Allmaras Model Research Articles

Friction factor and heat transfer prediction of rocket engine cooling channels in numerical simulations with high roughness Reynolds number

In literature, it is widely recognized that surface roughness significantly influences friction and heat transfer. This effect is especially pronounced in additive manufactured components, which are increasingly important in the space sector. However, using numerical approaches to predict their performances is challenging because the correlations and the numerical models available for high roughness conditions have to be tuned with respect to the specific case. This study aims to benchmark existing modeling strategies and to compare the results against the experimental results of additively manufactured rocket engine cooling channels. To achieve this, the Spalart–Allmaras model equipped with the Boeing roughness correction was implemented in ANSYS Fluent and tested on various test conditions. The goal is to determine the best-fitting sand-grain parameter values that match experimental data in terms of friction factor and compare the heat transfer predictions regarding coolant temperature, wall temperature, and Nusselt number. Eventually, a correction of the turbulent Prandtl number was demonstrated to be needed. Data from literature and empirical correlations for high values of roughness Reynolds number are gathered and compared with the outcomes from this work, giving satisfying results.

Viscous-Layer Compressibility Correction for Two-Equation Reynolds-Averaged Navier–Stokes Models

The baseline two-equation Reynolds-averaged Navier–Stokes (RANS) models include fluid density but lack calibration for compressible flows, making them inadequate for high Mach numbers. Various compressibility corrections have been proposed to integrate the van Driest transformation or the semilocal transformation, i.e., a given compressible law of the wall, into the RANS formulation. Prior work has focused mainly on the logarithmic layer, but upon evaluating these log-layer compressibility corrections, we find that they do not significantly improve skin friction estimates. To overcome this challenge, we develop viscous-layer compressibility corrections. We do that by altering the dissipation terms. These corrections conform the RANS model to the semilocal scaling, resulting in more accurate predictions of mean velocity and temperature in a posteriori tests. Although not the primary focus of this study, we also find that the baseline one-equation Spalart–Allmaras model, which was proposed before the concept of semilocal scaling, produces results consistent with the semilocal scaling in a posteriori tests without requiring any compressibility correction.

Turbulence effects in the topology optimization of compressible subsonic flow

AbstractTurbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds‐Averaged Navier–Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre‐Averaged Navier–Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart–Allmaras model, which differs from the usual Spalart–Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization.

Evaluation of turbulence models for the prediction of flow properties in vegetated channels

The performance of turbulence models was investigated to predict the flow and turbulence features of the vegetated channel using computational fluid dynamics (CFD). The Ansys Fluent, CFD software was implemented for the numerical studies. The flow was three-dimensional, incompressible, steady, and turbulent. Ten turbulence models, provided by Ansys Fluent, were implemented for the comparative study. The numerical model was validated against an experimental study conducted in the literature. The numerical studies show that the Renormalization group k–ε model is the most successful model for predicting the flow characteristics of the vegetated channel with a Root Mean Square Error (RMSE) value of 0.2752. At the same time, the Reynolds Stress Model gives the least successful predictive performance, indicated by an RMSE value of 0.4302. Moreover, the Spalart–Allmaras (S–A) model offers the shortest computation time with a value of 6652.393 s, whereas the Shear Stress Transport k–ω model proves to be the most time-consuming with a value of 11 952.219 s. The velocity of water flow in a channel is not uniform as it is slower at the surface of leaves and faster in the free zones. The maximum velocity is observed in the middle section of the channel, below the leaf, and between the roots with the value of u = 0.1158 m/s. Furthermore, the characteristics of turbulence in a channel are influenced by several factors such as channel geometry, flow velocity, and vegetation distribution. As a result, the presence of vegetation in a channel affects the flow and turbulence characteristics of the water significantly.

Numerical and experimental investigations of flow separation control through a linear compressor cascade

Modern large-scale gas turbines are equipped with high-pressure ratio compressors to increase engine work and its overall efficiency. Flow separation and energy losses are also two interrelated phenomenon associated with changes in compressor loading level and performance. This paper examines therefore the control of flow separation using a passive-control technique. An arced divergent-convergent slot grooved from the blade pressure side to its suction side was adopted to control flow separation, reducing the losses through a linear compressor cascade. The spanwise location of the slot was selected based on CFD simulations where the corner separation was predicted. The slot height in the spanwise direction was selected to be 8% of the blade height at the end-wall side. The present work was performed experimentally and numerically at an inlet Reynolds number,Rec=ρV∞C/μ=2.98×105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{ec}=\\rho {V}_{\\infty }C/\\mu =2.98\ imes {10}^{5}$$\\end{document}, covering a wide range of incidence angles from +6∘to-6∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+ 6^{ \\circ } {\ ext{ to}} - 6^{ \\circ }$$\\end{document}. The experimental work was carried out using a linear cascade test section consisting of six NACA 65-009 blade profiles integrated into a low-speed wind tunnel. A five-hole pressure probe system was used to obtain main flow parameters. Numerically, four turbulence models, including Spalart–Allmaras (S–A) model, Realizable (R k-ε) model, Shear-Stress Transport (SST k-ω) model, and Reynolds Stress model (RSM) were tested to predict the velocity and pressure fields. Good agreement between the experimental measurements and the numerical results, which were obtained using the RSM turbulence model in terms of velocity profiles and total pressure downstream of blades. It was observed also that the use of the arced-slotted blades for positive incident angles was more effective in reducing the separation than the negative and zero incident angles, approaching a maximum value of 33% for 6° with enhanced blade loading reaching 17.6%. It is to be concluded that, the use of arced slotted blade improves the compressor performance specially for positive incident angles.

