# Combined Experimental and CFD Approach of Two-Phase Flow Driven by Low Thermal Gradients in Wine Tanks: Application to Light Lees Resuspension

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## Abstract

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## 1. Introduction

_{room}> T

_{wine}or negative T

_{room}< T

_{wine}) between the container and the outside of the container. If these low gradients induce a resuspension of the lees, then, by extension, higher gradients will contribute even more. In a second step, a numerical study was carried out to ascertain whether the laboratory results could be extrapolated to full-scale tanks. For this purpose, Computational Fluid Dynamics (CFD) calculations were performed using a calculation code based on the finite volume method and a two-phase flow model (the wine and the light lees, respectively).

## 2. Experimental Procedure: Highlighting the Thermal Resuspension Process of Light Lees

#### 2.1. Flow Dynamics Within the Wine Bulk

^{−3}) which were likely to produce sufficient light scattering and subsequent facilitate efficient traceability of the flow.

#### 2.2. Settling Dynamics of the Light Lees

^{−3}[6] (i.e., higher than that of the wine). Given that density of lees is significantly higher than that of the liquid phase, it should be considered a serious obstacle to their resuspension in the wine bulk. For such small solid particles, the settling velocity typically obeys the so-called Stokes velocity, according to the following relationship:

_{2}(with the temperature T being expressed in K):

^{−1}. By using a particle image velocimetry (PIV) measurement system, including a Litron Nd:YAG laser and a CCD video camera identical to that used in a previous study [19], the velocity field was properly determined in the wine receptacle. The maximum recorded wine velocities were close to 1.2 mm·s

^{−1}(i.e., in the order of 10

^{3}times higher than the settling velocities) [20]. It can thus be concluded that the gravitational sedimentation rates of the light lees alone cannot influence their resuspension in the wine bulk under the effect of the low thermal gradients.

#### 2.3. Resuspension of Light Lees

## 3. Numerical Procedure: Application of CFD to a Full-Scale Wine Tank

#### 3.1. Heat Transfer and Numerical Methods

^{®}software. The mesh consisted of about 15,000 hexahedral and tetrahedral cells. The unstructured mesh was refined on the wall where a high resolution boundary layer is required. while it is coarser in the far field, as seen in Figure 4. The problem is considered to be axisymmetric and time-dependent, but not isothermal.

^{®}commercial code was used to calculate the anisothermal flow in the 2D calculation domain. Convective exchanges require the activation of the energy equation to take into account thermal transfer phenomena. Depending on the wine-growing region, not all wine cellars are thermo-regulated; the temperature of the ambient air in cellars can fluctuate daily [21]. Such fluctuations can thus affect the wine temperature by conduction through the wall of the tanks, vats or barrels. In order to mimic these thermal fluctuations, a subroutine was implemented in the CFD code which modulates the temperature of the tank wall according to the time of the day, according to the scheme displayed in Figure 5.

_{w2}, which is directly in contact with the wine. This parameter will be the thermal boundary condition of the numerical problem. Its determination is based on the conservation of the heat supply through the different environments crossed, expressed hereafter:

_{w2}:

_{w2}will be possible once the convective exchange coefficients have been accurately estimated. The respective convective coefficients are deduced from the Nusselt number Nu:

_{c2}at the inside surface of the tank, we used the value determined in similar enological conditions [8], namely h

_{c2}= 30 W·m

^{−2}·K

^{−1}. For the external convective coefficient, which is a forced convection one, we assumed that the tank was exposed to a constant wind velocity of V ≈ 1 m·s

^{−1}within the cellar. In such a case, the Nusselt number reported to the tank diameter in Equation (6) can be estimated as:

^{2}·s

^{−1}).

_{wine}= T

_{lees}= 12 °C. Gradually, a heat transfer by convection took place between the walls of the tank and the wine, resulting in a change in its density. In order to model as accurately as possible the slightest change in density as a function of temperature, we created a database specific to the thermo-physical properties of both wine and lees.

#### 3.2. Equations and Numerical Scheme

#### 3.3. Numerical Results

^{−1}) were observed at t = 18 h along the axis of symmetry of the tank. We can also note that the velocity profile for t = 6h merged with that of t = 24 h, transition time between positive and negative gradients.

#### 3.4. Contribution of the Wine Mixing Dynamics on the Resuspension of Light Lees

^{−1}, against 2.15 mm·s

^{−1}for the wine. A key finding is that the average velocity of the wine was about 31% higher than that of the lees, which have a higher density. It should be noted, however, that the actual lees velocity was up to 250 times higher than the settling velocity previously determined using the Stokes equation (1). Moreover, it should be noted that the lees granulometry did not induce a sufficient sedimentation rate to oppose the vortex structures and the natural convection flow velocities involved. This implies that as long as the wine tank is not subjected to thermal equilibrium (identical temperature between the wine and the outside of the tank), the lees will not settle to the bottom of the tank. Finally, the numerical results confirmed that the laboratory results can be extrapolated to full-scale tanks, and that a small thermal gradient is sufficient to resuspend the light lees.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

