Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of b...Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of backward-facing step (BFS).The simulation results were validated with particle image velocimetry (PIV) measurements and direct numerical simulation (DNS).This LES simulation was carried out with a Reynolds number of 9000 in a pressurized water tunnel with an expansion ratio of 2.00.The results indicate that the LES model can reveal largescale vortex motion although with a larger grid-cell size.However,the LES model tends to overestimate the top wall separation and the Reynolds stress components for the BFS flow simulation without a sufficiently fine grid.Overall,LES is a potential tool for simulating separated flow controlled by large-scale vortices.展开更多
In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uni...In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uniform external magnetic field was applied to the flow and strength of magnetic field was varied with different values of dimensionless parameter Hartmann number (Ha=0,10,20,30,40).Three different electrical conductivity models were used to see the effects of MHD nanofluid flow.Besides,five different inclination angles between 0°-90° is used for the external magnetic field.The problem geometry is a backward-facing step which is used in many engineering applications where flow separation and reattachment phenomenon occurs.Mixed type convective heat transfer of backward-facing step was examined with various values of Richardson number (Ri=0.01,0.1,1,10) and four different nanoparticle volume fractions (Ф=0.01,0.015,0.020,0.025) considering different electrical conductivity models.Finite element method via commercial code COMSOL was used for computations.Results indicate that the addition of nanoparticles enhanced heat transfer significantly.Also increasing magnetic field strength and inclination angle increased heat transfer rate.Effects of different electrical conductivity models were also investigated and it was observed that they have significant effects on the fluid flow and heat transfer characteristics in the presence of magnetic field.展开更多
The backward-facing step is a critical problem existing in many engineering and industrial applications.In this study,a semi-porous baffle(the root of the baffle is a porous medium and the tip is solid) is placed behi...The backward-facing step is a critical problem existing in many engineering and industrial applications.In this study,a semi-porous baffle(the root of the baffle is a porous medium and the tip is solid) is placed behind the step.The effects of the length of the porous part,and the baffle location on the energy transfer and pressure drop are studied in different Reynolds numbers(Re=100,200,300,400,500).The effect of the Darcy number of the porous medium on the aforementioned parameters is also investigated.Both the local maximum and average relative Nusselt numbers(divided by the Nusselt of the base case with no baffle at the same Reynolds) and relative pressure drop(calculated as the relative Nusselt number) are reported.The results show that by adoption of the proper length of the porous medium,the average relative and maximum local Nusselt numbers could be enhanced by 20% and 90%,respectively.Low permeable porous media give better energy transfer.For example,porous media with Da=10^(-5) give 30% better maximum local Nusselt number and about 7% higher average Nusselt number with respect to the same case with Da=10^(-2).展开更多
The mixing and combustion characteristics in a cavity flameholding combustor under inlet Mach number 2.92 are numerically investigated with ethylene injection.Dimensionless distance is defined as the ratio of the actu...The mixing and combustion characteristics in a cavity flameholding combustor under inlet Mach number 2.92 are numerically investigated with ethylene injection.Dimensionless distance is defined as the ratio of the actual distance to the height of the combustor entrance.The cavity shear-layer mode,the lifted cavity shear-layer mode,and jet wake mode with upstream separation are observed respectively with dimensionless distance equals to 1.5,4.5,and 7.5.In both non-reacting and reacting flow fields,the numerical results are essentially in agreement with the schlieren photography,flame chemiluminescence images,and wall pressure,which verify the reliability of the numerical method.The results of non-reacting flow fields show that the BackwardFacing Step(BFS)can promote the flow separation downstream at a fixed distance.The more forward the separation position is,the larger the separation zone is in the non-reacting flow field.Furthermore,the larger the separation zone is,the higher the intensity of combustion in the reacting flow field is.A reasonable distance can reduce the total pressure loss generated by the shock waves in the combustor.The flame presents remarkable three-dimensional characteristics in the reacting flow fields.When dimensionless distance equals to 4.5,there are flames near the side wall above the cavity and it is difficult for the flame stabilization in the center of the combustor,while the combustion intensity in the center of the combustor is higher than that near the side wall when dimensionless distance equals to 7.5.In the cavity flameholding combustors with a backward-facing step,the higher combustion intensity may bring much total pressure loss to the combustor.Thus,it is a good choice to achieve better thrust performance when dimensionless distance equals to 4.5 compared to the other two combustors.展开更多
The tile-type electromagnetic actuator(TEA)and stripe-type electromagnetic actuator(SEA)are applied to the active control of the perturbation energy in the liquid metal flow over a backward-facing step(BFS).Three cont...The tile-type electromagnetic actuator(TEA)and stripe-type electromagnetic actuator(SEA)are applied to the active control of the perturbation energy in the liquid metal flow over a backward-facing step(BFS).Three control strategies consisting of base flow control(BFC),linear model control(LMC)and combined model control(CMC)are considered to change the amplification rate of the perturbation energy.CMC is the combination of BFC and LMC.SEA is utilized in BFC to produce the streamwise Lorentz force thus adjusting the amplification rate via modifying the flow structures,and the magnitude of the maximum amplification rate could reach to 6 orders.TEA is used in LMC to reduce the magnitude of the amplification rate via the wall-normalwise Lorentz force,and the magnitude could be decreased by 2 orders.Both TEA and SEA are employed in CMC where the magnitude of the amplification rate could be diminished by 3 orders.In other words,the control strategy of CMC could capably alter the flow instability of the liquid metal flow.展开更多
