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Rail. Eng. Science (2022) 30(2):221–241 https://doi.org/10.1007/s40534-022-00271-4 Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from moving model experiments 1 1 2,3 4 • • • Jinfeng Wu Xiaozhen Li C. S. Cai Dejun Liu Received: 19 October 2021 / Revised: 11 January 2022 / Accepted: 17 January 2022 / Published online: 5 March 2022 The Author(s) 2022 Abstract In a strong crosswind, the wake of a bridge approaching and leaving the wake of the bridge tower, tower will lead to an abrupt change of the aerodynamic which should not be neglected. forces acting on a vehicle passing through it, which may result in problems related to the transportation safety. This Keywords Vehicle aerodynamics Wind tunnel test study investigates the transient aerodynamic characteristics Moving train Bridge tower Shielding effect Sudden of a high-speed train moving in a truss girder bridge and change mechanism Truss bridge passing by a bridge tower in a wind tunnel. The scaled ratio of the train, bridge, and tower are 1:30. Effects of various parameters such as the incoming wind speed, train speed, and yaw angle on the aerodynamic performance of the train were considered. Then the sudden change mechanism of 1 Introduction aerodynamic loads on the train when it crosses over the tower was further discussed. The results show that the The dynamic performance and safety of rail transportation bridge tower has an apparent shielding effect on the train are of great concern for long-span bridge development passing through it, with the inﬂuencing width being larger subjected to crosswinds. With the continuous improvement than the width of the tower. The train speed is the main of train speed, not only the aerodynamic resistance of the factor affecting the inﬂuencing width of aerodynamic train increases sharply, but a series of aerodynamic prob- coefﬁcients, and the mutation amplitude is mainly related lems that endanger the train operation safety and reduce the to the yaw angle obtained by changing the incoming wind comfort of passengers appear to be solved urgently. These speed or train speed. The vehicle movement introduces an aerodynamic challenges are associated with a high-speed asymmetry of loading on the train in the process of train passing through tunnels, bridge towers, and encoun- tering one another. The running safety of the train and the coupling effect among the crosswind, moving vehicle, and bridge structure are greatly concerned issues and have been & Xiaozhen Li investigated by many scholars [1–4]. Xu and Guo [5] and xzhli@swjtu.edu.cn Cai and Chen [6] built a three-dimensional wind-road Department of Bridge Engineering, School of Civil vehicle-bridge framework to analyze the dynamic respon- Engineering, Southwest Jiaotong University, Chengdu, China ses of the vehicle-bridge system in a windy environment. Li et al. [7] established a wind-vehicle-bridge coupled Department of Bridge Engineering, School of Transportation, model for railway vehicles. Xu et al. [8, 9] developed a Southeast University, Nanjing, Jiangsu, China vehicle-track modeling method to simulate the dynamic Department of Civil and Environmental Engineering, interaction. Liu et al. [10] then extended the safety analysis Louisiana State University, Baton Rouge, LA 70803, USA of the vehicle on the railway bridge by taking into account College of Civil Engineering and Architecture, Jiaxing of the vibration effect of the track structure and accordingly University, Jiaxing 314001, Zhejiang, China 123 222 J. Wu et al. proposed a wind-train-track-bridge interaction system for aerodynamic forces and moments on the vehicle. Research research. on the aerodynamic characteristics of vehicles has been The bridge engineering community has presently technically able to study the moving condition, and the entered a new era which the construction of bridges train speed has been greatly improved as a result. crossing mountainous and oceanic terrain or connecting As far as the bridge towers are concerned, a vehicle islands needs to be addressed [11, 12]. Long-span bridges crossing the wake of the tower may experience a sudden are favored by designers because of its strong crossing change in the aerodynamic loads on it which can poten- ability and convenient navigation. The spans of the sus- tially cause serious trafﬁc accidents. Several researchers pension and cable-stayed bridges have been challenging have attempted to qualitatively exhibit the variation of new limits. The size of the bridge tower also increases with aerodynamic forces on vehicles as they pass through the a large proportion even reaching tens of meters along the wake of the tower [27–29]. Results reported in Charuvisit longitudinal bridge direction. The existence of the bridge et al. [30] indicated that there was an asymmetry in the tower will change the windy environment around the deck variation of the aerodynamic loads when the vehicle was [13, 14]. The authentic aerodynamic forces of the vehicle approaching and leaving the tower wake. In Argentini et al. are determined by the ﬂow ﬁeld around it. In this scenario, [31], a description of aerodynamic loads on a high-sided the sudden change of transverse wind speed in the tower vehicle located in the wake of a bluff tower was presented region is more likely to induce the lateral instability of for the cases with and without localized wind shielding vehicles and handling/controllability problem for the driver near the tower. Wang et al. [32] simulated the aerodynamic [15, 16]. This lies in the dramatic change of aerodynamic forces on a stationary road vehicle in the wake of a bridge forces acting on the vehicle as it passes through the bridge tower using CFD and compared the simulation results with tower. When the vehicle drives through the tower, the wind tunnel test results for the ﬁrst time. vehicle will be tightly blocked. The wind loads acting on However, the results of the aforementioned studies are the vehicle will decrease as it enters the tower region, and mainly focused on vehicles at exposed sites such as then increase as it leaves the region, experiencing a sharp exposed bridges, ground surfaces, viaducts, and embank- change with a high risk that the vehicle can be turned over. ments. Only a few studies have been carried out on vehi- The ﬂow ﬁeld near the tower region is complicated. For cles running across a complicated bridge structure such as a better evaluation of the running safety of the vehicle and truss girder bridge, which is instinctively different in improving the ride comfort of passengers as well as to structure and the interferences arising from it must be provide perspectives for accident prevention, the study on considered. The design of a truss bridge can result in sig- the aerodynamic characteristics of the vehicle crossing the niﬁcantly different ﬂow patterns in crosswind conditions. wake of the bridge tower is of critical importance. The atmospheric boundary layer (ABL) differs signiﬁ- The characteristics of the aerodynamic forces acting on cantly from that of largely exposed bridges as well as the the vehicle can be achieved through computational ﬂuid aerodynamics of vehicles immersed in them, requiring the dynamics (CFD), wind tunnel experiments, and full model aerodynamic forces of vehicles running inside a truss ﬁeld tests. Due to the complexity, high cost, and difﬁculty bridge to be investigated as a standalone study. For the of implementation of the actual vehicle test, the former two consideration of transient vehicle movement, which is methods are commonly adopted. The aerodynamic forces inherently different from stationary testing, a long travel acting on a vehicle model were typically obtained using