Prediction of High-Mach-Number Flutter Instabilities for the NACA0012 Benchmark Wing

M OST fluid flows of engineering interest are turbulent, and while numerous advances have been made in the numerical solution of the Navier–Stokes equations, known as computational fluid dynamics (CFD), turbulent flows still present challenges for today’s methods. Turbulent flows are characterized by a very wide range of scales in both time and space.Most of the kinetic energy of a turbulent flow is stored in the large-scale structures of the flow. In contrast, kinetic energy is dissipated as heat at the smallest scales. Although the much more computationally intensive large eddy simulations (LES) and direct numerical simulations (DNS) are performed in research environments, simulations that resolve the Reynolds-averaged Navier–Stokes (RANS) equations are still required for rapid engineering results. The size of the smallest length scales, and therefore the maximum allowable CFD grid spacing to completely resolve all turbulence, is inversely proportional to Re. So for a three-dimensional simulation, the number of grid points must scale with Re [1]. Because such fine grids and small time steps are not practical with today’s computers, compromises must be made that approximate certain aspects of the physics. Most CFD methods solve the steady or unsteady RANS (URANS) equations, as illustrated in Fig. 1. Essentially, only the mean flow is solved on the computational mesh, and the turbulent physics are replaced by closure models of varying sophistication. URANS–based methods include simple algebraic models like Baldwin–Lomax, one-equation models like Baldwin–Barth and Spalart–Allmaras, and two-equation models such as k-! and k-! shear stress transport (SST). These turbulence models tend to be heuristic and rely on nonphysical constants that are “tuned” to specific flows, such as airfoils at low angles of attack. That is, the results from the model are iteratively compared against experimental data, and the constants are adjusted until the computational results agree with the experiment. Although they perform well for those cases, they fail to accurately predict unsteady flows dominated by viscous effects, as in the case of static and dynamic stall [2,3] or bluffbody flows. Hybrid RANS/LESmethods provide away to achieve some of the advantages of LES for separated and highly vortical flowfields while retaining the computational efficiency of URANS methods. Baurle et al. [4] developed the idea that URANS and LES methods can be linearly blended by some smooth function to form a hybrid model. This idea of blending was used in 2006 by Sanchez-Rocha et al. [5], who used the k-! SST RANSmodel as the basis for a hybrid method within an existing LES code to resolve wall-bounded turbulence. Sanchez-Rocha et al. demonstrated this capability with simulations of a NACA 0015 airfoil in static and dynamic stall at a Reynolds number of 1 10. A more common approach is to incorporate an LES model into a URANS code to capture subgrid scales, so that where grid resolution permits, LES-like results are obtained. Strictly speaking, LES requires that the resolved scales extend into the inertial subrange. These scales, and those smaller, are more universal, meaning that their physics depends less on the particular geometry. Such universal scales are more amenable to modeling, since even when heuristics are used, they should be valid for a larger range of flows. The drawback of LES is that in order to directly solve for the larger turbulent scales, it requiresmuch finer grids and smaller time steps than URANS computations. In most engineering applications, LES remains far too computationally expensive for routine use.On coarse grids that are usually only suitable forURANS applications, hybrid methods of this variety can capture larger turbulent eddies in the interior of the flow (away from boundaries), thus providing a better approximation of the true physics than URANS alone. Detached eddy simulation (DES) is a commonhybrid formulation, inwhich the turbulence near walls ismodeledwithMenter’s k-!SST [6] or Spalart–Allmaras [7] URANS turbulence models. However, it must be noted that DESmodels are separate and distinct from hybrid methods like those of Sanchez-Rocha et al. [5] in that they lack a dedicated subgrid-scale model. Instead, the URANS equations perform “double-duty” as theLESmodel bymodifying a length scale used in the destruction terms [8,9]. For this effort, the RANS–LES hybrid model developed by Sanchez-Rocha et al. [5,10] has been extended and evaluated within an unstructured CFD methodology. Comparisons with experimental data, as well as published LES and structured CFD simulations, were used to verify and expand the base of knowledge of unstructured hybrid RANS–LES methods. Emphasis is placed on the improvement of the aerodynamic performance quantities (forces and moments) through more accurate prediction of the pressure distribution and separation location on the cylinder.

