Application of a lattice Boltzmann method combined with a Smagorinsky turbulence model to spatially resolved heat flux inside a refrigerated vehicle

Abstract

a b s t r a c tIn this work the simulation of velocity and temperature distributions inside a refrigerated vehicle is evaluated. For this purpose a 3D double distribution lattice Boltzmann method (LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator is coupled by the buoyancy force calculated with the Boussinesq approximation. This LBM is extended by a Smagorinsky subgrid method, which numerically stabilizes the BGK scheme for low resolutions and high Reynolds and Rayleigh numbers. Besides validation against the two benchmark cases porous plate and natural convection in a square cavity evaluated at resolutions of y + ≈ 2 for Ra numbers between 10 3 and 10 10 , the method and its implementation are tested via comparison with experimental data for a refrigerated vehicle at Re ≈ 53 000.The aim of the investigation is to provide a deeper understanding of the refrigerated vehicle's insulation processes including its thermal performance under turbulent flow conditions. Therefore, we extend this method by the half lattice division scheme for conjugate heat transfer to simulate in the geometry of a refrigerated vehicle including its insulation walls. This newly developed method combination enables us to accurately predict velocity and temperature distributions inside the cooled loading area, while spatially resolving the heat flux through the insulation walls. We simulate the time dependent heating process of the open door test and validate against measurements at four characteristic velocity and 13 temperature positions in the truck. (M. Gaedtke). are complex material requirements which, in addition to the insulation, include static stability, load securing as well as resistance against vibrational stress.According to Smale [2] most simulations and models for the representation of a velocity and temperature distribution in the field of applied cooling of geometries between 1974 and 2006 have shown low accuracy and large deviations from experimental data. Tabsoba et al. [3] studied the influence of the k-ϵ turbulence model against the Reynolds stress model, where they indicated the k-ϵ model to fail at the prediction of certain flow characteristics in ventilated enclosures. Ambaw [4] summarized studies on the cooling of harvested food, indicating some progress being made between 2006 and 2013 with the accuracy of the models. With simulations mainly based on Reynolds averaging turbulence models as the k-ϵ or shear stress transport (SST) model [5][6][7][8], he also came to the conclusion, that a clear increase in the accuracy of turbulent 3D simulations within complex cooled geometries compared with experimental data has still to come.According to James [9] first simulations of the open door tests have been carried out by Tso et al. [10]. Tso's simulated temperatures deviate from experimental recordings by up to 4 K at a temperature difference of about 26 K. Son [11] showed an approximation to the validation data up to 1.13 K in the simulation of the velocity and temperature distribution in the interior of a filled...

Numerical study on the application of vacuum insulation panels and a latent heat storage for refrigerated vehicles with a large Eddy lattice Boltzmann method

“…In this work we use the double distribution thermal LBM (DDT-LBM) including a Smagorinsky turbulence model as described in detail in our previous study [11], in which we also presented a rigorous validation of the model itself as well as its implementation in the open source code OpenLB. This validation study included -a grid convergence study showing that the scheme is second order in space by comparing it with the analytical solution of the porous plate problem, -a comparison with the benchmark of natural convection in a square cavity for different Rayleigh numbers from laminar to turbulent natural convection, -and a comparison with measurements for the refrigerated transporter, which is also investigated in the current manuscript.…”

“…As in our previous work [11], the Smagorinsky sub-gridscale model introduced to the LBM by Hou et al [15] is used. Following Hou et al, the viscosity ν in Eq.…”

“…As in our previous work [11] Latt's [22] regularized boundary approach is used for pressure and velocity boundary conditions. A constant temperature boundary condition is implemented as described in [20] and the outflow boundary condition for the temperature is used as recommended by Junk and Yang [18].…”

“…The AC's outlet and suction side are shown in green and orange, respectively. Adapted from [11] unit is installed, which can be used for both, heating and cooling purposes with a full-load volume flow ofV = 990 m/h 3 and a heating and cooling capacity of Q = 950 W. The energy supply of the transport refrigeration system can be provided either by the diesel engine installed in the vehicle during the journey or externally by 400 V three-phase current during longer rest periods.…”

“…In addition, spatially resolved measurements without influencing the wall properties or the flow properties in the system are costly if not hardly possible. In a previous study Gaedtke et al [11] showed the applicability of a double distribution thermal LBM to the simulation of a refrigerated vehicle's insulation. By replacing the widely applied Reynolds averaging turbulence model with a large eddy turbulence model and transiently resolving the flow field, the refrigerated vehicle's walls and their conjugate heat transfer, they found much closer accordance to measured data than previous studies [17,26].…”