Unsteady Navier Research Articles

High-resolution strategy for localized method of approximate particular solutions to solve unsteady Navier–Stokes problems

In this paper, a high resolution strategy for the localized method of approximate particular solutions (LMAPS) is proposed. In order to avoid solving large and ill-conditioned equations, in the original LMAPS, low-order linear equations are solved by choosing the support region containing five nearest points. In order to improve the accuracy and stability of numerical calculation, for the LMAPS, a high-resolution strategy with limiters is proposed by choosing upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate. This method is suitable for solving the Navier–Stokes equations with high Reynolds number.

Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel

The unsteady characteristics of the second throat of a transonic wind tunnel have an important influence on the design and test of the wind tunnel. Therefore, the forced oscillation characteristics were studied by a numerical simulation method. The governing equation was the viscous compressible unsteady Navier–Stokes equation. Under the sinusoidal pressure disturbance of the computational domain exit, the shock wave presents a clear forced oscillation state, and the shock wave periodically changes its position. Under a pressure disturbance of 1%, the shock wave displacement reaches 150 mm. Additionally, overshoot occurs when the shock moves upstream or downstream. The shock-boundary layer interference is very sensitive to the motion characteristics of the shock wave, resulting in a transformation of the flow field symmetry. The flow field downstream of the shock wave exhibits periodic structural changes. Compared with the pressure change at the outlet, the pressure change near the shock wave has a phase delay. The increasing disturbance near the shock wave shows a clear amplification effect. The pressure disturbance near the shock wave had an obvious amplification effect, and its fluctuation amount reached 16% under the pressure disturbance of 1%. The variation trend of the second throat wall force, wavefront Mach number, and Mach number in the test section with time is similar to that of the downstream disturbance, but it does not have a complete follow-up effect, which indicates that the pressure disturbance can propagate into the test section through the boundary layer or the shock gap. Nevertheless, the second throat choking can still control the Mach number stability of the test section. The dynamic characteristics of shock oscillation are related to the amplitude and frequency of the applied pressure disturbance. The shock displacement decreases with the increase in the excitation frequency. When the excitation frequency is higher than 125 Hz, the flow field basically does not change.

Airfoil optimization for rotors operating in the ultra-low Reynolds number regime

Ultra-low Reynolds number aerodynamics has gained significant attention in recent times, primarily due to the proliferation of micro-aerial vehicles and their utilization in low-density environments such as the Martian atmosphere and high altitudes in Earth's atmosphere. The Martian atmosphere presents a unique combination of low Reynolds numbers and high subsonic Mach numbers, necessitating the use of unconventional airfoil designs in this regime. This study focuses on optimizing airfoils for rotors operating in the compressible ultra-low Reynolds number regime. We demonstrate the capability of XFOIL, a panel method code incorporating an integral boundary layer formulation, to accurately predict airfoil loads when the flow remains attached. We determine the optimal camber and maximum camber positions by analyzing the four digits, two percent thickness, National Advisory Committee for Aeronautics XX02 airfoil family using XFOIL. Subsequently, we employ a multi-objective optimization approach, utilizing a Class Shape Transformation airfoil parameterization to maximize lift and minimize drag. We select several points from the resulting Pareto front and evaluate their performance through unsteady compressible Navier–Stokes simulations. Our findings reveal that incorporating sharp leading-edge variations in these airfoil designs enhances the peak efficiency by over 10%, primarily attributable to the development of laminar separation bubbles on the suction side of the airfoils. Importantly, these modified airfoils maintain favorable performance at low angles of attack.

Numerical investigation of the self-induced unsteadiness phenomenon in the impeller of a high-loading centrifugal compressor

Unsteady flow phenomena are common in turbomachinery and have serious impacts on its stable operation. This paper reports a self-induced unsteady phenomenon inside a centrifugal impeller due to strong secondary flow that has not been previously reported. A high-loading centrifugal impeller is selected as the research object, an accurate three-dimensional model is established, and exhaustive numerical simulations are performed based on unsteady compressible Navier–Stokes equations. The unsteady performance of the compressor is measured in detail during the experiment, and the experimental results are compared with the numerical simulation results to verify the reliability of the numerical simulation method. The results of the unsteady pressure signal show the existence of unsteady phenomenon when the operating point is far away from the choke boundary. The power spectrum results of the unsteady pressure distribution at the impeller blade tip are analyzed, and two different modes of this unsteady phenomenon are confirmed. Higher-order frequency characteristics are not observed near the stall boundary. The detailed analysis of the flow field inside the impeller clarifies that the instability of the interface formed between the secondary flow and the main flow induces this unsteady phenomenon. This unsteady pressure disturbance propagates inside the blade passage through pressure waves, which contributes to the instability of the interface and the existence of this self-induced unsteady phenomenon.

