Kinetic Energy Flux Research Articles

The Crab Pulsar: Origin of the Crab Nebula’s Radio Pairs

Abstract Previously, we constructed a model—essentially a plausibility argument—in which the Crab Pulsar produces a spatially separated ion dominated and pair plasma dominated, magnetically striped relativistic wind, with the ion wind’s kinetic energy and electromagnetic Poynting fluxes being comparable. In this paper, the polar cap ion–photon pair production of that model is replaced with pair production by ion curvature synchrotron photons. The first primary ion curvature photons, and, contrary to conventional wisdom, also the first primary electron curvature photons, do not immediately convert into pairs. The primary beam particles continue to accelerate, and the actual photons that convert into pairs, which then short out the parallel electric field and terminate the acceleration, are produced by the further accelerated, higher energy particles. Simple estimates of the ensuing pair production cascade give pair multiplicities—the number of pairs per primary beam particle—of M ± ≈ 6–8 × 104, comparable to standard calculations, but much less than the 3 × 106 value deduced by Rees and Gunn in order to sustain the Crab Nebula’s N ± ≈ 1051 radio-emitting pairs against adiabatic expansion energy losses. Using a simple spin-down evolution model for the pulsar’s rotation frequency, the time-integrated pair cascade production driven by the primary ion beam can produce the N ± ≈ 1051 radio pairs, whereas the primary electron beam produces about an order of magnitude fewer pairs.

Lagrangian Investigation of Wave-Driven Turbulence in the Ocean Surface Boundary Layer

AbstractTurbulent processes in the ocean surface boundary layer (OSBL) play a key role in weather and climate systems. This study explores a Lagrangian analysis of wave-driven OSBL turbulence, based on a large-eddy simulation (LES) model coupled to a Lagrangian stochastic model (LSM). Langmuir turbulence (LT) is captured by Craik–Leibovich wave forcing that generates LT through the Craik–Leibovich type 2 (CL2) mechanism. Breaking wave (BW) effects are modeled by a surface turbulent kinetic energy flux that is constrained by wind energy input to surface waves. Unresolved LES subgrid-scale (SGS) motions are simulated with the LSM to be energetically consistent with the SGS model of the LES. With LT, Lagrangian autocorrelations of velocities reveal three distinct turbulent time scales: an integral, a dispersive mixing, and a coherent structure time. Coherent structures due to LT result in relatively narrow peaks of Lagrangian frequency velocity spectra. With and without waves, the high-frequency spectral tail is consistent with expectations for the inertial subrange, but BWs substantially increase spectral levels at high frequencies. Consistently, over short times, particle-pair dispersion results agree with the Richardson–Obukhov law, and near-surface dispersion is significantly enhanced because of BWs. Over longer times, our dispersion results are consistent with Taylor dispersion. In this case, turbulent diffusivities are substantially larger with LT in the crosswind direction, but reduced in the along-wind direction because of enhanced turbulent transport by LT that reduces mean Eulerian shear. Our results indicate that the Lagrangian analysis framework is effective and physically intuitive to characterize OSBL turbulence.

MHD simulations of the formation and propagation of protostellar jets to observational length-scales

We present 2.5-D global, ideal MHD simulations of magnetically and rotationally driven protostellar jets from Keplerian accretion discs, wherein only the initial magnetic field strength at the inner radius of the disc, $B_{\rm i}$, is varied. Using the AMR-MHD code AZEUS, we self-consistently follow the jet evolution into the observational regime ($>10^3\,\mathrm{AU}$) with a spatial dynamic range of $\sim6.5\times10^5$. The simulations reveal a three-component outflow: 1) A hot, dense, super-fast and highly magnetised 'jet core'; 2) a cold, rarefied, trans-fast and highly magnetised 'sheath' surrounding the jet core and extending to a tangential discontinuity; and 3) a warm, dense, trans-slow and weakly magnetised shocked ambient medium entrained by the advancing bow shock. The simulations reveal power-law relationships between $B_{\rm i}$ and the jet advance speed, $v_{\rm jet}$, the average jet rotation speed, $\langle v_\varphi\rangle$, as well as fluxes of mass, momentum, and kinetic energy. Quantities that do not depend on $B_{\rm i}$ include the plasma-$\beta$ of the transported material which, in all cases, seems to asymptote to order unity. Jets are launched by a combination of the 'magnetic tower' and 'bead-on-a-wire' mechanisms, with the former accounting for most of the jet acceleration---even for strong fields---and continuing well beyond the fast magnetosonic point. At no time does the leading bow shock leave the domain and, as such, these simulations generate large-scale jets that reproduce many of the observed properties of protostellar jets including their characteristic speeds and transported fluxes.

