Turbulence Model Parameters Research Articles

Research on turbulence model parameters for the prediction of waterjet propulsion pump hydrodynamic performance

Abstract The hydrodynamic performance of waterjet propulsion pumps has an important impact on improving the speed of waterjet propulsion ships. High-precision prediction of the hydrodynamic performance of water-jet propulsion pumps based on CFD is of great significance to improving the pump design quality. Based on the Reynolds-averaged Naiver-Stokes equation, this paper conducts a grid-independence verification on a water jet propulsion pump based on hydrodynamic test data, uses the Latin hypercube sampling method to generate SST k-ω turbulence model parameter space calculation samples, performs steady-state calculation on all samples, analyzes the sensitivity of changes in the parameters of the turbulence model to the prediction of the external characteristics of the waterjet propulsion pump, and finally obtains the influence of changes in the parameters of the turbulence model on the prediction of the external characteristics of the pump. Among them, the sensitivities of the three parameters β *, β1 and a1 are higher. The results show that the prediction accuracy of the external characteristics of the water jet propulsion pump can be effectively improved by correcting these three highly sensitive parameters, and the correction values of the three key parameters are obtained. The prediction error of the external characteristics of the water jet propulsion pump is reduced from 4.3% to less than 2.1%. A feedforward neural network is used to establish a mapping model between the three turbulence model parameters and the head coefficient and power coefficient of the waterjet propulsion pump in order to achieve rapid prediction. The genetic algorithm is applied to optimize the weights, thresholds and other coefficients in the neural network, thereby improving the prediction accuracy. Based on the optimized neural network, the genetic algorithm is used to optimize the three turbulence model parameters, and the optimized coefficients are obtained. The optimized turbulence model parameters are put into the hydrodynamic model for RANS simulation to verify the degree of optimization of the model coefficients by the genetic algorithm.

Data assimilation method and application of shear stress transport turbulence model for complex separation of internal shock boundary layer flow

Data assimilation method and application of shear stress transport turbulence model for complex separation of internal shock boundary layer flow

Fluid Flow and Effect of Turbulence Model on Large-Sized Triple-Offset Butterfly Valve

The performance a valve has been frequently estimated with numerical methods owing to limitations such as cost and place. In this study, for the triple-offset butterfly valves, the different sizes in various disc-opening cases was numerically conducted using different turbulence models of the two-equation turbulence models of k–ε, k-ω, and Reynolds stress model. The numerical calculations were validated against experimentally obtained valve flow test results. The numerical effect with the different turbulence models were analyzed with respect to the disc-opening cases. From the numerical analysis, the Reynolds stress model exhibits the most pronounced turbulence effects among the various turbulence models showing higher value of Reynolds normal stress near the valve disc region. The sensitivity of the turbulence model constants was examined using the 300 mm valve to observe the sensitivity of the turbulence model parameters in the two-equation turbulence models.

Uncertainty quantification and identification of SST turbulence model parameters based on Bayesian optimization algorithm in supersonic flow

AbstractThe Reynolds‐Averaged Navier–Stokes (RANS) model is the main model in engineering applications today. However, the normal value of the closure coefficient of the RANS turbulence model is determined based on some simple basic flows and may no longer be applicable for complex flows. In this paper, the closure coefficient of shear stress transport (SST) turbulence model is recalibrated by combining Bayesian method and particle swarm optimization algorithm, so as to improve the numerical simulation accuracy of wall pressure in supersonic flow. First, the obtained prior samples were numerically calculated, and the Sobol index of the closure coefficient was calculated by sensitivity analysis method to characterize the sensitivity of the wall pressure to the model parameters. Second, combined with the uncertainty of propagation parameters by non‐intrusive polynomial chaos (NIPC). Finally, Bayesian optimization is used to quantify the uncertainty and obtain the maximum likelihood function estimation and optimal parameters. The results show that the maximum relative error of wall pressure predicted by the SST turbulence model decreases from 29.71% to 9.00%, and the average relative error decreases from 9.86% to 3.67% through the parameter calibration of Bayesian optimization method. In addition, the system evaluated the calibration effect of three criteria, and the calibration results parameters under the three criteria were all better than the calculated results of the nominal values. Meanwhile, the velocity profile and density profile of the flow field were also analyzed. Finally, the same calibration method was applied to the supersonic hollow cylinder and BSL (Baseline) turbulence model, and the same calibration results were obtained, which verified the universality of the calibration method.

