Numerical Simulation of Condensation Heat Transfer and Structural Optimization in Dryer of Paper Machine

Numerical Simulation of Condensation Heat Transfer and Structural Optimization in Dryer of Paper Machine

Mingliang-Zheng

^1†

Received June 22, 2020; Received in revised form August 3, 2020; Accepted August 5, 2020

ABSTRACT

In order to improve the heat transfer efficiency of the multi-channel dryer, based on the Navier-Stokes equations and the standard two equation kinetic-ε (epsilon) turbulent model, the Volume of Fluid model in fluent software was used to simulate the two-phase flow field of the condensation heat transfer in a micro-channel of dryer, the structural optimization and the influence of process parameters on the uniformity of temperature distribution were analyzed. The results showed that the saturated water vapor began to condense and release heat when it entered the channel, and with the flow of water vapor in the channel, the channel surface presented a certain range of temperature distribution, the condensate converged at the bottom of the channel and the liquid film gradually thickened along the channel. In general, the heat transfer coefficient of the multi- channel dryer is high, and the temperature difference between the inlet and outlet of the channel can be reduced by the reverse convection heat transfer in the multi-channel dryer with double inlet, the relationship between the speed of dryer and the average condensation heat transfer coefficient shows an increasing trend of slope decreasing.

Keywords: Multi-channel dryer, numerical simulation, condensation heat transfer, structural optimization

Printed in Korea http://dx.doi.org/10.7584/JKTAPPI.2020.08.52.4.20

1 School of Electrical and Mechanical Engineering, Taihu University of Wuxi, Wuxi, 214064, China, Lecturer

† Corresponding Author: E-mail: [email protected] (Address: School of Electrical and Mechanical Engineering, Taihu University of Wuxi, Wuxi, 214064, China)

1. Introduction

In the paper-making process, the drying section has the largest energy consumption,

¹⁾

and the dryer is the key equipment of the drying section, whose heat transfer performance plays a decisive role in

the energy consumption of the whole drying sec-

tion. In order to overcome the poor drainage of

condensate water in traditional dryer, the multi-

channel dryer

^2-4)

through many microchannels to

increase the heat transfer area and provide the

outflow channel, which can improve the heat

transfer efficiency to a certain extent. The con- densation heat transfer of forced flow in the multi-channel dryer is the key thermophysical process of drying, whose heat transfer coefficient is affected by the law of gas-liquid two-phase flow of steam condensation. Therefore, the analysis of heat flow field in the dryer channel is of great value to the deep understanding of the essence of condensation.

Because of the heavy workload and high cost of the experimental method to determine the conden- sation heat transfer of the dryer, the CFD (compu- tational fluid dynamics)

⁵⁾

simulation method can quickly obtain the detailed and quantitative analysis of the influence of structural parameters on the heat transfer and resistance performance. Shin et al.

⁶⁾

studied the flow and heat transfer characteris- tics of steam condensation in a single horizontal channel of a multi-channel dryer, and found that the condensation heat transfer coefficient was best when the height width ratio was 1 :3; Dong and Zhang

⁷⁾

and Chang et al.

⁸⁾

used fluent to explore the flow characteristics in a multi-channel dryer, and studied the influence of gas-phase and liquid- phase conversion rate on the two phase flow pat- tern; Zhang

⁹⁾

found the pressure drop was the smallest when the flow pattern was annular flow or annular mist flow; Lu

¹⁰⁾

found that the average condensation heat transfer coefficient was the largest when the height width ratio was 1:1; Yan et

al.

^11,12)

carried out the numerical simulation on the

condensation heat transfer and structural param- eters, and found that the two-phase flow pattern was consistent with the Tandon diagram, and the increase of steam mass flow rate would weaken the effect of height width ratio on condensation heat transfer. However, there were few reports about the condensation heat transfer of multi-channel dryer considering the speed, and the rotation state was the actual working condition of the dryer, which was an important process parameter of heat

transfer. Therefore, in order to improve the heat transfer efficiency of the dryer, this paper used FLUENT software to carry out the three-dimen- sional flow simulation, structural optimization and rotation effect analysis for microchannel of dryer.

Specifically, we use gambit function of FLUENT to create geometric model and mesh, then the VOF model in fluent software is used to simulate the two-phase flow field of the condensation heat transfer, finally, we get the distribution laws of temperature, velocity and liquid volume.

2. Physical Model, Mesh Division and Calculation Method of Dryer

2.1 Physical model and mesh division

The structure of the multi-channel dryer used in the calculation was shown in Fig. 1. Because of the symmetrical distribution and the structure and properties of each channel were the same, so their heat transfer characteristics should be similar and we could study the flow field distribution of a channel to predict the overall performance. Taking the diameter, length and thickness of gray cast iron dryer were Φ800 mm×1,200 mm×30 mm, considering the rotating condition, the size of a

Fig. 1. Structure of multi-channel drying cylinder.

channel was shown in Table 1. Gambit software was used to create geometric model and divide grid. In order to ensure the calculation accuracy, the hexahedral structured grid division and local encryption were adopted. The number of grids was 756,000, the grid division was shown in Fig. 2. The steam was along the Z axis to flow, the origin was on the Z axis and 900 mm away from the steam channel.