Physics of “Cold” Disk Accretion onto Black Holes Driven by Magnetized Winds

Disk accretion onto black holes is accompanied by collimated outflows (jets). In active galactic nuclei (AGN), the kinetic energy flux of the jet (jet power or kinetic luminosity) may exceed the bolometric luminosity of the disk by a few orders of magnitude. This may be explained in the framework of the so called “cold” disk accretion. In this regime of accretion, the disk is radiatively inefficient because practically all the energy released at the accretion is carried out by the magnetized wind. This wind also provides efficient loss of the angular momentum by the matter in the disk. In this review, the physics of the accretion driven by the wind is considered from first principles. It is shown that the magnetized wind can efficiently carry out angular momentum and energy of the matter of the disk. The conditions when this process dominates conventional loss of the angular momentum due to turbulent viscosity are discussed. The “cold” accretion occurs when the viscous stresses in the disk can be neglected in comparison with impact of the wind on the accretion. Two problems crucial for survival of the model of “cold” accretion are considered. The first one is existence of the magnetohydrodynamical solutions for disk accretion purely due to the angular momentum loss by the wind. Another problem is the ability of the model to reproduce observations which demonstrate existence of the sources with kinetic power of jets 2–3 orders of magnitude exceeding the bolometric luminosity of disks. The solutions of the problem in similar prescriptions and numerical solutions without such an assumption are discussed. Calculations of the “unavoidable” radiation from the “cold” disk and the ratio of the jet power of the SMBH to the bolometric luminosity of the accretion disk around a super massive black hole are given in the framework of the Shakura and Sunyaev paradigm of an optically thick α -disk. The exploration of the Fundamental Plane of Black Holes allows us to obtain semi empirical equations that determine the bolometric luminosity and the ratio of the luminosities as functions of the black hole mass and accretion rate.

Ratio of the jet power to the bolometric luminosity of the disk during accretion onto a black hole

Disk accretion onto black holes is accompanied by collimated outflows (jets). In active galactic nuclei (AGN), the kinetic energy flux of the jet (jet power or kinetic luminosity) may exceed the bolometric luminosity of the disk by a few orders of magnitude. This may be explained in the framework of the so-called “cold” disk accretion when the only source of the AGN energy is the energy released by accretion. The radiation from the disk is suppressed because the disk wind carries out almost all the angular momentum and the gravitational energy of the accreting material. In this paper, we calculate the “unavoidable” radiation from the “cold” disk and the ratio of the kinetic energy power of the outflow to the bolometric luminosity of the accretion disk around a super massive black hole in the framework of the Shakura and Sunyaev paradigm of an optically thick [Formula: see text]-disk. The exploration of the Fundamental Plane of Black Holes allows us to obtain equations that define the bolometric luminosity and the ratio of the luminosities as functions of the black hole mass and accretion rate. The application of our equations in the case of the M87 jet demonstrates good agreement with observations. In the case of Sgr A*, these equations allow us to predict the kinetic energy flux from the disk around the Galactic supermassive black hole.

The Effect of Helicity on Kinetic Energy Cascade in Compressible Helical Turbulence

Helicity plays an important role in the nonlinear dynamic process of compressible helical turbulence. We carry out direct numerical simulations (DNS) of compressible helical turbulence with different mean helicity at the grid resolution of 512(3) and try to explore the physical mechanism of kinetic energy cascade under the effect of helicity. The filtering method of coarse-graining is employed for scale decomposition to get kinetic energy flux. We get some novel conclusions in contrast to pre-existing knowledge in incompressible helical turbulence. Firstly, helicity also hinders the process of compressible kinetic energy cascade and reduces viscous dissipation. Secondly, helicity weakens some exclusive features, such as coupling between compressible and solenoidal mode of fluctuating velocity, energy transformation between kinetic energy and internal energy, and shocklets which appear only in compressible turbulence and serves as the role of constraint.

