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Numerical analysis of aerodynamic characteristics of high-speed train with different train nose lengths
International Journal of Heat and Mass Transfer 127 (2018) 188–199
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Numerical analysis of aerodynamic characteristics of high-speed train with different train nose lengths Jiqiang Niu a, Yueming Wang a, Lei Zhang b,⇑, Yanping Yuan a a b
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, Hunan, China
a r t i c l e
i n f o
Article history: Received 16 March 2018 Received in revised form 21 June 2018 Accepted 13 August 2018
Keywords: High-speed train Train nose length Aerodynamic performance Flow structure Boundary layer
a b s t r a c t In this study, based on the SST j-x turbulent model, the IDDES method is used to simulate the unsteady aerodynamic performance of trains with respect to different lengths of the tapered nose of the train (8 m and 12 m). The numerical simulation used in this study is verified through wind tunnel tests. The effects of the length of the tapered nose of the train on the aerodynamic performance, such as the train forces, boundary layer, velocity distribution, pressure distribution, and flow structure around the train, are elucidated via comparing and analyzing the obtained results. The results indicate that the effect of the length of the tapered nose of the train on the drag force of the tail car and lift force of the head car is stronger than the effect on other cars, and the Cd value of the tail car decreases by 30.53% and the Cl value of the head car increases by 87.98%. Increase in the length of the tapered nose of the train decreases the fluctuation of the drag and lift forces of the train, especially the head car. It is also observed that the boundary layer thickness around the train is decreased with the increase in the length of the tapered nose of the train. Moreover, it is observed that vortex drag is the primary factor in the aerodynamic drag of the tail car and that vortex drag primarily depends on the length of the tapered nose of the train. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction With the increase in train speed, train aerodynamic problems become very obvious; for example, the train aerodynamic drag increases significantly, which will not only cut the efficiency of railway transportation, increase energy consumption, and waste resources but also produce more noise, influencing the surrounding environment. Previous research shows that the shape of a high-speed train is closely related to the train’s aerodynamic performance, that the characteristics of train drag and lift force are significantly related to the shape of the train head, and that the train nose length has a great effect on improving the train aerodynamic performance [1–3]. To date, some scholars have studied the effect of the train nose length on the train aerodynamic performance. Choi and Kim [4] studied the effects of the train nose length on the aerodynamic drag of trains traveling in tunnels with the speed increasing from 100 to 200 km/h and found that the aerodynamic drag is reduced by up to approximately 50% by changing the nose from a blunt to a streamlined shape. Hemida and Krajnovic´ [5] investigated ⇑ Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.041 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
the influence of the nose shape on the train flow structures under a crosswind and found that highly unsteady three-dimensional flow around the nose yielded more vortex structures in the wake in the short-nose simulation, which resulted in a surface flow that differed from that in the case of a long-nose train and influenced the dominant frequencies that arose due to the shear layer instabilities. Chen et al. [6] found that the influence of different nose lengths on the surface pressure on the train body was mainly concentrated at the front and rear of the train, and the amplitudes of the lateral force and overturning moment were also influenced by the nose length, with the strongest effect on the head car and a stronger effect on the middle car than on the tail car by simulating the flow and pressure waves caused by two trains with different nose lengths passing each other in a tunnel. Chen et al. [7] compared and discussed the pressure distribution on the train surface, vortex development around the train, and variation of the velocity field around the train with different nose lengths under a strong crosswind and analyzed the variations in the aerodynamic force coefficients with different nose lengths. Chen et al. [8] studied the influence of the train nose length on the aerodynamic properties using the detached-eddy simulation (DES) method and found that the total drag coefficient, strength of vortex shedding, and strength of the wake flow decreased with increases in the train
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nose length and a minor positive pressure area was generated in the nose cone compared to a shorter train nose. Ku et al. [9] studied the optimization of the cross-sectional area distribution of a highspeed train nose of various lengths in order to minimize the micropressure-wave intensity at the tunnel exit and found that some optimal shapes divide one large compression wave into two small waves by causing a strong expansion effect between the front and rear ends. Tian [10] analyzed the formation mechanism of aerodynamic drag of high-speed trains, put forward some reduction measures, and found that adopting a streamlined train shape is the most effective measure to reduce the aerodynamic drag. Tian [11] studied the influence of a streamlined head shape on the air pressure pulse from two trains passing each other and found that as the length of the streamlined train head increases, the amplitude of the air pressure pulse decreases logarithmically while the absolute value of the aerodynamic drag and lift of head-car decrease linearly and the aerodynamic drag of the tail-car decrease by quadratic. Chen et al. [12] studied the aerodynamic drag of maglev trains of different shapes in an evacuated tube with different vacuum pressures and blockage ratios and found that there were no obvious differences in the aerodynamic drag reduction among different streamlined head shapes. Some other scholars also studied the effect of train length on the train aerodynamic characteristics [13–16]. The purpose of the investigation reported in this paper was to analyze the flow field around a high-speed train with different lengths of train nose and also to study the effect of the train nose length on the aerodynamic characteristics of the train. This paper is organized as follows: the train model, numerical method, grid description, size and boundary conditions of the computational region, and data process are introduced in Section 2. The validation of the algorithm is described in Section 3. The aerodynamic characteristics of the train and the effect of the train nose length on the aerodynamic performance of trains as well as the flow structure around trains are described in Section 4. Finally, Section 5 presents the conclusions drawn based on the results.
2. Numerical model 2.1. Train model In this study, trains with two different lengths of the train nose were used as models for the numerical simulations (see Fig. 1a). The models, including the streamlined area, windshield, and bogie, used for the numerical simulation were simplified in accordance with the CEN standard (2009, 2010) [17,18], and the subgrade was also modelled. The dimensions of the train with a short train nose are shown in Fig. 1b, and the length (Ltr) and height (H, distance from the upper surface of the train to the top surface of
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the rail, TOR) of a full-scale model of the train were 77 and 3.7 m, respectively. The streamlined length of the primary type of high speed train is approximately within the range of 5–15 m, such as the Shinkansen train in Japan, TGV in French, ICE in Germany, and CRH in China. The main difference in the dimensions of the two types of trains is the length of the train nose: 8 and 12 m, respectively, as shown in Fig. 1c. Fig. 1c also shows that the two trains with different lengths of train nose both have a width of 3.4 m. 2.2. Numerical method In this simulation, the unsteady flow field around trains with different lengths of the train nose was simulated by IDDES based on the Shear Stress Transport (SST) j-x turbulence model. This method has been widely used to simulate train aerodynamic performance and is very effective [19–22]. The IDDES method is a combination of the delayed detached eddy simulation (DDES) method and wall-modelling in the large eddy simulation (LES) method and considers the characteristics of the turbulent incoming flow. The DDES method is derived from the DES method by introducing a delay function to prevent the LES method from being used in the boundary layer and to ensure that the Reynoldsaveraged Navier–Stokes equations are used in the boundary layer; this can cause modelled-stress depletion and grid-induced separation. Compared to the case for the DDES grid scale, the IDDES grid scale further reduces the sub-grid viscosity in the log layer. Other advantages of using IDDES to simulate train unsteady aerodynamic performance have been described in detail in previous studies in Refs. [16,21]. More information about IDDES and a description of it can be found in studies in Refs. [23–25]. In this study, a pressure-based solver selected in Fluent was used for the numerical simulation. The gradients were computed for the control volumes around the cells using the least-squares method. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm was used to solve the pressure and velocity coupling equations. The bounded central differencing scheme and the second-order upwind scheme were used to solve the momentum equation and the j-x equations, respectively. The unsteady calculation method of the dual-time-step format was used for time discretization, with the physical time step being 1 104 s, in keeping with studies in Refs. [8,16,26,27], and the second-order implicit scheme was used for the transient formulation. For each time step, the number of iterations was 30, and the residual of each turbulent equation was at least 106. 2.3. Grid generation In this study, a hexahedral-dominated mesh was generated around the train using the open-source CFD toolbox OpenFOAM
Fig. 1. Dimensions of the full-scale train: (a) 3D train model including streamlined train head, windshield, and bogie; (b) size and position of the train relative to the subgrade; (c) size of the train streamlined area.
