RNG k-e model

Our group has made extensive use of the RNG k-e model (Nijemeisland and Dixon, 2004), which is derived from the instantaneous Navier-Stokes equations using the Renormalization Group method (Yakhot and Orszag, 1986) as opposed to the standard k-e model, which is based on Reynolds averaging. The... 

The RNG model provides its own energy balance, which is based on the energy balance of the standard k-e model with similar changes as for the k and e balances. The RNG k-e model energy balance is defined as a transport equation for enthalpy. There are four contributions to the total change in enthalpy the temperature gradient, the total pressure differential, the internal stress, and the source term, including contributions from reaction, etc. In the traditional turbulent heat transfer model, the Prandtl number is fixed and user-defined the RNG model treats it as a variable dependent on the turbulent viscosity. It was found experimentally that the turbulent Prandtl number is indeed a function of the molecular Prandtl number and the viscosity (Kays, 1994). 

The Fluent code with the RSM turbulence model, predict very well the pressure drop in cyclones and can be used in cyclone design for any operational conditions (Figs. 3, 5, 7 and 8). In the CFD numerical calculations a very small pressme drop deviation were observed, with less than 3% of deviation at different inlet velocity which probably in the same magnitude of the experimental error. The CFD simulations with RNG k-e turbulence model still yield a reasonably good prediction (Figs. 3, 5, 7 and 8) with the deviation about 14-20% of an experimental data. It considerably tolerable since the RNG k-e model is much less on computational time required compared to the complicated RSM tmbulence model. In all cases of the simulation the RNG k-< model considerably underestimates the cyclone pressme drop as revealed by Griffiths and Boysan [8], However under extreme temperature (>850 K) there is no significant difference between RNG k-< and RSM model prediction. 

Compared with Equation 4.6, Equation 4.12 contains the term -pUi Uj, the so-called Reynolds stress, which represents the effect of turbulence and must be modeled by the CFD code. Limited computational resources restrict the direct simulation of these fluctuations, at least for the moment. Therefore the transport equations are commonly modified to account for the averaged fluctuating velocity components. Three commonly applied turbulence modeling approaches have been used in the CFD model of spray drying system, i.e., k-Q model (Launder and Spalding 1972, 1974), RNG k-e model (Yakhot and Orszag 1986), and a Reynolds stress model (RSM) (Launder et al. 1975). 

The standard k-e model focuses on mechanisms that affect the turbulent kinetic energy. Robusmess, economy, and reasonable accuracy over a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations. The RNG k-e model was derived using a rigorous statistical technique (called Re-Normalization Group theory). It is similar in form to the standard k-e model, but the effect of swirl on turbulence is included in the RNG mode enhancing the accuracy for swirling flows. 

Currently the widely used turbulence models are standard K-s model, RNG K-e model and the Reynolds stress model (RSM). Standard K-s model is based on isotropic turbulence model, its simulation result error of separator flow field is large (Shan Yongbo, 2005). RNG K-s model has improved with a standard K-s model, but there are still larger defects. To improve the cyclone vortex field strength prediction results a greater extent, algebraic stress turbulence model based... 

The second difference is that the realizable k-e model uses different source and sink terms in the transport equation for eddy dissipation. The resulting equation is considerably different from the one nsed for both the standard and RNG k-e models. The modified prediction of e, along with the modified calculation for p,t, makes this turbulence model snperior to the other k-e models for a number of applications. In particular, the model does better in predicting the spreading rate of round jets, such as those emitted from a rotating impeller blade. 

The turbulent effects are described by a modified (RNG) k-e model [66, 82, 96-98]. For model validation experimental LDA data characterizing a standard vessel of laboratory scale, as reported by Engeskaug [22], is used. The simulations considered in this section have been reported by Engeskaug [22], Druecker [17] and Jakobsen [43]. 

In order to validate the accxuracy of this information soiuce s product ( FLUENT/UNS ) for this kind of flow prediction, a straight five-fin labyrinth knife seal with a nominal clearance of 1.11 mm between the labyrinfli seal and the shroud was analyzed. The computational model was axisymmetric, with specification of the pressure ratio (1.5) across the seal as imposed boimdary conditions. The working fluid was assumed to be air, with density computed via the ideal gas law and fluid properties (viscosity, thermal conductivity, and heat capacity) expressed as a function of temperature. Turbulence was modeled using the RNG k-e model. The CFD model was run at several different rotor speeds and the windage heating was computed and compared with the experimental data. 

The Realizable k-e model ensures the positivity of normal stresses ( realizable ) by making the empirical constants of k-e turbulence model, C, a function of the mean flow (mean deformation) and the turbulence (/c, ) while the Boussinesq theory used in the standard and RNG k-e model allows for negative normal stresses. The Realizable k-e model is more accurate in the prediction of the spreading rate of both planar and round jets. Kang et al (2008) used a Realizable k-e model to simulate the hydrodynamics in the membrane filtration zone of pilot and full-scale MBRs. 

---