The Giants Arcs as Modeled by the Superbubbles

The giant arcs in the clusters of galaxies are modeled in the framework of the superbubbles. The density of the intracluster medium is assumed to follow a hyperbolic behavior. The analytical law of motion is function of the elapsed time and the polar angle. As a consequence the flux of kinetic energy in the expanding thin layer decreases with increasing polar angle making the giant arc invisible to the astronomical observations. In order to calibrate the arcsec-parsec conversion three cosmologies are analyzed.

Interstellar Medium Parameters in Front of the External Bow Shock

We know that it is the front of the Earth’s bow shock where the solar wind kinetic energy flux is transformed into the other kinds the most intensively. In our previous studies, we obtained important relationships that enable calculating the key parameters at transition through the Earth’s bow shock front. One of the most important sources of information on physical processes at the heliosphere boundary are the Voyager 1 and 2 spacecrafts. Since both the solar wind and interstellar medium are supersonic streams, two shocks are formed when flowing around the heliopause. The internal shock, in which the solar wind decelerates to subsonic velocity, is called the heliospheric shock. In the external bow shock, the interstellar gas supersonic flux is decelerated. The aim of this paper is to generalize the previously obtained equations to the processes in the external bow shock region. If Voyager-1 was equipped with a greater set of measuring instruments, we could have already provided estimations of the interstellar medium key parameters, and described in physical terms what this medium is, using relationships and equations from our studies.

Energy-Based Water Droplet Impact Erosion Studies of Laser-Treated Austenitic and Martensitic Steels and their Applications

Abstract High-power diode laser (HPDL) surface treatments of high-manganese austenitic and high-chromium martensitic steel round specimens have been carried out, and their resistance to water droplet impact erosion (WDIE) in air was evaluated as per ASTM G73-10, Standard Test Method for Liquid Impingement Erosion Using Rotating Apparatus. This is because the water droplets always travel along with a fluid medium, either steam or air, and these are influenced by inertial, Coriolis, and centrifugal forces, which are missing in a vacuum. Because of these forces, the water droplets elongate and may break before hitting a target, resulting in WDIE damages entirely different from those in a vacuum. The WDIE damages on the test specimens were observed on the leading edge towards the suction side, where the boundary layer is attached, and the pressure gradients are high. These are similar to those occurring on the blades of an axial flow compressor of a gas turbine, a low-pressure steam turbine, and a helicopter rotor, because their leading edges are round. The WDIE testing is based on water droplet kinetic energy (KEd) and kinetic energy flux (KEfd). It has been proved experimentally that the product of KEd and KEfd can predict WDIE damages in a material, and this product can be used to compare the WDIE test results of different materials received from different laboratories. It is observed from the test results that the resistance to WDIE of HPDL-treated high-manganese austenitic steel (Hadfield’s steel) has reduced drastically, whereas that of high-chromium martensitic stainless steel has improved manifold. Fine microstructure and increased martensitic contents in high-chromium martensitic stainless steel after HPDL treatment are the main reasons for its improved performance, whereas the coarse microstructure having microcracks in HPDL-treated Hadfield’s steel is responsible for poor performance.

Estimating the effect of rainfall on the surface temperature of a tropical lake

Abstract. We make use of a unique high-quality, long-term observational dataset on a tropical lake to assess the effect of rainfall on lake surface temperature. The lake in question is Lake Kivu, one of the African Great Lakes, and was selected for its remarkably uniform climate and availability of multi-year over-lake meteorological observations. Rain may have a cooling effect on the lake surface by lowering the near-surface air temperature, by the direct rain heat flux into the lake, by mixing the lake surface layer through the flux of kinetic energy and by convective mixing of the lake surface layer. The potential importance of the rainfall effect is discussed in terms of both heat flux and kinetic energy flux. To estimate the rainfall effect on the mean diurnal cycle of lake surface temperature, the data are binned into categories of daily rainfall amount. They are further filtered based on comparable values of daily mean net radiation, which reduces the influence of radiative-flux differences. Our results indicate that days with heavy rainfall may experience a reduction in lake surface temperature of approximately 0.3 K by the end of the day compared to days with light to moderate rainfall. Overall this study highlights a new potential control on lake surface temperature and suggests that further efforts are needed to quantify this effect in other regions and to include this process in land surface models used for atmospheric prediction.