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4.1, which has been widely and successfully applied in aerodynamic numerical simulation of trains [8,21,28]. Some similar examples about grid independence have been carried out in the previous review study by Ref. [16]. In this study, to ensure that the mesh density is suitable for the calculation the mesh independent analysis is conducted in this section. Three densities are used in mesh independent analysis such as coarse, medium, and fine; the details of the initial mesh around a train are presented in Table 1, and the mesh around a train with different types of mesh densities is shown in Fig. 2. Fig. 3 shows the mesh around the train in the case of medium density. The smallest mesh size used on the 1:8 scaled train model surface was 0.977 mm. To ensure the accuracy of the solution, two refinement boxes were added around the train; the dimensions of these two boxes were about 64.9 H 2 H 1.5 H and 40 H 3 H 2 H, respectively, as shown in Fig. 3a. The cell size in the two refinement boxes are 15.6 mm and 7.8 mm, respectively. In order to simulate the flow field close to the train
surface, for the initial mesh, 10 prism layers were added to the boundary layer of the train; the thickness of the first prism layer close to the train surface was approximately 0.1 mm, as shown in Fig. 3b. The surface mesh on the streamlined head and bogie is shown in Fig. 3c and d, respectively. Based on the preliminary steady state calculation results, the adaptive mesh technique in Fluent was employed to adjust the meshes around the train to ensure that the averaged y+ of the cell in the first layer adjacent to the train surface was approximately 1–10. 2.4. Computational region and boundary condition Fig. 4 shows the dimensions of the computational region, which satisfied the requirements of the CEN standard (2009, 2010) [17,18]. As shown in Fig. 4, the top and side faces of the
Table 1 Different cases considered in mesh independent analysis. Items
Coarse
Medium
Fine
Number of volume meshes Size of the smallest mesh on train surface/mm Number of prism layers Smallest thickness of the first boundary layer/mm Maximum mesh size in two fine refinement boxes/mm
19 105 823 1.95
25 110 062 0.977–1.95
38 952 413 0.977
10 0.195
10 0.0977–0.195
10 0.0977
15.6/7.8
15.6/7.8
7.8/3.9
Coarse
Fig. 4. Boundary conditions and size of computational region.
Medium
Fine
Fig. 2. Mesh around train with different types of mesh densities.
Fig. 3. Grid around the train: (a) grid for computational region, (b) grid in prism layer, (c) grid on the train streamlined head, and (d) grid on the bogie.
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computational domain were considered as the slip wall boundary, while the slip speed was the incoming flow velocity in the x-direction. Avoiding the interference of the ground effect on the flow field at the bottom of a train, the bottom face (ground) was considered as the slip wall boundary. The back face was considered as the pressure outlet boundary, while the reference pressure Pout was taken to be 1 atm. To describe the characteristics of the incoming flow, the turbulent kinetic energy, j, and the specific dissipation rate, x, were selected in the Turbulence Specification Method of Fluent. These parameters were calculated using Eqs. (1) and (2), respectively.
j ¼ 3=2ðIUm Þ2
ð1Þ
x ¼ j1=2 =ð0:07H C 1=4 Þ
ð2Þ
where the average the wind speed, Um, was 60 m/s; I, the turbulence intensity of the incoming flow, was 0.1%, which is the value measured in the wind tunnel test [29,30]; the characteristic length, H, was the height of the train; and the empirical constant, C, was taken to be 0.09.
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where D, L, p, and u are the mean drag, lift force, static pressure, and velocity, respectively. Further, Cd, Cl, Cp, and Cv are the mean drag coefficient, lift coefficient, pressure coefficient, and velocity coefficient, respectively. In addition, the reference pressure, p1, was considered to be 1 atm and the air density, q, was considered to be 1.225 kg/m3. Finally, the reference area, S, was considered to be 0.175 m2. In this study, the non-dimensional time ‘‘tUm/S1/2” was used to deal with these fluctuating parameters related to the flow field around the train such as the force, pressure, and velocity [8,21,27,30]. The drag coefficient and lift coefficient of the train with a long train nose are shown in Fig. 5. It can be seen that the mean Cd and Cl value of the train remains nearly constant after a non-dimensional time of 70, which means that the flow field has been fully developed and stabilized. Therefore, the force, pressure, and other parameters were all calculated by taking the average value for the non-dimensional time interval of 70–270.
3. Algorithm verification and mesh independence 3.1. Algorithm verification
2.5. Data processing For the convenience of comparative analysis, some coefficients are defined as follows according to CEN 2010 and CEN2013 (2010, 2013) [13,14]:
C d ¼ D=ð0:5qU 2m SÞ
ð3Þ
C l ¼ L=ð0:5qU 2m SÞ
ð4Þ
C p ¼ ðp p1 Þ=ð0:5qU 2m Þ
ð5Þ
C v ¼ u=U m
ð6Þ
Wind tunnel tests with a 1:8 scaled model of a CRH2c train were performed in Refs. [29,31]. To verify the reliability of the numerical method used in this paper, the same wind tunnel and train model were used for the numerical simulations here, the numerical simulation was constructed as the wind tunnel test, and the scaled train models used for algorithm verification are shown in Fig. 6. To get the characteristics of incoming flow, a Cobra probe was arranged at a height of 0.2 m from the centre region of the floor: both the static and the dynamic pressure gradient along the tunnel axis were less than or equal to 0.01/m, and the turbulence intensity was less than 1%. Three six-component balances (TH1001A, TH1001B, and TH1001C) made at China Aerodynamic
Fig. 5. Non-dimensional time history curves for Cd and Cl of train with long train nose.
Fig. 6. 1:8 scaled train model used for algorithm verification: (a) train model in wind tunnel; (b) train model used for numerical simulations.
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Table 2 Comparison of average aerodynamic force coefficients obtained from simulations and test. Case
Numerical simulation Wind tunnel test [29] e/%
Cd
Cl
Head car
Tail car
Head car
Tail car
0.1394 0.145 4.02
0.1620 0.163 0.62
0.0321 0.046 43.30
0.1313 0.097 26.12
Research and Development Center and an electronic pressure scanning valve (range of 7 kPa and accuracy of 0.08%) produced by Scanivalve were used to collect the train aerodynamic forces and train surface pressure, respectively. An HY scan 2004 system was used to collect and process the test data. If the numerical simulation results are sufficiently close to those of the wind tunnel test, the algorithm used in this paper can be considered appropriate. As shown in Table 2, the maximum error in the Cl values between the wind tunnel test and the numerical simulation can be up to 43%; this large error could possibly be ascribed to the train model in the wind tunnel not arriving exactly on a horizontal plane although the train model was installed according to the requirement, and the measurement is also considered with respect to a horizontal plane. Further, numerical simulation and experiments are not identical with respect to installation, and the complex structure of the bottom of the train and the distance between the train and the ballast also contribute to it, which meant that the accuracy of the flow field simulation was not high [32–34]. Table 2 also shows that the maximum error in the Cd values obtained from the wind tunnel test and the numerical simulation was about 4%. However, the deviation was within the acceptable scope of the project. The above illustrates that the mesh size and simulation method used in this study were suitable for achieving accurate numerical results.
CNumerical simulation CWind tunnel 100% e ¼ CWind tunnel
ð7Þ
where e is the error between numerical results and experimental data, CNumerical simulation and CWind tunnel are the aerodynamic force coefficients of the numerical simulation and wind tunnel, respectively.
Fig. 7. Mean pressure distribution on the symmetry line of the train: (a) head car; (b) tail car.
As shown in Fig. 7, the distribution of the mean pressure coefficients on the symmetry line of the train in the simulation is in agreement with the experimental result, although individual measurement points show large deviations. 3.2. Mesh independence The mean Cd and Cl of the train with respect to three types of mesh densities and error (e) between numerical simulation results and wind tunnel data are presented in Table 3. Information regarding the mesh density has been provided in Table 1. The results in Table 3 indicate that the effect of the mesh density on the aerodynamic force coefficient of the train is evident, but the difference in the aerodynamic force coefficient of the train between two mesh densities decreases as the mesh density increases, the maximum error of Cd for each car between the medium case and fine case is 1.54%, the maximum error of Cl for each car except the middle car between the medium case and fine case is 2.49%. The error of Cl for the middle car between the medium case and fine case can be up to 6.32%, the reason for the above problems maybe the fact that the direction of the lift of the middle car to proceed from negative to positive, and the flow at the bottom of the middle car is complex. In terms of determining the aerodynamic force of the train, a medium mesh density is considered appropriate for simulating the aerodynamic forces in this study. The mean values of Cp and Cv along the train with three types of mesh densities are shown in Fig. 8. As shown in Fig. 8a and b, there is no evident difference in pressure on the side of the train among these three types of mesh densities, but the effect of the mesh density on the velocity along the side of the train is relatively large, and the difference decreases with an increase in the mesh density, and the difference of Cv along Line-1 between the medium mesh density and fine mesh density is relatively small. Fig. 8c and d show that the effect of the mesh density on the pressure on both the side and top surfaces of the train is negligible. As shown in Fig. 8e, certain difference exist in terms of pressure at the bottom of the train, especially in the region surrounding the bogie, but the difference between the medium mesh density and fine mesh density is negligible. In conclusion, the difference in velocity distribution along the train between the medium mesh density and the fine mesh density is relatively somewhat evident, but the effect of the mesh density on the other parameters in the flow field around the train becomes insignificant. Therefore, the medium mesh density can be used to simulate the aerodynamic performance of the train. In this study, the boundary layer thickness (d99) is defined as the distance from the position of 0.99Um to the train surface. The boundary layer around the trains with three different types of mesh densities was presented in Fig. 9. As shown in Fig. 9a, with an increase in the mesh density, the d99 of the train decreases, and nearly no difference of d99 between the medium and fine mesh densities exists. Fig. 8b shows that the d99 of the train increases with increase in the mesh density, and the difference of d99 between the medium and fine mesh densities is less than 0.34%. Both Fig. 9a and b show that the profiles of the boundary layer along the trains with three types of mesh densities has no
Table 3 Mean value of Cd and Cl of the train for three types of mesh densities and errors. Case
Coarse Medium Fine
Cd/e (%)
Cl/e (%)
Head car
Middle car
Tail car
Head car
Middle car
Tail car
0.1294/10.76 0.1394/3.86 0.1410/2.76
0.0778 0.0801 0.0812
0.1433/12.09 0.1620/0.61 0.1645/0.92
0.0626/36.09 0.0321/30.22 0.0313/31.96
0.0120 0.0095 0.0101
0.1061/9.24 0.1313/35.36 0.1291/33.09
J. Niu et al. / International Journal of Heat and Mass Transfer 127 (2018) 188–199
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Fig. 8. Distribution of mean Cp and Cv along the train with three types of mesh densities: (a) Cp along Line-1, (b) Cv along Line-1, (c) top surface of the train, (d) side surface of the train, and (e) bottom surface of the train.
