Delayed Detached Eddy Simulation Research Articles

On the application of higher-order Backward Difference (BDF) methods for computing turbulent flows

The Backward Differentiation Formulae (BDF) of orders one to six are implemented in an in-house three-dimensional finite-volume (FVM) compressible flow code that operates on unstructured meshes. The lower-upper symmetric Gauss-Seidel (LUSGS) implicit relaxation technique based on the splitting of convective Jacobians is used to obtain a variable-order stable implementation in the solver. The temporal order of accuracy of the implemented schemes is verified using the Method of Manufactured Solutions (MoMS). Practical engineering flow problems are simulated to investigate the operational stability of BDF methods so that these can be used as a cheaper alternative to multi-stage methods in RANS, hybrid RANS-LES, and LES implementations. Steady-state flow simulations of supersonic flow over a flat plate and high Reynolds number flow over a NACA-0012 airfoil show that algorithm with BDF schemes of orders 1-5 is stable at high CFL numbers (700-1000) and produces a converged solution. Stokes' second problem and a high-resolution delayed detached eddy simulation (DDES) of flow over a 3D circular cylinder using the BDF1-BDF6 methods demonstrate the use of these higher-order temporal schemes in unsteady laminar and turbulent flows. It is concluded that BDF methods of orders 3-5 can be practically employed to achieve higher levels of temporal accuracy in flow simulations when the level of spatial accuracy is also high (ENO/WENO schemes, spectral methods, etc.) in hybrid RANS-LES, LES or DNS. Even without higher-order spatial accuracy, the same BDF schemes can be used in Adaptive Time-stepping (ATS) methods to obtain prescribed temporal accuracy efficiently by algorithmically switching between the different schemes.

Numerical investigation of turbulent flow and mixed convection around a wavy cylinder

The performance of different scale-resolving simulation (SRS) models in resolving the turbulent flow structures and forced convection around a wavy cylinder (TFWC) at subcritical Re = 3000 is compared firstly. The SRS models include the SST scale adaptive simulation (SAS), the SST delayed detached-eddy simulation (DDES), and the production-limited DDES (PL-DDES) models. The simulation results on a coarse grid resolution testify that the PL-DDES model is superior to the SAS and DDES models. Another primary purpose is exploring the turbulent flow and mixed convection around a wavy cylinder using the PL-DDES model. For the contra flow (Richardson number = −0.3), the Strouhal number, the drag coefficient, and the Root-Mean-Square (RMS) lift coefficient decrease, but the length of the recirculation zone increases. In contrast, it is inverse results in the parallel flow (Richardson number = 0.3). Due to the buoyancy effect, the region of the 3 d flow structures in the contra flow and the parallel flow are respectively larger and smaller than those in the non-buoyancy flow. The laminar mixed convection is dominant around the cylinder in the contra flow. The turbulent mixed convection plays an essential role in the wake region for the parallel flow. In the windward region, the laminar mixed convection is dominant for both flows. The Nusselt number decreases and increases in the contra flow and the parallel flow, respectively.

Aerodynamic and Acoustic Simulations of Thick Flatback Airfoils Employing High Order DES Methods

AbstractThe results of high fidelity aerodynamic and acoustic computations of thick flatback airfoils are reported in the present paper. The studies are conducted on a flatback airfoil having a relative thickness of 30% with the blunt trailing edge thickness of 10% relative to chord. Delayed Detached‐Eddy Simulation (DDES) approaches in combination with high order (5th) flux discretization WENO (Weighted Essentially Non‐Oscillatory) and Riemann solver are employed. Two variants of the DES length scale calculation methods are compared. The results are validated against experimental data with good accuracy. The studies provide guideline on the mesh and turbulence modeling selection for flatback airfoil simulations. The results indicate that the wake breakdown is strongly influenced by the spanwise resolution of the mesh, which directly contributes to the prediction accuracy especially for drag force and noise emission. The Reynolds normal stress and the Reynolds stress component have the largest contributions on the mixing process, while the contribution of the component is minimal. Proper orthogonal decomposition is further performed to gain deeper insights into the wake characteristics.

