To assess the aerodynamic performance and vibration characteristics of rotor blades during rotation,a study of unsteady blade surface forces is conducted in a low-speed axial flow compressor under a rotating coordinat...To assess the aerodynamic performance and vibration characteristics of rotor blades during rotation,a study of unsteady blade surface forces is conducted in a low-speed axial flow compressor under a rotating coordinate system.The capture,modulation,and acquisition of unsteady blade surface forces are achieved by using pressure sensors and strain gauges attached to the rotor blades,in conjunction with a wireless telemetry system.Based on the measurement reliability verification,this approach allows for the determination of the static pressure distribution on rotor blade surfaces,enabling the quantitative description of loadability at different spanwise positions along the blade chord.Effects caused by the factors such as Tip Leakage Flow(TLF)and flow separation can be perceived and reflected in the trends of static pressure on the blade surfaces.Simultaneously,the dynamic characteristics of unsteady pressure and stress on the blade surfaces are analyzed.The results indicate that only the pressure signals measured at the mid-chord of the blade tip can distinctly detect the unsteady frequency of TLF due to the oscillation of the low-pressure spot on the pressure surface.Subsequently,with the help of one-dimensional continuous wavelet analysis method,it can be inferred that as the compressor enters stall,the sensors are capable of capturing stall cell frequency under a rotating coordinate system.Furthermore,the stress at the blade root is higher than that at the blade tip,and the frequency band of the vibration can also be measured by the pressure sensors fixed on the casing wall in a stationary frame.While the compressor stalls,the stress at the blade root can be higher,which can provide valuable guidance for monitoring the lifecycle of compressor blades.展开更多
Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the...Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is developed,which maintains the fidelity of the Navier-Stokes solution for unsteady flow and of the moving-medium Ffowcs Williams-Hawkings(FW-H)formulation for capturing tonal noise.Furthermore,this on-the-fly approach enables a unified architecture for discreteadjoint sensitivity analysis encompassing both aerodynamics and aeroacoustics,facilitating effective multi-objective weighted optimizations.Subsequently,this proposed methodology is applied to perform trade-off optimizations between aerodynamics and aeroacoustics for a propeller by employing varying weighting factors to comprehend their influence on optimal configurations.The results demonstrate a positive correlation between efficiency and noise sensitivities,and thus indicate an inherent synchronicity where pursing noise reduction through purely aeroacoustic optimization inevitably entails sacrificing aerodynamic efficiency.However,by effectively incorporating appropriate weighting factors(recommended to range from 0.25 to 0.5)into the multi-objective function combined with both aerodynamics and aeroacoustics,it becomes feasible to achieve efficiency enhancement and noise reduction simultaneously.Key findings show that reducing blade planform size and equipping“rotated-S”shaped airfoil profiles in the tip region can effectively restrain noise levels while maintaining aerodynamic performance.展开更多
Unsteady aerodynamic characteristics at high angles of attack are of great importance to the design and development of advanced fighter aircraft, which are characterized by post-stall maneuverability with multiple Deg...Unsteady aerodynamic characteristics at high angles of attack are of great importance to the design and development of advanced fighter aircraft, which are characterized by post-stall maneuverability with multiple Degrees-of-Freedom(multi-DOF) and complex flow field structure.In this paper, a special kind of cable-driven parallel mechanism is firstly utilized as a new suspension method to conduct unsteady dynamic wind tunnel tests at high angles of attack, thereby providing experimental aerodynamic data. These tests include a wide range of multi-DOF coupled oscillatory motions with various amplitudes and frequencies. Then, for aerodynamic modeling and analysis, a novel data-driven Feature-Level Attention Recurrent neural network(FLAR) is proposed. This model incorporates a specially designed feature-level attention module that focuses on the state variables affecting the aerodynamic coefficients, thereby enhancing the physical interpretability of the aerodynamic model. Subsequently, spin maneuver simulations, using a mathematical model as the baseline, are conducted to validate the effectiveness of the FLAR. Finally, the results on wind tunnel data reveal that the FLAR accurately predicts aerodynamic coefficients, and observations through the visualization of attention scores identify the key state variables that affect the aerodynamic coefficients. It is concluded that the proposed FLAR enhances the interpretability of the aerodynamic model while achieving good prediction accuracy and generalization capability for multi-DOF coupling motion at high angles of attack.展开更多
