Mean Kinetic Energy Research Articles

Characterizing tilt effects on wind plants

Tilting the nacelle of a wind turbine modifies entrainment into the wind plant and impacts total efficiency. Wakes are deflected vertically by tilt and in the case of large angles can disrupt entertainment from the undisturbed flow or dissipate on the ground. The effect of nacelle tilt on wake behavior is investigated in a series of wind tunnel experiments for the first time. Scale model turbines with a hub height and a diameter of 12 cm are arranged in a Cartesian array composed of four rows of three turbines each. The tilt angle was varied in the third turbine row from −15° to 15° in chosen 5° increments. Stereo particle image velocimetry measurements of the instantaneous velocity field were recorded at four locations for each angle. Tilted wakes are described in terms of the average streamwise velocity, vertical velocity, and Reynolds stresses. Mean kinetic energy quantities are presented, and conditional sampling is employed to quantify the importance of sweep to ejection events in vertical momentum transfer. Additionally, the effect of nacelle tilt on net power production is presented and compared to existing models. Numerical simulations accurately predict losses in net efficiency for positive angles but diverge for negative tilt angles. The results demonstrate that the tilt angle influences wake magnitude, displacement, and recovery. Positive angles deflect wakes above the wind plant, while negative angles encourage entrainment into the wind plant and exhibit rapid recovery.

Kinetic energy balance in turbulent particle-laden channel flow

The present study investigates the influence of particle additives on the transfer, conversion, and dissipation of kinetic energy (KE) of a turbulent gas–solid channel flow. We derived the equations of KE, mean-flow KE, and turbulent KE (TKE) of the particle-laden flow and further performed two-way coupled direct numerical simulations of channel flow laden with four-million particles with Stokes number St = 30 (corresponding to a mass loading ratio of around one) with an Eulerian–Lagrangian approach. We found that, in the unladen flow, more than half of the input energy is directly dissipated in the mean flow, whereas the rest is converted to maintain the turbulence. By contrast, in the laden flow, both mean dissipation and energy supply are comparable with the unladen flow. However, the turbulence production is greatly reduced in the particle-laden flow. Another sink term due to the presence of the particle–fluid interactions corresponds to the rest loss of the total energy supply. The results reveal the particle-induced redistribution of mean KE, which is transferred from the mean flow to particles in the channel core, whereas the flow gains energy from particles in the near-wall region. In total, there is a loss of the mean-flow energy due to the presence of the inertial particles. Regarding TKE balance, the particles, gaining energy from the mean flow, transfer the energy to the fluid across the channel, which contributes around one third of the TKE source. The present results provide a general picture of KE balance of a particle-laden channel flow.

Reduced-order modelling of radiative transfer effects on Rayleigh–Bénard convection in a cubic cell

This paper presents a reduced-order modelling strategy for Rayleigh-Benard convection of a radiating gas, based on the proper orthogonal decomposition (POD). Direct numerical simulation (DNS) of coupled natural convection and radiative transfer in a cubic Rayleigh-Benard cell is performed for an air/H 2 O/CO 2 mixture at room temperature and at a Rayleigh number of 10 7. It is shown that radiative transfer between the isothermal walls and the gas triggers a convection growth outside the boundary-layers. Mean and turbulent kinetic energy increase with radiation, as well as temperature fluctuations to a lesser extent. As in the uncoupled case, the large-scale circulation (LSC) settles in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, and experiences occasional brief reorientations which are rotations of π/2 of the LSC in the horizontal plane. A POD analysis is conducted and reveals that the dominant POD eigenfunctions are preserved with radiation while POD eigenvalues are increased. Two POD-based reduced-order models including radiative transfer effects are then derived: the first one is based on coupled DNS data while the second one is an a priori model based on uncoupled DNS data. Owing to the weak temperature differences, radiation effects on mode amplitudes are linear in the models. Both models capture the increase in energy with radiation and are able to reproduce the low-frequency dynamics of reorientations and the high-frequency dynamics associated with the LSC velocity observed in the coupled DNS.

