# Simulation of Vapor-Liquid Separation in the Orifice-Baffle Header under Various Operating Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

_{in}) is 12 g/s. The vapor leakage from the orifice because of the liquid impact is one of the main reasons that deteriorate the vapor-liquid separation performance. Moreover, the vortex in the header increases the local mass flux, thereafter decreasing the droplet diameter. With the increasing of ṁ

_{in}, the dominant force of the droplet in the vertical direction switches from F

_{G}to F

_{D2}.

## 1. Introduction

^{2}∙s), LSC has a higher heat transfer coefficient and 30.5–52.6% lower pressure drop, simultaneously. They further pinpointed that LSC has superior comprehensive performance in terms of penalty factor and minimum entropy generation number [5]. Li et al. [6] discovered that the condenser inserted with a T-junction unit can improve the heat transfer capacity by approximately 5.1%. At the level of the thermal systems, LSC also exhibits its advances in air conditioning systems, heat pump, and organic Rankine cycle (ORC). Chen et al. [7] found that the Energy Efficiency Ratio (EER) at cooling mode and Coefficient of Performance (COP) at heating mode in an air conditioning with LSC are 9.8% and 7.3% higher than these in baseline system, respectively. They further pointed out that using LSC can reduce avoidable exergy destruction of the compressor by 45.5% [8]. Li et al. [6] found that the refrigeration system with LSC results in a higher COP by 6.6% compared to a conventional condenser. Chen et al. [9] revealed that the heat pump with LSC has a higher COP and lower power consumption. Lu et al. [10] concluded that the ORC with LSC achieves a 21.43% lower average electricity production cost than conventional ORC. In short, liquid-separation condensation is a promising technology that enables the improvement of both the condenser performance and thermal system efficiency.

_{L}) can be 100% at low inlet mass flux, and it reduces with the increasing of the inlet mass flux or inlet quality. However, in the T-junction header, the liquid and vapor can only be separated one, which limited the improvement of HTC in LSC.

## 2. Model Description

#### 2.1. Computational Domain and Boundary Condition

_{1}, I

_{2}, I

_{3}, I

_{4}, B

_{1}, B

_{2}, and B

_{3}from top to bottom. Furthermore, the orifice is not assigned on the right side of the baffle to avoid the direct liquid impact. The boundary condition at the inlets and outlets are set as velocity inlet and pressure outlet, respectively. The velocity of each phase is calculated using the void fraction model proposed by EI Hajal et al. [18] and compiled by a user-defined function (UDF). The pressure difference between the branch outlet P

_{B}and the orifice P

_{O}approximately equals to the pressure drop in the next two paths of the LSC [17].

#### 2.2. Methematical Method

^{−5}s. The governing equations are discretized by the Finite Volume Method (FVM). Furthermore, the residuals through every time step iterations are all lower than 10

^{−4}. The discrete scheme and the under-relaxation factor as well as other details are found in our previous research [16].

#### 2.3. Mesh-Sensitive Test and Model Validation

_{L,O}) changes insignificantly. Hence, to balance the calculation consumption and the accuracy of the numerical model, the mesh number of 2.03 million is selected, in which the minimum orthogonal quality, the maximum ortho skew and the aspect ratio are 0.54, 0.43 and 2.53, respectively.

#### 2.4. Evaluation Indicator

_{L}) and the vapor leakage ratio (F

_{V}). F

_{L}is defined as the ratio of the liquid drainage from the orifice to the inlet, as shown in Equation (11). Similarly, F

_{V}is defined as Equation (12).

## 3. Results and Discussion

_{in}) are 45 °C and 0.5, respectively. To investigate its features under various conditions, the inlet mass flow rate (ṁ

_{in}) is set in the range of 9–21 g/s based on scenarios in the air conditioning.

#### 3.1. Performance of the Header and Flow Characteristics in the Orifices

_{in}is depicted in Figure 4. It can be observed that with the increasing of ṁ

_{in}, η increases firstly to the maximum value of 51.94% at ṁ

_{in}= 12 g/s and then decreases. When ṁ

_{in}is larger than 15 g/s, the degradation of η becomes severer. It becomes 29.99% at ṁ

_{in}= 21 g/s. This will be discussed in the following section. The pressure difference (ΔP) crossing the orifice-baffle, which is one of the main driving forces for the liquid drainage [16], increases with the increasing of ṁ

_{in}. This is because more liquid flows towards the right side of the orifice-baffle, leading to an increase in the height of the liquid film above the orifice-baffle. Thereafter, the static pressure above the orifice-baffle increases.

