The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulenc...The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case).展开更多
An experimental study was conducted to visualize the flow field and confirm the transitional Reynolds number from laminar to turbulent flow, as distilled water flows through quartz glass microtubes with inner diameter...An experimental study was conducted to visualize the flow field and confirm the transitional Reynolds number from laminar to turbulent flow, as distilled water flows through quartz glass microtubes with inner diameter 315 and 520 μm. With gentian violet as colorant, the flow field pictures in the microtube, and therefore, is shot by a CCD camera with a microscope at different Reynolds numbers. Pressure drop data were also used to characterize the friction factor for those microtubes in the Reynolds number range of 200–2300. The experimental results clearly showed that the flow in the microtube was the laminar state and the friction factors agreed well with the Poiseuille equations when the Reynolds number was low. As the Reynolds number was larger than 1200 and 1500 for the microtube with inner diameter 315 and 520 μm, respectively, the friction factor departed from the classical laminar solution due to the earlier transition from laminar to tubulent flow. The flow turned into full turbulent when the Reynolds number reached 1500–1800.展开更多
Turbulent fluidized bed proves effective in industrial processes due to superior heat and mass transfer and chemical reaction performance. However, understanding the transition to turbulent fluidization remains limite...Turbulent fluidized bed proves effective in industrial processes due to superior heat and mass transfer and chemical reaction performance. However, understanding the transition to turbulent fluidization remains limited, especially at temperatures exceeding 1000 ℃, making it challenging to develop high-temperature fluidized bed applications. This paper presents an experimental investigation on the turbulent fluidization onset velocity (U_(c)), measured in a 30 mm diameter bed using corundum particles with average diameters from 0.68 mm to 1.58 mm in temperatures from ambient to 1600 ℃. Experimental results reveal that U_(c) increases with temperature up to 600 ℃, stabilizes within the 600–1200 ℃ range, and then decreases above 1200 ℃, demonstrating the varying relative significance of hydrodynamic and interparticle forces at different temperatures. To help design and operate high-temperature applications of turbulent fluidization, we developed U_(c) correlations based on experimental data from both literature sources and this study, covering temperatures of up to 1600 ℃ and particles of Groups A to D.展开更多
To control the transition process in a laminar separation bubble(LSB)over an ultra-high load compressor blade at a Re of 1.5×10^(5),the effects of wall heat transfer were considered and numerically investigated b...To control the transition process in a laminar separation bubble(LSB)over an ultra-high load compressor blade at a Re of 1.5×10^(5),the effects of wall heat transfer were considered and numerically investigated by large eddy simulations(LES).Compared with the adiabatic wall condition,the local kinematic viscosity of airflow was reduced by wall cooling;thus the effects of turbulent dissipation on the growth of fluctuations were weakened.As such,the transition occurred much earlier,and the size of LSB became smaller.On the cooled surface,the spanwise vortices deformed much more rapidly and the size of hairpin vortex structures was decreased.Furthermore,the rolling-up of 3D hairpin vortices and the ejection and sweeping process very close to the blade surface was weakened.Correspondingly,the aerodynamic losses of the compressor blade were reduced by 18.2%and 38.4%for the two cooled wall conditions.The results demonstrated the feasibility of wall cooling in controlling the transition within an LSB and reducing the aerodynamic loss of an ultra-highly loaded compressor blade.展开更多
Since 1970s,several experimental works revealed that the cavitation sheet inception does not occur at the minimum pressure location but further downstream at the location of a laminar/turbulent transition.Most of the ...Since 1970s,several experimental works revealed that the cavitation sheet inception does not occur at the minimum pressure location but further downstream at the location of a laminar/turbulent transition.Most of the cavitation models use the saturation vapour pressure as a threshold to initiate the production of vapour and therefore,are not able to capture such flows.In this paper,three modifications of the Schnerr and Sauer cavitation model are proposed and coupled with an algebraic laminar/turbulent transition model.Application to a NACA 16012 profile shows the ability of the modifications to move the cavitation inception at the right location compared with the experiment.One of them,based on the multiplication of the evaporation term by the square of the turbulent intensity seems promising.展开更多
The shock wave boundary layer interaction on the suction side of transonic compressor blade is one of the main objectives of TFAST project(Transition Location Effect on Shock Wave Boundary Layer Interaction).In order ...The shock wave boundary layer interaction on the suction side of transonic compressor blade is one of the main objectives of TFAST project(Transition Location Effect on Shock Wave Boundary Layer Interaction).In order to investigate the flow structure on the suction side of a profile,a design of a generic test section in linear transonic wind tunnel was proposed.The experimental and numerical results for the flow structure investigations are shown for the flow conditions as the existing ones on the suction side of the compressor profile.Near the sidewalls the suction slots are applied for the corner flow structure control.It allows to control the Axial Velocity Density Ratio(AVDR),important parameter for compressor cascade investigations.Numerical results for Explicit Algebraic Reynolds Stress Model with transition modeling are compared with oil flow visualization,schlieren and Pressure Sensitive Paint.Boundary layer transition location is detected by Temperature Sensitive Paint.展开更多