Wake characteristics of complex-shaped snow particles: Comparison of numerical simulations with fixed snowflakes to time-resolved particle tracking velocimetry experiments with free-falling analogs

Experimental and numerical approaches have their own advantages and limitations, in particular, when dealing with complex phenomena such as snow particles falling at moderate Reynolds numbers (Re). Time-resolved, three-dimensional particle tracking velocimetry (4D-PTV) experiments of free-falling, three-dimensional (3D)-printed snowflakes' analogs shed light on the elaborate falling dynamics of irregular snow particles but present a lower resolution (tracer seeding density) and a limited field of view (domain size) to fully capture the wake flow. Delayed-detached eddy simulations of fixed snow particles do not realistically represent all the physics of a falling ice particle, especially for cases with unsteady falling attitudes, but accurately predict the drag coefficient and capture the wake characteristics for steadily falling snowflakes. In this work, we compare both approaches on time- and space-averaged flow quantities in the snowflake wake. First, we cross validate the two approaches for low Re cases, where close agreement of the wake features is expected, and second, we assess how strongly the unsteady falling motion perturbs the average wake pattern as compared to a fixed particle at higher Re. For steadily falling snowflakes, the fixed-particle model can properly represent the wake flow with errors within the experimental uncertainty (±15%). At moderate/high Re (unsteady falling motion), larger differences are present. Applying a co-moving frame to the experimental data to account for the particle movement or filtering the numerical data on larger grids reduces these differences only to some extent, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.

Numerical investigation of flow deflectors for the improvement of condensing air flux through the air-conditioning unit on high-speed trains

It has been observed that the condensing air flux through the air-conditioning (AC) unit on a running high-speed train significantly decreases due to the shear stream flowing over the train roof. Insufficient condensing air may put the AC under a risk of overheating. In this study, four shapes of flow deflectors that are able to alleviate the flux drop are designed and investigated using experimentally validated Delayed Detached Eddy Simulation (DDES). Numerical results show that the air flux drop mainly depends on the cross-sectional shape of deflectors, which changes the flow conditions above AC condensing outlets, including the properties of the negative pressure region and the incident angle of the high-speed shear flow produced by the train operation. Meanwhile, the extra aerodynamic drag brought by the installation of deflectors is computed and analyzed. The results presented in this paper can be applied to the design of the AC system, as well as other equipment requiring active convective cooling, on higher speed trains.

Predicting the High-Angle-of-Attack Characteristics of a Delta Wing at Low Speed

Ensuring the safe operation of new supersonic transport aircraft requires understanding their stability during takeoff and landing. These phases involve flying at subsonic speeds and high angles of attack, where the aerodynamics are characterized by unsteady vortical flow. This work assesses the accuracy of Reynolds-averaged Navier–Stokes (RANS) and delayed detached eddy simulations (DDES) at predicting the vortex-dominated flow over a delta wing for angles of attack up to and past stall. The delta wing has an aspect ratio of 2 and is a simplified representation of a supersonic transport wing. The predicted aerodynamic coefficients are compared with experimental data, focusing on the shape of the pitching moment curve. In addition, a steadiness metric is formulated to distinguish between steady and unsteady angles of attack. It is found that RANS accurately predicts vortex effects in the steady regime but is inaccurate at high angles of attack where the flow is unsteady. DDES is more reliable in the unsteady regime, but the computational cost is at least 100 times that of RANS. Predicting the pitching moment at the highest angles of attack is difficult even with DDES on a 69-million-cell mesh. These results provide guidelines for choosing the appropriate fidelity depending on the flow characteristics, the required accuracy, and the computational budget.

