Enhancing One-Equation Turbulence Models for Delta Wings by Gene Expression Programming

This paper presents flow measurements on four delta wing configurations which are differentiated by their leading edge profiles; sharp-edged, small, medium, and large radius. The experiments were performed as a part of the European Vortex Flow Experiment-2 campaign. Tests were conducted at speeds of 20.63 m/s and 41.23 m/s representing Reynolds numbers of 1 × 106 and 2 × 106, respectively. In this paper, oil flow visualization data are presented for the four wings together with particle image velocimetry results for the large radius wing. The study has identified interesting features of the interrelationship between the conventional leading edge primary vortex and the occurrence and development of the inner vortex on the round-edged delta wings. The effects of Reynolds number, angle of attack, and leading-edge radii on both vortex systems are discussed in detail.

This study establishes a compressible continuous adjoint data assimilation (C2ADA) approach for reproducing a complete mean flow from sparse wall pressure observations. The model-form error induced by the Boussinesq approximation is corrected by the addition of a spatially varying additive forcing term. The linear part of the eddy viscosity, computed using the conventional Reynolds-averaged Navier–Stokes model, is incorporated for ensuring the well-posedness of the optimization. The model is derived theoretically to minimize discrepancies between the wall pressure measurements and the numerical predictions of the primary-adjoint system, thereby enabling determination of the optimal contribution of the Reynolds force vector. The effects of divergence schemes and turbulence models are investigated by examining flow over a 30P30N airfoil. The C2ADA model, employing two distinct schemes, demonstrates significant improvements in velocity estimation, but the first-order scheme introduces excessive dissipation, resulting in an under-prediction of spanwise vorticity. The C2ADA model combined with different eddy-viscosity models uniquely recovers the Reynolds force vectors and obtains mean fields that outperform those achieved solely through conventional eddy viscosity models. The practicability of the C2ADA model for capturing complex flow phenomena is confirmed by applying it to study three-dimensional flow over a 65° delta wing. Despite limited wall pressure observations, the C2ADA model has shown a notable improvement in accurately estimating the intensity and location of both the primary and secondary vortices. Recovery errors in the apex region are significantly diminished by incorporating a paucity of observations account for the effect of inboard vortex. The study broadens the applicability of continuous adjoint-based approaches for modeling compressible flow, as our C2ADA approach is easily implemented in existing computational fluid dynamics solvers and has significantly higher computational efficiency than other approaches.

PurposeThe purpose of this study is to investigate the flow on blunt-edged delta wing Vortex Flow Experiment (VFE-2) configuration in wind tunnel testing. The flow characteristics of this wing exhibits differently from sharp-edges where the primary vortex developed at certain chord-wise position from the wing apex.Design/methodology/approachA model of VFE-2 wing has been replicated with the main chord length of 1.3 meters with two sets of leading-edge radius. The experiments were performed in Universiti Teknologi Malaysia wind tunnel sized of 2 × 1.5 m2 test section with maximum speeds of 80 m/s. To investigate the effects of leading-edge radius, Reynolds number and angle of attack, the experiments were carried out at 1 × 106 and 2 × 106 Reynolds number based on mean aerodynamic chord length. Three measurement techniques were used on the wing, i.e. flow visualization, surface and off-surface pressure measurement.FindingsThis study has observed that the inner vortex has first developed inboard of the wing at low angle of attack. At moderate angle of attacks, the primary vortex is then developed in the leading-edge region, at the same time, the inner vortex also well-developed inboard of the wing. When the angle of attacks is further increased, primary vortex becomes very prominent in the leading edge and the inner vortex has disappeared.Originality/valueThe research results provide a better understanding into the effects of angle of attacks, Reynolds number and leading-edge bluntness on delta wing flow topology, particularly the interaction between the primary vortex and the inner vortex.

The significance of spillways is to allow the flood to be safely discharged from downstream. There is a strong correlation between the poor design of spillways and the failures of dams. In order to address this concern, the present study investigates the flow over the Nazloo-ogee spillway using the CFD 3D numerical model and an artificial intelligence method called Gene Expression Programming (GEP). In a physical model, discharge and flow depths were calculated for 21 different total heads. Among different turbulence models, the RNG turbulence model achieved the maximum compatibility in computational fluid dynamic simulation. In addition, GEP was used to estimate Q, in which 70% of collected data was dedicated to training and 30% to testing. R2, RMSE, and MAE were obtained as performance criteria, and the new mathematical equation for the prediction of discharge was obtained using this model. Finally, the numerical model and GEP outputs were compared with the experimental data. According to the results, the numerical model and GEP exhibited a high level of correspondence in simulating flow over an ogee-crested spillway.