Impacts of early/late South China Sea summer monsoon withdrawal on tropical cyclone genesis over the western North Pacific

This study reveals a significant in-phase relationship between the South China Sea summer monsoon (SCSSM) withdrawal date and tropical cyclone (TC) genesis over the western North Pacific (WNP). The number of TCs generated over the WNP from mid-September to mid-October is positively correlated with the SCSSM withdrawal date during the period of 1979–2016. The decreased (increased) number of TCs generated during early (late) SCSSM withdrawal years is attributed to both internal atmospheric dynamics and external sea surface temperature (SST) forcing. Through dynamic (Rossby wave response) and thermodynamic (increased moisture) processes, the warm SST anomalies during late withdrawal years over the tropical WNP contribute to maintaining the monsoon trough (MT) in the boreal autumn and moisturizing the mid-level atmosphere, providing a favorable environment for TC genesis. The remaining MT can facilitate the conversion of mean kinetic energy into eddy kinetic energy (EKE) and enhance synoptic-scale waves. In addition, upper-level baroclinic energy conversion also contributes to EKE development. Both barotropic and baroclinic processes favor TC genesis over the WNP. In contrast, colder SSTs during early withdrawal years induce the early withdrawal of the MT, leading to depressed enhancement of the EKE and weakening the northwestward propagation of synoptic-scale waves. Hence, fewer (more) TCs tend to be generated during early (late) withdrawal years.

Wake Statistics of Different-Scale Wind Turbines under Turbulent Boundary Layer Inflow

Subscale wind turbines can be installed in the field for the development of wind technologies, for which the blade aerodynamics can be designed in a way similar to that of a full-scale wind turbine. However, it is not clear whether the wake of a subscale turbine, which is located closer to the ground and faces different incoming turbulence, is also similar to that of a full-scale wind turbine. In this work we investigate the wakes from a full-scale wind turbine of rotor diameter 80 m and a subscale wind turbine of rotor diameter of 27 m using large-eddy simulation with the turbine blades and nacelle modeled using actuator surface models. The blade aerodynamics of the two turbines are the same. In the simulations, the two turbines also face the same turbulent boundary inflows. The computed results show differences between the two turbines for both velocity deficits and turbine-added turbulence kinetic energy. Such differences are further analyzed by examining the mean kinetic energy equation.

Cosmic Ray Dissociation of Molecular Hydrogen and Dense Cloud Chemistry

Abstract Dissociation of molecular hydrogen by secondary electrons produced by cosmic ray or X-ray ionization plays a crucial role in the chemistry of the densest part of molecular clouds. Here we study the effect of the mean kinetic energy of secondary electrons on this process. We compare predictions using a range of secondary electron energies and predictions of the cross sections with the values in the UMIST database. We find that the predicted column densities change by nearly one dex.

Time dependence of quantum correlation functions.

In the past few years, the exponential expansion analysis of time autocorrelation functions has provided profound insight into the leading microscopic processes driving the atomic-scale dynamics and has made it possible to highlight the presence and the role of various relaxation channels through which the fundamental correlation functions decay with time. Here we apply this method to the determination of the full time dependence of a correlation function c(t) in a quantum system at nonzero temperature, by making explicit its relationship with its Kubo transform c_{K}(t), which in some cases can be approximately computed with the presently available quantum simulation techniques. We obtain an exact expression for c(t) in terms of the exponential modes that describe the time behavior of c_{K}(t). The relative importance of the various modes in determining the overall shape of c(t) can then be studied in detail. This work extends to the full time domain the results of a previous paper [Guarini et al., Phys. Rev. Lett. 123, 135301 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.135301], in which we employed the same method to calculate the zero time value of the velocity autocorrelation function, to obtain a microscopic description of the quantum mean kinetic energy in a fluid. In particular, we show that the decay constants and the frequencies of the dominant microscopic modes of c(t) are the same as those of c_{K}(t), but the dynamics of the quantum system also contains an additional term decaying on a time scale determined solely by temperature of the system.

