Instantaneous Flow Structures Research Articles

Eddy viscosity enhanced temporal direct deconvolution model for temporal large-eddy simulation of turbulent channel flow

In this work, a novel eddy viscosity enhanced temporal direct deconvolution model (TDDM) is proposed for temporal large-eddy simulation (TLES) of turbulent channel flow at large filter widths. To improve the accuracy of the constant eddy viscosity (CEV) model, particularly in the near-wall region, a damping function is incorporated to refine its performance. Moreover, a spatial filtering strategy is introduced to reduce the aliasing errors associated with the computation of subfilter-scale (SFS) stress, thereby enhancing numerical stability. In the a posteriori study, the accuracy of the CEV model is assessed comprehensively by comparing the TLES results with corresponding temporally filtered direct numerical simulation data. The results demonstrate that the CEV-enhanced TDDM provides accurate predictions across various statistical properties of velocity, instantaneous flow structures, kinetic energy spectra, and SFS energy fluxes. The coefficient sensitivity analysis of the CEV model reveals that the model coefficient significantly influences low Reynolds number flows, while its impact on high Reynolds number flows is relatively small. TLES on coarse grids demonstrate that the CEV-enhanced TDDM exhibits strong robustness and accuracy at different grid resolutions. Additionally, the CEV-enhanced TDDM in high Reynolds number flows is stable and accurate at remarkably large filter widths.

Characteristics of the jet shear layer of a round elevated jet in crossflow

The present research aims at an experimental study to investigate the effect of velocity ratio (R) on the evolution of elevated round jet issued from a stack having an aspect ratio (AR) of 9.0 in a uniform crossflow at a Reynolds number of 2000. The experiments are conducted in a low-speed, recirculating water tunnel. Laser Doppler Velocimetry (LDV) is employed to characterize the water tunnel. Particle Image Velocimetry (PIV) is used to measure the flow field, and the dye visualization technique is utilized to capture the accompanying instantaneous flow structures. Depending on the velocity ratio (R = 0.16 - 1.5), distinct jet shear layer (JSL) structures are observed in the symmetric plane (XY), confirmed by both the flow visualization and PIV data. These structures include clockwise vortices, anticlockwise vortices, swing-induced mushroom vortices, and jet-like vortices. For R<0.5, entrainment of a substantial amount of jet fluid into the stack-wake region (downwash) has been observed. At R=0.5, the streak image captured in the wall parallel plane reveals the ring-like vortices that appear to wrap around the jet core while upright vortices are detected downstream on the lee side of the jet. Additionally, variations in average velocity and turbulent fluctuations in the near field, contingent on different velocity ratios, are discussed.

Flow characteristic investigation of localized arc filament plasma assisted turbulent jet and Bunsen flame

Localized arc filament plasma actuators (LAFPAs) have shown the capability to alter the entrainment of freestream air into a jet. This paper presents an investigation into the effects of LAFPAs on the air jet and methane/air premixed Bunsen flames at different Reynolds numbers. The flow disturbance covering the laminar to turbulent transient conditions was generated by a high voltage plasma discharge system of LAFPAs. The high speed Z-type Schlieren technique was applied to visualize the instantaneous flow and flame structures, and an optical flow algorithm was used to estimate the velocity distribution and further analyze the turbulent effect induced by the plasma. The results illustrate that, in the presence of LAFPA operation, the turbulence jet was accelerated and the jet mixing enhanced. Meanwhile, with the help of LAFPAs, the global consumption burning velocity increased significantly by the area enhancement via plasma–flame interaction. The flame front response to the flow disturbance consists of more surface stretch and flame separation. Furthermore, turbulence spectra analysis of the images reveals a considerable increase in turbulent fluctuations in both cold flow and reacting flow.