With the help of the area rule the flow around delta wings and swallow-tailed wings in the transonic range is referred to the flow around (equivalent) bodies of revolution. Since the critical Mach-numbers — the limits of the transonic range and the linerarizable subsonic and supersonic region — lie quite near unity, the transonic properties can be determined by the calculation of the critical Mach-numbers, the calculation in the linearized ranges, and at Mach-number 1. For the latter the “parabolic method” [6] is used and applied together with a transonic method of characteristics to various bodies. The lower critical Mach-number is determined with sufficient accuracy by the linear theory. For the upper critical Mach-number the formula of Oswatitsch-Sjodin [15] is used.

SummaryMeasurements of wing buffeting, using root strain gauges, were made in the Nasa Langley 0-3 m cryogenic windtunnel to refine techniques which will be used in larger cryogenic facilities such as the United States National Transonic Facility (NTF) and the European Transonic Windtunnel (ETW). The questions addressed included the relative importance variations in frequency parameter and Reynolds number, the choice of model material (considering both stiffness and damping) and the effects of static aeroelastic distortion.The main series of tests was made on three half models of slender 65° delta wings with a sharp leading edge. The three delta wings had the same planform but widely differing bending stiffnesses and frequencies (obtained by varying both the material and the thickness of the wings). It was known that the steady flow on this configuration would be insensitive to variations in Reynolds number. On this wing at vortex breakdown the spectrum of the unsteady excitation is unusual, having a sharp peak at particular frequency parameter.Additional tests were made on one unswept half-wing of aspect ratio 1·5 with an NPL 9510 aerofoil section, known to be sensitive to variations in Reynolds number at transonic speeds. The test Mach numbers were M = 0·21 and 0·35 for the delta wings and to M = 0·30 for the unswept wing. On this wing the unsteady excitation spectrum is fairly flat (as on most wings). Hence correct representation of the frequency parameter is not particularly important.

Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers

Reynolds-averaged turbulence models have become one of the most important and popular techniques for practical engineering applications in aeronautics and astronautics. However, the poor performance in the prediction of flow separations restricts its application ranges due to the traditional linearity and equilibrium hypotheses that constitute the equation of Reynolds stress in turbulence modeling. In this study, an artificial neural network-based quadratic constitutive (ANN-QCR) Reynolds stress model is proposed for simulating turbulent flows with separations by using the field inversion and machine learning technique (FIML) with high-fidelity experimental data. In particular, the Reynolds stress is decomposed into linear and non-linear parts, respectively. The former is evaluated by the Spalart–Allmaras model with a correction factor imposed on the production term to account for the non-equilibrium effect, while the latter is a quadratic constitutive term with a self-calibrated factor. These correction factors are predicted by an artificial neural network (ANN) depending on the local flow features. The unified framework of FIML updates the weights of ANN-QCR directly by the gradient-based discrete adjoint method, ensuring consistency between the field inversion and the neural network training. The data-augmented ANN-QCR turbulence model is well validated through several separated turbulent flows induced by adverse pressure gradients, shock wave boundary interfaces, higher angles of attack, and higher Reynolds numbers (Re). With the optimization target at lift coefficients, the established model also improves the predictive performance in other flow quantities, such as drag coefficients and pressure distributions. In addition, this model captures the development of separation bubbles better with the increase in the angle of attack. Benefiting from the compatibility and convergence of forward simulation, the generalization capability of the present ANN-QCR model is successfully validated in various numerical simulations of separated turbulent flow problems across a wide range of attack angles and Reynolds numbers with good accuracy.

