optimizes the performance of existing or new engines without adding control hardware to ensure the safe operation of the engine on the premise of safe operation of the engine and without adding control hardware, so as to achieve the optimum and maximum performance potential of an engine or a comprehensive performance index (Valdivia et al., 2014). This has become the main way to improve engine performance. Therefore, it is very important to study the advanced engine control mode and control method to improve the overall performance level of aeroengines in China, and to follow up and catch up with advanced aeroengine control technology elsewhere (Gong et al., 2018).

The new generation fighter must have a wider flight envelope, higher flexibility and mobility, and better economy. To achieve this goal, the air ventilation and cooling system must be able to provide more powerful and lasting power, which also creates new and higher requirements for the control of the ventilation and cooling system (Antcliff et al., 2016). The genetic algorithm is a mature global optimization method with high robustness and wide applicability (Fetouh & Zaky, 2017). Because of its advantages of not being restricted by the nature of the problem, such as continuity or differentiability, and being able to deal with complex problems that are difficult to solve with traditional optimization algorithms, it fully demonstrates its great potential in solving control system optimization, which has attracted great attention in the field of control (Chao et al., 2011). Genetic algorithm has been widely used in various fields such as the field of control, linear and non-linear, optimization, robustness, adaptivity, sliding mode, fuzzy logic, neural network, parameter estimation and system identification, model linearization and controller order reduction, robot arm control and trajectory planning. As an effective global parallel optimization search tool, the genetic algorithm has the characteristics of not depending on the specific domain of the problem, optimizing without gradient information, not requiring explicit function form, not requiring initial value, implicit parallel operation, and convergence to global optimal solution with probability. Genetic algorithm is especially suitable for large-scale, highly nonlinear, non analytic optimization problems. Because of these characteristics of the genetic algorithm, the genetic algorithm has been continuously used in aeroengine optimization, including in component optimization, engine structural parameters optimization, impeller flow field aerodynamic design, engine regulation optimization, etc. Based on the above, this paper builds a ventilation and cooling model of the aircraft piston engine based on the genetic algorithm, and optimizes the ventilation and cooling program control of aircraft piston engines (Zhu et al., 2017). The paper presents a genetic-algorithm-based optimization method for ventilation and cooling of aircraft piston engines. Firstly, the engine cooling model is established. The principle of the aircraft piston engine is analyzed, and the ventilation and cooling program of the aircraft piston engine is optimized using the genetic algorithm. The results show that this method can effectively optimize the ventilation and cooling program of the aircraft piston engine, and optimize the maximum failure rate of the ventilation and cooling program of the aircraft piston engine. Compared with similar methods, it has some advantages.

2. Materials and methods

The aircraft piston engine’s ventilation and cooling model (CRFM) is composed of condenser, radiator, and fan. With the continuous improvement of people’s living standards and the increasingly compact design of engines, the vibration and noise ride (NVH) of the engine and its accessories have been given more and more attention in the industry as a whole. As a key component affecting engine power and durability, the impact of vibration and noise caused by CRFM on NVH performance of the whole machine, cannot be ignored (Duggal & Djordjevic, 2004).

2.1. Ventilation and cooling model of the aircraft piston engine

The CRFM studied in this paper is shown in Figure 1. CRFM is connected to the aircraft frame by four rubber dampers. In the simulation analysis, CRFM is simplified as a rigid body with six degrees of freedom, and rubber damper is simplified as a spring with linear elasticity along three orthogonal axes in space, i.e. the $u$, $v$, and $w$ axes of the rubber damper, with constant damping. In order to simulate the actual operating conditions, the external excitation caused by aircraft frame and fan lamp is simplified as a sinusoidal load with fixed amplitude and frequency (Zhu et al., 2017).

Figure 1. Picture of CRFM.

