The stability of the static mode of compressible gas convection is analyzed in the linear approximation with heating from below. The obtained data are compared with the results of solving the system of complete nonlin...The stability of the static mode of compressible gas convection is analyzed in the linear approximation with heating from below. The obtained data are compared with the results of solving the system of complete nonlinear equations describing convective flows of compressible gas. The features of the constructed neutral curve are discussed.展开更多
A detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate...A detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate（TDR） is made. The Rayleigh number（Ra） in our simulations ranges up to 5×10^10 and Prandtl number（Pr） is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the ＂temperature islands＂, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number（Nu） and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb 〈 δθ（3 D） 〈 δθ（2 D） and all three heights obey a universal power-law relation z ~Ra^-0.30. In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb（near top and bottom plates respectively） as the ＂mid region＂ and the rest as the ＂side region＂, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs w展开更多
The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a comb...The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a combined space-time separa- tion involving spatial separation r and time delay T, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu（r, v） has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.展开更多
This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular sec...This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section.The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method,taking into account the Darcy–Brinkman model for porous medium.It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial,transient,and semi-steady.The features of each step are provided in detail.The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper)inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate.In contrast,as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide)inside the chamber increased,convection heat transfer rate improved.At the same time,it was observed that the use of both nano-fluids(single and hybrid)in the porous environment of the aluminum foam could improve convection.展开更多
High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） varying between （...High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） varying between （1, 0.3） and （20.8, 6.3）. For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse （GL） model together with the empirical finite conductivity cor- rection factorf（X） were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells＇ aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357＋O.525Ra0.168, can be used to de- scribe Nu∞（Ra）. The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.展开更多
By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means tha...By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.展开更多
We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity ...We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.展开更多
Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up t...Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.展开更多
In addition to the hierarchical-structure (H-S) model, this paper further explores the most intensive intermittent structure of Rayleigh-Bénard convection at the high Ra numbers proportional to temperature. With ...In addition to the hierarchical-structure (H-S) model, this paper further explores the most intensive intermittent structure of Rayleigh-Bénard convection at the high Ra numbers proportional to temperature. With respect to the discovery and by means of the scale, both of Bolgiano, there are two regions of the structure holding the absolute scaling law given by Ching’s paper. Through theoretic analysis of data, this paper indicates that the regions act as two local intensive intermittent structures, by which the statistical absolute scaling performance of region is induced, rather than the statistical result of the entire time series in belief since 1941. In terms of statistical theory, the local structure in fluid, therefore, is the essence governing the absolute scaling performance of region, especially in high intensity.展开更多
In the present paper, the effect of variable fluid properties （density, viscosity, thermal conductivity and specific heat） on the convection in the classical Rayleigh-Benard problem is investigated. The investigatio...In the present paper, the effect of variable fluid properties （density, viscosity, thermal conductivity and specific heat） on the convection in the classical Rayleigh-Benard problem is investigated. The investigation concerns water, air, and engine oil by taking into account the variation of fluid properties with temperature. The results are obtained by numerically solving the governing equations, using the SIMPLE algorithm and covering large temperature differences. It is found that the critical Rayleigh number increases as the temperature difference increases considering all fluid properties variable. However, when the fluid properties are kept constant, calculated at the mean temperature, and only density is considered variable, the critical Rayleigh number either decreases or remains constant.展开更多
Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( PO...Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile,a low-dimensional model( LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits,streamline and isothermal predicted by LDM,it is suggested that the error between LDM and DNS is still large.展开更多
Natural convection driven by the temperature difference of horizontal top and bottom surfaces of an enclosure containing air, Pr = 0.7, and fins of different arrangements at different lengths is studied numerically fo...Natural convection driven by the temperature difference of horizontal top and bottom surfaces of an enclosure containing air, Pr = 0.7, and fins of different arrangements at different lengths is studied numerically for Ra = 105 and 5 × 10^5. Evolution of heat transfer rates （Nusselt number） is illustrated along with various, steady or unsteady, cellular flow structures and temperature patterns. The effect of fin length and placement on flow regime and heat transfer is established. Different fin orientations at the walls are observed to introduce considerable unsteadiness in some cases, requiring close investigation in order to design systems for specific purposes.展开更多