2.2 System dynamics model

It was considered that the condensation flow of dryer was a three-dimensional compressible unsteady two-phase turbulence (gas and liquid) under rotation. Any fluid flow follows the Navier Stokes basic equations, for multiphase flow, VOF model

¹³⁾

has been widely used to trace the phase interface in numerical simulation of two-phase flow process. Its control equations include:

(1) Continuity equations



  

  

  

 

   

t u x

v y

w

z 0 [1]

Here u, v, w are the velocity components of veloc- ity vector on axis, ρ is fluid density. 

V

(2) Momentum equations



     

 



  

( )

( ) ( )

( )

( )

  

 

u

t div uV div gradu p x S v

t div vV d

u

 

 iiv gradv p y S w

t div wV div gradw p z

( )

v

( )

( ) ( )



 



  

  

 



     

  SS

S F

w

l

l v





 





 



 



   

 

^v

0 5 . ( )

[2]

Here μ is viscosity coefficient, p is microelement pressure, S

u

, S

v

, S

w

are the components of general- ized source items caused by volume force and viscous force, κ is surface curvature, α

l

is liquid surface tension coefficient, F

v

is volume fraction of gas phase, ρ

l

is liquid density, ρ

v

is vapor density.

(3) Temperature equation



    

( )

( ) ( )

 C T 

t

^p

div C TV div k gradT Q

p T

 g  [3]

Here k is turbulent kinetic energy, g is gravita- tional acceleration, C

p

is specific heat at constant pressure, and Q

T

is condensation heat per unit vol- ume.

(4) k-ε equations



  

  

  

 

  



 

( ) ( )

[( ) ]

( )

    







k t

k

x x

k x

G G Y

t

i

i i

t

k i

k b M



  

  

 

 







( )

[( ) ]

( )

  





  

i

i i

t

k i

s k s b s

x x x

K k G G G K k

1 3 2

2

 





 

 

[4]

S 

Table 1. Main dimensions

Name Length (mm) Width (mm) Height (mm)

Steam channel 1,000 13.5 4.5

Dryer wall 1,000 13.5 1

Cooling water channel 1,000 13.5 15.5

Fig. 2. Grid generation of model.

Here ε is dissipation rate, μ

t

is turbulent viscosity coefficient, G

k

is velocity turbulent kinetic energy, G

b

is buoyancy turbulent kinetic energy, Y

M

is pul- sating expansion, K is dissipation coefficient, and σ is turbulent Prandtl number.

(5) VOF equation



   



  

  

F

t div FV m

m

F T T T T T F T T

T T T

l l e

l

e

l l

s s

g g s

s

( ) ,

,

,



 

 



s

ss



 



 

[5]

Here m

e

is condensation quality source term, F

l

is volume fraction of liquid phase, and F

l

+ F

v

=1, β is adjustment coefficient, T

s

is steam saturation tem- perature.

2.3 Boundary condition setting and calculation method

The steam inlet boundary used the mass flow rate, the coolant inlet boundary used the mass flow, and their outlet boundary used the pressure.

The initial inlet mass flow rate of water vapor was 30 kg/(m

²

·s), the initial inlet mass flow of cooling water was 0.062 kg/s, the turbulence intensity was 5%, the initial outlet pressure was 0 Pa, and the steam saturation temperature was 120℃. The physical parameters of water vapor and cooling water could be directly selected in the material library of FLUENT software. Turning on fram- emotion and setting the corresponding rotation speed of the channel. In the VOF model, the implicit body force option was enabled in order to improve the convergence of calculation. The solver was set to double precision and unsteady state. The VOR equation was in HRIC

⁵⁾

format, the PISO

⁵⁾

algorithm was used for the coupling of pressure and velocity, the Gauss order-reduction algorithm was used for the parameters gradient in cell, the

body forced weight algorithm was used for the spatial discretization of pressure, the second order upwind algorithm was used for the discretization of momentum equations, energy equation, turbulent kinetic energy and turbulent dissipation equations.

3. Numerical Simulation Results

3.1 Temperature distribution

When the speed was 50 r/min, the temperature distribution is as shown in Fig. 3. The channel surface had a temperature distribution field with high temperature at the inlet, low temperature at the outlet and continuous change of temperature in the middle part. When the water vapor at the outlet, there was a certain temperature difference in whole channel, which indicated the steam con- denses and exotherms in the channel.

3.2 Velocity distribution

When the speed was 50 r/min, the velocity distri- bution was as shown in Fig. 4. The velocity of the channel middle part (section center) was higher, and the velocity decreased gradually from the middle part to the wall. The difference of flow velocity distribution is mainly caused by pressure drop. The bottom of left side and the top of right side in Fig. 4 are not 90 degree, which are caused

Fig. 3. The overall temperature distribution.

by the turbulence of steam and condensate. The top and bottom thickness of orange color are thicker both sides in Fig. 4, which are caused by the pressure drop along the channel wall is gentle and along the center of channel is volatile.