Aircraft with slender bodies and swept lifting surfaces, flying at high angles of attack, often have regions of three-dimensi onal separated flow characterized by strong off-body vortices. One approach to numerically simulate this class of high Reynolds number flows is to use the Reynolds-averaged Navier-Stokes equations (RANS), together with a turbulence model. Many turbulence models have been utilized for the RANS equations, however most are developed and calibrated for configurations with attached boundary layers or flows with shockinduced separation. In order to apply these models to separated flows with strong off-body vortices, modifications are usually necessary. This investigation examines the development and application of these modifications for both the algebraic Baldwin-Lomax turbulence model, and the one-equation Spalart-Allmaxas model. The implementation of these modified models differs among several production computational fluid dynamics (CFD) codes, as do their computed results. Model behavior in predicting crossflow separation for an ogive cylinder, and leadingedge separation for a delta wing are examined. The flowfields for the ogive cylinder and delta wing geometries are simulated at 20° and 15° angle of attack respectively. Both configurations are computed at subsonic flow speeds, however applications to transonic and supersonic wingbody configurations are discussed. Comparisons are made with experimental surface pressure measurements, and surface oil-flow visualizations where available.

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-state Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65° swept, sharp-edged, cropped delta wing of zero thickness at 20° angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 106, the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown.\nThe effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied.\nComparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2 π eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment.\nThe second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65° swept model and an 80° swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock.\nComparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

Appropriate design parameters need to be determined for unmanned aerial vehicles that can perform kamikaze missions. In this study, a UAV with 3 different wing configurations and a fuselage and tail wings were designed, and the flow around the wing was examined using computational fluid mechanics. Advanced modeling techniques were employed to simulate and analyze the aerodynamic behavior of these configurations. The effect of angle of attack (AoA), wing positioning on the fuselage, and wing configurations were investigated. Due to the effect of the wing sweep angle, high-pressure values in the arrow-angle wing were lower than in rectangular and trapezoidal wings. In a similar situation, the flow separation on the arrow-angle wing is less advanced towards the wing tip. When the wing type and connection location were examined, the highest ${{C}_{l}}/{{C}_{d}}$ ratio was obtained in the trapezoidal model connected to the fuselage in the middle. The results of numerical wing models compared with the theoretical lift coefficient were consistent. Trapezoidal and rectangular wings had a high lift coefficient, but after ${{15}^{\circ }}$ of AoA, the lift coefficient decreased. At angles of attack beyond ${{15}^{\circ }}$, the arrow-angle wing still has an increasing lift coefficient. As the angle of attack increased, the drag coefficient was also enhanced. The lowest drag coefficient occurred in the arrow-angle wing model. Up to ${{5}^{\circ }}$of AoA, all wing models raised the ${{C}_{l}}/{{C}_{d}}$ ratio. The ${{C}_{l}}/{{C}_{d}}$ ratio decreased at higher angles of attack. As a result of the examination, it would be more correct to choose trapezoidal and arrow-angle wings.

Effect of delta wing on the particle flow in a novel gas supersonic separator

Application of an evolutionary algorithm to LES modelling of turbulent transport in premixed flames

Delta wing is a triangular-shaped platform that can be applied into the unmanned aerial vehicle (UAV) or drone applications. However, the flow above the delta wing is governed by complex leading-edge vortex structures which result in complicated aerodynamics behaviour. At higher angles of attack, the vortex burst can take place when the swirling flow is unable to sustain the adverse pressure gradient. More studies are needed to understand these vortex phenomena. This paper addresses an experimental study of active flow control called propeller on a generic 55° swept angle sharp-edged delta wing model. In this experiment, a propeller was placed at two different locations. The first location was at the apex of the wing while the second position was at the rear of the wing. The experiments were conducted in a 1.5 × 2.0 m2 closed-loop wind tunnel facility at Universiti Teknologi Malaysia. The freestream velocities were set at 20 m/s and 25 m/s. The research consisted of an intensive surface pressure measurement above the wing surface to investigate the effects of rotating propeller towards the leading-edge vortex. The experiments were divided into four configurations. The clean wing configuration was performed without the propeller and followed by pusher-propeller configuration using 10-inch 9-inch propellers. The final configuration was the tractor-propeller with a 10-inch propeller. The results emphasise the influences of the propeller size and its location corresponding to vortex properties above the delta-winged UAV model. The findings had indicated that the vortex peak is increased when the propeller is installed for both pusher and tractor configurations. The results also indicate that the pressure coefficient is increased when the propeller advance ratio increases.

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes