Flux Injection Research Articles

Alkaline flux dissociation in blast furnace tuyere bird’s nest: Part 1: CaO dissolution kinetics and slag physicochemical evolution in the coal-coke-slag

In the pursuit of optimizing smelting efficiency and minimizing carbon emissions in blast furnace operations, the strategic introduction of the tuyere alkaline flux injection, particularly in managing the viscosity of the coal-coke-slag in the bird’s nest region, is investigated. This study focused on exploring the dynamics of CaO dissolution within the slag of the coal-coke-slag in the bird’s nest area of a 2200 m3 blast furnace in China, particularly under conditions of instability. Quantitative analysis revealed that at 1550 °C, the CaO maximal dissolution capacity reached 62.05 wt%, with an average rate constant of dissolution observed at 4.65 × 10−4 s−1. The dissolution mechanism was characterized by interfacial dissociation, mass transfer diffusion, and the attainment of a dynamic equilibrium, predominantly influenced by the Ca2+ concentration gradient within the slag. This process facilitates the depolymerization of the slag’s network structure, heavily influenced by the aluminum oxide tetrahedron, effectively reducing slag viscosity. Further, the study quantified the optimal CaO injection content through the tuyere, suggesting a range of 4.00–5.32 kg/tHM, contingent on the use of high-quality raw fuel and advanced high wind temperature technology. This work contributes valuable theoretical insights towards enhancing the efficiency and sustainability of smelting operations, applicable to both conventional and high pellet blast furnaces, marking a significant step forward in the development of low-carbon metallurgical processes.

A mixed nonlocal finite element model for thermo‐poro‐elasto‐plastic simulation of porous media with multiphase fluid flow

SummaryA new mixed nonlocal finite element framework is developed for nonlinear thermo‐poro‐elasto‐plastic simulation of porous media with multiphase pore fluid flow and thermal coupling. The solid‐fluid interaction is accounted for using the mixture theory of Biot based on the volume fractions concept. Different sources of nolinearities arising from the multiphase fluid flow effects, advective‐diffusive heat transfer, inelastic deformation, fluid flux injection induced mechanical tractions, solid skeleton deformation permeability dependence, and temperature dependent viscosity are included in developing a robust numerical solver for the targeted coupled multiphysics problem. To address the effect of microstructure in inelastic localized deformation behaviour with dilational softening, a nonlocal plasticity model is proposed based on a characteristic length scale which rectifies the non‐physical pathological mesh dependence problem encountered in conventional plasticity. The accuracy and strength of the developed model is shown with comparing the obtained numerical results of a benchmark bilateral compression test with existing published data in the literature. To show the versatility and robustness of the developed computational framework in modelling the geomechanics of real‐case engineering practices, large scale thermo‐hydro‐mechanical (THM) subsurface stimulation processes with applications in enhanced oil recovery (EOR) are effectively simulated and the targeted enhanced recovery and performances are demonstrated. The current formulation does not include phase transformation modelling capability, and therefore, the developed models may not be applicable for simulation of the engineering processes that involve phase change behaviour (e.g., steam injection).

Particle injection methods in 3D-PIC MCC simulations applied to plasma grid biasing

In negative ion sources for the ITER Neutral Beam Injection system, the co-extraction of electrons is one of the main limiting factors. The current of co-extracted electrons can be decreased by applying a positive bias voltage to the Plasma Grid (PG) with respect to its source walls. Simulations using three-dimensional Particle-in-Cell Monte Carlo Collision (3D-PIC MCC) model are a powerful tool for studying the extraction region of such ion sources. However, the inclusion of both PG and source walls in the simulation domain is difficult due to numerical constraints. This study uses the 3D-PIC MCC code ONIX to explore the effects of particle injection models on plasma characteristics, using a flux injection model to regulate particle influx for a flat transition in potential from the bulk plasma to the simulation domain. Biasing of the PG above floating potential is possible using the flux injection scheme and results in a notable reduction in co-extracted electrons, corroborating with established experimental observations.

