Generalized TEMOM Scheme for Solving the Population Balance Equation

Yu, Mingzhou; Liu, Yueyan; Lin, Jianzhong; Seipenbusch, Martin

doi:10.1080/02786826.2015.1093598

Cited by 28 publications

(28 citation statements)

References 47 publications

(104 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In previous studies (Xie and He 2014;Yu et al 2015c), it has been revealed that different approximations of collision kernel using the same order of Taylor series and the same expansion point are almost equivalent. Therefore, the error of collision kernel expanded in part in the original TEMOM (Yu et al 2008) is equivalent to that of the collision kernel expanded as a whole (Chen et al 2014).…”

Section: ½26mentioning

confidence: 99%

“…Based on the above analysis, the system error of TEMOM model is where L is a constant, which can be regarded as the maximum of the third derivative of Chen et al 2014;Yu et al 2015c). Since M 0 , M 1 , M 2 , and u are calculated accurately, the key point of error estimation is how to calculate the third order particle moment M 3 and the third derivative of collision kernel.…”

Section: System Error Of Temom Modelmentioning

confidence: 99%

See 1 more Smart Citation

Error estimation of TEMOM for Brownian coagulation

Xie

2016

Aerosol Science and Technology

View full text Add to dashboard Cite

In the present study, the error estimation of Taylor series expansion method of moment (TEMOM) for particle population balance equation due to Brownian coagulation is proposed. The approximation introduced by Taylor series polynomials has two parts: one is the approximation of nonlinear collision kernel, and the other is the approximation of higher and fractional particle moment. The results show that the two kinds of errors have the same order in the original TEMOM model, which is related to the third derivative of collision kernel and the first four integer order particle moments, i.e., M 0 , M 1 , M 2 , and M 3 . Based on the lognormal size distribution assumption, the system errors are obtained for different TEMOM models due to Brownian coagulation; and all the errors are small and acceptable. The results have confirmed the validity of TEMOM model. EDITORNicole Riemer

show abstract

Section: ½26mentioning

confidence: 99%

Section: System Error Of Temom Modelmentioning

confidence: 99%

Error estimation of TEMOM for Brownian coagulation

Xie

2016

Aerosol Science and Technology

View full text Add to dashboard Cite

show abstract

“…This is accomplished using a Taylor-series expansion technique for the TEMOM by employing two methods. One method is obtaining the solution for the PBE by constructing a closure moment model; implicit moments are present in the converted equations, and they can be arbitrarily approximately substituted with closure functions, such as in Yu et al (2015). The second method is obtaining the PBE resolution by directly expanding (Chen et al 2014).…”

Section: Theorymentioning

confidence: 99%

An Efficient Algorithm Scheme for Implementing the TEMOM for Resolving Aerosol Dynamics

Liu

Koivisto

2017

Aerosol Sci Eng

Self Cite

View full text Add to dashboard Cite

This paper presents a new algorithm scheme for implementing the Taylor-series expansion method of moments (TEMOM), which is a general method for solving the population balance equation. Instead of deriving moment ordinary differential equations (ODEs) for particular aerosol dynamics, the new numerical algorithm develops a subroutine that corresponds to types of kernels of aerosol dynamics rather than a particular kernel. Consequently, the TEMOM can be conveniently applied to types of dynamics rather than a particular dynamics, and the derivation from the PBE to moment ODEs is avoided. A key aspect to the new algorithm scheme is that the particle kernels are written in a general form, allowing for a universal expression of aerosol dynamics. The closure of ODEs for moments was accomplished by implementing a new Taylor-series expansion closure function with two varying parameters H and /, which enables the TEMOM applicable to any type of moment sequence. The feasibility of the new algorithm scheme was verified by comparing it with other recognized methods for six classic aerosol dynamics. The new algorithm scheme makes the TEMOM much easier to be used for users as compared to its original version (Aerosol Sci Tech 49(2015):1021-1036). The idea of the algorithm scheme can be applied to other nonquadrature-based methods of moments.

show abstract

“…Although the geometric mean volume, ( m 1 2 /( m 0 3/2 m 1 1/2 ), seems more reasonable than the averaged volume, it cannot reach the expected level in the TEMOM. The theoretical analysis of selecting these two volumes as Taylor-series expansion points has been conducted in [29] and [30] , in which the averaged volume has been verified as a more precise measure. Although the highest order of moments in Eq.…”

Section: Mathematical Modelmentioning

confidence: 99%

A new analytical solution for agglomerate growth undergoing Brownian coagulation

Liu

Jin

et al. 2016

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWe proposed a new analytical solution for a population balance equation for fractal-like agglomerates. The new analytical solution applies to agglomerates with any mass fractal dimensions. Two well-known numerical methods, including the Taylor-series expansion method of moments and the quadrature method of moments, were selected as references. The reliability of the analytical solution with three mass fractal dimensions of 1.0, 2.0, and 3.0 in the continuum-slip regime was verified. The accuracy of the new analytical solution is affected by both the Knudsen number and the mass fractal dimension. The new analytical solution can be further improved in accuracy by introducing a correction factor to the originally derived mathematical formula. The new analytical solution was finally confirmed to possess potential for replacing the numerical solution in the continuum-slip regime.

show abstract

Generalized TEMOM Scheme for Solving the Population Balance Equation

Cited by 28 publications

References 47 publications

Error estimation of TEMOM for Brownian coagulation

Error estimation of TEMOM for Brownian coagulation

An Efficient Algorithm Scheme for Implementing the TEMOM for Resolving Aerosol Dynamics

A new analytical solution for agglomerate growth undergoing Brownian coagulation

Contact Info

Product

Resources

About