A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust th...A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust the amplification rate of the perturbation energy.The amplification mechanisms are investigated numerically via analyzing the characteristics of the terms in the Reynolds-Orr equation which describes the growth rate of the perturbation energy.The results demonstrate that the main convective term always promotes the increase in the growth rate while the viscous terms usually play the reverse role.The contours of the product of the wall-normalwise and streamwise perturbation velocities distribute on both sides of the isoline,which represents the zero wall-normalwise gradient of the streamwise velocity in the base flow,due to the Kelvin-Helmholtz(KH)instability.For the case without control,the isoline downstream the reattachment point of the primary separation bubble is closer to the lower wall,and thus the viscous term near the lower wall might suppress the amplification rate.For the case in which the body force only acts on the secondary separation bubble,the secondary separation bubble is removed,and the magnitude of the negative wall-normalwise gradient of the base flow streamwise velocity decreases along the streamwise direction,and thus the growth rate of the perturbation energy is smaller than that for the case without control.For the case where the body force acts on both the separation bubbles,the secondary separation bubble is removed,the isoline stays in the central part of the channel,and thereby the viscous term has less effects on the amplification rate of which the peak value could be the maximum one for some control number.展开更多
A model that uses the operator splitting technique based on Eulerian-Lagrangian method and embeds the k-ε turbulence mode is developed. The model is used to simulate a two dimensional flow over a backward-facing step...A model that uses the operator splitting technique based on Eulerian-Lagrangian method and embeds the k-ε turbulence mode is developed. The model is used to simulate a two dimensional flow over a backward-facing step with triangular mesh discrete flow field. The convection operator is solved with the characteristic method and the diffusion operator and pressure-Poisson equation are solved by finite element method. The results from the example showed that numerical results are well agreed with the experimental data,and that the method can be adapted to simulate complex turbulent flow with strong non-linear convection. The treatment of boundary conditions is also studied in the paper.展开更多
Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent fl...Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent flow controlled by large eddy,in which the effect of small eddy could be negligible as an approximation.The grid dimension could easily satisfy the resolution requirement to describe the characteristics of a large eddy flow.Therefore,direct numerical simulation of N-S equations to obtain the turbulent flow field on the coarse grid could be realized.Numerical simulation of a two-dimensional flow over a backward-facing step at a Reynolds number Re=44000 was conducted using Euler-Lagrange finite element scheme based on the efficient operator-splitting method(OSFEM).The flow field was descretized by triangle meshes with 16669 nodes.The overall computational time only took 150 min on a PC.Both the characteristics of time-averaged and instantaneous turbulent flow were simultaneously obtained.The analysis showed that the calculated results were in good agreement with the test data.Hence,the DNS approach could become the reality to solve the complex turbulent flow with high Reynolds numbers in practical engineering.展开更多
Unsteady behaviors of the large-scale vortical structure superimposed in the turbulent separated and reattaching flow over a backward-facing step were convincingly delineated by performing simultaneous measurements of...Unsteady behaviors of the large-scale vortical structure superimposed in the turbulent separated and reattaching flow over a backward-facing step were convincingly delineated by performing simultaneous measurements of the wall pressure fluctuations and visualizations of the flow. Toward this end, a synchronized instrumentation system integrated with the microphone array and the high-speed camera was established. The smoke-wire technique was employed to visualize the unsteady events. A thorough analysis based on the wall pressure fluctuations disclosed that the large-scale vortical structure shedding at the frequency of fH/Uo = 0.064 gave a primary contribution to the wall pressure fluctuations, and consequently dominated unsteady behaviors of the turbulent shear layer. The convection velocity of the large-scale vortical structure was determined as Uc =0.55 U0. The instantaneous flow visualizations and wall pressure were compared in a straightforward manner. Below the separation bubble and the reattachment zone, the negative peak of the time-varying wall pressure was in phase with passage of the local large-scale vortical structure. In the redeveloping turbulent boundary layer, the decaying large-scale vortical structure was clearly revealed.展开更多
Flow over a backward-facing step was studied to investigate the effect of large-scale vortex structures on sediment incipience. The transient flow velocity field at the downstream of the backward-facing step was obtai...Flow over a backward-facing step was studied to investigate the effect of large-scale vortex structures on sediment incipience. The transient flow velocity field at the downstream of the backward-facing step was obtained using the technique of Particle Tracking Velocimetry （PTV）. The optical amplification technique was employed to measure the instantaneous flow velocities near the bed and the instantaneous bed shear stress was given. The experimental observations revealed a new insight into the oscillation of the large-scale structure and the three-dimensional characteristics of the flow. In particular, very high turbulence intensity, instantaneous horizontal velocity near the bed and the bed shear stress near the reattachment point were observed. The sediment incipient probability obtained from the sequent images of sediment particles near the bed indicates that the critical instantaneous shear stress of the sediment incipience is independent of flow conditions.展开更多