It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow contro...It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified e^(N)method,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.展开更多
Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this ...Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this paper, the hydrodynamic coefficients of an AUV in non-dimensional depths of 0.75, 1, 1.5, 2, and 4D are obtained for movement close to the free-surface. Reynolds Averaged Navier Stokes Equations(RANS) are discretized using the finite volume approach and the water-surface effects modeled using the Volume of Fraction(VOF) method. As the operating speeds of AUVs are usually low, the boundary layer over them is not fully laminar or fully turbulent, so the effect of boundary layer transition from laminar to turbulent flow was considered in the simulations. Two different turbulence/transition models were used: 1) a full-turbulence model, the k-ε model, and 2) a turbulence/transition model, Menter's Transition-SST model. The results show that the Menter's Transition-SST model has a better consistency with experimental results. In addition, the wave-making effects of these bodies are studied at different immersion depths in the sea-surface vicinity or at finite depths. It is observed that the relevant pitch moments and lift coefficients are non-zero for these axi-symmetric bodies when they move close to the sea-surface. This is not expected for greater depths.展开更多
Experimental techniques for imaging laminar-turbulent transition of boundary layers using IR thermography are presented for both flight and wind tunnel test environments. A brief overview of other transition detection...Experimental techniques for imaging laminar-turbulent transition of boundary layers using IR thermography are presented for both flight and wind tunnel test environments. A brief overview of other transition detection techniques is discussed as motivation. A direct comparison is made between IR thermography and naphthalene flow visualization. A technique for obtaining quantitative transition location is presented.展开更多
By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growt...By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.展开更多
Three-dimensional compressible flow simulationswere conducted to develop a Hyperloop pod. Thenovelty is the usage of Gamma transition model, in whichthe transition from laminar to turbulent flow can be predicted.First...Three-dimensional compressible flow simulationswere conducted to develop a Hyperloop pod. Thenovelty is the usage of Gamma transition model, in whichthe transition from laminar to turbulent flow can be predicted.First, a mesh dependency study was undertaken,showing second-order convergence with respect to themesh refinement. Second, an aerodynamic analysis for twodesigns, short and optimized, was conducted with thetraveling speed 125 m/s at the system pressure 0.15 bar.The concept of the short model was to delay the transitionto decrease the frictional drag;meanwhile that of theoptimized design was to minimize the pressure drag bydecreasing the frontal area and introduce the transitionmore toward the front of the pod. The computed resultsshow that the transition of the short model occurred moreon the rear side due to the pod shape, which resulted in 8%smaller frictional drag coefficient than that for the optimizedmodel. The pressure drag for the optimized designwas 24% smaller than that for the short design, half ofwhich is due to the decrease in the frontal area, and theother half is due to the smoothed rear-end shape. The totaldrag for the optimized model was 14% smaller than that forthe short model. Finally, the influence of the systempressure was investigated. As the system pressure and theReynolds number increase, the frictional drag coefficientincreases, and the transition point moves toward the front,which are the typical phenomena observed in the transitionregime.展开更多
Turbulence is a century-old physics problem,and the prediction of laminar-turbulent transition remains a major challenge in computational fluid dynamics(CFD).This paper proposes a new conceptual multiscale-structure f...Turbulence is a century-old physics problem,and the prediction of laminar-turbulent transition remains a major challenge in computational fluid dynamics(CFD).This paper proposes a new conceptual multiscale-structure flow system consisting of a nonturbulent part and two types of turbulent eddies with different properties.The stability criterion for turbulent transition flows,based on the principle of compromise-in-competition between viscosity and inertia,is used to obtain model closure.The multiscale-structure concept and stability criterion are the characteristics of the dual-eddy energy-minimization multiscale(EMMS)-based turbulence model.The solved heterogeneous structure parameters and energy dissipation rate are analyzed,which reveal the laminar-turbulent transition process.To validate the dual-eddy EMMS-based turbulence model,three benchmark problems,namely,the transitional flows over the flat plate boundary layer with zero pressure gradient,NACA0012,and Aerospatiale-A airfoils,were simulated.The simulation was performed by combining the optimized results from the proposed model with the equations of the well-known κ-ω shear stress transfer(SST)turbulence model.The numerical results show that the dual-eddy EMMS-based turbulence model improves the prediction in the laminar-turbulent transition process.This demonstrates the soundness of using the multiscale-structure concept in turbulent flows to establish the turbulence transition model by considering the principle of compromise-in-competition between viscosity and inertia.展开更多
文摘The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case).
