Spalart-Allmaras Turbulence Model Research Articles

A generalised wall function including compressibility and pressure-gradient terms for the Spalart–Allmaras turbulence model

ABSTRACTSpalart-Allmaras (SA) model is a low Reynolds number (Re) model, which means that the first off-wall grid point should be placed in the viscous sub-layer with . This restriction of placing the first off-wall grid point so close to the wall leads to an increase in the mesh size, and thus the computation. The wall function approach is an alternative to this problem. The standard wall function method usually employed has a limitation for cases that involve high adverse pressure gradient and compressibility. This limits its use to the non-separated flows only. The present work focuses on the formulation of the generalised wall function given by Shih et al. [A generalized wall function; 1999] and applies it to the SA turbulence model, with some modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when directly using the Shih et al. model. Several flows, with zero pressure gradient to those with adverse pressure gradient leading to flow separation, are solved with the proposed wall treatment, with relatively coarse grids involving beyond 50 and up to 100 for certain cases. It is concluded that the results in each case are close to those obtained by the low-Re SA model, despite the use of much coarser meshes.

Validation of Higher-Order Interactional Aerodynamics Simulations on Full Helicopter Configurations

Time-accurate numerical predictions of the interactional aerodynamics between NASA's generic ROBIN fuselage and its four-bladed rotor were performed using the recently developed Reynolds-averaged Navier–Stokes solver HAMSTR. Two stencil-based reconstruction schemes (MUSCL, WENO), a second-order temporal accuracy, and the Spalart–Allmaras turbulence model were used. Three-dimensional volume meshes were created in a robust manner from two-dimensional unstructured surface grids using Hamiltonian paths and strands on nearbody domains. Grid connectivity was established between nearbody and background domains in an overset fashion. Two previously researched operational conditions were reproduced, i. e., a near-hover case and a medium-speed forward flight case at an advance ratio of 0.151. The results were compared with various experimental and numerical references and were found to be in good agreement with both. The comparison included the analysis of the rotor wake structure, tip-vortex trajectories, steady and dynamic fuselage pressure distributions in longitudinal and lateral directions, and rotor inflow predictions.

Lift/Drag Characteristics of Different Ice Accretion Airfoil

Aircraft icing has influence on the preliminary safety and performance evaluation of airplane. In this paper, based on different ice shapes (none, rime, mixed), the aerodynamic models of airfoil are established to analyze. Various lift/drag characteristics are obtained by numerical simulation using computational fluid dynamics (CFD) under different icing conditions. Navier-Stokes (N-S) equation and Spalart-Allmaras (S-A) turbulence model are adopted. The results show: 1. It’s obvious that lift-drag characteristics are different under various ice shapes. The lift coefficient (α=0° ∼7°): CL none>CL rime>CL mixed, the drag coefficient (α=0° ∼7°): CD none<CD rime<CD mixed. 2. At the same angle of attack (α=6°), lift/drag characteristics in the condition of different ice shapes are different. The pressure gradient at the leading edge is ▽p none>Vp rime>▽p mixed, which has important effect on the speed of airstream flow and the flow separation at the front zone of airfoil.

A modified Taylor Galerkin scheme for turbulent compressible flow simulation

As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The Characteristic Based Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).&nbsp

Numerical study of mixed-phase ice crystal icing based on Eulerian method

Ice crystals mainly cause compressor blades icing, and it is difficult to reveal the icing mechanism by experimental methods. Therefore, an Eulerian method was used to study ice crystal icing on a wedge airfoil in this paper. The calculation process was divided into three parts. First, the air flow field was calculated by Spalart-Allmaras turbulence model. Then the Eulerian method was used to obtain the trajectory of ice crystal and droplet. At last, the Messinger model was used to calculate the ice shape. The feasibility of the numerical method was verified by the NRC&rsquo;s experiments. Then the effect of pressure on icing was analyzed. It could be found that the lower the pressure, the stronger the sublimation (evaporation) of ice crystals (droplets), and the more obvious the icing was. In addition, the ratio of LWC/TWC (Liquid Water Content/ Total Water Content) had a great effect on icing. It also could be found that too little or too much liquid water was not conductive for icing. The conclusions obtained by calculation were basically consistent with the NRC&rsquo;s. The method in this paper could provide some reference for the subsequent study of engine icing mechanism or the design of anti-icing system.