The flow over a backward-facing step(BFS)is a typical separation and reattachment flow.Its flow structures and unsteady mechanisms are still not well explored.In this paper,the global velocity fields of a BFS are obta...The flow over a backward-facing step(BFS)is a typical separation and reattachment flow.Its flow structures and unsteady mechanisms are still not well explored.In this paper,the global velocity fields of a BFS are obtained by a synchronous particle image velocimetry(PIV)system with Reh=5345(Reynolds number)and Er=2(expansion ratio).Flow structures are distinguished and defined by the fraction of the negative velocity(upn).The reattachment zone(Lr)is quantitatively defined as(u0.9,u/0.1)on the bottom wall.Spatial distribution of the large-scale vortices couples well with the divided flow structures and their temporal evolution presenting four stages(forming,developing,shedding and redeveloping)when travel downstream.The unsteady motions with various low frequencies are well explained by the coherent vortices and flow structures.Among the unsteady low frequency motions,the Kelvin Helmholtz(KH)vortices and the oscillation of Xr(OX)come likely from the free shear layer.The KH vortices contribute to the unsteadiness of the temporal flow,and the OX is the primary response to the vortical fluctuations.展开更多
Wall pressure fluctuations in turbulent boundary layer flow over backward-facing step with and without entrainment were investigated. Digital array pressure sensors and multi-arrayed microphones were employed to acqui...Wall pressure fluctuations in turbulent boundary layer flow over backward-facing step with and without entrainment were investigated. Digital array pressure sensors and multi-arrayed microphones were employed to acquire the time-averaged static pressure and fluctuating pressure, respectively. The differences of two flows were scrutinized in terms of static pressure characteristics, pressure fluctuations, cross-correlation and coherence of wall pressure. Introduction of the entrainment increased scale of large-scale vortical structure and reduced its convection velocity. However, shedding frequency of large-scale vortical structures was found to be the same for both flows.展开更多
Particle diffusion in large eddy structures with various Stokes number was analyzed numerically for the two-dimensional gas-particle turbulent flow over a backward-facing step. The continuous phase simulation was anal...Particle diffusion in large eddy structures with various Stokes number was analyzed numerically for the two-dimensional gas-particle turbulent flow over a backward-facing step. The continuous phase simulation was analyzed using the large eddy simulation (LES) method while the particle phase was analyzed by the Lagrangian method. The spatial and temporal results were used to analyze the evolution of the large eddy coherent structures and the vortex-particle interactions. The effect of the particle Stokes number on the in-stantaneous particle concentration distributions was also discussed. The simulations of the single-phase flow reproduced the character of the separation and reattachment flow and the essential features of the coherent structures. Numerous and complex vortex structures appeared at the high Reynolds number. Furthermore, the simulation shows that the Stokes number plays an important role in the particle dispersion and the instanta-neous particle distribution. The continuous phase time-averaged results and the particle phase time-averaged results obtained from the LES analysis agree well with previous experimental data.展开更多
The present study focuses on the flow of a yield-stress(Bingham)nanofluid,consisting of suspended Fe3O4 nanoparticles,subjected to a magnetic field in a backward-facing step duct(BFS)configuration.The duct is equipped...The present study focuses on the flow of a yield-stress(Bingham)nanofluid,consisting of suspended Fe3O4 nanoparticles,subjected to a magnetic field in a backward-facing step duct(BFS)configuration.The duct is equipped with a cylindrical obstacle,where the lower wall is kept at a constant temperature.The yield-stress nanofluid enters this duct at a cold temperature with fully developed velocity.The aim of the present investigation is to explore the influence of flow velocity(Re=10 to 200),nanoparticle concentration(ϕ=0 to 0.1),magnetic field intensity(Ha=0 to 100),and its inclination angle(γ=0 to 90)and nanofluid yield stress(Bn=0 to 20)on the thermal and hydrodynamic efficiency inside the backward-facing step.The numerical results have been obtained by resolving the momentum and energy balance equations using the Galerkin finite element method.The obtained results have indicated that an increase in Reynolds number and nanoparticle volume fraction enhances heat transfer.In contrast,a significant reduction is observed with an increase in Hartmann and Bingham numbers,resulting in quasi-immobilization of the fluid under the magnetic influence and radical solidification of this type of fluid,accompanied by the suppression of the vortex zone downstream of the cylindrical obstacle.This study sheds light on the complexity of this magnetically influenced fluid,with potential implications in various engineering and materials science fields.展开更多
Taking a C1x motor with a backward-facing step which can generate a typical corner vortex as a reference,a numerical methodology using large eddy simulation was established in this study.Based on this methodology,the ...Taking a C1x motor with a backward-facing step which can generate a typical corner vortex as a reference,a numerical methodology using large eddy simulation was established in this study.Based on this methodology,the position of the backward-facing step of the motor was computed and analyzed to determine a basic configuration.Two key geometrical parameters,the head cavity angle and submerged nozzle cavity height,were subsequently introduced.Their effects on the corner vortex motion and their interactions with the acoustic pressure downstream of the backward-facing step were analyzed.The phenomena of vortex acoustic coupling and characteristics of pressure oscillations were further explored.The results show that the maximum error between the simulations and experimental data on the dominant frequency of pressure oscillations is 5.23%,which indicates that the numerical methodology built in this study is highly accurate.When the step is located at less than 5/8 of the total length of the combustion chamber,vortex acoustic coupling occurs,which can increase the pressure oscillations in the motor.Both the vorticity and the scale of vortices in the downstream step increase when the head cavity angle is greater than 24°,which increases the amplitude of the pressure oscillation by maximum 63.0%.The submerged nozzle cavity mainly affects the vortices in the cavity itself rather than those in the downstream step.When the height of the cavity increases from 10 to 20 mm,the pressure oscillation amplitude under the main frequency increases by 39.1%.As this height continues to increase,the amplitude of pressure oscillations increases but the primary frequency decreases.展开更多