The centroid coordinate system $Gc-XYZ$ is defined as follows. The origin $Gc$ is located at the centroid (CG) of the CRFM model, and the X axis is along the axis of the fan motor, and its positive direction points to the front of the aircraft. The Z axis is vertical, its positive direction is vertical, and the Y axis is determined by the right-hand rule. The elastic principal axis coordinate system $Gc-uvw$ of rubber dampers is defined as follows. The origin GR is located at the center of mass of each damper block, and u, v, and w are the three elastic principal axis directions of each damper block, respectively. If CRFM centroid displacement is defined as the displacement of the centroid along the XYZ axis, and x, y, z, and the rotated angular displacements $\theta x$, $\theta y$, $\theta z$ around the XYZ axis are recorded as X, then $X={\left(\begin{array}{cccccc}x& y& z& {\theta }_x& {\theta }_y& {\theta }_z\end{array}\right)}^T$.

Using Newton’s laws of motion, the motion equation of CEFM model in ventilation and cooling can be written as (1) $MX=RF+EF$(1) where RF is the reaction force and moment acting on CRFM at the supporting point, and EF is the external force and moment acting on CRFM directly.

Suppose $J_x$, $J_y$, $J_z$, $J_{xy}$, $J_{xz}$, and $J_{yz}$ are the product of inertia and rotational inertia of CRFM model during ventilation and cooling, then the inertia matrix is (2) $M=\left(\begin{array}{cccccc}m& 0& 0& 0& 0& 0\\ 0& m& 0& 0& 0& 0\\ 0& 0& m& 0& 0& 0\\ 0& 0& 0& J_x& -J_{xy}& -J_{xz}\\ 0& 0& 0& -J_{xy}& J_y& -J_{yz}\\ 0& 0& 0& -J_{xz}& -J_{yz}& J_z\end{array}\right)$(2) where m is a vector. The relationship among the displacement $D{r}_i$ in the local coordinate system $Gr-uvw$, the displacement $D{c}_i$ in the centroid coordinate $Gc-\text{XYZ}$, and the displacement X of the CRFM centroid for the suspended points of the ith vibration absorber are as follows: (3) $\begin{array}{rl}D{r}_i& =B_{i}D{c}_i=B_i{E}_{i}X\end{array}$(3) (4) $\begin{array}{rl}{E}_i& =\left(\begin{array}{cccccc}\text{1}& \text{0}& \text{0}& \text{0}& z_i& -y_i\\ 0& 1& 0& -z_i& 0& x_i\\ 0& 0& 1& y_i& -x_i& 0\end{array}\right)=\left(\begin{array}{ccc}1& ⋮& r_i\end{array}\right)\end{array}$(4) (5) $\begin{array}{rl}{B}_i& =\left(\begin{array}{ccc}\cos {\alpha }_{i1}& \cos {\beta }_{i1}& \cos {\gamma }_{i1}\\ \cos {\alpha }_{i2}& \cos {\beta }_{i2}& \cos {\gamma }_{i2}\\ \cos {\alpha }_{i3}& \cos {\beta }_{i3}& \cos {\gamma }_{i3}\end{array}\right)\end{array}$(5) (6) $\begin{array}{rl}{r}_i& =\left(\begin{array}{ccc}0& z_i& -y_i\\ -z_i& 0& x_i\\ y_i& -x_i& 0\end{array}\right)\end{array}$(6) where $B_i$, $E_i$, and $r_i$ are the directional cosine matrices of the three elastic principal axes of the ith vibration absorber in the GC coordinate system, and $x_i$, $y_i$, and $z_i$ are the coordinates of the suspended points of the ith vibration absorber in the centroid coordinate system $Gc-\text{XYZ}$.

