Conjugate heat transfer through nano scale porous media to optimize vacuum insulation panels with lattice Boltzmann methods

TLDR: A new holistic approach provides a distinct advantage over similar porous media approaches by providing direct control and tuning of particle packing characteristics such as aggregate size, shape and pore size distributions and studying their influence directly on conduction and radiation independently.

Abstract: Due to reduced thermal conductivity, vacuum insulation panels (VIPs) provide significant thermal insulation performance. Our novel vacuum panels operate at reduced pressure and are filled with a powder of precipitated silicic acid to further hinder convection and provide static stability against atmospheric pressure. To obtain an in depth understanding of heat transfer mechanisms, their interactions and their dependencies inside VIPs, detailed microscale simulations are conducted. Particle characteristics for silica are used with a discrete element method (DEM) simulation, using open source software Yade-DEM, to generate a periodic compressed packing of precipitated silicic acid particles. This aggregate packing is then imported into OpenLB (openlb.net) as a fully resolved geometry, and used to study the effects on heat transfer at the microscale. A three dimensional Lattice Boltzmann method (LBM) for conjugated heat transfer is implemented with open source software OpenLB, which is extended to include radiative heat transport. The infrared intensity distribution is solved and coupled with the temperature through the emissivity, absorption and scattering of the studied media using the radiative transfer equation by means of LBM. This new holistic approach provides a distinct advantage over similar porous media approaches by providing direct control and tuning of particle packing characteristics such as aggregate size, shape and pore size distributions and studying their influence directly on conduction and radiation independently. Our aim is to generate one holistic tool which can be used to generate silica geometry and then simulate automatically the thermal conductivity through the generated geometry.

Figures

Fig. 8. Heat conductivity breakdown due to air, radiation and through the solid material.

Fig. 10. Temperature distribution through periodic packing of silica aggregates.

Table 1 Comparison of thermal conductivity λ of high performance thermal insulation materials [3] (EPS and XPS are expanded and extruded polystyrene respectively).

Fig. 4. Thermal conductivity measurement system composed of: [1] insulated enclosure, [2] vacuum pump, [3] thermostat, [4] pressure sensor, [5] measurement electronics and laptop.

Fig. 9. Radiation distribution through periodic packing of silica aggregates.

Table 2 Measurement uncertainty for temperature sensors.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Conjugate heat transfer through nano scale porous media to optimize vacuum insulation panels with lattice boltzmann methods" ?

This aggregate packing is then imported into OpenLB ( openlb. net ) as a fully resolved geometry, and used to study the effects on heat transfer at the microscale. The infrared intensity distribution is solved and coupled with the temperature through the emissivity, absorption and scattering of the studied media using the radiative transfer equation by means of LBM. This new holistic approach provides a distinct advantage over similar porous media approaches by providing direct control and tuning of particle packing characteristics such as aggregate size, shape and pore size distributions and studying their influence directly on conduction and radiation independently. 

Q2. What is the thermal transfer due to radiation at higher pressures?

At higher pressures, the number of air particles also increases and thus absorption of radiation increases and the heat flux due to radiation decreases slightly. 

Q3. What is the coupling term for the gas?

The coupling term arises from the increased heat transport bridging between neighboring particles or fibers on the micro-scale and increases as the heat conductivity of the gas and solid increases. 

Q4. What is the process for generating the geometry?

Since the entire process for generating the geometry is procedural and parameter driven, multiple geometries can be generated based on the same base geometry. 

Q5. What is the way to understand the effects of different packing geometries on the individual?

In order to understand effects of different packing geometries such as porosity and aggregate size on the individual contributions that make up the heat transfer through the VIP, a high fidelity model of the packing geometry is required. 

Q6. What is the effect of the pressure inside the VIP on the heat transfer?

As the pressure inside the VIP decreases, the heat transfer through the fluid decreases inversely proportional to the Knudsen number in (18) [7,27]. 

Q7. What is the equilibriumfunction for the heat transfer through a VIP?

(12)Heat transfer through a VIP is composed of the heat transfer through gas λG (convection), through solid λS (conduction), through radiation λR and a coupling term λC . 

Q8. What is the first method of generating the geometry?

The first method generates the geometry based on idealized elementary units or fractal geometry, the second based on inhomogeneous procedurally generated geometry. 

Q9. What is the thermal conductivity of a standard polystyrene board?

To calculate thermal conductivity as a function of temperature and density the following equation from Zarr et al. [31] holds for the standard material. 

Q10. What is the advantage of the three dimensional geometry generation method?

The three dimensional geometry generation method implemented provides a distinct advantage over other porous media approaches by allowing direct control and tuning of particle packing characteristics such as aggregate size, shape and pore size distributions and studying their influence directly on conduction and radiation independently. 

Q11. What is the holistic approach to silica?

Their holistic approach is composed of two parts, the first generates the silica particle geometry with YADE, the second simulates the effective thermal conductivity through the geometry usingOpenLB 

Q12. What is the effective heat conductivity of the solid qs and the fluid qf?

The effective heat conductivity λeff though the resolved packing is calculated byλeff = qeffL ∆T(14)where L is the cell length,∆T is the temperature difference between the upper (Γt ) and lower boundary (Γb) and the effective heat flux qeff is given byqeff = qs + qf + qr . (15)The heat fluxes for the solid qs and for the fluid qf are calculated by the temperature distribution’s first momentum in (6). 

Q13. What is the way to determine the thermal conductivity of a test plate?

To confirm grid independence, a simplified geometry, shown in Fig. 6, considering a single sphere between two plates, is used to evaluate the effective thermal conductivity. 

Q14. How is the thermal conductivity of the VIP panels measured?

The VIP panels compressed with 25 and 30 bar closely follow the simulations with compression levels 0 and 2 respectively, both with a relative error of 3.7%. 

Q15. What is the method for generating VIP nanostructure geometry?

Rochais et al. [9] also present a method for procedural generation of VIP nanostructure geometry based primarily on the fractal dimension and repetitions of periodic base structures (square-shaped, diamond-shaped, brick-shaped).