An in-depth examination of flow structures organization downstream of a delta-winglet pair vortex generator under laminar, transitional, and turbulent flow regimes

In the present study, we experimentally investigate the time-averaged and time-evolving flow structures generated downstream of a delta-winglet pair vortex generator in an airflow channel. The Stereoscopic Particle Image Velocimetry technique is used to measure the velocity fields in the cross-sectional planes at various axial positions along the channel. The analysis of time-averaged flow topology shows that the flow is predominantly composed of two main counter-rotating longitudinal vortices under laminar, transitional, and turbulent regimes. While the time-averaged flow behavior might appear simple, the real-time organization of the instantaneous flow structures presents more complex features. The study of the flow's temporal evolution indicates that the transition from laminar to turbulent regime is controlled by a meandering mechanism referred to the motion of the main vortex centers around their axis and the emergence of secondary structures that evolve periodically over time.

Analysis of performance and flow structures of cycloidal rotors under different pitch-pivot-point and blade camber conditions

The performance and unsteady vortical flows of a 2-bladed cycloidal propeller are investigated using the SST γ−Re‾θt transition model, under different pitch-pivot-point and blade camber conditions. Firstly, it shows that the results of the present computations match well with the previous numerical data and experiments, in terms of the instantaneous performance and internal flow structures. Then, due to the moderate propulsive force and low power, the cycloidal rotor with a pitch-pivot-point of x/c = 0.25 maximize the efficiency. Moving the pitching location to the leading edge increases the lift and leads to the earlier flow separation on the blade surface. However, as the pitch-pivot-point shifts to the middle chord, the power of the cycloidal rotor increases dramatically because of the massive flow separation, leading to the degradation of the performance. Simultaneously, the symmetrical profiles, involving NACA0012 and 0015, are recommended due to the wide operation condition with high efficiency. The thick symmetrical and asymmetrical airfoils produce the worst performance due to the large power that is consumed. Furthermore, owing to the change of the rotating speed only, the advance coefficient effect is more obvious than the Reynolds number. When analyzing the performance of the rotating system at any position, one should consider the performance, pressure difference, near-wall flows and forces (lift and drag) of each blade.

Bulk Cavitation in Model Gasoline Injectors and Their Correlation with the Instantaneous Liquid Flow Field

It is well established that spray characteristics from automotive injectors depend on, among other factors, whether cavitation arises in the injector nozzle. Bulk cavitation, which refers to the cavitation development distant from walls and thus far from the streamline curvature associated with salient points on a wall, has not been thoroughly investigated experimentally in injector nozzles. Consequently, it is not clear what is causing this phenomenon. The research objective of this study was to visualize cavitation in three different injector models (designated as Type A, Type B, and Type C) and quantify the liquid flow field in relation to the bulk cavitation phenomenon. In all models, bulk cavitation was present. We expected this bulk cavitation to be associated with a swirling flow with its axis parallel to that of the nozzle. However, liquid velocity measurements obtained through particle image velocimetry (PIV) demonstrated the absence of a swirling flow structure in the mean flow field just upstream of the nozzle exit, at a plane normal to the hypothetical axis of the injector. Consequently, we applied proper orthogonal decomposition (POD) to analyze the instantaneous liquid velocity data records in order to capture the dominant coherent structures potentially related to cavitation. It was found that the most energetic mode of the liquid flow field corresponded to the expected instantaneous swirling flow structure when bulk cavitation was present in the flow.

The effect of transverse inclination angle on hydrodynamic characteristics of two tandem circular cylinders in an X arrangement

A numerical investigation of the flow around two stationary circular cylinders in an X arrangement, with a Reynolds number of Re = 3900 and a spacing ratio of L/D = 4.0, is conducted using Large-Eddy Simulation. Eight different transverse inclination angles (α = 0°–30°) are considered to investigate their effects on several aspects, including the time-averaged drag coefficient (Cd-ave), root-mean-square lift coefficient (Cl-rms), Strouhal number (St), instantaneous flow structure, and time-averaged pressure distribution. The numerical results demonstrate that when the inclination angle exceeds a critical value of αc = 12.5°–15°, the flow pattern in the gap between two cylinders transitions from the reattachment regime to the co-shedding regime. This flow transition indicates that the wake vortex periodically detaches from the upstream cylinder and impinges on the downstream cylinder, resulting in a sharp increase in force coefficients, especially for the downstream one. When compared with α = 15°–30°, the force coefficients for both cylinders at α = 0°–12.5° are reduced, which is favorable to the structural stability. Furthermore, an increase in α leads to a monotonic rise in Cd-ave for the downstream cylinder. This can be primarily attributed to the amplified pressure coefficient on the front face of the downstream cylinder, which is caused by the reduced shielding effect from the upstream one.

