In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is st...In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations.展开更多
The vortex structure plays a significant role in the investigation of the turbulent drag reduction effect of the viscoelastic turbulent flow.This paper aims to find out an optimal vortex identification method for the ...The vortex structure plays a significant role in the investigation of the turbulent drag reduction effect of the viscoelastic turbulent flow.This paper aims to find out an optimal vortex identification method for the viscoelastic turbulent flows,and then studies the turbulent drag reduction mechanism by analyzing the characteristics of the identified vortex structures in the turbulent flows of the viscoelastic fluids.The Q,λ2,Liutex,Omega(Ω)and Omega-Liutex(ΩR)methods are adopted for the identification of vortex structures in the forced homogeneous isotropic turbulence(FHIT)with/without the polymer additive,respectively.The comparison among these five methods shows that the threshold values for the Q,λ2 and Liutex methods should be specially adjusted so as to suitably describe the strong and weak vortex structures in the FHIT of both the Newtonian and viscoelastic fluids,while a fixed threshold value of 0.52 for theΩandΩR methods is effective for both the Newtonian and viscoelastic fluids.The comparison between the identified vortex structures in the FHIT with and without the polymer additive indicates that theΩandΩR methods are more appropriate for the vortex identification because their dimensionless values with a fixed range from 0 to 1 can avoid the effect of the different ranges of the Q,λ2 and∣R∣(for the Liutex method)for the Newtonian and viscoelastic fluids.This also illustrates that theΩandΩR methods can be extended to identify the vortex structures in the turbulent flow of the viscoelastic fluid.Finally,the characteristics of the vortex structures in the FHIT of the viscoelastic fluid are analyzed by utilizing theΩandΩR methods.The results show that both the strong and weak vortex structures are inhibited by increasing the concentration of the polymer solution and by decreasing the Weissenberg number,especially for the weak vortex structures.展开更多
The concept of vortex is crucial in both understanding and modeling of turbulence.For large eddy simulation(LES),the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid ...The concept of vortex is crucial in both understanding and modeling of turbulence.For large eddy simulation(LES),the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid stress models.Even though the rotating motions of fluids,i.e.,vortices or eddies are central in developing turbulent models,vortex identification methods are seldom used in these models.In this study,we develop a new subgrid model based on the Liutex vector,a new quantity introduced to decompose fluid motions into rigid rotation,pure shear and stretching,and thus identify vortices.The new model is then applied in a decaying homogeneous isotropic turbulence(DHIT)and a turbulent channel flow at Reynolds number Reτ=180.It is shown that the new model can predict accurate energy spectra compared with experiments in DHIT and give a well-matched velocity profile in turbulent channel flow without changing the form of the model.Future directions include improvement of the Liutex based model,for example developing anisotropic subgrid models,and its applications in various turbulent flows.展开更多
The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed ...The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed to obtain the axinlly symmetrical solution of theNavier-Stokes equations of motion in the form of an infinite set of nonlinear partial differen-tial equations of the second order. For the present we solve the zeroth order approximation.By using the method of Fourier transform, we get a nonlinear nitegro-differential equationfor the amplitude function in the wave number space.It is also the dynamical equation forthe energy spectrum. By choosing a suitable initial condition, we solve this equation numerically. The energyspectrum function and the energy transfer spectrum function thus calculated satisfy the spec-trum form of the karman-Howarth equation exactly. We Lave computed the energy spectrumfunction, the energy transfer function the decay of turbulent energy, the integral scale, Taylormicroscale, the double and triple velocity correlations on the whole range from the initialperiod to the final period of decay. As a whole all these calculated statistical physicalquantities agree with experiments very wall except a few cases with small discrepancies at largeseparations.展开更多
As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the e...As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.展开更多
In the present paper,based upon the statistical vorticity structure theory of homogeneous isotropic turbulence,it is proposed that homogeneous isotropic turbulence has the property of similarity in the period of decay...In the present paper,based upon the statistical vorticity structure theory of homogeneous isotropic turbulence,it is proposed that homogeneous isotropic turbulence has the property of similarity in the period of decay,and the similarity-length is determined by the magnitude of velocity fluctuation and the generalized Taylor's microscale of turbulence which is closely related to the characteristic length of the vortex Introducing the condition of pseudo-similarity,this paper starts from the Navier-Stokes equations of motion to study homogeneous isotropic turbulence.In the calculations,the velocity fluctuation is assumed to be periodic in space with the period being proportional to the generalized Taylor's microscale of turbulence The calculations in the physical space are transformed to that in the spectral space by expanding the velocity fluctuation and other physical quantities into Fourier series.Utilizing the fast Fourier transform,the forward difference formulae and the leap-frog difference foumulae,we study the homogeneous isotropic turbulence in the whole period of decay for the different grid Reynolds numbers.Agreements between the calculations and the experimental data are satisfactory.展开更多
Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is pres...Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav- iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.展开更多
By introducing the Fourier filters, we analyse the correlation between large- and small-scale velocity components in homogeneous isotropic turbulence theoretically. We show that different Fourier filters act similarly...By introducing the Fourier filters, we analyse the correlation between large- and small-scale velocity components in homogeneous isotropic turbulence theoretically. We show that different Fourier filters act similarly on this multiscale correlation with a ＂natural＂ mechanism of removing the physical correlations between large- and small-scale velocity components. This conclusion calls for the further investigation on the Hilbert-Huang decomposition to investigate the mechanism of Marusic et al （2008）.展开更多
A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condi...A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condition is constructed by reversing the velocity field in space,i.e.,the time-reversed turbulence.It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process.This description is consistent to the velocity derivative skewness Sk.However,compared with Sk,it is easier to be obtained,and it is expected to be extended to anisotropic turbulence.Furthermore,this description also works for the resolved velocity field,which means that it can be used in engineering turbulent flows.The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.展开更多
Homogeneous isotropic turbulence has been playing a key role in the research of turbulence theory.And the pseudo-spectral method is the most popular numerical method to simulate this type of flow fields in a periodic ...Homogeneous isotropic turbulence has been playing a key role in the research of turbulence theory.And the pseudo-spectral method is the most popular numerical method to simulate this type of flow fields in a periodic box,where fast Fourier transform(FFT)is mostly effective.However,the bottle-neck in this method is the memory of computer,which motivates us to construct a memory-saving algorithm for spectral method in present paper.Inevitably,more times of FFT are needed as compensation.In the most memory-saving situation,only 6 three-dimension arrays are employed in the code.The cost of computation is increased by a factor of 4,and that 38 FFTs are needed per time step instead of the previous 9 FFTs.A simulation of isotropic turbulence on 20483 grid can be implemented on a 256G distributed memory clusters through this method.展开更多
基金the National Natural Science Foundation of China (Grant 11772128)the Fundamental Research Funds for the Central Universities (Grants 2017MS022 and 2018ZD09).
文摘In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51706050,51806051).
文摘The vortex structure plays a significant role in the investigation of the turbulent drag reduction effect of the viscoelastic turbulent flow.This paper aims to find out an optimal vortex identification method for the viscoelastic turbulent flows,and then studies the turbulent drag reduction mechanism by analyzing the characteristics of the identified vortex structures in the turbulent flows of the viscoelastic fluids.The Q,λ2,Liutex,Omega(Ω)and Omega-Liutex(ΩR)methods are adopted for the identification of vortex structures in the forced homogeneous isotropic turbulence(FHIT)with/without the polymer additive,respectively.The comparison among these five methods shows that the threshold values for the Q,λ2 and Liutex methods should be specially adjusted so as to suitably describe the strong and weak vortex structures in the FHIT of both the Newtonian and viscoelastic fluids,while a fixed threshold value of 0.52 for theΩandΩR methods is effective for both the Newtonian and viscoelastic fluids.The comparison between the identified vortex structures in the FHIT with and without the polymer additive indicates that theΩandΩR methods are more appropriate for the vortex identification because their dimensionless values with a fixed range from 0 to 1 can avoid the effect of the different ranges of the Q,λ2 and∣R∣(for the Liutex method)for the Newtonian and viscoelastic fluids.This also illustrates that theΩandΩR methods can be extended to identify the vortex structures in the turbulent flow of the viscoelastic fluid.Finally,the characteristics of the vortex structures in the FHIT of the viscoelastic fluid are analyzed by utilizing theΩandΩR methods.The results show that both the strong and weak vortex structures are inhibited by increasing the concentration of the polymer solution and by decreasing the Weissenberg number,especially for the weak vortex structures.
基金Project supported by the National Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.22KJB130011)the Supercomputing Center in Yancheng(Grant No.FW(W)20221001).
