Time-averaged Quantities Research Articles

Comparison between shear-driven and pressure-driven oscillatory flows over ripples

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

Uncertainty quantification of time-average quantities of chaotic systems using sensitivity-enhanced polynomial chaos expansion.

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed sensitivity-enhanced generalized polynomial chaos expansion, se-gPC, to quantify efficiently this effect. se-gPC is an extension of gPC expansion, enriched with the sensitivity of the time-averaged quantities with respect to the stochastic variables. To compute these sensitivities, the adjoint of the shadowing operator is derived in the frequency domain. Coupling the adjoint operator with gPC provides an efficient uncertainty quantification algorithm, which, in its simplest form, has computational cost that is independent of the number of random variables. The method is applied to the Kuramoto-Sivashinsky equationand is found to produce results that match very well with Monte Carlo simulations. The efficiency of the proposed method significantly outperforms sparse-grid approaches, such as Smolyak quadrature. These properties make the method suitable for application to other dynamical systems with many stochastic parameters.

On the laminar wake of curved plates

Numerical simulations are performed to investigate the effect of the Reynolds number (Re) on flow over curved plates. Concave and convex plates, obtained by introducing curvature on a flat plate, are analyzed in the Reynolds number range 0.1 ≤Re≤ 120. It is observed that for a concave plate, the separation point is dependent on Re, while for a convex plate, the flow separates from the outermost tips for all Reynolds numbers. The analysis of time-averaged quantities reveals that concave and convex plates behave differently for the same Reynolds number. In the steady flow regime, visualization of streamlines reveals the presence of a recirculation bubble on the front side of the concave plate, even for the lowest Reynolds number (Re = 0.1). However, at higher Reynolds numbers (Re = 110, 120), the near wake of concave plate witnesses secondary and tertiary recirculating entities. The present simulations also report the unique phenomenon of vortex realignment and divergence of vortex street in the wake of a concave plate. For a convex plate, the vortex realignment is followed by the movement of upper and lower vortices as two parallel vortex streets. The existence of multiple instabilities is another highlight in the near and far wakes of the concave plate, some of which arise due to the secondary vortex interactions. A comprehensive analysis further reveals a handful of novel phenomenal occurrences in the wake of concave surfaces.

Direct numerical simulation of turbulent jet in regular waves: A comparison between circular and non-circular cross-sections

Direct numerical simulations of circular and non-circular jets (square and rectangular) when released into regular waves are performed and reported in this article. In case of a rectangular jet, two different orientations of the nozzle have been simulated i.e major axis parallel (case 1) and perpendicular (case 2) to wave advancement direction. An analysis of the leading vortex ring reveals that axis switching in a rectangular jet takes place irrespective of nozzle orientation with respect to wave advancement direction. The axis switching is absent in the square jet. Further, the roll-up frequency of the non-circular jets is found less than the circular jet. Also, the roll-up frequency is independent of the orientation of the rectangular jet with respect to the wave direction. The braid region shows that the number of counter-rotating pairs are four for all the cases, however, the lateral jets are three for circular, square and case 1 of rectangular jets. The lateral jets in case 2 of the rectangular jet remain four due to change in orientation of the lateral jets owing to change in the nozzle orientation. The time-averaged quantities suggest increased mixing and entrainment in the rectangular jet as compared to circular jet. The highest mixing and shortest potential core are observed in case 2 of the rectangular jet. Therefore, for better mixing, the rectangular nozzle should be placed in the ocean outfall such that its major axis remains perpendicular to the direction of wave advancement.

Two-phase flow simulations of surface waves in wind-forced conditions

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn–Hilliard volume-of-fluid model to capture the dynamics of the air–sea interface at geophysically relevant Reynolds numbers. It employs a hybrid filtered/averaging improved detached eddy simulation method to model turbulence and utilizes a continuum model to account for surface tension if the diffuse interface is under-resolved by the grid. A numerical wind-wave tank is introduced, and results obtained for two known wind-wave conditions are analyzed in comparison to experimental data at matched Reynolds numbers. The focus of the comparison is on both time-averaged and wave-coherent quantities, and includes pressure, velocity as well as modeled and resolved Reynolds stresses. In general, numerical predictions agree well with the experimental measurements and reproduce many wave-dependent flow features. Reynolds stresses near the water surface are found to be especially important in modulating the critical layer height. It is concluded that the diffusive interface approach proves to be a promising method for future studies of air–sea interface dynamics in geophysically relevant flows.

CFD-DEM Evaluation of the Clustering Behavior in a Riser-the Effect of the Drag Force Model.