Numerical Study of Variable Camber Continuous Trailing Edge Flap at Off-Design Conditions

Numerical simulations are performed to study the outboard airfoil of advanced technology regional aircraft (ATRA) wings with five different variable camber continuous trailing edge flap (VCCTEF) configurations. The computational study aims to improve the aerodynamic efficiency of the airfoil under cruise conditions. The design of outboard airfoil complies with the hybrid laminar flow control design criteria. This work is unique in terms of analysis of the effects of VCCTEF on the ATRA wing’s outboard airfoil during the off-design condition. The Reynolds–Averaged Navier–Stokes equations coupled with the Spalart-Allmaras turbulence model are employed to perform the simulations for the baseline case and VCCTEF configurations. The current computational study is performed at an altitude of 10 km with a cruise Mach number of 0.77 and a Reynolds number of 2.16 × 107. Amongst all five configurations of VCCTEF airfoils studied, a flap having a parabolic profile (VCCTEF 123) configuration shows the maximum airfoil efficiency and resulted in an increase of 6.3% as compared to the baseline airfoil.

The stall of different ice accretion airfoil

Ice along the leading edge of upper surfaces have detrimental effects on performance and control of an aircraft. Various icing shapes airfoil have various influence on aerodynamic characteristics and stall phenomenon. The mechanics model, of which ice accretion zone is on the leading edge, is produced by the assembly of various ice shapes (rime ice and mixed ice) and NACA0012 airfoil, In order to analyse the cause of stall phenomenon. The Reynolds averaged Navier-Stokes (N-S) equations are solved using Spalart-Allmaras (S-A) turbulence models the entire flow field. The results show: 1) the stalling angle of attack is various in case of various ice shapes on the leading edge. The stalling angle of attack is 15.5° in case of none ice, about 9° in case of rime ice and about 7.8° in case of mixed ice. 2) The way of airflow separation is different in case of various ice shapes on the leading edge. The vortex zone is expanded from the trailing edge to the leading edge in case of rime ice. Both vortex zones at the leading edge and the trailing edge are expanding meanwhile into one vortex zone in case of mixed ice.

Numerical investigation on interactive FIO of two-tandem cylinders for hydrokinetic energy harnessing

Flow induced oscillations (FIO) of two rough, rigid, tandem-cylinders on springs are investigated for hydrokinetic power conversion at Reynolds number 30,000 ≤ Re ≤ 120,000. Passive turbulence control (PTC) in the form of roughness strips is applied to enhance FIO and increase the power harness efficiency of the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) converter. Numerical simulations are performed using two-dimensional, Unsteady Reynolds-Averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model. The center-to-center spacing ratio d/D of the two cylinders is set as 2.0 or 2.57 with mass ratio m* = 1.343, damping ratio ζ = 0.26, and stiffness K = 1,200N/m. Amplitude response, frequency response, interaction, energy harvesting, and conversion efficiency are presented and discussed. Results are compared to experimental data for validation and reveal how the interaction of two tandem cylinders may enhance the harnessed power. CFD provides complementary valuable information on visualization of wake and vortex structures. The main conclusions are: (1) In the VIV region at Re = 60,000, the amplitude response, frequency response, harnessed power, and power conversion efficiency of the upstream cylinder is the same for the two spacing ratios tested. Due to the shedding effect, the motion of the downstream cylinder for spacing ratio d/D = 2.0 is more severely suppressed than spacing ratio d/D = 2.57, which reduces the harnessed power and conversion efficiency for the downstream cylinder. (2) In the galloping region at Re = 110,000, due to the different timing of impingement of the shed vortices on the downstream cylinder, the upstream cylinder harnesses more power and has higher energy conversion efficiency for spacing ratio d/D = 2.0 than d/D = 2.57.