Short-term, linear, and non-linear local effects of the tides on the surface dynamics in a new, high-resolution model of the Mediterranean Sea circulation

The tides in the Mediterranean Sea are generally weaker than in other regions of the world ocean, but are locally intensified in passages with complex bathymetry, such as the Gibraltar Strait and the Sicily Channel. To date, a detailed understanding of their effects on the circulation, on the short time scales relevant to forecasting, is still missing, due to the lack of specific observations, and of basin-scale, numerical models explicitly accounting for the tidal forcing. The present investigation attempts to bridge this gap, using a newly developed forecasting model of the circulation of the Mediterranean Sea-Black Sea system that includes the effects of the main diurnal and semidiurnal astronomical tides. After validating the model barotropic tidal dynamics through comparison with the results of a tidal inversion software and historical data, a fully baroclinic run is analyzed, with focus on the Mediterranean Sea dynamics. The run covers the period 19 March–30 April 2018 and is initialized and forced with realistic fields produced by state-of-the-art operational models. After verifying that the modelled circulation and hydrology agree with available remote and in situ observations, attention is focused on short-time effects of the tidal forcing on the local circulation. Tides are found to significantly modulate transports not only across the Strait of Gibraltar and the Sicily Channel, as expected, but also across the Corsica Channel and the Otranto Strait. Tidal effects also modify relevant features of the circulation inside the basin, inducing local modulations of some of the main currents and exciting topographic waves that eventually get trapped over shallow bathymetric features, producing diurnal rotations of the flow patterns. Examples of the latter dynamics are found over the Adventure Bank and the Malta Plateau, in the Sicily Channel, and in the eastern portions of the Corsica Channel and the Otranto Strait. Furthermore, in several locations (Sicily Channel, Corsica Channel, Messina Strait, North Adriatic Sea), spectral analysis of the mean kinetic energy reveals the presence of spectral peaks corresponding to periods of about 8 and 6 h, which can only be interpreted as harmonics (overtides and compound tides) of the diurnal and semidiurnal tidal components, generated through non-linear interactions. This shows that, contrary to a widespread assumption, tidal effects in the Mediterranean cannot be linearly superimposed on the basin circulation.

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.

Energetics of Seamount Wakes. Part I: Energy Exchange

AbstractSeamounts have been theorized to act as “stirring rods,” converting barotropic flow into an unsteady wake, turbulence, and diapycnal mixing. The energetics of these processes are not well understood, but they may have implications for basin-scale mixing calculations. This study presents the results of a series of simulations for idealized seamounts in steady barotropic flow, with varying degrees of stratification and rotation. The kinetic energy within each simulation domain is decomposed into the mean kinetic energy, unsteady eddy energy, and turbulent kinetic energy; evolution equations are derived for each. Within the evolution equations, energy exchange terms arise, which relate the various forms of kinetic energy and potential energy. Key exchange terms, such as the rate at which the mean flow is converted into eddy energy, are compared across the Froude–Rossby parameter space. It is shown that the conversion terms associated with mesoscale motions are a function of the Burger number, which is consistent with a quasigeostrophic flow regime. Conversely, conversion terms associated with turbulent processes scale with the product of the Froude and Rossby number. The amount of energy extracted from the mean flows suggests that wake effects may be significant for the parameter range and model assumptions studied. These results suggest that some seamounts may indeed act as oceanic stirring rods.

Compressible plane turbulent wakes under pressure gradients evolving in a constant area section

Development of statistically two-dimensional (2-D) turbulent wakes under pressure gradients is a common feature of many industrial and aerodynamic flows. The usual set-up is to generate a wake, and study its development through a passage with a variable area; if the downstream area decreases (increases) a favourable pressure gradient or FPG (adverse pressure gradient or APG) is imposed. In applications such as in turbomachinery, however, the wakes develop in a periodic constant area passage in the stator–rotor gap and with an imposed pressure gradient. To study these flows, here, we develop a canonical set-up for this new kind of wake evolution in FPG and APG of different strengths by placing a 2-D flat plate normal to the flow in a periodic constant area passage and a fixed inflow mass flux. Employing compressible direct numerical simulations, we impose pressure gradients through a ramped body force term to the momentum and total energy equations while the wake is allowed to develop spatially in a region of fixed width. The resultant mean velocity statistics, wake width, energy budgets and entropy generation rates are scrutinised to assess the effect of the pressure gradients, and where possible, the similarities and differences to the conventional case of variable area pressure gradients are discussed. The results show that the effect of a constant area pressure gradient on flow statistics is non-trivial, resulting from significant density changes. The pressure gradients also have an effect on the different energy budgets, which produces a gain for FPG and loss for APG in the mean kinetic energy. Consequently, the entropy generation rate diminishes and augments for the FPG and APG, respectively, compared to the zero pressure gradient. Finally, the effect of different passage heights ( ) relative to the wake half-width ( ) is studied using large eddy simulations. We find that wake width and hence the spreading, depends primarily on the wake–wake interaction for small and pressure gradients for larger , and this has implications for the design of turbomachinery.