_{L,O}and ṁ

_{V,O,}are analyzed, as shown in Figure 5. As mentioned above, there exists a strong liquid impact at the right side of the baffle, O

_{2}, being the furthest away from the liquid impact, has a higher ṁ

_{L,O}than O

_{1}and O

_{3}. Different from η that is peaked at ṁ

_{in}= 12 g/s, the peak of ṁ

_{L,O}= 3.75 g/s appears at ṁ

_{in}= 15 g/s. This is explained as: compared to ṁ

_{in}= 12 g/s, ṁ

_{in}= 15 g/s has a higher ṁ

_{L,O}because of a larger driving force, but its F

_{L}is much smaller owing to the more liquid within ṁ

_{in}, leading to a lower η given that F

_{V}in these two cases are negligible (see Figure 5b). ṁ

_{L,O}maintains at around 3.30 g/s when ṁ

_{in}is 18 g/s and 21 g/s. Meanwhile, ṁ

_{V,O}weakens the vapor-liquid separation performance, derived from Equations (11) and (12). As seen in Figure 5b, ṁ

_{V,O}has an opposite trend to ṁ

_{L,O}. It decreases at first when ṁ

_{in}is smaller than 15 g/s and then increases to 0.15 g/s at ṁ

_{in}= 21 g/s. The vapor only leakage about 0.02 g/s and 0.01 g/s as ṁ

_{in}equals to 12 g/s and 15 g/s, respectively. This is due to the liquid film above the orifice-baffle in these two cases being able to resist the impact of the liquid flow from the wall, in which the orifices are rarely affected by the fluid impact and only a small amount of vapor leakage. Conversely, much vapor leakage out from the orifice under the other three ṁ

_{in}because of the unstable liquid film above the orifice-baffle. Moreover, the vapor is escaped out from O

_{2}is less than that from O

_{1}and O

_{3}owing to its farthest distance away from the liquid impact.

_{2}are significantly different from those in O

_{1}and O

_{3}. When ṁ

_{in}is between 9–15 g/s, the vapor velocity in O

_{2}is normally lower than 1.5 m/s and it mostly exists near the wall of the orifice. As ṁ

_{in}increases, the vapor with high velocity begins to appear in O

_{2}, which indicates more vapor leakage. This phenomenon is mainly due to the induced stronger liquid impact on the orifice-baffle at higher ṁ

_{in}. As a result, the liquid film above the orifice-baffle is unable to resist the liquid impact and meanwhile the interactions between the liquid and vapor becomes intensive, leading to the increasing of ṁ

_{V,O}. As for O

_{1}and O

_{3}that are closer to the liquid impact region, they are more likely to have a higher vapor velocity. As shown in Figure 6b, the velocity of the vapor in O

_{1}and O

_{3}can be up to 3 m/s as ṁ

_{in}= 9 g/s. However, with more liquid accumulated on the orifice-baffle (Figure 6c,d), the effect of the fluid impact on these two orifices weakens, with only a little vapor leakage out from the orifices. Further increasing ṁ

_{in}(Figure 6e,f), the liquid impact is enhanced again, contributing to a higher vapor velocity in O

_{1}and O

_{3}. Summarily, the effects of the liquid impact on the orifice are the competitions between the liquid film on the orifice-baffle and ṁ

_{in}. At the lower ṁ

_{in}, the liquid film is too thin to resist the liquid impact and, consequently, the vapor escapes from the orifices, whereas at the higher ṁ

_{in}, the interactions of the liquid and vapor are upgraded and the vapor is carried to the orifices by the liquid.