The continuous adjoint method to the γ−R˜eθt$$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model coupled with the Spalart–Allmaras model for compressible flows

AbstractThe continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the transition model (in three, non‐smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in‐house, vertex‐centered finite‐volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of “frozen transition” (assumption according to which the adjoint to the transition model equations are not solved) or “frozen turbulence” (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities.

A face-centred finite volume method for laminar and turbulent incompressible flows

This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the negative Spalart–Allmaras (SA) model and three novel convective stabilisations, inspired by Riemann solvers, are derived and compared numerically. The resulting method achieves first-order convergence of the velocity, the velocity-gradient tensor and the pressure. FCFV accurately predicts engineering quantities of interest, such as drag and lift, on unstructured meshes and, by avoiding gradient reconstruction, the method is less sensitive to mesh quality than other FV methods, even in the presence of highly distorted and stretched cells. A monolithic and a staggered solution strategies for the RANS-SA system are derived and compared numerically. Numerical benchmarks, involving laminar and turbulent, steady and transient cases are used to assess the performance, accuracy and robustness of the proposed FCFV method.

A field inversion and symbolic regression enhanced Spalart–Allmaras model for airfoil stall prediction

A data-driven turbulence modeling method based on symbolic regression (SR) is proposed in this paper to enhance the prediction accuracy of the Spalart–Allmaras (SA) model for airfoil stall. Unlike traditional methods that rely on neural networks and lack physical interpretability, this paper utilizes SR to establish an analytic expression mapping local flow field variables to the SA model correction factor β. The training data are obtained through field inversion with the discrete adjoint method in the flow field of the S809 airfoil. Additionally, a relearning approach proposed in this paper is applied to the SR process to address the issue arising from the multi-solution nature of field inversion. The SA model embedded with β, referred to as the SA-SR model, can be integrated into computational fluid dynamics solvers with negligible computational cost. The generalization performance of the SA-SR model is tested under various conditions and airfoil types. The results indicate that the new model improves the predictive capability for airfoil stall without compromising the performance of the baseline SA model for attached flows.

Effects of Reynolds Number on the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe=17.8 deg. The Reynolds number based on the body height was varied from 5×103 to 5×104. Prior to the Reynolds number investigation, a Reynolds-averaged Navier–Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart–Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe=17.8 deg notchback Ahmed body at Re=5×104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re≥1×104. The wake structure exhibited three regimes: symmetric (Re≤1×104), transitionally asymmetric (1×104<Re≤3.5×104), and fully asymmetric (Re>3.5×104) states. The wake asymmetry was attributed to an imbalance in entrainment from the sides and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Deep Reinforcement Learning-Augmented Spalart–Allmaras Turbulence Model: Application to a Turbulent Round Jet Flow

The purpose of this work is to explore the potential of deep reinforcement learning (DRL) as a black-box optimizer for turbulence model identification. For this, we consider a Reynolds-averaged Navier–Stokes (RANS) closure model of a round turbulent jet flow at a Reynolds number of 10,000. For this purpose, we augment the widely utilized Spalart–Allmaras turbulence model by introducing a source term that is identified by DRL. The algorithm is trained to maximize the alignment of the augmented RANS model velocity fields and time-averaged large eddy simulation (LES) reference data. It is shown that the alignment between the reference data and the results of the RANS simulation is improved by 48% using the Spalart–Allmaras model augmented with DRL compared to the standard model. The velocity field, jet spreading rate, and axial velocity decay exhibit substantially improved agreement with both the LES reference and literature data. In addition, we applied the trained model to a jet flow with a Reynolds number of 15,000, which improved the mean field alignment by 35%, demonstrating that the framework is applicable to unseen data of the same configuration at a higher Reynolds number. Overall, this work demonstrates that DRL is a promising method for RANS closure model identification. Hurdles and challenges associated with the presented methodology, such as high numerical cost, numerical stability, and sensitivity of hyperparameters are discussed in the study.

