Shear Stress Transport Model Research Articles

Burbujas de separación laminar en flujo en transición alrededor de perfiles Aerodinámicos

The purpose of this work is to apply the γ-Re θ turbulence model, which is one of the numerical methods of shear stress transport (SST) applicable to transient flow, to examine if it shows the expected laminar separation cells or bubbles. This condition is key in the way to guarantee that the numerical modeling of lift and drag forces in aerodynamic profiles is more faithful to corresponding experimental data. For this, several two-dimensional simulations implemented with OpenFOAM, a well-known Finite Volume Method (FVM) package, were carried out for a Reynolds number range between 1x10 4 and 5x10 , with the airfoils NACA0012, SG6043 and S826, in which the laminar separation bubbles usually form. Numerical results of lift and drag coefficients show correct prediction of experimental results and error is reduced by 3% when compared to other simulations. In particular, adequate performance of the model is observed for regions close to or greater than the angle of attack for which the aerodynamic profile stalls. On the other hand, the geometric footprint of the flow simulated with this γ-Re 5 transition SST model shows great improvement compared to previous studies regarding the formation of laminar separation bubbles, which in turn means better performance when calculating lift and drag coefficients. It is also concluded that laminar separation occurs in the three studied airfoils, being symmetric or asymmetric profiles.

Geometrical investigation of cooling channels with two alternated isothermal blocks under forced convective turbulent flow

The present work performs a numerical analysis of the geometrical investigation of a two-dimensional channel with two alternated isothermal rectangular blocks subjected to turbulent forced convective flows. Constructal Design associated with Exhaustive Search is used to investigate the influence of the geometry of the isothermal blocks over the performance of the cooling convective flows in a multi-objective viewpoint, i.e., considering the pressure drop and heat transfer rate. The time-averaged equations of continuity, momentum, and energy conservation are solved with the finite volume method. The k–omega shear stress transport model is used for the closure of turbulence. The effect of the two proposed degrees of freedom, the height/length ratio of the two blocks (H_{1}/L_{1} and H_{2}/L_{2}), is analyzed in relation to the proposed objectives. Regarding the thermal purpose, the geometry with the highest insertion into the channel led to the best performance, while the opposite configuration led to the best fluid dynamic performance. This behavior was similar to that previously found in the literature for forced convective laminar flows. For a multi-objective perspective, the use of technique for order preference by similarity to ideal solution indicated that asymmetric blocks led to the best multi-objective performance when both performance indicators had the same weight.

Two-equation turbulent viscosity model for simulation of transitional flows: An efficient artificial neural network strategy

Laminar-to-turbulent transition phenomena are ubiquitous in natural and industrial flows. As to the Reynolds-averaged Navier–Stokes (RANS) simulation method, the workhorse for accurate prediction of such flow regime boils down to the consideration of the transition effect in turbulence modeling. In this paper, an industrial–practical transition–turbulence model with excellent accuracy, robustness, and efficiency is established by the fully connected artificial neural network (ANN), which maps the relation between the RANS mean flow variables and an intermittency factor. A one-equation local correlation-based transition model coupled with Menter's shear stress transport (SST) model is taken as the benchmark. The present two-way coupling ANN model is trained with two National Advisory Committee for Aeronautics (NACA) airfoils, that is, NACA0012 and NACA2418, at various angles of attack and Mach numbers, while tested with the A-airfoil, NACA0015, and RAE 2822 supercritical airfoils in different flow states. The a posteriori test results manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress, and lift/drag/moment coefficient predicted by the ANN model are all in good agreement with those given by the benchmark transition-based SST model. Furthermore, the ANN model exhibits higher calculation efficiency and convergence speed than the traditional transition-predictive SST model. The present work may pave a new way for machine learning methods to be used in integrated transition–turbulence modeling toward industrial applications.