#### 3.2. Flow Characteristics in the Branch Outlet

_{B}and x

_{B}in the branch outlets are rather significant. The liquid mass flow rate in each branch outlet (ṁ

_{L,B}) increases with the increasing of ṁ

_{in}. Moreover, the liquid flows into the header and jets on the header wall of the header. A part of the liquid breaks up into droplets that are thereafter dragged into the branch outlets by the vapor, which is termed as “droplet entrainment”. A similar phenomenon was also found by Li [12] and Zheng [20]. Obviously, ṁ

_{L,B}in B

_{3}is remarkably higher than that in B

_{1}and B

_{2}. This is because the liquid flows to B

_{3}is not only by droplet entrainment, but also comes from the overflowing liquid from the orifice-baffle that cannot be drained promptly. However, the vapor in the branch outlet is more uniform than liquid owing to its lower inertia force. ṁ

_{V,B}in B

_{1}is slightly lower than B

_{2}and B

_{3}for the considered ṁ

_{in}.

_{4}and mixes in S

_{10}. Due to the inertia, the fluid gathers on the right side of the header and a vortex is generated on the left side, resulting in the vapor velocity on the left side being lower than that on the right side. After S

_{10}, the fluid continues to flow downwardly, and then a part of it is divided into the B

_{1}because of the suction of the branch outlet. The fluid is more accumulated at the lower part of B

_{1}due to the inertia (S

_{7}), in which the vortex exists above the B

_{1}and shows a vapor velocity non-uniform distribution. The other part of the fluid from I

_{4}that cannot enter B

_{1}in time will keep flowing in the header. In this way, the fluid also flows on the left side, resulting in a lower non-uniformity at S

_{11}. Similarly, the vapor velocity distribution in the next branch outlet (S

_{8}) and header (S

_{12}) are close to the S

_{7}and S

_{11}respectively. However, due to the diversion of the fluid, the vapor velocity decreases correspondingly. On the other hand, in the B

_{3}, the distribution of the vapor velocity is more uniform. This is mainly due to the fact that B

_{3}has a maximum mass flow rate than B

_{1}and B

_{2}, in which case the fluid can be fully fill at the B

_{3}, where there is no vortex generated. With the increase in ṁ

_{in}, not only does the velocity increase but it also improves the non-uniformity of the velocity distributions.

#### 3.3. Mechanism Model of Droplet

_{V,C}) is also proposed. The following assumptions are made for the droplets: (1) they are spherical; (2) they have the same diameter in the same branch outlet.

_{1}as an example, Figure 9 demonstrates d in the header and the vapor velocity in B

_{1}with and without vortex. It is observed that an increase in ṁ

_{in}leads to an enlarged droplet diameter and decreased vapor velocity simultaneously. In addition, the existence of the vortex decreases the droplet diameter by up to 1.76 times and increases the vapor velocity in the branch outlet by 35.10%, which significantly affects the forces of the droplet.

_{G}), the drag force (F

_{D2}) and the buoyancy force (F

_{B}) in the vertical direction as well as the drag force (F

_{D1}) in the axial direction. The details of these four forces are described in Appendix B. In these four forces, F

_{G}and F

_{B}are only dominated by d. Moreover d, the drag force (F

_{D1}and F

_{D2}) is also depended on the velocity. The higher mass flux represents the smaller droplet diameter. The drag force under different ṁ

_{in}is a result of the vapor velocity competing with d. As shown in Figure 11, the sum of forces in the vertical direction shows fluctuation with the increasing of ṁ

_{in}and the minimum value is 2.04 × 10

^{−4}N at ṁ

_{in}= 12 g/s, while the force in the axial increases monotonously. F

_{D1}and F

_{D2}increases with the increasing of ṁ

_{in}, which indicates the increasing rate of the velocity is larger than the decreasing rate of d. Meanwhile, F

_{G}and F

_{B}both decrease due to the droplet being smaller when increasing of ṁ

_{in}. F

_{G}at ṁ

_{in}= 21 g/s is only 1.02% to that at ṁ

_{in}= 12 g/s. Since F

_{G}and F

_{B}are only related to the density difference, F

_{G}is constantly 20.14 times higher than F

_{B}, which represents that in general, the force in the vertical upward is relatively small compared to the downward. Interestingly, the dominant force in the vertical direction switches from F

_{G}to F

_{D2}when ṁ

_{in}is higher than 12 g/s.

_{axial}and the vertical distance is the diameter of the branch outlet (d

_{B}), as shown in Figure 10. If the flowing time of droplet in the vertical direction t

_{vertical}is longer than that in the axial direction t

_{axial}, the droplet will be entrained to the branch outlet. Therefore, the critical point for the droplet entrainment is defined at t

_{vertical}= t

_{axial}. In this way, the critical vapor velocity (U

_{V,C}) required to entrain the droplet can be obtained when the droplet in the branch outlets is located in S

_{axial}, as calculated as in Equations (13)–(15).