On turbulent flow and aerodynamic noise of generic side-view mirror with cell-centred finite difference method

This paper investigates the turbulent flow and aerodynamic noise of a half-cylinder body mounted on a flat plate at using high-order cell-centred finite difference method with delayed detached-eddy simulation (DDES) and large-eddy simulation (LES). Transient flow patterns from the two simulations are found to be very different in consideration of the small-scale structures. The profiles of mean velocity, resolved turbulent kinetic energy and resolved Reynolds shear stress are found to be similar among all the simulations, indicating mean quantities are relatively insensitive to turbulence modelling and grid resolution. The power spectra density of the pressure fluctuations show that LES is more capable of resolving energies in high-frequency range than DDES. After computing the normalised wavenumber-frequency spectra of fluctuating pressure on the window, we further carried out the wavenumber-frequency decomposition to separate the acoustic and the hydrodynamic components from the pressure fluctuations. The energy distribution shows that the acoustic energy has a much slower decaying rate in the high-frequency range than the hydrodynamic energy. In addition, the space-averaged sound pressure levels of pressure fluctuations on the window indicate that the present simulation with a high-order method is able to improve the accuracy in predicting pressure spectra. Finally, we carry out proper orthogonal decomposition to extract the dominating features of the decomposed acoustic and hydrodynamic components of pressure fluctuation. Patterns of multi-scale turbulence in hydrodynamic modes and propagating wavefronts of cylinder shape in acoustic modes are identified. The present research indicates that a relatively coarse grid is still capable of resolving fluctuating quantities of energy-containing structures, and LES is suggested against DDES when near-wall aerodynamic noise is the main concern.

Detached eddy simulation of turbulent flow fields over steep hilly terrain

The verification and validation (V&V) of multi-fidelity turbulence models is crucial for the efficient and reliable industrial application of computational fluid dynamics (CFD). This study aims to evaluate the performance of detached eddy simulation (DES) modeling approaches embedded with various unsteady Reynolds Averaged Navier-Stokes (URANS) models in simulating the turbulent flow fields over a steep-sloped hill. And the high-fidelity numerical methodology based on the DES model was proposed and analyzed in the context of URANS modes, mesh resolution and sampling duration. In comparison with the experimental data, the shear stress transport (SST) k-ω based DDES (Delayed Detached eddy simulation) turbulence model (DDES SST k-ω) could better predict the profiles of mean velocity and turbulence fluctuation, while the Spalart-Allmaras (S-A) based DES and DDES turbulence models show its stronger capability to reproduce the spectral characteristics. Additionally, in contrast to DES S-A and DDES S-A, a larger time-averaged separation bubble was predicted by DES SST k-ω and DDES SST k-ω. Moreover, the instantaneous flow patterns such as the formation and evolution of turbulent eddies in the hill wake could be reasonably reproduced by DES S-A and DDES S-A. Furthermore, the numerical results obtained from DES models were sensitive to URANS modes and vertical mesh resolution but trivially affected by the increase in sampling time after reaching the statistical convergence.

Evaluation of CFD methodologies for prediction of flows around simplified and complex automotive models

A comprehensive evaluation of the predictive capability and computational costs of Reynolds Averaged Navier–Stokes (RANS), Unsteady RANS (URANS), Delayed Detached-Eddy Simulation (DDES), and Lattice-Boltzmann Method (LBM) methodologies was carried out for flow around the SAE notchback and the DrivAer fastback models. From the comparison, all methods predicted drag within roughly 10% of experimental values. However, this accuracy was misleading for RANS as the predicted flowfield deviated from both the unsteady methods and experiments in regions where flow separation was developing. This was especially true around the rotating wheel flows of the DrivAer model, where RANS predicted extensive separation around the rear wheels to the point that it changed the structure of the vehicle wake. In these regions of highly separated flow, the unsteady methods proved to be much more accurate and robust, although comparisons of the flow around the rotating wheels proved inconclusive as to which methods provided suitable predictive capabilities. Despite improved flow predictions, URANS and DDES proved to be significantly more expensive than RANS, while LBM provided comparable accuracy to URANS/DDES with substantially reduced costs.