Riser reactors are frequently applied in catalytic processes involving rapid catalyst deactivation. Typically heterogeneous flow structures prevail because of the clustering of particles, which impacts the quality of the gas-solid contact. This phenomenon results as a competition between fluid-particle interaction (i.e., drag) and particle-particle interaction (i.e., collisions). In this study, five drag force correlations were used in a combined computational fluid dynamics-discrete element method Immersed Boundary Model to predict the clustering. The simulation results were compared with experimental data obtained from a pseudo-2D riser in the fast fluidization regime. The clusters were detected on the basis of a core-wake approach using constant thresholds. Although good predictions for the global (solids volume fraction and mass flux) variables and cluster (spatial distribution, size, and number of clusters) variables were obtained with two of the approaches in most of the simulations, all the correlations show significant deviations in the onset of a pneumatic transport regime. However, the correlations of Felice (Int. J. Multiphase Flow1994, 20, 153-159) and Tang et al. [AIChE J.2015, 61 ( (2), ), 688-698] show the closest correspondence for the time-averaged quantities and the clustering behavior in the fast fluidization regime.

Heat and mass transfer processes of solid-state hydrogen discharging: a CFD study

This article deals with the numerical simulation of a two-dimensional instantaneous heat and mass transfer processes within a commonly used intermetallic compound (a.k.a. Mischmetal) packed in a unit disc of an annulus-disc reactors, during hydrogen gas desorption. Using the finite volumes technique bundled in the OpenFOAM® CFD code, temperature and amount of desorbed hydrogen and their time-averaged quantities inside the metal-hydride packed bed are obtained for various temperatures of fluids used in heat transfer, and several outlet pressure magnitudes. Using a set of numerical simulations, we have emphasized the impacts of both parameters on metal-hydride reactor performance related to discharging time. An excellent accord was recorded for the present simulations results compared against the literature-reported experimental data [20].

Large-eddy simulation of airflow dynamics around a cluster of buildings

The wind flow around the buildings with different rooftops is studied numerically using large-eddy simulation (LES). The filtered Navier-Stokes equations in LES are used to compute the large eddies, whereas the dynamic Smagorinsky subgrid-scale (SGS) model calculates the small eddies. A turbulent spot method is applied for the synthesis of artificial turbulent fields at the inlet. In this separated and reattached flow, our aim is to analyze the wakes’ vortical structure along with the buildings of different heights and shapes. A large number of engineering applications involve precise predictions of the airflow around buildings to ensure performance and safety. To validate the numerical solver, a comparison is performed with the earlier reported numerical and experimental data. The turbulent flow characteristics are discussed in terms of instantaneous flow structure and time-averaged statistical flow quantities. All the cases are simulated for a Reynolds number [Formula: see text] to understand the turbulent airflow patterns. The flow shows a separable bubble at the leading edge of the rooftop of the building that leads to recirculation at the lee side of the first row of buildings. Due to the recirculation, the suction arises near the leading edge of the building to assure a continuous flow of air around the obstacles. Further, Reynold stresses show high momentum fluxes in the frontal region of the buildings.

Experimental investigation of three-dimensional effects in cavitating flows with time-resolved stereo particle image velocimetry

The present paper is devoted to characterizing the three-dimensional effects in a cavitating flow generated in a venturi-type profile. Experimental measurements based on 2D3C (two-dimensional-three-component) stereoscopic particle image velocimetry are conducted to obtain the three components of the velocity field in multiple vertical planes aligned with the main flow direction, from the center of the channel to the side walls. Time-resolved acquisitions are conducted, so not only time-averaged quantities but also velocity fluctuations can be discussed. The attention was focused on configurations of cloud cavitation, where the attached cavity experiences large-scale periodical oscillations and shedding of clouds of vapor. Although the water channel is purely two-dimensional, some significant flow velocities in the third direction (depth of the test section) were measured. Some of those velocities were found to be related to small differences between the boundary conditions on the two sides, such as minor gaps between the sides and the bottom wall, while others reflect intrinsic three-dimensional mechanisms inside the cavitation area, such as side jets that contribute to the periodical instability process. These mechanisms are discussed, and a possible 3D (three-dimensional) structure of the cavitating flow is proposed.