distance for the vehicle is required such that it can com- stationary scaled models in the initial stage of the study plete an acceleration and deceleration process. Thus, the [17–20]. By considering the moving nature of vehicles with scaled ratio of the bridge needs to be accordingly smaller, critical disruptions to aerodynamic performance, a more and the bridge model is relatively longer than that of typ- appropriate experimental system which can deal with ical bridges. This in turn requires the wind tunnel to be able moving aerodynamic problems is in need which can reveal to accommodate the device in it. Li et al. [33] developed a the real-time characteristics of aerodynamic forces acting novel test system composed of a steel-truss bridge model, a on the vehicle [21–23]. Bocciolone et al. [24] attempted to CRH3 train model, a motion driving system, and a test achieve this by releasing a train model from a speciﬁcally instrumentation and acquisition system to measure the designed ramp to mimic its acceleration. To explore wind aerodynamic characteristics of a high-speed train passing induced forces and pressures on the vehicle model, Dori- through a truss bridge. The scaled ratio of both the bridge gatti et al. [25] considered in detail the differences between and the vehicle was 1:30. In accompanying work by Wang moving model experiments and static experiments. In et al. [34], the shielding effect from the truss bridge on the recognizing the technical challenges and limitations, Xiang aerodynamic forces of the vehicle was further experimen- et al. [26] designed a relatively long and smooth guide-way tally investigated with vehicle both being stationary and to minimize the experimental errors for testing the moving and was compared with the simulation results from Rail. Eng. Science (2022) 30(2):221–241 Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 223 a numerical CFD model using the dynamic mesh method. three-car train model composed of a head car, a middle car, Inﬂuencing factors of the incoming wind speed, train and a tail car, as shown in Fig. 1. The simpliﬁcation was speed, and wind angle on the transient vehicle aerodynamic based on the work by Cooper [36], which suggests that a characteristics were also investigated. Yao et al. [35] decrease in length will not alter the aerodynamic charac- adopted a new overset mesh approach to consider the teristics of the ﬂow as long as the total length remains motion of trains and its effect on the aerodynamics of the above the limit, because the certain distance of the ﬂow train-truss bridge system under crosswinds. The computed characteristics downstream the nose (less than a head car results were validated with the measured ones from wind length) is more or less constant. Therefore, the middle car tunnel experiments. In addition to considering the complex was used to simulate the fairly long middle car body of the supper structure of the bridge, introducing the bridge tower train, and the head car and the tail car, as their names can produce a sudden change in the aerodynamic forces on imply, were used to model the front car and the rear car, the vehicle passing through it. However, the sudden change respectively. In addition, the head car and the tail car were mechanism of the aerodynamic forces acting on the vehicle basically used as transitional segments as their streamlined is rarely studied, yet these are of great importance for geometric shape can weaken the effect of the ambient ﬂow designers to have a comprehensive understanding of the around them. The ﬂow structure around the middle car is aerodynamic characteristics of vehicles on bridges and/or recognized more stable, thus the aerodynamic forces acting for managers to adopt effective countermeasures to ensure on the middle car were tested in this study. the trafﬁc safety on the bridge. Further simpliﬁcations, such as neglecting the mirrors, In this study, an experimental investigation into the windshield wipers, and mechanical parts, were made dur- changes in aerodynamic loads on a high-speed train due to ing the train model production process. The wheelsets and the presence of the bridge tower is presented while also the bogies were also excluded in the modeling. In order to considering train motion. An innovative moving vehicle reduce the inertia effect as much as possible in the accel- device which can apply measurements with shelters (e.g., eration and deceleration processes, the train model adopted the truss bridge, bridge tower, oncoming vehicle, wind a light wood material for the car body and had it hollowed barrier, and tunnel), compel the vehicle to a high driving to achieve weight loss, while the high-quality wood could speed, and adjust incoming wind directions, was devel- achieve high stiffness to ensure the accuracy of the aero- oped. A truss girder and a typical high-speed train geom- dynamic measurements on the train model. The length of etry were selected as the prototype with bridge towers at each car model is 500 mm, and there is a small gap both sides of the deck with a scaled ratio of the bridge, between them to ensure the measurement of the aerody- train, and tower of 1:30. Systematic experiments were namic loads on the middle car that is independent. The performed to investigate the variation of aerodynamic mass of the head car, middle car, and tail car is 700, 980, forces on the train as well as its sudden change mechanism and 820 g, respectively. as the train passes through the wake of the bridge tower. This investigation considers the inﬂuences of various 2.2 Bridge deck model parameters such as the incoming wind speed, train speed, and yaw angle which represents the ﬁrst step toward a There is mutual aerodynamic interference between vehicles larger research project. The ﬁnal goal of this research is, in and bridges under crosswinds. Some achievements have fact, to put forward effective countermeasures like wind been made in the research of aerodynamic characteristics barriers to address issues associated with the sudden of trains in exposed environment, such as on the ground, change in aerodynamic loads on the train and to assess the subgrade, viaduct, or an open bridge structure [37–41]. running safety of the train and the riding comfort of pas- However, only a few studies have been carried out on the sengers when the train is approaching and leaving the wake aerodynamic interference effects of complex bridge struc- of the tower, which will be discussed in detail in its tures (such as truss girder bridge) on trains. In recent years, accompanying paper. due to the consideration of economy and trafﬁc volume, the advantages of highway-railway bridges are more and more obvious, and they are favored by bridge designers. Dif- 2 Models and experimental conﬁguration ferent from the open bridge structure, when wind ﬂows through the truss girder bridge, the unique form of the 2.1 Train model structure will result in complex ﬂow characteristics around it, which also has a great impact on the aerodynamic In consideration of the common high-speed train types characteristics of trains running inside the bridge. running in the Chinese railway, a typical train prototype A long-span cable-stayed bridge on the Shanghai-Nan- was employed in the experiment and was simpliﬁed into a tong HSR (high-speed railway) was selected as the bridge Rail. Eng. Science (2022) 30(2):221–241 224 J. Wu et al. Head car Middle car Tail car (a) (b) 500 500 500 110 Fig. 1 Three-car train model (unit: mm): a elevation view; b end view prototype to investigate the effect of a bridge deck on the with a test section of 22.5 m in width, 36.0 m in length, aerodynamic loads on a train. The total length of the deck and 4.5 m in height, respectively. This