The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-...The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls.An initial linear temperature profile is assumed.A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters.For a relatively small height,isobaric convection is found to take place,which is taken over by an adiabatic mode when the height exceeds the critical value,or by a super-adiabatic mode in case of a relatively high temperature gradient.In the adiabatic mode,convective flow develops due to adiabatic processes given a stable initial stratification.An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature.Moreover,an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases.These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations.A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank.In the presence of convective flows,the vaporized fuel is mixed with the oxidizer(air)forming a gas-vapor medium.However,if the volumetric concentration of fuel vapor(hydrocarbon)is in the interval between the lower and upper concentration limits of ignition,then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency.展开更多
This paper conducts a Large Eddy Simulation (LES) of Rayleigh Bénard convection in a cubic cavity based on the WMLES S-Omega subgrid-scale model. For a cubic cavity with a vertical temperature difference of 6.7...This paper conducts a Large Eddy Simulation (LES) of Rayleigh Bénard convection in a cubic cavity based on the WMLES S-Omega subgrid-scale model. For a cubic cavity with a vertical temperature difference of 6.7°C and 20°C, the velocity pulsation profiles and the mean velocity profiles of the vertical section in the middle of the cubic cavity were simulated, respectively. And they are consistent with the experiment results. Furthermore, the mean velocity field of the vertical cross-section in the middle of the cavity was calculated. Structures of the mean velocity field in the two cases are similar. A counterclockwise large vortex is found to occupy the cavity, and there are two small clockwise vortices in the lower left and upper right corners, and the mean velocity fields at two different temperature differences are consistent with the experimental results. The two-dimensional instantaneous temperature field and mean temperature field with different cross-sections in the z-direction, as well as the three-dimensional instantaneous isothermal surface structure, indicate that the large-scale circulation motion within the cubic cavity is moving diagonally. In addition, the structure of the mean streamline also illustrates this viewpoint. For the reverse vortex formed at two corners in the mean streamline structure, we used the Q criterion to identify and obtain two vortex structures similar to boomerangs. The basic turbulent structure in RB thermal convection includes the rising and falling plumes generated by buoyancy effects.展开更多
Logarithmic boundary layers have been observed in different regions in turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are no...Logarithmic boundary layers have been observed in different regions in turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we perform three-dimensional simulations of turbulence in a slim-box without the front and back walls with aspect ratio, width:depth:height=L:D:H=1:1/6:1width:depth:height=L:D:H=1:1/6:1 (respectively corresponding to xx, yy and zz coordinates), in the Rayleigh number Ra=[1×10^8,1×10^10]Ra=[1×10^8,1×10^10] for Prandtl number Pr=0.7Pr=0.7. To investigate the structures of the viscous and thermal boundary layers, we examine the velocity profiles in the streamwise and vertical directions (i.e. UU and WW) along with the mean temperature profile throughout the plume-impacting, plume-ejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length, e^+u=e^+0(z^+)3/2[1+(z^+/z^+sub)4]^1/4eu+=e^+0(z+)3/2[1+(z+/zsub+)4]1/4, as proposed by She et al.(J Fluid Mech, 2017), though it is neither \pb type nor logarithmic. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, AA, can be described by composition of the thermal stress length ■■θ0■θ0■ and the thicknesses of thermal boundary layer z■subzsub■ and z?bufzbuf■, i.e. A■z?sub/(■■θ0z■buf3/2)A■zsub?/(■θ0■zbuf^3/2). The adverse pressure gradient responsible for turning the wind direction contributes to intensively emitting plumes and the logarithmic temperature profile at the plume-ejecting region. The Nusselt number scaling and the local heat flux in the slim box are consistent with previous results of the confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation in a fixed plane.展开更多
We propose a theoretical model for spatial variations of the temperature varianceσ2(z,r)(z is the dis-tance from the sample bottom and r the radial coordinate)in turbulent Rayleigh-Bénard convection(RBC).Adaptin...We propose a theoretical model for spatial variations of the temperature varianceσ2(z,r)(z is the dis-tance from the sample bottom and r the radial coordinate)in turbulent Rayleigh-Bénard convection(RBC).Adapting the“attached-eddy”modelofshearflowtothe plumesofRBC,wederivedanequationforσ2 which is based on the universal scaling of the normalized RBC temperature spectra.This equation in-cludes both logarithmic and power-law dependences on z/λth,whereλth is the thermal boundary layer thickness.The equation parameters depend on r and the Prandtl number Pr,but have only an extremelyweak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for thetemperature variance profile in turbulent RBC.展开更多