We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in´a square cavity by direct numerical simulations.The Rayleigh number range is 1×10^(8)≤Ra≤...We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in´a square cavity by direct numerical simulations.The Rayleigh number range is 1×10^(8)≤Ra≤1×10^(13),and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max∼(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10^(9),the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10^(10),the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV∼Ra−0.14±0.01.展开更多
We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibr...We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibration frequency range 0<ω<1400.The triangular rough elements are uniformly distributed over the top and bottom surfaces,and the vibration is applied in the horizontal direction.It is shown that under the combined action of roughness and horizontal vibration,with increasing the vibration frequency ω,the heat transfer is initially decreased a little and then greatly enhanced after ω exceeds the critical value.The physical reason for massive heat-transfer-enhancement is that high frequency vibration destabilizes thermal boundary layers(BL)over rough surfaces,triggers abundant emissions of thermal plumes,and strengthens the motion of large-scale circulation(LSC),which consequently thins the thickness of thermal BL and heightens the convective transport.In addition,it is shown that vibration-induced heat-transfer-enhancement can obviously affect the scaling behavior between the heat flux and the Rayleigh number,and the scaling exponent increases with increasing ω,whereas the influence of vibration on the scaling behavior between the intensity of LSC and Ra is very weak.展开更多
Rough-surface Rayleigh-Benard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratioГ=2.Three types of fractal roughness elements,which are marked as nl,n2...Rough-surface Rayleigh-Benard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratioГ=2.Three types of fractal roughness elements,which are marked as nl,n2 and n3,are constructed based on the Koch curve and sparsely mounted on both the plates,where n denotes the level of the roughness.The considered Rayleigh numbers Ra range from 10^(7)to 10^(11)with Prandtl number Pr=1.Two regimes are identified for cases nl,n2.In Regime I,the scaling exponentsβin the effective Nusselt number Nu vs Ra scaling Nu~Ra^(β)reach up to about 0.4.However,when Ra is larger than a critical value Ra_(c),the flow enters RegimeⅡ,with p saturating back to a value close to the smooth-wall case(0.3).Rac is found to increase with increasing n,and for case n3,only Regime I is identified in the studied Ra range.The extension of Regime I in case n3 is due to the fact that at high Ra,the smallest roughness elements can play a role to disrupt the thermal boundary layers.The thermal dissipation rate is studied and it is found that the increasedβin Regime I is related with enhanced thermal dissipation rate in the bulk.An interesting finding is that no clear convection roll structures can be identified for the rough cases,which is different from the smooth case where well-organized convection rolls can be found.This difference is further quantified by the detailed analysis of the plume statistics,and it is found that the horizontal profiles of plume density and velocity are relatively flattened due to the absence of clear convection rolls.展开更多
The aim of this paper is to develop an efficient numerical method to compute the eigenvalues of the stability analysis of a problem describing the motion of a fluid within a cylindrical container heated non-homogeneou...The aim of this paper is to develop an efficient numerical method to compute the eigenvalues of the stability analysis of a problem describing the motion of a fluid within a cylindrical container heated non-homogeneously from below.An axisymmetric stationary motion settles in,at certain values of the external parameters appearing in the set of partial differential equations modeling the problem.This basic solution is computed by discretizing the equations with a Chebyshev collocation method.Its linear stability is formulated with a generalized eigenvalue problem.The numerical approach(generalized Arnoldi method)uses the idea of preconditioning the eigenvalue problem with a modified Cayley transformation before applying the Arnoldi method.Previous works have dealt with transformations requiring regularity to one of the submatrices.In this article we extend those results to the case in which that submatrix is singular.This method allows a fast computation of the critical eigenvalues which determine whether the steady flow is stable or unstable.The algorithm based on this method is compared to the QZ method and is found to be computationally more efficient.The reliability of the computed eigenvalues in terms of stability is confirmed via pseudospectra calculations.展开更多
文摘The stability of the static mode of compressible gas convection is analyzed in the linear approximation with heating from below. The obtained data are compared with the results of solving the system of complete nonlinear equations describing convective flows of compressible gas. The features of the constructed neutral curve are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11772362 and 11452002)the Special Scientific Research Fund for Super Computing in the Joint Fund of the National Natural Science Foundation of Chinathe People’s Government of Guangdong Province(Phase Ⅱ,Grant No.nsfc2015 570)
文摘A detailed comparative numerical study between the two-dimensional（2 D） and quasi-two-dimensional（quasi-2 D）turbulent Rayleigh–B＇enard（RB） convection on flow state, heat transfer, and thermal dissipation rate（TDR） is made. The Rayleigh number（Ra） in our simulations ranges up to 5×10^10 and Prandtl number（Pr） is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the ＂temperature islands＂, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number（Nu） and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb 〈 δθ（3 D） 〈 δθ（2 D） and all three heights obey a universal power-law relation z ~Ra^-0.30. In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb（near top and bottom plates respectively） as the ＂mid region＂ and the rest as the ＂side region＂, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs w
基金supported in part by RGC of Hong Kong SAR (HKUST-605013)
文摘The recent development of the elliptic model （He, et al. Phy. Rev. E, 2006）, which predicts that the space-time correlation function Cu（r, r） in a turbulent flow has a scaling form Cu（rE, 0） with re being a combined space-time separa- tion involving spatial separation r and time delay T, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu（r, v） has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.