Analysis of turbulence intensity in the megacity of Beijing by High-frequency observations on a 325-m Tower

Turbulent flow over complex urban morphology poses challenges to utilization of distributed wind energy in cities. In this paper, turbulence intensity (TI), which is often used to guide wind turbine design and evaluate wind power production, is analyzed by high-frequency observations on a 325-m tower located in the downtown of Beijing, China. The results show that the characteristics of TI, including the diurnal variation, the statistical distribution, and the relations between TI and wind speeds near the ground are significantly different from these at higher heights. It is also found that the normal turbulence model (NTM) with the parameters recommended by the IEC standard cannot fit the data well. The new NTM parameters are given by the least-square fittings. Besides, a three-parameter model is found to fit the data well and performs slightly better than the NTM with the least-square fitting parameters. This research indicates that the NTM parameters in the IEC standard should be re-evaluated in urban areas, and different turbulence model parameters are recommended for higher and lower hub heights.

Effect of Turbulence Model and Spray Parameters on Kerosene Fuelled Scramjet Combustor

Numerical simulations are carried out for scramjet combustor with fuel injector struts to evaluate its performance for ground test conditions. Simulations were carried out for non-reacting and reacting flow with equivalence ratio of 1.0. CFD predicted top wall pressure compared reasonably well with experimental results except the upstream (ahead of the fuel injection) regions of the combustor where CFD has predicted higher values compared to the measured values. Effect of various spray distribution and turbulence models on wall pressure distribution and performance of the combustor studied. SST-kw turbulence model has predicted close to experimental data at upstream of combustion compared to k-e, k-w turbulence models. The net calculated combustion efficiency and achieved thrust at exit of combustor are 3% and 2.7% respectively higher in k-w compared to SST-kw though total pressure recovery in all three cases are almost similar.

Real-Time Simulation of CNG Engine and After-Treatment System Cold Start Part 1: Transient Engine-Out Emission Prediction Using a Stochastic Reactor Model

<div class="section abstract"><div class="htmlview paragraph">During cold start of natural gas engines, increased methane and formaldehyde emissions can be released due to flame quenching on cold cylinder walls, misfiring and the catalyst not being fully active at low temperatures. Euro 6 legislation does not regulate methane and formaldehyde emissions. New limits for these two pollutants have been proposed by CLOVE consortium for Euro 7 scenarios. These proposals indicate tougher requirements for aftertreatment systems of natural gas engines.</div><div class="htmlview paragraph">In the present study, a zero-dimensional model for real-time engine-out emission prediction for transient engine cold start is presented. The model incorporates the stochastic reactor model for spark ignition engines and tabulated chemistry. The tabulated chemistry approach allows to account for the physical and chemical properties of natural gas fuels in detail by using a-priori generated laminar flame speed and combustion chemistry look-up tables. The turbulence-chemistry interaction within the combustion chamber is predicted using a K-k turbulence model. The optimum turbulence model parameters are trained by matching the experimental cylinder pressure and engine-out emissions of nine steady-state operating points.</div><div class="htmlview paragraph">Subsequently, the trained engine model is applied for predicting engine-out emissions of a WLTP passenger car engine cold start. The predicted engine-out emissions comprise nitrogen oxide, carbon monoxide, carbon dioxide, unburnt methane, formaldehyde, and hydrogen. The simulation results are validated by comparing to transient engine measurements at different ambient temperatures (-7°C, 0°C, 8°C and 20°C). Additionally, the sensitivity of engine-out emissions towards air-fuel-ratio (λ=1.0 and λ=1.3) and natural gas quality (H-Gas and L-Gas) is investigated.</div></div>

