In an endeavor to establish a connection between the mean velocity profile in compressible wall-bounded turbulence and its incompressible analogue,a refined version of the Trettel and Larsson's(TL)transformation i...In an endeavor to establish a connection between the mean velocity profile in compressible wall-bounded turbulence and its incompressible analogue,a refined version of the Trettel and Larsson's(TL)transformation is systematically derived and rigorously assessed across diverse flow scenarios.Incorporating the recently proposed intrinsic compressibility effects and modeling the multi-layer structure of mixing lengths,the proposed transformation demonstrates exceptional performance in collapsing 57canonical flow cases,including cooled channel and pipe flows,channel flows with pseudo heat sources,as well as adiabatic and diabatic boundary layer flows.Furthermore,the transformation seamlessly extends to low Reynolds number cooled channel and pipe flows,achieving a level of accuracy unparalleled by other transformations in the current state-of-the-art.展开更多
This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incomp...This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows.It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold.Regarding the vortex orientation,the inclination angle remains similar.However,as the wall-normal distance increases,a more and more obvious distinction is noticed for its orientation with respect to the spanwise(z)direction.It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification,i.e.,vortices rotating in the−z direction for the total velocity field and in the z direction for the fluctuating one.These observations function as a reasonable explanation for various remarks in previous studies.展开更多
Based on direct numerical simulation (DNS) data of the straight ducts,namely square and rectangular annular ducts,detailed analyses were conducted for the mean streamwise velocity,relevant velocity scales,and turbulen...Based on direct numerical simulation (DNS) data of the straight ducts,namely square and rectangular annular ducts,detailed analyses were conducted for the mean streamwise velocity,relevant velocity scales,and turbulence statistics.It is concluded that turbulent boundary layers (TBL) should be broadly classified into three types (Type-A,-B,and-C) in terms of their distribution patterns of the time-averaged local wall-shear stress (τw) or the mean local frictional velocity (uτ).With reference to the Type-A TBL analysis by von Karman in developing the law-of-the-wall using the time-averaged local frictional velocity (uτ) as scale,the current study extended the approach to the Type-B TBL and obtained the analytical expressions for streamwise velocity in the inner-layer using ensemble-averaged frictional velocity (ūτ) as scale.These analytical formulae were formed by introducing the general damping and enhancing functions.Further,the research applied a near-wall DNS-guided integration to the governing equations of Type-B TBL and quantitatively proved the correctness and accuracy of the inner-layer analytical expressions for this type.展开更多
The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbu...The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence. The spectra are calculated from direct numerical simulation （DNS） of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the nearwall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number Rer can be as low as 1000. The properties of the inner and outer peaks in the spanwise spec- tra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number, which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity.展开更多
In-depth analyses of existing direct numerical simulations(DNS)data led to a logical and important classification of generic turbulent boundary layers(TBLs),namely Type-A,-B and-C TBL,based on the distribution pattern...In-depth analyses of existing direct numerical simulations(DNS)data led to a logical and important classification of generic turbulent boundary layers(TBLs),namely Type-A,-B and-C TBL,based on the distribution patterns of the time-averaged wall-shear stress.Among these types,Type-A TBL and its related law formulations were investigated in terms of the analytical velocity profiles independent on Reynolds number(Re).These formulations were benchmarked by the DNS data of turbulence on a zero-pressure-gradient flat-plate(ZPGFP).With reference to the analysis from von Karman in developing the traditional law-of-the-wall,the current study first physically distinguished the time-averaged local scale used by von Karman from the time-space-averaged scale defined in the current paper,and then derived the governing equations with the Re—independency under the time-space-averaged scales.Based on the indicator function(IDF)and TBL thickness,the sublayer partitions were quantitatively defined.The analytical formulations for entire ZPGFP TBL were derived,including the formula in the inner,buffer,semi-logarithmic(semi-log)and wake layers.The research profoundly understood the damping phenomenon and its controlling mechanism in the TBL with its associated mathematical expressions,namely the damping function under both linear and logarithmic coordinates.Based on these understandings and the quantified TBL partitions,the analytical formulations for the entire ZPGFP TBL were established and were further proved being uniform and consistent under both the time-averaged local and the time-space-averaged scales.Comparing to the traditional law,these formulations were validated by the existing DNS data with more accuracy and wider applicability.The findings advance the current understandings of the conventional TBL theory and its well-known foundation of law-of-the-wall.展开更多