文摘An experimental study was conducted to visualize the flow field and confirm the transitional Reynolds number from laminar to turbulent flow, as distilled water flows through quartz glass microtubes with inner diameter 315 and 520 μm. With gentian violet as colorant, the flow field pictures in the microtube, and therefore, is shot by a CCD camera with a microscope at different Reynolds numbers. Pressure drop data were also used to characterize the friction factor for those microtubes in the Reynolds number range of 200–2300. The experimental results clearly showed that the flow in the microtube was the laminar state and the friction factors agreed well with the Poiseuille equations when the Reynolds number was low. As the Reynolds number was larger than 1200 and 1500 for the microtube with inner diameter 315 and 520 μm, respectively, the friction factor departed from the classical laminar solution due to the earlier transition from laminar to tubulent flow. The flow turned into full turbulent when the Reynolds number reached 1500–1800.
基金supported by the National Natural Science Foundation of China(grant No.U22A20410).
文摘Turbulent fluidized bed proves effective in industrial processes due to superior heat and mass transfer and chemical reaction performance. However, understanding the transition to turbulent fluidization remains limited, especially at temperatures exceeding 1000 ℃, making it challenging to develop high-temperature fluidized bed applications. This paper presents an experimental investigation on the turbulent fluidization onset velocity (U_(c)), measured in a 30 mm diameter bed using corundum particles with average diameters from 0.68 mm to 1.58 mm in temperatures from ambient to 1600 ℃. Experimental results reveal that U_(c) increases with temperature up to 600 ℃, stabilizes within the 600–1200 ℃ range, and then decreases above 1200 ℃, demonstrating the varying relative significance of hydrodynamic and interparticle forces at different temperatures. To help design and operate high-temperature applications of turbulent fluidization, we developed U_(c) correlations based on experimental data from both literature sources and this study, covering temperatures of up to 1600 ℃ and particles of Groups A to D.
基金the financial support of the Science Center for Gas Turbine Project(2022-B-Ⅱ-008)Open project of the State Key Laboratory of Aerodynamics(SKLA-20190105)。
文摘To control the transition process in a laminar separation bubble(LSB)over an ultra-high load compressor blade at a Re of 1.5×10^(5),the effects of wall heat transfer were considered and numerically investigated by large eddy simulations(LES).Compared with the adiabatic wall condition,the local kinematic viscosity of airflow was reduced by wall cooling;thus the effects of turbulent dissipation on the growth of fluctuations were weakened.As such,the transition occurred much earlier,and the size of LSB became smaller.On the cooled surface,the spanwise vortices deformed much more rapidly and the size of hairpin vortex structures was decreased.Furthermore,the rolling-up of 3D hairpin vortices and the ejection and sweeping process very close to the blade surface was weakened.Correspondingly,the aerodynamic losses of the compressor blade were reduced by 18.2%and 38.4%for the two cooled wall conditions.The results demonstrated the feasibility of wall cooling in controlling the transition within an LSB and reducing the aerodynamic loss of an ultra-highly loaded compressor blade.
文摘Since 1970s,several experimental works revealed that the cavitation sheet inception does not occur at the minimum pressure location but further downstream at the location of a laminar/turbulent transition.Most of the cavitation models use the saturation vapour pressure as a threshold to initiate the production of vapour and therefore,are not able to capture such flows.In this paper,three modifications of the Schnerr and Sauer cavitation model are proposed and coupled with an algebraic laminar/turbulent transition model.Application to a NACA 16012 profile shows the ability of the modifications to move the cavitation inception at the right location compared with the experiment.One of them,based on the multiplication of the evaporation term by the square of the turbulent intensity seems promising.
基金supported by 7 EU framework projectproject of acronym TFAST(Transition Location Effect on Shock Wave Boundary Layer Interaction)+1 种基金supported in part by PL-Grid InfrastructureNumerical simulations are carried out in Academic Computer Centre(TASK)in Gdansk
文摘The shock wave boundary layer interaction on the suction side of transonic compressor blade is one of the main objectives of TFAST project(Transition Location Effect on Shock Wave Boundary Layer Interaction).In order to investigate the flow structure on the suction side of a profile,a design of a generic test section in linear transonic wind tunnel was proposed.The experimental and numerical results for the flow structure investigations are shown for the flow conditions as the existing ones on the suction side of the compressor profile.Near the sidewalls the suction slots are applied for the corner flow structure control.It allows to control the Axial Velocity Density Ratio(AVDR),important parameter for compressor cascade investigations.Numerical results for Explicit Algebraic Reynolds Stress Model with transition modeling are compared with oil flow visualization,schlieren and Pressure Sensitive Paint.Boundary layer transition location is detected by Temperature Sensitive Paint.