Validation of Pronghorn Pressure Drop Correlations Against Pebble Bed Experiments

The verification and validation of Pronghorn is imperative for predicting the fluid velocity, pressure, and temperature in advanced reactors, specifically high-temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, multidimensional thermal-hydraulic code developed by Idaho National Laboratory. The Pronghorn incompressible Navier-Stokes equations are validated by using the pressure drop measurements and axial velocity averaged from the particle image velocimetry data obtained at the engineering-scale pebble bed facility at Texas A&M University. Pronghorn and STAR-CCM+ porous media models using the Handley, Kerntechnischer Ausschuss, and Carman correlations comparably estimate the pressure drop better than other functions with a maximum 3.34% average relative difference compared to the experimental measurements. The precise average pebble bed porosity estimation has a large impact on the pressure drop. The implementation of the volume-averaged porosity in several sectors, with each sector’s thickness larger than the representative elementary length, has the potential to improve pressure drop modeling or provide more detailed velocity profiles in nuclear reactors with high aspect ratios. The wall effects can be considered using this approach, applying the relatively higher volume-averaged porosity near walls. In addition, the pressure gradients and volume- or surface-averaged axial velocities from the realizable two-layer and shear stress transport models are in good agreement with the porous media simulations and particle image velocimetry data.

Three-dimensional numerical analysis and experimental confirmation for investigating the ground-based lateral droplet ejection toward microgravity simulation

Rapid in situ manufacturing is significant in space exploration. Droplet-based printing technology with micrometer accuracy has great potential in space due to the advantages of convenient transportation, customized metal material, and good environmental adaptability. It could achieve the ground microgravity simulation by a small Bond number (Bo < 1). The present work proposes a new method to evaluate the reliability of the ground microgravity simulation in the lateral metallic droplet-based ejection. The three-dimensional model is developed to numerically analyze the droplet ejection dynamic process coupled with the volume of fluid method and the k–ω shear stress transport model. The model accuracy and efficiency are improved by the local fine grid. In addition, the computation is validated by the cryogenic alloy droplet ejection experiments and theoretical analysis. The proposed theoretical analysis equation has good agreement with the SnPb alloy droplet ejection trajectory. Reynolds number (Re), Weber number (We), Froude number (Fr), Ohnesorge number (Oh), and breakup length (Lb) are used to analyze the gravity influences on the droplet ejection process of different materials, nozzle length–diameter ratios, and crucible fluid unfilled heights. The ejection direction has little effect on the aluminum droplet formation time and breakup length and the gravity effect increases with the length–diameter ratio and unfilled heights. In simulated results, the minimum We number of the aluminum droplet formation is 0.22 and the cryogenic alloy droplet formation is 0.19. The reliability of ground physical microgravity simulation is dependent on material selection, and aluminum is more suitable than the cryogenic and SnPb alloys.

Numerical simulation of propulsive aerodynamic profiles

The problem of creating high-lift propulsive aerodynamic is considered. A method was developed for constructing an aerodynamic profile by solving the inverse problem of aerodynamics. The dependence of the lifting force of this profile on the volume of air sucked from its upper surface and from the angle of attack is studied. The profile under study was developed on the basis of the well-known Griffin/Goldschmid profile with air suction at the upper critical point. Three aerodynamic profiles have been developed. The first profile has a flat lower surface to obtain the ground effect. The second profile is similar to the first but has a slit nozzle near the trailing edge. The third profile is similar to the second but has a non-flat bottom surface and increased thickness. The solution of the inverse problem of aerodynamics was used to construct aerodynamic profiles within the model of an ideal gas. The pressure distribution on the upper part of the profile, its construction height and the range of angles of attack are from 0° to 16°, as well as the degree of rarefaction up to 0.5 atm in the gap through which the air was taken were set. For the second and third profiles, the ratio of the amount of air ejected through the nozzle to the amount of air taken from the upper surface of the profile was set. This ratio ranged from 50 % to 200 %. Numerical calculations were performed for each variant using the Spalart-Allmaras turbulence models and the Transition Shear Stress Transport (SST) and Langtry model. The parameters of the turbulence models were adjusted according to known reference data. The Reynolds number was in the range of 1.5·105–1.5·106. The profiles have a high lift coefficient Cy = 3–3.4 which is achieved when creating a vacuum in the air intake of 0.5 atm. Cy depends on the angle of attack almost linearly up to the maximum values. The greater the air flow through the slot nozzle, the greater is the Cy at a vacuum in the air intake of 0.5 atm. Significance for practical application. The developed profiles have a large thickness and create traction. These profiles are convenient to use in aircraft with large internal volumes, for example, those running on hydrogen fuel.