A STATISTICAL ANALYSIS BETWEEN CMES AND FLARES OVER THE SOLAR CYCLE 24

The correlations between the parameters of Coronal Mass Ejections (CMEs) and Solar Flares (SFs) during the solar cycle 24 are investigated. To do this, we first collect the CMEs and SFs sample over the period from December 1, 2008 to April 30, 2017. The CMEs data were obtained from the Solar and Heliospheric Observatory/ Large Angle Spectrometric Coronagraph (SOHO / LASCO) database while the soft X-ray flares data sets are taken from Hinode/XRT mission. Then, we compile a sample of 519 CMEs associated flares by applying temporal and spatial conditions. We statistically analyze our sample of CMEs associated flares and divide them into two types: after-CMEs and before-CMEs based on their start time. The CMEs and flares properties show that there were significant features in all physical properties such as (kinetic energy, speed and acceleration) between two flare-associated CME types. We investigated the relation between the CMEs kinetic energy and flare flux. The correlation coefficient for this relation is R= 0.40, which is considered as weak relation.

Numerical Analysis of Nonlocal Convection—Comparison with Three-dimensional Numerical Simulations of Efficient Turbulent Convection

We compare 1D nonlocal turbulent convection models with 3D hydrodynamic numerical simulations. We study the validity of closure models and turbulent coefficients by varying the Prandtl number, the P$\acute{e}$clet number, and the depth of the convection zone. Four closure models of the fourth-order moments are evaluated with the 3D simulation data. The performance of the closure models varies among different cases and different fourth-order moments. We solve the dynamic equations of moments together with equations of the thermal structure. Unfortunately, we cannot obtain steady-state solutions when these closure models of fourth-order moments are adopted. The numerical solutions of the down-gradient approximations of the third-order moments, on the other hand, are robust. We calibrate the coefficients of the 1D down-gradient model from the 3D simulation data. The calibrated coefficients are more robust in the cases of deep convection zones. Finally we have compared the 1D steady-state solutions with the 3D simulation results. The 1D model has captured many features appearing in the 3D simulations : (1) $\nabla-\nabla_{a}$ has a U-shape with a minimum value at the lower part of the convection zone. (2) There exists a bump for $\nabla-\nabla_{a}$ near the top of the convection zone when the P$\acute{e}$clet number is large. (3) The temperature gradient can be sub-adiabatic due to the nonlocal effect. Apart from these similarities, the prediction on the kinetic energy flux, however, is unsatisfactory.

Performance of second-moment differential stress and flux models for natural convection in an enclosure

In this paper the relative performance of two different differential stress and flux models for computing natural convection in an enclosure is examined. One model is the low-Reynolds number differential stress and flux model and the other model is a recently developed elliptic blending based differential stress and flux model. The primary emphasis of the study is placed on investigating the accuracy of the both models for the turbulent natural convection in an enclosure. Both models are used to predict turbulent natural convections in a square cavity with hot and cold side walls and conducting top and bottom walls (Ra = 1.58 × 109). The relative performance between both models is examined through comparing their solutions with the experimental data. It is shown that both models predict the vertical mean velocity component and mean temperature well. It is also shown that the low-Reynolds number differential stress and flux model slightly under-predicts the turbulent kinetic energy and vertical turbulent heat flux. It is also noted that the implementation of the elliptic blending second moment model is easier since this model does not contain any wall-related parameters and damping functions.

A method for reducing mean flow in oscillating-grid turbulence

Oscillating-grid turbulence (OGT) is an experimental tool that has been widely used to study the role of turbulent fluctuations under conditions of small mean flow. We report experiments to investigate the structure of the turbulent flow produced by an oscillating grid, using velocity measurements obtained through the application of two-dimensional particle image velocimetry in the vertical plane through the centre of the grid. Ensemble averages of the fluid velocity measurements at specific stages of the grid’s oscillation indicate that mean flow is induced in OGT by the merging of grid-induced jets close to the tank sidewalls. The installation of an open-ended ‘inner box’ (with its top edge positioned just below the bottom of the grid’s oscillation) is shown to inhibit the merging of the jets, thereby resulting in a reduction in the magnitude of the mean flow within the interior of the inner box region. Measurements of the time-averaged root-mean-square turbulent velocity components and the time-averaged turbulent kinetic energy flux indicate that the installation of the inner box results in turbulence that is in good agreement with the well-established models of OGT across the central 50% of the inner box’s width, but that distinct anisotropic regions exist adjacent to the vertical sidewalls. We anticipate that this simple amendment to reduce the mean flow present in OGT can be readily used in future work that utilises OGT to isolate the effects of turbulent fluctuations from those of the mean flow.Graphical abstract