large-scaled wind model is 14,000 mm with 30 truss sections, each of which tunnel, on one hand, can increase the scale ratio of the is 593.3 mm in height and 466.7 mm in length, respec- model so that some small accessories can be accurately tively, as shown in Fig. 2a. The truss plane is triangle- simulated. On the other hand, it can adapt to the wind shaped with vertical web members. The cross-section is tunnel test requirements of super long-span bridges. The constant, and the width of the deck is 1,200 mm with the achievable maximum mean wind speed in the tunnel can distance of 600 mm between two adjacent truss planes (see reach 16.5 m/s, and the minimum mean wind speed can be Fig. 2b). as low as 1 m/s. The bridge deck model is made of wood with high Capitalizing on the large width of the test section, an rigidity and was manufactured based on simpliﬁcations by innovative testing device which can accelerate the train neglecting handrails, side and central protection rails and model to a high driving speed and adjust incoming wind maintenance channels. The deck is separated from the directions was developed, as displayed in Fig. 3. Based on upper train model so that the aerodynamic force measure- this device, a series of wind tunnel experiments were ments on the train cannot be affected by the lower deck. performed on a moving train model, to investigate how the aerodynamic forces on the train vary as it was crossing the 2.3 Experimental conﬁguration wake of a tower. The train model was placed inside the truss girder, and it was only moving on the windward side. The wind tunnel tests were carried out in the XNJD-3 wind The total length of the bridge deck model is 14,000 mm, tunnel at Southwest Jiaotong University. The XNJD-3 wind and is divided into four segments for installation, between tunnel is a large closed type boundary layer wind tunnel, which there is a small gap to separate them from each (a) 466.7 134 36.7 14,000 (466.7×30) (b) Wind Train model Truss plane Truss plane 1,200 Fig. 2 Bridge deck model (unit: mm): a side view; b cross section Rail. Eng. Science (2022) 30(2):221–241 64.8 36.7 46.7 73.3 216.5 593.3 593.3 115 Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 225 Tower Seg. #1 Displacement Seg. #2 Seg. #3 Seg. #4 Train model Guideway restrictor Deck model Servo motor Pulley Conveyor belt Support column 7,933 3,267 3,733 3,733 3,267 (466.7×7) (466.7×8) (466.7×8) (466.7×7) 14,000 19,500 20,500 Fig. 3 Schematic diagram of experimental conﬁguration (unit: mm) other. The bridge system and the entire testing system are middle car. The signal receiver is mounted on the head erected by support columns. The side and middle segments car to collect data from sensor via the connecting cable. contain 7 and 8 internodes, respectively. In order to prevent Then, the signal receiver transmits the data to a remote the train model from rushing out of the guide-way due to computer synchronously and wirelessly which, compared the inertial effect, displacement restrictors are set at both to most of the conventional long wire experiments, not ends of it. The distance between the restrictors i.e., the only ensures the stability of the ﬂow ﬁeld around the actual operating distance for the train model is 19,500 mm, vehicle model, but avoids the potential safety problems and the total length of the guide-way is 20,500 mm. caused by wire winding or towing. More importantly, the The train model is actuated by a servo motor with wireless data acquisition method provides a good premise transmissions by pulleys and a synchronous conveyor belt, for testing on vehicles passing through shelters such as which is made of aluminum alloy material as ﬂat and very bridge towers or wind barriers. The whole device makes rigid, ensuring smooth operation of the train model. The the aerodynamic tests on trains more convenient and train model can accurately run at a set speed, and maintain accurate, and details about the testing device can be this speed after the acceleration is completed. The interval referred to Li et al. [33]. of both the acceleration and the deceleration is 0.5 s. Taking into account the operating distance for the train 2.4 Wind tunnel test on site model, the maximum running speed is set to be 15 m/s to ensure that the actual performing of the train model is Figure 5 shows the relative position of tower models to the within the testing area. It also guarantees the interval of a deck. The distances between the tower center and two ends certain constant speed when the train model moves is long of the deck are 6,067 and 7,933 mm, respectively. The enough for signal processing and aerodynamics analyses. tower models are made of wood, 2,800 mm in height, and The motion system can realize bi-directional driving of are set on both sides of the deck model. The lateral and vehicles, forward and backward, greatly improving the longitudinal width of the tower cross-section are 505 and efﬁciency of tests and test cases. 660 mm, respectively. The data acquisition system is another important The motion system can drive vehicles in both directions, component of the whole testing device. It is mainly forward or backward, which greatly improves the efﬁ- ciency of the tests. The forward direction is the default composed of a force testing balance, a sensor, a signal receiver, and a connecting cable, as shown in Fig. 4.The positive direction set by the test module, as shown in force testing balance is installed at the centroid of the Fig. 5, then the backward direction is the opposite direction middle car to measure the aerodynamic forces of the of motion. According to the time history curve of the Rail. Eng. Science (2022) 30(2):221–241 2,800 226 J. Wu et al. (a) (b) Signal receiver Force testing balance Sensor Connecting cable Fig. 4 Data acquisition system: a signal receiver in the head car; b force testing balance in the middle car [31] Forward moving Control room (a) Wind direction Tower model Bridge deck model Train model Guideway (b) Tower model Bridge deck model Train model Guideway 6,067 7,933 Fig. 5 Experimental conﬁguration with tower models (unit: mm): a top view; b side view Rail. Eng. Science (2022) 30(2):221–241 100 Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 227 longitudinal force coefﬁcient, the operating direction can -V x be distinguished. The incoming direction of wind w is assigned to be res perpendicular to the deck, and a is deﬁned as the wind y y angle i.e., the angle between the incoming wind velocity U and the deck. The relationship between a and w is a ¼ 90 w, and the wind angle discussed in this study is 90 . The sampling frequency is set to be 1,024 Hz, which is applicable for data analysis under different train speeds. In y order to minimize the systematic errors and ensure the stability of the test system, each case was repeatedly tested x for three times. The in-situ wind tunnel experiments of the three-car train model passing through the tower are shown in Fig. 6. Fig. 7 Wind loads and velocity vector diagram on train model 2 2 2 U ¼ U þ V ; ð1aÞ res 3 Data process U ¼ U sin b; ð1bÞ res The wind forces and moments acting on the train model b ¼ arctanðU=VÞ; ð1cÞ can be measured by the force testing balance. The direc- where b is the yaw angle. tions of wind loads and velocity vector diagram of train model are displayed in Fig. 7. In this study, only the lift 3.1 Deﬁnition of train aerodynamic coefﬁcients force F , the side force F , and the rolling moment M are L S R investigated, corresponding to F , F , and M in Fig. 7, x y z There are two typical deﬁnitions for train aerodynamic respectively. The relationship between the wind velocity U coefﬁcients. One is deﬁned according to the incoming and the relative