When the vertical displacement excitation $z(t)$ is applied to the aircraft frame, if the displacement of the suspension point of each damper is the same as the excitation displacement of the aircraft frame, then the suspension point of the damper i has displacement $D{c}_{bottomi}={\left\{\begin{array}{ccc}0& 0& z(t)\end{array}\right\}}^T$ in the $Gc-\text{XYZ}$ coordinate system. The relationship $f_{ri}$ between the force and the deformation of the ith damper in its local coordinate $Gr-uvw$ is as follows: (7) $\begin{array}{rl}{f}_{ri}& =k_i(D{r}_i-D{r}_{bottomi})=k_i(B_{i}D{c}_{bottomi})\\ & =\left[\begin{array}{cc}{k}_i{B}_i& k_i{B}_i{r}_i\end{array}\right]X-k_i{B}_{i}D{c}_{bottomi}\end{array}$(7) In the formula, $k_i$ is the complex stiffness matrix of the damping block i in its elastic principal axis coordinate system $Gr-uvw$: (8) $k_i=\left(\begin{array}{ccc}{k}_u& 0& 0\\ 0& k_v& 0\\ 0& 0& k_w\end{array}\right)$(8) The counterforce $R{F}_{fi}$ and countermoment $R{F}_{ti}$ of the ith damper on CRFM is (9) $\begin{array}{rl}R{F}_{fi}& =\left\{\begin{array}{c}R{F}_{fi}\\ R{F}_{ti}\end{array}\right\}\\ & =\left(\begin{array}{cc}-B_i^T{k}_i{B}_i& -B_i^T{B}_i{r}_i\\ -r_i^T{B}_i^T{k}_i{B}_i& -r_i^T{B}_i^T{k}_i{B}_i{r}_i\end{array}\right)X\\ & +\left(\begin{array}{c}{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\\ r_i^T{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\end{array}\right)\end{array}$(9) Thus the motion equation of CEFM model in ventilation and cooling can be written as (10) $\begin{array}{rl}MX& =RF+EF\\ & =\sum _{i=1}^n\left(\begin{array}{cc}-B_i^T{k}_i{B}_i& -B_i^T{k}_i{B}_i{r}_i\\ -r_i^T{B}_i^T{k}_i{B}_i& -r_i^T{B}_i^T{k}_i{B}_{i}r\end{array}\right)X\\ & +\sum _{i=1}^n\left(\begin{array}{c}{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\\ r_i^T{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\end{array}\right)+EF\end{array}$(10) (11) $MX+KX=F+EF$(11) where (12) $\begin{array}{rl}F& =\left\{\begin{array}{c}\sum _{i=1}^n{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\\ \sum _{i=1}^n{r}_i^T{B}_i^T{k}_i{B}_{i}D{c}_{bottomi}\end{array}\right\}\end{array}$(12) (13) $\begin{array}{rl}K& =\sum _{i=1}^n\left(\begin{array}{cc}{B}_i^T{k}_i{B}_i& -B_i^T{k}_i{B}_i{r}_i\\ r_i^T{B}_i^T{k}_i{B}_i& r_i^T{B}_i^T{k}_i{B}_i{r}_i\end{array}\right)\end{array}$(13) In the CEFM centroid coordinate system $Gc-\text{XYZ}$, according to the inertia matrix and mode matrix of CEFM model, the energy distribution of the CEFM model in ventilation and cooling can be obtained (Meenakshisundaram et al., 2017). It is written in matrix form and defined as energy distribution matrix Deep. When the CEFM model vibrates in the jth mode, the percentage of energy allocated by the kth generalized coordinate to the total energy of the CEFM model is (14) $Deep(k,j)=\frac{\frac{1}{2}{\omega }_j^2\sum _{l=1}^6[M(k,l)\varphi (k,j)\varphi (l,j)]}{\frac{1}{2}{\omega }_j^2\sum _{k=1}^6\sum _{l=1}^6[M(k,l)\varphi (k,j)\varphi (l,j)]}$(14) where $\varphi (k,j)$ and $\varphi (l,j)$ are the kth and $l$th elements of the ith mode of vibration, $M(k,l)$ is the kth row and the lth column element of the inertia matrix of the CEFM model in ventilation and cooling, and ${\omega }_j^2$ is the natural frequency of the jth order. The dominant direction of the CEFM model in ventilation and cooling can be identified according to the values of the elements in each column of the matrix (Kazemi et al., 2018).

2.2. Optimization of ventilation and cooling of aircraft piston engine based on genetic algorithm

After understanding the ventilation and cooling principle based on cefm model, the ventilation and cooling scheme of aircraft piston engine is optimized by genetic algorithm.

