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Numerical Simulation of Volatile Organic Compounds during Condensation in a Vertical Tube^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Physical Model

_{z}is very small relative to R (Figure 1). At the entrance of the tube, comes a flow of vapor-air mixture with a uniform temperature T

_{in}, uniform pressure P

_{in}and vapor mass fraction W

_{in}. The wall of the tube is cooled by convective in contact with an external fluid (air) at temperature T

_{e}.

- The flow of the gas mixture is laminar and stationary.
- The flows are two-dimensional and ax symmetric.
- The radiation and effects of Duffour and Soret are negligible.
- The boundary layer approximations are valid for both phases.
- The gas mixture is considered perfect gas.
- The liquid-vapor interface is mobile, without wave, in local thermodynamic equilibrium and impermeable to dry air.
- The effect of the liquid superficial tension is negligible.

## 3. Equations

#### 3.1. Liquid Phae

#### 3.2. Gas Phase

#### 3.3. Boundary Conditions and Interface

- Condition at the tube inlet (z = 0)

- Condition at the wall of the tube (r = R):

- Condition at the central axis of the tube (r = 0):

- Condition at the liquid-vapor interface ($r=R-{\delta}_{z}$)

#### 3.4. Numerical Resolution

## 4. Presentation of Results

#### 4.1. Effect of Temperature Difference ΔT

_{in}= 1 atm, Re

_{in}= 2000, ${W}_{in}^{n-bu\mathrm{tan}ol}=0.05,{\mathrm{W}}_{\mathrm{in}}^{\mathrm{propanol}}=0.25$ and ΔT is varied in the range [25 °C–35 °C].

_{bulk}for different deviations ΔT, the increase of this temperature difference decreases the cooling external temperature, and consequently a decrease of mixture temperature along the tube. This finding is well indicated in Figure 3 which shows the variation of the Nusselt number along the tube. At the tube inlet, it is noted that the heat transfer is higher when the temperature difference is large, then it decreases and becomes independent of the ΔT at the end of condensation

_{in}− T

_{e}on the bulk mass fraction W

_{bulk}is shown in Figure 4. At the tube inlet, it is noted that the bulk mass fraction for each compound retains its input value, and then decreases with the increasing of this temperature difference along the tube because of the vapor condensation.

_{in}− T

_{e}signifies a decrease in external fluid cooling temperature T

_{e}which causes an increase in the amount of condensed vapor away from the entrance, and consequently a greater thickness.

_{bulk}= 0.25 to 0.024 i.e., a decrease in mass fraction of 91% against 0.05 to 0.0093 i.e., with a decrease in mass fraction of 85% for the n-butanol vapor.

#### 4.2. Effect of Reynolds Number Re_{in}

_{in}= 1 atm.

_{bulk}and the local Nusselt number N

_{uz}for the ternary mixture (n-butanol propanol-air). It is noted that the temperature and the local Nusselt number of the mixture increase with the Reynolds number because the transfers between the vapor-air mixture and the liquid-vapor interface increase with the convection.

_{bulk}and the liquid film thickness δ

_{z}. It is found that the increase in the Reynolds number increases the mixture fraction of the two vapors, this is explained by the fact that the convective transfers in the vapor phase increase with the speed at which the steam mixture flows towards the vapor interface (Figure 9) which favors the increase of the condensed mass and consequently a thicker liquid film (Figure 10).

## 5. Conclusions

- Transfers are more intense at the entrance of the tube for the ternary mixture and promote heat and mass exchanges resulting in a large number of Nusselt which will gradually decrease to the exit where the curve meets at the end of condensation.
- The Nusselt number, the condensation rate and the film thickness increase with the temperature difference ΔT = T
_{in}− T_{e} - The increase in the Reynolds number at the inlet leads to an increase in the liquid film thickness, the Nusselt number and a decrease in the condensation rate.

## References

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**MDPI and ACS Style**

Hammami, Y.E.; Zine-Dine, K.; Mir, R.; Midiouni, T.; Hssain, M.A.
Numerical Simulation of Volatile Organic Compounds during Condensation in a Vertical Tube. *Proceedings* **2019**, *38*, 21.
https://doi.org/10.3390/proceedings2019038021

**AMA Style**

Hammami YE, Zine-Dine K, Mir R, Midiouni T, Hssain MA.
Numerical Simulation of Volatile Organic Compounds during Condensation in a Vertical Tube. *Proceedings*. 2019; 38(1):21.
https://doi.org/10.3390/proceedings2019038021

**Chicago/Turabian Style**

Hammami, Youness El, Kaoutar Zine-Dine, Rachid Mir, Touria Midiouni, and Mustapha Ait Hssain.
2019. "Numerical Simulation of Volatile Organic Compounds during Condensation in a Vertical Tube" *Proceedings* 38, no. 1: 21.
https://doi.org/10.3390/proceedings2019038021