Large-eddy simulation of airflow dynamics around a cluster of buildings

The wind flow around the buildings with different rooftops is studied numerically using large-eddy simulation (LES). The filtered Navier-Stokes equations in LES are used to compute the large eddies, whereas the dynamic Smagorinsky subgrid-scale (SGS) model calculates the small eddies. A turbulent spot method is applied for the synthesis of artificial turbulent fields at the inlet. In this separated and reattached flow, our aim is to analyze the wakes’ vortical structure along with the buildings of different heights and shapes. A large number of engineering applications involve precise predictions of the airflow around buildings to ensure performance and safety. To validate the numerical solver, a comparison is performed with the earlier reported numerical and experimental data. The turbulent flow characteristics are discussed in terms of instantaneous flow structure and time-averaged statistical flow quantities. All the cases are simulated for a Reynolds number [Formula: see text] to understand the turbulent airflow patterns. The flow shows a separable bubble at the leading edge of the rooftop of the building that leads to recirculation at the lee side of the first row of buildings. Due to the recirculation, the suction arises near the leading edge of the building to assure a continuous flow of air around the obstacles. Further, Reynold stresses show high momentum fluxes in the frontal region of the buildings.

Lamb dilatation and its hydrodynamic viscous flux in near-wall incompressible flows

In this paper, we introduce a new physical concept referred to as the wall-normal Lamb dilatation flux (WNLDF), which is defined as the wall-normal derivative of the Lamb dilatation (namely, the divergence of the Lamb vector) multiplied by the dynamic viscosity for incompressible viscous flows. It is proved that the boundary Lamb dilatation flux (BLDF, namely the wall-normal Lamb dilatation flux at the wall) is determined by the boundary enstrophy flux (BEF) and the surface curvature-induced contribution. As the first step to explore this new concept, the present study only considers flow past a stationary no-slip flat wall without curvature-fluid dynamic coupling effects. It is found that the temporal–spatial evolution rate of the WNLDF is contributed by four source terms, which can be explicitly expressed by using the fundamental surface quantities including skin friction (or surface vorticity) and surface pressure. Therefore, the instantaneous near-wall flow structures are directly related to the WNLDF in both laminar and turbulent flows. As an example, for the turbulent channel flow at Reτ=180, the intensification of the temporal–spatial evolution rate of the WNLDF is caused by the strong wall-normal velocity event (SWNVE) associated with quasi-streamwise vortices and high intermittency of the viscous sublayer. In addition, near the SWNVE, this evolution rate is mainly contributed by the dot product of skin friction and surface enstrophy gradient, as well as the coupling between the skin friction divergence and the boundary enstrophy. The exact results presented in this paper could provide new physical insights into complex near-wall flows.

Effects of turbulence intensity and integral length scale on the surface pressure on a rectangular 5:1 cylinder

This paper presents the LES of the turbulence effects on the flow over a two-dimensional rectangular 5:1 cylinder. The homogeneous and isotropic inflow turbulence fields are generated by the Iterating-Reshaping based Consistent Discrete Random Flow Generation (IRCDRFG) technique. A total of nine numerical cases with the inflow turbulence intensity equal to 5.0%, 7.5%, and 10.0%, and the ratio of integral length scale to cylinder depth (L/D) equal to 1, 2, and 4 are simulated respectively. The LES tool well reproduces both the instantaneous and time-averaged flow structures in the near cylinder area. The sizes of the mean separation bubble on the cylinder surface are noticed to decrease and be closer to the leading edge with the higher turbulence intensity and the lower L/D, which contributes to the shift of location with the minimum mean value and that with the maximum RMS value of the surface pressure. Besides, the consistent drag force results with different inflow conditions are obtained, which have strong connection with the following correlation results of surface pressure in different directions. Additionally, the PSD analysis shows that the low-frequency energy of the fluctuating pressure is significantly increased with the presence of the incoming large-scale turbulence field.

