On the forced convective flow inside thermal collectors enhanced by porous media: from macro to micro-channels

Purpose Aiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered. Design/methodology/approach The general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid. Findings The analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers. Originality/value A general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

Global dissipative solutions of the defocusing isothermal Euler–Langevin–Korteweg equations

We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler–Langevin–Korteweg system, which corresponds to the Euler–Korteweg system of compressible quantum fluids with an isothermal pressure law and a linear drag term with respect to the velocity. In particular, the isothermal feature prevents the energy and the BD-entropy from being positive. Adapting standard approximation arguments we first show the existence of global weak solutions to the defocusing isothermal Navier–Stokes–Langevin–Korteweg system. Introducing a relative entropy function satisfying a Gronwall-type inequality we then perform the inviscid limit to obtain the existence of dissipative solutions of the Euler–Langevin–Korteweg system.

ON THE CHARACTER OF AN ARTIFICIAL SATELLITE DRAG UNDER VARIOUS STATES OF SOLAR AND GEOMAGNETIC ACTIVITY

Purpose: The artificial satellites drag in the atmosphere remains an urgent problem to date. In this work, the artificial satellites data are used in order to study the atmosphere state under various manifestations of solar and geomagnetic activity. The selected satelites were moving uncontrollable being good indicators of the upper atmosphere state. The B-star (drag term) drag coefficient is used in this work. This term is used in the SGP and SDP models to take into account the resistance of the atmosphere to the satelite orbital motion. The data of the drag of two artificial satellites, one moving in elliptical and the other in circular orbits at midlatitudes (orbital plane angles of 58°-60°) were considered. These data include the end of the 23rd solar activity cycle, as well as the growth, the maximum and the decay phases of the 24th solar cycle (years 2005–2017). Seven periods of anomalous drag of the satellites were analyzed. They are: 4 monthly periods (two in 2005 and two in 2011) and 3 yearly periods (within 19.07.2014 to 22.08.2015), five-year long (2005–2010) and six-year long (2011–2017) periods. Design/methodology/approach: The periodogram analysis was made. This allowed to reveal the periodic processes in changes in the state of the atmosphere of different duration. The correlation coefficients of the B-star drag term with the indices of solar and geomagnetic activity were calculated. The analysis of extreme drag of the satellites in the periods of the increased solar and geomagnetic activity (intervals of observation lasting a month) was made. Findings: Using the solar and geomagnetic data we found that some month-long part of the anomalous drag periods were followed by flares on the Sun and the arrival of the coronal mass ejections into the near-Earth space. At time intervals of yearlong observations the highest values (0.5-0.7) were obtained for the coefficients of the B-star parameter correlation with the solar activity indices – solar radiation at the wavelength of 10.7 cm, F10.7, and Lyman alpha radiation, Lα. At monthly time intervals, the largest values of the correlation coefficients were obtained for the B-stars with the electron fluxes with energies above 0.6 and 2 MeV, E, (0.3-0.5), the Lyman alpha radiation, Lα, (0.58–0.73 for a сircular orbit satellite), and the solar constant, TSI, (0.3–0.6), as well as the geomagnetic storms intensity index, Dst , (0.66–0.69). Periodogram calculations show the presence of a whole spectrum of periods in the deceleration of a circular orbit satellite and a dedicated period for an elliptical orbit satellite. Conclusions: The B-star drag term dependences on the indices of solar and geomagnetic activity during some periods of their intensification for the 23–24 cycles of solar activity are considered. The periodogram analysis made together with the analysis of the conditions and parameters of space weather allows to see the general and more detailed picture of the solar and geomagnetic activity influence on the change in the motion of the satellite in the atmosphere. The B-star drag term helps to consider only the atmosphere influence on the artificial satellite movement in the near-Earth space. Key words: artificial satellite, atmosphere, artificial satellite drag, solar activity, geomagnetic activity, space weather

Dynamic Simulation of a Mooring Catenary Based on the Lumped-Mass Approach: OpenModelica and Python Implementations

In this paper, the theoretical background behind the formulation and solution of a discretized lumped-mass mathematical-model of the physically continuous and inelastic mooring catenary is re-visited. The drag term of the Morison equation is used to determine the fluid loads, and the sea-bed interaction is prescribed as vertical spring loads on the interacting nodes. Numerical solution to the equation of motion is sought through a finite-difference method. The initial conditions are determined using the catenary theory, the instantaneous boundary conditions are prescribed, and the in-elasticity of the mooring segments is specified as the constraint equation. The solution procedure is then implemented as both Python and Modelica code. Results of the Modelica simulation are then compared with those generated using the popular ocean-engineering software, Orcaflex. Finally, conclusions are drawn based on the analysis of simulation results. The codes and results are made available for download.