significant difference. However in Fig. 9c, the difference in the profile of the boundary layer appears along the shoulder of the train, especially the boundary layer in C-3, and a significant difference exists in the profile of the boundary layer between the coarse mesh and the other two types of mesh densities. Therefore, the medium mesh is sufficient for simulating the train boundary layer. The flow structure around the train is shown in Fig. 10, which indicates the existence of several vortices around the train, particularly in the area towards the rear of the train. It indicates that the size of the vortex around the train is determined owing to the mesh density to a certain degree, and as the mesh density increases, the size of the vortex around the train increases. However, the distribution of the vortices around the train is not affected via the mesh density.
4. Results and discussion 4.1. Analysis of aerodynamic forces For the convenience of comparative analysis, the standard deviation (SD) values of the aerodynamic force coefficients were proposed in this study and were used to evaluate the amplitude and degree of fluctuation of the force coefficients, respectively [8,16,21,30]. The formula to calculate the SD is defined as follows,
which has also been described in detail in Ref. [35]. The difference between the numerical results and experimental data (e0 ) is also defined as follows:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X xsd ¼ t ðxi lÞ2 N i¼1 Cshort Clong 100% e0 ¼ Cshort
ð8Þ
ð9Þ
where xsd is the SD, N is the number of samples, xi is the individual sample, the subscript i is the order of the sample data, and it is between 1 and N, l is the average of the samples, Cshort and Clong are the aerodynamic force coefficients and their SD of the numerical simulation and wind tunnel, respectively. Table 4 shows the mean value and e0 in the Cd, and Cl values of the trains with different lengths of the train nose. As shown in Table 4, the increase of the train nose length decreases the Cd values of the whole train by 9.77%, especially for the head and tail cars, with the maximum reductions being 7.5 and 15.89%, respectively. The effect of the length of the tapered nose of the train on the Cd value of the tail car in the whole train is significantly smaller than for the other cars, and the train nose length has little effect on the middle car. Table 4 also shows that the effect of the train nose
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Fig. 9. Boundary layer around the trains with three types of mesh densities: (a) development of the boundary layer along the train in the longitudinal section; (b) development of the boundary layer along the train in the horizontal section H-3; (c) thicknesses of the boundary layer of the middle cross-sections of the head car, middle car, and tail car (C-1, C-2, and C-3).
Fig. 10. Iso-surface plot of Q-criteria collared using mean velocity U (Q = 50,000): (a) top view, (b) side view, and (c) 3D view of flow structure around the train.
length has a greater impact on the Cl value of each car in the train than on the Cd value, and the increase in the train nose length increases the Cl values of the head car and middle car, with the maximum growth being 68.06 and 691.67%, respectively, but decreases the Cl value of the tail car by 32.04%. It may be that the structure at the bottom of the train is complex and has a
multiple-time-scale, which would cause the flow field at the bottom of the train to be complicated and changeable. The above results indicate that the lift forces of the cars in the whole train differ significantly one another and can be disturbed easily by the flow characteristics, which will be described in detail in Section 4.2.
J. Niu et al. / International Journal of Heat and Mass Transfer 127 (2018) 188–199 Table 4 Mean value and e0 in the aerodynamic force coefficient of trains with different lengths of the train nose. Type
Length of the train nose
Mean value Head car
Middle car
Tail car
Total
Cd
Short (8 m) Long (12 m) e0 /%
0.1507 0.1394 7.5
0.0795 0.0801 0.75
0.1926 0.1620 15.89
0.4228 0.3815 9.77
Cl
Short (8 m) Long (12 m) e0 /%
0.0191 0.0321 68.06
0.0012 0.0095 691.67
0.1932 0.1313 32.04
0.1729 0.0897 48.12
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reducing the fluctuations in the Cd and Cl values of the train and reveals a phenomenon in which the fluctuations in both Cd and Cl of the tail car are strongest, followed by those of the middle car, while the head car shows the smallest fluctuations, and the above regularity is not affected by the train nose length. Table 5 also shows that the fluctuation in both Cd and Cl of each car in the train decreases with increases of the train nose length, and train nose length has the largest effect on the head car, followed by the middle car and finally the tail car, with the maximum reductions being above 41, 21, and 5%, respectively.
4.2. Effect of the train nose length on flow field around train Table 5 SD and e0 in aerodynamic force coefficient of trains with different lengths of the train nose. Type
Length of the train nose
SD value Head car
Middle car
Tail car
Total
Cd
Short (8 m) Long (12 m) e0 /%
0.0097 0.0057 41.24
0.0119 0.0094 21.01
0.0121 0.0112 7.44
0.0337 0.0263 21.96
Cl
Short (8 m) Long (12 m) e0 /%
0.0138 0.0070 49.28
0.0150 0.0112 25.33
0.0199 0.0189 5.03
0.0487 0.0371 23.82
The SD values of the aerodynamic force coefficients for the two different lengths of the train nose are shown in Table 5. It shows that an increase in the train nose length is an effective method of
The boundary layer around trains with two types of lengths of the train nose is shown in Fig. 11, which indicates that d99 increases along the train. As shown in Fig. 11a, in addition to the area around the train head and tail, there is no obvious difference in the thickness of the boundary layer along the train between the two types of trains, which can also be observed in Region 1 of Fig. 11b. Fig. 11b shows that the d99 around the corner of the train decreases significantly with increases in the length of the train nose, for example in Regions 2 and 3, and the effect is more obvious from the head to the tail. The green line in Fig. 11c is the boundary layer of the train in the horizontal section of H-4, which shows that both the value and growth of d99 around the train with the short train nose (1.43 W for the train head and 1.65 W for the train tail) is larger than that with the long train nose (1.34 W for the train head and 1.52 W for the train tail), and for the two special fixedpoint points shown in Fig. 11c, long train nose decreases the d99
Fig. 11. Boundary layer around trains with different lengths of the train nose: (a) development of the boundary layer along the train on the longitudinal section; (b) thicknesses of the boundary layer of the middle cross-sections of the head car, middle car, and tail car (C-1, C-2, and C-3); (c) development of the boundary layer along the train in different horizontal sections (H-1, H-2, H-3, and H-4).
