Keywords

1 Introduction

The State Council of China has announced its ambitious plan to raise the speed of high-speed trains (HSTs) to 400 km/h and even 600 km/h. One of the obstacles for such HSTs to be commercially viable is the rapidly rising aerodynamic drag with train speed. There have been a great number of attempts, as reported in the literature, on the aerodynamic drag reduction of HSTs using various passive techniques, e.g., aerodynamic shape optimizations [1, 2], vortex generator [3] and non-smooth surface [4]. These investigations have achieved a great success. However, when shaping vehicle bodies has reached or approached its optimum, it is active control that can potentially reduce aerodynamic drag significantly further. This has been demonstrated by our recent campaign on the active DR of Ahmed bodies [5, 6], in which the optimal combinations of actuations achieved maximum DRs of 32% and 21% for the high and low-drag regimes, respectively, based on the artificial intelligence (AI) control. Active DR, especially AI-based, for a high-speed train has been rarely studied. Note that both Ahmed bodies and HST tail car are critical geometries, i.e. the bluff body geometries that exhibit sharp flow transition when changing one of the geometrical parameters [7, 8]. One may naturally surmise that the knowledge we have gained from the study of Ahmed bodies might be to a certain extent applicable for HSTs. This work aims to address this issue and to develop an AI-based active DR technique, following our strategies deployed for the DR of Ahmed bodies, for a high-speed maglev train using combined steady jets.

2 Experimental Details

Experiments are conducted in a closed-circuit wind tunnel with a test section of 1.0 m high, 0.8 m wide and 5.6 m long. Experimental setup is schematically shown in Fig. 1. A 1/20 scaled highly streamlined three-car maglev HST model is examined, which has an overall length of 1.8 m, a width of 0.184 m and a height of 0.21 m. The Reynolds number Re investigated is 4.0 × 105 based on the square root of the model cross-section area. The model is supported by two cylindrical posts mounted on the head and tail trains. The other end of each supporting post is connected to a force balance, which is fixed on an aluminum plate mounted on a fixed frame outside and isolated from the wind tunnel. The total aerodynamic drag of the model is captured from the two force balances. Sixty pressure taps, connected to two pressure scanners, are distributed on the tail car to measure the surface pressure distribution.

Fig. 1
A schematic diagram of an experimental setup presents an object on the support pillar with a windshield, freestream flow in the left direction, force balances at the bottom of the pillars, and a wind tunnel wall between the object and the aluminum plane.

Schematics of experimental setup

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3 Results and Discussion

Over 90 different steady blowing actuations are investigated in Open-loop control experiment. Nevertheless, only twelve of them can achieve drag reduction. These actuations, referred to as Si (i = 1, 2, …, 12), are distributed in four specific areas (Fig. 2a), denoted as Ai (i = 1, 2, …, 4). The actuation outlet is 1 mm in width and 23–42 mm in length. The blowing angles θsi of Si are defined with respect to the streamwise direction. The net power saving S is calculated by (\(\Delta FU_{\infty } - 0.5 \rho Q_{Si} V_{Si}^{2} - p_{si} A_{si} V_{si}\))/FD \(U_{\infty }\), where ΔF is the reduced drag under control, \({\text{Q}}_{\text{Si}}\) is the flow rate of Si, VSi is the jet exit velocity, psi is the mean static pressure of Si, \({\text{A}}_{\text{si}}\) is the outlet area of Si, and FD is the drag of the baseline flow. Positive value of DR or S represents drag reduced or power saved. Open-loop control results indicate that individual actuation S1, distributed in area A3 with θs1 = 105°, can produce a maximum DR of 7% but S is only −5%. Under this control, the surface pressure has been greatly increased as shown in Fig. 3a. The variation of surface pressure \(\Delta {C}_{p}={C}_{p,ctr}-{C}_{p,un}\), where \({C}_{p,ctr}\) represents surface pressure under control and \({C}_{p,un}\) represents surface pressure in baseline flow. As the pressure taps get closer to the tail nose, \(\Delta {C}_{p}\) increase gradually. \({C}_{p1}\), the pressure taps in the symmetry plane and is closest to the tail nose, increases about 80%. \(\Delta {C}_{p10}\) and \(\Delta {C}_{p17}\) are 16% and 13%, respectively. It indicates that the jet from actuation S1 weaken the longitudinal vortices above those two surfaces. While, the surface pressure recovers only in the area not far from the jet. Pressure taps away from S1 remain consistent between baseline flow and controlled flow. When blowing angle of S1 is adjusted to θs1 = 90°, S can achieve 4% when DR = 6%.

