Turbulence, single-phase flow

Beattie, D. R. M., 1983, An Extension of Single Phase Flow Turbulent Pipe Flow Concepts to Two-Phase Flow, Ph.D. thesis, University of New South Wales, Sydney, Australia. (3)... 

In Chap. 3 the problems of single-phase flow are considered. Detailed data on flows of incompressible fluid and gas in smooth and rough micro-channels are presented. The chapter focuses on the transition from laminar to turbulent flow, and the thermal effects that cause oscillatory regimes. 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

D. The Simulation of Processes in a Turbulent Single-Phase Flow... 

The number of equations to be solved is, among other things, related to the turbulence model chosen (in comparison with the k-e model, the RSM involves five more differential equations). The number of equations further depends on the character of the simulation whether it is 3-D, 21/2-D, or just 2-D (see below, under The domain and the grid ). In the case of two-phase flow simulations, the use of two-fluid models implies doubling the number of NS equations required for single-phase flow. All this may urge the development of more efficient solution algorithms. Recent developments in computer hardware (faster processors, parallel platforms) make this possible indeed. 

In the current state of the art, almost all multiphase CFD models available in commercial codes use some type of turbulence model based on extending models originally developed for single-phase flows. Such CFD models are thus meant to describe fully turbulent flows (as opposed to laminar or transitional flows). Nevertheless, many of these models have not been validated... 

The "correlative" multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a "multilevel" approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

In order for a model to be closured, the total number of independent equations has to match the total number of independent variables. For a single-phase flow, the typical independent equations include the continuity equation, momentum equation, energy equation, equation of state for compressible flow, equations for turbulence characteristics in turbulent flows, and relations for laminar transport coefficients (e.g., fJL = f(T)). The typical independent variables may include density, pressure, velocity, temperature, turbulence characteristics, and some laminar transport coefficients. Since the velocity of gas is a vector, the number of independent variables associated with the velocity depends on the number of components of the velocity in question. Similar consideration is also applied to the momentum equation, which is normally written in a vectorial form. 

The fluxes of mass, momentum, and energy of phase k transported in a laminar or turbulent multiphase flow can be expressed in terms of the local gradients and the transport coefficients. In a gas-solid multiphase flow, the transport coefficients of the gas phase may be reasonably represented by those in a single-phase flow although certain modifications... 

Me Effective turbulent viscosity in a single phase flow... 

Most attempts at modeling complex, turbulent multiphase flows rely on the practices followed for single-phase flows, with some ad hoc modifications to account... 

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