Influence of Interpolation Scheme on the Accuracy of Overset Method for Computing Rudder-Propeller Interaction

Abstract The overset method and associated interpolation schemes are usually thoroughly verified only on synthetic or academic test cases for which conclusions might not directly translate to real engineering problems. In the present work, an overset grid method is used to simulate a rudder-propeller flow, for which a comprehensive verification and validation study is performed. Three overset-related interpolation schemes (first order inverse distance, second order nearest cell gradient and third order least squares) are tested to quantify and qualify numerical errors on integral quantities, mass imbalance, flow features and rudder pressure distributions. The performance overhead is also measured to help make accuracy versus performance balance decisions. Rigorous solution verification is performed to estimate time and space Discretization, iterative and statistical uncertainties. Validation of the propeller-rudder flow against experimental data is also done. The results show that, while the choice of interpolation scheme has minimal impact on time-averaged integral quantities (like propeller and rudder forces), they do influence the smoothness of the time signals, with the first order scheme resulting in large intensity high-frequency temporal oscillations. Lower order interpolation methods also produce more interpolation artifacts in fringe cells, which are then convected downstream. Mass imbalance is also affected by the interpolation scheme, with higher order schemes such as the third order least squares approach resulting in an order of magnitude lower flux errors. The limitations of first order schemes do not, however, result in significant lower computational overhead, with the second order nearest cell gradient being even cheaper than the inverse distance scheme in the tested implementation. Lastly, validation shows promising results with rudder forces within 10% of the experiments.

Riblet Performance Beneath Transitional and Turbulent Boundary Layers at Low Reynolds Numbers

Several high-resolution scale-resolving simulations are carried out to examine the effect of riblets on the mean and turbulent statistics of a zero-pressure-gradient boundary layer. The Reynolds number is chosen such that the riblets are exposed to both the transitional and turbulent regimes of the boundary layer. This is in contrast to the turbulent channel flow or fully turbulent boundary layers studied in the literature. The boundary layer is subjected to freestream turbulence and roughness tripping. The transition process and the extent of the turbulent regime on the riblets are altered by tripping the boundary layer with an isolated hemispherical roughness element. The influence of the riblets on the transition onset and the viscous drag reduction is demonstrated through time-averaged, phase-averaged, and instantaneous flow quantities. The effect of the V-shaped riblets with both sharp and curved tips (and valleys) is also explored. With riblets, the viscous drag in the turbulent regime is reduced by 4–6% when compared to a smooth surface, and the efficacy of sharp V-shaped riblets is shown to be marginally higher than for the curved riblets. In the transitional flow regime, the coherent structures over riblets are predominantly spanwise oriented. In particular, a separated shear layer forms over the riblet leading edge as the flow encounters an abrupt surface transition from the smooth surface onto the riblets. A leading-edge ramp is shown to effectively minimize the additional spurt in the turbulent kinetic energy and the associated losses incurred due to this abrupt surface change.

Mean flow reconstruction of unsteady flows using physics-informed neural networks

Abstract Data assimilation of flow measurements is an essential tool for extracting information in fluid dynamics problems. Recent works have shown that the physics-informed neural networks (PINNs) enable the reconstruction of unsteady fluid flows, governed by the Navier–Stokes equations, if the network is given enough flow measurements that are appropriately distributed in time and space. In many practical applications, however, experimental measurements involve only time-averaged quantities or their higher order statistics which are governed by the under-determined Reynolds-averaged Navier–Stokes (RANS) equations. In this study, we perform PINN-based reconstruction of time-averaged quantities of an unsteady flow from sparse velocity data. The applied technique leverages the time-averaged velocity data to infer unknown closure quantities (curl of unsteady RANS forcing), as well as to interpolate the fields from sparse measurements. Furthermore, the method’s capabilities are extended further to the assimilation of Reynolds stresses where PINNs successfully interpolate the data to complete the velocity as well as the stresses fields and gain insight into the pressure field of the investigated flow.

Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach

We present a frequency-domain method for computing the sensitivities of time-averaged quantities of chaotic systems with respect to input parameters. Such sensitivities cannot be computed by conventional adjoint analysis tools, because the presence of positive Lyapunov exponents leads to exponential growth of the adjoint variables. The proposed method is based on the well established least-square shadowing (LSS) approach [1], that formulates the evaluation of sensitivities as an optimisation problem, thereby avoiding the exponential growth of the solution. All existing formulations of LSS (and its variants) are in the time domain. In the present paper, we reformulate the LSS method in the frequency (Fourier) space using harmonic balancing. The resulting system is closed using periodicity. The new method is tested on the Kuramoto-Sivashinsky system and the results match with those obtained using the standard time-domain formulation. The storage and computing requirements of the direct solution grow rapidly with the size of the system. To mitigate these requirements, we propose a resolvent-based iterative approach that needs much less storage. Application to the Kuramoto-Sivashinsky system gave accurate results with low computational cost. Truncating the large frequencies with small energy content from the harmonic balancing operator did not affect the accuracy of the computed sensitivities. Further work is needed to assess the performance and scalability of the proposed method.