This study presents a two-dimensional,transient model to simulate the flow and thermal behavior of CO_(2) within a fracturing wellbore.The model accounts for high-velocity flow within the tubing and radial heat exchan...This study presents a two-dimensional,transient model to simulate the flow and thermal behavior of CO_(2) within a fracturing wellbore.The model accounts for high-velocity flow within the tubing and radial heat exchange between the wellbore and surrounding formation.It captures the temporal evolution of temperature,pressure,flow velocity,and fluid density,enabling detailed analysis of phase transitions along different tubing sections.The influence of key operational and geological parameters,including wellhead pressure,injection velocity,inlet temperature,and formation temperature gradient,on the wellbore’s thermal and pressure fields is systematically investigated.Results indicate that due to intense convective transport by the high-speed CO_(2) flow,the temperature and velocity within the tubing are primarily governed by the inlet temperature and injection velocity,with relatively minor influence from radial heat transfer with the formation.The pressure,flow velocity,and density of CO_(2) within the tubing are strongly dependent on wellhead conditions.Frictional losses and well depth contribute to pressure variations,particularly in the horizontal section of the wellbore,where a noticeable pressurization effect increases the fluid density.During injection,liquid CO_(2) initially undergoes a rapid transition to a supercritical state,with the depth at which this phase change occurs stabilizing as injection progresses.展开更多
Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of un...Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.展开更多
The study presents an experimental exploration into the mode transition of an overunder TBCC(Turbine-Based Combined Cycle)inlet,with a specific emphasis on the flow characteristics at off-design transition Mach number...The study presents an experimental exploration into the mode transition of an overunder TBCC(Turbine-Based Combined Cycle)inlet,with a specific emphasis on the flow characteristics at off-design transition Mach number.A systematic investigation was undertaken into the mode transition characteristics in both unthrottled and throttled conditions within a highspeed duct,employing high speed Schlieren and dynamic pressure acquisition systems.The results show that the high-speed duct faced flow oscillations primarily dictated by the separation bubble near the duct entrance during the downward rotation of splitter,leading to the duct’s unstart under the unthrottled condition.During the splitter’s reverse rotation,a notable hysteresis of unstart/restart of the high-speed duct was observed.Conversely,hysteresis vanishes when the initial flowfield nears the critical state owing to downstream throttling.Moreover,the oscillatory diversity,a distinctive characteristic of the high-speed duct,was firstly observed during the mode transition induced by throttling.The flow evolution was divided into four stages:an initial instability stage characterized by low-frequency oscillations below 255 Hz induced by shock train self-excitation oscillation and high-frequency oscillations around 1367 Hz caused by the movement of separation bubble.This stage is succeeded by the“big buzz”phase,comprised of pressure accumulation/release within the overflow-free duct and shock motion outside the duct to retain dynamic flow balance.The dominant frequency escalated with the increase of the internal contraction ratio in the range of 280 Hz to 400 Hz.This was followed by a high-frequency oscillation stage around 453 Hz dominated by a large internal contraction ratio with low pulsating energy,accompanied by a continuous supersonic overflow.Lastly,as the splitter gradually intersected the boundary layer of the first-stage compression surface,the capture area and the turbulence intensity of the incoming flow underwent a sudden shift,leading to a more diverse flow oscillation within the duct,manifested as various forms of mixed buzz.展开更多
Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft ...Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.展开更多
The unsteady 3D flow fields in a single-stage transonic compressor under designed conditions are simulated numerically to investigate the effects of the curved rotors on the stage performance and the aerodynamic inter...The unsteady 3D flow fields in a single-stage transonic compressor under designed conditions are simulated numerically to investigate the effects of the curved rotors on the stage performance and the aerodynamic interaction between the blade rows. The results show that, compared to the compressor with unurved rotors, the compressor under scrutiny acquires remarkable increases in efficiency with significantly reduced amplitudes of the time-dependent fluctuation. The amplitude of the pressure fluctuation around the stator leading edge decreases at both endwalls, but increases at the mid-span in the curved rotors. The pressure fluctuation near the stator leading edge, therefore, becomes more uniform in the radial direction of this compressor. Except for the leading edge area, the pressure fluctuatinn amplitude declines remarkably in the tip region of stator surface downstream of the curved rotor, but hardly changes in the middle and at the hub.展开更多