UDC 532.517.4 The results of numerical simulation of fully developed turbulent flow in a channel with the cube on the lower wall (for the characteristic Reynolds number Re = 40,000) within the framework of the traditional approach to the solution of unsteady Reynolds-averaged Navier-Stokes equations (URANS) in combination with the semiempirical Spalart-Allmaras turbulence model (with a correction for rotation) have been presented. A de- tailed comparative analysis of the results of numerical simulation of local and integral flow characteristics and the Martinuzzi experimental data has shown that the self-oscillating regime of flow past the cube is a su- perposition of oscillations of the arms of a horseshoe vortex and the rear arched and detached vortex struc- tures. Using fast Fourier transformation, it has been found that the oscillations are of a bimodal character in the longitudinal and vertical directions, whereas in the transverse direction, they are of a unimodal character. Introduction. The problem on unsteady flow past a cube in a narrow channel with the fully developed turbu- lent flow being formed at the inlet is of particular interest for testing today's calculation algorithms of computational hydrodynamics. In this case channel flow is of a self-oscillating character and is distinguished by a complex vortex structure (Fig. 1). Flow separation begins ahead of the cube and further develops from its frontal face side and on the lateral walls. A horseshoe vortex that interacts with the near wake of the cube results. We recognize the following basic large-scale flow elements for their subsequent analysis and comparison to experimental data: 1) a horseshoe vor- tex; 2) a vortex ensemble consisting of a vortex attached to the face side of the cube and two columnar vortices near the lateral walls; 3) a rear detached vortex; 4) an attached vortex behind the end wall of the cube, which is not iden- tified in the Martinuzzi experiment, as should be noted, but is visualized in many calculations; 5) an arched vortex with two oppositely rotating bends, which is formed in the near wake. Experimental data to which we compare results of numerical investigations were obtained by Martinuzzi (1) and have been introduced into the ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) databank (2). About ten large-scale numerical investigations based on solution of steady and unsteady Reynolds-aver- aged Navier-Stokes equations (RANS ⁄ URANS) and on application of the large-eddy model (see, e.g., (3-5)) have been carried out over a period of 15 years. It is noteworthy that, except for the results obtained by Durbin with the V2F turbulence model (6), none of the works gives satisfactory agreement between the results of calculations within the framework of the RANS ⁄ URANS methodology and the experimental data. This work is primarily aimed at substantiating the applicability of the URANS approach to the prediction of turbulent separated flows. The commercial FLUENT v6.3 package (7) is used. Preliminary verification and approval of the package with a catalog of semiempirical models realized in it, which were carried out on two-dimensional test problems such as flow past a circular cylinder (8) and circulation flow in a square cavity with a moving upper bound- ary (9, 10), have shown satisfactory correlation with experimental data, when the two-parametric model of shear-stress transfer MSST and the Spalart-Allmaras (SA) vortex-viscosity model were selected. It has been shown in (8-10) that the SA model in its traditional formulation substantially overstates turbulent-viscosity values, which renders it unsuit- able for calculations of turbulent separated flows. For further testing, we have selected the SA model modified with allowance for rotation.

A great number of supersonic aircrafts use delta wings. Since 1950, delta wings have been studied well and it has been observed that there appear two large counter-rotating leading edge vortices when delta wing structure flies at high angles of attack. These vortices are responsible for additional lift and they also provide a very high stall incidence to the wing. At high Mach numbers, compressibility advances leading edge separation and also expands the magnitude of the primary vortex. Shock waves appearing due to high-speed flow over the delta wing result in drastic changes in the flow characteristics. Although supersonic jets use delta wing configurations but most of the time they fly at subsonic speeds and hence the focus of present study is on both subsonic as well as supersonic regimes. The present study consist of numerical simulations of the flow-field over a compound delta wing at various Mach numbers ranging from 0.3 to 2.0 and angles of attack ranging from 0° to 15° using the computational model established in previous research [1]. Reynolds Averaged Navier-Stokes (RANS) based steady-state computations were carried out. Spalart Allmaras (SA) turbulence model is considered due to its less computational cost and good performance for simulating external flows. Since the study involves supersonic Mach numbers, compressibility was also incorporated in the computational model. The study with various freestream Mach numbers shows that there is a sudden change in flow fields with an increase in the Mach number for the range of 0.8 to 1.3. The flow near to the delta wing surface beneath the primary vortex becomes completely supersonic and shock waves appear when the flow reaches Mach number 0.85. Due to this shock wave formation, flow fields become more complex. At high Mach number because of the stronger magnitude of the primary vortex which prevents the evolution of the inner separation, the secondary vortex disappears. The results also confirm the hypothesis of vortex breakdown which is also responsible for the nonlinear behavior of flow characteristics over the wing when there is an increase in Mach number.

