Reynolds-averaged Navier-Stokes Model Research Articles

Experimental and numerical simulations of air quality in an urban canopy: Effects of roof shapes and atmospheric stability

The roof shapes of buildings and atmospheric stability play vital roles in dispersing and transporting pollutants in urban canopies. This study investigated the influence of roof shapes and atmospheric stability through experimental and numerical simulations. Wind flow and gas diffusion simulations were conducted around buildings in urban canopies using wind tunnel experiments and computational fluid dynamic models based on Reynolds-averaged Navier–Stokes models. Four building roof shapes and three atmospheric stability conditions were used in this study. The results of the experiment and numerical simulations were validated using quantitative computational models based on the validation metrics. The numerical simulation results corresponded with the experimental results for the flow and dispersion. The simulation results showed that the flow velocity of the slanted roof was higher than that of the other roof shapes. The pollutants accumulated near the slanted and pitched roofs' leeward side were higher than those in the flat and hip-shaped roofs. Pollutants in the building increased under stable atmospheric conditions and decreased under unstable atmospheric conditions.

Modeling radial turbine performance under pulsating flow by machine learning method

This work presents the development and application of a machine learning model to predict the unsteady performance of a turbocharger radial turbine subject to on-engine pulsating flow conditions. The model proposed, based on a fully connected neural network, predicts the instantaneous turbine torque and circumferentially-averaged relative inflow angle when given, as only inputs, the total pressure and temperature pulses and the time derivative of the total pressure pulse upstream of the turbine. The training data set for the model is obtained from an experimentally-validated Reynolds-averaged Navier-Stokes model and consists of various operating conditions characterized by different pulse amplitudes and frequencies. Heat transfer effects are neglected by the use of adiabatic boundary conditions while the rotational speed of the rotor is otherwise maintained fixed. Based on the results obtained, the model is shown capable of accurately predicting the turbine torque and local properties of the flow, such as the relative inflow angle, with a high degree of accuracy (coefficient of determination larger than 0.98 ). At first, the model is tested for both interpolation and extrapolation conditions. Given a training data set constituted by only three pulses characterized by different amplitudes, the model accurately predicts the turbine performance both for conditions inside and outside the range of amplitudes of the training data set. Lastly, the model is trained with a larger data set, including both variations of the pulse amplitude and frequency, in order to predict the performance of the turbine subject to a more general pulse shape. The error indicators show an improvement with respect to the extrapolation case due to the larger size of the training data set, showing also a great capability of the model to predict the unsteady performance of the turbine for a more general pulse shape. The model represents a fast and efficient approach for predicting the unsteady turbine performance as compared to more complex experimental set-ups and time-consuming 3D numerical simulations and a valid alternative to the more common 0D-1D models.

Space-filling single square and square fractal grids induced turbulence: Reynolds stress model parameters-optimization

The employment of grid-induced turbulent flow structures as a passive means of augmenting solid-fluid heat transfer is receiving considerable attention, especially in HVAC applications. However, there presently exists a gap in simulation approaches, where industry-accessible CFD packages are unable to accurately express crucial second-order turbulent flow statistics generated by space-filling single square grids (SSGs) and square fractal grids (SFGs). The present study reports a successful application of a revised Reynolds Stress Model (RSM), which accurately replicates the streamwise distributions of centerline mean flow velocity and turbulence intensity in the lee of one SSG (operating under three different flow Reynolds number ReDh) and five geometrically different SFG test cases after undergoing Nelder-Mead downhill simplex optimization of key RSM kernel parameters. The optimized RSM presents a disagreement of, at worst, 4.30% and 9.98%, respectively against experimental hot-wire anemometry measurements of first-order and second-order statistics, and is the first known instance of the RSM being validated for turbulence intensity predictions of SSG- and SFG-induced turbulence. Examination of RSM parameters reveals that the pre-factors for the rates of turbulence dissipation production and destruction (C1,ε and C2,ε) hold greatest effect on simulation accuracy, with additional optimization of the turbulent viscosity pre-factor (Cμ) required for SFG cases. This is attributed to the effect of enhanced turbulent transport due to the cascading and multiscale nature of SFG turbulence, which insofar could not be replicated by Reynolds-Averaged Navier-Stokes (RANS) models. The values of optimized C1,ε, C2,ε, and Cμ range between 1.057 to 1.697, 2.226 to 2.556, and 0.17 to 2.27, respectively. This leads to the largest deviation of −26.6%, 33.1%, and 200% for C1,ε, C2,ε, and Cμ, respectively, when compared to their corresponding default values. With regards to the sensitivity of this parameter set on grid design, it is shown that the grid's fractal iteration number N and thickness ratio tr have greatest influence on the variation of C1,ε, C2,ε, and Cμ, while the effect of ReDh is insignificant. Overall, this study presents an alternative approach to capture the anisotropic and inhomogeneous nature of SSG- and SFG-induced turbulence for industrial heat-transfer applications via an accessible RANS package, which was previously constrained to expensive DNS and LES studies.