A full-span free-wake method is coupled with an unsteady panel method to accurately predict the unsteady aerodynamics of helicopter rotor blades in hover and forward flight. The unsteady potential-based panel method i...A full-span free-wake method is coupled with an unsteady panel method to accurately predict the unsteady aerodynamics of helicopter rotor blades in hover and forward flight. The unsteady potential-based panel method is used to consider aerodynamics of finite thickness multi-bladed rotors, and the full-span free-wake method is applied to simulating dynamics of rotor wake. These methods are tightly coupled through trailing-edge Kutta condition and by converting doublet-wake panels to full-span vortex filaments. A velocity-field integration technique is also adopted to overcome singularity problem during the interaction between the rotor wake and blades. Helicopter rotors including Caradonna–Tung, UH-60A, and AH-1G rotors, are simulated in hover and forward flight to validate the accuracy of this approach. The predicted aerodynamic loads of rotor blades agree well with available measured data and computational fluid dynamics （CFD） results, and the unsteady dynamics of rotor wake is also well simulated. Compared to CFD, the present method obtains accurate results more efficiently and is suitable to rotorcraft aeroelastic analysis.展开更多
The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is p...The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.展开更多
Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous f...Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.展开更多
Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme wi...Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme without using any turbulence model.A series of distinguished unsteady phenomena for a thin 2-D transonic airfoil flow were presented.Due to continuous adverse pressure gradient in the subsonic flow downstream of the sonic line,the unsteady separated boundary layer with main vortex and secondary vortex was developed at the rear of the airfoil.At the trailing edge,the vortex-shedding was characterized by periodical connection of the main vortex and secondary vortex on the other side of the airfoil.The unsteady separation and vortex-shedding occurred with the same period.On the airfoil surface,the average pulse pressure related to the unsteady supersonic region was obviously smaller than that related to the vortex-shedding at the trailing edge.With the attack angle increasing from 0°to 2°,the frequency of vortex-shedding decreases about 4.2%.At last,the turbulence intensity and many second-order statistics in the wake region were investigated.展开更多
The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and th...The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and the three dimensional unsteady turbulent simulation concerning the rotor-stator interaction is executed by a Navier-Stoke solver embedded with k -ε turbulence model and with appropriate moving interface boundary conditions. Detecting points are distributed in the flow passage in different radial and circumferential positions to capture the static pressure fluctuation character for one cycle of the impeller. The time-domain spectrums show that the static pressure curves are periodic and have five peaks and five valleys. With the radius increasing, the pressure fluctuation peak-to-peak values in the impeller are increasing, and reach the maximum value on the interface. In the casing flow passage, those values are about 7% of local static pressure except some ones near the tongue. The values become decreasingly in the diffuser pipe. The frequency spectrums transformed by fast Fourier transform （FFT） show that the dominant frequency is approximate with the blade passing frequency, and the pressure fluctuations in impeller passage have high frequency content while those in casing ones have no such information.展开更多
The impulse and self starting characteristics of a mixed-compression hypersonic inlet designed at Mach number of 6.5 are studied by applying the unsteady computational fluid dynamics （CFD） method. The full Navier–S...The impulse and self starting characteristics of a mixed-compression hypersonic inlet designed at Mach number of 6.5 are studied by applying the unsteady computational fluid dynamics （CFD） method. The full Navier–Stokes equations are solved with the assumption of viscous perfect gas model, and the shear-stress transport （SST） k–x two-equation Reynolds averaged Navier– Stokes （RANS） model is used for turbulence modeling. Results indicate that during impulse starting, the flow field is divided into three zones with different aerodynamic parameters by primary shock and upstream-facing shock. The separation bubble on the shoulder of ramp undergoes a generating, growing, swallowing and disappearing process in sequence. But a separation bubble at the entrance of inlet exists until the freestream velocity is accelerated to the starting Mach number during self starting. The mass flux distribution of flow field is non-uniform because of the interaction between shock and boundary layer, so that the mass flow rate at throat is unsteady during impulse starting. The duration of impulse starting process increases almost linearly with the decrease of freestream Mach number but rises abruptly when the freestream Mach number approaches the starting Mach number. The accelerating performance of booster almost has no influence on the self starting ability of hypersonic inlet.展开更多
