Reynolds average simulations

Even nowadays, a DNS of the turbulent flow in, e.g., a lab-scale stirred vessel at a low Reynolds number (Re = 8,000) still takes approximately 3 months on 8 processors and more than 17 GB of memory (Sommerfeld and Decker, 2004). Hence, the turbulent flows in such applications are usually simulated with the help of the Reynolds Averaged Navier- Stokes (RANS) equations (see, e.g., Tennekes and Lumley, 1972) which deliver an averaged representation of the flow only. This may lead, however, to poor results as to small-scale phenomena, since many of the latter are nonlinearly dependent on the flow field (Rielly and Marquis, 2001). 

Results of Reynolds Averaged Navier- Stokes Simulations... 

Thus, the reactor will be perfectly mixed if and only if = at every spatial location in the reactor. As noted earlier, unless we conduct a DNS, we will not compute the instantaneous mixture fraction in the CFD simulation. Instead, if we use a RANS model, we will compute the ensemble- or Reynolds-average mixture fraction, denoted by ( ). Thus, the first state variable needed to describe macromixing in this system is ( ). If the system is perfectly macromixed, ( ) = < at every point in the reactor. The second state variable will be used to describe the degree of local micromixing, and is the mixture-fraction variance (maximum value of the variance at any point in the reactor is ( )(1 — ( )), and varies from zero in the feed streams to a maximum of 1/4 when ( ) = 1/2. 

This chapter is devoted to methods for describing the turbulent transport of passive scalars. The basic transport equations resulting from Reynolds averaging have been derived in earlier chapters and contain unclosed terms that must be modeled. Thus the available models for these terms are the primary focus of this chapter. However, to begin the discussion, we first review transport models based on the direct numerical simulation of the Navier-Stokes equation, and other models that do not require one-point closures. The presentation of turbulent transport models in this chapter is not intended to be comprehensive. Instead, the emphasis is on the differences between particular classes of models, and how they relate to models for turbulent reacting flow. A more detailed discussion of turbulent-flow models can be found in Pope (2000). For practical advice on choosing appropriate models for particular flows, the reader may wish to consult Wilcox (1993). 

The reduction of the turbulent-reacting-flow problem to a turbulent-scalar-mixing problem represents a significant computational simplification. However, at high Reynolds numbers, the direct numerical simulation (DNS) of (5.100) is still intractable.86 Instead, for most practical applications, the Reynolds-averaged transport equation developed in... 

In turbulent reactive flows, the chemical species and temperature fluctuate in time and space. As a result, any variable can be decomposed in its mean and fluctuation. In Reynolds-averaged Navier-Stokes (RANS) simulations, only the means of the variables are computed. Therefore, a method to obtain a turbulent database (containing the means of species, temperature, etc.) from the laminar data is needed. In this work, the mean variables are calculated by PDF-averaging their laminar values with an assumed shape PDF function. For details the reader is referred to Refs. [16, 17]. In the combustion model, transport equations for the mean and variances of the mixture fraction and the progress variable and the mean mass fraction of NO are solved. More details about this turbulent implementation of the flamelet combustion model can also be found in Ref. [20],... 

The three main numerical approaches used in turbulence combustion modeling are Reynolds averaged Navier Stokes (RANS) where all turbulent scales are modeled, direct numerical simulations (DNS) where all scales are resolved and large eddy simulations (LES) where larger scales are explicitly computed whereas the effects of smaller ones are modeled ... 

To simulate turbulent flows, Reynolds-averaged Navier-Stokes (RANS) equations form the basis for most codes. Several turbulence models are usually provided. A new turbulence model may also usually be incorporated via user-defined routines. Recently, many of the commercial CFD codes have announced the inclusion of large eddy simulation (LES) capabilities. Considering the importance of rotating equipment used in reactor engineering applications, the ability to handle multiple reference frames or sliding meshes is important. Most leading commercial CFD codes provide... 

If such an approach becomes widespread it will be even more necessary to calibrate and understand its merits and drawbacks by using detailed and accurate computational modelling techniques that have been thoroughly validated, such as Large Eddy Simulation methods (Rodi, 1997 [541]), stochastic simulation methods (Hort et al., 2002 [276] Turfus, 1988 [622]), and time-dependent Reynolds-averaged models. 

In other cases the application of this concept has been further extended simulating faster turbulent fluctuations that are within the turbulence spectrum. For such dynamic simulations, using Reynolds averaged models, the Ic-quantity represents the turbulent kinetic energy accumulated on the fraction of the spectrum that is represented by the modeled scales. Therefore, to compare the simulated results obtained with this type of models with experimental data, that is averaged over a sufficient time period to give steady-state data (representing the whole spectrum of turbulence), both the modeled and the resolved scales have to be considered [68]. 

Three different theoretical approaches have been established describing turbulent flows in general, as outlined in sect 1.3. These methods are the direct numerical simulations (DNS), large eddy simulations (LES), and the Reynolds average Navier-Stokes (RANS) approach. 

When dealing with turbulent flows all the relevant dimensionless numbers are evaluated with the available quantities. For example, in DNS, the fluid and particle instantaneous velocities will be employed, whereas in large-eddy simulation (LES) or in Reynolds-average Navier-Stokes-equations (RANS) simulations the filtered or Reynolds-average values will be used. 

---