Combustion behavior of co-injecting flux, pulverized coal, and natural gas in blast furnace and its influence on blast furnace smelting

The integration of advanced high-ratio pellet ore smelting technology with flux injection at the blast furnace tuyere offers significant carbon emission and air pollution reductions for iron and steel manufacturers. This study presents a comprehensive thermogravimetric analysis and burnout rate assessment of Russian Bituminous Coal (RB) and flux mixtures across varying mass ratios, alongside a detailed exploration of the catalytic mechanisms of three distinct fluxes on RB combustion. The findings reveal that lime, when added to the coal-flux blend, markedly enhances the overall combustion characteristic index and catalytic impact, more so than limestone or dolomite. The optimal lime admixture of 5 % resulted in a peak S value of 6.30 and a burnout rate of 70.63 %, constituting an increase of 7.64 % over the base case without flux. Lime's superior catalytic performance is attributed to its higher content of calcium-containing compounds, which amplify catalytic activity through increased Ca2+ ion exchange with carboxyl groups. Mathematical model calculations considering the combustion rate of the pulverized coal show that: after the addition of 5 % lime, there is a 133.43 t/d increase in iron production, compared to the 11,323.98 t/d without the addition of flux. When the lime addition amount is 7 %, the proportion of sintered ore in the blast furnace decreases by 6.53 %, and the coke saving is 2.8 kg/t. This research is expected to enhance the understanding of pulverized coal combustion when amalgamated with basic fluxes and serve as a theoretical foundation for optimizing industrial applications.

Influence of different particle injection methods on plasma sheath with strong production of negative ion in one-dimensional PIC simulation

Particle injection is necessary to maintain the plasma source term in particle-in-cell (PIC) simulation. There are two commonly used particle injection methods, namely, a) constant flux injection, in which a fixed number of ion-electron pairs are injected each time step, and b) pair re-injection, in which the number of ion-electron pairs injected is according to the number of positive ions removed. Different injection methods may bring big difference to the simulation results. Therefore, the appropriate particle injection method must be selected according to the object and purpose of simulation to obtain the correct result. In this paper, a 1D3V (one dimension in space and three dimensions in velocity space) PIC model is used to analyze the evolution of plasma in the formation of space charge limited (SCL) sheath and reverse sheath with the condition of surface production, and the differences of the two particle injection methods are compared. It is found that the simulation result with pair re-injection does not match experiment result.

Hierarchical Morphing Control of an Ultra-Lightweight Electro-Actuated Polymer Telescope with Thin-Film Actuators.

This paper explores advanced shape control techniques for ultra-lightweight electro-actuated polymers with composite ferroelectric thin films. It begins with an overview of PVDF-TrFE film actuators used in the development of thin-shell composites, emphasizing the need to overcome constraints related to the electrode size for successful scalability. Strain generation in thin-film actuators is investigated, including conventional electrode-based methods and non-contact electron flux excitation. Numerical studies incorporate experimentally calibrated ferroelectric parameters, modeling non-contact actuation with an equivalent circuit representation. The potential distribution generated by electron flux injection highlights its potential for reducing print-through actuation issues. Additionally, the paper outlines a vision for the future of large thin-shell reflectors by integrating the discussed methods for charging ferroelectric polymer films. A hierarchical control strategy is proposed, combining macro- and micro-scale techniques to rectify shape errors in lightweight reflectors. These strategies offer the potential to enhance precision and performance in future spaceborne observation systems, benefiting space exploration and communication technologies.

Comparison of non-reactive flow fields in conventional swirl-air combustion and swirl distributed combustion