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around the train in the horizontal section of H-4 by 6.3% and 7.9%, respectively, which means that with the development of the boundary layer along the train, the effect of the train nose length is considerably significant. The width of the black line in the horizontal section of H-3 in the wake of train with a short train nose (1.832 W) is bigger than that with a long train nose (1.491 W), which means that the strength of the wake of the train with a short train nose is greater. As shown in the small windows in Fig. 11c, the distance of the blue lines at two side of the train tail with the short train nose in the nearest place (1.025 W) is smaller than that with the long train nose (1.087 W), which means that the short train nose accelerates the airflow around the streamlined area of the tail car, exacerbates the separation of airflow here, and increases the negative pressure in the area behind the train, the above mentioned condition will increase the pressure drag of the tail car. Because the increase of the boundary layer thickness causes the aerodynamic drag to increase, the above difference in boundary layer thickness can explain why the aerodynamic drag of the train with a short train nose is greater than that with the long train nose. Through calculation, it is observed that the ratio of the pressure drag and viscous skin friction drag for the head car, middle car, and tail car with short train nose is 0.903, 1.215, and 4.999, respectively, and the ratio of the pressure drag and viscous skin friction drag for the head car, middle car, and tail car with long train nose is 1.495, 0.9, and 5.935, respectively. Based on the above results, it is observed that the ratio of the pressure drag and the viscous skin friction drag of the car increases from head car to tail car, and also increases with the increase in the train nose length. The transient vortex structure was described by the iso-surface of the constant Q, which has been used for describing the flow structure around trains and has been used widely in studies of the aerodynamic performance of trains [5,16,21,36]. Detailed introduction about the value of Q has been given in Ref. [37]. Iso-surfaces corresponding to the Q-criterion are presented in Fig. 12, which shows that the vortices around the train increase and strengthen from the train head to the train tail. The big difference is that Vortices 1 and 2 around the train with a short train nose are bigger and stronger than those with a long train nose. Considering that these shedding vortices would cause the train
aerodynamic forces to fluctuate, the difference in the vortices around the train head and train tail can explain why an increase in the length of the train nose causes a decrease in the fluctuation of the aerodynamic forces. Fig. 12 also shows that more vortices appear around the middle car in the train with a short train nose relative to the one with the long train nose, which is the main cause of the high fluctuation of the aerodynamic forces in the middle car of the train with a short train nose. Because vortex drag is the main component of the aerodynamic drag, the above phenomena can also indicate that the aerodynamic drag of the train with a short train nose is greater than that with a long train nose. Fig. 13 shows the flow structure around the train tail with two types of lengths of the train nose. As shown in Fig. 13a, there are two main differences in the sizes of the vortices around the train tail between the two lengths of the train nose. One is that the size of Vortices 1 around the train tail with a short train nose is bigger than that with a long train nose, which is due to the large separation of flow caused by the large change in gradient of the train shape, leading to the formation of a big negative pressure in this area, which can be observed in Region 1 of Fig. 13c. Fig. 13b shows that the area of low velocity (Region-2) with respect to the train with a long nose is larger than that with a short train nose, which may be because the flow at the top of the train nose is directed farther by the profile of the upper surface train with a long train nose, which blocks and decreases the airflow under the train nose (Region-2). Fig. 13c also shows that the size and the strength of the negative pressure at the upper of the train and behind the train tail with short train nose length is larger than those with long train nose; this phenomenon can also be used to explain the reason why the aerodynamic drag and lift of the tail car with short train nose is larger than that with long train nose. Fig. 14 shows the Cp value along the train on the train upper and side surfaces. As shown in Fig. 14, the big difference of Cp along the upper surface of the trains with the two types of lengths of the train nose appears in regions around the train head and train tail, and there are basically no differences in other regions. This is due to the difference in the separation point and the reattachment point of the airflow near the train surface between the trains with two types of lengths of the train nose. The flow separation around the train head with a short train nose (around S-2 in
Fig. 12. Iso-surfaces corresponding to the Q-criterion, rendered for mean velocity, Um (Q = 100 000): (a) instantaneous vortex structure around entire train; (b) side view of vortex structure around train head; (c) top view of vortex structure around train head.
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(a)
(b)
Short
Short
Vortices-1
Region-1
Region-2
Vortices-2
Long
Long
(c)
Region-1
Short
Long Region-2
Fig. 13. Flow structure around the train tail: (a) flow streamlines (the train surface and streamlines are colored by pressure and velocity, respectively); (b) velocity contour; (c) pressure contour. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 14. Cp distribution along the trains with two different lengths of the train nose: (a) train upper surface; (b) train side surface.
Fig. 14a and S-10 in Fig. 13b) is earlier than that with a long train nose (around L-2 in Fig. 14a and L-6 in Fig. 14b), which causes an increase in the pressure aerodynamic drag of the head car with the
short train nose. The flow separation around the train tail with the short train nose (around S-3 in Fig. 14a and S-7 in Fig. 14b) is later than that with the long train nose (around L-3 in Fig. 14a and L-7
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Fig. 15. Distribution of Cp and Cv along Line 1 at one side of the train with two different lengths of the train nose: (a) distribution of Cp along Line 1; (b) distribution of Cv along Line 1.
(a)
in Fig. 14b), but the aerodynamic drag of the tail car with the short train nose is bigger than that with the long train nose, which means that vortex drag is the main factor in the aerodynamic drag of the tail car. Fig. 15 shows the pressure coefficient (Cp) and velocity coefficient (Cv) along Line 1 at one side of the train with two different lengths of the train nose. As can be observed from Fig. 15a, the minimum difference exists in Cp along Line 1, besides the region around the train head, and Cp along Line 1 close to the train head with the short train nose is larger than that in the case of the head car with the long train nose, which indicates that the separation of airflow is strongly affected by the shape of the train, which can also be observed in Region 1 of Figs. 15b and 16a. The difference of Cp around the train tail between the two types of train nose lengths is small relative to those around the train head, which also can be observed in Fig. 16a and c. Unlike Cp along Line 1, the primary differences in Cv are concentrated in the area after the middle car, and the largest difference appears in the area at a distance of 0.8 Ltr from the tip of the train nose: Cv along the train with the long train nose is considerably smaller than that with the short train nose; however, in the train wake area, the law of Cv around the train is opposite to that in the area just mentioned. The above mentioned details also explain why the wake of the train with a short train nose is larger in size and strength than that with a long train nose, which can be observed in Fig. 16b.
Short Region-1 Long
(b) Short Region-2 Long
(c)
3.67H
4.71W
4.13H
Short
5.44W
4.16W Long
5.29W
Fig. 16. Flow field around the trains: (a) distribution of pressure on train surface; (b), and (c) are the velocity and pressure contour on the horizontal plane height of 0.324 H from the top surface of the rail, respectively.
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5. Conclusions The aerodynamic performance and flow fields for three-car trains with two different lengths of the train nose, that is, short and long, were simulated without yaw angle. The conclusions drawn from the obtained results are as follows: 1. The effect of the train nose length on the drag of the tail car and lift force of the head car is stronger than the effect on other cars, and when the length of the train nose increases from 8 to 12 m, the Cd value of the tail car decreases by 30.53% and the Cl value of the head car increases by 87.98%. The aerodynamic forces of the middle car are the least influenced by the train nose length. Increasing the train nose length can effectively reduce the fluctuation of Cd and Cl of the train, especially for the head car, and the effect of the train nose length decreases from the head car to the tail car in turn. 2. The profile of the boundary layer is influenced by the train nose length, and d99 around the corner of the train decreases significantly with increases of the train nose length. Both the value and the growth of d99 along the train with the train nose length are bigger than those with the long train nose. Negative pressure formed by large separation around the train with the short train nose is bigger than that with the long train nose. In addition, vortex drag is the main factor in the aerodynamic drag of the tail car, and vortex drag mainly depends on the train nose length. 3. The effect of the train nose length on the train surface pressure is concentrated in the train head and train tail, and the magnitude of variation of the train surface pressure caused by the train with a short train nose is bigger than that with a long train nose. The effect of the train nose length on the pressure distribution around the train head and velocity distribution around the train tail is most significant relative to other regions. Conflict of interest The authors declare that they have no conflict of interest. Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities of China (2682018CX14), the National Natural Science Foundation of China (51605397) and Sichuan Province Youth Science and Technology Innovation Team Program (2017TD0017). References [1] J.A. Schetz, Aerodynamics of high-speed trains, Annu. Rev. Fluid Mech. 33 (1) (2001) 371–414. [2] R.S. Raghunathan, H.D. Kim, T. Setoguchi, Aerodynamics of high-speed railway train, Prog. Aerosp. Sci. 38 (6–7) (2002) 469–514. [3] H. Tian, Study evolvement of train aerodynamics in China, J. Traffic Transp. Eng. 1 (4) (2006) 1–9. [4] J.K. Choi, K.H. Kim, Effects of nose shape and tunnel cross-sectional area on aerodynamic drag of train traveling in tunnels, Tunn. Undergr. Space Technol. 41 (2014) 62–73. [5] H. Hemida, S. Krajnovic´, LES study of the influence of a train-nose shape on the flow structures under cross-wind conditions, J. Fluids Eng. 130 (9) (2008) 091101. [6] H. Hemida, S. Krajnovic´, LES study of the influence of the nose shape and yaw angles on flow structures around trains, J. Wind Eng. Ind. Aerodyn. 98 (1) (2010) 34–46. [7] X.D. Chen, T.H. Liu, X.S. Zhou, W.H. Li, T.Z. Xie, Z.W. Chen, Analysis of the aerodynamic effects of different nose lengths on two trains intersecting in a tunnel at 350 km/h, Tunn. Undergr. Space Technol. 66 (2017) 77–90. [8] Z. Chen, T. Liu, Z. Jiang, Z. Guo, J. Zhang, Comparative analysis of the effect of different nose lengths on train aerodynamic performance under crosswind, J. Fluids Struct. 78 (2018) 69–85.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Numerical analysis of aerodynamic characteristics of high-speed train with different train nose lengths Jiqiang Niu a, Yueming Wang a, Lei Zhang b,⇑, Yanping Yuan a a b