Planar optode observation method for the effect of raindrop on dissolved oxygen and pH diffusion of air–water interface

The air–water interface is an important boundary where material exchanges, it has important influence on ecosystem and biogeochemical cycle. The rain can change the balance of interface, improve the exchange rate of gas flux, and make the distribution of dissolved oxygen and pH around the interface change in horizontal and vertical direction. Based on planar sensing film with highly spatial and temporal resolution which can provide the characteristics of two-dimensional distribution information, we carry out the simulation experiment of raindrops about oxygen and pH distribution in air–water interface using double parameters planar optode. The experimental data are analyzed from the gas transfer velocity, the kinetic energy flux and the sea-air flux of oxygen. The results show that rainfall process plays an important role in adjusting dissolved oxygen and pH of the surface water, the raindrop can break the balance of micro surface of water–gas interface mechanism, increase the gas transfer velocity and promote the dissolution of oxygen in the atmosphere in water to make a average increase of about 2.3 mg/L in vertical direction 23 mm. The impact of rainfall on pH of the water surface within 12 mm is relatively obvious, the pH value decreased by an average of 0.2–0.4 units, indicating that the raindrop promoted the migration of the atmosphere in the air–water interface, and the dissolved CO2 caused the surface water acidification. This study provides a novel technical method for understanding the influence of raindrops on the dissolved oxygen concentration and pH of the surface water in low wind-impacting area and static-water area. This study provides a novel technical method for understanding the influence of raindrops on the dissolved oxygen concentration and pH of the surface water in low wind impacting area and static water area.

Large-eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity

In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add $\nu_\mathrm{ren} \propto \Pi_u^{1/3} (\pi/\Delta)^{-1/3}$ to the kinematic viscosity; here $\Pi_u$ is the turbulent kinetic energy flux, and $\Delta$ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a $128^3$ grid and compare the results with direct numerical simulation (DNS) on a $512^3$ grid. There is a good agreement between the LES and DNS results on the evolution of kinetic energy and entropy, spectra and fluxes of velocity and temperature fields, and the isosurfaces of temperature. We also show the capability of our LES to simulate thermal convection at very high Rayleigh numbers and exhibit some results for $\mathrm{Ra=10^{18}}$.

Mass, momentum, and energy transfer in supersonic aerosol deposition processes

Aerosol deposition (AD) can lead to the formation of dense coatings via deposition of particles from a gas flow; in AD the aerosol is passed through a converging-diverging nozzle, facilitating inertial particle impaction on a desired substrate at supersonic particle velocities. Unique from thermal spray methods, AD can be applied near room temperature and unique from cold spray, in AD the aerosol is typically at atmospheric pressure upstream of the nozzle. Though AD has been successfully demonstrated previously, a number of aspects related to particle motion in AD systems remain poorly understood. In this work, we simulated compressible flow field profiles and particle trajectories for typical AD working conditions for a slit type converging-diverging nozzle with a planar substrate. In examining the fluid flow profile, we show that the velocity and pressure profiles, as well as the shock structure are sensitive to the upstream and downstream operating pressures of the nozzle. These ultimately affect particle impaction speed. Importantly, in AD, the particle drag regime is dynamic; both particle Knudsen numbers and Mach numbers can vary by orders of magnitude. To aid particle trajectory simulations, we trained a neural network to predict the drag force on the particles based on existing experimental data, theoretical limits, and new direct simulation Monte Carlo (DMSC) results. The neural network based drag law, which depends upon both Mach and Knudsen numbers, shows better agreement with the DSMC simulation data than pre-existing correlations. With it, particle trajectory simulation results reveal that for a given particle density, there exists an optimal particle diameter to maximize particle impaction speed. We also find that in AD particles undergo size dependent inertial focusing, i.e. there is a particular particle diameter where the particle deposition linewidth is minimized. Particles smaller than this diameter are underfocused, and particles larger than this are overfocused, and hence have larger deposition linewidths in both cases. Using trajectory simulations, we additionally developed a framework that can be used to evaluate the position-dependent mass, momentum and kinetic energy fluxes to the deposition substrate for any aerosol size distribution function upstream of the nozzle. It is shown for typical aerosol concentrations achievable in the laboratory, the kinetic energy flux can approach a magnitude normally observed in convective heat transfer with phase change, hence translational kinetic energy to thermal energy transfer in AD is likely a key contributor to the formation of dense coatings.