2.2.1. Fitness function

In genetic algorithm, fitness function is used to evaluate the merits and demerits of individuals. Its design reflects the optimal goal of the algorithm, and is also the key to establishing the CEFM model using the genetic algorithm. According to the principle that the linear dynamic response of the CEFM model should conform to the nonlinear dynamic response, the fitness function is chosen as the time integral of the square of the normalized data difference between the nonlinear dynamic response and the linear dynamic response (Chowdhury & Garai, 2017). The optimum index for evaluating the individual program in the ventilation and cooling program of CEFM model is as follows: (15) $\begin{array}{rl}{J}_i& =\sum _{K=0}^N[{\overline{N}}_{f1}^2(K^f)+{\overline{N}}_{f2}^2(K^f)]\\ & +\sum _{K=0}^N[{\overline{N}}_{c1}^2(K^f)+{\overline{N}}_{c2}^2(K^f)]\end{array}$(15) where (16) $\begin{array}{rl}{\overline{N}}_{f1}(K^f)& =[N_{f21}(K^f)-{\tilde{N}}_{f11}(K^f)]\times a_1\end{array}$(16) (17) $\begin{array}{rl}{\overline{N}}_{f2}(K^f)& =[N_{c22}(K^f)-{\tilde{N}}_{c12}(K^f)]\times a_2\end{array}$(17) (18) $\begin{array}{rl}{\overline{N}}_{c1}(K^f)& =[N_{f21}(K^f)-{\tilde{N}}_{c11}(K^f)]\times a_3\end{array}$(18) (19) $\begin{array}{rl}{\overline{N}}_{c2}(K^f)& =N_{c22}(K^f)-{\tilde{N}}_{c12}(K^f)\end{array}$(19) (20) $\begin{array}{rl}{a}_1& =\frac{{\tilde{N}}_{f11}(N^f)}{{\tilde{N}}_{f12}(N^f)}\end{array}$(20) (21) $\begin{array}{rl}{a}_1& =\frac{{\tilde{N}}_{f11}(N^f)}{{\tilde{N}}_{f12}(N^f)}\end{array}$(21) (22) $\begin{array}{rl}{a}_3& =\frac{{\tilde{N}}_{c11}(N^f)}{{\tilde{N}}_{c12}(N^f)}\end{array}$(22) where K is the sampling time, N is the increment, ${\tilde{N}}_{f12}$ is the increment of the fan speed after normalization, ${\tilde{N}}_{c12}$ is the increment of the compressor speed after normalization, subscript 11 represents the output of the nonlinear system when the main fuel flow steps, subscript 12 represents the output of the nonlinear system when the tail nozzle area steps, subscript 21 represents the output of the linear system when the main fuel flow unit steps, subscript 22 represents the output of linear system when the tail nozzle area unit steps. N is the total sampling time, $a_1$, $a_2$, and $a_3$ are the output normalization coefficients selected to make the optimal index independent of the range of quantities. When ${\tilde{N}}_{f1}({\tilde{N}}_{c1})$ is the main fuel flow unit step, the difference between the speed of normalized linear system fan (compressor) and the speed of nonlinear system fan (compressor); ${\tilde{N}}_{f2}({\tilde{N}}_{c2})$ is the difference between the speed of the normalized linear system fan (compressor) and the speed of the nonlinear system fan (compressor) when the unit of tail nozzle area steps; $\overline{N}$ series represents the difference before normalization. Individual fitness $f_i$ is defined as the reciprocal of the optimal index $J_i$, that is, in the process of f = 3 optimization, the smaller the optimal index, the greater the individual fitness. Through genetic operators, the greater the fitness of individuals, the greater the probability that their individual characteristics are inherited by the next generation.

2.2.2. Genetic operator

The genetic algorithm is an adaptive heuristic global search algorithm based on the idea of bionic evolution. It searches for the global optimal solution through the evolutionary process of basic genetic operations such as selection, crossover, and mutation (Ruan et al., 2017).

In the design process, 10-ary floating-point coding is adopted. The location element in the ventilation and cooling program of the aircraft piston engine is taken as the optimized parameter, and the size of the population is set as M.

