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Application of mean age distribution method

in mixing design optimization

Thanh Tinh Tran1*

, Hye Kyeong Jang1, Wook Ryol Hwang

1

1School of Mechanical & Aerospace Engineering, Gyeongsang National University,Jinju 660-701, Gyeongnam, South Korea

*Corresponding author. Email: trantt@gnu.ac.kr

Abstract: The numerous applications of mixing can be found in chemical, cosmetic,pharmaceutical and food industries. The mixing efficiency is a key target that needs to be

carefully considered when a mixing system is designed. This study will present the application of

mean age distribution method in mixing design optimization.

In order to estimate the efficiency of a mixing system, the residence-time [1] of a tracer hasbeen widely used in numerous studies. But this method just gives the mean residence time of a

tracer at the outlet, and provides no information of spatial distribution inside the computational

domain. Another limitation of this method is time-dependent which takes more computational

time.

Base on the transport equation for the tracer species , Liu & Tilton (2010) [2] introduce thetransport or conservation equation for mean age

[ ( )]

where the mean age is defined by

; and , , are the turbulent momentumdiffusivity, turbulent Schmidt number and molecular diffusivity, respectively. The transport

equation of mean age is in the same conservation form as the steady transport equation for

momentum, so can be solved as a scalar with the same CFD solver. Due to steady transportequation, this mean age distribution (MAD) method also has lower computational cost than the

residence time method.

Having an inlet and an outlet (even though very small value of mass flow rate) is the priority

requirement of MAD method. The boundary conditions for mean age are: at inlet; and at wall or outlet.

The MAD method is implemented in ANSYS Fluent V14.5 by using the User-Defined

Function [3]. A 2D stirred vessel with dimensions is considered for the testcase as showed in figure 1. The artificialimpeller, which is imposed a profile velocity, has a

diameter , and a clearance from the bottom. The turbulentmodel is used in this study.

The figures 3 & 4 show that MAD contour is not same as velocity field. The left side closes to

the inlet, so has small value of mean age; while the right side contains high value of mean age,

especially inside the circulation. The area-weighted probability density function of MAD infigure 2 gives more inside information of mean age: the left and right peaks correspond to the

left and right sides of vessel, respectively.

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MAD is successfully installed in ANSYS Fluent and excellent in unveiling the closed

circulations or the deadzones which are needed to eliminate in the design optimization. This

technique has large potential for numerous applications not only in mixing industries, but also inmaterial process and the other fluidic devices.

Key words: Mean Age Distribution, tracer species, mixing, design optimization

Figure 1: Configuration & mesh Figure 2: Probability density function of MAD

Figure 3: Velocity field Figure 4: Contour of MAD (blue color: 0 to 18800)

ACKNOWLEDMENT

This work has been supported by the National Research Foundation of Korea (NRF-2013R1A1A2A100057693) funded by the Ministry of Education and by Support Program forCommercialization of R&D Outcomes (2013A000023) funded by the Ministry of Science, ICT andFuture Planning.

REFERENCES

[1] Danckwerts P.V. Continuous flow systems Distribution of residence times. Chem. Eng. Sci.1953, 2:1-13.[2] Liu M. and Tilton J.N. Spatial distributions of mean age and higher moments in steady continuous flows.

AIChE J.2010, 56: 2561-2572.

[3] ANSYS Fluent UDF Manual V14.5, 2012.

inlet outlet