Numerical investigation to analyse the effect of fin shape on performance of finned tube heat exchanger

Numerical investigations are carried out to determine the effect of change in geometrical parameter of annular fin on thermal and hydraulic characteristics. Fin shape is changed by varying horizontal diameter of fin. Three different cases of annular fin are investigated corresponding to fin diameter ratio (X) of 0.65, 0.85 and 1. Turbulence is modelled using k-ω shear stress transport model. Relative assessment of tube with annular fin of different horizontal diameter (D01) is done for 2500 < Re < 13000. The comparison of Nusselt number reveals that circular tube with annular fin enhances heat transfer rate. Nusselt number augments by 35% and 10% in case of annular fin with diameter ratio of 0.65 and 0.85 as compared to that of annular fin with diameter ratio of 1.00 for 2500 < Re< 13000. Pressure drop augments with increase in horizontal diameter of fin and Reynolds number. Annular fin with diameter ratio of 0.65 performs better in terms of heat transfer and pressure penalty as compared to other cases for range of reported Reynolds number.

Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model’s input parameters. We develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model’s response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow.

Numerical Investigation of Supersonic Air-to-Air Ejectors Including Design Effects on Entrainment Efficiency

Abstract The objective of this work is to develop and validate a computational fluid dynamics (CFD) model of a supersonic air ejector, a device largely used in aircraft, and to determine how its efficiency behaves when some of its geometric parameters vary, fully exploring the physical phenomena of the problem. It is important to highlight that in the aeronautical industry the competitiveness of any device intrinsically relies on its efficiency, such that a CFD model for an ejector is indispensable for proper design. This paper presents a study of several turbulence models Rk–ε en, Rk–ε std, k–ω shear stress transport (SST), Spalart–Allmaras (SA), and generalized k–ω (GEKO). A validation process was conducted by comparing CFD results with two supersonic air ejector experiments. The turbulence model was also validated with these experiments, and it was concluded that the k–ω GEKO model is able to reproduce the physics of the supersonic air ejector problem with greater fidelity than traditional turbulence models in terms of entrainment ratio, with a 6% relative error reduction in relation to the traditional k–ω SST model, which has been considered by multiple authors as the best Reynolds-averaged Navier–Stokes (RANS) approach in ejector's CFD studies. After this validation process, the sensitivity of ejector efficiency to two geometric parameters was evaluated: the nozzle exit position and the ejector mixing chamber height.

Numerical study of flow separation control over a circular hump using synthetic jet actuators

This study deals with the wall resolved Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation of boundary layer flow separation over a circular hump model and its active control. An array of Synthetic Jet Actuators (SJAs) is implemented in the hump model to introduce a train of vortex rings into the boundary layer to control flow separation. The OpenFOAM solver is used to numerically simulate and analyze the fluid flow using the k–ω shear stress transport model. Hot wire anemometry and particle image velocimetry measurements are carried out to evaluate the accuracy of the URANS technique as well as the effectiveness of SJAs by comparing numerical predictions to experimental data. The time-averaged results are in a good agreement with experimental results and demonstrate a successful application of SJAs to delay the flow separation by the interactions of vortical structures with the separated shear flow. The three-dimensional simulation also reveals that near wall coherent flow structures (streamwise and spanwise vortices) are responsible for the wall shear stress components. The results can be used to better understand the performance of SJAs and to further improve future actuator configurations.