Parametric instability in propagating flames and the impact of hydrogen enrichment on the onset of secondary instability

A self-excited acoustic instability of laminar premixed flames propagating in an open-ended tube with a length of 700 mm and a radius of 10 mm was simulated by solving the reacting unsteady compressible Navier–Stokes equations, to understand the way of massive acoustic generation and its onset behaviors. Four fuel–air mixtures with an equivalence ratio of 1.2 were considered, namely, methane–air and methane–hydrogen–air mixtures, to identify the role of hydrogen in rich methane–air mixture. Parametric instability, which generated huge acoustic disturbance and violent flame pulsations, was observed only for a particular methane–hydrogen–air mixture with RH = 0.2, consistent with previously reported experimental observations. For the investigation of the reinforcement mechanism of acoustic instability under parametric instability, the flame surface area modulation was examined. It was found that violent subharmonic flame front pulsations could strongly modulate the flame surface area in the fundamental mode, resulting in a fluctuating heat release rate and increased thermoacoustic coupling. When hydrogen addition was small, attaining a higher level of primary instability, which is the precursor of the parametric instability, was more dominant than increasing the threshold level for the onset of the parametric instability. With larger hydrogen addition, the increase in the threshold level was more dominant than attaining a higher level of the primary instability. In particular, as the flame propagation time decreased, the level of the primary instability was saturated in larger hydrogen addition. This study elucidates the mechanism for the acoustic generation of propagating flames under the parametric instability, and the effects of hydrogen enrichment within rich methane–air mixtures.

Wall-Resolved Large-Eddy Simulation of Flow over a Parametric Set of Gaussian Bumps

Wall-resolved large-eddy simulations were carried out for the flow over a parametric set of Gaussian bumps, which are representative of surfaces generating smooth-body separation. The geometry and flow conditions were motivated by an experimental investigation, which was conducted in order to provide data for validating numerical approaches. Because the high-Reynolds-number and three-dimensional shape of the experimental model is challenging, even for approximate numerical techniques, a prior investigation was initiated in order to provide benchmark results that are accessible via wall-resolved large-eddy simulation. It was found that by increasing the bump height, the Reynolds number could be reduced, and flow separation would occur. The modified bump now serves as a surrogate for the original Gaussian bump, producing smooth-body separation. In the present study, solutions are obtained to the unsteady three-dimensional compressible Navier–Stokes equations utilizing a high-fidelity computational scheme and an implicit time-marching approach. A series of simulations is carried out for bumps of varying heights, for both the three-dimensional configuration and a spanwise-periodic subset, corresponding to flow at the midspan. A number of metrics are provided to attest to the accuracy of simulations. Comparisons are made between the spanwise-periodic subset and the three-dimensional configuration, and features of the flowfields are described. The generation of an arch vortex structure evolving about the speed bump geometry is elucidated.

Deflector shape impact on aero-acoustic noise generation and propagation

The acoustic pressure level generated during lift-off and the associated vibrations can significantly affect the payload of a launch vehicle. Optimizing the plume deflector is one of the most effective methods to reduce this noise. Considering the Vega launcher as a case of study, different deflectors are studied: flat, inclined at 30°, and wedge. The approach followed is to use the unsteady Navier–Stokes equations to solve both the noise generation and the propagation. First, it has been observed that the blast wave, due to the ignition overpressure, is independent of the deflector geometry. However, the predominant acoustic waves are due to the impact of the jet with the deflectors. The analysis has shown that the flat deflector generates more shock waves and propagates the acoustic waves equally in all directions so that more acoustic loads reach the fairing. The inclined deflector causes a plate shock and intermediate tail shocks and redirects the flow towards one side of the launcher. Finally, the wedge deflector generates a detached shock wave with a higher pressure increase than the inclined deflector. However, as the flow is redirected towards the two sides, a lower OASPL reaches the fairing. In the same way, the pressure distribution over the fairing surface has shown that the wedge deflector is acoustically more efficient for this case of study. The acoustic effectiveness of deflectors has been demonstrated compared to the case without a deflector. Therefore, deflectors are advised to be included on the launch platform to improve payload comfort and reliability on the launchers.