Assessment of different turbulence models on the large scale internal heated water pool natural convection simulation

In vessel retention (IVR) is treated as one of the strategies in the severe accident management aspect for the safety of nuclear reactor. The investigation of internal heated melt pool natural convection behavior is important for providing the reference for the IVR strategy. Various researchers conducted internal heated melt pool simulation with focusing on the different aspects and conditions. Based on the previous research, the large scale internal heated melt pool flow behavior located in the turbulence flow region and turbulence models used could affect the simulation result of the internal heated melt pool. Therefore, it is important to conduct the simulation of comprehensive assessment of different turbulence models on the melt pool simulation. In this work, the simulation of large scale internal heated water pool, which is one of the COPRA (COrium Pool Research Apparatus) water tests, is conducted by using ANSYS FLUENT 18.2. The large scale internal heated water pool transient behavior is investigated. The effect of various turbulence models on the internal heated water pool simulation is investigated. This work could provide better understanding of temperature distribution and velocity distribution of large scale internal heated water pool natural convection behavior from the numerical aspect. Based on the current simulation, Realizable k-epsilon turbulence model with the consideration of full buoyancy effects, RNG k-epsilon turbulence model with the consideration of full buoyancy effects, DES (Spalart-Allmaras) turbulence model and DES (SST k-omega) turbulence model are recommended for the simulation of large scale internal heated water pool. This work could bring the benefits for the further study on the numerical investigation of large scale internal heated water pool natural convection behavior.

Low Speed Numerical Aerodynamic Analysis of New Designed 3D Transport Aircraft

In this study a new airfoil is designed by using aerodynamic features of the NACA 0012 airfoil and numerical calculation is conducted by using Spalart–Allmaras Turbulence Model and calculated lift and drag coefficients are compare with experimental result to correlate numerical calculation accuracy of CDF model. Then, according to the new airfoil data, a three dimensional aircraft fuselage, and its wings are designed and, tail section is designed by using NACA 0012 airfoil. Finally, 3D model aircraft are simulated for cruise flight, climb and descent at the angle of attack +10 and -10 degrees respectively. The simulation results are interpreted in terms of fluid dynamics. It is observed that during the ascension and descent of the aircraft, very large vortices are formed by the low pressure effect occurring at the rear upper or lower part of the fuselage. Vortexes originating from the rear body are given with the wing tip vortexes in the same figures but the vortex due to the back of the fuselage is found to be very large compared to the wingtip. Furthermore, for each simulation, the formation of the wingtip vortexes are investigated and presented. It is observed that during ascending the vortex formation is formed in roll up and roll down in the phase of descending.

A painless intrusive polynomial chaos method with RANS-based applications

This paper presents a method for the quantification of uncertainty propagation using intrusive Polynomial Chaos Expansion (iPCE). Contrary to commonly implemented intrusive methods built on a problem specific-approach that depends on the governing PDEs, the proposed method, although intrusive in nature, can easily be implemented to any system of equations. A proper mathematical framework is developed that performs the derivation and numerical solution of the iPCE equations with little additional effort, avoiding the laborious mathematical and software development commonly associated with intrusive approaches. Computational cost, convergence and stability properties are analyzed in detail and discussed. The proposed uncertainty quantification (UQ) method is applied to the Reynolds-Averaged Navier–Stokes (RANS) equations, coupled with the Spalart–Allmaras turbulence model and results are compared with those of the non-intrusive PCE (niPCE).