Drift Characteristics of Metal Ions in Helium in an External Electric Field

The results of Monte Carlo calculations of the drift characteristics of metal ions (Li, Be, Al, Fe, Cu, W, Hg, and Au) in a constant uniform electric field 1 < E/N < 1000 Td in helium are presented. The dependences of the mobility, longitudinal and transverse diffusion coefficients, and mean kinetic energy of ions, as well as their longitudinal and transverse temperatures, on the electric field strength are given.

Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.

Response of Total and Eddy Kinetic Energy to the Recent Spinup of the Beaufort Gyre

AbstractThe Beaufort Gyre in the Arctic Ocean has spun up over the past two decades in response to changes of the wind forcing and sea ice conditions, accumulating a significant amount of freshwater. Here a simulation performed with a high-resolution, eddy-resolving model is analyzed in order to provide a detailed description of the total and eddy kinetic energy and their response to this spinup of the gyre. On average, and in contrast to the typical open ocean conditions, the levels of mean and eddy kinetic energy are of the same order of magnitude, and the eddy kinetic energy is only intensified along the boundary and in the subsurface. In response to the strong anomalous atmospheric conditions in 2007, the gyre spins up and the mean kinetic energy almost doubles, while the eddy kinetic energy does not increase significantly for a long time period. This is because the isopycnals are able to flatten and the gyre expands outwards, reducing the potential for baroclinic instability. These results have implications for understanding the mechanisms at play for equilibrating the Beaufort Gyre and the variability and future changes of the Arctic freshwater system.

Dependence of Information Entropy of Uniform Fermi Systems on Correlations and Thermal Effects

The influence of correlations of uniform Fermi systems (nuclear matter, electron gas and liquid 3He) on Shannon's information entropy, S, is studied. It is found that, for three different Fermi systems with different particle interactions, the correlated part of S (Soor) depends on the correlation parameter of the systems or on the discontinuity gap of the momentum distribution through two parameter expressions. The values of the parameters characterize the strength of the correlations. A two parameter expression also holds between Scor and the mean kinetic energy (K) of the Fermi system. The study of thermal effects on the uncorrelated electron gas leads to a relation between the thermal part of S (Sthermai) and the fundamental quantities of temperature, thermodynamical entropy and the mean kinetic energy. It is found that, in the case of low temperature limit, the expression connecting Sthermai with Κ is the same to the one which connects Scor with K. Thus, regardless of the reason (correlations or thermal) that changes K, S takes almost the same value.

Semi-Lagrangian Vlasov simulation of the interaction between femtosecond chirped and double laser pulses with a thin plasma slab

The wakefield generation and electrons acceleration in the interaction of femtosecond chirped and double laser pulses with an underdense thin plasma slab is examined by numerical solution of the relativistic Vlasov-Maxwell system of equations using the backward semi-Lagrangian method (BSL). Unlike particle-in-cell methods, the BSL method is free of numerical noise and provides an accurate representation of the distribution function, even in very low density regions of phase space where acceleration and trapping occur. The effect of density fluctuations in low density regions of phase space are important, since they affect the acceleration processes over the following interactions. Therefore, a detailed structure of the distribution function is needed to investigate this process in these regions, which only can be obtained by Vlasov codes. Excitation of wakefields by chirped, chirp free, and double pulse lasers in an underdense plasma slab are simulated using the BSL code and the results are compared. It is shown that by making use of chirped laser pulses, the mean kinetic energy of plasma electrons can be enhanced up to 40% compared with the chirp free case. The investigation of wakefield generation by double laser pulses with a time repetition equal to one plasma period, exhibits amplification of wakefield amplitude after the entrance of the second laser pulse into plasma slab.

Kinetic energy of oxygen atoms in water and in silica hydrogel

The effect of temperature on the mean kinetic energy of Oxygen, Ke(O), in silica hydrogel (constituting of water confined in a silica Xerogel matrix) was computed between 5 and 325 K. The results are higher by up to 40% than those deduced from a recent deep inelastic neutron scattering (DINS) measurement. Note that when the mean kinetic energy of Hydrogen Ke(H) was computed using the same method a good agreement was obtained with the DINS measurement. This seems to indicate that the measured Ke(O) values are strongly underestimated due to the DINS method of analysis of the n-scattering intensities as discussed in the text.