Numerical study on the indoor flow field and ventilation performance in the power room of a hybrid locomotive that passes through a tunnel

Under the background of energy saving, emission reduction, and green transportation, the electrification construction of railway lines is difficult owing to long cycles and high costs. Hybrid locomotives have emerged as fuel locomotives that can run on electrified lines and that achieve energy saving, emission reduction, and railway emergency on non-electrified lines. Train power equipment is highly integrated in the locomotive power room, which leads to the ventilation and heat dissipation performance of indoor high-heat equipment becoming one of the main factors that affect the safe operation of trains. This study focuses on the flow field and ventilation of locomotive power rooms in railway vehicle/tunnel systems and explores the variation of the ventilation flow rate and flow field in a power room when trains pass through a tunnel at different speeds. Based on the unsteady Reynold-averaged Navier–Stokes (RANS) equations and shear-stress transformation (SST) k-ω turbulence model, the relative motion between a train and a tunnel is simulated by sliding mesh, and the related algorithm settings are verified through experiments. The results show that: train speed is linearly related to the air inlet flow rate, and trains have a critical speed, which affects the original indoor air-cooling circulation system. This critical speed is reduced by the tunnel environment; The propagation and superposition of the pressure wave in a tunnel have no evident effect on the flow rate of the power room vent; Train speed is negatively correlated with the fan efficiency; thus, it deteriorates the fan efficiency in the tunnel environment; The symmetrical distribution of ventilation openings in a power room can effectively balance the fresh-air flow, but it is not conducive to cooling equipment located near the locomotive. These conclusions can contribute to improving future designs of the ventilation systems of hybrid electric locomotive power rooms.

Numerical Modeling of Supersonic Combustion of Hydrogen in the Wake Region of a Strut

Numerical modeling of combustion of a sonic hydrogen stream injected into a supersonic stream of air using a strut is presented. Results are obtained by numerically solving unsteady, compressible, turbulent Navier-Stokes equations, using Unstructured Finite Volume Method (UFVM) incorporating RNG based κ−ε two equation model and time integration using three stage Runge Kutta method. Reaction is modeled using an eight step H2-air chemistry. The developed numerical procedure is based on the implicit treatment of chemical source terms by preconditioning and solved along with unsteady turbulent Navier Stokes equations explicitly. Code is validated against a standard wall jet experimental data and is successfully used to model the reacting flow field resulting due to combustion of hydrogen in the wake region of strut placed in heated supersonic air stream.

Novel computational fluid dynamics-finite element analysis solution for the study of flexible material wave energy converters

The use of flexible materials for primary mover and power takeoff of wave energy converters (WECs) has attracted considerable attention in recent years, owing to their potential to enhance the reliability, survivability, and wave energy conversion efficiency. Although some reduced order models have been used to study the fluid–structure interaction (FSI) responses of flexible wave energy converters (fWECs), they are somehow inappropriate due to their limited accuracy and applicability span. To gain a deeper understanding of the physical mechanisms in fWECs, a high-fidelity approach is required. In this work, we build up a fluid–structure interaction analysis framework based on computational fluid dynamics and a finite element analysis method. The incompressible viscous flow is resolved by solving three-dimensional unsteady Navier–Stokes equations with a finite volume approach. The structure dynamics are solved by a finite element method, taking the nonlinear behavior of flexible material into consideration. A strong coupling strategy is utilized to enhance the numerical stability and convergence of the iterative process. We demonstrate the present FSI tool is able to provide rich flow field information and structural response details, such as the velocity, pressure, and structural stress distribution. This is illustrated through several case studies, including two types of fWECs. The unsteady wave–structure-interaction and the associated nonlinear phenomena are also accurately captured by this tool.