Bayesian uncertainty quantification analysis of the SST model for transonic flow around airfoils simulation

Transonic flow simulation is a common but complex task in engineering, and poses a great challenge to computational fluid dynamics using the Reynolds-averaged Navier–Stokes approach. One of the important factors influencing the complexity of this task is the uncertainty introduced by turbulence models. In this paper, to improve the performance of the shear stress transport model, a Bayesian uncertainty quantification analysis of turbulence model parameters is carried out on transonic flow around the RAE2822 airfoil and the ONERA M6 wing. First, the Sobol indices are obtained for sensitivity analysis, the results of which show that the pressure coefficients are mainly sensitive to four parameters a1, κ, β⁎, and β1. A posterior uncertainty analysis is then performed based on the pressure coefficients of two-dimensional sections. The maximum a posteriori estimates from the two examples indicate opposite trends for the predicted shock wave positions. In the predictions for RAE2822, the shock wave position is advanced, while in those for ONERA M6, it is delayed. The estimates from RAE2822 enable a better prediction capability at a small angle of attack, while those from ONERA M6 enables an ability to simulate flow with separation at a large angle of attack, mainly because of the increase in a1. In practical engineering applications, the choice between the two sets of calibrated parameters to achieve the best simulation results may be facilitated by reference to experimental data.

Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning

The paper considers the slope flow simulation and the problem of finding the optimal parameter values of this mathematical model. The slope flow is modeled using the finite volume method applied to the Reynolds-averaged Navier–Stokes equations with closure in the form of the k−ωSST turbulence model. The optimal values of the turbulence model coefficients for free surface gravity multiphase flows were found using the global search algorithm. Calibration was performed to increase the similarity of the experimental and calculated velocity profiles. The Root Mean Square Error (RMSE) of derivation between the calculated flow velocity profile and the experimental one is considered as the objective function in the optimization problem. The calibration of the turbulence model coefficients for calculating the free surface flows on test slopes using the multiphase model for interphase tracking has not been performed previously. To solve the multi-extremal optimization problem arising from the search for the minimum of the loss function for the flow velocity profile, we apply a new optimization approach using a Peano curve to reduce the dimensionality of the problem. To speed up the optimization procedure, the objective function was approximated using an artificial neural network. Thus, an interdisciplinary approach was applied which allowed the optimal values of six turbulence model parameters to be found using OpenFOAM and Globalizer software.

Analysis of adaptive mesh refinement in a turbulent buoyant helium plume

AbstractThe study evaluates OpenFOAM's adaptive mesh refinement (AMR) capabilities and accuracy when applied to numerical simulations of turbulent buoyant flows. To this purpose, large eddy simulations of Sandia's turbulent helium plume test case are considered, a scenario with similar characteristics (in terms of air entrainment and vortex shedding) to those encountered in large‐scale fires. Comparison is made of the relative accuracy (in terms of both first and second order statistics), the predicted puffing frequencies and the computing times of numerical simulations using AMR and static meshes. Additionally, a sensitivity study on different AMR parameters is conducted and an evaluation of the performance of the dynamic Smagorinsky model when combined with AMR is made. Overall, the predictions of AMR are very satisfactory, in terms of both accuracy and computing times, compared to the use of static meshes of different sizes. Nevertheless, it is observed that a careful choice of a static mesh can result in equally accurate predictions with comparable, or even smaller, computing times than AMR for the case at hand. Additionally, the use of AMR slightly modified the entrainment characteristics in the near‐field region of the plume and (significantly) altered some of the, dynamically determined, turbulence model parameters.