Simultaneous measurements of inertial acceleration and flow structures during coarse-grain entrainment under steady currents

An instrumented smart sediment particle (SSP) is used to investigate the entrainment of spherical coarse grains resting on a rough bed comprising semi-spherical elements. The SSP contains electronic sensors facilitating the direct measurement of tri-axial accelerations. The instantaneous flow field is measured simultaneously using two-dimensional particle tracking velocimetry (PTV), enabling joint analysis of accelerations and flow structures during entrainment. Two different initial placement positions of the SSP are tested. Both particle vibration and complete entrainment events are observed in experiments. Results show larger maximum acceleration and longer duration of motion with more significant obstruction by surrounding bed roughness, which entails greater momentum transfer at the initiation of entrainment. During vibration events, acceleration can occasionally reach the threshold value but with no entrainment because of the low persistence of relevant flow features inducing energy transfer. Further analysis on instantaneous flow structures indicates that, at the threshold flow condition, the occurrence and persistence of the “sweep-outward interaction” quadrant motion sequence (i.e. Q4-Q1 sequence) in front the particle, combined with the transient increase of vorticity due to the passage of clockwise vortices above the particle, is the key to energy transfer and complete entrainment. The Q4-Q1 sequence may either be caused by the lower half of anti-clockwise vortices or occur independently. Generally, the joint analysis of acceleration and flow structures provides a new perspective to studying coarse grain entrainment, especially a potential to relate near-bed flow structures to the status of particle motion in the future.

Numerical investigation of h-Darrieus wind turbine aerodynamics at different tip speed ratios

PurposeThe purpose of the paper is to predict the aerodynamic performance of a complete scale model H-Darrieus vertical axis wind turbine (VAWT) with end plates at different operating conditions. This paper aims at understanding the flow physics around a model VAWT for three different tip speed ratios corresponding to three different flow regimes.Design/methodology/approachThis study achieves a first three-dimensional hybrid lattice Boltzmann method/very large eddy simulation (LBM-VLES) model for a complete scaled model VAWT with end plates and mast using the solver PowerFLOW. The power curve predicted from the numerical simulations is compared with the experimental data collected at Erlangen University. This study highlights the complexity of the turbulent flow features that are seen at three different operational regimes of the turbine using instantaneous flow structures, mean velocity, pressure iso-contours, blade loading and skin friction plots.FindingsThe power curve predicted using the LBM-VLES approach and setup provides a good overall match with the experimental power curve, with the peak and drop after the operational point being captured. Variable turbulent flow structures are seen over the azimuthal revolution that depends on the tip speed ratio (TSR). Significant dynamic stall structures are seen in the upwind phase and at the end of the downwind phase of rotation in the deep stall regime. Strong blade wake interactions and turbulent flow structures are seen inside the rotor at higher TSRs.Research limitations/implicationsThe computational cost and time for such high-fidelity simulations using the LBM-VLES remains expensive. Each simulation requires around a week using supercomputing facilities. Further studies need to be performed to improve analytical VAWT models using inputs/calibration from high fidelity simulation databases. As a future work, the impact of turbulent and nonuniform inflow conditions that are more representative of a typical urban environment also needs to be investigated.Practical implicationsThe LBM methodology is shown to be a reliable approach for VAWT power prediction. Dynamic stall and blade wake interactions reduce the aerodynamic performance of a VAWT. An ideal operation close to the peak of the power curve should be favored based on the local wind resource, as this point exhibits a smoother variation of forces improving operational performance. The 3D flow features also exhibit a significant wake asymmetry that could impact the optimal layout of VAWT clusters to increase their power density. The present work also highlights the importance of 3D simulations of the complete model including the support structures such as end plates and mast.Social implicationsAccurate predictions of power performance for Darrieus VAWTs could help in better siting of wind turbines thus improving return of investment and reducing levelized cost of energy. It could promote the development of onsite electricity generation, especially for industrial sites/urban areas and renew interest for VAWT wind farms.Originality/valueA first high-fidelity simulation of a complete VAWT with end plates and supporting structures has been performed using the LBM approach and compared with experimental data. The 3D flow physics has been analyzed at different operating regimes of the turbine. These physical insights and prediction capabilities of this approach could be useful for commercial VAWT manufacturers.