Large eddy simulations of the effect of vertical staggering in large wind farms

AbstractIn order to study the effect of vertical staggering in large wind farms, large eddy simulations (LES) of large wind farms with a regular turbine layout aligned with the given wind direction were conducted. In the simulations, we varied the hub heights of consecutive downstream rows to create vertically staggered wind farms. We analysed the effect of streamwise and spanwise turbine spacing, the wind farm layout, the turbine rotor diameter, and hub height difference between consecutive downstream turbine rows on the average power output. We find that vertical staggering significantly increases the power production in the entrance region of large wind farms and is more effective when the streamwise turbine spacing and turbine diameter are smaller. Surprisingly, vertical staggering does not significantly improve the power production in the fully developed regime of the wind farm. The reason is that the downward vertical kinetic energy flux, which brings high velocity fluid from above the wind farm towards the hub height plane, does not increase due to vertical staggering. Thus, the shorter wind turbines are effectively sheltered from the atmospheric flow above the wind farm that supplies the energy, which limits the benefit of vertical staggering. In some cases, a vertically staggered wind farm even produced less power than the corresponding non vertically staggered reference wind farm. In such cases, the production of shorter turbines is significantly negatively impacted while the production of the taller turbine is only increased marginally.

Higher-order moments with turbulent length-scales and anisotropy associated with flow over dune shapes in tidal environment

The purpose of this research paper is to investigate the third-order moments of velocity fluctuations, turbulent kinetic energy (TKE) fluxes, turbulence dissipation rate, turbulent length scales, and Reynolds stress anisotropy in the wake regions over two artificial upstream-facing bed forms. For the structure having a smaller flow-facing slope (slanting forward-facing structure, named as SFFS), the maximum flow intermittency is 0.6% with a maximum flow reversal frequency of 0.24 Hz, whereas for the greater flow-facing sloped structure (vertical forward-facing structure, named as VFFS), up to 70% flow intermittency is noticed just downstream of the corresponding crest location with a maximum of 28 Hz flow reversal frequency. A strong negative M30 (stream-wise flux of stream-wise normal stress) and a strong positive M03 (vertical flux of vertical normal stress), implying the occurrence of ejection events, take place above the flow separation region along the generated shear layer. However, near the lee-surface, positive M30 and negative M03 imply the presence of sweep events. For both the cases, maximum of normalized TKE (κ) is generated in the vicinity of crest location, which spread over the retarding flow region near-bed of the trough and wake-flow region downstream of the crest. The production of turbulence is mainly concentrated at the interface of intense ejection and sweep dominated zones over the trough region for the VFFS case, and for the other bed form, i.e., SFFS case, maximum turbulence production is concentrated at the near-bed crest location. Near the bed, the length-scale of eddies in the inertial sub-range decreases substantially compared to that in the upstream. It is seen that in the region of negative kinetic energy production, local maximum anisotropy is found, especially for b11,22,33S and b11,22,33V components. Interestingly, at the corresponding crest points for SFFS and VFFS, maximum affinity toward the one-component isotropy is measured almost throughout the vertical height. However, a clear increasing trend in the affinity to a better isotropy; i.e., the three-dimensional isotropy is identified as the vertical height increases up to z ≈ 3 cm above the bed when a fair downstream location for the VFFS case is considered. A special look toward the investigation of possible connection of the flow region with negative TKE production with the stream anisotropy shows that a substantial increase in the degree of anisotropy (Ad) in the anisotropy invariant maps of the negative TKE production takes place for both the cases, when compared to that for the positive TKE production region.

Energy balance analysis of model-scale vessel with open and ducted propeller configuration

This paper focuses on performance analysis of a model scale vessel equipped with an open versus a ducted propeller in self-propulsion using a control volume analysis of energy, applied on Computational Fluid Dynamics (CFD) results. An energy balance analysis decompose the delivered power for each system into internal and turbulent kinetic energy fluxes, i.e. viscous losses, transverse kinetic energy losses, and pressure work and axial kinetic energy fluxes. Such a decomposition can facilitate understanding of system performance and pinpoint enhancement possibilities. For this specific case it is shown that the much higher required power for the ducted propeller configuration to the largest extent is due to higher viscous losses, caused by mainly propeller duct and different rudder configuration. The energy balance analysis is a post-processing tool with the only additional requirement of solving the energy equation, which can be employed with any CFD-code based on commonly available variables.