On the numerical assessment of flow losses and secondary flows in Pelton turbine manifolds

Different methods combining analytical guidelines, numerical simulations, and the manufacturer’s experience are employed to design and optimise the distributor manifold of a Pelton turbine. All these methods have in common to assume undisturbed straight inflow to the manifold, thus neglecting the upstream flow conditions. Our numerical simulations executed with the open-source code OpenFOAM v2012 show that the insufficient consideration of the upstream flow situation may lead to inaccurate predictions of the manifold flow. Five turbulence models were tested in our simulations, and the inflow turbulence intensity was varied from 1% to 10%. The flow quality was assessed by evaluating the head loss coefficient from total pressure drop, the head loss coefficient from the entropy production, the secondary velocity ratio upstream the injectors and the mass flow imbalances in the injectors. The study of turbulence models revealed that the k-ω Shear Stress Transport model predicted the head loss and secondary flows with reasonable accuracy. Also, the computationally less expensive model of Spalart-Allmaras leads to similar results and therefore emerges as an appropriate model for optimisation. The simulations with varying inflow turbulence intensity levels indicate a flow pattern change, if the specified inflow turbulence intensity is less than 4%. Below this value of inflow turbulence intensity, a significant increase of the secondary flow upstream of the injectors was observed.

Near Field Decay of Mach 2 Elliptical Jet in the Presence of Tangentially Injected Secondary Swirling Flow

This investigation explores the mixing promoting capability of tangentially injected secondary swirling flow on a Mach 2 elliptical jet issuing from an elliptical nozzle of aspect ratio 2. A detailed three-dimensional numerical analysis was carried out for the combination of different levels of pressure gradient at the nozzle exit and five swirl numbers. Reynolds-Averaged Navier-Stokes equation along with Shear Stress Transport model was solved to predict the flow filed. The presence of secondary swirling flow created large pressure gradient in the direction perpendicular to jet axis, resulting in enhanced mass entrainment leading to high spread of the controlled jet compared to the uncontrolled jet. Also, the secondary jet increased the turbulence level in the flow field for all the cases studied compared to that of free jet case, leading to a reduction in jet core length. The swirl number and the pressure gradient at the nozzle exit is found to have a strong effect on the core length reduction. A maximum of about 70% reduction in core length was achieved for nozzle pressure ratio 4 with secondary flow of swirl number 5.

프란시스 수차 모델 내 흡출관의 내부 유동 특성에 미치는 공기 주입구의 영향

Swirling flow inside draft tube at part load condition during cavitation inception induces large pressure fluctuations. For suppression of the draft tube surge, fins with air injection holes are employed on the draft tube wall. The protrusion of air injection holes obstructs the incoming flow and creates flow complexities near the holes. The present study transiently investigates the effect of protrusion of these holes on the performance and flow phenomena of the Francis turbine numerically. Reynolds averaged Navier-Stokes (RANS) equations are solved along with a two-phase mixture model using Scale Adaptive Simulation Shear Stress Transport (SAS-SST) model to solve the turbulent flows. The numerical methodology is then verified by an experiment based on the International Standard (IEC 60193) norms. The hole protrusion reduces the efficiency of the turbine and exhibits higher strength of the vortex rope which is minimized using fins without holes. The swirl number is reduced by about 34% for the draft tube without holes. The random pressure fluctuations caused by the hole’s intrusiveness are also suppressed when the holes are removed.