Investigation of Mixing Characteristics of the Transverse Jet in a Supersonic Combustor at Low Mach Inflow Condition

LES is used in the present work to simulate and unfold unsteady flow dynamics and mixing characteristics in a cavity-based supersonic combustor at low Mach numbers. In the combustor, a transverse jet is injected ahead of the cavity. Two inflow Mach numbers (Ma=1.2 and Ma=2.5) are numerically investigated. Fine instantaneous and average mixing flow structures are well identified and analyzed by LES. The mixing performance is also studied and compared. The simulation results show that penetration is dominated by jet/freestream momentum flux ratio, even though the inflow Mach number varies. It is also demonstrated that for a jet at low Mach inflow, a higher coefficient of pressure is attained. While around the jet location, a much higher peak of the mixing vorticity efficiency is obtained for low Mach inflow, which is of fundamental importance to the near-field mixing.

Experimental Study on Wake Characteristics of Secondary Grooved Cylinders with Different Depths

In this study, the flow field of a new secondary-grooved cylinder is determined by using particle image velocimetry (PIV) to understand the wake characteristics at different depths of the secondary grooved cylinders. In order to analyze the wake characteristic behind the secondary grooved cylinder with different depths, time-averaged streamlines, time-averaged velocity, RMS velocity, Reynolds stress, turbulent kinetic energy, and instantaneous flow structures are employed. The recirculation zone for secondary grooved cylinders with different depths decreases when compared to the smooth cylinder; the peak magnitudes of flow velocity fluctuation intensity and transverse velocity fluctuation intensity for secondary grooved cylinders with different depths are reduced and the locations appear delayed. Furthermore, in contrast to the smooth cylinder, the secondary grooved cylinders with different depths' Reynolds stress and turbulent kinetic energy are increased by the wake flow, and the transient large-scale vortex is split into several smaller-scale vortices behind the secondary grooved cylinders. The results obtained for the above flow structure are more significant when h/D = 0.05 for the secondary grooved cylinder.

Physical mechanisms behind the extreme wind pressures on two tandem square cylinders

The extreme wind pressure might lead to local or overall structural failures. The physical mechanisms behind extreme pressures on two tandem square cylinders are investigated using large-eddy simulation at a Reynolds number of 8 × 104. The spacing ratio P/B ranges from 1.1 to 5 (P: cylinders’ center distance; B: side length). The aerodynamic coefficients, flow patterns, mean and fluctuating pressure coefficients, pressure skewness and kurtosis, and instantaneous flow structures are analyzed. The extreme negative pressures are induced by the intermittent appearance of strong vortices attached to the cylinder surfaces. “Gap vortex” and “wall vortex” are responsible for the extreme pressure at the gap-sides of two cylinders in the single mode (1 < P/B < 2). “Corner vortex” would cause extreme negative pressure near the front corners of the upstream cylinder and the rear corners of both cylinders at most spacings. At the reattached (2 ≤ P/B < 4) and binary (4 ≤ P/B ≤ 5) modes, the Karman vortex released from the rear corner of the downstream cylinders leads to extreme pressure on the rear surface. As the spacing increases, the extreme pressure on non-Gaussian-pressure regions is generally strengthened but the three-dimensionality in vortex structures and instantaneous pressure distributions roughly declines.

An LES study of the wake flow dynamics and heat transfer characteristics of two side-by-side finite wall-mounted square cylinders

This paper studies the wake flow dynamics and heat transfer characteristics of two side-by-side finite wall-mounted square cylinders through large-eddy simulations at Reynolds and Prandtl numbers of Re = 1.2 × 104 and Pr = 0.7. The influence of normalized center-to-center distances between cylinders (S/d, where d is the side of the cylindersʹ cross-section) is investigated for S/d = 2–5, while both cylinders pose an identical aspect ratio of AR = 7. First, the numerical approach is validated against the published experimental data. Then the instantaneous and time-mean wake flow structures, as well as the global quantities, turbulence statistics and heat transfer are studied. It is found that the biased/flip-flop flow at S/d = 2 turns into anti-phase coupled vortex shedding flow at S/d ≥ 3. This flow regime transition induces a relatively sharp change in drag coefficient and vortex shedding frequency, minimum values at S/d = 2 and maximum values at S/d = 3. The Nusselt number mildly changes at S/d ≥ 3. The turbulent deflected gap flow at S/d = 2 results in inequality of drag forces on and heat transfer from two cylinders. That is, the drag coefficient and Nusselt number are larger for the cylinder towards which the gap-flow is deflected. It is also shown that swinging the deflected gap flow at S/d = 2 is a more intense source of turbulence than the vortex shedding from lateral faces, albeit the Reynolds stress is magnified with increasing S/d. The flow interference is steadily reduced with S/d, almost faded at S/d = 5.