Aerodynamic and aeroacoustic behavior of span-wise wavy trailing edge modified SNL 100 m blade

The aerodynamic and aeroacoustic behaviors of wavy trailing edge modified flatback wind turbine blade have been investigated through numerical simulation. Previous studies have demonstrated aerodynamic and aeroacoustic benefits of the span-wise wavy trailing edge modification on the flatback trailing edge. The previous two-dimensional airfoil test cases have been extended to a complete set of design parametric study. Aerodynamic and aeroacoustic characteristics of the parametric study have been discussed, relying on the wave size, including recently added cases. Furthermore, in the current study, the wavy trailing edge modification has been applied to the Sandia flatback blade called “SNL100-03FB” and tested in rotating blade conditions. Several variations of the wavy trailing edge design have been tested for a range of wind speeds using an overset computation domain. The numerical simulation employs the in-house developed Navier–Stokes solver, OVERTURNS, as well as Graphics Processing Unit (GPU)-accelerated solver, GPURANS3D. Both are hybrid Reynolds Averaged Navier Stokes (RANS)/Large Eddy Simulation (LES) simulation; delayed detached eddy simulation has been used with the Spalart–Allmaras turbulent model and modified [Formula: see text] laminar–turbulent transition model.

On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust

A classic approach to Computational Fluid Dynamics (CFD) is to perform simulations with a fixed set of variables in order to account for parameters and boundary conditions. However, experiments and real-life performance are subject to variability in their conditions. In recent years, the interest of performing simulations under uncertainty is increasing, but this is not yet a common rule, and simulations with lack of information are still taking place. This procedure could be missing details such as whether sources of uncertainty affect dramatic parts in the simulation of the flow. One of the reasons of avoiding to quantify uncertainties is that they usually require to run an unaffordable number of CFD simulations to develop the study.To face this problem, Non-Intrusive Uncertainty Quantification (UQ) has been applied to 3D Reynolds-Averaged Navier-Stokes simulations of an under-expanded jet from an aircraft exhaust with the Spalart-Allmaras turbulent model, in order to assess the impact of inaccuracies and quality in the simulation. To save a large number of computations, sparse grids are used to compute the integrals and built surrogates for UQ. Results show that some regions of the jet plume can be more sensitive than others to variance in both physical and turbulence model parameters. The Spalart-Allmaras turbulent model is demonstrated to have an accurate performance with respect to other turbulent models in RANS, LES and experimental data, and the contribution of a large variance in its parameter is analysed. This investigation explicitly outlines, exhibits and proves the details of the relationship between diverse sources of input uncertainty, the sensitivity of different quantities of interest to said uncertainties and the spatial distribution arising due to their propagation in the simulation of the high-speed jet flow. This analysis represents first numerical study that provides evidence for this heuristic observation.

Numerical investigation of freestream flow effects on thrust vector control performance

Abstract The current research attempted to apply a numerical investigation for external freestream-flow influence on thrust-vector control. The freestream-flow Mach numbers varying from 0.05 to 1.1 were studied at different flow conditions. Computational modeling and simulation of a converging diverging nozzle with shock-vector control structure was achieved with utilizing the Unsteady-RANS approach and Spalart-Allmaras turbulence model. The present investigation has shown that, freestream-flow is an essential parameter on performance of shock-vector nozzle. Numerical results demonstrate that, increasing freestream Mach number would reduce the thrust-vectoring effectiveness. Furthermore, optimizing fluidic-injection angle would decrease the negative influence of external freestream-flow on thrust-vectoring performance. Besides, increasing secondary-pressure ratio and decreasing nozzle-pressure ratio at different freestream-flows would reduce response time of starting fluidic thrust-vector process. In addition, to conduct the improvement of the future aero-engine designs, the present research attempted to create a database of different external-flows with main parameters that have effects on thrust-vector control.

Experimental and Numerical Investigation of Optimized Blade Tip Shapes—Part II: Tip Flow Analysis and Loss Mechanisms

