The motivation of this study is to investigate the turbulence-chemistry interactions by using probability density function （PDF） method. A consistent hybrid Reynolds Averaged Navier-Stokes （RANS）/PDF method is use...The motivation of this study is to investigate the turbulence-chemistry interactions by using probability density function （PDF） method. A consistent hybrid Reynolds Averaged Navier-Stokes （RANS）/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity-frequency-composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo （MC） method combined with the finite volume （FV） method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models.展开更多
The present study aims at the investigation of the effects of turbulence-chemistry interaction on combus- tion instabilities using a probability density function （PDF） method. The instantaneous quantities in the flo...The present study aims at the investigation of the effects of turbulence-chemistry interaction on combus- tion instabilities using a probability density function （PDF） method. The instantaneous quantities in the flow field were decomposed into the Favre-averaged variables and the stochastic fluctuations, which were calculated by unsteady Reynolds averaged Navier-Stokes （U-RANS） equations and the PDF model, respectively. A joint fluctuating velocity- frequency-composition PDF was used. The governing equa- tions are solved by a consistent hybrid finite volume/Monte- Carlo algorithm on triangular unstructured meshes. A non- reacting flow behind a triangular-shaped bluff body flame stabilizer in a rectilinear combustor was simulated by the present method. The results demonstrate the capability of the present method to capture the large-scale coherent struc- tures. The triple decomposition was performed, by divid- ing the coherent Favre-averaged velocity into time-averaged value and periodical coherent part, to analyze the coherent and incoherent contributions to Reynolds stresses. A sim- ple modification to the coefficients in the turbulent frequency model will help to improve the simulation results. Unsteady flow fields were depicted by streamlines and vorticity con- tours. Moreover, the association between turbulence produc- tion and vorticity saddle points is illustrated.展开更多
对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针...对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针对受高斯白噪声激励的非线性随机系统,将福克-普朗克-柯尔莫哥洛夫(Fokker-PlanckKolmogrov, FPK)方程作为研究工具,提出一种基于多高斯闭合法(MGC)的PDF控制方法。首先,根据目标PDF的形状构造一个由多个高斯型PDF相叠加的PDF;然后,构造一个优化问题,使得该PDF逼近目标PDF;进一步,通过求解FPK方程得到被控系统的状态方程;最后,结合原始状态方程求得控制函数,实现对目标PDF的追踪控制。针对不同类型目标PDF进行的仿真结果表明了所提出方法的可行性和有效性。展开更多
为了研究LHCb 7 TeV W+、W-和Z实验数据对CT14HERA2部分子分布函数(Parton Distribution Functions,PDFs)的影响,首先将收集到的数据进行了理论预测并将其和实验测量结果进行了比较,在误差允许的范围内理论和实验符合的很好。其次,用误...为了研究LHCb 7 TeV W+、W-和Z实验数据对CT14HERA2部分子分布函数(Parton Distribution Functions,PDFs)的影响,首先将收集到的数据进行了理论预测并将其和实验测量结果进行了比较,在误差允许的范围内理论和实验符合的很好。其次,用误差PDFs更新软件包(Error PDFs Updated Method Package,EPUMP)更新了CT14HERA2 PDFs,并和全局拟合的PDFs进行了比较。最后,加入协方差矩阵后的实验数据可以在较大和较小的x区域减少d(x,Q)/u(x,Q)误差,同时也对CT14HERA2 PDFs进行了优化。验证结果表明,LHCb 7 TeV W+、W-和Z产生的实验数据在较大的x区域对g(x,Q)、d(x,Q)、d(x,Q)/u(x,Q)、d(x,Q)/u(x,Q)、u(x,Q)、d(x,Q)和u(x,Q)PDFs的中心值约束较大,可以用前4个误差PDFs代替原来全局拟合或优化后得到的56个误差集。展开更多
Based on the maximunl-entropy （ME） principle, a new power spectral estimator for random waves is derived in the form of S（ω）=a/8H^2^-（2π）^（d＋2）exp[-b（2π/ω）^n],1）y solving a variational problem subject ...Based on the maximunl-entropy （ME） principle, a new power spectral estimator for random waves is derived in the form of S（ω）=a/8H^2^-（2π）^（d＋2）exp[-b（2π/ω）^n],1）y solving a variational problem subject to some quite general constraints. This robust method is comprehensive enough to describe the wave spectra even in extreme wave conditions and is superior to periodogranl method that is not suit＇able to process comparatively short or intensively unsteady signals for its tremendous boundary effect and some inherent defects of FKF. Fortunately, the newly derived method for spectral estimation works fairly well, even though the sample data sets are very short and unsteady, and the reliability and efficiency of this spectral estimator have been preliminarily proved.展开更多
In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochas...In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker Planck Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.展开更多
The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real...The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.展开更多
输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫...输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫项的一维Burgers方程出发推导一个精确的单点速度PDF输运方程,并分别用两个模型封闭该方程中的条件对流项和条件扩散项,获得模化PDF输运方程。然后分别用基于网格的Monte Carlo随机粒子法、原始积分矩法和文章发展的线性积分矩法等3种数值解法求解模化PDF输运方程。数值实验表明,所发展的输运概率密度函数方法可用于研究B.urgers湍流的统计特性。3种数值解法中,线性积分矩法和原始积分矩法均可获得和直接数值模拟相似的结果,且线性积分矩法比原始积分矩法的计算效率更高。Monte Carlo方法的计算结果在带随机外力项的Burgers方程算例中不太理想,这或许和该方法为保持单位网格内颗粒数不变而频繁地增删粒子从而引入数值扰动有关。展开更多
基金The project supported by the National Natural Science Foundation of China (50506028)Action Scheme for Invigorating Education Towards the twenty-first century
文摘The motivation of this study is to investigate the turbulence-chemistry interactions by using probability density function （PDF） method. A consistent hybrid Reynolds Averaged Navier-Stokes （RANS）/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity-frequency-composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo （MC） method combined with the finite volume （FV） method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models.