Presented in this paper is a mathematical model to calculate the probability of the sediment incipient motion, in which the effects of the fluctuating pressure and the seepage are considered. The instantaneous bed she...Presented in this paper is a mathematical model to calculate the probability of the sediment incipient motion, in which the effects of the fluctuating pressure and the seepage are considered. The instantaneous bed shear velocity and the pressure gradient on the bed downstream of the backward-facing step flow are obtained according to the PIV measurements. It is found that the instantaneous pressure gradient on the bed obeys normal distribution. The probability of the sediment incipient motion on the bed downstream of the backward-facing step flow is given by the mathematical model. The predicted results agree well with the experiment in the region downstream of the reattachment point while a large discrepancy between the theory and experiment is seen in the region near the reattachment point. The possible reasons for this discrepancy are discussed.展开更多
The separating/reattaching flow over an axisymmetric backward-facing step is analyzed experimentally by means of particle image velocimetry （PIV）, The main purpose of the measurements is the investigation of the mea...The separating/reattaching flow over an axisymmetric backward-facing step is analyzed experimentally by means of particle image velocimetry （PIV）, The main purpose of the measurements is the investigation of the mean flow field as well as of the Reynolds stress distributions at a Mach number of 0,7 and at a Reynolds number of 3,3 x 10s based on the step height, Due to the strong progress of optical flow measurements in the last years it was possible to resolve all flow scales down to 180 μm （≈1% of the step height） with high precision, Thanks to the high spatial resolution it was found for the first time that the Reynolds stress distribution features a local minimum between the first part of the shear layer and a region inside the recirculation region, This implies a more complex wake dynamics than assumed before,展开更多
Dilute gas-particle turbulent flows over a backward-facing step are numerically simulated by Large Eddy Simulation (LES) for the continuous phase and Lagran- gian particle trajectory method for the particle phase. Pre...Dilute gas-particle turbulent flows over a backward-facing step are numerically simulated by Large Eddy Simulation (LES) for the continuous phase and Lagran- gian particle trajectory method for the particle phase. Predicted results of mean velocities and fluctuating velocities of both phases agree well with the experimental data, and demonstrate that the main characteristics of the flow are accurately captured by the simulations. Characteristics of separation and reattachments as well as essential features of the coherent structure are obtained, in which the processes of vortex roll up, growth, pairing and breaking up are shown in details. Particle dispersions are then investigated through particles’ instantaneous distri- butions in coherent structure as well as the mean and fluctuating properties of particle number density (PND). The predicted mean PND agree well with experiment results. For small particles, the instantaneous distributions show much preferential concentration, while their mean PND shows more uniform distribution in down- stream region. On the contrary, for large particles, their instantaneous distributions are much uniform (without clear preferential concentration) due to less effect of large eddy coherent, while their mean PND across the section is not uniform for more particles are distributed in the main flow region. The preferential concentra- tion of particles by the large-scale eddies can lead to a high fluctuating PND.展开更多
A numerical study on mixing of hydrogen injected into a supersonic air stream has been performed by solving two-dimensional full Navier-Stokes equations. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme ...A numerical study on mixing of hydrogen injected into a supersonic air stream has been performed by solving two-dimensional full Navier-Stokes equations. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. The main objectives of this study are to increase the mixing efficiency and flame holding capability of a supersonic combustor. The performance of combustor has been investigated by varying the hydrogen injection angle made with the direction of air stream considering anti-clockwise direction as positive. The injector position from left boundary, backward-facing step height and the inlet width of air stream are kept constant. The results show that upstream of injector the mixing is dominated by recirculation and in downstream the mixing is dominated by mass concentration of hydrogen. Upstream recirculation is dominant for injecting angle 600 and 900 . Incorporating the various effects, perpendicular injection shows the maximum mixing efficiency and its large upstream recirculation region has a good flame holding capability.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51379128)
文摘Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of backward-facing step (BFS).The simulation results were validated with particle image velocimetry (PIV) measurements and direct numerical simulation (DNS).This LES simulation was carried out with a Reynolds number of 9000 in a pressurized water tunnel with an expansion ratio of 2.00.The results indicate that the LES model can reveal largescale vortex motion although with a larger grid-cell size.However,the LES model tends to overestimate the top wall separation and the Reynolds stress components for the BFS flow simulation without a sufficiently fine grid.Overall,LES is a potential tool for simulating separated flow controlled by large-scale vortices.