Numerical simulation of single/double liquid jets in supersonic crossflows

This study investigates the mixing processes of liquid jets in supersonic crossflows at a Mach number of 2.1 by using numerical simulations that employ the Coupled Level-Set/Volume-of-Fluid (CLSVOF) method, which is based on the Delayed Detached Eddy Simulation (DDES). The instantaneous spray morphology from the simulations agreed well with the experimental data. The spray presents the ‘Ω’ shape when viewed from the front, and the maximum error in the penetration depth was 15% from a side perspective. The direction of the air movement determined the shape of the liquid column shearing and breaking. In turn, the breaking process of the liquid jet significantly affects the structure of the air flow. Three-dimensional flow around the liquid column occurred when the supersonic incoming flow impinged on the liquid column, ultimately forming counter-rotating vortex pairs (CVP) in the inner region of the spray. Evolution of the reverse vortex pair accelerated the mixing process of the spray. Single liquid jet was used as a basis to further study double jets in Mach 2.1 airflow. The results show that the breaking length and penetration depth of the downstream jet are significantly improved.

CFD Investigation on Hydrodynamic Resistance of a Novel Subsea Shuttle Tanker

The Subsea Shuttle Tanker (SST) was proposed by Equinor as an alternative to subsea pipelines and surface tankers for the transportation of liquid carbon dioxide (CO2) from existing offshore/land facilities to marginal subsea fields. In contrast to highly weather-dependent surface tanker operations, the SST can operate in any condition underwater. Low resistance is paramount to achieving maximum range. In this paper, the resistance of the SST at an operating forward speed of 6 knots (3.09 m/s) and subject to an incoming current velocity of 1 m/s is computed using Computational Fluid Dynamics (CFD). The Delayed Detached Eddy Simulation (DDES) method is used. This method combines features of Reynolds-Averaged Navier–Stokes Simulation (RANS) in the attached boundary layer parts at the near-wall regions, and Large Eddy Simulation (LES) at the unsteady, separated regions near to the propeller. The force required to overcome forward resistance is calculated to be 222 kN and agrees well with experimental measurements available in the open literature. The corresponding power consumption is calculated to be 927 kW, highlighting the high efficiency of the SST. The method presented in this paper is general and can be used for resistance optimization studies of any underwater vessel.

Numerical investigations of vortex formation on a generic multiple-swept-wing configuration

For an improvement of the flight stability characteristics of high-agility aircraft, the comprehension of the vortex development, behavior and break down is important. Therefore, numerical investigations on low aspect ratio, multiple-swept-wing configurations are performed in this study to analyze the influence of the numerical method on the vortex formation. The discussed configurations are based on a triple- and double-delta wing planform. Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and delayed detached eddy simulations (DDES) are performed for both configurations. The simulations are executed at Re = 3.0times 10^6, symmetric freestream conditions, and an angle of attack of alpha = 16^circ, for consistency with reference wind tunnel data. For the triple-delta-wing configuration, the results of the DDES show a satisfying accordance to the experiments compared to URANS, especially for the flow field and the pitching moment coefficient. For the double-delta-wing configuration, the URANS simulation provides reliable results with low deviation of the aerodynamic coefficients and high precision for the flow field development with respect to the experimental data.

Comparative numerical study of aerodynamic heating and performance of transonic hyperloop pods with different noses

Delayed detached eddy simulation (DDES) using a shear stress transport (SST) k-ω turbulence model was used to investigate the aerodynamic and temperature characteristics of hyperloop pods with different nose shapes, namely conical, spherical, and ellipsoidal, at transonic speed in a tube with pressure of 0.01 atm. The employed numerical model was validated by the results of a wind tunnel test and grid resolution, and the unsteady aerodynamic behaviours of the different pods in the tubes were analyzed and compared. The pods with the spherical and conical noses were found to generate the lowest aerodynamic pressure and friction drags, respectively. In addition, the effects of the nose shape on the maximum temperature and pressure in the tube were more significant in the deceleration stage than in other stages, and were least pronounced for the pod with the spherical nose. The pod with the ellipsoidal nose generated the lowest minimum temperature and pressure. In addition, the flow field around the pod tail was more sensitive to the nose shape compared with that around the pod head, with a high-temperature and pressure area generated around the tails of the conical- and ellipsoidal-nose pods. The observations indicate that a conical nose affords the best aerodynamic behavior of a transonic hyperloop pod in an evacuated tube.

