The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact soluti...The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.展开更多
The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is ...The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.展开更多
This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the ...This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.展开更多
In order to investigate the aerodynamics of a high speed low pressure turbine works in high Mach number and low Reynold number environment,the effect of freestream turbulence(FST)on the boundary layer development on t...In order to investigate the aerodynamics of a high speed low pressure turbine works in high Mach number and low Reynold number environment,the effect of freestream turbulence(FST)on the boundary layer development on the high speed low pressure turbine under different Reynolds numbers(Re)is numerically investigated.Large eddy simulation is adopted here with a subgrid scale model of Wall Adapting Local Eddy viscosity(WALE).Cases with Re ranging from 100000 to 400000 under an exit Mach number(Ma)of 0.87 have been considered at low and high FST levels.A low Ma case(0.17)under very low Re has also been studied under both low and high FST.It is found that higher Re or FST level leads to earlier transition.Re has a greater effect than FST on the development of boundary layer.The effect of FST on the boundary layer depends on the Re.The boundary layer development shows totally different behaviors under different Ma.A separation bubble could be formed under low Ma while no attachment could be detected under high Ma.The FST has a stronger effect on the separated boundary layer under low Ma,which could eliminate the separation in the present study.For all the cases under low FST,the Kelvin-Helmholtz instability is the dominate mechanism in the transition process.For the low Ma case with high FST,the streamwise streaks play a dominant role in the transition process.For the high Ma cases with high FST,both the streamwise streaks and Kelvin-Helmholtz instability work in the transition process.The streamwise streaks play a more important role when the Re increased.展开更多
Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence...Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence theory.The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon,however,cannot generally be met in practice,and thus discrepancy is often observed between the f law and direct numerical simulation(DNS)results of boundary layers in wall bounded turbulence,especially for moderate to low Reynolds number flows.Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion.Actually,Liutex is free from viscous dissipation and thus independent of Reynolds number,relaxing the very high Reynold number assumption of K41.Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000),both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law,which is obviously much better than the turbulence energy spectrum,while vorticity and other popular vortex identification methods,Q criterion for example,do not possess such a distinguished feature due to stretching and shearing contamination.展开更多
This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on...This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.展开更多
基金Xi’an University of Architecture and Technology(Grant no.002/2040221134).
文摘The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.
基金supported by grants from the National Key Research and Development Program of China(Grant No.2016YFA0401200)the National Natural Science Foundation of China(Grant Nos.12072230,11672204,91952301,and 11732011).
文摘The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.
文摘This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.
基金supported by the National Science and Technology Major Project of China (No. 2017-Ⅱ-0008-0022,2019-Ⅱ-008-0028)
文摘In order to investigate the aerodynamics of a high speed low pressure turbine works in high Mach number and low Reynold number environment,the effect of freestream turbulence(FST)on the boundary layer development on the high speed low pressure turbine under different Reynolds numbers(Re)is numerically investigated.Large eddy simulation is adopted here with a subgrid scale model of Wall Adapting Local Eddy viscosity(WALE).Cases with Re ranging from 100000 to 400000 under an exit Mach number(Ma)of 0.87 have been considered at low and high FST levels.A low Ma case(0.17)under very low Re has also been studied under both low and high FST.It is found that higher Re or FST level leads to earlier transition.Re has a greater effect than FST on the development of boundary layer.The effect of FST on the boundary layer depends on the Re.The boundary layer development shows totally different behaviors under different Ma.A separation bubble could be formed under low Ma while no attachment could be detected under high Ma.The FST has a stronger effect on the separated boundary layer under low Ma,which could eliminate the separation in the present study.For all the cases under low FST,the Kelvin-Helmholtz instability is the dominate mechanism in the transition process.For the low Ma case with high FST,the streamwise streaks play a dominant role in the transition process.For the high Ma cases with high FST,both the streamwise streaks and Kelvin-Helmholtz instability work in the transition process.The streamwise streaks play a more important role when the Re increased.
文摘Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence theory.The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon,however,cannot generally be met in practice,and thus discrepancy is often observed between the f law and direct numerical simulation(DNS)results of boundary layers in wall bounded turbulence,especially for moderate to low Reynolds number flows.Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion.Actually,Liutex is free from viscous dissipation and thus independent of Reynolds number,relaxing the very high Reynold number assumption of K41.Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000),both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law,which is obviously much better than the turbulence energy spectrum,while vorticity and other popular vortex identification methods,Q criterion for example,do not possess such a distinguished feature due to stretching and shearing contamination.
基金supported jointly by the Centre National de la Recherche Scientifiquethe Korea Science and Engineering Foundation
文摘This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.