Numerical Investigation of Flow around Two Tandem Cylinders in the Upper Transition Reynolds Number Regime Using Modal Analysis

Flow around two tandem cylinders at Re = 3.6 × 106 for different center-to-center spacing ratio (L/D) is investigated numerically using two-dimensional (2D) Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations combined with a standard k−ω SST turbulence model. The instantaneous flow structures around the cylinders, hydrodynamic forces on the cylinders and Strouhal number (St) are analyzed and discussed. Dynamic Mode Decomposition (DMD) is used to extract the spatiotemporal information of the coherent flow structures in the wake regions behind the upstream (UC) and downstream (DC) cylinders. A sparsity-promoted algorithm is implemented to select the dominant modes which contribute the most to the dynamics of the system. Based on the dominant modes, a reduced-order representation of the flows is built. A comparison of the lift and drag force–time histories, obtained by simulation results and the reduced-order representations, shows a high capability of the latter to reproduce the surrounding flow and hydrodynamic properties of the tandem cylinders at the high Reynolds number.

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.

Flow mechanism of self-recirculating casing treatment in a low-reaction transonic compressor rotor

Casing treatment is used to ensure the stability of an aeroengine compressor when it is operated away from its design point. However, currently, there is little published data about the effect of casing treatment on highly loaded axial compressors. In this study, unsteady numerical simulations are applied to explore the flow mechanism responsible for the stability enhancement of a low-reaction (LR) transonic compressor rotor with ultra-high loading owing to self-recirculating casing treatment (SRCT). A special SRCT configuration is designed based on the suction effect, which can simultaneously improve the stall margin and aerodynamic performance. Radial skew in the direction of blade rotation is employed to enhance the control outcomes further. The results show that the best skew angle for stall margin and performance improvement is 45 degrees. Further analysis of the instantaneous flow structures reveals that for the smooth casing, the mechanism by which tip leakage vortex (TLV) breakdown, TSV, and blade loading interact induces periodic oscillations of the tip flow field. As the unsteady suction effect introduced by the SRCT dominates the evolution processes of vortical structures, the original oscillation frequency is converted into the SRCT-induced excitation frequency. Furthermore, a substantial amount of double-leakage flow is inhaled into the recirculation channel without rolling up into the adjacent TLV, which dampens the shock/TLV interaction and the formation of downstream TSVs. The blockage along the pressure side caused by the aforementioned large-scale vortices is effectively eliminated.

Aerodynamic characteristics of double-connected train groups composed of different kinds of high-speed trains under crosswinds: A comparison study

As train speeds continuously increase, the crosswind stability of high-speed trains (HSTs) has been a prominent research topic. Benefiting from advances in railway technology, the coupled operation of different HSTs has been proven to be permissible, but the crosswind performance of double-connected train groups composed of different kinds of HSTs has rarely been studied. This paper therefore studied the differences in the aerodynamic performance of double-connected train groups composed of same and different train units under crosswinds. We employed an improved delayed detached-eddy simulation (IDDES) method to investigate the flow features around different groups of double-connected train. Two one-eighth-scale standard HSTs—Train 1 (T 1) and Train 2 (T 2)—currently operating in China were selected to form different group configurations for double-connected trains: T 1-T 1 (Case 1–1), T 1-T 2 (Case 1–2), T 2-T 1 (Case 2–1), and T 2-T 2 (Case 2–2). First, the reliability of the numerical algorithm and mesh independence were verified to ensure the accuracy of the numerical results. Second, the aerodynamic force coefficients, time-averaged, and instantaneous flow structures of different double-connected train group types were compared and analyzed.