3.3 Liquid (condensate) volume distribution

When the speed was 50 r/min and the simulation time was 10 s, the condensate of wall distribution was as shown in Fig. 5. Due to gravity, the con- densate converged at the bottom of the channel.

Along the direction of steam flow, the amount of condensation gradually increased, and the liquid film gradually thickened, but relative to the chan- nel width, the liquid film was still very thin.

All told, through the condensation heat transfer in a microchannel with one-way injecting, the temperature in the whole channel was still high especially the paper was wide, the energy was not fully utilized, the temperature distribution from the inlet to the outlet was in a range of variation, and the liquid film with a certain thickness distri-

bution, which would lead to serious temperature heterogeneity on the surface of dryer and affected the paper quality.

4. Structural Optimization

In order to further improve the temperature uni- formity and heat transfer performance of the dryer, one-way injecting was changed to two-way injecting, as shown in Fig. 6. In the improved multi-channel dryer, the outer shell was matched with the inner cylinder to form a gas-liquid two- phase flow channel. The steam entered the channel along both two-way driven by subsequent high-pressure steam, then the steam started con- densing to form a gas-liquid two-phase flow. The condensate entered the outlet pipe through the ponding ring at the end to outflow dryer.

The size of optimized channel was designed as 1,000 mm×6.75 mm×4.5 mm×2. The grid gen- eration was in Fig. 7. The initial and boundary Fig. 4. The velocity distribution of inlet and outlet.

(a) Inlet (b) Outlet

Fig. 5. Liquid volume distribution.

conditions were the same as above. When the speed was 50 r/min, the temperature distribution was as shown in Fig. 8. Comparing the results of Fig. 8 and Fig. 3, the deviation of surface tempera- ture in Fig. 8 is (451-343=208K), the deviation of surface temperature in Fig. 3 is (451-303=248K), so the multichannel dryer with two-way injecting could effectively improve the uniformity of sur- face temperature. Because of the two-way inject- ing, the high temperature steam entered to two inlets. On the one hand, the steam heat was

transmitted to the outer surface of the dryer to dry the wet paper; on the other hand, the con- vection heat transfer was formed in the two channels, which greatly reduced the uneven heat transfer on the surface of the dryer. Comparing with one-way injecting, there was still a tem- perature difference between the inlet and the outlet, but the temperature difference could be reduced due to the countercurrent operation of the two channels.

In order to discuss the influence of key process 1. Intake pipe, 2. Cylinder head at working side, 3. Shell of drying cylinder, 4. Inner

cylinder of drying cylinder, 5. Cylinder head at operating side, 6. Hydrosphere, 7. Water outlet pipe

Fig. 6. Exploded view of two-way injecting vapor into multi-port dryer.

Fig. 7. Grid generation of optimized structure. Fig. 8. The overall temperature distribution of

optimized structure.

parameters on condensation heat transfer effi- ciency, we introduced the average condensation heat transfer coefficient

¹⁴⁾

:

h  A T T





(

_{steam wall}

) [6]

Here Φ is heat exchange of channel, T

steam

is inlet temperature, T

wall

is wall temperature, A is heat transfer area.

In order to study the influence of speed on the condensation heat transfer characteristics, fixing the other parameters unchanged, setting the speed was 23, 32, 39, 45 and 50 r/min for numerical simulation of the optimized channel. The relation- ship between the average condensation heat transfer coefficient and the speed was shown in Fig. 9. The average condensation heat transfer coefficient increased with the increase of the speed, however, the slope was smaller and smaller, which was caused by the relative balance between the liquid film thickness and the turbulence intensity.

The speed was increased, the turbulence was strengthened, and the heat transfer coefficient was increased, but the liquid film thickness was increased, so the increase of the average conden- sation heat transfer coefficient was limited. There-

fore, simply increasing the “speed” was not the best measure to improve the heat transfer perfor- mance of the dryer. We should comprehensively select the optimal process parameters according to the resource consumption.

5. Conclusions

Based on the numerical simulation of the con- densation heat transfer flow field in a microchannel of the paper machine dryer, the volume fraction, temperature and velocity distribution of the two- phase flow in the channel were known. The main results were as follows:

(1) Under a certain steam flow rate, the liquid film was obviously affected by gravity in a microchannel of dryer, and more was distrib- uted in the bottom; the outer wall temperature of the dryer at the inlet was high, which decreased gradually along the direction of steam flow, but the temperature at the outlet was still high.

(2) After using the structure optimization with two-way injecting, the steam formed a con- vection heat transfer model in two channels, which greatly reduced the uneven heat trans- fer on the surface of the dryer.

(3) The condensation heat transfer coefficient of the multi-channel dryer with two-way injecting increased with the increase of dryer speed, but the slope was smaller and smaller, and it would remain stable eventually, which was determined by the film thickness and turbulence intensity.

Further, we could continue to study the specific influence of more structure and process parameters on the heat transfer performance, and carry out the design and application of the multi-channel dryer with high-performance.

Fig. 9. Effect of rotating speed on average

condensation heat transfer coefficient.

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