In order to calculate the unsteady aerodynamic characteristics of a tilt-rotor in a conver- sion mode, a virtual blade model （VBM） and an real blade model （RBM） are established respec- tively. A new multi-layer mo...In order to calculate the unsteady aerodynamic characteristics of a tilt-rotor in a conver- sion mode, a virtual blade model （VBM） and an real blade model （RBM） are established respec- tively. A new multi-layer moving-embedded grid technique is proposed to reduce the numerical dissipation of the tilt-rotor wake in a conversion mode. In this method, a grid system generated abound the rotor accounts for rigid blade motions, and a new searching scheme named adaptive inverse map （AIM） is established to search corresponding donor elements in the present moving- embedded grid system to translate information among the different computational zones. A dual-time method is employed to fulfill unsteady calculations on the flowfield of the tilt-rotor, and a second-order centered difference scheme considering artificial viscosity is used to calculate the flux. In order to improve the computing efficiency, the single program multiple data （SPMD） model parallel acceleration technology is adopted, according to the characteristic of the current grid system. The lift and drag coefficients of an NACA0012 airfoil, the dynamic pressure distributions below a typical rotor plane, and the sectional pressure distributions on a three-bladed Branum- Tung tilt-rotor in hover flight are calculated respectively, and the present VBM and RBM are val- idated by comparing the calculated results with available experimental data. Then, unsteady aero- dynamic forces and flowfields of an XV-15 tilt-rotor in different modes, such as a fixed conversion mode at different tilt angles （15°, 30°, 60°） and a whole conversion mode which converses from 0° to 90°, are numerically simulated by the VBM and RBM respectively. By analyses and comparisons on the simulated results of unsteady aerodynamic forces of the tilt-rotor in different modes, some meaningful conclusions about distorted blade-tip vortex distribution and unsteady aerodynamic force variation in a conversion mode are obtained, and these investigation results could provide a good foundation for tilt-rotor aircraft design in the future.展开更多
Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determ...Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines （SVMs） based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle.-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as sele, ction of input variables, selection of output variables and determination of SVM parameters. The least squares SVM （LS-SVM） models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfving learning and generalization performance of LS-SVMs.展开更多
Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of...Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.展开更多
The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized secon...The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.展开更多
An improved delayed detached eddy simulation （IDDES） method based on the k-x-SST （shear stress transport） turbulence model was applied to predict the unsteady vortex breakdown past an 80o/65o double-delta wing （...An improved delayed detached eddy simulation （IDDES） method based on the k-x-SST （shear stress transport） turbulence model was applied to predict the unsteady vortex breakdown past an 80o/65o double-delta wing （DDW）, where the angles of attack （AOAs） range from 30° to 40°. Firstly, the IDDES model and the relative numerical methods were validated by simulating the massively separated flow around an NACA0021 straight wing at the AOA of 60°. The fluctuation properties of the lift and pressure coefficients were analyzed and compared with the available measurements. For the DDW case, the computations were compared with such mea-surements as the mean lift, drag, pitching moment, pressure coefficients and breakdown locations. Furthermore, the unsteady properties were investigated in detail, such as the frequencies of force and moments, pressure fluctuation on the upper surface, typical vortex breakdown patterns at three moments, and the distributions of kinetic turbulence energy at a stream wise section. Two dominated modes are observed, in which their Strouhal numbers are 1.0 at the AOAs of 30°, 32° and 34° and 0.7 at the AOAs of 36o, 38° and 40°. The breakdown vortex always moves upstream and downstream and its types change alternatively. Furthermore, the vortex can be identified as breakdown or not through the mean pressure, root mean square of pressure, or even through correlation analysis.展开更多
Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-e...Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.展开更多
基金funded by the National Natural Science Foundation of China(Nos.U24A20138 and No.52376039)the Beijing Natural Science Foundation,China(JQ24017)+1 种基金the National Science and Technology Major Project of China(Nos.J2019-II-0005-0025 and Y2022-II-0002-0005)the Special Fund for the Member of Youth Innovation Promotion Association of Chinese Academy of Sciences,China(No.2018173).