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, Hunan, China
a r t i c l e
i n f o
Article history: Received 16 March 2018 Received in revised form 21 June 2018 Accepted 13 August 2018
Keywords: High-speed train Train nose length Aerodynamic performance Flow structure Boundary layer
a b s t r a c t In this study, based on the SST j-x turbulent model, the IDDES method is used to simulate the unsteady aerodynamic performance of trains with respect to different lengths of the tapered nose of the train (8 m and 12 m). The numerical simulation used in this study is verified through wind tunnel tests. The effects of the length of the tapered nose of the train on the aerodynamic performance, such as the train forces, boundary layer, velocity distribution, pressure distribution, and flow structure around the train, are elucidated via comparing and analyzing the obtained results. The results indicate that the effect of the length of the tapered nose of the train on the drag force of the tail car and lift force of the head car is stronger than the effect on other cars, and the Cd value of the tail car decreases by 30.53% and the Cl value of the head car increases by 87.98%. Increase in the length of the tapered nose of the train decreases the fluctuation of the drag and lift forces of the train, especially the head car. It is also observed that the boundary layer thickness around the train is decreased with the increase in the length of the tapered nose of the train. Moreover, it is observed that vortex drag is the primary factor in the aerodynamic drag of the tail car and that vortex drag primarily depends on the length of the tapered nose of the train. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction With the increase in train speed, train aerodynamic problems become very obvious; for example, the train aerodynamic drag increases significantly, which will not only cut the efficiency of railway transportation, increase energy consumption, and waste resources but also produce more noise, influencing the surrounding environment. Previous research shows that the shape of a high-speed train is closely related to the train’s aerodynamic performance, that the characteristics of train drag and lift force are significantly related to the shape of the train head, and that the train nose length has a great effect on improving the train aerodynamic performance [1–3]. To date, some scholars have studied the effect of the train nose length on the train aerodynamic performance. Choi and Kim [4] studied the effects of the train nose length on the aerodynamic drag of trains traveling in tunnels with the speed increasing from 100 to 200 km/h and found that the aerodynamic drag is reduced by up to approximately 50% by changing the nose from a blunt to a streamlined shape. Hemida and Krajnovic´ [5] investigated ⇑ Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.041 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
the influence of the nose shape on the train flow structures under a crosswind and found that highly unsteady three-dimensional flow around the nose yielded more vortex structures in the wake in the short-nose simulation, which resulted in a surface flow that differed from that in the case of a long-nose train and influenced the dominant frequencies that arose due to the shear layer instabilities. Chen et al. [6] found that the influence of different nose lengths on the surface pressure on the train body was mainly concentrated at the front and rear of the train, and the amplitudes of the lateral force and overturning moment were also influenced by the nose length, with the strongest effect on the head car and a stronger effect on the middle car than on the tail car by simulating the flow and pressure waves caused by two trains with different nose lengths passing each other in a tunnel. Chen et al. [7] compared and discussed the pressure distribution on the train surface, vortex development around the train, and variation of the velocity field around the train with different nose lengths under a strong crosswind and analyzed the variations in the aerodynamic force coefficients with different nose lengths. Chen et al. [8] studied the influence of the train nose length on the aerodynamic properties using the detached-eddy simulation (DES) method and found that the total drag coefficient, strength of vortex shedding, and strength of the wake flow decreased with increases in the train
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nose length and a minor positive pressure area was generated in the nose cone compared to a shorter train nose. Ku et al. [9] studied the optimization of the cross-sectional area distribution of a highspeed train nose of various lengths in order to minimize the micropressure-wave intensity at the tunnel exit and found that some optimal shapes divide one large compression wave into two small waves by causing a strong expansion effect between the front and rear ends. Tian [10] analyzed the formation mechanism of aerodynamic drag of high-speed trains, put forward some reduction measures, and found that adopting a streamlined train shape is the most effective measure to reduce the aerodynamic drag. Tian [11] studied the influence of a streamlined head shape on the air pressure pulse from two trains passing each other and found that as the length of the streamlined train head increases, the amplitude of the air pressure pulse decreases logarithmically while the absolute value of the aerodynamic drag and lift of head-car decrease linearly and the aerodynamic drag of the tail-car decrease by quadratic. Chen et al. [12] studied the aerodynamic drag of maglev trains of different shapes in an evacuated tube with different vacuum pressures and blockage ratios and found that there were no obvious differences in the aerodynamic drag reduction among different streamlined head shapes. Some other scholars also studied the effect of train length on the train aerodynamic characteristics [13–16]. The purpose of the investigation reported in this paper was to analyze the flow field around a high-speed train with different lengths of train nose and also to study the effect of the train nose length on the aerodynamic characteristics of the train. This paper is organized as follows: the train model, numerical method, grid description, size and boundary conditions of the computational region, and data process are introduced in Section 2. The validation of the algorithm is described in Section 3. The aerodynamic characteristics of the train and the effect of the train nose length on the aerodynamic performance of trains as well as the flow structure around trains are described in Section 4. Finally, Section 5 presents the conclusions drawn based on the results.
2. Numerical model 2.1. Train model In this study, trains with two different lengths of the train nose were used as models for the numerical simulations (see Fig. 1a). The models, including the streamlined area, windshield, and bogie, used for the numerical simulation were simplified in accordance with the CEN standard (2009, 2010) [17,18], and the subgrade was also modelled. The dimensions of the train with a short train nose are shown in Fig. 1b, and the length (Ltr) and height (H, distance from the upper surface of the train to the top surface of
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the rail, TOR) of a full-scale model of the train were 77 and 3.7 m, respectively. The streamlined length of the primary type of high speed train is approximately within the range of 5–15 m, such as the Shinkansen train in Japan, TGV in French, ICE in Germany, and CRH in China. The main difference in the dimensions of the two types of trains is the length of the train nose: 8 and 12 m, respectively, as shown in Fig. 1c. Fig. 1c also shows that the two trains with different lengths of train nose both have a width of 3.4 m. 2.2. Numerical method In this simulation, the unsteady flow field around trains with different lengths of the train nose was simulated by IDDES based on the Shear Stress Transport (SST) j-x turbulence model. This method has been widely used to simulate train aerodynamic performance and is very effective [19–22]. The IDDES method is a combination of the delayed detached eddy simulation (DDES) method and wall-modelling in the large eddy simulation (LES) method and considers the characteristics of the turbulent incoming flow. The DDES method is derived from the DES method by introducing a delay function to prevent the LES method from being used in the boundary layer and to ensure that the Reynoldsaveraged Navier–Stokes equations are used in the boundary layer; this can cause modelled-stress depletion and grid-induced separation. Compared to the case for the DDES grid scale, the IDDES grid scale further reduces the sub-grid viscosity in the log layer. Other advantages of using IDDES to simulate train unsteady aerodynamic performance have been described in detail in previous studies in Refs. [16,21]. More information about IDDES and a description of it can be found in studies in Refs. [23–25]. In this study, a pressure-based solver selected in Fluent was used for the numerical simulation. The gradients were computed for the control volumes around the cells using the least-squares method. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm was used to solve the pressure and velocity coupling equations. The bounded central differencing scheme and the second-order upwind scheme were used to solve the momentum equation and the j-x equations, respectively. The unsteady calculation method of the dual-time-step format was used for time discretization, with the physical time step being 1 104 s, in keeping with studies in Refs. [8,16,26,27], and the second-order implicit scheme was used for the transient formulation. For each time step, the number of iterations was 30, and the residual of each turbulent equation was at least 106. 2.3. Grid generation In this study, a hexahedral-dominated mesh was generated around the train using the open-source CFD toolbox OpenFOAM
Fig. 1. Dimensions of the full-scale train: (a) 3D train model including streamlined train head, windshield, and bogie; (b) size and position of the train relative to the subgrade; (c) size of the train streamlined area.