Environmental contours for wind-resistant bridge design in complex terrain

Accurate estimation of the extreme wind fields is crucial for long-span bridge design. The current practice is focused on estimating the extreme mean wind speed, neglecting the inherent uncertainty in the turbulence model parameters. However, full-scale measurements on bridges show that such uncertainties are significant and should be considered in design. Here, the environmental contour method (ECM) is used to obtain long-term extreme wind fields considering uncertainties from the mean wind speed, turbulence intensities and spectral parameters measured at the Sulafjord Bridge site. Design contours of combinations of wind field parameters are obtained for target return periods of 4, 50 and 100 years. The contours are based on a proposed probabilistic modeling strategy that combines hindcast mesoscale simulations and field measurements. The contour estimates are also compared with state-of-the-art design values from the design recommendations. It is concluded that the environmental contours provide a more complete and yet intuitive description of the wind field at the bridge site compared to the current design methodology. The ECM is found suitable for obtaining design wind fields at new long-span bridge sites as it makes use of the limited site data more efficiently and it is still easy-to-use for the practicing engineer.

Global sensitivity analysis and uncertainty quantification of soot formation in an n-dodecane spray flame

Quantifying the uncertainty of soot formation in a turbulent combustion simulation remains a challenging task. In this work, global sensitivity analysis and uncertainty quantification of soot formation in the widely known Spray-A flame have been carried out. The numerical simulation reasonably predicts the measured penetration length, ignition delay, flame lift-off length, and soot volume fraction at quasi-steady state, providing a good baseline for the subsequent analysis. The active subspace method has been applied to perform global sensitivity analysis, with the peak soot volume fraction on centerline (PSVF-c) and the axial location of the peak soot volume fraction on centerline (LPSVF-c) at 4 ms being chosen as the quantities of interest (QoIs), and the parameters in soot and turbulence model being considered as the uncertainty inputs. It is found that at the early stage of the spray flame, e.g., 1 ms after the start of injection, more than one dimensional active subspace is needed to characterize the input space, while the active subspace tends to one dimension as the spray flame approaches the quasi-steady state. At the quasi-steady state of the spray flame, surface growth rate parameter is the controlling parameter for PSVF-c. Meanwhile, LPSVF-c is controlled by turbulence model parameters. Uncertainty quantification for soot formation is performed by constructing the response surfaces in the active subspace to map the input parameters to the QoIs. The 95% confidence interval due to the uncertainty of turbulence model, soot model and the overall uncertainty of these two models are [6.64,6.91], [6.59,8.05] and [6.52,8.02] ppm for PSVF-c, and [78.17,81.02], [79.39,80.21] and [78.26,81.22] mm for LPSVF-c. This work demonstrates the potential of using the active subspace method for global sensitivity analysis and uncertainty quantification of the soot formation in turbulent spray flames.

Error Quantification for the Assessment of Data-Driven Turbulence Models

Data-driven turbulence modelling is becoming common practice in the field of fluid mechanics. Complex machine learning methods are applied to large high fidelity data sets in an attempt to discover relationships between mean flow features and turbulence model parameters. However, a clear discrepancy is emerging between complex models that appear to fit the high fidelity data well a priori and simpler models which subsequently hold up in a posteriori testing through CFD simulations. With this in mind, a novel error quantification technique is proposed consisting of an upper and lower bound, against which data-driven turbulence models can be systematically assessed. At the lower bound is models that are linear in either the full set or a subset of the input features, where feature selection is used to determine the best model. Any machine learning technique must be able to improve on this performance for the extra complexity in training to be of practical use. The upper bound is found by the stable insertion of the high fidelity data for the Reynolds stresses into CFD simulation. Three machine learning methods, Gene Expression Programming, Deep Neural Networks and Gaussian Mixtures Models are presented and assessed on this error quantification technique. We further show that for the simple canonical cases often used to develop data-driven methods, lower bound linear models can provide very satisfactory accuracy and stability with limited scope for substantial improvement through more complex machine learning methods.

Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES

ABSTRACT The objective of this study is to obtain accurate flow field analysis results in a short computational time by using data assimilation, which increases the accuracy of Reynolds averaged Navier-Stokes (RANS) simulations with low grid resolution. The large-eddy simulation (LES) results are assimilated into RANS simulations. In those simulations, the turbulence-model parameters are optimised by an ensemble Kalman filter with a proposed method for adaptive hyperparameter optimisation. The target of calculations is the flow field around a square cylinder of the Reynolds number of approximately . Only the surface pressure of the square cylinder is used as an observation variable. For this shape, the assimilated RANS flow field is similar to that given by the LES analysis, and the drag coefficient reproducibility is improved by . The turbulence-model parameters are also used in the analyses of different cross-sectional shape and are found to improve the reproducibility of the flow field.

Bayesian Uncertainty Reduction of Generalised k-ω Turbulence Model for Prediction of Film-Cooling Effectiveness

In this study, Reynolds-averaged Navier-Stokes (RANS) simulations were carried out to predict the film cooling effectiveness of an inclined round jet in crossflow using turbulence model parameters optimised based on measurement data. The posterior distributions of the generalised (GEKO) turbulence model parameters were estimated using a computationally efficient surrogate model with the Markov chain Monte Carlo method, which provides a framework for probabilistic parameter estimation based on measurement data. The results show that using the maximum a posterior parameters for a blowing ratio of 0.5 gives better predictions than using the default parameters of the GEKO model. The estimated parameters were then applied to flows with a higher blowing ratio and different hole geometry to evaluate the generalisation performance. In both cases, the results were improved by properly predicting the spread of the cooling flow.

Uncertainty analysis and calibration of SST turbulence model for free shear layer in cavity-ramp flow

The development and reattachment of the free shear layer in supersonic flows have been a widely encountered phenomenon in engineering, and are gaining increasing interest from researchers who investigate such complex flow structures using numerical simulation methods. Among these methods, Reynolds Averaged Navier-Stokes (RANS) still plays an important role in application problems. However, the uncertainty of the parameters in RANS turbulence model affects the reliability and accuracy of predictions. Therefore, the purpose of this study is to conduct a detailed uncertainty analysis of the parameters in the shear-stress transport (SST) turbulence model for the free shear layer in a cavity-ramp flow. In the current study, uncertainty quantification was conducted with the construction of a surrogate model between the parameters and calculation results using the non-intrusive polynomial chaos (NIPC) method. Next, for sensitivity analysis, the Sobol index of each parameter was calculated to identify the key parameters mainly responsible for the uncertainty. Based on the above results, Bayesian inference was employed to calibrate these key parameters by leveraging experimental data. The results show that the calculated wall pressure and skin friction of the ramp suffer a non-negligible uncertainty caused by the model parameters, and parameters a1, σω2, β2, κ, and β1 are identified as the key parameters in this type of flow. Subsequently, the calibrated values for the key parameters are obtained through Bayesian inference, which could significantly improve prediction results in the original case. Furthermore, the applicability of the SST model with calibrated parameters is verified under different free-stream conditions.

Calibration of \u03ba-\u03b5 turbulence model for thermal\u2013hydraulic analyses in rib-roughened narrow rectangular channels using genetic algorithm

Nowadays, applications of turbulent fluid flow in removing high heat flux in rib-roughened narrow channels are drawing much interest. In this work, an improved version of the κ-ε turbulence model is proposed for better prediction of thermal–hydraulic characteristics of flow inside rib-roughened (pitch-to-rib height (p/k) ratio = 10 and 20) narrow channels (channel height, H = 1.2 mm and 3.2 mm). For this, the four turbulence model parameters, Cμ, Cε1, Cε2, and σk, are calibrated. These parameters are adjustable empirical constants provided for controlling the accuracy of the turbulence model results when needed. The simulated data are used to develop correlations between the relative errors in predicting the friction factor (f), Nusselt number (Nu), and the model parameters using a multivariate nonlinear regression method. These correlations are used to optimize the errors using genetic algorithm. Results reveal that the calibrated parameters are not the same for all the narrow channel configurations. After calibration, the overall predictive improvements are up to 35.83% and 27.30% for p/k = 10 and p/k = 20 respectively when H = 1.2 mm. Also, up to 15.48% and 18.05% improvements are obtained for p/k = 10 and p/k = 20 respectively when H = 3.2 mm. The role of the two parameters Cε1 and Cε2 are found to be of primary importance. Furthermore, three types of nanofluids i.e. Al2O3-water, CuO-water, and TiO2-water are studied using the calibrated model to check the potentiality of heat transfer enhancement. Among them, CuO-water nanofluid is predicted to have around 1.32 times higher value of Nu than pure water for the same narrow channel configuration.Article Highlightsκ-ε turbulence model is calibrated for rib-roughened narrow rectangular channels using genetic algorithm.Cε1 and Cε2 are the most influential parameters on the performance of the model inside rib-roughened narrow channel.Suggested calibration process is more effective for channel height of 1.2 mm than 3.2 mm.