A deep neural network approach for parameterized PDEs and Bayesian inverse problems

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems. However, MCMC techniques are computationally challenging as they require a prohibitive number of forward PDE solves. The goal of this paper is to introduce a fractional deep neural network (fDNN) based approach for the forward solves within an MCMC routine. Moreover, we discuss some approximation error estimates. We illustrate the efficiency of fDNN on inverse problems governed by nonlinear elliptic PDEs and the unsteady Navier–Stokes equations. In the former case, two examples are discussed, respectively depending on two and 100 parameters, with significant observed savings. The unsteady Navier–Stokes example illustrates that fDNN can outperform existing DNNs, doing a better job of capturing essential features such as vortex shedding.

Existence, uniqueness, and asymptotic stability results for the 3-D steady and unsteady Navier–Stokes equations on multi-connected domains with inhomogeneous boundary conditions

We consider both stationary and time-dependent solutions of the 3-D Navier–Stokes equations (NSE) on a multi-connected bounded domain Ω ⊂ R 3 with inhomogeneous boundary values on ∂ Ω = Γ; here Γ is a union of disjoint surfaces Γ 0 , Γ 1 , … , Γ l . Our starting point is Leray’s classic problem, which is to find a weak solution u ∈ H 1 ( Ω ) of the stationary problem assuming that on the boundary u = β ∈ H 1 / 2 ( Γ ). The general flux condition ∑ j = 0 l ∫ Γ j β · n d S = 0 must be satisfied due to compatibility considerations. Early results on this problem including the initial results in (J. Math. Pures Appl. 12 (1933) 1–82) assumed the more restrictive flux condition ∫ Γ j β · n d S = 0 for each j = 1 , … , l. More recent results, of which those in (An Introduction to the Mathematical Theory of the Navier–Stokes Equations, vol. II 1994 Springer–Verlag) and (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) are particularly representative, assume only the general flux condition in exchange for size restrictions on the data. In this paper we also assume only the general flux condition throughout, and for virtually the same size restrictions on the data as in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) we obtain the existence of a weak solution that matches that found in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) when the assumptions imposed here and those assumed in (In Lectures on the Analysis of Nonlinear Partial Differential Equations 2013 237–290 Int. Press) are both met; additionally we demonstrate that this solution is unique. For slightly stronger size restrictions we obtain the existence and uniqueness of solutions of both Leray’s problem and global mild solutions of the corresponding time-dependent problem, while showing that both the stationary and time-dependent solutions we construct are a bit stronger than weak solutions. The settings in which we establish our results allow us to culminate our discussion by showing that our time-dependent solutions converge to each other exponentially in time, so that in particular our stationary solutions are asymptotically stable. We also discuss additional features which allow for data of increased size on certain domains, including those which are thin in a generalized sense.

Strong shock solutions in symmetric wedge flows: Unphysical or unstable?

This paper investigates the strong shock solutions in a supersonic wedge experimentally, analytically, and numerically. Experiments and computations are conducted on scaled-down models for the two types of shock reflection to be possible. The time-resolved schlieren observation of the flow evolution revealed that the shock formation is a highly dynamic transition of the starting shock from a strong Mach reflection (MR) to a weak regular reflection (RR) via a strong RR reflection over a constant shock wave angle for a wedge angle less than the detachment criterion angle for the shock transition. However, when the wedge angle is greater than the detachment criterion angle, the shock moves over the wedge with the MR structures of diminishing Mach stem height at a constant incident shock wave angle. These intermediate shock reflections are found to be unstable and oscillate at high amplitude and low frequencies to upstream pressure fluctuations. The nature of the intermediate shock reflection during the shock transition over the wedge has also been studied using an unsteady second-order two-dimensional compressible Navier–Stokes solver code with shear stress transport k-ω turbulence modeling. The computed flow parameters around the intermediate shock reflections confirmed that these are indeed strong shock reflections believed to be unphysical in steady wedge flows.

