Reynolds-averaged Navier-Stokes Closures Research Articles

Large-eddy simulation of turbulent non-Newtonian flows: A comparison with state-of-the-art RANS closures

In the present research, a comparative study of improved Large-Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) closures are carried out with the focus on the influence of terms accounting for the effect of Non-Newtonian (NN) power-law fluid rheology. Using different available databases for shear-thinning turbulent pipe flows, a new set of calibrated constants is proposed for the four-equation k-ε-ζ-f RANS model which results in improved overall performance compared to the original constants. Analyzing the results, the accuracy of this model in comparison with the conventional RANS models, to the first degree, is attributed to its intrinsic ability to account for the wall damping effect, which resulted in about 50% improvement in turbulent kinetic energy prediction with respect to the other RANS models, and then, to the extra NN terms leading to the more accurate prediction of the drag-reduction phenomenon. However, the sensitivity of this model results to the model constants is high which can question the validity of the constants for more practical high-Reynolds-number problems. On the other hand, LES models provided more reliable results with the best performance shown by the Dynamic Lagrangian (DL) SGS closure, especially in predicting mean apparent viscosity and second-order statistics. Both NN k-ε-ζ-f RANS and DL LES models demonstrated great potential for non-Newtonian turbulent flows and the choice between them would be based on the level of accuracy required and the limitation of computational costs.

LES predictions of confinement effect on swirling flow generated by single helical axial swirler

PurposeFor higher swirling flows (swirl > 0.5), flow confinement significantly impacts fluid flow, flame stability, flame length and heat transfer, especially when the confinement ratio is less than 9. Past numerical studies on helical axial swirler type systems are limited to non-reacting or reacting flows type Reynolds averaged Navier Stokes closure models, mostly are non-parametric studies. Effects of parametric studies like swirl angle and confinement on the unsteady flow field, either numerical or experimental, are very minimal. The purpose of this paper is to document modeling practices for a large eddy simulation (LES) type grid, predict the confinement effects of a single swirler lean direct injection (LDI) system and validate with literature data.Design/methodology/approachThe first part of the paper discusses the approach followed for numerical modelling of LES with the minimum number of cells required across critical sections to capture the spectrum of turbulent energy with good accuracy. The numerical model includes all flow developing sections of the LDI swirler, right from the axial setting chamber to the exit of the flame tube, and its length is effectively modelled to match the experimental data. The computational model predicts unsteady features like vortex breakdown bubble, represented by a strong recirculation zone anchored downstream of the fuel nozzle. It is interesting to note that the LES is effective in predicting the secondary recirculation zones in the divergent section as well as at the corners of the tube wall.FindingsThe predictions of a single helical axial swirler with a vane tip angle of 60°, with a duct size of 2 × 2 square inches, are compared with the experimental data at several axial locations as well as with centerline data. Both mean and unsteady turbulent quantities obtained through the numerical simulations are validated with the experimental data (Cai et al., 2005). The methodology is extended to the confinements effect on mean flow characteristics. The time scale and length scale are useful parameters to get the desired results. The results show that with an increase in the confinement ratio, the recirculation length increases proportionally. A sample of three cases has been documented in this paper.Originality/valueThe novelty of the paper is the modelling practices (grid/unsteady models) for a parametric study of LDI are established, and the mean confinement effects are validated with experimental data. The spectrum of turbulent energies is well captured by LES, and trends are aligned with experimental data. The methodology can be extended to reacting flows also to study the effect of swirl angle, fuel injection on aerodynamics, droplet characteristics and emissions.