文摘To assess the aerodynamic performance and vibration characteristics of rotor blades during rotation,a study of unsteady blade surface forces is conducted in a low-speed axial flow compressor under a rotating coordinate system.The capture,modulation,and acquisition of unsteady blade surface forces are achieved by using pressure sensors and strain gauges attached to the rotor blades,in conjunction with a wireless telemetry system.Based on the measurement reliability verification,this approach allows for the determination of the static pressure distribution on rotor blade surfaces,enabling the quantitative description of loadability at different spanwise positions along the blade chord.Effects caused by the factors such as Tip Leakage Flow(TLF)and flow separation can be perceived and reflected in the trends of static pressure on the blade surfaces.Simultaneously,the dynamic characteristics of unsteady pressure and stress on the blade surfaces are analyzed.The results indicate that only the pressure signals measured at the mid-chord of the blade tip can distinctly detect the unsteady frequency of TLF due to the oscillation of the low-pressure spot on the pressure surface.Subsequently,with the help of one-dimensional continuous wavelet analysis method,it can be inferred that as the compressor enters stall,the sensors are capable of capturing stall cell frequency under a rotating coordinate system.Furthermore,the stress at the blade root is higher than that at the blade tip,and the frequency band of the vibration can also be measured by the pressure sensors fixed on the casing wall in a stationary frame.While the compressor stalls,the stress at the blade root can be higher,which can provide valuable guidance for monitoring the lifecycle of compressor blades.
基金supported by the National Science and Technology Major Project,China(No.Y2019-I-0018-0017)the National Natural Science Foundation of China(No.11602200)+1 种基金Hunan Innovative Province Construction Special Fund,China(No.2021GK1020)the Priority Academic Program Development of Jiangsu Higher Education Institutions,China。
文摘Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is developed,which maintains the fidelity of the Navier-Stokes solution for unsteady flow and of the moving-medium Ffowcs Williams-Hawkings(FW-H)formulation for capturing tonal noise.Furthermore,this on-the-fly approach enables a unified architecture for discreteadjoint sensitivity analysis encompassing both aerodynamics and aeroacoustics,facilitating effective multi-objective weighted optimizations.Subsequently,this proposed methodology is applied to perform trade-off optimizations between aerodynamics and aeroacoustics for a propeller by employing varying weighting factors to comprehend their influence on optimal configurations.The results demonstrate a positive correlation between efficiency and noise sensitivities,and thus indicate an inherent synchronicity where pursing noise reduction through purely aeroacoustic optimization inevitably entails sacrificing aerodynamic efficiency.However,by effectively incorporating appropriate weighting factors(recommended to range from 0.25 to 0.5)into the multi-objective function combined with both aerodynamics and aeroacoustics,it becomes feasible to achieve efficiency enhancement and noise reduction simultaneously.Key findings show that reducing blade planform size and equipping“rotated-S”shaped airfoil profiles in the tip region can effectively restrain noise levels while maintaining aerodynamic performance.
基金supported by the National Natural Science Foundation of China(Nos.12172315,12072304,11702232)the Fujian Provincial Natural Science Foundation,China(No.2021J01050)the Aeronautical Science Foundation of China(No.20220013068002).
文摘Unsteady aerodynamic characteristics at high angles of attack are of great importance to the design and development of advanced fighter aircraft, which are characterized by post-stall maneuverability with multiple Degrees-of-Freedom(multi-DOF) and complex flow field structure.In this paper, a special kind of cable-driven parallel mechanism is firstly utilized as a new suspension method to conduct unsteady dynamic wind tunnel tests at high angles of attack, thereby providing experimental aerodynamic data. These tests include a wide range of multi-DOF coupled oscillatory motions with various amplitudes and frequencies. Then, for aerodynamic modeling and analysis, a novel data-driven Feature-Level Attention Recurrent neural network(FLAR) is proposed. This model incorporates a specially designed feature-level attention module that focuses on the state variables affecting the aerodynamic coefficients, thereby enhancing the physical interpretability of the aerodynamic model. Subsequently, spin maneuver simulations, using a mathematical model as the baseline, are conducted to validate the effectiveness of the FLAR. Finally, the results on wind tunnel data reveal that the FLAR accurately predicts aerodynamic coefficients, and observations through the visualization of attention scores identify the key state variables that affect the aerodynamic coefficients. It is concluded that the proposed FLAR enhances the interpretability of the aerodynamic model while achieving good prediction accuracy and generalization capability for multi-DOF coupling motion at high angles of attack.