文摘This study numerically investigates the impact of porous materials,nano-particle types,and their concentrations on transient natural convection heat transfer of nano-fluid inside a porous chamber with a triangular section.The governing equations of the two-phase mixture model are separated on the computational domain and solved using the Finite Volume Method,taking into account the Darcy–Brinkman model for porous medium.It was observed that convection heat transfer inside the triangular chamber consists of three stages named initial,transient,and semi-steady.The features of each step are provided in detail.The results suggested that the use of a hybrid nano-fluid(water/aluminum oxide-cooper)inside a porous glass material and an increase in volume fraction of nano-particles have adverse effects on heat transfer rate.In contrast,as the nano-particle volume fraction of the single nano-fluid(water/aluminum oxide)inside the chamber increased,convection heat transfer rate improved.At the same time,it was observed that the use of both nano-fluids(single and hybrid)in the porous environment of the aluminum foam could improve convection.
基金supported by the National Natural Science Foundation of China (Grant Nos.11222222, 11161160554 and 11002085)Innovation Program of Shanghai Municipal Education Commission (Grant No.13YZ008)Shanghai Program for Innovative Research Team in Universities
文摘High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard （RB） convection have been made in rectangular cells of water （Prandtl number Pr ≈ 5 and 7） with aspect ratios （F~, Fy） varying between （1, 0.3） and （20.8, 6.3）. For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse （GL） model together with the empirical finite conductivity cor- rection factorf（X） were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells＇ aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357＋O.525Ra0.168, can be used to de- scribe Nu∞（Ra）. The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.
文摘By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.
文摘We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.
基金Supported by the Natural Science Foundation of Henan Province(092300410150)the Key Youth Teacher Foundation of Department Education of Henan Province(2011GGJS-210)the Key Youth Teacher Foundation of Huanghuai University
文摘Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.
文摘In addition to the hierarchical-structure (H-S) model, this paper further explores the most intensive intermittent structure of Rayleigh-Bénard convection at the high Ra numbers proportional to temperature. With respect to the discovery and by means of the scale, both of Bolgiano, there are two regions of the structure holding the absolute scaling law given by Ching’s paper. Through theoretic analysis of data, this paper indicates that the regions act as two local intensive intermittent structures, by which the statistical absolute scaling performance of region is induced, rather than the statistical result of the entire time series in belief since 1941. In terms of statistical theory, the local structure in fluid, therefore, is the essence governing the absolute scaling performance of region, especially in high intensity.
文摘In the present paper, the effect of variable fluid properties （density, viscosity, thermal conductivity and specific heat） on the convection in the classical Rayleigh-Benard problem is investigated. The investigation concerns water, air, and engine oil by taking into account the variation of fluid properties with temperature. The results are obtained by numerically solving the governing equations, using the SIMPLE algorithm and covering large temperature differences. It is found that the critical Rayleigh number increases as the temperature difference increases considering all fluid properties variable. However, when the fluid properties are kept constant, calculated at the mean temperature, and only density is considered variable, the critical Rayleigh number either decreases or remains constant.
基金Sponsored by the National Natural Science Foundation of China(Grant o.51576051)
文摘Direct numerical simulation based on OpenFOAM is carried out for two-dimensional RayleighBénard( RB) convection in a square domain at high Rayleigh number of 107 and Pr = 0.71. Proper orthogonal decomposition( POD) is used to analyze the flow and temperature characteristics from POD energy spectrum and eigenmodes. The results show that the energy spectrum converges fast and the scale of vortex structures captured by eigenmodes becomes smaller as the eigenmode order increases. Meanwhile,a low-dimensional model( LDM) for RB convection is derived based on POD eigenmodes used as a basis of Galerkin project of Navier-Stokes-Boussinesq equations. LDM is built based on different number of eigenmodes and through the analysis of phase portraits,streamline and isothermal predicted by LDM,it is suggested that the error between LDM and DNS is still large.
文摘Natural convection driven by the temperature difference of horizontal top and bottom surfaces of an enclosure containing air, Pr = 0.7, and fins of different arrangements at different lengths is studied numerically for Ra = 105 and 5 × 10^5. Evolution of heat transfer rates （Nusselt number） is illustrated along with various, steady or unsteady, cellular flow structures and temperature patterns. The effect of fin length and placement on flow regime and heat transfer is established. Different fin orientations at the walls are observed to introduce considerable unsteadiness in some cases, requiring close investigation in order to design systems for specific purposes.