In this paper,we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress.Specifically,with a theoretic...In this paper,we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress.Specifically,with a theoretical or empirical relation of the total stress,the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region[h〇,h\].The formulas are validated using direct numerical simulation data of turbulent channel and boundary layer flows,and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than 2%.The present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near-wall statistics are very difficult to measure accurately.展开更多
Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physic...Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physical mechanism of the stretch and compression of multi-scale vortex structures in the wall-bounded turbulence, the topological characteristics of turbulence statistics in logarithmic layer were illustrated by local-averaged velocity structure function. During coherent structures bursting, results reveal that the topological structures of velocity gradients, velocity strain rates and vorticities behave as antisymmetric quadrupole modes. A three-layer antisymmetric quadrupole vortex packet confirms that there is a tight relationship between the outer layer and the near-wall layer.展开更多
In order to manipulate the large-scale coherent structures in the wall-bounded turbulence and reduce the skin-friction,an active-control experimental investigation is performed by using the synchronous and asynchronou...In order to manipulate the large-scale coherent structures in the wall-bounded turbulence and reduce the skin-friction,an active-control experimental investigation is performed by using the synchronous and asynchronous vibrations of double piezoelectric vibrators embedded spanwisely on a smooth flat plate surface.A TSI-IFA300 hot-wire anemometer and a TSI-1621 A-Tl.5 hot-wire probe are used to measure the time series of the instantaneous velocity at different locations.The influences of the vibrations on the wall-bounded turbulence are compared in a multi-scale point of view.A disturbance Reynolds Number Red=pd2 f/μis introduced to represent the disturbance.A probability density functions(PDFs)of the multi-scale components of the turbulence velocity and the multi-scale conditional phase-averaged waveform are studied in detail using the wavelet transform.The results show that the maximum drag reduction rate 18.54%is obtained at 100 V/160 Hz and Red=0.54 in the asynchronous vibration mode.The disturbances generated by the vibrators have a significant influence on the sweep events of the burst.The asynchronous vibration model is more effective than the synchronous vibration one.A possible physical mechanism is suggested to explain why the disturbance frequency of 160 Hz leads to an optimal parameter set for the drag reduction.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 p展开更多
Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical vortex-representation notion.This work focuses on the effectiveness of the local identification criteria in the vor...Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical vortex-representation notion.This work focuses on the effectiveness of the local identification criteria in the vortex representation of wall-bounded turbulence.Basically,five local identification criteria regarding vortex strength and three criteria for vortex axis are considered.Instead of separately evaluating the two classes of criteria,the current work defines vortex vectors by arbitrarily combining the vortex strength and vortex axis expressed by various criteria,and attempts to figure out the most effective one regarding the vortex representation.The effectiveness of these vortex vectors is evaluated based on two aspects:first,the alignment of the vortex axis and vortex iso-surface should be well established,which benefits the simplification of the vortex filaments;second,vortices could be viewed as the"gene code"of turbulent flows,which means reconstructing the velocity fields based on them should be effective.For the first aspect,the differential geometry method is employed to describe the vortex isosurface-axis alignment property quantitatively.For the second aspect,the Biot-Savart law is employed to accomplish the vortex-to-velocity reconstruction.Results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.展开更多
基金supported by the Research Grants Council(RGC)of the Government of Hong Kong Special Administrative Region(HKSAR)with RGC/ECS Project(Grant No.26200222)RGC/GRF Project(Grant No.16201023)+3 种基金RGC/STG Project(Grant No.STG2/E-605/23-N)Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011779)Guangdong Province Science and Technology Plan Project(Grant No.2023A0505030005)Center for Ocean Research in Hong Kong and Macao,a joint research center between Laoshan Laboratory and HKUST,and the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone(Grant No.HZQBKCZYB-2020083).