基金funded by National Natural Science Foundation of China(Mechanisms of proppant-carrying transport by magnetic cross-linked microparticle grids and their degradation patterns in CO_(2) fractured cracks).
文摘This study presents a two-dimensional,transient model to simulate the flow and thermal behavior of CO_(2) within a fracturing wellbore.The model accounts for high-velocity flow within the tubing and radial heat exchange between the wellbore and surrounding formation.It captures the temporal evolution of temperature,pressure,flow velocity,and fluid density,enabling detailed analysis of phase transitions along different tubing sections.The influence of key operational and geological parameters,including wellhead pressure,injection velocity,inlet temperature,and formation temperature gradient,on the wellbore’s thermal and pressure fields is systematically investigated.Results indicate that due to intense convective transport by the high-speed CO_(2) flow,the temperature and velocity within the tubing are primarily governed by the inlet temperature and injection velocity,with relatively minor influence from radial heat transfer with the formation.The pressure,flow velocity,and density of CO_(2) within the tubing are strongly dependent on wellhead conditions.Frictional losses and well depth contribute to pressure variations,particularly in the horizontal section of the wellbore,where a noticeable pressurization effect increases the fluid density.During injection,liquid CO_(2) initially undergoes a rapid transition to a supercritical state,with the depth at which this phase change occurs stabilizing as injection progresses.
基金supported by the National Natural Science Foundation of China(No.92252201)the Fundamental Research Funds for the Central Universitiesthe Academic Excellence Foundation of Beihang University(BUAA)for PhD Students。
文摘Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.
基金funded by the National Natural Science Foundation of China(Nos.12025202,U20A2070 and 12172175)the National Science and Technology Major Project,China(No.J2019-Ⅱ-0014-0035)+2 种基金the Postdoctoral Fellowship Program of CPSF,China(No.GZB20230970)the Science Center for Gas Turbine Project,China(Nos.P2022-C-Ⅱ-002-001 and P2022-A-Ⅱ-002-001)the Young Scientific and Technological Talents Project of Jiangsu Association for Science and Technology,China(No.TJ-2021-052).
文摘The study presents an experimental exploration into the mode transition of an overunder TBCC(Turbine-Based Combined Cycle)inlet,with a specific emphasis on the flow characteristics at off-design transition Mach number.A systematic investigation was undertaken into the mode transition characteristics in both unthrottled and throttled conditions within a highspeed duct,employing high speed Schlieren and dynamic pressure acquisition systems.The results show that the high-speed duct faced flow oscillations primarily dictated by the separation bubble near the duct entrance during the downward rotation of splitter,leading to the duct’s unstart under the unthrottled condition.During the splitter’s reverse rotation,a notable hysteresis of unstart/restart of the high-speed duct was observed.Conversely,hysteresis vanishes when the initial flowfield nears the critical state owing to downstream throttling.Moreover,the oscillatory diversity,a distinctive characteristic of the high-speed duct,was firstly observed during the mode transition induced by throttling.The flow evolution was divided into four stages:an initial instability stage characterized by low-frequency oscillations below 255 Hz induced by shock train self-excitation oscillation and high-frequency oscillations around 1367 Hz caused by the movement of separation bubble.This stage is succeeded by the“big buzz”phase,comprised of pressure accumulation/release within the overflow-free duct and shock motion outside the duct to retain dynamic flow balance.The dominant frequency escalated with the increase of the internal contraction ratio in the range of 280 Hz to 400 Hz.This was followed by a high-frequency oscillation stage around 453 Hz dominated by a large internal contraction ratio with low pulsating energy,accompanied by a continuous supersonic overflow.Lastly,as the splitter gradually intersected the boundary layer of the first-stage compression surface,the capture area and the turbulence intensity of the incoming flow underwent a sudden shift,leading to a more diverse flow oscillation within the duct,manifested as various forms of mixed buzz.
基金supported in part by the National Natural Science Foundation of China (No. 12202363)。
文摘Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.