D | Diameter of the tank, m |

${d}_{l}$ | Average lees diameter, m |

e | Wall tank thickness, m |

$\overrightarrow{F}$ | External body forces, N |

$Gr$ | Grashof number |

H | Height of the tank, m |

${h}_{c1}$ | Convective heat transfer coefficient of air, W·m^{−2}·K^{−1} |

${h}_{c2}$ | Convective heat transfer coefficient of wine, W·m^{−2}·K^{−1} |

Nu | Nusselt number |

$p$ | Static pressure, Pa |

$Pr$ | Prandtl number |

$r$ | Radial coordinate |

$Ra$ | Raleigh number |

${S}_{m}$ | Mass added to the continuous phase from the dispersed second phase |

T_{w1} | Temperature of the outer surface of the tank, K |

T_{w2} | Temperature of the inner surface of the tank, K |

T_{1} | Air temperature, K |

T_{2} | Wine temperature, K |

${\mathsf{\nu}}_{\mathrm{x}}$ | Axial velocity, m·s^{−1} |

${\mathsf{\nu}}_{\mathrm{r}}$ | Radial velocity, m·s^{−1} |

$x$ | Axial coordinate |

${\lambda}_{air}$ | Thermal conductivity of air, W·m^{−1}·K^{−1} |

${\lambda}_{wine}$ | Thermal conductivity of wine, W·m^{−1}·K^{−1} |

${\mu}_{w}$ | Dynamic viscosity of wine, kg·m^{−1}·s^{−1} |

${\rho}_{l}$ | Density of lees, kg·m^{−3} |

${\rho}_{w}$ | Density of wine, kg·m^{−3} |

ϕ | Heat flux, W·m^{−2} |

$\rho $ | Density, kg·m^{−3} |

$g$ | Gravitational acceleration, m·s^{−2} |

ν | Kinematic viscosity, m^{2}·s^{−1} |

β | Thermal expansion coefficient, K^{−1} |

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**Figure 1.**Flow behavior within the wine bulk, and flow directions near the bottom surface of the container, under a low positive thermal gradient of +3 °C (left), and a low negative thermal gradient of −3 °C (right), respectively 15 min after the start of the heating/cooling process of the room.

**Figure 2.**Micrographs taken through Scanning Electron Microscopy (SEM) showing the nearly monodisperse size distribution of light lees (magnification ×2000 left–×10,000 right).

**Figure 3.**Resuspension process of light lees under low positive thermal gradient +3 °C (left) and low negative thermal gradient −3 °C (right), 15 min after the start of the heating/cooling process of the room.

**Figure 4.**Volume fraction of light lees in the liquid bulk (

**a**). Superposition of the geometry of the tank (left) and the mesh of the fluid domain (right) (

**b**). Meshing of the fluid domain and detail of the refinement of the mesh close to the wall (

**c**).

**Figure 6.**Sketch of the heat transfer mode (

**a**), and electrical analogy of the thermal resistances (

**b**), with φ being the total resistance against heat transfer, T

_{1}the ambient air temperature outside the tank, T

_{2}the wine temperature, T

_{w1}the temperature of the external wall of the tank and T

_{w2}the temperature of the inner wall, h

_{c1}the external convective coefficient, h

_{c2}the internal convective coefficient, and ${\lambda}_{w}$ the thermal conductivity of the tank wall whose thickness is denoted $e$.

**Figure 7.**Evolution of the temperature of the wine over a 24 h cycle (

**a**), and corresponding streamline patterns (

**b**).

**Figure 8.**Axial velocity of the wine at 6, 12, 18 and 24 h, respectively, as plotted along a horizontal axis at y = 210 cm.

**Figure 9.**Time evolution of the volume fraction of lees throughout the first 12 h of the 24 h cycle (at 1 h, 3 h, 6 h and 12 h, respectively).

**Figure 10.**Comparison of the axial velocities of wine and lees, at t = 6 h and t = 18 h, as plotted along a horizontal axis, at y = 110 cm.

**Table 1.**Thermo-physical properties of the various materials, with Pr defined as the ratio of kinematic viscosity to thermal diffusivity.

Kinematic Viscosity, ν (m^{2}·s^{−1}) | Thermal Conductivity, λ (W·m^{−1}·K^{−1}) | Thermal Expansion Coefficient, β (K^{−1}) | Prandtl Number, Pr | |
---|---|---|---|---|

Stainless steel | — | 16 | — | — |

Air | 1.57·10^{−5} | 0.0262 | — | 0.7 |

Wine | 1.25·10^{−6} | 0.46 | 8·10^{−4} | 9.4 |

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**MDPI and ACS Style**

Bogard, F.; Beaumont, F.; Vasserot, Y.; Simescu-Lazar, F.; Nsom, B.; Liger-Belair, G.; Polidori, G.
Combined Experimental and CFD Approach of Two-Phase Flow Driven by Low Thermal Gradients in Wine Tanks: Application to Light Lees Resuspension. *Foods* **2020**, *9*, 865.
https://doi.org/10.3390/foods9070865

**AMA Style**

Bogard F, Beaumont F, Vasserot Y, Simescu-Lazar F, Nsom B, Liger-Belair G, Polidori G.
Combined Experimental and CFD Approach of Two-Phase Flow Driven by Low Thermal Gradients in Wine Tanks: Application to Light Lees Resuspension. *Foods*. 2020; 9(7):865.
https://doi.org/10.3390/foods9070865

**Chicago/Turabian Style**

Bogard, Fabien, Fabien Beaumont, Yann Vasserot, Florica Simescu-Lazar, Blaise Nsom, Gérard Liger-Belair, and Guillaume Polidori.
2020. "Combined Experimental and CFD Approach of Two-Phase Flow Driven by Low Thermal Gradients in Wine Tanks: Application to Light Lees Resuspension" *Foods* 9, no. 7: 865.
https://doi.org/10.3390/foods9070865