scholarly journals A bimodal temom model for particle Brownian coagulation in the continuum-slip regime

2016 ◽  
Vol 20 (3) ◽  
pp. 927-932
Author(s):  
Qing He ◽  
Jin Li ◽  
Tingting Kong ◽  
Mingliang Xie
Keyword(s):  
Asymptotic Behavior ◽  
Series Expansion ◽  
Correction Factor ◽  
Taylor Series ◽  
Volume Fraction ◽  
Taylor Series Expansion ◽  
Number Concentration ◽  
Brownian Coagulation ◽  
Slip Regime ◽  
The Continuum

In this paper, a bimodal Taylor-series expansion moment of method is proposed to deal with Brownian coagulation in the continuum-slip regime, where the non-linear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that both the number concentration and volume fraction decrease with time in the smaller mode due to the intra and inter coagulation, and the asymptotic behavior of the larger mode is as same as that in the continuum regime.

scholarly journals An improved particle population balance equation in the continuum-slip regime

2016 ◽  
Vol 20 (3) ◽  
pp. 921-926 ◽  
Author(s):  
Mingliang Xie ◽  
Jin Li ◽  
Tingting Kong ◽  
Qing He
Keyword(s):  
Asymptotic Behavior ◽  
Correction Factor ◽  
Balance Equation ◽  
Present Model ◽  
Population Balance ◽  
Population Balance Equation ◽  
Brownian Coagulation ◽  
Slip Regime ◽  
Particle Population ◽  
The Continuum

An improved moment model is proposed to solve the population balance equation for Brownian coagulation in the continuum-slip regime, and it reduces to a known one in open literature when the non-linear terms in the slip correction factor are ignored. The present model shows same asymptotic behavior as that in the continuum regime.

scholarly journals Steady-state solutions for particles undergoing Brownian coagulation and breakage by the TEMOM model

2018 ◽  
Vol 22 (4) ◽  
pp. 1595-1600
Author(s):  
Qing He ◽  
Jiang Lin
Keyword(s):  
Particle Size ◽  
Steady State ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Equal Size ◽  
Steady State Distribution ◽  
State Distribution ◽  
Brownian Coagulation ◽  
Steady State Solutions

When coagulation and breakage proceed simultaneously, a steady-state distribution may exist due to the opposite effects on particle size. In this paper, a moment model using Taylor-series expansion technology for particles undergoing Brownian coagulation and equal size multiple breakage is proposed, then the steady-state solutions of this model are obtained.

scholarly journals The asymptotic stability of the Taylor-series expansion method of moment model for Brownian coagulation

2018 ◽  
Vol 22 (4) ◽  
pp. 1651-1657
Author(s):  
Mingliang Xie ◽  
Tingting Kong ◽  
Jin Li ◽  
Jiang Lin
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Perturbation Equation ◽  
Method Of Moment ◽  
Brownian Coagulation ◽  
Asymptotic Stable ◽  
The Stability ◽  
Series Expansion Method

In the present study, the linear stability of population balance equation due to Brownian motion is analyzed with the Taylor-series expansion method of moment. Under certain conditions, the stability of the Taylor-series expansion method of moment model is reduced to a well-studied problem involving eigenvalues of matrices. Based on the principle of dimensional analysis, the perturbation equation is solved asymptotically. The results show that the Taylor-series expansion method of moment model is asymptotic stable, which implies that the asymptotic solution is uniqueness, and supports the self-preserving size distribution hypothesis theoretically.

scholarly journals High concentration Brownian coagulation in jet flow using two enhancement formulations

2012 ◽  
Vol 16 (5) ◽  
pp. 1519-1523
Author(s):  
Pei-Feng Lin ◽  
Di-Chong Wu ◽  
Ze-Fei Zhu
Keyword(s):  
Volume Fraction ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
High Volume ◽  
Jet Flow ◽  
High Concentration ◽  
Brownian Coagulation ◽  
Planar Jet ◽  
Ultra Fine Particle ◽  
The One

Ultra-fine particle coagulation by Brownian motion at high concentration in planar jet flow is simulated. A Taylor-Series Expansion Method of Moments is employed to solve the particle general dynamic equation. The volume fraction gets high value, very closes to that at the nozzle exit. As the vortex pairing develops, the high volume fraction region rolls out and mixes with the low value region. The enhancement factor given by Trzeciak et al. will be less than one at some specific outer positions, which seems to be less accurate than the one given by Heine et al.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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