文摘It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified e^(N)method,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.
文摘Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this paper, the hydrodynamic coefficients of an AUV in non-dimensional depths of 0.75, 1, 1.5, 2, and 4D are obtained for movement close to the free-surface. Reynolds Averaged Navier Stokes Equations(RANS) are discretized using the finite volume approach and the water-surface effects modeled using the Volume of Fraction(VOF) method. As the operating speeds of AUVs are usually low, the boundary layer over them is not fully laminar or fully turbulent, so the effect of boundary layer transition from laminar to turbulent flow was considered in the simulations. Two different turbulence/transition models were used: 1) a full-turbulence model, the k-ε model, and 2) a turbulence/transition model, Menter's Transition-SST model. The results show that the Menter's Transition-SST model has a better consistency with experimental results. In addition, the wave-making effects of these bodies are studied at different immersion depths in the sea-surface vicinity or at finite depths. It is observed that the relevant pitch moments and lift coefficients are non-zero for these axi-symmetric bodies when they move close to the sea-surface. This is not expected for greater depths.
文摘Experimental techniques for imaging laminar-turbulent transition of boundary layers using IR thermography are presented for both flight and wind tunnel test environments. A brief overview of other transition detection techniques is discussed as motivation. A direct comparison is made between IR thermography and naphthalene flow visualization. A technique for obtaining quantitative transition location is presented.
基金Project supported by the National Natural Science Foundation of China(Nos.91752203,11490553,and 11602148)
文摘By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.
基金The authors acknowledge all the members of the Swissloop Team for their great endeavor to compete in the Hyperloop pod Competition and to push the Hyperloop technology forward.The authors gratefully acknowledge Connova AG for their support in manufacturing of the pod.
文摘Three-dimensional compressible flow simulationswere conducted to develop a Hyperloop pod. Thenovelty is the usage of Gamma transition model, in whichthe transition from laminar to turbulent flow can be predicted.First, a mesh dependency study was undertaken,showing second-order convergence with respect to themesh refinement. Second, an aerodynamic analysis for twodesigns, short and optimized, was conducted with thetraveling speed 125 m/s at the system pressure 0.15 bar.The concept of the short model was to delay the transitionto decrease the frictional drag;meanwhile that of theoptimized design was to minimize the pressure drag bydecreasing the frontal area and introduce the transitionmore toward the front of the pod. The computed resultsshow that the transition of the short model occurred moreon the rear side due to the pod shape, which resulted in 8%smaller frictional drag coefficient than that for the optimizedmodel. The pressure drag for the optimized designwas 24% smaller than that for the short design, half ofwhich is due to the decrease in the frontal area, and theother half is due to the smoothed rear-end shape. The totaldrag for the optimized model was 14% smaller than that forthe short model. Finally, the influence of the systempressure was investigated. As the system pressure and theReynolds number increase, the frictional drag coefficientincreases, and the transition point moves toward the front,which are the typical phenomena observed in the transitionregime.
基金financially supported by the National Key R&D Program of China(No.2018YFB1500902)National Numerical Wind Tunnel Project of China(No.NNW2020ZT1-A20)+1 种基金National Natural Science Foundation of China(Nos.51776212,91434113)Chinese Academy of Sciences(No.QYZDB-SSW-SYS029).
文摘Turbulence is a century-old physics problem,and the prediction of laminar-turbulent transition remains a major challenge in computational fluid dynamics(CFD).This paper proposes a new conceptual multiscale-structure flow system consisting of a nonturbulent part and two types of turbulent eddies with different properties.The stability criterion for turbulent transition flows,based on the principle of compromise-in-competition between viscosity and inertia,is used to obtain model closure.The multiscale-structure concept and stability criterion are the characteristics of the dual-eddy energy-minimization multiscale(EMMS)-based turbulence model.The solved heterogeneous structure parameters and energy dissipation rate are analyzed,which reveal the laminar-turbulent transition process.To validate the dual-eddy EMMS-based turbulence model,three benchmark problems,namely,the transitional flows over the flat plate boundary layer with zero pressure gradient,NACA0012,and Aerospatiale-A airfoils,were simulated.The simulation was performed by combining the optimized results from the proposed model with the equations of the well-known κ-ω shear stress transfer(SST)turbulence model.The numerical results show that the dual-eddy EMMS-based turbulence model improves the prediction in the laminar-turbulent transition process.This demonstrates the soundness of using the multiscale-structure concept in turbulent flows to establish the turbulence transition model by considering the principle of compromise-in-competition between viscosity and inertia.