基金National Natural Science Foundation of China (506460210) Chinese Specialized Research Fund for the Doctoral Program of Higher Education (20060213007)Development Program for Outstanding Young Teachers in Harbin Institute of Technology (HITQNJS.2006.046)
文摘The unsteady 3D flow fields in a single-stage transonic compressor under designed conditions are simulated numerically to investigate the effects of the curved rotors on the stage performance and the aerodynamic interaction between the blade rows. The results show that, compared to the compressor with unurved rotors, the compressor under scrutiny acquires remarkable increases in efficiency with significantly reduced amplitudes of the time-dependent fluctuation. The amplitude of the pressure fluctuation around the stator leading edge decreases at both endwalls, but increases at the mid-span in the curved rotors. The pressure fluctuation near the stator leading edge, therefore, becomes more uniform in the radial direction of this compressor. Except for the leading edge area, the pressure fluctuatinn amplitude declines remarkably in the tip region of stator surface downstream of the curved rotor, but hardly changes in the middle and at the hub.
文摘A full-span free-wake method is coupled with an unsteady panel method to accurately predict the unsteady aerodynamics of helicopter rotor blades in hover and forward flight. The unsteady potential-based panel method is used to consider aerodynamics of finite thickness multi-bladed rotors, and the full-span free-wake method is applied to simulating dynamics of rotor wake. These methods are tightly coupled through trailing-edge Kutta condition and by converting doublet-wake panels to full-span vortex filaments. A velocity-field integration technique is also adopted to overcome singularity problem during the interaction between the rotor wake and blades. Helicopter rotors including Caradonna–Tung, UH-60A, and AH-1G rotors, are simulated in hover and forward flight to validate the accuracy of this approach. The predicted aerodynamic loads of rotor blades agree well with available measured data and computational fluid dynamics （CFD） results, and the unsteady dynamics of rotor wake is also well simulated. Compared to CFD, the present method obtains accurate results more efficiently and is suitable to rotorcraft aeroelastic analysis.
基金supported by the National Natural Science Foundation of China (No. 90716011)
文摘The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.
基金Supported by the National Natural Science Foundation of China(10372043,11172134)the Fundingof Jiangsu Innovation Program for Graduate Education(CXZZ11-0192)~~
文摘Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.
基金Programme of Introducing Talents of Discipline to Universities(B08009)
文摘Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme without using any turbulence model.A series of distinguished unsteady phenomena for a thin 2-D transonic airfoil flow were presented.Due to continuous adverse pressure gradient in the subsonic flow downstream of the sonic line,the unsteady separated boundary layer with main vortex and secondary vortex was developed at the rear of the airfoil.At the trailing edge,the vortex-shedding was characterized by periodical connection of the main vortex and secondary vortex on the other side of the airfoil.The unsteady separation and vortex-shedding occurred with the same period.On the airfoil surface,the average pulse pressure related to the unsteady supersonic region was obviously smaller than that related to the vortex-shedding at the trailing edge.With the attack angle increasing from 0°to 2°,the frequency of vortex-shedding decreases about 4.2%.At last,the turbulence intensity and many second-order statistics in the wake region were investigated.
基金supported by National Outstanding Young Scientists Funds of China (Grand No.50825902)
文摘The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and the three dimensional unsteady turbulent simulation concerning the rotor-stator interaction is executed by a Navier-Stoke solver embedded with k -ε turbulence model and with appropriate moving interface boundary conditions. Detecting points are distributed in the flow passage in different radial and circumferential positions to capture the static pressure fluctuation character for one cycle of the impeller. The time-domain spectrums show that the static pressure curves are periodic and have five peaks and five valleys. With the radius increasing, the pressure fluctuation peak-to-peak values in the impeller are increasing, and reach the maximum value on the interface. In the casing flow passage, those values are about 7% of local static pressure except some ones near the tongue. The values become decreasingly in the diffuser pipe. The frequency spectrums transformed by fast Fourier transform （FFT） show that the dominant frequency is approximate with the blade passing frequency, and the pressure fluctuations in impeller passage have high frequency content while those in casing ones have no such information.