基金the National Natural Science Foundation of China(Grant No.11772362)the Shenzhen Fundamental Research Program(Grant No.JCYJ20190807160413162)the Fundamental Research Funds for the Central Universities,Sun Yat-sen University,China(Grant No.19lgzd15).
文摘We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in´a square cavity by direct numerical simulations.The Rayleigh number range is 1×10^(8)≤Ra≤1×10^(13),and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max∼(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10^(9),the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10^(10),the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV∼Ra−0.14±0.01.
基金supported by the National Natural Science Foundation of China(Grant Nos.11988102,92052201,91852202,H825204,and 11972220)the Program of Shanghai Academic Research Leader(Grant No.19XD1421400)+1 种基金Shanghai Science and Technology Program(Grant Nos.19JC1412802 and 20ZR14I9800)China Postdoctoral Science Foundation(Grant No.2020M681259).
文摘We carried out direct numerical simulations of turbulent Rayleigh-Benard convection(RBC)with accounting for both the roughness and the external vibration over the Rayleigh number range 10^(7)≤Ra≤10^(11) and the vibration frequency range 0<ω<1400.The triangular rough elements are uniformly distributed over the top and bottom surfaces,and the vibration is applied in the horizontal direction.It is shown that under the combined action of roughness and horizontal vibration,with increasing the vibration frequency ω,the heat transfer is initially decreased a little and then greatly enhanced after ω exceeds the critical value.The physical reason for massive heat-transfer-enhancement is that high frequency vibration destabilizes thermal boundary layers(BL)over rough surfaces,triggers abundant emissions of thermal plumes,and strengthens the motion of large-scale circulation(LSC),which consequently thins the thickness of thermal BL and heightens the convective transport.In addition,it is shown that vibration-induced heat-transfer-enhancement can obviously affect the scaling behavior between the heat flux and the Rayleigh number,and the scaling exponent increases with increasing ω,whereas the influence of vibration on the scaling behavior between the intensity of LSC and Ra is very weak.
基金Projects supported by the National Natural Science Foundation of China(Grant Nos.11772323,91952103 and 11621202).
文摘Rough-surface Rayleigh-Benard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratioГ=2.Three types of fractal roughness elements,which are marked as nl,n2 and n3,are constructed based on the Koch curve and sparsely mounted on both the plates,where n denotes the level of the roughness.The considered Rayleigh numbers Ra range from 10^(7)to 10^(11)with Prandtl number Pr=1.Two regimes are identified for cases nl,n2.In Regime I,the scaling exponentsβin the effective Nusselt number Nu vs Ra scaling Nu~Ra^(β)reach up to about 0.4.However,when Ra is larger than a critical value Ra_(c),the flow enters RegimeⅡ,with p saturating back to a value close to the smooth-wall case(0.3).Rac is found to increase with increasing n,and for case n3,only Regime I is identified in the studied Ra range.The extension of Regime I in case n3 is due to the fact that at high Ra,the smallest roughness elements can play a role to disrupt the thermal boundary layers.The thermal dissipation rate is studied and it is found that the increasedβin Regime I is related with enhanced thermal dissipation rate in the bulk.An interesting finding is that no clear convection roll structures can be identified for the rough cases,which is different from the smooth case where well-organized convection rolls can be found.This difference is further quantified by the detailed analysis of the plume statistics,and it is found that the horizontal profiles of plume density and velocity are relatively flattened due to the absence of clear convection rolls.
基金the Research Grants MCYT(Spanish Government)MTM2006-14843-C02-01 and CCYT(JC Castilla-La Mancha)PAC-05-005which include FEDER funds.AMM thanks support by Grants from CSIC(PI-200650I224)+1 种基金Comunidad de Madrid(SIMUMAT S-0505-ESP-0158)Junta de Castilla-La Mancha(PAC-05-005-2).
文摘The aim of this paper is to develop an efficient numerical method to compute the eigenvalues of the stability analysis of a problem describing the motion of a fluid within a cylindrical container heated non-homogeneously from below.An axisymmetric stationary motion settles in,at certain values of the external parameters appearing in the set of partial differential equations modeling the problem.This basic solution is computed by discretizing the equations with a Chebyshev collocation method.Its linear stability is formulated with a generalized eigenvalue problem.The numerical approach(generalized Arnoldi method)uses the idea of preconditioning the eigenvalue problem with a modified Cayley transformation before applying the Arnoldi method.Previous works have dealt with transformations requiring regularity to one of the submatrices.In this article we extend those results to the case in which that submatrix is singular.This method allows a fast computation of the critical eigenvalues which determine whether the steady flow is stable or unstable.The algorithm based on this method is compared to the QZ method and is found to be computationally more efficient.The reliability of the computed eigenvalues in terms of stability is confirmed via pseudospectra calculations.