Improving modeling of submerged canopy flows with a vortex-based Spalart–Allmaras model

Accurately modeling the hydrodynamics of submerged canopies is crucial for predicting sediment dynamics and geomorphodynamics. This paper introduces vortex-based Spalart–Allmaras (VBSA) models, considering the spatial structure of canopy-scale vortices and stem wakes. The VBSA models are innovative in incorporating the physics of canopy-overflow interaction. They were validated using experimental data across a wide range of velocities and canopy densities, and their performance was compared with other turbulence models (i.e., previous SA models and k-ε model). Despite lacking high-order numerical schemes, the VBSA models outperform other turbulence models, exhibiting less numerical dissipation and better replication of mean velocity and Reynolds shear stress profiles in the vortex penetration space and below the surface. A sensitivity analysis was conducted to identify optimal values for new model parameters. Analyses suggest that the porous canopy layer suppresses the mixing efficiency by reducing the turbulence length scale. The analysis of eddy viscosity flux balance reveals that the eddy viscosity is transferred to the canopy layer from the overflow by the canopy-scale vortices and is destructed in the canopy, with production being less important, particularly in large submergence scenarios.

Replicating transition with modified Spalart–Allmaras model

An algebraic transition model has been developed to preserve the “flow-structure-adaptive” characteristics in “Reynolds-Averaged Navier–Stokes” (RANS) computations for multiple transition mechanisms. The formulation is convenient and plausible in a sense that it relies on the local flow information to trigger transition employing an algebraic intermittency parameter γ rather than a γ-transport equation. The turbulence intensity Tu appearing in γ has been evaluated locally using an empirical relation for the turbulent kinetic energy k, resolving the interaction between local and free-stream turbulence intensities. Splitting γ into low and elevated Tu regimes assists in calibrating the model coefficients as well as minimizing the “trial-and-error” inconsistency, involved in most of the correlation-based transition models for initiating proper simulations. The γ function is directly fed into the production term of a modified Spalart–Allmaras (MSA) turbulence model. The artifact is pivotal to precisely representing the relevant physical aspects of the flow, such as the bypass, natural and separation-induced transitions, and boundary layer (BL) separation and shock BL interactions. Numerical results demonstrate that the MSA transition model maintains decent agreement with other transition and non-transition models available in the literature.

Are random forests better suited than neural networks to augment RANS turbulence models?

Machine-learning (ML) techniques have bloomed in recent years, especially in fluid mechanics applications. In this paper, we trained, validated and compared two types of ML-based models to augment Reynolds-averaged Navier–Stokes (RANS) simulations. The methodology was tested in a series of flows around bumps, characterized by different levels of flow separation and curvatures. Initially, the ML-based models were trained in three configurations presenting attached flow, small and moderate separation and tested in two configurations presenting incipient and large separation. The output quantity of the machine-learning model is the turbulent viscosity as done in Volpiani et al. (2022). The new models based on artificial neural networks (NN) and random forest (RF) improved the results if compared to the baseline Spalart–Allmaras model, in terms of velocity field and skin-friction profiles. We noted that NN has better extrapolation properties than RF, but the skin-friction distribution can present small oscillations when using certain input features. These oscillations can be reduced if the RF model is employed. One major advantages of RF is that raw quantities can be given as input features, avoiding normalization issues (such as division by zero) and allowing a larger number of universal inputs. At the end, we propose a mixed NN-RF model that combines the strengths of each method and, as a result, improves considerably the RANS prediction capability, even for a case with strong separation where the Boussinesq hypothesis (and therefore the eddy-viscosity assumption) lacks accuracy.

Design and Analysis of UAV Profile for Agriculture and Surveying Application

This study represents the aerodynamic design of an Unmanned aerial vehicle intended for surveillance or agriculture with a maximum take weight of 125 kg. Weight estimation and constraint analysis were done based on the Mission profile. Design of Computer-Aided Design (CAD) models were generated for three different configurations using CATIA V5R20 as a high wing, mid-wing, and low wing. Flow analysis was done for the above configurations at various angles of attack. ANSYS 15 was used for the flow Analysis. A Tetrahedron element meshed the model with the minimum required orthogonal quality. Five microns were given to the initial layer height of the prism mesh. Spalart Allmaras model is used as the Turbulence model in the solver. The aerodynamic characteristics of the above configuration obtained from Computational Fluid Dynamics (CFD) results were compared with the DATCOM program and validated with the wind tunnel experimental test data. The open-circuited suction-type Subsonic wind tunnel was employed for the test. The aerodynamic properties for the angle of attack in the range of -2° to 14° angle of attack are calculated using a six-component balance. The study aims to find the Unmanned Aerial Vehicle (UAV) configuration based on the aerodynamic characteristics obtained from the CFD and DATCOM results. High-wing UAVs have better aerodynamic efficiency than the other two configurations.