文摘The concept of vortex is crucial in both understanding and modeling of turbulence.For large eddy simulation(LES),the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid stress models.Even though the rotating motions of fluids,i.e.,vortices or eddies are central in developing turbulent models,vortex identification methods are seldom used in these models.In this study,we develop a new subgrid model based on the Liutex vector,a new quantity introduced to decompose fluid motions into rigid rotation,pure shear and stretching,and thus identify vortices.The new model is then applied in a decaying homogeneous isotropic turbulence(DHIT)and a turbulent channel flow at Reynolds number Reτ=180.It is shown that the new model can predict accurate energy spectra compared with experiments in DHIT and give a well-matched velocity profile in turbulent channel flow without changing the form of the model.Future directions include improvement of the Liutex based model,for example developing anisotropic subgrid models,and its applications in various turbulent flows.
文摘The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed to obtain the axinlly symmetrical solution of theNavier-Stokes equations of motion in the form of an infinite set of nonlinear partial differen-tial equations of the second order. For the present we solve the zeroth order approximation.By using the method of Fourier transform, we get a nonlinear nitegro-differential equationfor the amplitude function in the wave number space.It is also the dynamical equation forthe energy spectrum. By choosing a suitable initial condition, we solve this equation numerically. The energyspectrum function and the energy transfer spectrum function thus calculated satisfy the spec-trum form of the karman-Howarth equation exactly. We Lave computed the energy spectrumfunction, the energy transfer function the decay of turbulent energy, the integral scale, Taylormicroscale, the double and triple velocity correlations on the whole range from the initialperiod to the final period of decay. As a whole all these calculated statistical physicalquantities agree with experiments very wall except a few cases with small discrepancies at largeseparations.
文摘As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.
文摘In the present paper,based upon the statistical vorticity structure theory of homogeneous isotropic turbulence,it is proposed that homogeneous isotropic turbulence has the property of similarity in the period of decay,and the similarity-length is determined by the magnitude of velocity fluctuation and the generalized Taylor's microscale of turbulence which is closely related to the characteristic length of the vortex Introducing the condition of pseudo-similarity,this paper starts from the Navier-Stokes equations of motion to study homogeneous isotropic turbulence.In the calculations,the velocity fluctuation is assumed to be periodic in space with the period being proportional to the generalized Taylor's microscale of turbulence The calculations in the physical space are transformed to that in the spectral space by expanding the velocity fluctuation and other physical quantities into Fourier series.Utilizing the fast Fourier transform,the forward difference formulae and the leap-frog difference foumulae,we study the homogeneous isotropic turbulence in the whole period of decay for the different grid Reynolds numbers.Agreements between the calculations and the experimental data are satisfactory.
基金supported by the National Natural Science Foundation of China(Nos.11572025,11202013,and 51420105008)
文摘Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav- iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.
基金supported by the National Natural Science Foundation of China(11202013 and51420105008)
文摘By introducing the Fourier filters, we analyse the correlation between large- and small-scale velocity components in homogeneous isotropic turbulence theoretically. We show that different Fourier filters act similarly on this multiscale correlation with a ＂natural＂ mechanism of removing the physical correlations between large- and small-scale velocity components. This conclusion calls for the further investigation on the Hilbert-Huang decomposition to investigate the mechanism of Marusic et al （2008）.
基金the National Natural Science Foundation of China(Nos.12002318 and51976203)the Central Government Guides Local Science and Technology Development Fund Projects(No.YDZX20191400002850)the Science Foundation of North University of China(No.XJJ201929)。
文摘A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condition is constructed by reversing the velocity field in space,i.e.,the time-reversed turbulence.It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process.This description is consistent to the velocity derivative skewness Sk.However,compared with Sk,it is easier to be obtained,and it is expected to be extended to anisotropic turbulence.Furthermore,this description also works for the resolved velocity field,which means that it can be used in engineering turbulent flows.The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.
基金support from National Natural Science Funds for Distinguished Young Scholar group under Grant No.10921202National Climb Plan under Grant No.2009CB724100.
文摘Homogeneous isotropic turbulence has been playing a key role in the research of turbulence theory.And the pseudo-spectral method is the most popular numerical method to simulate this type of flow fields in a periodic box,where fast Fourier transform(FFT)is mostly effective.However,the bottle-neck in this method is the memory of computer,which motivates us to construct a memory-saving algorithm for spectral method in present paper.Inevitably,more times of FFT are needed as compensation.In the most memory-saving situation,only 6 three-dimension arrays are employed in the code.The cost of computation is increased by a factor of 4,and that 38 FFTs are needed per time step instead of the previous 9 FFTs.A simulation of isotropic turbulence on 20483 grid can be implemented on a 256G distributed memory clusters through this method.