_{V,C}is highly correlated to the velocity of both phases in the header, the vapor velocity in the branch and d U

_{V,C}at the different axial locations under various ṁ

_{in}is plotted in Figure 12. Clearly, the larger S

_{axial}requires a higher U

_{V,C}to entrain the droplet and the growth rate of the U

_{V,C}decreases as the S

_{axial}increases. Moreover, under the same axial location, for the droplet to be dragged to the branch outlet needs a higher U

_{V,C}when ṁ

_{in}is increased. This is mainly due to the smaller d at higher ṁ

_{in}, causing the larger acceleration and the shorter flow time t

_{vertical}in the vertical direction.

## 4. Conclusions

- (1)
- The vapor-liquid separation efficiency maintains superior at the inlet mass flow rate of 9–15 g/s and then deteriorated as beyond 15 g/s. The maximum η are 51.94% at the inlet mass flow rate of 12 g/s;
- (2)
- The liquid impact on the orifice-baffle results in the vapor leakage from the orifice. It becomes more intensive and is the main reason that deteriorates the separation performance when the inlet mass flow rate is higher than 15 g/s;
- (3)
- The liquid maldistribution in the branch outlets is mainly because of the overflowing in B
_{3}that can be up to 4.36 g/s at the inlet mass flow rate of 21 g/s, whereas the vapor is more uniform distribution in the branch outlets owing to its lower inertia; - (4)
- The vortex in the header causes a decrease in the droplet diameter and an increase in the vapor velocity significantly in the branch outlet. The dominant force of the droplet in the vertical direction changes from F
_{G}to F_{D2}as ṁ_{in}increases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | |

a_{vertical} | Acceleration in the vertical direction, m/s^{2} |

C_{d} | Drag force coefficient |

C_{1ε} | Empirical constants, 1.42 |

C_{2ε} | Empirical constants, 1.68 |

C_{μ} | Empirical constants, 0.0845 |

d | Diameter, mm |

F | Drainage (leakage) rate ratio |

F_{B} | Buoyancy force, N |

F_{D1} | Drag force (axial), N |

F_{D2} | Drag force (vertical), N |

F_{G} | Gravitational force, N |

f | The friction factor of the vapor |

G_{k} | Generation of turbulent kinetic energy |

g | Gravitational acceleration, m/s^{2} |

ṁ | Mass flow rate, kg/s |

ΔP | Pressure difference, Pa |

Re | Reynold number |

S_{axial} | Axial distance, m |

t | Time, s |

t_{vertical} | Droplet flow time in the vertical direction, s |

t_{axial} | Droplet flow time in the axial direction, s |

U | Velocity, m/s |

Greek Symbol | |

α | Volume fraction |

ε | Turbulence kinetic dissipation, m^{2}/s^{3} |

η | Vapor-liquid separation efficiency |

μ | Dynamic viscosity, kg/(m^{2}·s^{2}) |

μ_{t} | Turbulence kinetic viscosity, kg/(m^{2}·s^{2}) |

ρ | Density, kg/m^{3} |

σ | Surface tension coefficient N/m |

σ_{k} | Empirical constants, 1.0 |

σ_{ε} | Empirical constants, 1.2 |

Subscript | |

B | Branch outlet |

C | Critical |

H | Header |

in | Inlet |

L | Liquid |

O | Orifice outlet |

S | Supercritical |

V | Vapor |

## Appendix A

_{L,S}, U

_{V,S}, ρ

_{V}, f represents the surface tension surface tension, the supercritical velocity of liquid, the supercritical velocity of vapor, vapor density and the friction factor of the vapor.

## Appendix B

_{D1}), the gravitation force (F

_{G}), the buoyancy force (F

_{B}) and the drag force in the vertical direction (F

_{D2}). They are evaluated as follow:

_{V,H}, U

_{L,H}and U

_{V,B}represent the vapor velocity and the droplet velocity in the header and the vapor velocity in the branch outlet, respectively. d is the droplet diameter. C

_{d}is the drag force coefficient for the droplet, which is calculated by the classical model proposed by Schiller and Naumann [22], as shown in Equation (A9).