Fig. 2
2 schematic diagrams of an experimental setup. A. It presents the tail part from the back view with surface areas A. 1, 2, 3, and 4 marked. B. It presents the tail part from a side view with points C p 1, 2, 3, 4, 5, 6, 7, 8, and 9 marked on the top, and points c p 10 to 23 marked on the side.

a The areas A1 – A4 for the arrangement of actuations. b Measurement locations Cp1 – Cp23 of surface pressure

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Fig. 3
6 dot plots of the delta C p versus pressure tap number. 1. It presents a decline up to 0, and then a stable trend. 2. It presents a varying trend from 10 to 0. 3. It presents a varying trend from 20 to 0. 4. It presents the highest value of 35. 5. It presents a stable trend between 0 and 10.

Variation in Cp1 − Cp23 under the optimal control of a S1; b the most efficient control

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The AI control system, consisting of the sensing (force balances), actuations (blowing jets) and control (linear-genetic-programming-algorithm-based controller) units as well as the plant, is used to find the optimal blowing ratios of seven actuations with a view to maximizing the DR and S. Unsupervised learning of the optimal control is converged after 10 generations. Each generation consists of 100 samples. Each sample is tested for 40 s to estimate the cost J (J = − ΔF – C*S + 0.4), which C = 0.1 is the weighted constant aiming to teach control units the importance of power saving. A lower J denotes a better control effect. The learning curve is shown in Fig. 4, in which the square symbol represents the minimum cost Jn (the subscript ‘n’ denotes the generation number) in each generation. Although the 100 samples of first generation are generated randomly, the AI system achieves the minimum cost J1 = 0.32 corresponding to a DR of 8%, which is slightly larger than the maximum DR produced by the individual S1 in the open-loop control experiment. As it evolves to the fourth generation, the cost declines to J4 = 0.31 and achieves a DR = 8%. The cost of fifth generation keeps decreasing to J5 = 0.3 and achieves a DR = 9%. The costs of 7–10th generation remain unchanged and converge to an optimal cost Jopt = 0.29. The optimal combination can produce a DR of 10%.

Fig. 4
An area graph of J versus n presents values of J 0 equal to J 1 equal to 0.32, J 4 equal to 0.31, J 5 equal to 0.30, and J option equal to 0.29. A declining trend of the intensity.

Learning curve of AI control based on TGP

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Nevertheless, there is nearly no net power saving under the optimal combination. Based on analysis of the data generated from the learning process, a most efficient combination is found to yield a maximum S of 5%, with a DR of 6%. This sacrifice in DR which results in an increasement in S is achieved by cutting down the blowing ratios of actuations. Specifically, the input power of the most efficient combination is only 20% of that of the optimal combination. The surface pressure variation under this most efficient combination is shown in Fig. 3b. The largest \(\Delta {C}_{p}\) appears at side surface, which may be connected to the weakening of the pair of longitudinal vortices formed at the lateral sides of the tail. Under optimal power saving combination, the pressure surface is recovered not only near the actuation, but also at far upstream area. Thus, the combination achieves a considerable DR with a very low input energy.

4 Conclusions

An extensive investigation on the active DR of a HSMT model using distributed jets has been conducted. In the open-loop control experiment, over 90 actuations, deployed at different locations of the tail car, had been investigated, in which the dependence of DR on their θsi and blowing ratio has been examined. The individual jet may achieve a maximum DR of 7% and a maximum net energy saving S of 4%. The surface pressure recovers greatly in the symmetry plane and slightly in the side surfaces. The pressure taps in the symmetry plane and nearest to tail nose can achieve a ∆Cp of 80%. With seven jets blowing simultaneously, an AI control system is deployed to find the best strategies in terms of their blowing ratios to maximize the DR of the model with the net power saving considered. An optimal strategy has been found to achieve DR = 10% after 10 generations of the learning process, though without net power saving. It is found that a small sacrifice in DR may achieve a much larger S. The most efficient control achieves S = 5% with a DR of 6%. The surface pressure recovers most in the side surface under this control. Work is under way to unveil the altered wake structures or the DR mechanisms under the optimal and the most efficient controls.