Detailed Analysis of the Effects of Spacer Grid and Mixing Vanes on Turbulence in a PWR Subchannel Under DFFB Conditions Based on DNS Data

Spacer grids and mixing vanes exhibit a significant role in the thermal hydraulics of pressurized water reactors (PWRs), especially in the post loss-of-coolant accident regimes. A detailed analysis of the contrasting upstream and downstream turbulent flow features is of great importance to both system codes and computational fluid dynamics (CFD)–Reynolds-averaged Navier–Stokes (RANS) modeling. Further, with the advent of supercomputing resources and machine learning research, a data-driven approach to turbulence modeling is gaining popularity. However, owing to the complexities associated with large-scale, high-fidelity data collection capabilities, the application of machine learning–based turbulence models has been limited to simple geometries. In this work, using a highly scalable CFD code PHASTA, we have collected data from direct numerical simulations of a PWR subchannel with high spatial and temporal resolution. From the collected data we extract key turbulent flow features, including mean velocities and Reynolds stresses that highlight the effects of spacer grids and mixing vanes on downstream turbulence in a typical PWR subchannel. An invariant analysis of the anisotropic stress tensor is also presented, which further elucidates their effect on the nature of turbulence in the immediate upstream and downstream vicinity. The high-resolution data from the simulations are archived and intended for the development of data-driven RANS closure models that are capable of capturing the evolution of anisotropy in PWR subchannels.

Conjugate Heat Transfer and Fluid Flow Modeling for Liquid Microjet Impingement Cooling with Alternating Feeding and Draining Channels

Liquid microjet impingement cooling has shown the potential to be the solution for heat removal from electronic devices such as very-large-scale integration (VLSI) chips. The post-impingement dynamics of the jet, specifically the interaction between the liquid fronts on the surface engendered by the jets is a critical criterion improving the heat transfer characteristics. While some seminally important experimental studies have investigated this attribute, the amount of accurate data and analysis is limited by the shortcomings of real-life experiments. In this article, numerical investigations into the fluid dynamics and heat transfer in microjet cooling systems are carried out. Specifically, this paper addresses the question regarding the necessary fidelity of the simulations. Different Reynolds-averaged Navier–Stokes (RANS) models are compared to the Large Eddy Simulations (LES) simulation and the potential fidelity of different eddy-viscosity-based closures is clearly shown. Recommendations are made regarding the RANS closures that should give the best performance. It is demonstrated that the transition Shear Stress Transport (SST) model and k - ω SST model both show excellent ability to predict the local or average Nu, and also local level pressure coefficient f with less than 5% difference in the range of 30 < Red < 4000, compared with the reference LES model. For the experimental measurements in the range of 130 < Red < 1400, the LES model, transition SST model and k - ω SST model all show less than 25% prediction error. Moreover, it is shown that the validity of the unit cell assumption for the temperature and flow distribution depends on the flow rate.

Data-Free and Data-Driven RANS Predictions with Quantified Uncertainty

For the purpose of estimating the epistemic model-form uncertainty in Reynolds-Averaged Navier-Stokes closures, we propose two transport equations to locally perturb the Reynolds stress tensor of a given baseline eddy-viscosity model. The spatial structure of the perturbations is determined by the proposed transport equations, and thus does not have to be inferred from full-field reference data. Depending on a small number of model parameters and the local flow conditions, a ’return to eddy viscosity’ is described, and the underlying baseline state can be recovered. In order to make predictions with quantified uncertainty, we identify two separate methods, i.e. a data-free and data-driven approach. In the former no reference data is required and computationally inexpensive intervals are computed. When reference data is available, Bayesian inference can be applied to obtained informed distributions of the model parameters and simulation output.

Vortical structures and pressure pulsations in draft tube of a Francis-99 turbine at part load: RANS and hybrid RANS/LES analysis