Wavelet transform is used to analyze the scaling rule of temperature data (passive scalar) in Rayleigh Bénard convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can f...Wavelet transform is used to analyze the scaling rule of temperature data (passive scalar) in Rayleigh Bénard convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can find the obtained scaling exponent agrees well with the one obtained from the temperature data in a experiment of wind tunnel. And then we propose a newly defined formula based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data. The obtained results demonstrate that we can correctly extract ξ(q) by using the method which is named as wavelet transform maximum modulus (WTMM).展开更多
We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC)in order to study the influence of the periodic(PD)and confined(CF)samples on the heat transport Nu.The ...We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC)in order to study the influence of the periodic(PD)and confined(CF)samples on the heat transport Nu.The numerical study is conducted with the Rayleigh number(Ra)varied in the range 10^(6)≤Ra≤10^(9) at a fixed Prandtl number Pr=4.3 and aspect ratio Γ=2 with the no-slip(NS)and freeslip(FS)plates.There exists a zonal flow for Ra≥3×10^(6) with the free-slip plates in the periodic sample.In all the other cases,the flow is the closed large-scale circulation(closed LSC).The striking features are that the heat transport Nu is influenced and the temperature profiles do not be influenced when the flow pattern is zonal flow.展开更多
Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity,...Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.展开更多
In this paper,we develop and test a unified hybrid LES/URANS turbulence model with two different Large Eddy Simulation(LES)turbulence models.The numerical algorithm is based on the Boundary Element Method.In the exist...In this paper,we develop and test a unified hybrid LES/URANS turbulence model with two different Large Eddy Simulation(LES)turbulence models.The numerical algorithm is based on the Boundary Element Method.In the existing hybrid LES/URANS turbulence model we implemented a new Smagorinsky LES turbulence model.The hybrid LES/URANS turbulence model is unified,which means that the LES/URANS interface is changed dynamically during simulation using a physical quantity.In order to define the interface between LES and unsteady Reynolds Averaged Navier Stokes(URANS)zones during the simulation,we use the Reynolds number based on turbulent kinetic energy as a switching criterion.This means that the flow characteristics define where the sub-grid scale or URANS effective viscosity and thermal conductivity are used in the governing equations in the next time step.In unified hybrid turbulence models,only one set of governing equations is used for LES and URANS regions.The developed hybrid LES/URANS model was tested on non-isothermal,unsteady and turbulent Rayleigh-Bénard Convection and compared with an existing model,where LES is based on turbulent kinetic energy.The hybrid turbulence model was implemented within a numerical algorithm based on the Boundary-Domain Integral Method,where a single domain and sub-domain approaches were used.The numerical algorithm uses governing equations written in a velocity-vorticity form.The false transient time scheme is used for the kinematics equation.展开更多
In this paper the influence of an impressed Coriolis force field on the configuration of a turbulent Rayleigh-Bénard convection problem is investigated in an experimental and numerical study. The main purpose of ...In this paper the influence of an impressed Coriolis force field on the configuration of a turbulent Rayleigh-Bénard convection problem is investigated in an experimental and numerical study. The main purpose of both studies lie on the analysis of a possible stabilising effect of a Coriolis acceleration on the turbulent unsteady structures inside the fluid. The relative Coriolis acceleration which is caused in the atmosphere by the earth rotation is realised in the experimental study by a uniform-rotational movement of the setup in a large-scale centrifuge under hyper-gravity. The same conditions as in the atmosphere in the beginning of a twister or hurricane should be realised in the experiment. The investigated Rayleigh numbers lie between 2.33 × 106 ≤ Ra ≤ 4.32 × 107.展开更多
Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities i...Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer. A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Béard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Blot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Blot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below.展开更多
Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied nu- merically.The convective instabilities in the system of Silicon Oil(10cSt)and Fluorinert(FC70)liquids have been analyzed.The cr...Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied nu- merically.The convective instabilities in the system of Silicon Oil(10cSt)and Fluorinert(FC70)liquids have been analyzed.The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0.Numerical results show that the instability of the two-layer system depends strongly on its depth ratio.When the depth ratio increases,the instability mode changes from mechanical coupling to thermal coupling.Between these two typical coupling modes, a time-dependent oscillation is detected.Nevertheless,traveling wave states are found in the case of oscillatory instability.The oscillation mode results from the competition between Rayleigh instability and Marangoni effect.展开更多