The leakage flows within the gap between the tips of unshrouded rotor blades and the stationary casing of high-speed turbines are the source of significant aerodynamic losses and thermal stresses. In the pursuit for higher component performance and reliability, shaping the tip geometry offers a considerable potential to modulate the rotor tip flows and to weaken the heat transfer onto the blade and casing. Nevertheless, a critical shortage of combined experimental and numerical studies addressing the flow and loss generation mechanisms of advanced tip profiles persists in the open literature. A comprehensive study is presented in this two-part paper that investigates the influence of blade tip geometry on the aerothermodynamics of a high-speed turbine. An experimental and numerical campaign has been performed on a high-pressure turbine stage adopting three different blade tip profiles. The aerothermal performance of two optimized tip geometries (one with a full three-dimensional contoured shape and the other featuring a multicavity squealer-like tip) is compared against that of a regular squealer geometry. In the second part of this paper, we report a detailed analysis on the aerodynamics of the turbine as a function of the blade tip geometry. Reynolds-averaged Navier-Stokes (RANS) simulations, adopting the Spalart–Allmaras turbulence model and experimental boundary conditions, were run on high-density unstructured meshes using the numecafine/open solver. The simulations were validated against time-averaged and time-resolved experimental data collected in an instrumented turbine stage specifically setup for the simultaneous testing of multiple blade tips at scaled engine-representative conditions. The tip flow physics is explored to explain variations in turbine performance as a function of the tip geometry. Denton's mixing loss model is applied to the predicted tip gap aerodynamic field to identify and quantify the loss reduction mechanisms of the alternative tip designs. An advanced method based on the local triple decomposition of relative motion is used to track the location, size and intensity of the vortical flow structures arising from the interaction between the tip leakage flow and the main gas path. Ultimately, the comparison between the unconventional tip profiles and the baseline squealer tip highlights distinct aerodynamic features in the associated gap flow field. The flow analysis provides guidelines for the designer to assess the impact of specific tip design strategies on the turbine aerodynamics and rotor heat transfer.

Effect of RANS Method on the Stall Onset Prediction by an Eigenvalue Approach

The eigenvalue approach is a recently developed compressor stability model used to predict stall onset. In this model, the flow field from a Reynolds-averaged Navier–Stokes (RANS) simulation provides the basic flow. This paper presents the effect of the RANS methods (including the computational grid, the turbulence model, and the spatial discretization scheme) on the eigenvalue and investigates the most influencing flow structures to the eigenvalue. The test compressor was the transonic compressor of NASA Rotor 37. Three individual meshes with different grid densities were used to validate the grid independence, and the results indicated that RANS simulation and eigenvalue calculation obtain grid independence at the same grid density. Then, the effect of four turbulence models (including Spalart–Allmaras (SA) turbulence model, two different k–ε models with the extended wall function model (EWFKE), and the Yang–Shih model (YSKE), and k–ω shear stress transport (SST) model), and three spatial discretization schemes (the central scheme, the flux difference splitting (FDS) scheme, and the symmetric total variation diminishing (STVD)) was also studied. Further investigation showed that the SA turbulence model combined with the STVD scheme provided the best stall point prediction, with a relative error of 0.05%. Detailed exploration of the three-dimensional flow field revealed that there were two flow patterns near the blade tip necessary for precisely predicting stall onset: the flow blockage generated by the shockwave-tip leakage vortex (TLV) interaction, and the trailing edge separation and corresponding wake flow. The effect of the blockage was greater than the effect of the trailing edge flow.

Multi-point aerodynamic shape optimization of cars based on continuous adjoint

This article presents a continuous adjoint-enabled, gradient-based optimization tool for multi-point, multi-objective industrial optimization problems and its application to the shape optimization of a concept car. Apart from the adjoint to the incompressible Reynolds-averaged Navier–Stokes equations, the adjoint to the Spalart–Allmaras turbulence model equation is also solved, in order to support the optimization with accurate gradients. Part of the mathematical development related to the sensitivity derivative terms resulting from the differentiation of the Reynolds-averaged Navier–Stokes (RANS) variant of the Spalart–Allmaras model when using an adjoint formulation consisting of field integrals is presented for the first time in the literature. In the industrial application, two operating points are considered, corresponding to two flow velocity angles with respect to the car symmetry plane, with a different objective (drag and yaw moment coefficients) for each of them. With the aforesaid targets, the Pareto front of optimal solutions is computed and discussed. Each point on this front is computed by minimizing a single objective function, resulting from the linear combination of the objective functions defined on the different operating points, using appropriate weights. Finally, some of the Pareto front members are re-evaluated using delayed detached eddy simulation (DDEs). The overall optimization tool is developed in the open-source CFD toolbox OpenFOAM.