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.

Evaluation of computational fluid dynamics models for predicting pediatric upper airway airflow characteristics.

Computational fluid dynamics (CFD) has the potential for use as a clinical tool to predict the aerodynamics and respiratory function in the upper airway (UA) of children; however, careful selection of validated computational models is necessary. This study constructed a 3D model of the pediatric UA based on cone beam computed tomography (CBCT) imaging. The pediatric UA was 3D printed for pressure and velocity experiments, which were used as reference standards to validate the CFD simulation models. Static wall pressure and velocity distribution inside of the UA under inhale airflow rates from 0 to 266.67mL/s were studied by CFD simulations based on the large eddy simulation (LES) model and four Reynolds-averaged Navier-Stokes (RANS) models. Our results showed that the LES performed best for pressure prediction; however, it was much more time-consuming than the four RANS models. Among the RANS models, the Low Reynolds number (LRN) SST k-ω model had the best overall performance at a series of airflow rates. Central flow velocity determined by particle image velocimetry was 3.617m/s, while velocities predicted by the LES, LRN SST k-ω, and k-ω models were 3.681, 3.532, and 3.439m/s, respectively. All models predicted jet flow in the oropharynx. These results suggest that the above CFD models have acceptable accuracy for predicting pediatric UA aerodynamics and that the LRN SST k-ω model has the most potential for clinical application in pediatric respiratory studies.

Aspect ratio and combined installation in fluidic oscillator-crossflow interactions

This paper describes a computational study of fluidic oscillator-crossflow interactions. Fluidic oscillators are high potential active flow control devices, which offer promise for cooling and flow separation. Previous experimental studies have investigated the internal/external flow fields of fluidic oscillators. This improved the understanding of three-dimensional flow fields; however, this has been limited to single aspect ratio nozzles in single variable installations. Research has not analyzed the effects of varying both oscillator parameters and installation conditions. Therefore, the present aim is to enhance flow field understanding by examining three aspect ratio (AR) nozzles in default perpendicular condition and in a “skewed incline” configuration (β = 60°, α = 75°). An unsteady Reynolds averaged Navier Stokes model was validated with prior experimental data and then used to evaluate time-averaged and time-accurate flow fields at three different blowing ratios. Strouhal number analysis uncovers the effectiveness of parametric changes. Internal flow fields are presented, identifying key differences and similarities. External flow field analysis in regard to spreading angles 55°–65° observes greater wall-normal penetration for lower AR oscillators with improved spanwise penetration for larger AR's. The combined installation produces stronger primary vortices, improving penetration along the wall, while inclination keeps vortices close to the wall. Oscillator effectiveness is dependent on the application.

