Volume average technique for turbulent flow simulation and its application to room airflow prediction
Fluid motion turbulence is one of the most important transport phenomena occurring in engineering applications. Although turbulent flow is governed by a set of conservation equations for momentum, mass, and energy, a Direct Numerical Simulation (DNS) of the flow by solving these equations to include the finest scale motions is impossible due to the extremely large computer resources required. On the other hand, the Reynolds Averaged Modelling (RAM) method has many limitations which hinder its applications to turbulent flows of practical significance. Room airflow featuring co-existence of laminar and turbulence regimes is a typical example of a flow which is difficult to handle with the RAM method. A promising way to avoid the difficulty of the DNS method and the limitation of the RAM method is to use the Large Eddy Simulation (LES) method. In the present thesis, the drawbacks of previously developed techniques for the LES method, particularly those associated with the SGS modelling, are identified. Then a new so called Volume Average Technique (VAT) for turbulent flow simulation is proposed. The main features of the VAT are as follows: (1) The volume averaging approach instead of the more common filtering approach is employed to define solvable scale fields, so that coarse-graining in the LES and space discretization of the numerical scheme are achieved in a single procedure. (2) All components of the SGS Reynolds stress and SGS turbulent heat flux are modelled dynamically using the newly proposed Functional Scale Similarity (FSS) SGS model. The model is superior to many previously developed SGS models in that it can be applied to highly inhomogeneous and/or anisotropic, weak or multi-regime turbulent flows using a relatively coarse grid. (3) The so called SGS turbulent diffusion is identified and modelled as a separate mechanism to that of the SGS turbulent flux represented by the SGS Reynolds stress and SGS turbulent heat flux. The SGS turbulent diffusion is defined in the coarse-graining procedure, and responsible for most of the energy dissipation. (4) A new 3-D collocated scheme for the solution of viscous incompressible fluid flow, based on the SIMPLE and fractional-step methods is developed for the LES. Benchmark tests of the VAT are performed based on 2-D and 3-D lid-driven and 3-D buoyancy-driven cavity flows. Finally, as an example of a practical calculation, the VAT is applied to the LES of airflow in an enclosed air-conditioned room with a wall-mounted cooling inlet and an outlet on the opposite wall.