wind velocity to vehicle U is as follows: res mean wind speed perpendicular to the moving direction, Fig. 6 Wind tunnel test on site Rail. Eng. Science (2022) 30(2):221–241 Moving direction 228 J. Wu et al. which is convenient for further study, if any, such as the (a) Test 1 application of wind loads on vehicles in the coupled wind- Test 2 vehicle-bridge vibration analysis. The expressions are as Test 3 follows: C ¼ ; ð2aÞ L;I 0:5qU BL -6 C ¼ ; ð2bÞ S;I 0:5qU HL -12 -18 C ¼ ; ð2cÞ R;I 2 2 2 4 6 8 101214 0:5qU B L t (s) where C , C , and C are the lift force coefﬁcient, side L;I S;I R;I (b) Test 1 force coefﬁcient, and rolling moment coefﬁcient based on Test 2 the ﬁrst type of deﬁnition, respectively; q is the air density; Test 3 U is the incoming mean wind speed; B, H, and L stand for the width, height, and length of the middle car, respectively. The other deﬁnition is based on the resultant velocity of wind velocity and vehicle velocity -6 (see Fig. 7) and can be written as -12 C ¼ ; ð3aÞ L;II 0:5qU BL res -18 2 4 6 8 101214 C ¼ ; ð3bÞ t (s) S;II 0:5qU HL res (c) Test 1 M 0.8 Test 2 C ¼ ; ð3cÞ R;II 2 2 Test 3 0:5qU B L res 0.4 where C , C , and C are the lift force coefﬁcient, L;II S;II R;II 0.0 side force coefﬁcient, and rolling moment coefﬁcient based on the second type of deﬁnition, respectively. -0.4 On the basis of Eq. (1b), it can be easily deduced that -0.8 the aerodynamic coefﬁcients under these two deﬁnitions have the relation as follows: -1.2 24 68 10 12 14 C ¼ C sin b ði ¼ L; S; RÞ: ð4Þ i;II i;I t (s) The ﬁrst deﬁnition is mainly employed for analyzing the Fig. 8 Time history curves of three repeated tests: a lift force F ; b inﬂuences of factors on aerodynamic characteristics of the side force F ; c rolling moment M S R vehicle in this study, and C , C , and C are also L;I S;I R;I written as C , C , and C , respectively, in the following L S R Figure 8 shows the time history curves of the aerody- sections. namic loads on the train under three repeated tests with the train speed of 2 m/s and the incoming wind speed of 3.2 Stability analysis of system testing 10 m/s, respectively. Figure 9 displays the envelope anal- ysis curves of the repeated tests for the convenience of The stability of the test system related to the reliable results comparison. The signal under three repeat tests shows the of train aerodynamic coefﬁcients are investigated by coincide trend and characteristics points. It can be seen that comparing the repeatedly tested cases through model tests. the results under three identical tests are in good agree- On one hand, it is to conﬁrm the stability and consistency ment, i.e., the system has good stability which can meet the of system testing; on the other hand, it can ensure the basic test requirements. With a comprehensive analysis of effectiveness analysis of the target case, especially when three test results, one test curve is selected as the ﬁnal there are errors with signals in one of the tests. result for the case in this study. Rail. Eng. Science (2022) 30(2):221–241 F (N) F (N) M (Nm) S L R Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 229 which needs to be eliminated for better analysis of the data. (a) Test 1 Li et al. [33] indicated that using 0–10 Hz low pass ﬁlter can Test 2 effectively eliminate the inﬂuence of interferences to process Test 3 the original data. The ﬁltered results are presented in Fig. 10, and it can be found that the time histories of the aerodynamic coefﬁcients remain quite stable after ﬁltering. In order to investigate the variation of train aerodynamic -6 coefﬁcients in different movement stages (acceleration, -12 constant speed, and deceleration) and in the process of entering the truss girder and the tower area, the ﬁltered -18 2 4 6 8 10 12 14 time history curves are re-plotted in Fig. 11. t (s) The motion stages of the vehicle can be distinguished from (b) 18 the longitudinal force coefﬁcient. The total running distance Test 1 Test 2 is 14 m set by the motion system, and the intervals of both the Test 3 acceleration and the deceleration are 0.5 s. Thus, the dis- tances of the acceleration and the deceleration stage as well as the constant speed period can be calculated accordingly, as illustrated in Fig. 11.As shown by Fig. 11a, the vehicle is stationary, being basically zero. The vehicle starts to accel- -6 erate at 3.44 s with a negative acceleration owing to backward moving, opposite to the positive direction of the motion -12 system. At 3.94 s, the acceleration phase is completed, and 2 4 6 8 10 12 14 the vehicle reaches the set constant speed of 2 m/s. The t (s) interval the vehicle runs at the constant speed is 6.5 s, (c) Test 1 therefore, the theoretical time for initially decelerating of the 0.8 Test 2 vehicle should be 10.44 s, which is exactly consistent with Test 3 0.4 that in the longitudinal force coefﬁcient curve. The vehicle stops at 10.94 s, and the longitudinal force coefﬁcient returns 0.0 to around zero after the ﬂow ﬁeld is stable. According to the changes of aerodynamic coefﬁcients -0.4 and in each motion stage, the moving process of the vehicle -0.8 passing through the bridge with tower is segmented as follows: -1.2 246 8 10 12 14 S1: Stationary stage (vehicle outside the truss girder), t (s) V ¼ 0; S2: Acceleration stage, with an interval of 0.5 s; Fig. 9 Envelope curves of three repeated tests: a lift force F ; b side force F ; c rolling moment M S3: Constant speed stage (vehicle outside the truss S R girder); 3.3 Data analysis S4: Constant speed stage (vehicle entering the truss girder); There are a lot of interference factors in the process of S5: Constant speed stage (vehicle inside the truss girder); vehicle movement, such as rail irregularity, model vibration, S6: Constant speed stage (vehicle through the tower and inertia effect, which will have a great impact on the area); accuracy of the test. Some shielding and vibration isolation S7: Deceleration stage, with an interval of 0.5 s; measures have been taken in the test design, yet the intro- S8: Stationary stage (vehicle inside the truss girder). duction of interference signals cannot be completely avoi- From Fig. 11b–d, it is found that when the vehicle is ded. Figure 10 shows the original time history curves of entering the truss girder (S4) and passing through the tower train aerodynamic coefﬁcients under the train speed of 2 m/s (S6), the aerodynamic coefﬁcients of the vehicle change and the incoming wind speed of 10 m/s, where the longi- signiﬁcantly and both decrease (the rolling moment coef- tudinal force coefﬁcient deﬁned by C ¼ F =ð0:5qU BLÞ is z z ﬁcient considering the absolute value), which indicates that also given in Fig. 10d. It can be seen that the curve ﬂuctu- the presence of the truss girder and bridge tower have a ates strongly and obvious interferences exist in the test, clear shielding effect on the vehicle. The aerodynamic Rail. Eng. Science (2022) 30(2):221–241 M (Nm) F (N) F (N) R L 230 J. Wu et al. (a) (b) Original data Original data 0-10 Hz low pass filter 4 0-10 Hz low pass filter -2 -2 -4 -4 02468 10 12 14 16 02 46 8 10 12 14 16 t (s) t (s) (c) (d) Original data 2 Original data 0-10 Hz low pass filter 0-10 Hz low pass filter -5 -1 -10 -2 -15 0 2 4 6 8 101214 16 0 2 4 6 8 10 12 14 16 t (s) t (s) Fig. 10 Data ﬁltering processing: a lift force coefﬁcient C ; b side force coefﬁcient C ; c rolling moment coefﬁcient C ; d longitudinal force L S R coefﬁcient C coefﬁcients during other stages, including S1, S5, and S8, coefﬁcients of the vehicle have no obvious change due to are relatively stable. The ﬂow ﬁeld is not yet stable in the the instantaneity and short time interval, which is not initial 10.94–12.5 s in S8 since the vehicle has just stopped, promptly causing