Heat and momentum diffusion of ternary hybrid nanoparticles in a channel with dissimilar permeability's and moving porous walls: A Multi-linear regression

In recent times, the term Hybrid nanofluid is frequently used owing to its extraordinary influence on different science and engineering processes like therapeutic process, motorized investigational and electrical circuits where energy transference is significant and marine engineering etc. The objective of the present investigation is to supervise the heat and momentum diffusion of ternary hybrid nanoparticles in a channel with dissimilar permeability's and moving porous walls which enables the nanofluid to enter or exist during successive expansion or contractions. In this model, newly proposed Wu's slip circumstance is enforced on the down permeable wall of the channel and analyzed along with thermal radiation and convective heating. The flow and heat diffusion of ternary hybrid flow-1 (Carbon Nanotubes(CNT), Graphene, Aluminum oxide), ternary hybrid flow-2 (Copper oxide, Copper, magnetite), ternary hybrid nanofluid 3 (Paraffin wax, Sand, AA7072 aluminum alloy) water as base fluid is compared and analyzed. The unsteady Navier Stokes equations is converted to partial differential equation by via stream function and the vorticity equation further similarity conversions are used to convert the prevailing flow quantities into non-linear differential equations and then elucidated numerically by shooting procedure with Runge-Kutta (R-K 4th order). Linear Regression method (LRM) is used to model the solution for the flow variables. Outcomes obtained for axial velocity f′(χ) and temperature circulation θ(χ) are interpreted by the graph. Achieved outcomes are compared with existing studies. The topmost result of this investigation is found to be -The higher distribution of heat transmission rate is observed in Case-3 (Paraffin wax + Sand + AA7072) with rise in Bi, Since the particles interaction is higher. The second order slip is shown lesser friction in the Copper oxide + copper + magnetite compared to rest of the situations

Roughness-Resolved Large-Eddy Simulation of Additive Manufacturing-Like Channel Flows

Abstract In the last decade, progresses in additive manufacturing (AM) have paved the way for optimized heat exchangers whose disruptive design will heavily rely on predictive numerical simulations. However, due to typical roughness induced by AM, current wall models used in steady and unsteady 3D Navier–Stokes simulations do not take into account such characteristics. For the development and assessment of novel wall models for AM, a high-fidelity roughness-resolved large-eddy simulation (RRLES) database is built. This article describes the numerical setup and the methodology used for conducting RRLES, from surface generation to postprocessing. In addition, three different cases representing two printing directions plus a streamwise and spanwise isotropic case are investigated. While the roughness distributions are the same in the three cases, the effective slope (ES) is very different, and the impact of this parameter on turbulence and heat transfer is analyzed at different Reynolds numbers.

Study on Complex Wake Characteristics of Yawed Wind Turbine Using Actuator Line Method

In modern large-scale wind farms, power loss caused by the wake effect is more than 30%, and active yaw control can greatly reduce the influence of the wake effect by deflecting the wind turbine’s wake. The yawed wind turbine’s wake characteristics are complex, and a deep comprehension of a yawed turbine’s wake is necessary. The actuator line method combined with URANS (unsteady Reynold-averaged Navier–Stokes equations) is used to study the yawed wind turbine’s wake characteristics in this paper. Compared with an un-yawed wind turbine, a yawed one has two main characteristics, deflection and deformation. With an increasing yaw angle, turbine wake shows an increasing deflection. The results indicated that deflection at different height was different, the wake profile showed the biggest deflection at about the hub height, while the smallest deflection existed at the top and bottom of the yawed turbine’s wake. This can be visually demonstrated by the evolution of a kidney-shape velocity distribution at the vertical cross-section. Two-dimensional and three-dimensional presentations of velocity deficit distributions are presented in this paper. The evolution of an irregular kidney-shape distribution is discussed in this paper. It is formed by the momentum exchange caused by the counter-rotating vortex pair. The results indicated that the counter-rotating vortex pair was composed of the streamwise vortex flux brought by the tip vortex. Furthermore, when the wind turbine rotated clockwise and yawed clockwise, the negative vorticity of counter-rotating vortex first appeared in the upper left position.