Bayesian parameter estimation of SST model for shock wave-boundary layer interaction flows with different strengths

The Shock Wave-Boundary Layer Interaction (SWBLI) flow generated by compression corner widely occurs in engineering. As one of the primary methods in engineering, the Reynolds Averaged Navier-Stokes (RANS) methods usually cannot correctly predict strong SWBLI flows. In addition to the defects of the eddy viscosity assumption, the uncertainty of the closure coefficients in RANS models often significantly impacts the simulation results. This study performs parametric sensitivity analysis and Bayesian calibration on the closure coefficients of the Menter k-ω Shear-Stress Transport (SST) model based on the SWBLI with different strengths. Firstly, the parametric sensitivity on prediction results is analyzed using the Sobol index. The results indicate that the Sobol indices of wall pressure and skin friction exhibited opposite fluctuation trends with the increase of SWBLI strength. Then, the Bayesian uncertainty quantification method is adopted to obtain the posterior probability distributions and Maximum A Posteriori (MAP) estimates of the closure coefficients and the posterior uncertainty of the Quantities of Interests (QoIs). The results indicate that the prediction ability for strong SWBLI of the SST model is significantly improved by using the MAP estimates, and the relative errors of QoIs are reduced dramatically.

Modeling particle distribution in a ventilated room with modified discrete random walk methods

The airflow and micro-particle dispersion in a 3-D ventilated scaled room has been simulated numerically. The flow field was studied by the Eulerian method using a Reynolds Averaged Navier-Stokes model, and we used the Lagrangian approach to solve the equations of particle motion. The purpose is to evaluate and compare various discrete random walk methods (DRW) and continuous random walk methods (CRW) to evaluate particle concentration distribution in indoor environments. The isotropic DRW method’s performance has been compared with models in which anisotropy of turbulence is applied, including CRW and modified DRW models based on near-wall direct numerical simulation results, near-wall kinetic energy, and the helicity of the flow. The results reveal that the isotropic DRW method can predict particle concentration in the indoor environment, and using a modified DRW model is not necessary.

Model-form uncertainty quantification of Reynolds-averaged Navier–Stokes modeling of flows over a SD7003 airfoil

Reynolds-averaged Navier–Stokes (RANS) models are known to be inaccurate in complex flows, for instance, laminar-turbulent transition, and RANS uncertainty quantification (UQ) is essential to estimate the uncertainty in their predictions. In this study, a recent physics-based UQ framework that introduces eigenvalue, eigenvector, and turbulence kinetic energy perturbations to the modeled Reynolds stress tensor has been used to estimate the uncertainty in the flow field. We introduce a regression-based marker function that focuses on the turbulence kinetic energy perturbation for the simulation of laminar-turbulent transitional flows over an Selig–Donovan 7003 airfoil. We observed a monotonic behavior of the magnitude of the predicted uncertainty bounds varying with the turbulence kinetic energy perturbation. Importantly, the predicted uncertainty bounds show a synergy behavior that dramatically increases the size of uncertainty bounds and can successfully encompass the reference data when the eigenvalue perturbations are augmented with the marker function.

Investigation on corner stall prediction and flow control by blended blade and end wall technology in a compressor cascade based on modified Spalart–Allmaras model

Corner stall has a significant impact on the performance of compressor cascades, but it is difficult to predict precisely using conventional Reynolds-averaged Navier–Stokes models. In view of this, first, the Spalart–Allmaras (SA) turbulence model modified with helicity is recalibrated to predict corner stall accurately. The internal reasons why the modified SA model does not overestimate the extent and intensity of corner stall as the original SA model is further explored through the analysis of turbulence transport nature. The investigation of corner stall control in a modified National Advisory Committee for Aeronautics 65 cascade by the blended blade and end wall (BBEW) technology is then carried out using the recalibrated MSA model. The numerical results indicate that the BBEW technology can eliminate the separation vortex on the end wall and change the flow field from corner stall to corner separation. The best BBEW scheme reduces the total pressure loss coefficient by 14.13%. The BBEW technology can most significantly enhance the aerodynamic performance of the compressor cascade when the maximum BBEW thickness is close to the trailing edge. When the maximum BBEW thickness is in the same position, the control effect rises first and subsequently falls as the maximum BBEW thickness grows. These research results serve as a guide for choosing turbulence models and designing the BBEW schemes.