A Novel Personalized Pre-operational Transcatheter Aortic Valve Implantation (TAVI) Supporting Tool

Objective: Cardiac implants may have a strong influence on the hemodynamics of the circulatory system. In this study, we present a novel personalized pre-operational transcatheter aortic valve implantation support tool. The main objective is to investigate the impact of TAVI devices on blood flow patterns that develop in the patient-specific model of ascending aorta under physiological flow conditions in vitro. Methods: The presented preoperational TAVI support tool is based on additive manufacturing, optical imaging and fluid dynamics. Optical measurements are performed in an anatomically accurate silicone aortic model. Two different cases were investigated, namely pre-operational stenotic blood flow and post-operational blood flow conditions. A ventricular assist device is used to mimic the function of the heart. It is driven by a pneumatical pump. We aimed to quantify the amount of backflow, shear stresses and kinetic energy in proximity of the valves. Results: We investigate the blood flow characteristics for both pre- and post-operational cases. It is found that the spatially averaged peak mean kinetic energy (MKE) of the pre-operational case is around seven times higher compared to the post-operational case (358J/m3 vs 49J/m3). In the diastolic phase, even for the lower velocity magnitudes, MKE is higher for the pre-operational case. Analysing the turbulent kinetic energies (TKE) shows that TKE of the pathological case is about one order of magnitude higher than the post-operational case during the peak systole (178 J/m3 vs 20 J/m3). Conclusions: We conclude that the pathological case introduces more disorganized flow features as a result of high shear stress. Furthermore the regions in the vicinity of the stenosed valve are found more risky for the destruction of the red blood cells and platelet deformation. It is presented that the developed novel personalized TAVI support tool is beneficial for pre-operational planning. Potential blood flow complications can be estimated using the support tool. KEYWORD: e-P-28 The authors do not declare any conflict of interest.

An experimental study on the effects of winglets on the tip vortex interaction in the near wake of a model wind turbine

AbstractAn experimental study of the near wake up to four rotor diameters behind a model wind turbine rotor with two different wing tip configurations is performed. A straight‐cut wing tip and a downstream‐facing winglet shape are compared on the same two‐bladed rotor operated at its design tip speed ratio. Phase‐averaged measurements of the velocity vector are synchronized with the rotor position, visualizing the downstream location of tip vortex interaction for the two blade tip configurations. The mean streamwise velocity is found not to be strongly affected by the presence of winglet tip extensions, suggesting an insignificant effect of winglets on the time‐averaged inflow conditions of a possible downstream wind turbine. An analysis of the phase‐averaged vorticity, however, reveals a significantly earlier tip vortex interaction and breakup for the wingletted rotor. In contradistinction, the tip vortices formed behind the reference configuration are assessed to be more stable and start merging into larger turbulent structures significantly further downstream. These results indicate that an optimized winglet design can not only contribute to a higher energy extraction in a rotor's tip region but also can positively affect the wake's mean kinetic energy recovery by stimulating a faster tip vortex interaction.

Моделирование аккумуляции кинетической энергии внутренних волн в областях с большим отношением горизонтального и вертикального масштабов

Tidal forcing excites internal waves in the bulk of the ocean. Deep ocean is an example of a system with continuous stratification subject to large-scale periodic forcing. Owing to specific dispersion relation of internal waves, the domains bounded by sloping boundaries may support wave patterns with wave rays converging to closed trajectories (geometric attractors) as result of iterative focusing reflections. Previously the behavior of kinetic energy in wave attractors has been investigated in two-dimensional domain with comparable depth and length. As the geometric aspect ratio of the domain increases, the dynamic pattern of energy focusing may significantly evolve both in laminar and turbulent regimes. The present paper shows that the energy density in domains with large aspect ratio can significantly increase. In numerical simulations the input forcing has been introduced at global scale by prescribing small-amplitude deformations of the upper bound of the liquid domain. The evolution of internal wave motion in such system has been computed numerically for different values of the forcing amplitude. The behavior of the large-aspect-ratio system has been compared to the well-studied case of the system with depth-to-length ratio of order unity. A number of most typical situations has been analysed in terms of behavior of integral mechanical quantities such as total dissipation, mean kinetic energy and energy fluctuations in laminar and turbulent cases.