文摘The impulse and self starting characteristics of a mixed-compression hypersonic inlet designed at Mach number of 6.5 are studied by applying the unsteady computational fluid dynamics （CFD） method. The full Navier–Stokes equations are solved with the assumption of viscous perfect gas model, and the shear-stress transport （SST） k–x two-equation Reynolds averaged Navier– Stokes （RANS） model is used for turbulence modeling. Results indicate that during impulse starting, the flow field is divided into three zones with different aerodynamic parameters by primary shock and upstream-facing shock. The separation bubble on the shoulder of ramp undergoes a generating, growing, swallowing and disappearing process in sequence. But a separation bubble at the entrance of inlet exists until the freestream velocity is accelerated to the starting Mach number during self starting. The mass flux distribution of flow field is non-uniform because of the interaction between shock and boundary layer, so that the mass flow rate at throat is unsteady during impulse starting. The duration of impulse starting process increases almost linearly with the decrease of freestream Mach number but rises abruptly when the freestream Mach number approaches the starting Mach number. The accelerating performance of booster almost has no influence on the self starting ability of hypersonic inlet.
基金supported by the National Natural Science Foundation of China(No.11272150)
文摘In order to calculate the unsteady aerodynamic characteristics of a tilt-rotor in a conver- sion mode, a virtual blade model （VBM） and an real blade model （RBM） are established respec- tively. A new multi-layer moving-embedded grid technique is proposed to reduce the numerical dissipation of the tilt-rotor wake in a conversion mode. In this method, a grid system generated abound the rotor accounts for rigid blade motions, and a new searching scheme named adaptive inverse map （AIM） is established to search corresponding donor elements in the present moving- embedded grid system to translate information among the different computational zones. A dual-time method is employed to fulfill unsteady calculations on the flowfield of the tilt-rotor, and a second-order centered difference scheme considering artificial viscosity is used to calculate the flux. In order to improve the computing efficiency, the single program multiple data （SPMD） model parallel acceleration technology is adopted, according to the characteristic of the current grid system. The lift and drag coefficients of an NACA0012 airfoil, the dynamic pressure distributions below a typical rotor plane, and the sectional pressure distributions on a three-bladed Branum- Tung tilt-rotor in hover flight are calculated respectively, and the present VBM and RBM are val- idated by comparing the calculated results with available experimental data. Then, unsteady aero- dynamic forces and flowfields of an XV-15 tilt-rotor in different modes, such as a fixed conversion mode at different tilt angles （15°, 30°, 60°） and a whole conversion mode which converses from 0° to 90°, are numerically simulated by the VBM and RBM respectively. By analyses and comparisons on the simulated results of unsteady aerodynamic forces of the tilt-rotor in different modes, some meaningful conclusions about distorted blade-tip vortex distribution and unsteady aerodynamic force variation in a conversion mode are obtained, and these investigation results could provide a good foundation for tilt-rotor aircraft design in the future.
文摘Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines （SVMs） based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle.-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as sele, ction of input variables, selection of output variables and determination of SVM parameters. The least squares SVM （LS-SVM） models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfving learning and generalization performance of LS-SVMs.
基金Project(51375498)supported by the National Natural Science Foundation of China
文摘Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.
基金The project supported by the National Natural Science Foundation of China (10372007,10002003) and CNPC Innovation Fund
文摘The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.
基金co-supported by Innovative Foundation of CARDCthe National Natural Science Foundation of China (No. 11072129)
文摘An improved delayed detached eddy simulation （IDDES） method based on the k-x-SST （shear stress transport） turbulence model was applied to predict the unsteady vortex breakdown past an 80o/65o double-delta wing （DDW）, where the angles of attack （AOAs） range from 30° to 40°. Firstly, the IDDES model and the relative numerical methods were validated by simulating the massively separated flow around an NACA0021 straight wing at the AOA of 60°. The fluctuation properties of the lift and pressure coefficients were analyzed and compared with the available measurements. For the DDW case, the computations were compared with such mea-surements as the mean lift, drag, pitching moment, pressure coefficients and breakdown locations. Furthermore, the unsteady properties were investigated in detail, such as the frequencies of force and moments, pressure fluctuation on the upper surface, typical vortex breakdown patterns at three moments, and the distributions of kinetic turbulence energy at a stream wise section. Two dominated modes are observed, in which their Strouhal numbers are 1.0 at the AOAs of 30°, 32° and 34° and 0.7 at the AOAs of 36o, 38° and 40°. The breakdown vortex always moves upstream and downstream and its types change alternatively. Furthermore, the vortex can be identified as breakdown or not through the mean pressure, root mean square of pressure, or even through correlation analysis.
基金supported by the National Natural Science Foundation of China (10502030 and 90505005)Innovation and Support Foundation of Chinese Astronautics
文摘Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.
