Comparison of zonal RANS and LES for a non-isothermal ribbed channel flow
Introduction
With ever increasing power densities, numerical simulation is now playing a key role in electronic system cooling design. According to statistics, the major factor causing electronic system failure is elevated temperatures (see Bailey, 2003). Small increases in operating temperature (of the order of 10–15 °C) can lead to a 50% reduction in the life of devices (Viswanath et al., 2000). In addition, overheated components may malfunction. Therefore, accurate prediction of flow and heat transfer in electronic systems is essential for electronics thermal design.
There are several prototype flows for electronics systems. These include channel flows with ribs or cubes mounted on a wall. Such geometries are intended to represent, to various extents, idealized circuit boards populated with integrated circuits. Numerous experimental and numerical studies have been reported in the literature on these idealized geometry flows. For example, for a fully developed ribbed channel flow, at a Reynolds number (Re) of 14,200, Acharya et al. (1993) assess flow and heat transfer predictions. The standard linear k–ϵ and Speziale’s (1987) non-linear k–ϵ models are considered. Velocity and heat transfer results show that the two models perform similarly for this, essentially (in the time mean) two-dimensional (2D), flow. However, the non-linear generally improves the streamwise turbulence intensities. Iacovides and Raisee (1999) present flow and heat transfer results obtained from three low Re models for a Re = 4 × 104, 2D, ribbed channel flow and 3D square duct flows with Re = 5 × 104 and Re = 1 × 105. They conclude that the use of low-Re number turbulence models is essential for heat transfer predictions, and that the Reynolds stress model yields superior heat transfer predictions to those for the linear models investigated. Bredberg and Davidson (1999) numerically explore 2D–ribbed channel flows. Relative to linear model results, the Gatski and Speziale (1993) EASM with Abid et al. (1995) damping functions is found not to improve heat transfer predictions. Bredberg et al. (2000) further illustrate that the turbulence models evaluated give predictions with an excessive Reynolds number dependency. Ooi et al. (2002) simulate heat transfer in 3D–ribbed ducts. The one-equation Spalart and Allmaras (1994) (S–A) model is found to perform better than the zonal k–l/k–ϵ (the Wolfshtein (1969) k–l model, which has less severe grid requirements, is applied near walls and the k–ϵ model in the core region), but still underpredicts heat transfer.
The turbulent periodic flow over wall-mounted cubes in a channel is obviously more complex than a ribbed channel flow (see Meinders and Hanjalić, 1999). Hence, more expensive eddy resolving modelling approaches than RANS have been employed by researchers. For example, Mathey et al. (1999) perform Smagorinsky (1963) large Eddy simulations (LES). Predictions show reasonable agreement with measurements. For the same case, Schmidt and Thiele (2002) compare the flow-field predictions for LES, detached Eddy simulation (DES) (Spalart et al., 1997) and the high-Re EASM. With DES, near walls the S–A model is used and away from them LES is implemented. Use of the former removes the need for semi-grid resolution of the near-wall streak structures in the attached flow regions. Hence, theoretically, the approach allows the use of coarser grids. Schmidt and Thiele find that the LES, requiring a finer grid, gives better predictions than the DES and EASM on a coarser grid. Zhong et al. (2003) also visit the same cube case, but using the k–l based zonal LES (ZLES) of Tucker and Davidson (2004) and Smagorinsky LES. For the ZLES, reminiscent of DES, near walls k–l RANS modelling is used. Away from walls the Yoshizawa (1993) k–l LES method is applied. The ZLES flow and heat transfer results are encouraging, being comparable in accuracy to those from LES which uses a much finer grid.
The above review suggests that RANS model performances tend to be problem dependent. Also it suggests that owing to the strong relationship between heat transfer and near-wall turbulence level, it is important to model near-wall flow behaviour accurately. In real flows, this region is also buffeted by large, geometry dependent, coherent vortices. When dealing with such features, the RANS approach generally performs poorly. Bearing in mind these points, the foregoing literature suggests that to accurately predict separated flows over complex geometries, eddy resolving schemes such as LES, ZLES and DES have potential.
Since it is a relatively low Reynolds number flow relevant to electronics and other areas of industrial application, here the ribbed channel case of Acharya et al. (1993) is revisited. The predictive abilities of ZLES and DES is explored. To aid comparison, the S–A, zonal k–l/EASM and k–l/cubic RANS models are also tested. For the latter two zonal models, the Wolfshtein (1969) k–l model is used in the near-wall regions, the Gatski and Speziale, 1993, Craft et al., 1996 two-equation models being employed in the core. Use of the near-wall k–l model is attractive, reducing grid demands. Also maintaining the same simple near-wall k–l model for the RANS is helpful in discerning if there are any benefits from resolving the large eddies shed from the rib when the DES and ZLES approaches are used. Non-zonal RANS predictions for this case, using the low Reynolds number Launder–Sharma k–ϵ model and cubic model of Craft et al. (1996) can be found in Liu (2004). The current results, in the context of these simulations and the LES of Lo Iacono and Tucker (2004) will be discussed later.