文摘In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uniform external magnetic field was applied to the flow and strength of magnetic field was varied with different values of dimensionless parameter Hartmann number (Ha=0,10,20,30,40).Three different electrical conductivity models were used to see the effects of MHD nanofluid flow.Besides,five different inclination angles between 0°-90° is used for the external magnetic field.The problem geometry is a backward-facing step which is used in many engineering applications where flow separation and reattachment phenomenon occurs.Mixed type convective heat transfer of backward-facing step was examined with various values of Richardson number (Ri=0.01,0.1,1,10) and four different nanoparticle volume fractions (Ф=0.01,0.015,0.020,0.025) considering different electrical conductivity models.Finite element method via commercial code COMSOL was used for computations.Results indicate that the addition of nanoparticles enhanced heat transfer significantly.Also increasing magnetic field strength and inclination angle increased heat transfer rate.Effects of different electrical conductivity models were also investigated and it was observed that they have significant effects on the fluid flow and heat transfer characteristics in the presence of magnetic field.
文摘The backward-facing step is a critical problem existing in many engineering and industrial applications.In this study,a semi-porous baffle(the root of the baffle is a porous medium and the tip is solid) is placed behind the step.The effects of the length of the porous part,and the baffle location on the energy transfer and pressure drop are studied in different Reynolds numbers(Re=100,200,300,400,500).The effect of the Darcy number of the porous medium on the aforementioned parameters is also investigated.Both the local maximum and average relative Nusselt numbers(divided by the Nusselt of the base case with no baffle at the same Reynolds) and relative pressure drop(calculated as the relative Nusselt number) are reported.The results show that by adoption of the proper length of the porous medium,the average relative and maximum local Nusselt numbers could be enhanced by 20% and 90%,respectively.Low permeable porous media give better energy transfer.For example,porous media with Da=10^(-5) give 30% better maximum local Nusselt number and about 7% higher average Nusselt number with respect to the same case with Da=10^(-2).
基金supported by the National Natural Science Foundation of China(Nos.11925207 and 12002381)the Scientific Research Plan of the National University of Defense Technology in 2019,China(No.ZK19-02)the Science and Technology Foundation of State Key Laboratory,China(No.6142703200311).
文摘The mixing and combustion characteristics in a cavity flameholding combustor under inlet Mach number 2.92 are numerically investigated with ethylene injection.Dimensionless distance is defined as the ratio of the actual distance to the height of the combustor entrance.The cavity shear-layer mode,the lifted cavity shear-layer mode,and jet wake mode with upstream separation are observed respectively with dimensionless distance equals to 1.5,4.5,and 7.5.In both non-reacting and reacting flow fields,the numerical results are essentially in agreement with the schlieren photography,flame chemiluminescence images,and wall pressure,which verify the reliability of the numerical method.The results of non-reacting flow fields show that the BackwardFacing Step(BFS)can promote the flow separation downstream at a fixed distance.The more forward the separation position is,the larger the separation zone is in the non-reacting flow field.Furthermore,the larger the separation zone is,the higher the intensity of combustion in the reacting flow field is.A reasonable distance can reduce the total pressure loss generated by the shock waves in the combustor.The flame presents remarkable three-dimensional characteristics in the reacting flow fields.When dimensionless distance equals to 4.5,there are flames near the side wall above the cavity and it is difficult for the flame stabilization in the center of the combustor,while the combustion intensity in the center of the combustor is higher than that near the side wall when dimensionless distance equals to 7.5.In the cavity flameholding combustors with a backward-facing step,the higher combustion intensity may bring much total pressure loss to the combustor.Thus,it is a good choice to achieve better thrust performance when dimensionless distance equals to 4.5 compared to the other two combustors.