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4.1, which has been widely and successfully applied in aerodynamic numerical simulation of trains [8,21,28]. Some similar examples about grid independence have been carried out in the previous review study by Ref. [16]. In this study, to ensure that the mesh density is suitable for the calculation the mesh independent analysis is conducted in this section. Three densities are used in mesh independent analysis such as coarse, medium, and fine; the details of the initial mesh around a train are presented in Table 1, and the mesh around a train with different types of mesh densities is shown in Fig. 2. Fig. 3 shows the mesh around the train in the case of medium density. The smallest mesh size used on the 1:8 scaled train model surface was 0.977 mm. To ensure the accuracy of the solution, two refinement boxes were added around the train; the dimensions of these two boxes were about 64.9 H 2 H 1.5 H and 40 H 3 H 2 H, respectively, as shown in Fig. 3a. The cell size in the two refinement boxes are 15.6 mm and 7.8 mm, respectively. In order to simulate the flow field close to the train
surface, for the initial mesh, 10 prism layers were added to the boundary layer of the train; the thickness of the first prism layer close to the train surface was approximately 0.1 mm, as shown in Fig. 3b. The surface mesh on the streamlined head and bogie is shown in Fig. 3c and d, respectively. Based on the preliminary steady state calculation results, the adaptive mesh technique in Fluent was employed to adjust the meshes around the train to ensure that the averaged y+ of the cell in the first layer adjacent to the train surface was approximately 1–10. 2.4. Computational region and boundary condition Fig. 4 shows the dimensions of the computational region, which satisfied the requirements of the CEN standard (2009, 2010) [17,18]. As shown in Fig. 4, the top and side faces of the
Table 1 Different cases considered in mesh independent analysis. Items
Coarse
Medium
Fine
Number of volume meshes Size of the smallest mesh on train surface/mm Number of prism layers Smallest thickness of the first boundary layer/mm Maximum mesh size in two fine refinement boxes/mm
19 105 823 1.95
25 110 062 0.977–1.95
38 952 413 0.977
10 0.195
10 0.0977–0.195
10 0.0977
15.6/7.8
15.6/7.8
7.8/3.9
Coarse
Fig. 4. Boundary conditions and size of computational region.
Medium
Fine
Fig. 2. Mesh around train with different types of mesh densities.
Fig. 3. Grid around the train: (a) grid for computational region, (b) grid in prism layer, (c) grid on the train streamlined head, and (d) grid on the bogie.
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computational domain were considered as the slip wall boundary, while the slip speed was the incoming flow velocity in the x-direction. Avoiding the interference of the ground effect on the flow field at the bottom of a train, the bottom face (ground) was considered as the slip wall boundary. The back face was considered as the pressure outlet boundary, while the reference pressure Pout was taken to be 1 atm. To describe the characteristics of the incoming flow, the turbulent kinetic energy, j, and the specific dissipation rate, x, were selected in the Turbulence Specification Method of Fluent. These parameters were calculated using Eqs. (1) and (2), respectively.
j ¼ 3=2ðIUm Þ2
ð1Þ
x ¼ j1=2 =ð0:07H C 1=4 Þ
ð2Þ
where the average the wind speed, Um, was 60 m/s; I, the turbulence intensity of the incoming flow, was 0.1%, which is the value measured in the wind tunnel test [29,30]; the characteristic length, H, was the height of the train; and the empirical constant, C, was taken to be 0.09.
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where D, L, p, and u are the mean drag, lift force, static pressure, and velocity, respectively. Further, Cd, Cl, Cp, and Cv are the mean drag coefficient, lift coefficient, pressure coefficient, and velocity coefficient, respectively. In addition, the reference pressure, p1, was considered to be 1 atm and the air density, q, was considered to be 1.225 kg/m3. Finally, the reference area, S, was considered to be 0.175 m2. In this study, the non-dimensional time ‘‘tUm/S1/2” was used to deal with these fluctuating parameters related to the flow field around the train such as the force, pressure, and velocity [8,21,27,30]. The drag coefficient and lift coefficient of the train with a long train nose are shown in Fig. 5. It can be seen that the mean Cd and Cl value of the train remains nearly constant after a non-dimensional time of 70, which means that the flow field has been fully developed and stabilized. Therefore, the force, pressure, and other parameters were all calculated by taking the average value for the non-dimensional time interval of 70–270.
3. Algorithm verification and mesh independence 3.1. Algorithm verification
2.5. Data processing For the convenience of comparative analysis, some coefficients are defined as follows according to CEN 2010 and CEN2013 (2010, 2013) [13,14]:
C d ¼ D=ð0:5qU 2m SÞ
ð3Þ
C l ¼ L=ð0:5qU 2m SÞ
ð4Þ
C p ¼ ðp p1 Þ=ð0:5qU 2m Þ
ð5Þ
C v ¼ u=U m
ð6Þ
Wind tunnel tests with a 1:8 scaled model of a CRH2c train were performed in Refs. [29,31]. To verify the reliability of the numerical method used in this paper, the same wind tunnel and train model were used for the numerical simulations here, the numerical simulation was constructed as the wind tunnel test, and the scaled train models used for algorithm verification are shown in Fig. 6. To get the characteristics of incoming flow, a Cobra probe was arranged at a height of 0.2 m from the centre region of the floor: both the static and the dynamic pressure gradient along the tunnel axis were less than or equal to 0.01/m, and the turbulence intensity was less than 1%. Three six-component balances (TH1001A, TH1001B, and TH1001C) made at China Aerodynamic
Fig. 5. Non-dimensional time history curves for Cd and Cl of train with long train nose.
Fig. 6. 1:8 scaled train model used for algorithm verification: (a) train model in wind tunnel; (b) train model used for numerical simulations.
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Table 2 Comparison of average aerodynamic force coefficients obtained from simulations and test. Case
Numerical simulation Wind tunnel test [29] e/%
Cd
Cl
Head car
Tail car
Head car
Tail car
0.1394 0.145 4.02
0.1620 0.163 0.62
0.0321 0.046 43.30
0.1313 0.097 26.12
Research and Development Center and an electronic pressure scanning valve (range of 7 kPa and accuracy of 0.08%) produced by Scanivalve were used to collect the train aerodynamic forces and train surface pressure, respectively. An HY scan 2004 system was used to collect and process the test data. If the numerical simulation results are sufficiently close to those of the wind tunnel test, the algorithm used in this paper can be considered appropriate. As shown in Table 2, the maximum error in the Cl values between the wind tunnel test and the numerical simulation can be up to 43%; this large error could possibly be ascribed to the train model in the wind tunnel not arriving exactly on a horizontal plane although the train model was installed according to the requirement, and the measurement is also considered with respect to a horizontal plane. Further, numerical simulation and experiments are not identical with respect to installation, and the complex structure of the bottom of the train and the distance between the train and the ballast also contribute to it, which meant that the accuracy of the flow field simulation was not high [32–34]. Table 2 also shows that the maximum error in the Cd values obtained from the wind tunnel test and the numerical simulation was about 4%. However, the deviation was within the acceptable scope of the project. The above illustrates that the mesh size and simulation method used in this study were suitable for achieving accurate numerical results.
CNumerical simulation CWind tunnel 100% e ¼ CWind tunnel
ð7Þ
where e is the error between numerical results and experimental data, CNumerical simulation and CWind tunnel are the aerodynamic force coefficients of the numerical simulation and wind tunnel, respectively.
Fig. 7. Mean pressure distribution on the symmetry line of the train: (a) head car; (b) tail car.
As shown in Fig. 7, the distribution of the mean pressure coefficients on the symmetry line of the train in the simulation is in agreement with the experimental result, although individual measurement points show large deviations. 3.2. Mesh independence The mean Cd and Cl of the train with respect to three types of mesh densities and error (e) between numerical simulation results and wind tunnel data are presented in Table 3. Information regarding the mesh density has been provided in Table 1. The results in Table 3 indicate that the effect of the mesh density on the aerodynamic force coefficient of the train is evident, but the difference in the aerodynamic force coefficient of the train between two mesh densities decreases as the mesh density increases, the maximum error of Cd for each car between the medium case and fine case is 1.54%, the maximum error of Cl for each car except the middle car between the medium case and fine case is 2.49%. The error of Cl for the middle car between the medium case and fine case can be up to 6.32%, the reason for the above problems maybe the fact that the direction of the lift of the middle car to proceed from negative to positive, and the flow at the bottom of the middle car is complex. In terms of determining the aerodynamic force of the train, a medium mesh density is considered appropriate for simulating the aerodynamic forces in this study. The mean values of Cp and Cv along the train with three types of mesh densities are shown in Fig. 8. As shown in Fig. 8a and b, there is no evident difference in pressure on the side of the train among these three types of mesh densities, but the effect of the mesh density on the velocity along the side of the train is relatively large, and the difference decreases with an increase in the mesh density, and the difference of Cv along Line-1 between the medium mesh density and fine mesh density is relatively small. Fig. 8c and d show that the effect of the mesh density on the pressure on both the side and top surfaces of the train is negligible. As shown in Fig. 8e, certain difference exist in terms of pressure at the bottom of the train, especially in the region surrounding the bogie, but the difference between the medium mesh density and fine mesh density is negligible. In conclusion, the difference in velocity distribution along the train between the medium mesh density and the fine mesh density is relatively somewhat evident, but the effect of the mesh density on the other parameters in the flow field around the train becomes insignificant. Therefore, the medium mesh density can be used to simulate the aerodynamic performance of the train. In this study, the boundary layer thickness (d99) is defined as the distance from the position of 0.99Um to the train surface. The boundary layer around the trains with three different types of mesh densities was presented in Fig. 9. As shown in Fig. 9a, with an increase in the mesh density, the d99 of the train decreases, and nearly no difference of d99 between the medium and fine mesh densities exists. Fig. 8b shows that the d99 of the train increases with increase in the mesh density, and the difference of d99 between the medium and fine mesh densities is less than 0.34%. Both Fig. 9a and b show that the profiles of the boundary layer along the trains with three types of mesh densities has no
Table 3 Mean value of Cd and Cl of the train for three types of mesh densities and errors. Case
Coarse Medium Fine
Cd/e (%)
Cl/e (%)
Head car
Middle car
Tail car
Head car
Middle car
Tail car
0.1294/10.76 0.1394/3.86 0.1410/2.76
0.0778 0.0801 0.0812
0.1433/12.09 0.1620/0.61 0.1645/0.92
0.0626/36.09 0.0321/30.22 0.0313/31.96
0.0120 0.0095 0.0101
0.1061/9.24 0.1313/35.36 0.1291/33.09
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Fig. 8. Distribution of mean Cp and Cv along the train with three types of mesh densities: (a) Cp along Line-1, (b) Cv along Line-1, (c) top surface of the train, (d) side surface of the train, and (e) bottom surface of the train.