changes in the ﬂow. and hence, the period of 12.5–15 s is regarded as the steady From the above analysis, it can be seen that the aero- section of S8. One can ﬁnd that when the vehicle is sta- dynamic characteristics of the vehicle are closely related to tionary, the aerodynamic coefﬁcients in S1 are larger than the ﬂow ﬁeld, and the main factors leading to changes of it those in S8 (absolute value for C ) due to the shielding are shelters and vehicle motion. This study mainly dis- effect of truss bridge. The shielding effect is also found cusses the shielding effect by the bridge tower as well as when the train runs from the uncovered stage S3 to stage considering the inﬂuence of vehicle movement. S5. This indicates that whether the vehicle is in movement or not, the shielding effect of the truss structure should not 3.4 Reynolds number dependency be ignored. Similarly, the inﬂuence of the bridge tower on the vehicle crossing through it is also signiﬁcant, which The Reynolds number has a signiﬁcant effect on the ﬂow should be paid special attention to and considered in the around a vehicle model. In wind tunnel test, the inﬂuence of analysis of vehicle aerodynamics. the Reynolds number should be avoided or weakened to Putting aside the variations in the tower area, when the ensure the reliability of test results. Normally, it is assumed vehicle is enclosed in the truss girder (S5 to S8), the that the aerodynamic force measurements on vehicles are aerodynamic coefﬁcients change greatly and vary from independent from the Reynolds number when the Reynolds each other from vehicle movement to stop. Compared with number is beyond a critical value. An approximate critical the dynamic condition, the lift force coefﬁcient of the number in Baker [21]is6 9 10 , with wind tunnel tests on a vehicle in stationary state decreases, while the side force 1:50 scaled vehicle model. In the work by Li et al. [33], it has coefﬁcient and the rolling moment coefﬁcient increase (C been pointed out that when the Reynolds number goes beyond considering absolute value). In the acceleration and a critical one (about 4.5 9 10 ), the aerodynamic coefﬁcients deceleration stage (S2 and S7), the aerodynamic of the train model are considered less sensitive to the Reynolds Rail. Eng. Science (2022) 30(2):221–241 z Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 231 V=2 m/s V=0 m/s V=0 m/s (a) 1.8 3.44 3.94 10.44 10.94 S7: Deceleration stage S2: Acceleration stage 0.9 S1: Stationary stage (Outside the truss girder) 0.0 S8: Stationary stage -0.9 (Inside the truss girder) (b) 1.2 0.8 0.4 S3: Constant speed stage (Outside the truss girder) 0.0 (c) 1.2 S5: Constant speed stage 0.8 (Inside the truss girder) 0.4 S4: Constant speed stage (Entering the truss girder) 0.0 (d) 0.00 -0.03 -0.06 S6: Constant speed stage (Through the tower region) -0.09 -5 0 5 10 15 20 t (s) Fig. 11 Train aerodynamic coefﬁcients in different stages: a longitudinal force coefﬁcient C ; b lift force coefﬁcient C ; c side force coefﬁcient z L C ; d rolling moment coefﬁcient C S R number. In the case, the results are obtained under the con- the moving train passing through the bridge with and dition that only the train model movement are conducted on without tower (see Fig. 12). On one hand, it is to clearly the guide-way without considering the inﬂuence of the truss understand the mechanism of the shielding effect of the bridge structure, which is known that it will have a signiﬁcant tower on the aerodynamic performance of vehicles cross- effect on the ﬂow around the vehicle. Speciﬁcally, the exis- ing through it; on the other hand, it is to conﬁrm the tence of the bridge structure will enhance the turbulence of the validity and accuracy of the test device, especially when ﬂow inside the truss girder where the train model travels. there are shelters (such as towers, buildings, etc.) in the For the present investigation with bridge structure ﬁeld. involved, it is believed that the Reynolds number will get The time history curves of aerodynamic forces on the larger, far greater than the stated critical value of train under a certain driving speed can be converted into 4.5 9 10 , leading to the aerodynamic coefﬁcient mea- position curves through relevant processing of vehicle surement in a less Reynolds sensitive range. Therefore, the speed. The center of the tower model is referred as the Reynolds effect on aerodynamics measurements is location of 0 m. The locations where the train model is neglected in the following discussions. approaching the tower are referred as the negative region, while the locations where the train model is leaving the wake are referred as the positive region, no matter the train 4 Results model is moving forward or backward. For the conve- nience of description, the aerodynamic coefﬁcient curve is 4.1 Shielding effect of bridge tower roughly divided into three stages according to the position of the vehicle, namely, approaching tower, tower shielding The effects related to the presence of bridge tower are area, and leaving tower. investigated by comparing the aerodynamic coefﬁcients of Rail. Eng. Science (2022) 30(2):221–241 C C C S z R L 232 J. Wu et al. (a) 0.8 (b) 0.6 Without tower Without tower With tower With tower 0.6 0.4 0.4 0.2 0.0 0.2 0.0 -0.2 Tower width Tower width -0.4 -0.2 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 01234 Location (m) Location (m) (c) 0.02 Without tower With tower 0.00 -0.02 -0.04 -0.06 Tower width -0.08 -4 -3 -2 -1 0123 4 Location (m) Fig. 12 Aerodynamic coefﬁcients of train with and without tower: a lift force coefﬁcient C ; b side force coefﬁcient C ; c rolling moment L S coefﬁcient C The incoming wind speed and train speed in this section shielding effect on the train and has a signiﬁcant inﬂuence are 10 and 4 m/s, respectively. From Fig. 12, it is found on its aerodynamic characteristics. that the aerodynamic coefﬁcients away from the tower Another aspect of the shielding effect of the bridge region are well consistent with the case without tower, tower on the train is referred to the width of the sudden except a slight difference for the side force coefﬁcient change area, which is much larger than the width of the which is, however, within the scope of acceptance. Aero- tower itself, and the aerodynamic loads on the train present dynamic coefﬁcients of train experience great mutations asymmetry when it approaches and leaves the tower. when it is passing though the bridge tower. The curves of Changes of aerodynamic coefﬁcients when vehicles cross the lift force coefﬁcient and the side force coefﬁcient ﬁrst through the tower can be achieved by means of wind tunnel decrease as the vehicle approaches the tower wake and then test or CFD simulation [42–44]. However, there are few increase as it leaves the wake. The side force coefﬁcient discussions on the mechanism and inﬂuencing factors of even suffers a great decrease to negative area, indicating bridge tower shielding. the side force changing the direction of force on the train. It In this study, based on a long-span cable-stayed truss is disadvantageous for train safety and explains the com- girder bridge, the aerodynamics of vehicles crossing through plexity of ﬂow around the tower as well. While for the the wake of a tower were investigated via wind tunnel rolling moment coefﬁcient which is small, its absolute experiments. Two representative parameters, inﬂuencing value also experiences a sudden decrease and a sudden width d and mutation amplitude D, are deﬁned to further increase afterward as the train is passing behind the tower. study the sudden change mechanism of aerodynamic coef- Furthermore, the aerodynamic coefﬁcients reach their ﬁcients when passing by the bridge tower, as