基金Project supported by the National Natural Science Foundation of China(Grant No.U2141246)
文摘The tile-type electromagnetic actuator(TEA)and stripe-type electromagnetic actuator(SEA)are applied to the active control of the perturbation energy in the liquid metal flow over a backward-facing step(BFS).Three control strategies consisting of base flow control(BFC),linear model control(LMC)and combined model control(CMC)are considered to change the amplification rate of the perturbation energy.CMC is the combination of BFC and LMC.SEA is utilized in BFC to produce the streamwise Lorentz force thus adjusting the amplification rate via modifying the flow structures,and the magnitude of the maximum amplification rate could reach to 6 orders.TEA is used in LMC to reduce the magnitude of the amplification rate via the wall-normalwise Lorentz force,and the magnitude could be decreased by 2 orders.Both TEA and SEA are employed in CMC where the magnitude of the amplification rate could be diminished by 3 orders.In other words,the control strategy of CMC could capably alter the flow instability of the liquid metal flow.
基金the National Natural Science Foundation of China (Nos. 51776087 and 51979125)。
文摘A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust the amplification rate of the perturbation energy.The amplification mechanisms are investigated numerically via analyzing the characteristics of the terms in the Reynolds-Orr equation which describes the growth rate of the perturbation energy.The results demonstrate that the main convective term always promotes the increase in the growth rate while the viscous terms usually play the reverse role.The contours of the product of the wall-normalwise and streamwise perturbation velocities distribute on both sides of the isoline,which represents the zero wall-normalwise gradient of the streamwise velocity in the base flow,due to the Kelvin-Helmholtz(KH)instability.For the case without control,the isoline downstream the reattachment point of the primary separation bubble is closer to the lower wall,and thus the viscous term near the lower wall might suppress the amplification rate.For the case in which the body force only acts on the secondary separation bubble,the secondary separation bubble is removed,and the magnitude of the negative wall-normalwise gradient of the base flow streamwise velocity decreases along the streamwise direction,and thus the growth rate of the perturbation energy is smaller than that for the case without control.For the case where the body force acts on both the separation bubbles,the secondary separation bubble is removed,the isoline stays in the central part of the channel,and thereby the viscous term has less effects on the amplification rate of which the peak value could be the maximum one for some control number.
基金supported by the Key Technologies Research&Development Program of China in the11th Five-Year Plan(Grant No.2008BAB29B04)
文摘A model that uses the operator splitting technique based on Eulerian-Lagrangian method and embeds the k-ε turbulence mode is developed. The model is used to simulate a two dimensional flow over a backward-facing step with triangular mesh discrete flow field. The convection operator is solved with the characteristic method and the diffusion operator and pressure-Poisson equation are solved by finite element method. The results from the example showed that numerical results are well agreed with the experimental data,and that the method can be adapted to simulate complex turbulent flow with strong non-linear convection. The treatment of boundary conditions is also studied in the paper.
基金supported by the Major National Science and Technology Projects of China (Grant No. 2012ZX07506003)the Public Research and Development Project for Water Resource (Grant No. 201001030)
文摘Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent flow controlled by large eddy,in which the effect of small eddy could be negligible as an approximation.The grid dimension could easily satisfy the resolution requirement to describe the characteristics of a large eddy flow.Therefore,direct numerical simulation of N-S equations to obtain the turbulent flow field on the coarse grid could be realized.Numerical simulation of a two-dimensional flow over a backward-facing step at a Reynolds number Re=44000 was conducted using Euler-Lagrange finite element scheme based on the efficient operator-splitting method(OSFEM).The flow field was descretized by triangle meshes with 16669 nodes.The overall computational time only took 150 min on a PC.Both the characteristics of time-averaged and instantaneous turbulent flow were simultaneously obtained.The analysis showed that the calculated results were in good agreement with the test data.Hence,the DNS approach could become the reality to solve the complex turbulent flow with high Reynolds numbers in practical engineering.
文摘Unsteady behaviors of the large-scale vortical structure superimposed in the turbulent separated and reattaching flow over a backward-facing step were convincingly delineated by performing simultaneous measurements of the wall pressure fluctuations and visualizations of the flow. Toward this end, a synchronized instrumentation system integrated with the microphone array and the high-speed camera was established. The smoke-wire technique was employed to visualize the unsteady events. A thorough analysis based on the wall pressure fluctuations disclosed that the large-scale vortical structure shedding at the frequency of fH/Uo = 0.064 gave a primary contribution to the wall pressure fluctuations, and consequently dominated unsteady behaviors of the turbulent shear layer. The convection velocity of the large-scale vortical structure was determined as Uc =0.55 U0. The instantaneous flow visualizations and wall pressure were compared in a straightforward manner. Below the separation bubble and the reattachment zone, the negative peak of the time-varying wall pressure was in phase with passage of the local large-scale vortical structure. In the redeveloping turbulent boundary layer, the decaying large-scale vortical structure was clearly revealed.
基金Project supported by the National Natural Science Foundation of China(Grant No.10602017).