基金supported by the National Natural Science Foundation of China(Grant Nos.92152101,and 92152301)。
文摘In an endeavor to establish a connection between the mean velocity profile in compressible wall-bounded turbulence and its incompressible analogue,a refined version of the Trettel and Larsson's(TL)transformation is systematically derived and rigorously assessed across diverse flow scenarios.Incorporating the recently proposed intrinsic compressibility effects and modeling the multi-layer structure of mixing lengths,the proposed transformation demonstrates exceptional performance in collapsing 57canonical flow cases,including cooled channel and pipe flows,channel flows with pseudo heat sources,as well as adiabatic and diabatic boundary layer flows.Furthermore,the transformation seamlessly extends to low Reynolds number cooled channel and pipe flows,achieving a level of accuracy unparalleled by other transformations in the current state-of-the-art.
基金fund from the Research Grants Coun-cil(RGC)of the Government of Hong Kong Special Administra-tive Region(HKSAR)with RGC/ECS Project(No.26200222)the fund from Guangdong Basic and Applied Basic Research Foundation(No.2022A1515011779)the fund from the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooper-ation Zone(No.HZQB-KCZYB-2020083)。
文摘This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows.It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold.Regarding the vortex orientation,the inclination angle remains similar.However,as the wall-normal distance increases,a more and more obvious distinction is noticed for its orientation with respect to the spanwise(z)direction.It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification,i.e.,vortices rotating in the−z direction for the total velocity field and in the z direction for the fluctuating one.These observations function as a reasonable explanation for various remarks in previous studies.
基金the National Natural Science Foundation of China(91434112)the United Innovation Program of Shanghai Commercial Aircraft Engine(AR908)the Shanghai Thousand Talents Program(EZH2126503).
文摘Based on direct numerical simulation (DNS) data of the straight ducts,namely square and rectangular annular ducts,detailed analyses were conducted for the mean streamwise velocity,relevant velocity scales,and turbulence statistics.It is concluded that turbulent boundary layers (TBL) should be broadly classified into three types (Type-A,-B,and-C) in terms of their distribution patterns of the time-averaged local wall-shear stress (τw) or the mean local frictional velocity (uτ).With reference to the Type-A TBL analysis by von Karman in developing the law-of-the-wall using the time-averaged local frictional velocity (uτ) as scale,the current study extended the approach to the Type-B TBL and obtained the analytical expressions for streamwise velocity in the inner-layer using ensemble-averaged frictional velocity (ūτ) as scale.These analytical formulae were formed by introducing the general damping and enhancing functions.Further,the research applied a near-wall DNS-guided integration to the governing equations of Type-B TBL and quantitatively proved the correctness and accuracy of the inner-layer analytical expressions for this type.
基金supported by the National Natural Science Foundation of China (Grants 11302238, 11232011, 11572331, and 11490551)the support from the Strategic Priority Research Program (Grant XDB22040104)+1 种基金the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant QYZDJ-SSW-SYS002)the National Basic Research Program of China (973 Program 2013CB834100 : Nonlinear Science)
文摘The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence. The spectra are calculated from direct numerical simulation （DNS） of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the nearwall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number Rer can be as low as 1000. The properties of the inner and outer peaks in the spanwise spec- tra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number, which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity.
基金The work was supported by the Talent Recruiting Program at Fudan University(Grant No.EZH2126503)。
文摘In-depth analyses of existing direct numerical simulations(DNS)data led to a logical and important classification of generic turbulent boundary layers(TBLs),namely Type-A,-B and-C TBL,based on the distribution patterns of the time-averaged wall-shear stress.Among these types,Type-A TBL and its related law formulations were investigated in terms of the analytical velocity profiles independent on Reynolds number(Re).These formulations were benchmarked by the DNS data of turbulence on a zero-pressure-gradient flat-plate(ZPGFP).With reference to the analysis from von Karman in developing the traditional law-of-the-wall,the current study first physically distinguished the time-averaged local scale used by von Karman from the time-space-averaged scale defined in the current paper,and then derived the governing equations with the Re—independency under the time-space-averaged scales.Based on the indicator function(IDF)and TBL thickness,the sublayer partitions were quantitatively defined.The analytical formulations for entire ZPGFP TBL were derived,including the formula in the inner,buffer,semi-logarithmic(semi-log)and wake layers.The research profoundly understood the damping phenomenon and its controlling mechanism in the TBL with its associated mathematical expressions,namely the damping function under both linear and logarithmic coordinates.Based on these understandings and the quantified TBL partitions,the analytical formulations for the entire ZPGFP TBL were established and were further proved being uniform and consistent under both the time-averaged local and the time-space-averaged scales.Comparing to the traditional law,these formulations were validated by the existing DNS data with more accuracy and wider applicability.The findings advance the current understandings of the conventional TBL theory and its well-known foundation of law-of-the-wall.