Frozen propagation of Reynolds force vector from high-fidelity data into Reynolds-averaged simulations of secondary flows

Successful propagation of information from high-fidelity sources (i.e., direct numerical simulations and large-eddy simulations) into Reynolds-averaged Navier–Stokes (RANS) equations plays an important role in the emerging field of data-driven RANS modeling. Small errors carried in high-fidelity data can propagate amplified errors into the mean flow field, and higher Reynolds numbers worsen the error propagation. In this study, we compare a series of propagation methods for two cases of Prandtl's secondary flows of the second kind: square-duct flow at a low Reynolds number and roughness-induced secondary flow at a very high Reynolds number. We show that frozen treatments result in less error propagation than the implicit treatment of Reynolds stress tensor (RST), and for cases with very high Reynolds numbers, explicit and implicit treatments are not recommended. Inspired by the obtained results, we introduce the frozen treatment to the propagation of the Reynolds force vector (RFV), which leads to less error propagation. Specifically, for both cases at low and high Reynolds numbers, the propagation of RFV results in one order of magnitude lower error compared to the RST propagation. In the frozen treatment method, three different eddy-viscosity models are used to evaluate the effect of turbulent diffusion on error propagation. We show that, regardless of the baseline model, the frozen treatment of RFV results in less error propagation. We combined one extra correction term for turbulent kinetic energy with the frozen treatment of RFV, which makes our propagation technique capable of reproducing both velocity and turbulent kinetic energy fields similar to high-fidelity data.

Numerical Modeling of Interactions between Solitary Waves and Floating Breakwaters

In the current numerical work, a 2D wave tank has been planned to explain the shared impacts among three different solitary waves and three different floating breakwaters by applying Reynolds-Averaged Navier-Stokes models and the volume of fluid method. Three dissimilar floating breakwaters (i.e., square breakwater, circular breakwater, and modified breakwater) were chosen. A total of eighteen cases were investigated, including three different floating breakwaters, a solitary wave (SW) with three different wave heights, and two different densities of floating breakwaters. We achieved the production of a solitary wave by moving a wave paddle (WP) and the motion of floating breakwater in two various directions by applying two different codes as user-defined functions. The dynamic mesh technique has been employed for re-forming mesh during the motion of the wave paddle and the floating breakwater. The numerical calculations have been confirmed by some numerical, analytical, and experimental case studies. First, the generation of a SW using the WP movement and the free motion of a heaving round cylinder on the free surface of motionless water were modeled and validated. Additionally, the effects of various parameters, including floating breakwater shape, floating breakwater density, and solitary wave height, on the hydrodynamic performances of the floating breakwater, the floating breakwater’s motions, and the free-surface elevation were considered under various conditions.

Application of data-driven RANS model in simulating indoor airflow.

The indoor environment has a significant impact on our wellbeing. Accurate prediction of the indoor air distribution can help to create a good indoor environment. Reynolds-averaged Navier-Stokes (RANS) models are commonly used for indoor airflow prediction. However, the Boussinesq hypothesis used in the RANS model fails to account for indoor anisotropic flows. To solve this problem, this study developed a data-driven RANS model by using a nonlinear model from the literature. An artificial neural network (ANN) was used to determine the coefficients of high-order terms. Three typical indoor airflows were selected as the training set to develop the model. Four other cases were used as testing sets to verify the generalizability of the model. The results show that the data-driven model can better predict the distributions of air velocity, temperature, and turbulent kinetic energy for the indoor anisotropic flows than the original RANS model. This is because the nonlinear terms are accurately simulated by the ANN. This investigation concluded that the data-driven model can correctly predict indoor anisotropic flows and has reasonably good generalizability.