Recognizing the limitations of the conventional linear-eddy-viscosity (LEVM) Reynolds-averaged Navier–Stokes (RANS) models to reproduce complex three-dimensional unsteady flows in hydraulic machinery, we performed a comparative assessment of a second-moment (Re-stress model, RSM) RANS closure and a hybrid RANS/LES method in capturing the flow and vortical structures in the draft tube of a Francis hydroturbine at off-design conditions. Considered is a case of part load (PL) at a flow rate of only 35% of the best efficiency point (BEP) characterised by multiple unsteady vortex systems. Despite some remaining uncertainties in generating the inflow conditions, both approaches reproduced reasonably well the measured mean velocity and the rms of its fluctuations, as well as the pressure spectrum with peaks detecting the precessing vortex core. In contrast to the common LEVMs, the Re-stress closure showed sufficient receptivity to intrinsic unsteadiness and reproduced well the overall flow and vortical patterns as well as the associated pressure pulsations in accord with the experiments. The hybrid RANS/LES method gave similar predictions as the RSM, but resolving a wider range of scales, which however, showed no significant effect on the dynamics of the dominant processing vortex core and the pressure pulsations.

Extending the bounds of ‘steady’ RANS closures: Toward an instability-sensitive Reynolds stress model

The incapability of the conventional Unsteady RANS (Reynolds–Averaged Navier Stokes) models to adequately capture turbulence unsteadiness presents the prime motivation of the present work, which focuses on formulating an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ωh (ωh=ɛh/k). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part of the total viscous dissipation rate ɛ, defined as ɛh=ɛ−0.5ν∂2k/(∂xj∂xj) (Jakirlic and Hanjalic, 2002), by applying the derivation rules to the expression for ωh. The model capability to account for vortex length and time scales variability was enabled through an additional term in the corresponding length-scale determining equation, providing a selective enhancement of its production, pertinent particularly to the highly unsteady separated shear layer region, modeled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010). The present model formulation, termed as SRANS model (Sensitized RANS), does not comprise any parameter depending explicitly on grid spacing. The predictive capabilities of the newly proposed length-scale determining model equation, solved in conjunction with Jakirlic and Hanjalic’s (2002) Reynolds stress model equation, are presently demonstrated by computing the flow configurations of increasing complexity featured by boundary layer separation from sharp-edged and continuous curved surfaces: backward-facing step flow, flow over a wall-mounted fence, flow over smoothly contoured periodically arranged hills and flow in a 3-D diffuser. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence and the near-wall Reynolds stress anisotropy in a plane channel. In most cases considered the fluctuating velocity field was obtained starting from steady RANS results.

Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures

Estimation of the uncertainty in numerical predictions by Reynolds-averaged Navier-Stokes closures is a vital step in building confidence in such predictions. An approach to model-form uncertainty quantification that does not assume the eddy-viscosity hypothesis to be exact is proposed. The methodology for estimation of uncertainty is demonstrated for plane channel flow, for a duct with secondary flows, and for the shock/boundary-layer interaction over a transonic bump.

Flow in an impeller‐stirred tank using an immersed‐boundary method

AbstractThe moderate Reynolds number flow developing in a cylindrical unbaffled stirred tank is studied using direct numerical simulation (DNS) and the results are compared with available experimental data and Reynolds Averaged Navier–Stokes (RANS) solutions. The geometry of the impeller is handled using an immersed‐boundary procedure implemented in a solver written for cylindrical coordinates. This allows efficient simulation of the flow at a reasonable computational cost and accurate prediction of the mean and rms velocity fields. For this configuration, RANS performs poorly because of the low Reynolds and strongly unsteady and inhomogeneous nature of the flow: many different flow structures are produced, ranging from small‐scale vortices generated at the blade tips to large‐scale meridional recirculation. It is shown, in addition, that inaccurate results are produced by the wrong (computational) assumption that an impeller with n blades produces instantaneous fields with an n‐fold symmetry. Because simple stirred‐tank configurations (like the present one) have been recently used to assess the performance of several RANS closures, the main message of this study is that simple geometrical configurations and low Reynolds numbers are not benign parameters for such a task. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1109–1118, 2004

Generation of Inflow Conditions in a Reynolds-Averaged Navier-Stokes Closure

Generation of Inflow Conditions in a Reynolds-Averaged Navier-Stokes Closure

Generation of inflow conditions in Reynolds-averaged Navier-Stokes closure

Generation of inflow conditions in Reynolds-averaged Navier-Stokes closure