文摘Flow over a backward-facing step was studied to investigate the effect of large-scale vortex structures on sediment incipience. The transient flow velocity field at the downstream of the backward-facing step was obtained using the technique of Particle Tracking Velocimetry （PTV）. The optical amplification technique was employed to measure the instantaneous flow velocities near the bed and the instantaneous bed shear stress was given. The experimental observations revealed a new insight into the oscillation of the large-scale structure and the three-dimensional characteristics of the flow. In particular, very high turbulence intensity, instantaneous horizontal velocity near the bed and the bed shear stress near the reattachment point were observed. The sediment incipient probability obtained from the sequent images of sediment particles near the bed indicates that the critical instantaneous shear stress of the sediment incipience is independent of flow conditions.
基金Project supported by the National Natural Science Foundation of China(Grant No.51909169)The Science and Technology Support Program of Jiangsu Province(Grant No.SBK2019042181)+1 种基金the Guizhou Science and Technology Cooperation Support((2017)2865)the International S&T Cooperation Program of China(Grant No.2015DFA01000).
文摘The flow over a backward-facing step(BFS)is a typical separation and reattachment flow.Its flow structures and unsteady mechanisms are still not well explored.In this paper,the global velocity fields of a BFS are obtained by a synchronous particle image velocimetry(PIV)system with Reh=5345(Reynolds number)and Er=2(expansion ratio).Flow structures are distinguished and defined by the fraction of the negative velocity(upn).The reattachment zone(Lr)is quantitatively defined as(u0.9,u/0.1)on the bottom wall.Spatial distribution of the large-scale vortices couples well with the divided flow structures and their temporal evolution presenting four stages(forming,developing,shedding and redeveloping)when travel downstream.The unsteady motions with various low frequencies are well explained by the coherent vortices and flow structures.Among the unsteady low frequency motions,the Kelvin Helmholtz(KH)vortices and the oscillation of Xr(OX)come likely from the free shear layer.The KH vortices contribute to the unsteadiness of the temporal flow,and the OX is the primary response to the vortical fluctuations.
文摘Wall pressure fluctuations in turbulent boundary layer flow over backward-facing step with and without entrainment were investigated. Digital array pressure sensors and multi-arrayed microphones were employed to acquire the time-averaged static pressure and fluctuating pressure, respectively. The differences of two flows were scrutinized in terms of static pressure characteristics, pressure fluctuations, cross-correlation and coherence of wall pressure. Introduction of the entrainment increased scale of large-scale vortical structure and reduced its convection velocity. However, shedding frequency of large-scale vortical structures was found to be the same for both flows.
基金the National Natural Science Foundation of China (No.19972026)
文摘Particle diffusion in large eddy structures with various Stokes number was analyzed numerically for the two-dimensional gas-particle turbulent flow over a backward-facing step. The continuous phase simulation was analyzed using the large eddy simulation (LES) method while the particle phase was analyzed by the Lagrangian method. The spatial and temporal results were used to analyze the evolution of the large eddy coherent structures and the vortex-particle interactions. The effect of the particle Stokes number on the in-stantaneous particle concentration distributions was also discussed. The simulations of the single-phase flow reproduced the character of the separation and reattachment flow and the essential features of the coherent structures. Numerous and complex vortex structures appeared at the high Reynolds number. Furthermore, the simulation shows that the Stokes number plays an important role in the particle dispersion and the instanta-neous particle distribution. The continuous phase time-averaged results and the particle phase time-averaged results obtained from the LES analysis agree well with previous experimental data.
文摘The present study focuses on the flow of a yield-stress(Bingham)nanofluid,consisting of suspended Fe3O4 nanoparticles,subjected to a magnetic field in a backward-facing step duct(BFS)configuration.The duct is equipped with a cylindrical obstacle,where the lower wall is kept at a constant temperature.The yield-stress nanofluid enters this duct at a cold temperature with fully developed velocity.The aim of the present investigation is to explore the influence of flow velocity(Re=10 to 200),nanoparticle concentration(ϕ=0 to 0.1),magnetic field intensity(Ha=0 to 100),and its inclination angle(γ=0 to 90)and nanofluid yield stress(Bn=0 to 20)on the thermal and hydrodynamic efficiency inside the backward-facing step.The numerical results have been obtained by resolving the momentum and energy balance equations using the Galerkin finite element method.The obtained results have indicated that an increase in Reynolds number and nanoparticle volume fraction enhances heat transfer.In contrast,a significant reduction is observed with an increase in Hartmann and Bingham numbers,resulting in quasi-immobilization of the fluid under the magnetic influence and radical solidification of this type of fluid,accompanied by the suppression of the vortex zone downstream of the cylindrical obstacle.This study sheds light on the complexity of this magnetically influenced fluid,with potential implications in various engineering and materials science fields.