Influence of wave height on round jet in regular waves: Direct numerical simulations

The influence of wave height on the dynamics of a turbulent round jet is analyzed using direct numerical simulation. The vortex dynamics associated with the interaction of the jet with waves of different heights is compared using the swirling strength criterion and the contours of vorticity. An analysis of the vortex roll-up frequency reveals that it increases with increasing wave height. With an increase in the wave height, the deflection of the jet elevates, and therefore, the span of the vortex rings in the near-field reduces in the direction of wave propagation. Further, an analysis of the braid region reveals that the number of lateral jets reduces to three with increasing wave height despite the number of counter-rotating vortex pairs remaining as four. The longer time evolution suggests that as the jet moves from the crest to the zero down-crossing, the fluid in the far-field gets detached from the main jet flow for the stronger waves. The evaluation of the preferred mode reveals that it remains helical for all wave heights. The proper orthogonal decomposition (POD) establishes that the highest energy is captured by the modes of the highest wave height. Also, as the wave height increases, a fewer number of modes capture 90% of the energy. Further, contours of POD modes represent the jet oscillations as well as the kinetic energy gain in the shear layer and the far-field. The time-averaged quantities quantitatively demonstrate an increase in mixing and entrainment in the jet as the wave height increases.

Bragg–Cherenkov resonance and polaron-like decoupling of the Wigner solid on superfluid helium

Nonlinear polaron-like dynamics of the two-dimensional Wigner solid (WS) on superfluid 4He are theoretically analyzed in different models and transport regimes for their similarities and distinctions. The Bragg-Cherenkov (BC) resonant excitation of surface waves and WS decoupling from surface dimples were usually considered in terms of a dc transport model. At the same time, field-velocity characteristics of the WS are measured under ac conditions and presented for time-averaged quantities. Here the nonlinear equation of motion of the WS coupled to surface dimples is studied for ac conditions using two different approaches based on fixing the driving field or the output current. Both approaches are shown to give similar results for the first harmonics of major transport properties. In the ac theory, the BC resonances for dimple inertia and the momentum relaxation rate have asymmetrical shapes, which is in contrast with the results of dc models. Even a quite low driving frequency is shown to affect the amplitude of the BC resonance and decoupling of the WS. Above the BC threshold, the effective mass of surface dimples as a function of the velocity amplitude strongly oscillates indicating multiple recoupling processes.

Analytical Solutions to Temperature Field in Various Relative-Scale Media Subjected to a Reciprocating Motion Point Heat Source

To reveal the temperature rise evolution mechanism of isotropic media subjected to reciprocating motion constant-strength point heat source, various forms of analytical solutions are derived on the basis of differentiated relative scales, and non-dimensionalized parameters are designed to characterize the thermal distribution regularities by utilizing numerical calculations. Temperature rise curves of media subjected to a reciprocating motion point heat source allow similar quasi-steady-state characteristics to appear, which finally achieve a stable state, so that the values of surplus temperature oscillate around the constant time-average quantity. The time to reach quasi-steady state, the time-averaged quantity and the fluctuation amplitude of surplus temperature are comprehensively impacted by the dimensionless distance parameter γ, the convective heat transfer parameter ω and the velocity and travel parameter β. This work discusses influence rules of temperature evolution in various relative-scale media and further enriches the moving heat source theory.

Transition-based constrained large-eddy simulation method with application to an ultrahigh-lift low-pressure turbine cascade flow

A transition-predictive Reynolds-averaged Navier–Stokes (RANS) model is introduced as the Reynolds controlling condition to constrained large-eddy simulation (TrCLES) to improve the ability of this method to predict wall-bounded laminar–turbulent transition flows. In the TrCLES method, the constraint conditions for total Reynolds stress and heat flux are only imposed to the near-wall region in transitional and turbulent boundary layer. The newly proposed method recovers direct numerical simulation in the laminar boundary region, and retrieves the traditional large-eddy simulation method in the far-wall regions. The TrCLES method is validated in simulations of external flow around the Eppler 387 (E387) airfoil and internal flow past the ultrahigh-lift low-pressure turbine T106C cascade. The improved delayed detached-eddy simulation (IDDES) method, CLES method based on full-turbulence shear stress transport model and RANS method with a three-equation transition model are also evaluated in comparison with the available experimental and numerical data. As expected, the TrCLES method can predict laminar separation bubble and separation-induced transition process in both the E387 and T106C flows pretty well. In contrast, neither IDDES nor the original CLES can provide reasonable prediction for the laminar separation-induced transition phenomenon. The validity and fidelity of the TrCLES method are further verified by simulations of the T106C cascade flows in a wider range of exit Reynolds and Mach numbers. It is shown that the TrCLES method can not only predict the time-averaged aerodynamic quantities such as isentropic Mach number and exit kinetic energy loss very well, but also capture the laminar separation bubble and unsteady flow structures with satisfactory accuracy.