We present an experimental study of flow structures in turbulent Rayleigh-Bénard convection in annular cells of aspect ratiosΓ=1,2 and 4,and radius ratio 0.5.The convecting fluid is water with Prandtl number Pr=...We present an experimental study of flow structures in turbulent Rayleigh-Bénard convection in annular cells of aspect ratiosΓ=1,2 and 4,and radius ratio 0.5.The convecting fluid is water with Prandtl number Pr=4.3 and 5.3.Rayleigh number Ra ranges 4.8×10^(7)≤Ra≤4.5×10^(10).The dipole state(two-roll flow structure)forΓ=1 and the quadrupole state(fourroll flow structure)forΓ=2 and 4 are found by multi-temperature-probe measurement.Nusselt number Nu is described by a power-law scaling Nu=0.11Ra^(0.31),which is insensitive to the change of flow structures.However,the Reynolds number Re is influenced by increasing aspect ratios,where Re is found to scale with Ra andΓas Re~Ra^(0.46)Γ^(-0.52).The normalized amplitudes of two flow structures as a function of Ra exist difference.Based on relative weights of the first four modes using the Fourier analysis,we find that the first mode dominates inΓ=1 cell,but the second mode contains the most energy inΓ=2 and 4 cells.With increasingΓ,the flow structures exhibit different characteristics.展开更多
In this paper, we apply a scaling analysis of the maximum of the probability density function(pdf) of velocity increments, i.e., max() = max()up p u, for a velocity field of turbulent Rayleigh-Bénard convec...In this paper, we apply a scaling analysis of the maximum of the probability density function(pdf) of velocity increments, i.e., max() = max()up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, (1), in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T(x/ D) scales as T(x/ D)(x/ D), with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent (x, z) is strongly inhomogeneous in the x(horizontal) direction. The vertical-direction-averaged pdf scaling exponent (x) obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell's central region, (x, z) fluctuates around 0.37, which agrees well with (1) obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade()IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.展开更多
In this paper,we investigate the Lagrangian coherent structures(LCSs)and their heat-transport mechanism in turbulent Rayleigh-Bénard(RB)convection.Direct numerical simulations(DNS)are performed in a closed square...In this paper,we investigate the Lagrangian coherent structures(LCSs)and their heat-transport mechanism in turbulent Rayleigh-Bénard(RB)convection.Direct numerical simulations(DNS)are performed in a closed square cell with Rayleigh numbers(Ra)ranging from 10^(6) to 10^(9) and Prandtl(Pr)number fixed at Pr=0.7.First,our results show the power-law relationship between Nusselt number(Nu)and Ra,Nu=0.99Ra^(0.30±0.02),confirming the results from previous studies.To gain insights into the material transport,LCSs are extracted using the finite-time Lyapunov exponent(FTLE)method.Interestingly,lobe structures are widely present,and we elucidate their role in transporting heat from the corner rolls to large-scale circulation.Next,the relationships between LCSs and thermal plumes are examined,and we identify two behaviors of thermal plumes:first,most plumes transport along the LCSs;second,few plumes are exposed to the bulk and subsequently mix with the turbulent background.Furthermore,we quantify the heat flux along the LCSs,which contributes to about 85%of the total flux regardless of Ra.This suggests that LCSs play a significant role in heat transport.Finally,the viscous(thermal)dissipation rate along the LCSs is quantified,which is larger than 80%(60%)of the total value,suggesting that LCSs are responsible for the large viscous and thermal dissipations.展开更多
In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and the...In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.展开更多
In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymp...In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.展开更多
文摘The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls.An initial linear temperature profile is assumed.A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters.For a relatively small height,isobaric convection is found to take place,which is taken over by an adiabatic mode when the height exceeds the critical value,or by a super-adiabatic mode in case of a relatively high temperature gradient.In the adiabatic mode,convective flow develops due to adiabatic processes given a stable initial stratification.An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature.Moreover,an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases.These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations.A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank.In the presence of convective flows,the vaporized fuel is mixed with the oxidizer(air)forming a gas-vapor medium.However,if the volumetric concentration of fuel vapor(hydrocarbon)is in the interval between the lower and upper concentration limits of ignition,then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency.