significant difference. However in Fig. 9c, the difference in the profile of the boundary layer appears along the shoulder of the train, especially the boundary layer in C-3, and a significant difference exists in the profile of the boundary layer between the coarse mesh and the other two types of mesh densities. Therefore, the medium mesh is sufficient for simulating the train boundary layer. The flow structure around the train is shown in Fig. 10, which indicates the existence of several vortices around the train, particularly in the area towards the rear of the train. It indicates that the size of the vortex around the train is determined owing to the mesh density to a certain degree, and as the mesh density increases, the size of the vortex around the train increases. However, the distribution of the vortices around the train is not affected via the mesh density.
4. Results and discussion 4.1. Analysis of aerodynamic forces For the convenience of comparative analysis, the standard deviation (SD) values of the aerodynamic force coefficients were proposed in this study and were used to evaluate the amplitude and degree of fluctuation of the force coefficients, respectively [8,16,21,30]. The formula to calculate the SD is defined as follows,
which has also been described in detail in Ref. [35]. The difference between the numerical results and experimental data (e0 ) is also defined as follows:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X xsd ¼ t ðxi lÞ2 N i¼1 Cshort Clong 100% e0 ¼ Cshort
ð8Þ
ð9Þ
where xsd is the SD, N is the number of samples, xi is the individual sample, the subscript i is the order of the sample data, and it is between 1 and N, l is the average of the samples, Cshort and Clong are the aerodynamic force coefficients and their SD of the numerical simulation and wind tunnel, respectively. Table 4 shows the mean value and e0 in the Cd, and Cl values of the trains with different lengths of the train nose. As shown in Table 4, the increase of the train nose length decreases the Cd values of the whole train by 9.77%, especially for the head and tail cars, with the maximum reductions being 7.5 and 15.89%, respectively. The effect of the length of the tapered nose of the train on the Cd value of the tail car in the whole train is significantly smaller than for the other cars, and the train nose length has little effect on the middle car. Table 4 also shows that the effect of the train nose
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Fig. 9. Boundary layer around the trains with three types of mesh densities: (a) development of the boundary layer along the train in the longitudinal section; (b) development of the boundary layer along the train in the horizontal section H-3; (c) thicknesses of the boundary layer of the middle cross-sections of the head car, middle car, and tail car (C-1, C-2, and C-3).
Fig. 10. Iso-surface plot of Q-criteria collared using mean velocity U (Q = 50,000): (a) top view, (b) side view, and (c) 3D view of flow structure around the train.
length has a greater impact on the Cl value of each car in the train than on the Cd value, and the increase in the train nose length increases the Cl values of the head car and middle car, with the maximum growth being 68.06 and 691.67%, respectively, but decreases the Cl value of the tail car by 32.04%. It may be that the structure at the bottom of the train is complex and has a
multiple-time-scale, which would cause the flow field at the bottom of the train to be complicated and changeable. The above results indicate that the lift forces of the cars in the whole train differ significantly one another and can be disturbed easily by the flow characteristics, which will be described in detail in Section 4.2.
J. Niu et al. / International Journal of Heat and Mass Transfer 127 (2018) 188–199 Table 4 Mean value and e0 in the aerodynamic force coefficient of trains with different lengths of the train nose. Type
Length of the train nose
Mean value Head car
Middle car
Tail car
Total
Cd
Short (8 m) Long (12 m) e0 /%
0.1507 0.1394 7.5
0.0795 0.0801 0.75
0.1926 0.1620 15.89
0.4228 0.3815 9.77
Cl
Short (8 m) Long (12 m) e0 /%
0.0191 0.0321 68.06
0.0012 0.0095 691.67
0.1932 0.1313 32.04
0.1729 0.0897 48.12
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reducing the fluctuations in the Cd and Cl values of the train and reveals a phenomenon in which the fluctuations in both Cd and Cl of the tail car are strongest, followed by those of the middle car, while the head car shows the smallest fluctuations, and the above regularity is not affected by the train nose length. Table 5 also shows that the fluctuation in both Cd and Cl of each car in the train decreases with increases of the train nose length, and train nose length has the largest effect on the head car, followed by the middle car and finally the tail car, with the maximum reductions being above 41, 21, and 5%, respectively.
4.2. Effect of the train nose length on flow field around train Table 5 SD and e0 in aerodynamic force coefficient of trains with different lengths of the train nose. Type
Length of the train nose
SD value Head car
Middle car
Tail car
Total
Cd
Short (8 m) Long (12 m) e0 /%
0.0097 0.0057 41.24
0.0119 0.0094 21.01
0.0121 0.0112 7.44
0.0337 0.0263 21.96
Cl
Short (8 m) Long (12 m) e0 /%
0.0138 0.0070 49.28
0.0150 0.0112 25.33
0.0199 0.0189 5.03
0.0487 0.0371 23.82
The SD values of the aerodynamic force coefficients for the two different lengths of the train nose are shown in Table 5. It shows that an increase in the train nose length is an effective method of
The boundary layer around trains with two types of lengths of the train nose is shown in Fig. 11, which indicates that d99 increases along the train. As shown in Fig. 11a, in addition to the area around the train head and tail, there is no obvious difference in the thickness of the boundary layer along the train between the two types of trains, which can also be observed in Region 1 of Fig. 11b. Fig. 11b shows that the d99 around the corner of the train decreases significantly with increases in the length of the train nose, for example in Regions 2 and 3, and the effect is more obvious from the head to the tail. The green line in Fig. 11c is the boundary layer of the train in the horizontal section of H-4, which shows that both the value and growth of d99 around the train with the short train nose (1.43 W for the train head and 1.65 W for the train tail) is larger than that with the long train nose (1.34 W for the train head and 1.52 W for the train tail), and for the two special fixedpoint points shown in Fig. 11c, long train nose decreases the d99
Fig. 11. Boundary layer around trains with different lengths of the train nose: (a) development of the boundary layer along the train on the longitudinal section; (b) thicknesses of the boundary layer of the middle cross-sections of the head car, middle car, and tail car (C-1, C-2, and C-3); (c) development of the boundary layer along the train in different horizontal sections (H-1, H-2, H-3, and H-4).