Calibration of Spalart-Allmaras model for simulation of corner flow separation in linear compressor cascade

This study focuses on the calibration of Spalart--Allmaras turbulence model parameters using the Bayesian inference approach to reproduce experimental measurements of corner flow separation in linear compressor cascade. The quantity of interest selected for the calibration process is the pitchwise distribution of Mach number in the wake of the linear compressor cascade. The model parameters are assumed to be random variables obeying uniform prior probability distributions. Sensitivity analysis is used to rank the importance and select the most influential turbulence model parameters for the calibration process. The sensitivity ranking indicates that two model parameters cb1 and kappa are the most influential random variables resulting in a two--parameter Bayesian calibration process. The likelihood distribution is specified in the form of the Gauss distribution to include the experimental uncertainty. The likelihood distribution is used together with prior distribution to compute posterior probabilities of selected model parameters. The polynomial chaos expansion is employed as a surrogate model to reduce the cost of posterior calculation. Numerical simulations with calibrated turbulence parameters show a significant increase in the accuracy of Mach number profile prediction for separated flows in linear compressor cascade. Numerical simulations also demonstrate that the calibrated set of model coefficients produce accurate predictions of the total pressure and Mach number profiles for the range of incidence angles that were not part of the calibration process.

Numerical investigation of conventional and tapered Savonius hydrokinetic turbines for low-velocity hydropower application in an irrigation channel

In the present work, computational fluid dynamics simulation was carried out using ANSYS Fluent to study the performance of conventional and tapered turbine blades for hydrokinetic power generation. The sliding mesh technique is used to study the influence of taper on conventional Savonius turbine using the SST k-ω turbulence model and performance parameters were determined. The geometric parameters used in the present simulation for conventional and tapered turbine blades are aspect ratio and overlap ratio of 1.0 and 0.0. The inlet velocity and depth of water used for present simulation are 0.5 m/s and 103.6 mm for both conventional and tapered turbine blades. The results show that a 5% increase in the performance of a conventional turbine as compare to tapered turbine blade with a taper angle of 5°. The value of maximum coefficient of power for conventional Savonius turbine blade is 0.21 with a tip speed ratio 0.9. The flow field around the conventional and tapered turbine blades at different angular positions are analysed. It was found that there is a loss of energy at the exit side of the advancing blade for the case of tapered turbine, that leads to 5% reduction of performance as compared to the conventional turbine.

Determination of integral turbulence model parameters as applied to the calculation of flows in fuel assemblies of fast reactors in porous-body approximation

This work aimed to correct the integral turbulence model developed earlier for assemblies of smooth rods. Two variants of the fuel assembly design were considered. In the first variant, the fuel rods were spaced using spacer grids. The presence of a spacer grid does not require a change in the form of the system of equations but leads to a change in the form of the resistance tensor and the generation of turbulence in the spacer grid region. In the second variant, a wire-wrapped fuel bundle was analyzed. The presence of a wire-wrapped fuel bundle requires an additional term in the equation for the conservation of momentum and change in the form of the resistance tensor. The simulations were obtained by CFD code ANSYS CFX and aimed at the determination of parameters involved in an integral model of turbulence being developed for modeling nuclear-reactor cores and heat exchangers in anisotropic porous-body approximation.