shown in mutation peak values at the tower region, demonstrating Fig. 13. Taking one of the aerodynamic coefﬁcients as an that the presence of the bridge tower has an obvious example, when the train is in the region of approaching tower and leaving tower, the mean values of its aerodynamic Rail. Eng. Science (2022) 30(2):221–241 S Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 233 Tower shielding area are quantitatively compared with mean values from the 0.8 Approaching tower Leaving tower case without tower, as displayed in Fig. 14. The lift force 0.6 coefﬁcient decreases by 92%; the side force coefﬁcient decreases by 153%; and the rolling moment coefﬁcient 0.4 increases by 68%, quantitatively demonstrating an obvious 1 shielding effect of tower. In the region of approaching 0.2 tower and leaving tower, the mean values of the steady (x , y ) 2 2 (x , y ) 1 1 Δ sections are obtained, and horizontal lines with mean Δ 2 0.0 values intersect with the aerodynamic coefﬁcient curve, marked with red slashes in Fig. 12. Speciﬁcally, the width (x , y ) -0.2 p p of the sudden change area for the lift force coefﬁcient, side force coefﬁcient, and rolling moment coefﬁcient is 1.277, -0.4 1.551, and 1.856 m, respectively, as illustrated in Table 1. -6 -4 -2 0 2 4 6 One can ﬁnd that the width of the sudden change area for Location (m) each coefﬁcient is much larger than the tower width of Fig. 13 Deﬁnition of inﬂuencing width and mutation amplitude 0.660 m (abscissa range from - 0.330 to 0.330 m), increasing by 1.93, 2.35, and 2.81 times, respectively. In coefﬁcients are denoted by y and y , respectively, and 1 2 addition, the initial and last intersection point exactly state horizontal lines with mean values intersecting with the the asymmetry in the aerodynamic loads when the train is aerodynamic coefﬁcient curve can obtain points ðx ; y Þ and 1 1 approaching and leaving the wake, which is caused by the ðx ; y Þ. The minimum point of the aerodynamic coefﬁcient 2 2 vehicle relative movement to the tower, as has been in thesuddenchangeareaisdenoted by ðx ; y Þ. Then, some p p proposed by Charuvisit et al. [30] that the vehicle motion deﬁnitions are made as follows: modiﬁes the steady state aerodynamic condition and introduces an asymmetry in the aerodynamic loads on the Inﬂuencing width: vehicle when it passes through the tower. The asymmetric d ¼ x x ; ð5aÞ 1 p 1 results are clearly distinguished from the conventional static ones and will be detailed discussed in future work. d ¼ x x ; ð5bÞ 2 2 p d ¼ d þ d ¼ x x : ð5cÞ s 1 2 2 1 4.2 Effect of wind speed Mutation amplitude: D ¼ y y ; ð6aÞ 1 1 p When the effect of the Reynolds number is not taken into account, the aerodynamic coefﬁcient is the function of D ¼ y y ; ð6bÞ 2 2 p wind angle and yaw angle [21]. The wind angle discussed D ¼ðD þ D Þ=2: ð6cÞ m 1 2 in this study is 90 , therefore the aerodynamic coefﬁcient is only a function of yaw angle, which can be changed by Taking a further analysis on Fig. 12, the mutation peak changing the incoming wind speed or train speed. How- values of the aerodynamic coefﬁcients at the tower region ever, the aerodynamic characteristics of vehicles at the same yaw angle (composed of different wind speed and 0.4 train speed) are quite different. Therefore, it is necessary to Mean value 0.325 study the aerodynamic coefﬁcients of vehicles under dif- Mutation peak 0.3 0.264 ferent incoming wind speeds or vehicle speeds. When the 0.2 Table 1 Inﬂuencing width of sudden change area for case with tower 0.1 Items x (m) x (m) d (m) d =d 1 2 s s t 0.026 0.0 C - 0.574 0.703 1.277 1.93 -0.010 -0.031 C - 0.711 0.840 1.551 2.35 -0.1 C - 0.850 1.006 1.856 2.81 -0.141 -0.2 x and x are the initial and last intersecting positions, respectively; d 1 2 s C C is the inﬂuencing width of sudden change area; and d is the width of L S R t tower Fig. 14 Mutation peak and mean values of coefﬁcients Rail. Eng. Science (2022) 30(2):221–241 Peak/mean value of coefficients 234 J. Wu et al. (a) 1.0 (a) 2.5 U=4 m/s, β = 63.4° U=4 m/s, β = 18.4° U=6 m/s, β = 71.6° U=6 m/s, β = 26.6° 2.0 0.8 U=8 m/s, β = 76.0° U=8 m/s, β = 33.7° U=9 m/s, β = 77.5° U=9 m/s, β = 36.9° 1.5 U=10m/s, β = 78.7° 0.6 U=10m/s, β = 39.8° 1.0 0.4 0.5 0.2 0.0 0.0 -0.5 Tower width Tower width -0.2 -1.0 -5 -4 -3 -2 -1 0 1234 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Location (m) Location (m) (b) 1.6 U=4 m/s, β = 63.4° (b) 1.8 U=4 m/s, β = 18.4° U=6 m/s, β = 71.6° 1.2 U=6 m/s, β = 26.6° U=8 m/s, β = 76.0° 1.2 U=8 m/s, β = 33.7° U=9 m/s, β = 77.5° 0.8 U=9 m/s, β = 36.9° U=10m/s, β = 78.7° U=10m/s, β = 39.8° 0.4 0.6 0.0 0.0 -0.4 -0.6 -0.8 Tower width -1.2 Tower width -1.2 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Location (m) Location (m) 0.06 (c) (c) 0.24 U=4 m/s, β = 63.4° U=4 m/s, β = 18.4° U=6 m/s, β = 71.6° U=6 m/s, β = 26.6° 0.18 0.03 U=8 m/s, β = 76.0° U=8 m/s, β = 33.7° U=9 m/s, β = 77.5° U=9 m/s, β = 36.9° 0.12 U=10m/s, β = 78.7° 0.00 U=10m/s, β = 39.8° 0.06 -0.03 0.00 -0.06 -0.06 -0.09 -0.12 Tower width Tower width -0.18 -0.12 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Location (m) Location (m) Fig. 15 Aerodynamic coefﬁcients of train varying with wind speed at Fig. 16 Aerodynamic coefﬁcients of train varying with wind speed at low train speed of V = 2 m/s: a lift force coefﬁcient C ; b side force L high train speed of V = 12 m/s: a lift force coefﬁcient C ; b side force coefﬁcient C ; c rolling moment coefﬁcient C S R coefﬁcient C ; c rolling moment coefﬁcient C S R wind speed is 4-10 m/s, the aerodynamic coefﬁcients of signiﬁcantly with the incoming wind speed, except the side the train varying with the wind speed under a low train force coefﬁcient at the wind speed U = 4 m/s is negative, speed of V = 2 m/s and a high train speed of V = 12 m/s are which may be caused by the test contingency. In the pro- as shown in Figs. 15 and 16, respectively. cess of crossing through the tower, the aerodynamic coef- It can be seen from Fig. 15 that at low train speed, when ﬁcients of the train appear great mutations, yet no obvious the train is in the region of approaching tower, the aero- change with the wind speed. It is worth noting that under dynamic coefﬁcients of the vehicle generally do not change different wind speeds, the side force coefﬁcient decreases Rail. Eng. Science (2022) 30(2):221–241 C C C L C C R C L S Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 235 abruptly from positive value to negative value, and then 1.0 (a) V=2 m/s, β = 76.0° increases to positive value, changing direction continu- V=4 m/s, β = 63.4° ously, which will be extremely detrimental to the train 0.8 V=8 m/s, β = 45.0° operation safety. After the train leaves the tower, the V=10 m/s, β = 38.7° V=12 m/s, β = 33.7° 0.6 aerodynamic coefﬁcients of the vehicle return to the same as that in the region of approaching tower. 