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around the train in the horizontal section of H-4 by 6.3% and 7.9%, respectively, which means that with the development of the boundary layer along the train, the effect of the train nose length is considerably significant. The width of the black line in the horizontal section of H-3 in the wake of train with a short train nose (1.832 W) is bigger than that with a long train nose (1.491 W), which means that the strength of the wake of the train with a short train nose is greater. As shown in the small windows in Fig. 11c, the distance of the blue lines at two side of the train tail with the short train nose in the nearest place (1.025 W) is smaller than that with the long train nose (1.087 W), which means that the short train nose accelerates the airflow around the streamlined area of the tail car, exacerbates the separation of airflow here, and increases the negative pressure in the area behind the train, the above mentioned condition will increase the pressure drag of the tail car. Because the increase of the boundary layer thickness causes the aerodynamic drag to increase, the above difference in boundary layer thickness can explain why the aerodynamic drag of the train with a short train nose is greater than that with the long train nose. Through calculation, it is observed that the ratio of the pressure drag and viscous skin friction drag for the head car, middle car, and tail car with short train nose is 0.903, 1.215, and 4.999, respectively, and the ratio of the pressure drag and viscous skin friction drag for the head car, middle car, and tail car with long train nose is 1.495, 0.9, and 5.935, respectively. Based on the above results, it is observed that the ratio of the pressure drag and the viscous skin friction drag of the car increases from head car to tail car, and also increases with the increase in the train nose length. The transient vortex structure was described by the iso-surface of the constant Q, which has been used for describing the flow structure around trains and has been used widely in studies of the aerodynamic performance of trains [5,16,21,36]. Detailed introduction about the value of Q has been given in Ref. [37]. Iso-surfaces corresponding to the Q-criterion are presented in Fig. 12, which shows that the vortices around the train increase and strengthen from the train head to the train tail. The big difference is that Vortices 1 and 2 around the train with a short train nose are bigger and stronger than those with a long train nose. Considering that these shedding vortices would cause the train
aerodynamic forces to fluctuate, the difference in the vortices around the train head and train tail can explain why an increase in the length of the train nose causes a decrease in the fluctuation of the aerodynamic forces. Fig. 12 also shows that more vortices appear around the middle car in the train with a short train nose relative to the one with the long train nose, which is the main cause of the high fluctuation of the aerodynamic forces in the middle car of the train with a short train nose. Because vortex drag is the main component of the aerodynamic drag, the above phenomena can also indicate that the aerodynamic drag of the train with a short train nose is greater than that with a long train nose. Fig. 13 shows the flow structure around the train tail with two types of lengths of the train nose. As shown in Fig. 13a, there are two main differences in the sizes of the vortices around the train tail between the two lengths of the train nose. One is that the size of Vortices 1 around the train tail with a short train nose is bigger than that with a long train nose, which is due to the large separation of flow caused by the large change in gradient of the train shape, leading to the formation of a big negative pressure in this area, which can be observed in Region 1 of Fig. 13c. Fig. 13b shows that the area of low velocity (Region-2) with respect to the train with a long nose is larger than that with a short train nose, which may be because the flow at the top of the train nose is directed farther by the profile of the upper surface train with a long train nose, which blocks and decreases the airflow under the train nose (Region-2). Fig. 13c also shows that the size and the strength of the negative pressure at the upper of the train and behind the train tail with short train nose length is larger than those with long train nose; this phenomenon can also be used to explain the reason why the aerodynamic drag and lift of the tail car with short train nose is larger than that with long train nose. Fig. 14 shows the Cp value along the train on the train upper and side surfaces. As shown in Fig. 14, the big difference of Cp along the upper surface of the trains with the two types of lengths of the train nose appears in regions around the train head and train tail, and there are basically no differences in other regions. This is due to the difference in the separation point and the reattachment point of the airflow near the train surface between the trains with two types of lengths of the train nose. The flow separation around the train head with a short train nose (around S-2 in
Fig. 12. Iso-surfaces corresponding to the Q-criterion, rendered for mean velocity, Um (Q = 100 000): (a) instantaneous vortex structure around entire train; (b) side view of vortex structure around train head; (c) top view of vortex structure around train head.
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(a)
(b)
Short
Short
Vortices-1
Region-1
Region-2
Vortices-2
Long
Long
(c)
Region-1
Short
Long Region-2
Fig. 13. Flow structure around the train tail: (a) flow streamlines (the train surface and streamlines are colored by pressure and velocity, respectively); (b) velocity contour; (c) pressure contour. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 14. Cp distribution along the trains with two different lengths of the train nose: (a) train upper surface; (b) train side surface.
Fig. 14a and S-10 in Fig. 13b) is earlier than that with a long train nose (around L-2 in Fig. 14a and L-6 in Fig. 14b), which causes an increase in the pressure aerodynamic drag of the head car with the
short train nose. The flow separation around the train tail with the short train nose (around S-3 in Fig. 14a and S-7 in Fig. 14b) is later than that with the long train nose (around L-3 in Fig. 14a and L-7
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Fig. 15. Distribution of Cp and Cv along Line 1 at one side of the train with two different lengths of the train nose: (a) distribution of Cp along Line 1; (b) distribution of Cv along Line 1.
(a)
in Fig. 14b), but the aerodynamic drag of the tail car with the short train nose is bigger than that with the long train nose, which means that vortex drag is the main factor in the aerodynamic drag of the tail car. Fig. 15 shows the pressure coefficient (Cp) and velocity coefficient (Cv) along Line 1 at one side of the train with two different lengths of the train nose. As can be observed from Fig. 15a, the minimum difference exists in Cp along Line 1, besides the region around the train head, and Cp along Line 1 close to the train head with the short train nose is larger than that in the case of the head car with the long train nose, which indicates that the separation of airflow is strongly affected by the shape of the train, which can also be observed in Region 1 of Figs. 15b and 16a. The difference of Cp around the train tail between the two types of train nose lengths is small relative to those around the train head, which also can be observed in Fig. 16a and c. Unlike Cp along Line 1, the primary differences in Cv are concentrated in the area after the middle car, and the largest difference appears in the area at a distance of 0.8 Ltr from the tip of the train nose: Cv along the train with the long train nose is considerably smaller than that with the short train nose; however, in the train wake area, the law of Cv around the train is opposite to that in the area just mentioned. The above mentioned details also explain why the wake of the train with a short train nose is larger in size and strength than that with a long train nose, which can be observed in Fig. 16b.
Short Region-1 Long
(b) Short Region-2 Long
(c)
3.67H
4.71W
4.13H
Short
5.44W
4.16W Long
5.29W
Fig. 16. Flow field around the trains: (a) distribution of pressure on train surface; (b), and (c) are the velocity and pressure contour on the horizontal plane height of 0.324 H from the top surface of the rail, respectively.
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5. Conclusions The aerodynamic performance and flow fields for three-car trains with two different lengths of the train nose, that is, short and long, were simulated without yaw angle. The conclusions drawn from the obtained results are as follows: 1. The effect of the train nose length on the drag of the tail car and lift force of the head car is stronger than the effect on other cars, and when the length of the train nose increases from 8 to 12 m, the Cd value of the tail car decreases by 30.53% and the Cl value of the head car increases by 87.98%. The aerodynamic forces of the middle car are the least influenced by the train nose length. Increasing the train nose length can effectively reduce the fluctuation of Cd and Cl of the train, especially for the head car, and the effect of the train nose length decreases from the head car to the tail car in turn. 2. The profile of the boundary layer is influenced by the train nose length, and d99 around the corner of the train decreases significantly with increases of the train nose length. Both the value and the growth of d99 along the train with the train nose length are bigger than those with the long train nose. Negative pressure formed by large separation around the train with the short train nose is bigger than that with the long train nose. In addition, vortex drag is the main factor in the aerodynamic drag of the tail car, and vortex drag mainly depends on the train nose length. 3. The effect of the train nose length on the train surface pressure is concentrated in the train head and train tail, and the magnitude of variation of the train surface pressure caused by the train with a short train nose is bigger than that with a long train nose. The effect of the train nose length on the pressure distribution around the train head and velocity distribution around the train tail is most significant relative to other regions. Conflict of interest The authors declare that they have no conflict of interest. Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities of China (2682018CX14), the National Natural Science Foundation of China (51605397) and Sichuan Province Youth Science and Technology Innovation Team Program (2017TD0017). References [1] J.A. Schetz, Aerodynamics of high-speed trains, Annu. Rev. Fluid Mech. 33 (1) (2001) 371–414. [2] R.S. Raghunathan, H.D. Kim, T. Setoguchi, Aerodynamics of high-speed railway train, Prog. Aerosp. Sci. 38 (6–7) (2002) 469–514. [3] H. Tian, Study evolvement of train aerodynamics in China, J. Traffic Transp. Eng. 1 (4) (2006) 1–9. [4] J.K. Choi, K.H. Kim, Effects of nose shape and tunnel cross-sectional area on aerodynamic drag of train traveling in tunnels, Tunn. Undergr. Space Technol. 41 (2014) 62–73. [5] H. Hemida, S. Krajnovic´, LES study of the influence of a train-nose shape on the flow structures under cross-wind conditions, J. Fluids Eng. 130 (9) (2008) 091101. [6] H. Hemida, S. Krajnovic´, LES study of the influence of the nose shape and yaw angles on flow structures around trains, J. Wind Eng. Ind. Aerodyn. 98 (1) (2010) 34–46. [7] X.D. Chen, T.H. Liu, X.S. Zhou, W.H. Li, T.Z. Xie, Z.W. Chen, Analysis of the aerodynamic effects of different nose lengths on two trains intersecting in a tunnel at 350 km/h, Tunn. Undergr. Space Technol. 66 (2017) 77–90. [8] Z. Chen, T. Liu, Z. Jiang, Z. Guo, J. Zhang, Comparative analysis of the effect of different nose lengths on train aerodynamic performance under crosswind, J. Fluids Struct. 78 (2018) 69–85.
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