Constrained Recalibration of Reynolds-Averaged Navier–Stokes Models

The constants and functions in Reynolds-averaged Navier–Stokes (RANS) turbulence models are coupled. Consequently, modifications of a RANS model often negatively impact its basic calibrations, which is why machine-learned augmentations are often detrimental outside the training dataset. A solution to this is to identify the degrees of freedom that do not affect the basic calibrations and only modify these identified degrees of freedom when recalibrating the baseline model to accommodate a specific application. This approach is colloquially known as the “rubber-band” approach, which we formally call “constrained model recalibration” in this paper. To illustrate the efficacy of the approach, we identify the degrees of freedom in the Spalart–Allmaras model that do not affect the log law calibration. By subsequently interfacing data-based methods with these degrees of freedom, we train models to solve historically challenging flow scenarios, including the round-jet/plane-jet anomaly, airfoil stall, secondary flow separation, and recovery after separation. In addition to good performance inside the training dataset, the trained models yield similar performance as the baseline model outside the training dataset.

Verification and Validation of the Spalart Allmaras Model with Rotation and Curvature Correction for Incompressible and Compressbile Flows

The Spalart-Allmaras turbulence model is the model which gets the highest technological readiness level in the NASA turbulence model resource home page. The model is widely used to predict external incompressible and compressbile flows. Different corrections to this model incorporating additional physical effects are presented on the same home page. Unfortunately none of these corrections are available in the official OpenFOAM version. Furthermore, no publicly available repository which contains the full set of corrections suggested by Shur et al. [1] to account for curvature and rotation effects was found. In this technical note, the rotation and streamline curvature correction is incorporated into the Spalart-Allmaras model in order to overcome this limitation. The same equations as suggested in Shur et al. [1] are implemented and verified by means of the incompressible flow in a rotating channel, a 2D bump flow in a channel and a channel flow exhibiting a U-turn. Regarding the rotating channel flow and the flow in a U-turn some quantitative differences remain with respect to the results of Shur et al. [1]. For the rotating channel flow, a careful consistency check with respect to the analytical relations leading to the computation of the factor multiplied with the production term was made. No inconsistencies in the implementation where found. Unfortunately the exact reason for the differences between the present results compared to the computations of Shur et al. [1], was not found. The interested readers are encouraged to help to clarify these issues. In the fourth test case it is shown that the model predicts a more correct turbulent viscosity distribution in the transonic flow around a delta wing. Applying the streamline and curvature corrections to the Spalart-Allmaras model predicts an earlier vortex breakdown compared to the standard Spalart-Allmaras model for a high angle of attack configuration. The agreement with the reference experiments is much better when using the corrections proposed by Shur et al. [1] to the Spalart-Allmaras compared to the standard Splart-Allmaras model.

Fast flow prediction of airfoil dynamic stall based on Fourier neural operator

Dynamic stall on airfoil is of great importance in engineering applications. In the present work, Fourier neural operator (FNO) is applied to predict flow fields during the dynamic stall process of the NACA0012 airfoil. Two cases with different angles of attack are simulated by Reynolds averaged numerical simulation with the Spalart–Allmaras (SA) model at Re=4×104. A prediction model is directly constructed between the flow fields at several previous time nodes and that at the future time node by FNO. The prediction of sequence flow fields based on the iterative prediction strategy is achieved for the dynamic stall. The results show that FNO can achieve a fast and accurate prediction of streamwise velocity, normal velocity, pressure, and vorticity for both cases. The dynamics of vortices around the airfoil is analyzed to demonstrate the prediction accuracy of FNO. In addition, FNOs with different configurations are tested to achieve a lower error and a shorter training time-consuming.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.

Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil

In this paper, the NWT600 airfoil with a thickness ratio of 60% is taken as the research object. The aerodynamic performance of the airfoil is analyzed by experiments and numerical simulations. The results simulated by various turbulence models used in the 2D steady-state RANS method are compared, including the Spalart–Allmaras model, k-ω SST model, k-ε realizable model, and Reynolds stress (linear pressure-strain) model. The influence of blunt trailing-edge thickness on aerodynamic characteristics is studied by adding thickness symmetrically. The results show that even under the low subsonic flow with a Mach number of 0.149, the airflow is prone to severe separation. The aerodynamic performance of the airfoil is very different from that of the conventional thin airfoil. Although the 2D steady-state RANS models overestimate the pressure on the surface of the airfoil in most cases, it is qualitatively acceptable to predict the pressure distribution of the very thick airfoil. Numerical results simulated by the Reynolds stress model are in the best agreement with the experimental data. It is also found that symmetrically thickening the trailing edge effectively improves the maximum lift coefficient and reduces the drag coefficient at a small angle of attack.