2.2.2.1. Selection

A proportional selection operator is adopted, i.e. the probability of individual selection for each ventilation and cooling program is proportional to its fitness. If the fitness of individual $X_i$ in ventilation and cooling program is $f_i$, then the probability of individual $X_i$ being selected is (23) $P_{is}=\frac{f_i}{\sum _{j=1}^M{f}_i}(i=1,2,\dots ,M)$(23)

2.2.2.2. Crossover

The role of crossover operators is to allow two chromosomes to exchange some genes in some way, thus forming two new individuals (Blaifi et al., 2018). Using arithmetic crossover, two new individuals are generated from the linear combination of two individuals. Let two individuals be $X_A^t$ and $X_B^t$, respectively; the two new individuals generated by crossover operation are then: (24) $\begin{array}{r}{X}_A^{t+1}=T{X}_A^t+(1-T)X_B^t\end{array}$(24) (25) $\begin{array}{r}{X}_B^{t+1}=T{X}_B^t+(1-T)X_A^t\end{array}$(25) The crossover probability T is 0.9 and the crossover parameter a is set randomly.

2.2.2.3. Mutation

The function of the mutation operator is to generate new individuals to improve the local search ability of the algorithm and maintain the diversity of the population (Garcia-Bediaga et al., 2017). The maximum variation probability of the CEFM model is 0.1, and the minimum variation probability is 0.09. Thus the variation probability of individual $X_i$ with fitness $f_i$ is (26) $P_{ib}=0.1-\frac{f_1-f_{min}}{f_{max}-f_{min}}\times (0.1-0.09)$(26) where $f_{max}$ is the maximum fitness in the current evolutionary generation, and $f_{min}$ is the minimum fitness in the current evolutionary generation, that is, the greater the fitness, the lower the probability of individual variation and the greater the probability that individual characteristics are inherited by the next generation (Zhang et al., 2017).

2.2.2.4. Optimal individual retention strategy

In order to ensure the convergence of the algorithm and accelerate the convergence of the algorithm, the optimal individual retention strategy is adopted, which is to select the individual of the optimal ventilation and cooling program in the T generation of the CEFM model, and it does not participate in any genetic operation (Aziza & Krichen, 2018). The individual ventilation and cooling program is the best choice for the ventilation and cooling of the aircraft piston engine.

3. Results

3.1. The method in this paper is used to optimize the ventilation and cooling effect of aircraft engines

The ventilation performance optimization results of the ventilation and cooling system of the aircraft piston engine under different working conditions are compared. The test conditions include: engine off (enoff) with fan at 2470 r/min (condition 1); engine idle, and air conditioning on (enonacon) with fan at 2470 r/min (condition 2). Taking the ventilation and cooling system of an Lycoming aero piston engine as an example, the failure reduction rate of the cooling and ventilation program of the aircraft in mid-2018 under the control of this method is analyzed. The failure rate is related to the cooling power and vibration intensity. The larger the cooling power, the higher the vibration intensity and the higher the failure rate; the smaller the cooling power, the lower the vibration intensity and the lower the failure rate. The results are shown in Table 1.

Table 1. Ventilation and cooling effect of aircraft engine optimized by the method presented in this paper.

Month	Working condition 1/failure reduction rate	Working condition 2/failure reduction rate
1	0.03	0.02
2	0.02	0.02
3	0.03	0.02
4	0.02	0.02
5	0.03	0.02
6	0.02	0.02
7	0.03	0.02
8	0.02	0.02
9	0.03	0.03
10	0.02	0.02
11	0.03	0.02
12	0.02	0.02

According to Table 1, after optimization of the proposed method, the maximum failure reduction rate of the ventilation and cooling program of the Lycoming piston engine is 0.03 in different working conditions, and the failure reduction rate is relatively small. This shows that the method can greatly reduce ventilation and cooling program failure of the aircraft piston engine, and also verifies the effectiveness of this method.

In order to further analyze the application performance of the proposed method, an optimization method for an aircraft piston engine based on finite element analysis and an optimization design method for an engine control law based on aircraft/engine performance integration are compared with the method of this paper.

3.2. Comparison of fault rate

From optimizing the ventilation and cooling system of the Lycoming aircraft piston engine using an optimization method for aircraft piston engines based on finite element analysis and an optimization method for the engine control law based on aircraft/engine performance integration, the failure reduction rate of the ventilation and cooling program of this Lycoming aircraft piston engine is shown in Figures 2 and 3.

