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[ Article ]  
Journal of Korea Technical Association of the Pulp and Paper Industry  Vol. 52, No. 4, pp.2027  
Abbreviation: J. Korea TAPPI  
ISSN: 02533200 (Print)  
Print publication date 30 Aug 2020  
Received 22 Jun 2020 Revised 03 Aug 2020 Accepted 05 Aug 2020  
DOI: https://doi.org/10.7584/JKTAPPI.2020.08.52.4.20  
Numerical Simulation of Condensation Heat Transfer and Structural Optimization in Dryer of Paper Machine  
Mingliang Zheng^{†}
 
1School of Electrical and Mechanical Engineering, Taihu University of Wuxi, Wuxi, 214064, Lecturer, China  
Correspondence to : † Email: zhmlwxcstu@163.com (Address: School of Electrical and Mechanical Engineering, Taihu University of Wuxi, Wuxi, 214064, China)  
In order to improve the heat transfer efficiency of the multichannel dryer, based on the NavierStokes equations and the standard two equation kineticε (epsilon) turbulent model, the Volume of Fluid model in fluent software was used to simulate the twophase flow field of the condensation heat transfer in a microchannel 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 multichannel 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 multichannel 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: Multichannel dryer, numerical simulation, condensation heat transfer, structural optimization 
In the papermaking 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 section. In order to overcome the poor drainage of condensate water in traditional dryer, the multichannel dryer^{24)} 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 condensation heat transfer of forced flow in the multichannel dryer is the key thermophysical process of drying, whose heat transfer coefficient is affected by the law of gasliquid twophase 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 condensation heat transfer of the dryer, the CFD (computational 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 characteristics of steam condensation in a single horizontal channel of a multichannel 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 multichannel dryer, and studied the influence of gasphase and liquidphase conversion rate on the two phase flow pattern; 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 parameters, and found that the twophase 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 multichannel 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 threedimensional 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 twophase flow field of the condensation heat transfer, finally, we get the distribution laws of temperature, velocity and liquid volume.
The structure of the multichannel 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 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.
Name  Length (mm)  Width (mm)  Height (mm) 

Cooling water channel  1,000  13.5  15.5 
It was considered that the condensation flow of dryer was a threedimensional compressible unsteady twophase 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 twophase flow process. Its control equations include:
(1) Continuity equations
[1] 
Here u, v, w are the velocity components of velocity vector
(2) Momentum equations
[2] 
Here μ is viscosity coefficient, p is microelement pressure, S_{u}, S_{v}, S_{w} are the components of generalized source items
(3) Temperature equation
[3] 
Here k is turbulent kinetic energy, g is gravitational acceleration, C_{p} is specific heat at constant pressure, and Q_{T} is condensation heat per unit volume.
(4) kε equations
[4] 
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 pulsating expansion, K is dissipation coefficient, and σ is turbulent Prandtl number.
(5) VOF equation
[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 temperature.
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 framemotion 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 orderreduction 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.
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 condenses and exotherms in the channel.
When the speed was 50 r/min, the velocity distribution 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 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.
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 condensate 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 channel width, the liquid film was still very thin.
All told, through the condensation heat transfer in a microchannel with oneway 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 distribution, which would lead to serious temperature heterogeneity on the surface of dryer and affected the paper quality.
In order to further improve the temperature uniformity and heat transfer performance of the dryer, oneway injecting was changed to twoway injecting, as shown in Fig. 6. In the improved multichannel dryer, the outer shell was matched with the inner cylinder to form a gasliquid twophase flow channel. The steam entered the channel along both twoway driven by subsequent highpressure steam, then the steam started condensing to form a gasliquid twophase flow. The condensate entered the outlet pipe through the ponding ring at the end to outflow dryer.
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
The size of optimized channel was designed as 1,000 mm×6.75 mm×4.5 mm×2. The grid generation was in Fig. 7. The initial and boundary 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 temperature in Fig. 8 is (451343=208K), the deviation of surface temperature in Fig. 3 is (451303=248K), so the multichannel dryer with twoway injecting could effectively improve the uniformity of surface temperature. Because of the twoway injecting, 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 convection heat transfer was formed in the two channels, which greatly reduced the uneven heat transfer on the surface of the dryer. Comparing with oneway injecting, there was still a temperature 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 parameters on condensation heat transfer efficiency, we introduced the average condensation heat transfer coefficient^{14)}:
[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 relationship 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 condensation heat transfer coefficient was limited. Therefore, simply increasing the “speed” was not the best measure to improve the heat transfer performance of the dryer. We should comprehensively select the optimal process parameters according to the resource consumption.
Based on the numerical simulation of the condensation heat transfer flow field in a microchannel of the paper machine dryer, the volume fraction, temperature and velocity distribution of the twophase flow in the channel were known. The main results were as follows:
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 multichannel dryer with highperformance.
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