基金Sponsored by the Natural Science Foundation of Shaanxi Province (Grant No. S2025-JC-YB-0532)the Practice and Innovation Funds for Graduate Students of Northwestern Polytechnical University (PF2024044)
文摘Taking a C1x motor with a backward-facing step which can generate a typical corner vortex as a reference,a numerical methodology using large eddy simulation was established in this study.Based on this methodology,the position of the backward-facing step of the motor was computed and analyzed to determine a basic configuration.Two key geometrical parameters,the head cavity angle and submerged nozzle cavity height,were subsequently introduced.Their effects on the corner vortex motion and their interactions with the acoustic pressure downstream of the backward-facing step were analyzed.The phenomena of vortex acoustic coupling and characteristics of pressure oscillations were further explored.The results show that the maximum error between the simulations and experimental data on the dominant frequency of pressure oscillations is 5.23%,which indicates that the numerical methodology built in this study is highly accurate.When the step is located at less than 5/8 of the total length of the combustion chamber,vortex acoustic coupling occurs,which can increase the pressure oscillations in the motor.Both the vorticity and the scale of vortices in the downstream step increase when the head cavity angle is greater than 24°,which increases the amplitude of the pressure oscillation by maximum 63.0%.The submerged nozzle cavity mainly affects the vortices in the cavity itself rather than those in the downstream step.When the height of the cavity increases from 10 to 20 mm,the pressure oscillation amplitude under the main frequency increases by 39.1%.As this height continues to increase,the amplitude of pressure oscillations increases but the primary frequency decreases.
基金supported by the National Natural Science Foundation of China (Grant No.10602017)
文摘Presented in this paper is a mathematical model to calculate the probability of the sediment incipient motion, in which the effects of the fluctuating pressure and the seepage are considered. The instantaneous bed shear velocity and the pressure gradient on the bed downstream of the backward-facing step flow are obtained according to the PIV measurements. It is found that the instantaneous pressure gradient on the bed obeys normal distribution. The probability of the sediment incipient motion on the bed downstream of the backward-facing step flow is given by the mathematical model. The predicted results agree well with the experiment in the region downstream of the reattachment point while a large discrepancy between the theory and experiment is seen in the region near the reattachment point. The possible reasons for this discrepancy are discussed.
基金supported by the German Research Foundation DFG in the framework of the TRR40
文摘The separating/reattaching flow over an axisymmetric backward-facing step is analyzed experimentally by means of particle image velocimetry （PIV）, The main purpose of the measurements is the investigation of the mean flow field as well as of the Reynolds stress distributions at a Mach number of 0,7 and at a Reynolds number of 3,3 x 10s based on the step height, Due to the strong progress of optical flow measurements in the last years it was possible to resolve all flow scales down to 180 μm （≈1% of the step height） with high precision, Thanks to the high spatial resolution it was found for the first time that the Reynolds stress distribution features a local minimum between the first part of the shear layer and a region inside the recirculation region, This implies a more complex wake dynamics than assumed before,
基金the National Natural Science Foundation of China (Grant Nos. 19972036, 50172067) the Research Committee of The Hong Kong Polytechnic University (Grant No. A-DP99)
文摘Dilute gas-particle turbulent flows over a backward-facing step are numerically simulated by Large Eddy Simulation (LES) for the continuous phase and Lagran- gian particle trajectory method for the particle phase. Predicted results of mean velocities and fluctuating velocities of both phases agree well with the experimental data, and demonstrate that the main characteristics of the flow are accurately captured by the simulations. Characteristics of separation and reattachments as well as essential features of the coherent structure are obtained, in which the processes of vortex roll up, growth, pairing and breaking up are shown in details. Particle dispersions are then investigated through particles’ instantaneous distri- butions in coherent structure as well as the mean and fluctuating properties of particle number density (PND). The predicted mean PND agree well with experiment results. For small particles, the instantaneous distributions show much preferential concentration, while their mean PND shows more uniform distribution in down- stream region. On the contrary, for large particles, their instantaneous distributions are much uniform (without clear preferential concentration) due to less effect of large eddy coherent, while their mean PND across the section is not uniform for more particles are distributed in the main flow region. The preferential concentra- tion of particles by the large-scale eddies can lead to a high fluctuating PND.
文摘A numerical study on mixing of hydrogen injected into a supersonic air stream has been performed by solving two-dimensional full Navier-Stokes equations. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. The main objectives of this study are to increase the mixing efficiency and flame holding capability of a supersonic combustor. The performance of combustor has been investigated by varying the hydrogen injection angle made with the direction of air stream considering anti-clockwise direction as positive. The injector position from left boundary, backward-facing step height and the inlet width of air stream are kept constant. The results show that upstream of injector the mixing is dominated by recirculation and in downstream the mixing is dominated by mass concentration of hydrogen. Upstream recirculation is dominant for injecting angle 600 and 900 . Incorporating the various effects, perpendicular injection shows the maximum mixing efficiency and its large upstream recirculation region has a good flame holding capability.