0.4 It can be seen from Fig. 16 that at high train speed, when the train is approaching the tower, the aerodynamic 0.2 coefﬁcients of the vehicle ﬂuctuate notably with the change of wind speed, which is entirely different from that at low 0.0 train speed. On the whole, the lift force coefﬁcient Tower width decreases with the increase of wind speed. The side force -0.2 -5 -4 -3 -2 -1 0 1 2 3 4 5 coefﬁcient increases with the increase of wind speed and Location (m) changes from negative region to positive region. The rolling moment coefﬁcient decreases with the increase of 1.0 (b) V=2 m/s, β = 76.0° wind speed, changing direction from positive to negative V=4 m/s, β = 63.4° 0.8 value. The direction of the side force and rolling moment V=8 m/s, β = 45.0° on the train has changed. Under some combinations, V=10 m/s, β = 38.7° 0.6 V=12 m/s, β = 33.7° potential safety hazard may exist for train operation. In the 0.4 process of the train passing through the tower, the lift force coefﬁcient and the side force coefﬁcient have a distinct 0.2 mutation while the rolling moment coefﬁcient does not. In fact, the sudden change of the rolling moment coefﬁcient is 0.0 more serious, with the direction changing continuously -0.2 back and forth between the positive and negative area. The Tower width smaller the incoming wind speed, the greater the abrupt -0.4 -5 -4 -3 -2 -1 0 1 2 3 4 5 change of each aerodynamic coefﬁcient as well as the Location (m) ﬂuctuation, which has the reverse effect at high wind speeds. Compared with the low train speed case of V = 12 m/s, 0.04 (c) V=2 m/s, β = 76.0° it exactly shows the complexity of the ﬂow ﬁeld V=4 m/s, β = 63.4° around the bridge tower with the train running at a high 0.02 V=8 m/s, β = 45.0° train speed. The inﬂuence of the vehicle motion must be V=10 m/s, β = 38.7° V=12 m/s, β = 33.7° 0.00 considered. Meanwhile, the results are also consistent with that in Fig. 18c, i.e., the smaller the yaw angle (the smaller -0.02 the incoming wind speed), the larger the mutation amplitude of aerodynamic coefﬁcients when the train passes by the -0.04 bridge tower under a high train speed. When the train is leaving the tower, a local enlargement appears for the -0.06 Tower width aerodynamic coefﬁcients especially at a low incoming wind -0.08 speed, which is caused by the wake effect of the -5 -4 -3 -2 -1 0 1 2 3 4 5 bridge tower. Furthermore, the aerodynamic coefﬁcients Location (m) display asymmetry in the process of approaching and leaving the tower, consistent with the results in Charuvisit Fig. 17 Aerodynamic coefﬁcients of train varying with vehicle speed under the ﬁrst deﬁnition: a lift force coefﬁcient C ; b side force et al. [30]. L,I coefﬁcient C ; c rolling moment coefﬁcient C S,I R,I 4.3 Effect of train speed 8 m/s and the train speed is 2–12 m/s. We can ﬁnd that the variation law of vehicle aerodynamic coefﬁcients with the The ﬂow ﬁeld around a train in motion is quite different yaw angle is various with different deﬁnitions. Under the from that at rest. In order to better analyze the inﬂuence of second deﬁnition, when the train is approaching the tower, the vehicle movement on aerodynamic coefﬁcients, chan- the mean values of aerodynamic coefﬁcients are consistent ges of the aerodynamic coefﬁcients with the yaw angle with the changing laws in Li et al. [33], that is, the lift force (33.7 –76.0 ) under two deﬁnitions are shown in Figs. 17 coefﬁcient and the side force coefﬁcient increase, and the and 18, respectively, when the incoming wind speed is Rail. Eng. Science (2022) 30(2):221–241 S,I L,I R,I 236 J. Wu et al. signiﬁcantly with the train speed, which is completely 1.0 (a) V=2 m/s, β = 76.0° 2 different from that in the second deﬁnition after sin b V=4 m/s, β = 63.4° 0.8 conversion. When the train is in the tower shielding area, V=8 m/s, β = 45.0° V=10 m/s, β = 38.7° the aerodynamic coefﬁcients of the train all experience V=12 m/s, β = 33.7° 0.6 great mutations. Different from that in Sect. 4.2, the inﬂuencing widths of aerodynamic coefﬁcients under var- 0.4 ious train speeds are different. Generally, with the increase of the train speed, the inﬂuencing widths of aerodynamic 0.2 coefﬁcients in the tower shielding region increase. While in Sect. 4.2 where the train speed is constant, the difference of 0.0 Tower width the inﬂuencing width is not signiﬁcant, indicating that the -0.2 train speed is an important factor affecting the inﬂuencing -5 -4 -3 -2 -1 01 2345 widths of aerodynamic coefﬁcients. With the shielding Location (m) effect of the bridge tower, the lift force coefﬁcient ﬁrst decreases and then increases, and the mutation amplitudes (b) 1.0 V=2 m/s, β = 76.0° under different train speeds are various. The side force V=4 m/s, β = 63.4° 0.8 coefﬁcient experiences a sudden change with direction of V=8 m/s, β = 45.0° V=10 m/s, β = 38.7° the side force acting on the train changed continuously, and 0.6 V=12 m/s, β = 33.7° the mutation amplitudes vary little under various train 0.4 speeds. The rolling moment coefﬁcient presents an obvious ‘‘sudden change’’ phenomenon under low train speed, 0.2 while no obvious this kind of phenomenon at high train 0.0 speed, which are consistent with the results in Figs. 15c and 16c. -0.2 Tower width After the train leaves the bridge tower, the inﬂuence of -0.4 the tower shielding effect on wind forces on the train -5 -4 -3 -2 -1 0 1 2 3 4 5 gradually weakens. However, the aerodynamic coefﬁcients Location (m) of the train increase partially due to the vehicle movement, 0.04 (c) and the higher the train speed, the more obvious the partial V=2 m/s, β = 76.0° increase of the lift force coefﬁcient and the side force V=4 m/s, β = 63.4° 0.02 V=8 m/s, β = 45.0° coefﬁcient. After a certain distance away from the bridge V=10 m/s, β = 38.7° tower, the aerodynamic coefﬁcients of the vehicle return to V=12 m/s, β = 33.7° 0.00 that before entering the bridge tower area. The inﬂuencing widths of aerodynamic coefﬁcients -0.02 under the two deﬁnitions are consistent. The variation of -0.04 the inﬂuencing widths with the train speed is shown in -0.06 Tower width -0.08 -5 -4 -3 -2 -1 0 12345 Location (m) Fig. 18 Aerodynamic coefﬁcients of train varying with vehicle speed under the second deﬁnition: a lift force coefﬁcient C ; b side force L,II coefﬁcient C ; c rolling moment coefﬁcient C S,II R,II rolling moment coefﬁcient decreases with the increase of the yaw angle. 1 In this study, the ﬁrst deﬁnition is used to describe the aerodynamic characteristics of the train at different stages 02 4 6 8 10 12 14 when it passes through the bridge tower. It can be seen that V (m/s) when the train does not enter the tower region, the aero- dynamic coefﬁcients of the train do not change Fig. 19 Inﬂuencing widths varying with train speed (U = 8 m/s) Rail. Eng. Science (2022) 30(2):221–241 C C S,II L,II R,II d (m) Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 237 Fig. 19. It can be seen that the higher the train speed, the shown in Fig. 20. It can be seen that the inﬂuencing widths greater the inﬂuencing widths of the curve in tower of vehicle aerodynamic coefﬁcients vary little with the yaw shielding area. The inﬂuencing width of aerodynamic angle under low and high train speed, respectively, which coefﬁcients has a positive correlation with the train speed. suggests that the effect of the wind speed on the inﬂuencing From the perspective of the wave mechanism, the rela- width of aerodynamic coefﬁcients is not signiﬁcant at a tionship among the speed, wavelength k and frequency f is certain train speed. The inﬂuencing widths of aerodynamic V ¼ kf . The vibration frequency of the car body is con- coefﬁcients at high train speed are larger than that at low stant, hence the higher the train speed, the larger the train speed. Taking the wind speed of 4 m/s as an example, wavelength of the curve, and the greater the inﬂuencing the inﬂuencing widths of the lift force coefﬁcient, side width. When the train passes through the bridge tower, the force coefﬁcient, and rolling moment coefﬁcient under low inﬂuence range of the tower on the train covers several train speed are 0.816, 0.873, and 1.390 m, respectively, wavelengths, and the aerodynamic characteristics of the which are 1.23, 1.32, and 2.11 times the width of the bridge train within this range will be affected and reﬂected as tower itself (0.66 m). While under high train speed, the ‘‘sudden change’’. The inﬂuencing widths corresponding to inﬂuencing widths of the lift force coefﬁcient and the side the curves of different wavelengths are also inconsistent. force coefﬁcient are 3.904 and 4.387 m, respectively, The higher the train speed (the larger the