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**Figure 6.**(

**a**) Instructions and distributions of velocity and density in each orifice at (

**b**) 9 g/s, (

**c**) 12 g/s, (

**d**) 15 g/s, (

**e**) 18 g/s and (

**f**) 21 g/s.

Parameters | Equations | |
---|---|---|

Volume Fraction | $\frac{\partial}{\partial t}\left({\alpha}_{q}{\rho}_{q}\right)+\nabla \left({\alpha}_{q}{\rho}_{q}\overrightarrow{{u}_{q}}\right)=0$ | (1) |

${\alpha}_{\mathrm{L}}+{\alpha}_{\mathrm{V}}=1$ | (2) | |

Momentum | $\frac{\partial}{\partial t}\left(\rho \overrightarrow{u}\right)+\nabla \cdot \left(\rho \overrightarrow{u}\overrightarrow{u}\right)=-\nabla p+\nabla \cdot \left[\mu \left(\nabla \overrightarrow{u}+\nabla {\overrightarrow{u}}^{\mathrm{T}}\right)\right]+\rho \overrightarrow{g}+\overrightarrow{F}\mathsf{\sigma}$ | (3) |

Properties | $\rho ={\alpha}_{\mathrm{L}}{\rho}_{\mathrm{L}}+{\alpha}_{\mathrm{V}}{\rho}_{\mathrm{V}}$ | (4) |

$\mu ={\alpha}_{\mathrm{L}}{\mu}_{\mathrm{L}}+{\alpha}_{\mathrm{V}}{\mu}_{\mathrm{V}}$ | (5) | |

Turbulence kinetic k | $\frac{\partial}{\partial t}\left(\rho k\right)+\nabla \cdot \left(\rho \overrightarrow{u}k\right)=\nabla \cdot \left[\left(\mu +\frac{{\mu}_{\mathrm{t}}}{{\sigma}_{\mathrm{k}}}\right)\nabla k\right]+{G}_{\mathrm{k}}-\rho \epsilon $ | (6) |

Turbulence kinetic dissipation ε | $\frac{\partial}{\partial t}\left(\rho \epsilon \right)+\nabla \cdot \left(\rho \overrightarrow{u}\epsilon \right)=\nabla \cdot \left[\left(\mu +\frac{{\mu}_{\mathrm{t}}}{{\sigma}_{\mathsf{\epsilon}}}\right)\nabla \epsilon \right]+{C}_{1\mathsf{\epsilon}}\frac{\epsilon}{k}\left({G}_{\mathrm{k}}\right)-{C}_{2\mathsf{\epsilon}}\rho \frac{{\epsilon}^{2}}{k}$ | (7) |

Generation of turbulent kinetic energy G_{k} | ${G}_{\mathrm{k}}=\frac{{\mu}_{\mathrm{t}}\left(\nabla u+\nabla {u}^{\mathrm{T}}\right)}{\nabla u}$ | (8) |

Eddy viscosity μ_{t} | ${\mu}_{\mathrm{t}}=\rho {C}_{\mathsf{\mu}}\frac{{k}^{2}}{\epsilon}$ | (9) |

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**MDPI and ACS Style**

Huang, K.; Chen, J.; Chen, Y.; Luo, X.; Liang, Y.; He, J.; Yang, Z.
Simulation of Vapor-Liquid Separation in the Orifice-Baffle Header under Various Operating Conditions. *Appl. Sci.* **2022**, *12*, 7971.
https://doi.org/10.3390/app12167971

**AMA Style**

Huang K, Chen J, Chen Y, Luo X, Liang Y, He J, Yang Z.
Simulation of Vapor-Liquid Separation in the Orifice-Baffle Header under Various Operating Conditions. *Applied Sciences*. 2022; 12(16):7971.
https://doi.org/10.3390/app12167971

**Chicago/Turabian Style**

Huang, Kunteng, Jianyong Chen, Ying Chen, Xianglong Luo, Yingzong Liang, Jiacheng He, and Zhi Yang.
2022. "Simulation of Vapor-Liquid Separation in the Orifice-Baffle Header under Various Operating Conditions" *Applied Sciences* 12, no. 16: 7971.
https://doi.org/10.3390/app12167971