Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finel...Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.展开更多
The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time ...The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time Shan–Chen model is built to study the cavitation bubble collapse. Using this model, the cavitation phenomena induced by density perturbation are simulated to obtain the coexistence densities at certain temperature and to demonstrate the Young–Laplace equation. Then, the cavitation bubble collapse near a curved rigid wall and the consequent high-speed jet towards the wall are simulated. Moreover, the influences of initial pressure difference and bubble-wall distance on the cavitation bubble collapse are investigated.展开更多
Fresh cement mortar is a type of workable paste, which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering. In this paper, Papanastasiou＇s model for Bingham fluids...Fresh cement mortar is a type of workable paste, which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering. In this paper, Papanastasiou＇s model for Bingham fluids is solved by using the multiple- relaxation-time lattice Boltzmann model （MRT-LB）. Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou＇s model provides a good approximation of realistic Bingham plastics for values of m 〉 108. For lower values of m, Papanastasiou＇s model is valid for fluids between Bingham and Newtonian fluids. The MRT-LB model is validated by two benchmark problems： 2D steady Poiseuille flows and lid-driven cavity flows. Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability. We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle. Besides the rich flow structures obtained in this work, the dynamics fhi d force on the round particle is calculated. Results show that both the Reynolds number Re and the Bingham number Bn affect the drag coefficients Co, and a drag coefficient with Re and Bn being taken into account is proposed. The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed. Finally, the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields. These results help simulation of fresh concrete flowing in porous media.展开更多
In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of t...In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time （SRT） LBE model （Guo and Zhao in Phys Rev E 68：035302, 2003）. The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen （SC） model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.展开更多
In the paper we extend the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model pro- posed in [Europhys. Lctt., 2010, 90： 54003] so that it is suitable also for incompressible flows. To decrease tile artif...In the paper we extend the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model pro- posed in [Europhys. Lctt., 2010, 90： 54003] so that it is suitable also for incompressible flows. To decrease tile artificial oscillations, the convection term is discretized by the flux linfiter scheme with splitting technique. A new model is validated by some well-known benchmark tests, including Rie- mann problem and Couette flow, and satisfying agreements are obtained between the sinmlation results and ana.lytical ones. In order to show the merit of LB model over traditional methods, the non-equilibrium characteristics of system are solved. The simulation results are consistent with the physical analysis.展开更多
Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still sub...Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.展开更多
CO_(2) absorption into absorbents is a widely used method to reduce carbon emissions,in which the concentration gradient near the gas-liquid interface may induce Rayleigh convection(RC).Once RC occurs,the mass transfe...CO_(2) absorption into absorbents is a widely used method to reduce carbon emissions,in which the concentration gradient near the gas-liquid interface may induce Rayleigh convection(RC).Once RC occurs,the mass transfer rate will be significantly enhanced.Therefore,it is necessary to explore the mass transfer enhancement mechanism further and develop a penetration/surface divergence hybrid mass transfer model.In this study,we conduct research on the process of CO_(2) absorption into ethanol with RC.Firstly,we use a multi-relaxation time lattice Boltzmann method to simulate the absorption process and obtain the flow and concentration fields.And we also verify the reliability of the numerical simulation results by comparing with the experimental results.Then,we analyze the characteristics of non-uniform flow and concentration fields in RC.Moreover,we divide the near-interface region into diffusion-dominated and convection-dominated mass transfer zones by checking whether the horizontal average velocity is greater than 1.0×10^(-4) m·s^(-1).Furthermore,based on the differences in mass transfer mechanisms of the aforementioned two zones,we propose a penetration/surface divergence hybrid model to predict the instantaneous mass transfer coefficient.The prediction results demonstrate that the hybrid model can precisely predict the instantaneous mass transfer coefficient of the entire CO_(2) absorption process.Our proposed hybrid model provides a promising way to deal with the complex mass transfer problems with non-uniform flow and concentration fields.展开更多
In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limit...In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.展开更多