wavelength), the increased by 5.92 and 6.65 times, which is much larger smaller the slope of the sudden decrease, and the larger the than the width of the bridge tower. The higher the vehicle inﬂuencing width of aerodynamic coefﬁcients. One can speed, the larger the inﬂuencing width of the vehicle also ﬁnd that the inﬂuencing width of the rolling moment aerodynamic coefﬁcients. When the vehicle speed is con- coefﬁcient is larger than that of the lift force coefﬁcient and stant, the inﬂuencing width has no signiﬁcant change, the side force coefﬁcient, and the inﬂuencing width of the which also implies that the vehicle speed is a critical factor lift force coefﬁcient and the side force coefﬁcient is close affecting the inﬂuencing width of aerodynamic coefﬁ- to each other. cients. From Figs. 15 and 16, we can also ﬁnd that the Taking the inﬂuencing width of the side force coefﬁcient shielding effect of the bridge tower, reﬂected in the inﬂu- as an example, as shown in Table 2, when the train speed is encing width, has the greatest impact on the rolling 2 m/s, the inﬂuencing width in the tower shielding area is moment of the vehicle, and then the side force and the lift 0.80 m, 1.21 times of the width of the bridge tower; when force. the train speed is 12 m/s, the inﬂuencing width is 4.35 m, The variation of the mutation amplitude of aerodynamic 6.59 times of the width of the bridge tower. The inﬂuencing coefﬁcients with the yaw angle under the two deﬁnitions is width of aerodynamic coefﬁcients is positively correlated shown in Fig. 21. It was discovered that the variation trend of the mutation amplitude of aerodynamic coefﬁcients with with the train speed. the yaw angle is different under different deﬁnitions. 4.4 Effect of yaw angle Outside of the tower area, the changing law of the mutation amplitude under two deﬁnitions are inconsistent. In the By analyzing Figs. 15 and 16, the variations of the inﬂu- shelter area of the tower, the variation of the mutation encing width of aerodynamic coefﬁcients with the yaw amplitude of aerodynamic coefﬁcients with the yaw angle angle at low and high vehicle speeds are obtained, as is also related to the deﬁnition adopted. Under the ﬁrst deﬁnition, when 33:7 b 45 , the mutation amplitude of aerodynamic coefﬁcients decreases Table 2 Inﬂuencing widths of train aerodynamic coefﬁcients with the increase of the yaw angle (the rolling moment V (m/s) C C C L S R coefﬁcient considers the absolute value). While when 45 b 76:0 , the mutation amplitude began to level off d (m) d =d d (m) d =d d (m) d =d s s t s s t s s t with the increase of the yaw angle, which is consistent with 2 0.87 1.32 0.80 1.21 1.41 2.14 that in Sect. 4.4, that is, b¼45 is the critical yaw angle of 4 1.51 2.28 1.43 2.17 2.18 3.30 the mutation amplitude. Under the second deﬁnition, when 8 2.80 4.24 3.17 4.80 – – 33:7 b 76:0 , the mutation amplitude of aerodynamic 10 3.71 5.62 3.60 5.46 – – coefﬁcients increases with the increase of the yaw angle 12 3.97 6.02 4.35 6.59 – – with no critical value (the rolling moment coefﬁcient is not Rail. Eng. Science (2022) 30(2):221–241 238 J. Wu et al. (a) 6 (b) Low train speed Low train speed High train speed High train speed 0 0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 β (°) β (°) (c) Low train speed High train speed 10 20 30 40 50 60 70 80 90 β (°) Fig. 20 Inﬂuencing width of aerodynamic coefﬁcients varying with yaw angle: a lift force coefﬁcient; b side force coefﬁcient; c rolling moment coefﬁcient 0.7 obvious because of its small value), and it is close to the mutation amplitude in the ﬁrst deﬁnition when the yaw C C L,Ⅰ S,Ⅰ R,Ⅰ 0.6 C C L,Ⅱ R,Ⅱ angle is large (e.g., b¼76:0 ). S,Ⅱ 0.5 The curves of the mutation amplitude of aerodynamic coefﬁcients with the yaw angle at V = 2 m/s, V = 12 m/s, 0.4 and U = 8 m/s are plotted together and are shown in 0.3 Fig. 22. It can be seen that the mutation amplitude curves 0.2 of V = 2 m/s and V = 12 m/s are in good agreement with the trend under U = 8 m/s. Speciﬁcally, at small yaw angle, the 0.1 mutation amplitude of the lift force coefﬁcient and the side 0.0 force coefﬁcient decrease with the increase of the yaw angle, while the mutation amplitude of the rolling moment -0.1 30 40 50 60 70 80 coefﬁcient increases with the increase of the yaw angle. When b is between 40 to 45 , the mutation amplitude of aerodynamic coefﬁcients begins to ﬂatten. When b 45 , Fig. 21 Mutation amplitude of aerodynamic coefﬁcients varying with yaw angle under two deﬁnitions (U = 8 m/s) the mutation amplitude of aerodynamic coefﬁcients has no obvious change with the yaw angle. Rail. Eng. Science (2022) 30(2):221–241 d (m) d (m) d (m) Aerodynamic characteristics of a high-speed train crossing the wake of a bridge tower from… 239 (b) 1.6 (a) 1.2 U= 8 m/s U= 8 m/s V= 2 m/s & V= 12 m/s V= 2 m/s & V= 12 m/s 1.0 1.2 0.8 0.8 0.6 0.4 0.4 0.2 0.0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 (c) 0.00 -0.04 -0.08 -0.12 -0.16 U= 8 m/s V= 2 m/s & V= 12 m/s -0.20 10 20 30 40 50 60 70 80 90 Fig. 22 Mutation amplitude of aerodynamic coefﬁcients vary with yaw angle: a lift force coefﬁcient; b side force coefﬁcient; c rolling moment coefﬁcient aerodynamic coefﬁcients decrease ﬁrstly with the 5 Concluding remarks yaw angle increases, then tend to be stable when yaw angle beyond 45 . In this study, the wind tunnel experiments have been per- formed to obtain the aerodynamic forces acting on a The presented study represents the ﬁrst step of a larger moving train model as it passes by a bridge tower. The research project, which aims at investigating the sudden inﬂuences of wind speed, train speed, and yaw angle on the change mechanism of aerodynamic forces acting on trains shielding effect are analyzed by focusing on the inﬂuenced caused by the wake of the bridge tower, also considering width and mutation amplitude of aerodynamic coefﬁcients. train motions. The next step of the study will make a fur- The following conclusions can be drawn: ther discussion on the train aerodynamic performance as it passes through the wake with localized wind barriers near (1) The bridge tower shows an obvious shielding effect the tower. Moreover, with the further advancement of on the train passing through it, where the aerody- namic coefﬁcients of the train reach their mutation experiment capacity, aerodynamic characteristics of the head car with a more complicated ﬂow ﬁeld should be peak values with the train being behind the tower shielding area. investigated in future. (2) The inﬂuencing width of bridge tower shielding on Acknowledgements The authors would like to gratefully acknowl- train aerodynamic coefﬁcients is much larger than the edge the supports from the National Natural Science Foundation of width of the bridge tower itself and is considerably China (No. U1434205, 51708645) and Zhejiang Provincial Natural affected by the train speed while the incoming wind Science Foundation of China (No. LY19E080016). speed has little effect on it. Open Access This article is licensed under a Creative Commons (3) The mutation amplitude is signiﬁcantly inﬂuenced by Attribution 4.0 International License, which permits use, sharing, the train and wind speeds. In terms of yaw angle, the adaptation, distribution and reproduction in any medium or format, as absolute mutation amplitude in three force long as you give appropriate credit to the original author(s) and the Rail. Eng. Science (2022) 30(2):221–241 240 J. 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Railway Engineering Science – Springer Journals
Published: Jun 1, 2022
Keywords: Vehicle aerodynamics; Wind tunnel test; Moving train; Bridge tower; Shielding effect; Sudden change mechanism; Truss bridge
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