文摘This paper conducts a Large Eddy Simulation (LES) of Rayleigh Bénard convection in a cubic cavity based on the WMLES S-Omega subgrid-scale model. For a cubic cavity with a vertical temperature difference of 6.7°C and 20°C, the velocity pulsation profiles and the mean velocity profiles of the vertical section in the middle of the cubic cavity were simulated, respectively. And they are consistent with the experiment results. Furthermore, the mean velocity field of the vertical cross-section in the middle of the cavity was calculated. Structures of the mean velocity field in the two cases are similar. A counterclockwise large vortex is found to occupy the cavity, and there are two small clockwise vortices in the lower left and upper right corners, and the mean velocity fields at two different temperature differences are consistent with the experimental results. The two-dimensional instantaneous temperature field and mean temperature field with different cross-sections in the z-direction, as well as the three-dimensional instantaneous isothermal surface structure, indicate that the large-scale circulation motion within the cubic cavity is moving diagonally. In addition, the structure of the mean streamline also illustrates this viewpoint. For the reverse vortex formed at two corners in the mean streamline structure, we used the Q criterion to identify and obtain two vortex structures similar to boomerangs. The basic turbulent structure in RB thermal convection includes the rising and falling plumes generated by buoyancy effects.
基金The Project was supported by the National Natural Science Foundation of China (Grants 11452002, 11521091, and 11372362)MOST (China) 973 Project (Grant 2009CB724100).
文摘Logarithmic boundary layers have been observed in different regions in turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we perform three-dimensional simulations of turbulence in a slim-box without the front and back walls with aspect ratio, width:depth:height=L:D:H=1:1/6:1width:depth:height=L:D:H=1:1/6:1 (respectively corresponding to xx, yy and zz coordinates), in the Rayleigh number Ra=[1×10^8,1×10^10]Ra=[1×10^8,1×10^10] for Prandtl number Pr=0.7Pr=0.7. To investigate the structures of the viscous and thermal boundary layers, we examine the velocity profiles in the streamwise and vertical directions (i.e. UU and WW) along with the mean temperature profile throughout the plume-impacting, plume-ejecting, and wind-shearing regions. The velocity profile is successfully quantified by a two-layer function of a stress length, e^+u=e^+0(z^+)3/2[1+(z^+/z^+sub)4]^1/4eu+=e^+0(z+)3/2[1+(z+/zsub+)4]1/4, as proposed by She et al.(J Fluid Mech, 2017), though it is neither \pb type nor logarithmic. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, AA, can be described by composition of the thermal stress length ■■θ0■θ0■ and the thicknesses of thermal boundary layer z■subzsub■ and z?bufzbuf■, i.e. A■z?sub/(■■θ0z■buf3/2)A■zsub?/(■θ0■zbuf^3/2). The adverse pressure gradient responsible for turning the wind direction contributes to intensively emitting plumes and the logarithmic temperature profile at the plume-ejecting region. The Nusselt number scaling and the local heat flux in the slim box are consistent with previous results of the confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation in a fixed plane.
基金the National Natural Science Foundation of China(Grants 11772111 and91952101)the Max Planck Partner Group.