The Spalart–Allmaras (SA) turbulence model is one of the most popular models applied to compressors, but it often over-predicts blockage size and hence under-predicts the stall margin. In this paper, a novel modification to the SA model is proposed to improve the prediction of compressor near-stall flows. The modification is based on the dimensionless vortical pressure gradient, which identifies blockage cells featured by 3D swirling, adverse pressure gradient, and low-momentum flows. It unblocks the compressor passage by enhancing the eddy viscosity in the identified blockage cells; whereas in canonical 2D flows the modification is automatically switched off. The model coefficients are calibrated via Bayesian inference, which considers the uncertainties involved in experiments and computational fluid dynamics (CFD) simulations of turbomachinery. The rotor exit radial profile data of NASA Rotor 67 at peak-efficiency and near-stall points are used for calibration. The calibrated model is tested extensively in four compressors covering both tip blockage and corner separation as well as both industrial and laboratory Reynolds number and Mach number. For the NASA Rotor 67 and the TUDa-GLR-OpenStage, the proposed model predicts more accurate stall margins at all operating speeds due to the tip unblocking effect. For the BUAA Stage B rotor, the proposed model predicts the tip blockage size and thus the stall margin more accurately. For the LMFA NACA65 cascade, the proposed model with the quadratic constitutive relation (QCR) achieves significant improvement in predicting the exit profiles due to the unblocking effect on the corner separation. The proposed model, termed as SA-PGω in this work, is a promising engineering tool for future Reynolds-averaged Navier–Stokes (RANS) simulations of compressor near-stall flows.

A sliding mesh technique within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) computational framework is validated using the experimental dataset collected as part of the NASA Source Diagnostic Test (SDT) campaign. Two modeling approaches are explored: the unsteady Reynolds-Averaged Navier Stokes (URANS) with Spalart-Allmaras (SA) turbulence model closure, and a hybrid Reynolds-Averaged Navier Stokes/Large Eddy Simulation (RANS/LES) paradigm employing a Zonal Detached Eddy Simulation (ZDES) closure with enhanced shielding protection. Fan stage performance metrics, aerodynamic quantities and turbulent flow structures are analyzed in this work. Initial studies focusing on grid and time-step sensitivity are presented. Sensitivity to different variants of the SA turbulence model is analyzed, supporting the use of the baseline SA model in the production runs. Two conditions are analyzed in detail using URANS and hybrid RANS/LES (HRLES). Mean flow quantities are well-captured by both methods in the low-speed (approach) regime. While URANS misses all the upstream-propagating noise in the inlet due to the rotor-locked tones being evanescent in nature at subsonic fan tip speeds, HRLES captures this broadband component in its pressure field. At the high-speed (sideline) condition, URANS shows better agreement with the SDT data than HRLES in the interstage flow-field. In this regime, URANS captures the tonal content propagating through the inlet, since the tones are now cut-on. Both methods are suitable to capture fan stage performance metrics and mean flow quantities, but only HRLES is able to resolve the fine turbulent structures responsible for broadband noise. The results support the use of the sliding mesh technique implemented in this work for future turbomachinery applications within the LAVA solver framework.

In this paper we have confirmed that eddy viscosity turbulence models are inadequate to predict secondary vortical flows developed from corners in internal flows. To remedy this shortcoming, we have added the quadratic constitutive relation (QCR) of Spalart to the one- and two-equation SA and SST turbulence models, respectively. The results of QCR with the SA and SST turbulence models have been validated against experimental data of Davis and Gessner for supersonic flow through a square duct. The approach is shown to be simple to implement and overall agreement is seen to improve with the use of QCR. Introduction: Supersonic flow through a square duct is altered by secondary vortical flow developing from the corners. These secondary flows are generated by Reynolds stress gradients acting in the corner region and appear to have similar structure to those found in subsonic flow through square ducts (1-3). Such flow is representative of various airplane inlets and therefore it is important to understand and predict the impact of this secondary flow on inlet pressure recovery and distortion. An experimental study was performed at the University of Washington to gain a better understanding of how the secondary flow associated with corners affects local flow conditions in a square duct over the development length (3). This configuration was utilized in this study to validate and improve the RANS turbulence models utilized for corner flows at Boeing. Accurate prediction of the flow around and through the aircraft is essential for design improvement, risk mitigation, and wind-tunnel and flight test reduction. At Boeing, the RANS approach is used routinely for design and analysis of our configurations. While RANS has proven to be a powerful approach for flow-field prediction, it still has some shortcomings even for steady state flow predictions. The one- and two-equation SA (4) and SST (5) eddy viscosity turbulence models, respectively, are still the workhorses for routine applications. The Reynolds