基金The works of Xia and Zhang were supported by the National Natural Science Foundation of China(Grants 11822208,11772297,and 91852205)the Fundamental Research Funds for the central Universities.
文摘In this paper,we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress.Specifically,with a theoretical or empirical relation of the total stress,the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region[h〇,h\].The formulas are validated using direct numerical simulation data of turbulent channel and boundary layer flows,and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than 2%.The present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near-wall statistics are very difficult to measure accurately.
基金supported by the National Natural Science Fundation of China (11272233)National Basic Research Program (973 Program) (2012CB720101)2013 Opening Fund of LNM,Institute of Mechanics,Chinese Academy of Sciences
文摘Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physical mechanism of the stretch and compression of multi-scale vortex structures in the wall-bounded turbulence, the topological characteristics of turbulence statistics in logarithmic layer were illustrated by local-averaged velocity structure function. During coherent structures bursting, results reveal that the topological structures of velocity gradients, velocity strain rates and vorticities behave as antisymmetric quadrupole modes. A three-layer antisymmetric quadrupole vortex packet confirms that there is a tight relationship between the outer layer and the near-wall layer.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11732010,11972251,11872272,11902218 and 11802195).
文摘In order to manipulate the large-scale coherent structures in the wall-bounded turbulence and reduce the skin-friction,an active-control experimental investigation is performed by using the synchronous and asynchronous vibrations of double piezoelectric vibrators embedded spanwisely on a smooth flat plate surface.A TSI-IFA300 hot-wire anemometer and a TSI-1621 A-Tl.5 hot-wire probe are used to measure the time series of the instantaneous velocity at different locations.The influences of the vibrations on the wall-bounded turbulence are compared in a multi-scale point of view.A disturbance Reynolds Number Red=pd2 f/μis introduced to represent the disturbance.A probability density functions(PDFs)of the multi-scale components of the turbulence velocity and the multi-scale conditional phase-averaged waveform are studied in detail using the wavelet transform.The results show that the maximum drag reduction rate 18.54%is obtained at 100 V/160 Hz and Red=0.54 in the asynchronous vibration mode.The disturbances generated by the vibrators have a significant influence on the sweep events of the burst.The asynchronous vibration model is more effective than the synchronous vibration one.A possible physical mechanism is suggested to explain why the disturbance frequency of 160 Hz leads to an optimal parameter set for the drag reduction.
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 p
基金the National Natural Science Foundation of China(Grant Nos.11902371 and 91852204)China Postdoctoral Science Foundation(Grant No.2019M653172).
文摘Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical vortex-representation notion.This work focuses on the effectiveness of the local identification criteria in the vortex representation of wall-bounded turbulence.Basically,five local identification criteria regarding vortex strength and three criteria for vortex axis are considered.Instead of separately evaluating the two classes of criteria,the current work defines vortex vectors by arbitrarily combining the vortex strength and vortex axis expressed by various criteria,and attempts to figure out the most effective one regarding the vortex representation.The effectiveness of these vortex vectors is evaluated based on two aspects:first,the alignment of the vortex axis and vortex iso-surface should be well established,which benefits the simplification of the vortex filaments;second,vortices could be viewed as the"gene code"of turbulent flows,which means reconstructing the velocity fields based on them should be effective.For the first aspect,the differential geometry method is employed to describe the vortex isosurface-axis alignment property quantitatively.For the second aspect,the Biot-Savart law is employed to accomplish the vortex-to-velocity reconstruction.Results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.