Capturing transition and non-transition flows with a new shear stress transport model

A new Shear Stress Transport (SST) k-ω model is devised to integrate salient features of both the non-transitional SST k-ω model and correlation-based γ-Reθ transition model. An exceptionally simplified approach is applied to extend the New SST (NSST) model capabilities toward transition/non-transition predictions. Bradshaw’s stress-intensity factor Rb=-uv¯/k can be parameterized with the wall-distance dependent Reynolds numberRey=ky/v; however, as the Rey is replaced by a “flow-structure-adaptive” parameterRμ=vT/v, the resulting Rb is capable of capturing various transition phenomena naturally. The prospective stress-intensity parameter Rb=Rb(Rey,Rμ) is incorporated in the constitutive relations for eddy-viscosity vT and production termPk. The proposed formulation is intrinsically plausible, having a dramatic impact on the prediction of bypass, separation-induced and natural transitions together with non-transitional flows. An extra viscous-production term Pklim is added with the k-equation to ensure proper generation of k at the viscous sublayer when computing separation-induced transition over a Low-Reynolds Number (LRN) airfoil. Results demonstrate that the NSST k-ω model maintains an excellent consistency with both SST k-ω and γ-Reθ models.

Detached eddy simulation on the structure of swirling jet flow field

The improved delayed detached eddy simulation method with shear stress transport model was used to analyze the evolution of vortex structure, velocity and pressure fields of swirling jet. The influence of nozzle pressure drop on vortex structure development and turbulence pulsation was investigated. The development of vortex structure could be divided into three stages: Kelvin-Helmholtz (K-H) instability, transition stage and swirling flow instability. Swirling flow could significantly enhance radial turbulence pulsation and increase diffusion angle. At the downstream of the jet flow, turbulence pulsation dissipation was the main reason for jet velocity attenuation. With the increase of pressure drop, the jet velocity, pulsation amplitude and the symmetry of velocity distribution increased correspondingly. Meanwhile the pressure pulsation along with the axis and vortex transport intensity also increased significantly. When the jet distance exceeded about 9 times the dimensionless jet distance, the impact distance of swirling jet could not be improved effectively by increasing the pressure drop. However, it could effectively increase the swirl intensity and jet diffusion angle. The swirling jet is more suitable for radial horizontal drilling with large hole size, coalbed methane horizontal well cavity completion and roadway drilling and pressure relief, etc.

Numerical study of statistically developed gas-liquid intermittent flows by the lens of three-dimensional simulations

Two-phase intermittent flows are characterized by an alternation between a region almost fully occupied by liquid (a liquid plug) and another one composed by a gas bubble. This type of flow is frequently found in industry, particularly in the transportation of oil and gas through pipelines. Their dynamics is commonly modeled with a one-dimensional approach, since long pipelines are employed, making 2D or 3D simulations unfeasible. The models always require an assessment of wall and interfacial friction factors, which are usually obtained by empirical correlations. In this work, from full 3D velocity fields across statistically developed slug unit cells, flow parameters needed for 1D models were determined. For that, several three-dimensional numerical simulations were performed using the open source platform OpenFOAM®. The two-phase flow was determined within a computational domain corresponding to a single slug unit cell, with periodic boundary conditions under imposed pressure gradient and overall void fraction, employing the Volume of Fluid (VOF) method. Both laminar and turbulent flows were studied. Turbulence was modeled with the k-ω Shear Stress Transport (SST) model. The axial velocity profile along the cross section, as well as slug parameters, were compared with available experimental data, showing a quite good agreement. From the results validated by experimental data, friction factors and momentum flux parameters were determined, allowing the development of corrections to improve the available 1D models.

Prediction of Cavitation Performance over the Pump-Jet Propulsor Using Computational Fluid Dynamics and Hybrid Deep Learning Method