Effects of thermal stratification on natural convection in a symmetrically heated channel: Comparison of characteristic quantities between air and water

We present in this paper a numerical investigation on pure convection flow inside a vertical channel heated at symmetrically uniform heat flux and contained in an enclosure. This study aims to investigate how far we can use water to predict natural convection in an air filled channel especially in presence of thermal stratification. The 2D unsteady Navier–Stokes equations under Boussinesq approximation was solved numerically using Finite Differences Method. The investigation is made for moderate Rayleigh numbers in order to study the effect of stratification at the early stages of the flow development. A comparison in terms of flow and heat transfer characteristics is done between the two fluids. It is seen that natural convection heat transfer in such a configuration is more impacted by thermal stratification when air is used as the working fluid. Traditionally used water models to predict the natural convection of air may give rise to misinterpretations about the real phenomenon especially when stratification occurs. This study should also give some clarifications about the discrepancies raised in the literature between numerical and experimental results when both water and air are used.

Inertio-capillary rebound of a droplet impacting a fluid bath

The rebound of droplets impacting a deep fluid bath is studied both experimentally and theoretically. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. Measurements of the droplet trajectory and other rebound metrics are compared directly with the predictions of a linear quasipotential model, as well as fully resolved direct numerical simulations of the unsteady Navier–Stokes equations. Both models resolve the time-dependent bath and droplet shapes in addition to the droplet trajectory. In the quasipotential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to two sets of coupled damped linear harmonic oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in our parameter regime of interest. Starting from the inertio-capillary limit in which both gravitational and viscous effects are negligible, increases in gravity or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. The inertio-capillary limit defines an upper bound on the possible coefficient of restitution for droplet–bath impact, depending only on the Weber number. The quasipotential model is able to rationalize historical experimental measurements for the coefficient of restitution, first presented by Jayaratne & Mason (Proc. R. Soc. Lond.A, vol. 280, issue 1383, 1964, pp. 545–565).

Modified pressure and vorticity variables using Helmholtz decomposition for solution of the incompressible flow equations

Incompressible Navier–Stokes equations are reformulated using the Helmholtz decomposition of a velocity vector into rotational and potential components. By substituting the decomposed velocity in the time derivative term in a momentum equation, the potential component representing a gradient of a pressure-like term is combined with the gradient of the pressure modifying the physical pressure field. The rotational component representing a curl of a vortex-like vector is combined with the vorticity vector, making a non-physical vorticity vector that modifies the fluid viscosity. Thus, the unsteady Navier–Stokes equation is transformed into an explicitly steady-state form in terms of non-primitive variables. The stream function vector is governed by a parabolic equation in time, while the vorticity vector is governed by the Poisson function with a source term function of the convection stretching and time dependency of the physical flow vorticity. Therefore, the resulting system of equations is numerically independent of the cell Reynolds number stability condition that hunted the convection–diffusion Navier–Stokes equation. Numerical results are obtained for the two-dimensional driven cavity problem for Reynolds number of 1000 with 21 × 21, 41 × 41, 81 × 81, and 161 × 161 grid points. The computational grids correspond to cell Reynolds numbers 25, 12.5, 6.25, and 3.125, respectively. The computed results are smooth in all cases and validate the method.

On Improved Understanding of Airfoil Performance Evaluation Methods at Low Reynolds Numbers

Airfoil performance for the Eppler 387 airfoil at low Reynolds number ( to 460,000) is studied numerically and compared to existing experimental data. Two- and three-dimensional unsteady laminar Navier–Stokes simulations are performed to evaluate the large-scale dynamics of the flow. All cases show laminar separation of the boundary layer followed by the shedding of large coherent vortices resulting in reattachment only observed in the mean flow, referred to as bubble flapping. Integrated aerodynamic coefficients, pressure distributions, and separation–reattachment locations are presented and compared to experimental data. Absolute averaged section lift and drag errors in the range to 300,000 are 5 and 7%, respectively, and good agreement of the pressure distributions is obtained. Laminar separation locations are predicted within 2%-chord, and turbulent reattachment is on average predicted within 5%-chord of the experimental values, which is improved to 3%-chord when updated experimental data are used. The work illustrates that bubble flapping, and the resulting mean airfoil performance, can be analyzed using laminar unsteady Navier–Stokes simulations, and that it does not necessitate external disturbances or three-dimensional instabilities. The shear layer transition over airfoils is found to be dominated by two-dimensional vortex shedding resulting in unsteady reattachment.