文摘We propose a theoretical model for spatial variations of the temperature varianceσ2(z,r)(z is the dis-tance from the sample bottom and r the radial coordinate)in turbulent Rayleigh-Bénard convection(RBC).Adapting the“attached-eddy”modelofshearflowtothe plumesofRBC,wederivedanequationforσ2 which is based on the universal scaling of the normalized RBC temperature spectra.This equation in-cludes both logarithmic and power-law dependences on z/λth,whereλth is the thermal boundary layer thickness.The equation parameters depend on r and the Prandtl number Pr,but have only an extremelyweak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for thetemperature variance profile in turbulent RBC.
文摘Wavelet transform is used to analyze the scaling rule of temperature data (passive scalar) in Rayleigh Bénard convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can find the obtained scaling exponent agrees well with the one obtained from the temperature data in a experiment of wind tunnel. And then we propose a newly defined formula based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data. The obtained results demonstrate that we can correctly extract ξ(q) by using the method which is named as wavelet transform maximum modulus (WTMM).
基金supported by the Natural Science Foundation of Guangdong Province(Grant No.2020A1515011094)the Science,Technology and Innovation Commission of Shenzhen Municipality(Grant No.KQJSCX20180328165817522).
文摘We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC)in order to study the influence of the periodic(PD)and confined(CF)samples on the heat transport Nu.The numerical study is conducted with the Rayleigh number(Ra)varied in the range 10^(6)≤Ra≤10^(9) at a fixed Prandtl number Pr=4.3 and aspect ratio Γ=2 with the no-slip(NS)and freeslip(FS)plates.There exists a zonal flow for Ra≥3×10^(6) with the free-slip plates in the periodic sample.In all the other cases,the flow is the closed large-scale circulation(closed LSC).The striking features are that the heat transport Nu is influenced and the temperature profiles do not be influenced when the flow pattern is zonal flow.
文摘Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.
基金support from the Slovenian Research Agency(research core funding No.P2-0196).
文摘In this paper,we develop and test a unified hybrid LES/URANS turbulence model with two different Large Eddy Simulation(LES)turbulence models.The numerical algorithm is based on the Boundary Element Method.In the existing hybrid LES/URANS turbulence model we implemented a new Smagorinsky LES turbulence model.The hybrid LES/URANS turbulence model is unified,which means that the LES/URANS interface is changed dynamically during simulation using a physical quantity.In order to define the interface between LES and unsteady Reynolds Averaged Navier Stokes(URANS)zones during the simulation,we use the Reynolds number based on turbulent kinetic energy as a switching criterion.This means that the flow characteristics define where the sub-grid scale or URANS effective viscosity and thermal conductivity are used in the governing equations in the next time step.In unified hybrid turbulence models,only one set of governing equations is used for LES and URANS regions.The developed hybrid LES/URANS model was tested on non-isothermal,unsteady and turbulent Rayleigh-Bénard Convection and compared with an existing model,where LES is based on turbulent kinetic energy.The hybrid turbulence model was implemented within a numerical algorithm based on the Boundary-Domain Integral Method,where a single domain and sub-domain approaches were used.The numerical algorithm uses governing equations written in a velocity-vorticity form.The false transient time scheme is used for the kinematics equation.
文摘In this paper the influence of an impressed Coriolis force field on the configuration of a turbulent Rayleigh-Bénard convection problem is investigated in an experimental and numerical study. The main purpose of both studies lie on the analysis of a possible stabilising effect of a Coriolis acceleration on the turbulent unsteady structures inside the fluid. The relative Coriolis acceleration which is caused in the atmosphere by the earth rotation is realised in the experimental study by a uniform-rotational movement of the setup in a large-scale centrifuge under hyper-gravity. The same conditions as in the atmosphere in the beginning of a twister or hurricane should be realised in the experiment. The investigated Rayleigh numbers lie between 2.33 × 106 ≤ Ra ≤ 4.32 × 107.
基金The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05 and KGCX-SW-409) The English text was polished by Keren Wang.
文摘Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer. A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Béard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Blot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Blot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below.
基金The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)
文摘Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied nu- merically.The convective instabilities in the system of Silicon Oil(10cSt)and Fluorinert(FC70)liquids have been analyzed.The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0.Numerical results show that the instability of the two-layer system depends strongly on its depth ratio.When the depth ratio increases,the instability mode changes from mechanical coupling to thermal coupling.Between these two typical coupling modes, a time-dependent oscillation is detected.Nevertheless,traveling wave states are found in the case of oscillatory instability.The oscillation mode results from the competition between Rayleigh instability and Marangoni effect.