Density-induced CO2 dissolution - approaches to test a new hypothesis on a process relevant for epigenetic karstification

<p><strong>Density-induced CO<sub>2</sub> dissolution - approaches to test a new hypothesis on a process relevant for epigenetic karstification   </strong></p><p>A process which has not yet been discussed as relevant for epigenetic karstification in phreatic zones has been hypothesized in a publication by Scherzer et al. (2017). It refers to an enhanced CO<sub>2</sub> transport into the phreatic zone by density-induced convective dissolution. The phenomenon is well-known also in CO<sub>2</sub> geologic sequestration and is denoted there typically as solubility trapping. Scherzer et al. (2017) denote this process in caves as nerochytic speleogenesis (from nerochytic = sink in Greek), assuming it has relevance for epigenetic karstification under certain circumstances. This could be relevant in particular in caves where CO<sub>2</sub> concentrations are highly elevated and show strong seasonal fluctuations.</p><p>Thomas et al. (2015) have introduced a method to visualize fingering patterns of CO<sub>2</sub> convective dissolution in water with a pH-sensitive color indicator. We have used this approach to produce a set of experimental data in a laboratory flume of dimensions 60 cm x 40 cm x 1 cm. Our aim is to validate a numerical model that we implemented in the simulator DuMu<sup>x </sup>(www.dumux.org), which can later on be used for future studies as the basis for investigating the relevance of nerochytic speleogenesis for karstification.</p><p>We have applied atmospheres with varying concentrations of carbon dioxid as boundary conditions at the top of the flume and observed the onset times and fingering patterns, in particular we focused on the velocity of the fingers.</p><p>The Navier-Stokes model with water density dependent on CO<sub>2</sub> concentration is run in 2D, 3D and pseudo 3D, the latter referring to a 2D approach with a drag term in the momentum balance to account for wall friction at the front and the back plate. Without calibration or fitting of parameters, the results of the comparison between experiment and simulation show reasonable agreement both with respect to the onset of convective fingering and the number of fingers occurring.</p><p>References:</p><p>H. Scherzer, H. Class, K. Weishaupt, T. Sauerborn, O. Trötschler: Nerochytische Speläogenese: Konvektiver Vertikaltransport von gelöstem CO<sub>2</sub> - ein Antrieb für Verkarstung in der phreatischen Zone im Bedeckten Karst, Laichinger Höhlenfreund 52:29-35, ISSN 0344 6832, 2017.<br> </p><p>C. Thomas, L. Lemaigre, A. Zalts, A. D'Onofrio, A. De Wit: Experimental study of CO<sub>2</sub> convective dissolution: the effect of color indicators, International Journal of Greenhouse Gas Control 42:525-533,2015.</p>

Dynamics of heavy and buoyant underwater pendulums

The humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world situations, the dynamics of pendulums is not quite so simple, particularly with additional interactions between the pendulum and a surrounding fluid. Here we extend the realm of pendulum studies to include large amplitude oscillations of heavy and buoyant pendulums in a fluid. We performed experiments with massive and hollow cylindrical pendulums in water, and constructed a simple model that takes the buoyancy, added mass, fluid (nonlinear) drag and bearing friction into account. To first order, the model predicts the oscillation frequencies, peak decelerations and damping rate well. An interesting effect of the nonlinear drag captured well by the model is that, for heavy pendulums, the damping time shows a non-monotonic dependence on pendulum mass, reaching a minimum when the pendulum mass density is nearly twice that of the fluid. Small deviations from the model’s predictions are seen, particularly in the second and subsequent maxima of oscillations. Using time-resolved particle image velocimetry (TR-PIV), we reveal that these deviations likely arise due to the disturbed flow created by the pendulum at earlier times. The mean wake velocity obtained from PIV is used to model an extra drag term due to incoming wake flow. The revised model significantly improves the predictions for the second and subsequent oscillations.

Noetherian symmetries of noncentral forces with drag term

We consider the Noetherian symmetries of second-order ODEs subjected to forces with nonzero curl. Both position and velocity dependent forces are considered. In the former case, the first integrals are shown to follow from the symmetries of the celebrated Emden–Fowler equation.

Stochastic Linearization and its Application in Motion Analysis of Cylindrical Floating Structure With Bilge Boxes

To account for the viscous effects of damping devices, for instance, bilge keels or bilge boxes, on the motions of ships and offshore structures, Morison’s equation is often adopted as an empirical but practical approach in the design process. In order to combine the standard engineering panel method with the drag term in Morison’s equation, and remain in the frequency domain, the drag term has to be linearized based on, for instance, stochastic linearization. In this paper, the stochastic linearization scheme is implemented in an in-house code and verified through the comparison with the DNV GL software WADAM. The model test results of a large cylindrical FPSO with bilge box are used to calibrate the drag coefficients in the Morison’s equation. When the linearized drag forces are included, heave motion RAOs correspond better to the model test results. However, the predicted natural periods of heave motions are seen to be smaller than those obtained from model tests. It is suspected that the viscous flow separation around the bilge box increases the added mass of the unit beyond what is predicted by potential flow alone. Discussions are made on the effect of viscous added mass on the heave natural period. It is quite common to only include the damping effects in the motion analysis for large offshore structures and ignore the contribution of the viscous effects on the excitation force. For the considered cylindrical FPSO, this paper demonstrates that the viscous excitation force can be important in survival conditions.

Structural Analysis of Aquaculture Nets: Comparison and Validation of Different Numerical Modeling Approaches

The performance of three different numerical methods were compared and evaluated against data from physical model tests of nets subjected to a static load due to water currents. A parameter study of a simplified net cage model subjected to a steady flow was performed by all methods, varying the net solidity and the flow velocity. The three numerical methods applied models based on springs, trusses, or triangular finite elements. Hydrodynamic load calculations were based on the drag term in Morison's equation and the cross-flow principle. Different approaches to account for wake effects were applied. In general, the presented numerical methods should be able to calculate loads and deformations within acceptable tolerance limits for low to intermediate current flow velocities and net solidities, while numerical analyses of high solidity nets subjected to high current velocities tend to overpredict the drag loads acting on the structure. To accurately estimate hydrodynamic loads and structural response of net structures with high projected solidity, new knowledge and methods are needed.