Numerical Simulation of the Flow in the ONERA F1 Wind Tunnel

This paper presents the outcome of numerical simulations of the flowfield inside the ONERA F1 wind tunnel, which is a large-scale pressurized low-speed wind tunnel mostly used to investigate the takeoff and landing performance of aircrafts in high-lift configuration. The simulations were carried out under Reynolds-averaged Navier–Stokes modeling assumptions. Results were compared to available experimental data characterizing the tunnel flowfield, especially in the test section. The overall flow physics is well captured by the simulations. However, when looking at the result with a more demanding level of accuracy, some important characteristics of the velocity distribution in the test section, such as flow upwash and total pressure distribution, are not replicated. Reasons are discussed in the paper, and some recommendations are derived for future similar simulations.

Ensemble Kalman method for learning turbulence models from indirect observation data

In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-driven models in this category need full-field Reynolds stress data for training, which not only places stringent demand on the data generation but also makes the trained model ill-conditioned and lacks robustness. This difficulty can be alleviated by incorporating the Reynolds-averaged Navier–Stokes (RANS) solver in the training process. However, this would necessitate developing adjoint solvers of the RANS model, which requires extra effort in code development and maintenance. Given this difficulty, we present an ensemble Kalman method with an adaptive step size to train a neural-network-based turbulence model by using indirect observation data. To our knowledge, this is the first such attempt in turbulence modelling. The ensemble method is first verified on the flow in a square duct, where it correctly learns the underlying turbulence models from velocity data. Then the generalizability of the learned model is evaluated on a family of separated flows over periodic hills. It is demonstrated that the turbulence model learned in one flow can predict flows in similar configurations with varying slopes.

Development of Explainable Data-Driven Turbulence Models with Application to Liquid Fuel Nuclear Reactors

Liquid fuel nuclear reactors offer innovative possibilities in terms of nuclear reactor designs and passive safety systems. Molten Salts Reactors (MSRs) with a fast spectrum are a particular type of these reactors using liquid fuel. MSFRs often involve large open cavities in their core in which the liquid fuel circulates at a high speed to transport the heat generated by the nuclear reactions into the heat exchangers. This high-speed flow yields a turbulent field with large Reynolds numbers in the reactor core. Since the nuclear power, the neutron precursor’s transport and the thermal exchanges are strongly coupled in the MSFR’s core cavity, having accurate turbulent models for the liquid fuel flow is necessary to avoid introducing significant errors in the numerical simulations of these reactors. Nonetheless, high-accuracy simulations of the turbulent flow field in the reactor cavity of these reactors are usually prohibitively expensive in terms of computational resources, especially when performing multiphysics numerical calculations. Therefore, in this work, we propose a novel method using a modified genetic algorithm to optimize the calculation of the Reynolds Shear Stress Tensor (RST) used for turbulence modeling. The proposed optimization methodology is particularly suitable for advanced liquid fuel reactors such as the MSFRs since it allows the development of high-accuracy but still low-computational-cost turbulence models for the liquid fuel. We demonstrate the applicability of this approach by developing high accuracy Reynolds-Averaged Navier–Stokes (RANS) models (averaged flow error less than 5%) for a low and a large aspect ratio in a Backward-Facing Step (BFS) section particularly challenging for RANS models. The newly developed turbulence models better capture the flow field after the boundary layer tipping, over the extent of the recirculation bubble, and near the boundary layer reattachment region in both BFS configurations. The main reason for these improvements is that the developed models better capture the flow field turbulent anisotropy in the bulk region of the BFS. Then, we illustrate the interest in using this turbulence modeling approach for the case of an MSFR by quantifying the impact of the turbulence modeling on the reactor key parameters.

Numerical Study of Stratified Flames Using Reynolds Averaged Navier Stokes Modeling.