Rectangular cylinders with a ratio of 5:1 are extensively applied in engineering structures. Their aerodynamic characteristics, especially at high Reynolds numbers (Re), remain unclear. A series of force and wind pressure measurement tests at high Reynolds numbers are conducted on a 5:1 rectangular cylinder, with angles of attack ranging from 0° to 8°. The results show that the mean drag coefficient, moment coefficient, and Strouhal number exhibit significant Reynolds number effects, with noticeable angle of attack variations. At nonzero angles of attack, the probability density function curve of the lift coefficient changes from bimodal to unimodal with increasing Reynolds number, and the transition Reynolds number decreases with the increase in angles of attack. As the angle of attack increases, the vortex core on the upper surface moves downstream, whereas the opposite occurs on the lower surface. When the angle of attack equals or exceeds 2°, the reattachment point on the upper surface disappears. The effect of the Reynolds number on the mean pressure coefficient is negligible, whereas the fluctuating pressure coefficient at the rear of the upper and lower surfaces notably decreases with the increasing Reynolds number. The overall shape of the mean and fluctuating pressure coefficient distributions is unaffected by the Reynolds number. Vortex shedding dominates fluctuations of pressure on top and bottom surfaces. As the angle of attack increases, the pressure coefficient spectra minimum peak amplitude distribution shifts backward on the top surface and forward on the bottom, likely due to the movement of the vortex core.

Improved quadratic constitutive relation via turbulence anisotropy analysis and symbolic regression

Unsteady RANS and detached eddy simulation of the multiphase flow in a co-current spray drying

Several fighters suffer from tail buffet problems. The buffet phenomenon is the oscillation of aircraft surface components excited as a result of the interaction between the differential pressures associated with turbulent airflow, aircraft structures, and control surfaces. This paper presents the modeling and simulation of a steady-state one-way and two-way fluid–structure interaction for the tail buffet problem of an F/A−18 fighter. The commercial software ANSYS is used to conduct the simulations. The unsteady Reynolds-averaged Navier–Stokes equations with four turbulent models are used to model the fluid domain. Simulation results of two nonlinear eddy viscosity turbulence models were compared with those of two linear viscosity turbulence models and the experimental data. The two linear turbulence models are standard linear Wilcox and Spalart–Allmaras. The two nonlinear eddy viscosity models are nonlinear eddy viscosity model and Spalart–Allmaras model with rotation and rotation/curvature corrections. The nonlinear eddy viscosity model is based on the standard linear Wilcox model and uses the formulation of an explicit algebraic Reynolds stress model. The Spalart–Allmaras model with rotation and rotation/curvature corrections turbulence model is the modified Spalart–Allmaras model with a strain-vorticity-based production and curvature treatment. The finite element analysis to model the structural components was conducted by using shell elements. Based on the simulation results, it is concluded that the buffet problem could be simulated as a two-way fluid–structure interaction and by using the nonlinear eddy viscosity model turbulence model as those give better results than the other considered models.

The capability to accurately model fluid flow within rotating Taylor–Couette systems has a primary role in informing computational investigations of rotating machinery. There is considerable uncertainty regarding selection of modelling approach, including a suitable turbulence model, that can accurately resolve turbulence within such complex flows while remaining computationally feasible for industrially relevant applications. This paper presents a numerical comparison of axisymmetric and three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence models within ANSYS Fluent. The CFD geometries are representative of ones for which there are published experimental measurements. For the Taylor–Couette study, investigation into inner cylinder start-up procedure, based on previous published findings, confirmed that the final state of the flow is highly dependent on the initial conditions and acceleration rate. Once Taylor vortices form and stabilise, they are not disrupted by small steps in inner cylinder speed, allowing computationally efficient accelerations. Investigations into applying rotational periodicity were unsuccessful, resulting in a significantly reduced core velocity. Axisymmetric predictions provided reasonable agreement with experimental data only at low rotation rates. A good prediction of the velocity flow field was obtained for three-dimensional simulations of the full 360° domain with differences of less than 5% for radial velocities. Among the URANS models, the standard k-ω model and baseline Reynolds stress model (BSL-RSM) provided the closest agreement to published experimental data. In the paper, the developed Taylor–Couette turbulence modelling methodology is extended to a bearing chamber geometry. Analysis of the secondary vortex flow field is compared both qualitatively and quantitatively to published bearing chamber experimental measurements. Overall, whilst a good agreement is still found using the standard k-ω turbulence model, discrepancies arise with the BSL-RSM. However, for this more complex bearing chamber environment compared to a Taylor–Couette flow, the shear stress transport k-ω turbulence model provided the closest agreement and is recommended for future bearing chamber modelling.