A data assimilation model for turbulent flows using continuous adjoint formulation

A generalized data assimilation model for turbulent flows using the continuous adjoint formulation is proposed. Within this formulation, the Spalart–Allmaras turbulence model is modified by adding a correction function β as a spatially varying coefficient to the turbulence production term. The model-form error is thus corrected by optimizing the β distribution, using the adjoint equations and the corresponding boundary conditions, to minimize the discrepancy between the predictions and observations. In addition, a constraint is applied to drive β toward a large value to avoid the flow unsteadiness owing to the low eddy viscosity. The present adjoint-based data assimilation (ABDA) model is expected to be applicable to various flow conditions unsolvable by the simple optimization of the model constant. This model is fully equation-driven and is thus computationally cheaper than the discretized adjoint method, as well as convenient to be implemented in the existing computational fluid dynamics codes. The flow over a cylinder with synthetic observations, the free round jet, the flow over a hump, and the three-dimensional flow over a wall-mounted cube, all of which are challenging for original Reynolds-averaged Navier–Stokes simulations, are employed to successfully demonstrate the reliability and capacity of the present ABDA model. The first-order scheme applied to the adjoint equations exhibits little effects on the final assimilation results, but improves the robustness significantly, and drives β to another solution that can also minimize the cost function. The present ABDA model is efficient in the heavy assimilation work of different types of shear and separated flows.

Numerical study of potential application of active suction and blowing through blade tip perforation to reduction of helicopter rotor thickness noise

The article explains a new concept (called here ATNC – active thickness noise control) of the application of surface transpiration to the reduction of helicopter main rotor harmonic noise. The ATNC method is based on an introduction of four cavities covered by perforated plates (connected to pressure reservoirs) at the leading and trailing edges of the outer 20% of blade span. For an exemplary, two-bladed (NACA 0012 airfoil) model helicopter rotor of Purcell in low-lifting, hover conditions (tip Mach number MaT = 0.66 and collective θ = 1.5° ) the results of numerical simulations, based on the SPARC code (Spalart-Allmaras turbulence and Bohning-Doerffer transpiration models), prove that the acoustic pressure fluctuations are significantly reduced by ATNC in the near-field of blade tip. The peak amplitude is attenuated by more than 45%, with a reduction of the Overall Sound Pressure Level OASPL by 3.4 dB. It is shown also that the venting has not only a large impact on the acoustic radiation, but also on the aerodynamic performance of the rotor, expressed in terms of the torque penalty of 38%. The ATNC method proves to be a promising candidate as a mean of helicopter rotor thickness noise control, but not in the current arrangement.

Aerodynamics of a Transonic Airfoil in Ground Effect

The wing-in-ground-effect (WIG) aircraft operates with larger lift-to-drag ratio compared to a conventional aircraft at low subsonic Mach numbers. To increase traffic volume of WIG aircraft, one possible way is to increase flight speed, which can result in transonic flow. Currently studies on transonic flight in ground effect are few. The goal of this paper is to study aerodynamics and flow physics of typical transonic RAE2822 airfoil at angles of attack from 0 to 12 deg and Mach numbers from 0.5 to 0.8 in ground effect by varying the ground clearance. The compressible Reynolds-averaged Navier–Stokes equations with Spalart–Allmaras turbulence model are solved using FLUENT. For flight near the ground, some interesting shock formations are obtained due to transonic flow. For unsteady shock buffet on the upper surface, the buffet boundary in angle of attack (AOA)–Mach number plane shrinks with the decreasing ground clearance. Compared to the unbounded flowfield, there exists a steady shock on the lower surface of the airfoil in ground effect for low AOAs because the channel between the lower surface of the supercritical airfoil and the ground is of typical converging–diverging shape, resulting in decrease in lift and increase in drag.