Wind turbine response in waked inflow: A modelling benchmark against full-scale measurements

Predicting the power and loads of wind turbines in waked inflow conditions still presents a major modelling challenge. It requires the accurate modelling of the atmospheric flow conditions, wakes of upstream turbines and the response of the turbine of interest. Rigorous validations of model frameworks against measurements of utility-scale wind turbines in such scenarios remain limited to date. In this study, six models of different fidelity are compared against measurements from the DanAero experiment. The two benchmark cases feature a full-wake and partial-wake scenario, respectively. The simulations are compared against local pressure forces and inflow velocities measured on several blade sections of the downstream turbine, as well as met mast measurements and standard SCADA data. Regardless of the model fidelity, reasonable agreements are found in terms of the wake characteristics and turbine response. For instance, the azimuth variation of the mean aerodynamic forces acting on the blade was captured with a mean relative error of 15–20%. While various model-specific deficiencies could be identified, the study highlights the need for further full-scale measurement campaigns with even more extensive instrumentation. Furthermore, it is concluded that validations should not be limited to integrated and/or time-averaged quantities that conceal characteristic spatial or temporal variations.

Coherence of unsteady wake of periodically plunging airfoil

We present an experimental investigation of the flow structure in the near wake of a NACA0012 airfoil plunging sinusoidally at a chord Reynolds number of Re = 20 000 and for a wide range of reduced frequency k and Strouhal number based on peak-to-peak amplitude St. Estimated mean thrust coefficients using the mean and fluctuating velocity fields confirm the St2 dependence as well as a significant effect of the reduced frequency for k ≤ 1. Generally, time-averaged flow quantities are better correlated with St than k in the range tested (k ≤ 3.14 and St ≤ 0.24). Analysis of the streamwise flow and cross-flow in the near wake using two-point cross-correlations and proper orthogonal decomposition reveals that the unsteady characteristics are even better correlated with St than the mean flow quantities. The percentage energy of the fundamental wake modes of the streamwise flow and the flapping mode of the cross-flow increases with increasing St, but at different rates in the drag-producing and thrust-producing wakes. There are similarities to the wake synchronisation behind oscillating bodies. The spanwise-averaged cross-correlation coefficient in the measurement domain grows linearly for small St (in drag-producing wakes), and is nearly constant at a high value for larger St (in thrust-producing wakes). Results show that the Strouhal number is the most important parameter that determines the degree of two-dimensionality of the wake, and suggest that spanwise vortices are quasi-two-dimensional for St ≥ 0.05 and x/c ≤ 4. The implications for experimental gust generators using oscillating airfoils are discussed.

Thermal control of transonic shock-boundary layer interaction over a natural laminar flow airfoil

Implicit large eddy simulations are performed to show control of shock and boundary layer interaction over a natural laminar flow airfoil by harmonic heat transfer on the suction surface at a free-stream Mach number M∞=0.72 and angle of attack of α=0.38°, for which experimental/flight test results exist. Surface heat flux is added in a time-periodic manner with the exciter strip located at different locations in the vicinity of the shock location at x/c≈0.49 for the flow without any control. Four cases of localized excitation with Gaussian distribution centered at x/c=0.45, 0.48, 0.50, and 0.55 on the airfoil surface are considered, with a width of 10% chord. The effects of unsteady heat flux on shock strength, location, and modification of its structure are demonstrated by instantaneous and time-averaged flow quantities. Detailed vortical and entropy contour plots and numerical Schlieren indicate flow features, such as creation and propagation of Kutta waves and their interactions with the shock wave. Time-averaged load distributions reveal a shift in the location and strength of the shock, with altered lift and drag time histories. The Fourier transforms of lift and drag coefficients help explain the alteration of the strength and structures of the shock-induced unsteadiness. The imposed excitation results in an improvement of aerodynamic efficiency (lift to drag ratio). The numerical simulations follow the algorithm developed in Sengupta et al. [Comput. Fluids 88, 19–37 (2013)].