The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattic...The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and the Reynolds and Richardson numbers. temperature patterns change greatly with variations of展开更多
This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked co...This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked compressible fluids,a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system.The unnecessity of the modification for systems under strong shock is analyzed.The model is validated by some well-known benchmark tests,including thermal Couette flow,Riemann problem.The first system is unshocked and the latter is shocked.In both systems,the Prandtl number effects are checked.Satisfying agreements are obtained between new model results and analytical ones.展开更多
The two-dimensional Rayleigh-Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed fr...The two-dimensional Rayleigh-Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin-Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.展开更多
This present paper proposes aerodynamic forces and entropy generation characteristics on theflow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theflo...This present paper proposes aerodynamic forces and entropy generation characteristics on theflow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theflow loss mechanism.The block mesh refinement was adopted in which a higher accuracy was needed in parts of the domain characterized by complexflow.The interpolated bounce-back method was used to treat the irregular curve.This numerical method can effectively solve the complexflowfield simulation problems with reasonable accuracy and reli-ability by simulatingflow around plate and airfoil.Based on second law of thermo-dynamics,an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of theflowfield at any position.After that,a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 air-foil as the research object.For unsteady condition,entropy generation rate and the drag force are not linearly related any more.Losses due to steady effects mainly con-sider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shed-ding vortex.展开更多
基金This work is supported in part by the National Natural Science Foundation of China(U19B6003-04-01,42204132,41874130)R&D Department of CNPC(2022DQ0604-01)China Postdoctoral Science Foundation(2020M680667,2021T140661).
文摘Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11674173,81627802,11474161,11374155 and 11474001the Qing Lan Project
文摘The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time Shan–Chen model is built to study the cavitation bubble collapse. Using this model, the cavitation phenomena induced by density perturbation are simulated to obtain the coexistence densities at certain temperature and to demonstrate the Young–Laplace equation. Then, the cavitation bubble collapse near a curved rigid wall and the consequent high-speed jet towards the wall are simulated. Moreover, the influences of initial pressure difference and bubble-wall distance on the cavitation bubble collapse are investigated.
基金supported by the National Key Basic Research Program of China(Grant No.2010CB731504)the Natural Science Foundation of China(Grant Nos.11034010,11272048 and 51239006)+1 种基金European Commission Marie Curie Actions(Grant No.IRSES-294976)the State Key Laboratory of Hydroscience and Engineering(Grant No.2013-KY-2)
文摘Fresh cement mortar is a type of workable paste, which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering. In this paper, Papanastasiou＇s model for Bingham fluids is solved by using the multiple- relaxation-time lattice Boltzmann model （MRT-LB）. Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou＇s model provides a good approximation of realistic Bingham plastics for values of m 〉 108. For lower values of m, Papanastasiou＇s model is valid for fluids between Bingham and Newtonian fluids. The MRT-LB model is validated by two benchmark problems： 2D steady Poiseuille flows and lid-driven cavity flows. Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability. We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle. Besides the rich flow structures obtained in this work, the dynamics fhi d force on the round particle is calculated. Results show that both the Reynolds number Re and the Bingham number Bn affect the drag coefficients Co, and a drag coefficient with Re and Bn being taken into account is proposed. The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed. Finally, the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields. These results help simulation of fresh concrete flowing in porous media.
基金This work was financially supported by the National Natural Science Foundation of China （51125024） and the National Basic Research Programme of China （2011CB707305）.
文摘In this paper, a lattice Boltzmann equation （LBE） model with multiple-relaxation-time （MRT） colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time （SRT） LBE model （Guo and Zhao in Phys Rev E 68：035302, 2003）. The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen （SC） model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.
基金The authors would like to sincerely thank S. Succi and C. Lin for many instructive discussions. We acknowl- edge support of National Natural Science Foundation of China （under Grant Nos. 11075021 and 11047020）. A. G. Xu and G. C. Zhang acknowledge support of the Science Foundation of CAEP （Grant Nos. 2012B0101014 and 2011A0201002） and the Founda- tion of State Key Laboratory of Explosion Science and Technology （Grant No. KFJJ14-1M）.