Reynolds averaged Navier Stokes technique was used to develop a validated numerical model for stratified flames. The validation was carried out with the experimental data of the non-swirl flames of the Cambridge dual annulus swirl burner. The RNG k–ε turbulence model along with the SG-35 skeletal chemical mechanism was found to give a good prediction of scalar and vector quantities while resulting in the reduction of computational time by 99.75% in comparison with that required for large eddy simulation techniques used in the literature. The effect of stratification at a constant input power, global equivalence ratio, and Reynolds number was examined. At stratification ratios (SRs = ϕin/ϕout) 1 and 2, intense burning, marked by the higher OH concentration, was observed close to the bluff body. Beyond SR = 2, the region of intense burning shifts downstream away from the bluff body. This is a result of the high equivalence ratio in the inner annulus, which is beyond the rich flammability limit of methane–air flames, and as a result, the primary flame region is shifted downstream after the mixtures from inner and outer annulus have mixed properly to produce a mixture with the equivalence ratio in the flammability limit. The maximum temperature was found to increase by 24.1% when the SR is increased from 1 to 2 and the combustion efficiency was found to significantly improve by 267%. The highest maximum temperature of 2249 K is observed for the mildly stratified flame at SR = 2. Beyond SR = 2, the maximum temperature decreases, while the combustion efficiency increases slightly.

Calibration of RANS model constant based on data assimilation and accurate simulation of separated flow

To improve the prediction accuracy of separated flow based on the Reynolds Averaged Navier–Stokes model, the model constants of the baseline Reynolds stress model are calibrated by the ensemble Kalman filter data assimilation method. The separated flow in a diffuser is taken as the object, and the wall pressure coefficients of the diffuser are used as the driving data. The results show that the method that recalibrates the model constants based on data assimilation is easy to implement and is an effective method. The wall pressure coefficients and the separation regions of the diffuser predicted by the baseline Reynolds stress model with the default model constants deviate greatly from the experimental observations. By recalibrating the model constants, the prediction accuracy of separated flow based on the baseline Reynolds stress model is improved. This provides an idea for the accurate simulation of separated flow based on the Reynolds Averaged Navier–Stokes model in engineering applications.

Application and assessment of the improved delayed detached eddy simulation model to the cold spray process: Toward high fidelity computation fluid dynamics simulations

Despite many years of research about the comprehension of fluid-dynamic related phenomena and improvements in the performance of cold spray systems, ensuring high fidelity simulations of gas and particle flow remains a challenge. In this work, a detailed high fidelity modeling, namely, improved delayed detached eddy simulation, in axisymmetric geometries was proposed and compared with a more usual numerical framework, the Reynolds averaged Navier–Stokes model. After its validation against literature data in three different nozzle configurations, the new model could demonstrate more accurate predictions of phenomena such as oblique shocks, bow shock, and particle–gas flow coupling. Finally, thanks to the high fidelity numerical framework, a new nozzle geometry with a narrower extension of the particle jet was proposed and assessed.

Towards numerical simulation of high part load pulsations in Francis turbines

One of the most interesting operating points of Francis turbines is the high part load point, which is characterized by synchronous pressure pulsations of large amplitude. Physical mechanisms of these pulsations are not well understood. Experimental observations show that the frequency of the pulsations is 1.5 to 4 times higher than the runner rotation frequency and there exists a 180 degree phase shift of pressure signal measured in the spiral casing and in the draft tube. Numerical modeling this operating point is challenging as it has to account several complex phenomena: cavitation, rotating vortex rope and interaction of the turbine flow with the whole water system of the test rig. In the present paper we carried out a series of 1D-3D calculations of a model turbine in an attempt to simulate the high part load pulsations. 1D hydro-acoustic equations were used for the upstream waterways, while 3D Reynolds averaged Navier-Stokes model of two-phase mixture was used for the turbine. Although the main factors were taken into account, these computations were not able to capture the high part load pulsations. Namely, the frequency and amplitude of the pressure pulsations were significantly lower than those in the experiment, and there was no phase shift in turbine domain. In order to investigate the shortcomings of the present model, we considered a problem of propagation of disturbances in two-phase “liquid-gas” flows. Several 2D test cases were numerically investigated using both incompressible and compressible gaseous phase model. It was shown that in the absence of phase transfer the compressible model correctly represents the speed of sound in both homogeneous and stratified flow regimes. From the other hand, in case of phase transfer the model damps out propagation of pressure disturbances in upstream direction. This behavior explains the failure of the present 1D-3D model to correctly describe the acoustic properties of the two-phase flow in the draft tube, playing a crucial role in the development of high part load pulsations.