Static roughness element effects on protuberance full-span wing at micro aerial vehicle application

Although the tubercle wings provide good maneuverability at post-stall conditions, the aerodynamic performance at pre-stall angles is threatened by forming a laminar separation bubble at the trough section of the tubercle wing; consequently, the flight endurance and range are reduced. In the present study, the idea of passive flow control is introduced by using the distribution of static roughness elements on a full-span wing with a sinusoidal leading edge. Initially, the effect of roughness element length, height, and its location are studied at a pre-stall angle (16-degree). Their effect on the laminar separation bubble and vortex shedding formed behind the wing are also investigated. The Reynolds number is assumed to be equal to [Formula: see text] which is in the range of critical Reynolds number and matches to the micro aerial vehicles application. An improved hybrid model, improved delay detached eddy simulation IDDES, has been used to model the flow turbulence structure. In the extended transition region at low Reynolds numbers, the roughness bypassed the instability. Consequently, roughening the surface of the aerofoil increased the boundary layer’s flow momentum, making it more resistible to adverse pressure gradients. By suppressing the bubble, the static roughness element led to pre-stall flow control, which saw an increase in lift coefficient, [Formula: see text], and a decrease in drag coefficient, [Formula: see text]. The results have been demonstrated that the aerodynamic performance, [Formula: see text], has been improved approximately 22.7%, 38%, and 45% for [Formula: see text], and [Formula: see text], respectively. The optimal arrangement of static roughness elements could decline the size of the vortices and strengthen the cores associated with them. This claim can be interpreted with the vortex shedding frequency.

Investigation of fine viscous flow fields in ship planar motion mechanism tests by DDES and RANS methods

The fine large separated flow is a focus in the naval architecture and ocean engineering. In the present study, the CFD solver, naoe-FOAM-SJTU, coupled with delayed detached-eddy simulation (DDES) and Reynolds Averaged Navier-Stokes (RANS) is adopted to simulate the fine viscous flow field in the ship planar motion mechanism (PMM) tests for the benchmark model Yupeng Ship. This paper compares the time histories of forces/moment acting on the hull and their oscillation frequency obtained by Fast Fourier Transform. The predicted results are in good agreement with the experimental data. By comparing the turbulent kinetic energy (TKE) and eddy viscosity coefficient calculated by both numerical methods, the results show that the TKE and eddy viscosity coefficient obtained by DDES method are much less than that achieved by RANS approach. The capacity of four vortex identification methods to capture vortex structures is analyzed in this paper, indicating that the third generation of vortex identification methods (ΩR and Liutex methods) are more suitable for analyzing the flow mechanism in the viscous large separated flow field. The axial Liutex and streamlines on the cutting planes are used to depict the flow around the hull.

Delayed detached eddy simulation method for breaking bow waves of a surface combatant model with different trim angle

Sailing attitudes vary with different loading conditions for ships sailing in open sea, and the trim angle, either by bow or by stern, exerts considerable impact on the flow field around the ship. Currently, attention has primarily been focused on hull resistance and wave patterns while few studies have touched upon breaking bow wave under different trim conditions. This study aims to analyze the breaking bow wave of a surface combatant model with a length of 5.72 m DTMB (name of a surface combatant model) under different sailing attitudes at Fr = 0.35. The Delayed Detached Eddy Simulation (DDES) approach was adopted to study the breaking bow wave features such as plunging jet and air entrainment. The interface-compression algebraic Volume Of Fluid (VOF) method in OpenFOAM was used to capture the free surface. The Computational Fluid Dynamics (CFD) approach was firstly validated by comparing hull resistance and wave contour with the available experimental data. The study then delves into the influence of trim angles on breaking bow waves through simulations of the different conditions, i.e., 1 deg trim by bow, test condition and 1 deg trim by stern. The wave contour, breaking wave profile, vorticity field and the wake field at several transverse sections are then compared in three trim conditions, followed by an analysis of the initial evolution of bow wave breaking based on the turbulent kinetic energy and the vorticity field at four cross sections. The results suggest that trim by bow makes free surface sharper and wave amplitude larger in the breaking bow wave region. The reason is that trim by bow enlarges the attack angle of the bow, thus energizing the bow wave and generating a more violent free surface of bow wave breaking.