文摘In the paper we extend the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model pro- posed in [Europhys. Lctt., 2010, 90： 54003] so that it is suitable also for incompressible flows. To decrease tile artificial oscillations, the convection term is discretized by the flux linfiter scheme with splitting technique. A new model is validated by some well-known benchmark tests, including Rie- mann problem and Couette flow, and satisfying agreements are obtained between the sinmlation results and ana.lytical ones. In order to show the merit of LB model over traditional methods, the non-equilibrium characteristics of system are solved. The simulation results are consistent with the physical analysis.
基金supported by the National Natural Science Foundation of China(NSFC,Grant Numbers 10572106,10872153 and 11172219)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110013).
文摘Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.
基金the financial support of the National Natural Science Foundation of China(21706182)。
文摘CO_(2) absorption into absorbents is a widely used method to reduce carbon emissions,in which the concentration gradient near the gas-liquid interface may induce Rayleigh convection(RC).Once RC occurs,the mass transfer rate will be significantly enhanced.Therefore,it is necessary to explore the mass transfer enhancement mechanism further and develop a penetration/surface divergence hybrid mass transfer model.In this study,we conduct research on the process of CO_(2) absorption into ethanol with RC.Firstly,we use a multi-relaxation time lattice Boltzmann method to simulate the absorption process and obtain the flow and concentration fields.And we also verify the reliability of the numerical simulation results by comparing with the experimental results.Then,we analyze the characteristics of non-uniform flow and concentration fields in RC.Moreover,we divide the near-interface region into diffusion-dominated and convection-dominated mass transfer zones by checking whether the horizontal average velocity is greater than 1.0×10^(-4) m·s^(-1).Furthermore,based on the differences in mass transfer mechanisms of the aforementioned two zones,we propose a penetration/surface divergence hybrid model to predict the instantaneous mass transfer coefficient.The prediction results demonstrate that the hybrid model can precisely predict the instantaneous mass transfer coefficient of the entire CO_(2) absorption process.Our proposed hybrid model provides a promising way to deal with the complex mass transfer problems with non-uniform flow and concentration fields.
基金Supported by the Science Foundation of Laboratory of Computational Physics, Science Foundation of China Academy of Engineering Physics under Grant Nos. 2009A0102005, 2009B0101012National Basic Research Program of China under Grant No. 2007CB815105+1 种基金National Natural Science Foundation of China under Grant Nos. 11074300, 11075021, and 11074303the Fundamental Research Funds for the Central Universities under Grant No. 2010YS03
文摘In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann （LB） model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 60773195 and 51006040
文摘The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and the Reynolds and Richardson numbers. temperature patterns change greatly with variations of
文摘This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked compressible fluids,a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system.The unnecessity of the modification for systems under strong shock is analyzed.The model is validated by some well-known benchmark tests,including thermal Couette flow,Riemann problem.The first system is unshocked and the latter is shocked.In both systems,the Prandtl number effects are checked.Satisfying agreements are obtained between new model results and analytical ones.
文摘The two-dimensional Rayleigh-Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin-Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.
基金The authors gratefully acknowledge the support by the National Key R&D Program of China(No.2018YFB0606101)Thanks to SCTS/CGCL HPCC of HUST for providing computing resources and technical support.
文摘This present paper proposes aerodynamic forces and entropy generation characteristics on theflow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify theflow loss mechanism.The block mesh refinement was adopted in which a higher accuracy was needed in parts of the domain characterized by complexflow.The interpolated bounce-back method was used to treat the irregular curve.This numerical method can effectively solve the complexflowfield simulation problems with reasonable accuracy and reli-ability by simulatingflow around plate and airfoil.Based on second law of thermo-dynamics,an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of theflowfield at any position.After that,a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 air-foil as the research object.For unsteady condition,entropy generation rate and the drag force are not linearly related any more.Losses due to steady effects mainly con-sider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shed-ding vortex.