Section snippets
Governing equations
For incompressible flows, the governing equations for RANS and LES can be written in the following common Cartesian coordinate weakly conservative tensor forms:For RANS the tilde denotes a time- or ensemble-averaging operation. For LES it represents spatial filtering. The parameters α and β are, respectively, mean temperature and pressure gradients in the periodic streamwise direction
Results and discussion
It should be noted that, unless otherwise stated, the ZLES and DES results in this section use the coarser cross-stream grid, profiles for the two grids being remarkably similar.
Conclusions
RANS and hybrid RANS/LES approaches were used to simulate the flow and heat transfer in a ribbed channel. For the flow field, generally, ZLES and DES gave similar pleasing results. For RANS, the S–A, k–l/cubic and k–l/EASM models yielded satisfactory mean velocities. However, in the recirculation region the k–l/EASM underpredicted velocities. Except for the k–l/EASM, all other models predicted a reasonable (<8% error) reattachment length. Generally, as expected, in terms of flow structure, mean
References (28)
- et al.
Periodically developed flow and heat transfer in a ribbed duct
Int. J. Heat Mass Transfer
(1993) - et al.
Development and application of a cubic eddy-viscosity model of turbulence
Int. J. Heat Fluid Flow
(1996) - et al.
Recent progress in the computation of flow and heat transfer in internal cooling passages of turbine blades
Int. J. Heat Fluid Flow
(1999) - et al.
Vortex structure and heat transfer in turbulent flow over a wall-mounted matrix of cubes
Int. J. Heat Fluid Flow
(1999) - et al.
Reynolds averaged simulation of flow and heat transfer in ribbed ducts
Int. J. Heat Fluid Flow
(2002) - et al.
A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
Int. J. Heat Mass Transfer
(1972) - et al.
Comparison of numerical methods applied to the flow over wall-mounted cubes
Int. J. Heat Fluid Flow
(2002) - et al.
Zonal k–l based large eddy simulations
Computers and Fluids
(2004) The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient
Int. J. Heat Mass Transfer
(1969)- et al.
Prediction of nonequilibrium turbulent flows with explicit algebraic stress model
AIAA J.
(1995)
On explicit algebraic stress models for complex turbulent flows
J. Fluid Mech.
Cited by (29)
Embedded LES of thermal stratification effects on the airflow and concentration fields around an isolated high-rise building: Spectral and POD analyses
2021, Building and EnvironmentCitation Excerpt :It should be noted that all of the above-mentioned ELES studies have been performed under the isothermal stratification conditions. Liu et al. [40] used ELES for simulating non-isothermal ribbed channel flow. Based on their results, a more elongated wake region was predicted by ELES compared with the prediction made by LES model.
Impact of rib shape on heat transfer using LES
2021, Applied Mathematical ModellingLarge Eddy Simulations on Vertical Axis Hydrokinetic Turbines - Power coefficient analysis for various solidities
2020, Renewable EnergyCitation Excerpt :As shown by this equation, the reduced frequency and consequently the dynamic stall phenomenon in a VAHT is influenced by the TSR and the solidity of the VAHT. Even though its high computational cost, LES approach has shown its superior accuracy compared with RANS approach in various applications such as aerodynamic studies [21], combustion [22], meteorology [23], flow around hdyrofoil [24,25], and architectural fluid mechanics [26] but also for less standard applications dealing for instance with accurate rain measurements [27], electronic system cooling design [28], sediment transport [29], or process engineering [30]. LES is then an attractive approach to capture the flow dynamics and to correctly predict the power coefficient of a vertical axis turbine.
Large eddy simulation of turbine internal cooling ducts
2015, Computers and FluidsSimulation of an innovative internal design of a plate solar receiver: Comparison between RANS and LES results
2014, Solar EnergyCitation Excerpt :This could be attributed to the fact that the shape of the vortices matches the top hot riblets-enhanced surface, maximising the interaction of the vortices with the wall. These results also agree with the literature (Liu et al., 2006), which has shown that LES simulations provide more realistic results regarding thermal exchanges than RANS simulations. Finally, the overall performance along the simulated length was calculated for both simulations.
LES of heat transfer in electronics
2012, Applied Mathematical ModellingCitation Excerpt :Numerical dissipation used in this method stems from the discretisation of spatial and temporal terms and low level terms left fully implicit in the CFD code [43]. Previous work on these cases [44–46] provides considerable motivation to investigate reductions in mesh size and different discretisation schemes using hybrid RANS-(N)LES methods. The first reason is to reduce computation time, the second is that using NLES relies on suitable discretisation and the last that nonlinear LES may also benefit from higher numerical fidelity.