The cavitation performance of an oblique flow field is different from that under a pure axial flow field. This study analyzed the hydrodynamic performance, bearing force, and tip clearance flow field under different rotating speeds and different cavitation numbers in an oblique flow field. Furthermore, this study proposed a hybrid deep learning model CNN-Bi-LSTM to quickly and accurately predict the bearing force of a pump-jet propulsor (PJP), which will solve the problem of time-consuming calculation and consumption of considerable computing resources in traditional computational fluid dynamics. The Shear–Stress–Transport model and Reynolds-averaged Navier–Stokes equations were utilized to procure the training and testing datasets. The training and testing datasets were reasonably divided in the ratio of 7:3. The results show that the propulsion efficiency decreased more obviously under higher rotating speed conditions, with a maximum decrease of up to 13.59%. The small cavitation numbers 1.4721 and high oblique angle significantly impacted the efficiency reduction; the maximum efficiency loss exceeded 20%. Thus, a small cavitation number 1.4721 is extremely detrimental to the propulsion efficiency of the PJP due to the large cavitation area. Moreover, the intensity of the tip clearance vortex continuously increased with the rotating speed. The CNN-Bi-LSTM deep model successfully predicted the phase difference and trend change of the propulsor bearing force under different conditions. The prediction difference was large at the crest and trough of the bearing force, but it is within the acceptable error range.

Capturing transition around low-Reynolds number hydrofoil with zero-equation transition model

Compared with the local correlation-based shear stress transport (SST) γ−Reθ transition model (where SST k−ω transport equations are coupled with intermittency γ and transitional momentum-thickness Reynolds number Reθ transport equations), relatively simple and convenient modifications are applied to the parent SST k−ω model for computing natural and separation-induced transitions over the hydrofoil at a low-Reynolds number (LRN). The curiosity toward hydrofoil performance at an LRN has been enhanced by increasing attention to autonomous marine systems, deserving numerical simulations for transitional flow using computational fluid dynamics. With the newly devised transitional SST (T-SST) model, the viscous sublayer blending function F2 is slightly modified, and a stress-intensity parameter as a function of eddy-to-laminar viscosity ratio RT is introduced; intended formulations are plausible and have significant impacts on the transition prediction. Owing to the inherent potential for predicting bypass transition, two anisotropic versions of the v¯2−f(V2F) turbulence model are selected to evaluate their competencies in capturing separation-induced and natural transitions. Results demonstrate that natural transition prediction is more challenging than separation-induced transition for the V2F model. Nonetheless, the T-SST model performs consistently well in replicating both transitional phenomena.

Hypersonic Turbulent Flow Reynolds-Averaged Navier–Stokes Simulations with Roughness and Blowing Effects

Thermal protection systems experience severe thermal load during atmospheric reentry of hypersonic vehicles. Inherent to the ablation process, roughness and blowing effects may appear, affecting the performance of the heat shield. The modeling and the simulation of these effects in the hypersonic regime are challenging and rarely compared to experimental data. In this paper, Reynolds-averaged Navier–Stokes simulations of hypersonic turbulent boundary layers with roughness and blowing wall conditions are performed on Holden’s experimental configurations (“Studies of Surface Roughness and Blowing Effects on Hypersonic Turbulent Boundary Layers over Slender Cones,” 27th Aerospace Sciences Meeting, AIAA Paper 1989-0458, 1989). Using the shear stress transport model. Four experimental configurations, characterized by different levels of turbulence compressibility, are considered. A detailed discussion is proposed about the behavior of equivalent sand grain corrections and blowing corrections in combination with turbulence compressibility corrections. The predictions of skin-friction coefficients and Stanton numbers are in good agreement with Holden’s experimental data. These results show that the combination of the Zeman compressibility correction and roughness/blowing wall corrections is promising for the simulation of hypersonic boundary layers over rough walls with blowing.

Uncertainty analysis of turbulence model in capturing flows involving laminarization and retransition

Flows experiencing laminarization and retransition are universal and crucial in many engineering applications. The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow. Specifically, two commonly used turbulence models are considered: the Spalart-Allmaras (SA) one-equation model and the Menter Shear Stress Transport (SST) two-equation model. Thereby, a series of steady Reynolds Averaged Navier-Stokes (RANS) predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients. As a result, both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization. Using the non-intrusive polynomial chaos method, solution uncertainties in velocity, pressure, and surface friction are quantified and analyzed, which reveals that the SST model possesses much great uncertainty in the non-laminar regime, especially for the logarithmic law prediction. Besides, a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty, and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method. The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models. Furthermore, the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.