The one equation Spalart–Allmaras (SA) turbulence model in an extended modular form is presented. It is employed for the prediction of crosswind flow around the lip of a 90 deg sector of an intake with and without surface roughness. The flow features around the lip are complex. There exists a region of high streamline curvature. For this, the Richardson number would suggest complete degeneration to laminar flow. Also, there are regions of high favorable pressure gradient (FPG) sufficient to laminarize a turbulent boundary layer (BL). This is all terminated by a shock and followed by a laminar separation. Under these severe conditions, the SA model is insensitive to capturing the effects of laminarization and the reenergization of eddy viscosity. The latter promotes the momentum transfer and correct reattachment prior to the fan face. Through distinct modules, the SA model has been modified to account for the effect of laminarization and separation induced transition. The modules have been implemented in the Rolls-Royce HYDRA computational fluid dynamic (CFD) solver. They have been validated over a number of experimental test cases involving laminarization and also surface roughness. The validated modules are finally applied in unsteady Reynolds-averaged Navier–Stokes (URANS) mode to flow around an engine intake and comparisons made with measurements. Encouraging agreement is found and hence advances made towards a more reliable intake design framework.

The NASA juncture flow experiments were designed for the purpose of evaluating and improving the ability of computational fluid dynamics (CFD) simulations to predict the juncture region flow field of a wing-body configuration. The wind tunnel experiments provide critical information for testing the accuracy of various turbulence models in simulating the complex flow separation that occurs at the trailing edge of the juncture region. The purpose of this paper is to build on the previous CFD research in the literature on juncture region flow with a focus on implementation of a structured hexahedral mesh with lower computing requirements and several turbulence models, in particular the newly developed one equation Wray- Agarwal (WA) turbulence model. The results from the one equation Spalart Allmaras (SA) and Wray-Agarwal (WA) turbulence models as well as the two-equation �� − �� SST (Shear Stress Transport) model are compared with the experimental data. Computations are performed and compared for four angles of attack of -2.5, 0, 5 and 7.5 degree. More importantly, this paper also analyzes the accuracy of various turbulence models with nonlinear quadratic constitutive relation (QCR) for eddy viscosity in comparison to the linear Boussinesq assumption. The prediction of pressure coefficient at various span-wise locations of the wing and the separation bubble near the trailing edge of the juncture demonstrate the ability of the Wray-Agarwal model in accurately computing the wing-body juncture flow field. This is reinforced by prediction of velocity profiles and turbulent shear stresses upstream of the fuselage and near the separation region of the wing.

To develop an advanced way of designing transonic airfoils for industry, a reliable and user-friendly mesh generator and a robust CFD solver are necessary. Especially, the prediction of unsteady shock buffet phenomenon is always a focus for the CFD simulation of transonic airfoils. In this study, BOXERmesh (an automatic mesh generator) and NEWT (a robust CFD solver), which are developed by CFS (Cambridge Flow Solutions) in collaboration with MHI (Mitsubishi Heavy Industries), are used to perform the CFD simulation of NACA SC2-0714 transonic airfoil. CFD simulation is conducted at two different attack angles with Mach number as 0.74 and Reynold number as 1.5×107 (non-buffet: α=2°; shock buffet: α=3°). A hexahedral dominant mesh is generated by BOXERmesh with the cell number as 5.52 million. Both unsteady RANS (URANS) and LES are performed using the CFD solver NEWT. Specifically, the governing equation is discretized by central differencing scheme with 2nd order accuracy in space by applying Swanson and Turkel type artificial viscosity, and the Adams-Bashford time integration with the dual-time stepping method is applied for temporal discretization in the density-based solver. Results show CFD simulation could reproduce the time averaged chordwise distribution of pressure coefficient at the two conditions. Both URANS and LES successfully capture the unsteady shock buffet phenomenon when increasing attack angle from 2° to 3°. However, the calculated peak oscillation location and the shock buffet frequency are different between URANS and LES. Applying the same mesh resolution, URANS performances better than LES, with the deviation of the shock buffet frequency less than 6% (Exp.: 69 Hz; URANS: 73 Hz). The reason is considered as the wall-normal mesh refinement near the airfoil surface (y+∼66) being not enough for LES to accurately resolve the turbulence scale and capture the boundary layer separation behavior. On the other hand, URANS is thought to be enough to reproduce the periodic moving of the onset of boundary separation and to predict the main characteristics of the shock buffet phenomenon.

Numerical modelling of the effect of appendages on turbulent mixing in connected nuclear fuel subchannels