Figure 2. Failure reduction rate of ventilation and cooling program of an aircraft piston engine Based on finite element analysis.

Figure 3. Failure reduction rate of ventilation and cooling program optimized based on the optimum design method of engine control laws for aircraft/engine performance integration.

By comparing the data of Figures 2 and 3 and Table 1, it can be seen that the failure reduction rate of the ventilation and cooling program of this Lycoming aircraft piston engine is quite different after optimization of the three methods. After optimizing the ventilation and cooling system of Lycoming aircraft piston engine, the maximum failure reduction rate of the ventilation and cooling program is 0.19 and 0.24, respectively, that is, always greater than that of the proposed method. It can be seen that the optimization effect of the proposed method is the best.

3.3. Stability comparison

Taking stability as an evaluation index, the stability of the ventilation and cooling program of the Lycoming aircraft piston engine after optimization was evaluated in 2018. The stability comparison results of the three methods are shown in Table 2.

Table 2. Stability comparison results of three methods.

	Article method		Optimizing method for an aircraft piston engine based on finite element analysis		Optimum design method of engine control law based on aircraft/engine performance integration
Month	Working condition 1 (%)	Working condition 2 (%)	Working condition 1 (%)	Working condition 2 (%)	Working condition 1 (%)	Working condition 2 (%)
1	98.88	98.88	91.65	91.98	88.56	87.45
2	98.67	98.88	91.76	91.54	88.34	87.44
3	98.88	98.88	91.34	91.34	88.33	88.45
4	98.88	98.88	91.45	91.98	88.22	87.45
5	98.67	98.97	91.65	91.54	88.37	87.44
6	98.88	98.88	91.76	91.34	88.56	88.45
7	98.88	98.88	91.34	91.98	88.34	87.45
8	98.67	98.97	91.45	91.54	88.33	87.44
9	98.88	98.88	91.65	91.34	88.22	88.45
10	98.88	98.88	91.76	91.98	88.37	87.45
11	98.67	98.97	91.34	91.54	88.45	87.44
12	98.88	98.88	91.45	91.34	88.45	88.45

According to the data in Table 2, the maximum stability of the ventilation and cooling program of this Lycoming aircraft piston engine optimized by the proposed method is 98.88% and 98.97%, respectively, in different working conditions in 2018. The maximum stability of the ventilation and cooling program of this Lycoming aircraft piston engine in 2018 is always lower than that of the present method, which is based on the optimization method for a certain aircraft piston engine based on finite element analysis and the optimization method for an engine control law based on aircraft/engine performance integration. It can be seen that the stability of the optimized ventilation and cooling program of aircraft engine is the best.

3.4. Convergence comparison

Convergence reflects the efficiency of the three methods in optimizing the ventilation and cooling system of aircraft piston engines. The convergence of three methods for optimizing the ventilation and cooling system of an aircraft piston engine under two different operating conditions was tested many times. The results are shown in Table 3.

Table 3. Results of convergence of three methods.

	Article method		Optimizing Method of an Aircraft piston engine Based on Finite Element Analysis		Optimum design method of engine control law based on aircraft/engine performance integration
Test times	Working condition 1 (%)	Working condition 2 (%)	Working condition 1 (%)	Working condition 1 (%)	Working condition 2 (%)	Working condition 1 (%)
1	96.99	97.12	84.34	84.44	79.65	79.65
2	96.88	97.22	84.55	84.45	79.65	79.44
3	96.98	97.24	84.44	84.56	79.44	77.99
4	96.99	97.45	84.45	84.34	77.99	79.65
5	96.99	97.12	84.56	84.44	79.65	79.65
6	96.88	97.22	84.34	84.45	79.65	79.44
7	96.98	97.24	84.55	84.56	79.44	77.99
8	96.99	97.45	84.44	84.34	77.99	79.65
9	96.99	97.12	84.45	84.44	79.65	79.65
10	96.88	97.22	84.56	84.45	79.65	79.44
11	96.98	97.24	84.45	84.56	79.44	77.99
12	96.99	97.45	84.56	84.34	77.99	79.65
Mean value	96.96	97.26	84.47	84.45	79.18	79.18

According to the data in Table 3, the convergence mean of the proposed method is always greater than 95.00% under different conditions and repeated tests. However, the convergence mean of the optimization method based on finite element analysis and the optimization method based on the integration of aircraft and engine performance is always below 90.00%. The efficiency of the proposed method is fastest when the ventilation and cooling system of the aircraft piston engine is optimized.

4. Discussion

Based on the research in this paper, some suggestions for improving the development level of aeroengines in the future may be put forward.

4.1. Priority breakthrough in engine technology

Enhancing aeroengine research and development capability requires vigorous policy support; the aeroengine industry needs to be regarded as an indispensable pillar industry and a priority breakthrough industry for national defense. It is necessary to formulate short-term, medium-term, and long-term development plans for aeroengines. From now on, accelerating the development of the aeroengine industry should be included in plans for national economic and social development, and the continuity of the development of the aeroengine industry should be emphasized and maintained. It is necessary to increase the investment of funds. Besides the government’s investment of a large amount of funds, aeroengine research institutes and production enterprises should be encouraged. For those units that have made outstanding contributions, maintain leading positions in the industry, have good market prospects, and have the courage to tackle key research issues, it should strive to arrange for their listing as soon as possible, make full use of the securities market to raise funds, and solve the current situation of fund shortage.

4.2. High-tech talents are the key

It should intensify the introduction and training of talent, especially high-tech talent. Excellent talent should not only be paid a good salary, but also be provided with a good working environment. On the basis of using talents, we should pay attention to the re training of talents to avoid the shortage of talents caused by the aging of talents.

4.3. Increasing the renovation of key technologies and equipment

Increase investment in key technology transformation and key equipment update, and gradually eliminate obsolete equipment, so that the quality of product processing is mainly guaranteed by the technical level and sense of responsibility of workers, and gradually develop in the direction of taking technology as the main guarantee.

4.4. Improving management level

We should further improve the management level, mobilize enterprises to consciously improve the level of scientific research and manufacturing technology, and really use funds to improve scientific research capacity, manufacturing technology level and market development. Learn from the successful experience of scientific research institutes and combine with the development needs, jointly improve the level of national defense research and management, use funds to introduce scientific and technological personnel, advanced technology and advanced equipment, solve the key problems in scientific research, retrain scientific and technological personnel and workers, improve the quality of talents and expand the talent team. Provide satisfactory treatment in terms of working conditions and salary.

In this paper, genetic algorithm is applied to the optimization design of ventilation and cooling system of aircraft piston engine, so as to optimize the performance of aircraft piston engine. The test results show that the maximum fault reduction rate of the optimized ventilation cooling scheme of the piston engine is 0.03, which is relatively small under off design conditions. In 2018, the maximum stability of the optimized ventilation and cooling scheme of Lycoming piston engine is 98.88% and 98.97% respectively, and the average convergence value is always greater than 95.00%. It has good stability and high application value.

5. Conclusions

The poor working conditions require more and more cooling system of engine. The cooling system directly affects the reliability of the power system, working efficiency, and the life of components. Therefore, the matching of the cooling system of aeroengines is a key and difficult point in engine design research. This method mainly optimizes the ventilation and cooling program of aircraft piston engines using the genetic algorithm. Combined with the full text data, we can see that the genetic algorithm has the following advantages:

1. The ability to search quickly and randomly independently of the problem domain.

2. The search starts from the group and has potential parallelism, which allows simultaneous comparisons among multiple individuals.

3. The search is inspired by the evaluation function, and the process is simple.

4. Using probability mechanism to iterate is random.

5. It is scalable and easy to combine with other algorithms.

The genetic algorithm makes up for the shortcomings of traditional optimization technology, and demonstrates its characteristics and charm in solving and applying many problems in the field of oil and gas exploration and development. The modeling and simulation results for the ventilation and cooling of an aircraft piston engine based on the genetic algorithm show that the method can effectively optimize the ventilation and cooling program of the aircraft piston engine, and optimize the maximum failure rate of ventilation and cooling. Compared with similar methods, optimization efficiency has certain advantages.

Disclosure statement

No potential conflict of interest was reported by the authors.