Analysis of Trailing Vortex Structure and Turbulent Features of High-Speed Train in Vacuum Pipeline

Through the improved delay-detached eddy simulation (IDDES), this paper establishes a 1:1 model for a high-speed train, and simulates the transient state of the train running 600km/h in a vacuum pipeline with the pressure of 1,000Pa. The results show that, following the Ω criteria, a pair of counterrotating vortexes can be captured, which alternatively shed near the tip of the last carriage, and propagate over a long distance along the flow direction. The motion and expansion of the vortexes are clearly three-dimensional (3D). Judging by the physical meaning of vortexes, the high vorticity vortexes mainly concentrate near the tip of the last carriage, while the low vorticity vortexes scatter across the wake zone. The latter vortexes have a low dissipation rate and are dominated by rotation. The turbulent energy and Reynolds stress of the wake field are very obvious near the tip of the last carriage, and attenuate quickly along the flow direction. This means the vortexes near the tip of the last carriage face a strong shear effect, and undergo apparent dissipation. Low turbulent energy and Reynolds stress are distributed in the downstream far from the tip of the last carriage, i.e., the interaction zone between vortexes and the ground / inner pipe wall.

Study on the Applicability of URANS, Large Eddy Simulations, and Hybrid Large Eddy Simulations/RANS Models for Prediction of Hydrodynamics of Cyclone Separator

Abstract Cyclone separators are an integral part of many industrial processes. A good understanding of the flow features is paramount to efficiently use them. The turbulent fluid flow characteristics are modeled using unsteady Reynolds-averaged Navier–Stokes (URANS), large eddy simulations (LES), and hybrid LES/Reynolds–averaged Navier–Stokes (RANS) turbulent models. The hybrid LES/RANS approaches, namely, detached eddy simulation (DES), delayed detached eddy simulation (DDES), and improved delayed detached eddy simulation (IDDES) based on the k−ω SST RANS approaches are explored. The study is carried out for three different inlet velocities (v = 8, 16.1, and 32 m/s). The results from hybrid LES/RANS models are shown to be in good agreement with the experimental data available in the literature. Reduction in computational time and mesh size are the two main benefits of using hybrid LES/RANS models over the traditional LES methods. The Reynolds stresses are observed in order to understand the redistribution of turbulent energy in the flow field. The velocity profiles and vorticity quantities are explored to obtain a better understanding of the behavior of fluid flow in cyclone separators.

Spectral proper orthogonal decomposition of compressor tip leakage flow

To identify the spatiotemporal coherent structure of compressor tip leakage flow, spectral proper orthogonal decomposition (SPOD) is performed on the near-tip flow field and the blade surface pressure of a low-speed compressor rotor. The data used for the SPOD analysis are obtained by delayed-detached eddy simulation, which is validated against the experimental data. The investigated rotor near-tip flow field is governed by two tip leakage vortices (TLV), and the near-tip compressor passage can be divided into four zones: the formation of main TLV (Zone I), the main TLV breakdown (Zone II), the formation of tip blockage cell (Zone III), and the formation of secondary TLV (Zone IV). Modal analysis from SPOD shows that a major part of total disturbance energy comes from the main TLV oscillating mode in Zone I and the main TLV vortex shedding mode in Zone III, both of which are low-frequency and low-rank; on the contrary, modal components in Zones II and IV are broadband and non-low-rank. Unsteady blade forces are mainly generated by the impingement of the main TLV on the blade pressure surface in Zone III, rather than the detachment of the secondary TLV from the blade suction surface in Zone IV. These identified coherent structures provide valuable knowledge for the aerodynamic/aeroelastic effects, turbulence modeling, and reduced-order modeling of compressor tip leakage flow.

Numerical analysis of the wake of complex-shaped snow particles at moderate Reynolds number

Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This also has an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable, and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated delayed-detached eddy simulation model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries although the contribution of different momentum flux terms differs. These results represent a further step toward a deeper understanding the drag of complex-shaped particles.