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Simultaneous near-infrared measurement of temperature and flow fields of a thermal plume arising in water

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This study proposes a method for the concurrent visualization and measurement of three-dimensional (3D) temperature and flow fields in water, where a thermal plume arises from a small heat source. This method is based on near-infrared (NIR) absorption imaging with a two-orthogonal-direction telecentric system at a wavelength of 1150 nm. The acquired images in each direction were divided into absorbance images corresponding to the temperature field and particle shadow images through a background subtraction method. A non-axisymmetric inverse Abel transform was applied to the absorbance images in the two directions to reconstruct the 3D temperature fields. The temperature was determined based on the temperature dependence of the absorption coefficient of water at this wavelength. Simultaneously, the 3D flow fields were obtained by applying shadow-based particle tracking velocimetry (PTV), which includes particle identification, track interpolation, and particle 3D matching of the particle shadow images. The results demonstrated 3D transient temperature profiles within the plume and the effect of forced flow on its growth direction. In addition, the PTV results indicated that the trajectories were consistent with the mixed convection field, which was verified via numerical simulation.

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The authors thank Mr Kyohei Hanada for assistance with the data analysis. This work was supported by the Mitutoyo Association for Science and Technology (Grant Number R2002), Japan.

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Correspondence to The-Anh Nguyen.

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Appendix A: CFD simulation

Appendix A: CFD simulation

Quantitative experiments were confirmed through numerical simulations using COMSOL Multiphysics 5.6 software (COMSOL, Stockholm, Sweden).

The incompressible fluid flow is described by the governing equations, which include the mass conservation equation

$$\frac{\partial \rho }{{\partial t}} + \nabla \cdot (\rho \vec{\varvec{u}}) = 0,$$

the equation of momentum (Navier–Stokes equation) with Boussinesq approximation

$$\rho \frac{{\partial \vec{\varvec{u}}}}{\partial t} = \rho \vec{\varvec{u}} \cdot \nabla \vec{\varvec{u}} = \nabla \cdot (\eta \nabla \vec{\varvec{u}}) - \nabla p - \beta (T - T_0 )\vec{\varvec{g}},$$

and the equation of energy

$$\rho c\frac{\partial T}{{\partial t}} + \rho c\vec{\varvec{u}} \cdot \nabla T = \nabla \cdot k\nabla T,$$

where \(\vec{\varvec{u}}\) is the flow velocity vector, ρ is the specific mass density, p is the pressure, η is the dynamic viscosity, T0 is the initial temperature, \(\overrightarrow{\varvec{g}}\) is the acceleration due to gravity, and c is the specific heat capacity.

The energy equation computes the heat transfer in the plate, which can be expressed as follows:

$$\rho c\frac{\partial T}{{\partial t}} = \nabla \cdot k\nabla T + \dot{P},$$

where \(\dot{{P}}\) is the heat generation rate of the sphere.

A slip condition was applied to the top surface of the water as a boundary condition. A no-slip boundary condition was set for the plate surface and boundaries between the water and cuvette walls. As the initial condition, the pressure distribution was assumed to be hydrostatic, and \(\vec{\varvec{u}} = 0\) was implemented over the entire region. The initial temperature was 293.15 K for all geometric entities. The simulation considered an adiabatic boundary condition assumption for the analysis of heat transfer between the cuvette wall and water. The material properties used in the simulation are listed in Table 2.

Table 2 Physical properties of materials

The simulation comprised two parts:

  1. (1)

    Fluid flow inside the domain with Eqs. 12 and 13, using \(\beta (T - T_0 )\vec{\varvec{g}} = 0,\) with a volumetric flow rate V0 = Q = 90 mm3/s at inlet and outlet regions.

  2. (2)

    Coupling heat and mass transport equations (Eqs. 1215) to laminar flow, starting from the results of the first study. The initial temperature remained at 293.15 K throughout. The simulation used 894,594 grids, with negligible mesh size effect on results.

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Nguyen, TA., Kondo, K. & Kakuta, N. Simultaneous near-infrared measurement of temperature and flow fields of a thermal plume arising in water. J Vis (2024).

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