基金supported by the National Natural Science Foundation of China (50936005)the Fundamental Research Fundsfor the Central Universities (WK2090130008,WK2090130011)
文摘The present study aims at the investigation of the effects of turbulence-chemistry interaction on combus- tion instabilities using a probability density function （PDF） method. The instantaneous quantities in the flow field were decomposed into the Favre-averaged variables and the stochastic fluctuations, which were calculated by unsteady Reynolds averaged Navier-Stokes （U-RANS） equations and the PDF model, respectively. A joint fluctuating velocity- frequency-composition PDF was used. The governing equa- tions are solved by a consistent hybrid finite volume/Monte- Carlo algorithm on triangular unstructured meshes. A non- reacting flow behind a triangular-shaped bluff body flame stabilizer in a rectilinear combustor was simulated by the present method. The results demonstrate the capability of the present method to capture the large-scale coherent struc- tures. The triple decomposition was performed, by divid- ing the coherent Favre-averaged velocity into time-averaged value and periodical coherent part, to analyze the coherent and incoherent contributions to Reynolds stresses. A sim- ple modification to the coefficients in the turbulent frequency model will help to improve the simulation results. Unsteady flow fields were depicted by streamlines and vorticity con- tours. Moreover, the association between turbulence produc- tion and vorticity saddle points is illustrated.
文摘对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针对受高斯白噪声激励的非线性随机系统,将福克-普朗克-柯尔莫哥洛夫(Fokker-PlanckKolmogrov, FPK)方程作为研究工具,提出一种基于多高斯闭合法(MGC)的PDF控制方法。首先,根据目标PDF的形状构造一个由多个高斯型PDF相叠加的PDF;然后,构造一个优化问题,使得该PDF逼近目标PDF;进一步,通过求解FPK方程得到被控系统的状态方程;最后,结合原始状态方程求得控制函数,实现对目标PDF的追踪控制。针对不同类型目标PDF进行的仿真结果表明了所提出方法的可行性和有效性。
文摘为了研究LHCb 7 TeV W+、W-和Z实验数据对CT14HERA2部分子分布函数(Parton Distribution Functions,PDFs)的影响,首先将收集到的数据进行了理论预测并将其和实验测量结果进行了比较,在误差允许的范围内理论和实验符合的很好。其次,用误差PDFs更新软件包(Error PDFs Updated Method Package,EPUMP)更新了CT14HERA2 PDFs,并和全局拟合的PDFs进行了比较。最后,加入协方差矩阵后的实验数据可以在较大和较小的x区域减少d(x,Q)/u(x,Q)误差,同时也对CT14HERA2 PDFs进行了优化。验证结果表明,LHCb 7 TeV W+、W-和Z产生的实验数据在较大的x区域对g(x,Q)、d(x,Q)、d(x,Q)/u(x,Q)、d(x,Q)/u(x,Q)、u(x,Q)、d(x,Q)和u(x,Q)PDFs的中心值约束较大,可以用前4个误差PDFs代替原来全局拟合或优化后得到的56个误差集。
基金This research was financially supported by the National Natural Science Foundation of China(Grant No.50479028)a Research Fundfor Doctoral Programs of Higher Education of China(Grant No.20060423009)
文摘Based on the maximunl-entropy （ME） principle, a new power spectral estimator for random waves is derived in the form of S（ω）=a/8H^2^-（2π）^（d＋2）exp[-b（2π/ω）^n],1）y solving a variational problem subject to some quite general constraints. This robust method is comprehensive enough to describe the wave spectra even in extreme wave conditions and is superior to periodogranl method that is not suit＇able to process comparatively short or intensively unsteady signals for its tremendous boundary effect and some inherent defects of FKF. Fortunately, the newly derived method for spectral estimation works fairly well, even though the sample data sets are very short and unsteady, and the reliability and efficiency of this spectral estimator have been preliminarily proved.
文摘In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE), therefore the Fokker Planck Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity of the SDE, the type of δ correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China(Nos.11172233,11302169,11302170,and 11472212)the Fundamental Research Funds for the Central Universities(No.3102014JCQ01079)
文摘The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.
文摘输运概率密度函数(transported probability density function,TPDF)方法在湍流燃烧模拟中颇受重视,其优势是可以精确处理方程中的非线性化学源项。将这种方法应用于由一维随机Burgers方程控制的Burgers湍流。首先,从带非线性随机强迫项的一维Burgers方程出发推导一个精确的单点速度PDF输运方程,并分别用两个模型封闭该方程中的条件对流项和条件扩散项,获得模化PDF输运方程。然后分别用基于网格的Monte Carlo随机粒子法、原始积分矩法和文章发展的线性积分矩法等3种数值解法求解模化PDF输运方程。数值实验表明,所发展的输运概率密度函数方法可用于研究B.urgers湍流的统计特性。3种数值解法中,线性积分矩法和原始积分矩法均可获得和直接数值模拟相似的结果,且线性积分矩法比原始积分矩法的计算效率更高。Monte Carlo方法的计算结果在带随机外力项的Burgers方程算例中不太理想,这或许和该方法为保持单位网格内颗粒数不变而频繁地增删粒子从而引入数值扰动有关。