基金supported by the National Natural Science Foundation of China(Grants 11988102,11825204,92052201,91852202)the Program of Shanghai Academic Research Leader(Grant 19XD1421400)Science and Technology Innovation Plan Of Shanghai Science and Technology Commission(STCSM)(Project 19JC1412802).
文摘We present an experimental study of flow structures in turbulent Rayleigh-Bénard convection in annular cells of aspect ratiosΓ=1,2 and 4,and radius ratio 0.5.The convecting fluid is water with Prandtl number Pr=4.3 and 5.3.Rayleigh number Ra ranges 4.8×10^(7)≤Ra≤4.5×10^(10).The dipole state(two-roll flow structure)forΓ=1 and the quadrupole state(fourroll flow structure)forΓ=2 and 4 are found by multi-temperature-probe measurement.Nusselt number Nu is described by a power-law scaling Nu=0.11Ra^(0.31),which is insensitive to the change of flow structures.However,the Reynolds number Re is influenced by increasing aspect ratios,where Re is found to scale with Ra andΓas Re~Ra^(0.46)Γ^(-0.52).The normalized amplitudes of two flow structures as a function of Ra exist difference.Based on relative weights of the first four modes using the Fourier analysis,we find that the first mode dominates inΓ=1 cell,but the second mode contains the most energy inΓ=2 and 4 cells.With increasingΓ,the flow structures exhibit different characteristics.
基金supported by the Natural Science Foundation of China(Grant Nos.11102114,11202122 and 11222222)the Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ008,13YZ124)+1 种基金the Shanghai Shuguang Project(Grant No.13SG40)the Program for New Century Excellent Talents in University(Grant No.NCET-13-0)
文摘In this paper, we apply a scaling analysis of the maximum of the probability density function(pdf) of velocity increments, i.e., max() = max()up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, (1), in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T(x/ D) scales as T(x/ D)(x/ D), with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent (x, z) is strongly inhomogeneous in the x(horizontal) direction. The vertical-direction-averaged pdf scaling exponent (x) obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell's central region, (x, z) fluctuates around 0.37, which agrees well with (1) obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade()IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11732010, 92052201, 12072185, 91952102, 12032016)
文摘In this paper,we investigate the Lagrangian coherent structures(LCSs)and their heat-transport mechanism in turbulent Rayleigh-Bénard(RB)convection.Direct numerical simulations(DNS)are performed in a closed square cell with Rayleigh numbers(Ra)ranging from 10^(6) to 10^(9) and Prandtl(Pr)number fixed at Pr=0.7.First,our results show the power-law relationship between Nusselt number(Nu)and Ra,Nu=0.99Ra^(0.30±0.02),confirming the results from previous studies.To gain insights into the material transport,LCSs are extracted using the finite-time Lyapunov exponent(FTLE)method.Interestingly,lobe structures are widely present,and we elucidate their role in transporting heat from the corner rolls to large-scale circulation.Next,the relationships between LCSs and thermal plumes are examined,and we identify two behaviors of thermal plumes:first,most plumes transport along the LCSs;second,few plumes are exposed to the bulk and subsequently mix with the turbulent background.Furthermore,we quantify the heat flux along the LCSs,which contributes to about 85%of the total flux regardless of Ra.This suggests that LCSs play a significant role in heat transport.Finally,the viscous(thermal)dissipation rate along the LCSs is quantified,which is larger than 80%(60%)of the total value,suggesting that LCSs are responsible for the large viscous and thermal dissipations.
文摘In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.
基金Supported by National Basic Research Program of China(973 Program,Grant No.2011CB808002)National Natural Sciences Fundation of China(Grant No.11371042)+3 种基金BNSF(No.1132006)Beijing Education Committee Foundation(No.CIT&TCD20130312)HNNSF(112300410251,132300410250,132300410084)KYTF of Henan Education Commitee(2011GGJS-210)
文摘In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.