Flow field distribution in traditional swirl flow and simulated distributed reaction swirl flow configuration was examined at 3 kHz frequency using high-speed Particle Image Velocimetry (PIV). Non-reactive flow field conditions in distributed reaction zones were fostered from the conventional swirl flow case using the designed inlet mixture preparation with CO2 dilution of the inlet airstream that corresponded to the combustion case at a heat release intensity of 5.72 MW/m3-atm. High-speed imaging of flow fields was performed at a framing rate of 3000 frames/s using a Neodymium-doped Yttrium Lithium Fluoride (Nd:YLF) laser beam at 527 nm wavelength to capture the Mie scattering images of the flow field. Mean flow velocity obtained from the post-processing of raw PIV images showed higher momentum flux injection in the swirl distributed flow zone case as compared to the normal swirl flow case. Enhanced velocity fluctuations were also observed in both the axial and radial direction for the distributed swirl flow case resulting in higher turbulence for the examined condition. The distributed swirl flow case showed a prominent corner recirculation zone along with higher flow entrainment within the recirculation zone. Enhanced interaction of average streamlines with vortices was found in the swirl distributed flow case. Increased turbulent fluctuation in the two different spatial directions was responsible for higher Reynolds stress distribution (u′v′) in the distributed flow case, indicating improved mixing behavior at lower global oxygen concentrations from the carbon dioxide (CO2) dilution, and showed different length scales of turbulent eddies. Furthermore, the spatial local Damkӧhler number values for distributed flow case (for its implication in reacting case) were found to be less than unity. The results showed a shorter flow timescale than the corresponding chemical timescales in distributed reaction zone. These results help support substantiating the difference of reaction regimes on the Borghi diagram (plot of velocity fluctuation/ laminar flame speed versus the integral length scale/ flame thickness) between the distributed reaction zone (that possesses thickened reaction zone) and conventional swirl reaction flow regimes having corrugated flamelet zone.

Numerical simulation of non-isothermal supercritical water flow in ground pipeline and wellbore: An interactive sensitivity analysis and injection parameters optimization

Supercritical water injection is promising in enhanced heavy oil recovery, in which precise prediction and regulation of bottomhole parameters are the prerequisite for improving the recovery efficiency. However, dramatically changing thermophysical properties make it difficult to calculate the hydraulic and thermal resistances of supercritical water flow in ground pipeline and wellbore. In this work, a comprehensive mathematical model was established to simulate the non-isothermal flow of supercritical water from boiler outlet to bottomhole. Modified correlations of friction coefficients and convective heat transfer coefficients respectively developed for vertical and horizontal flow of supercritical water were coupled in momentum and energy conservation equations to calculate the hydraulic and thermal resistance. The model was validated by oilfield and laboratory data with the relative deviations of pressure and temperature less than 2%. The interactive sensitivity analysis was carried out by response surface method for injection parameters optimization. The results indicated that the heat loss in ground pipeline was comparable to that in wellbore once it reached 10 times longer than wellbore and should be taken into consideration. Increasing mass flux was found to be efficient for reducing the heat loss resulted from the decline of wellbore insulation. But there existed a matching combination of injection pressure and mass flux that making bottomhole temperature the highest. For a typical injection case with a poor insulation wellbore and limited injection temperature, a combination of high mass flux and low injection pressure was recommended for achieving targeted bottomhole temperature due to its high thermal efficiency.

Physicochemical properties of cinder and alkaline modification in tuyere birdnest region of blast furnace

An important factor in increasing gas utilization and lowering carbon emissions is the removal of cinder from the tuyere birdnest region of the blast furnace. Based on a 2200 m3 blast furnace in China, the physicochemical characteristics of cinder are investigated in this paper. Alkaline flux’s chemical modification and flux injection content are examined to alter the fluidity of cinder slag. Firstly, the basicity and aluminum content of cinder slag are 0.80 and 40.33%, respectively. The melting characteristic of cinder slag is high and the liquid phase fluidity is poor. Secondly, as the content of CaO, MgO, and FeO grow while the viscosity keeps declining, the melting temperature of the cinder first decreases and then rises, rises, and decreases. Compared to Mg2+, Ca2+ and Fe2+ have higher diffusion rates and a stronger interaction modification impact. The potential of flux modification is CaO + FeO > CaO + MgO > CaO > FeO > MgO. Finally, the optimum chemical modification occurs when the basicity of cinder slag is 1.05 and the FeO content is 0.40%. During regular blast furnace operation, 1.62 kg/tHM of limestone and 5.92 kg/tHM of basic oxygen furnace (BOF) slag are injected into the tuyere.

Photospheric signatures of retraction and reconnection in realistic magnetohydrodynamic simulations

Context. Magnetic flux emergence and cancelling in the quiet Sun is a frequently observed phenomenon. The two possible physical flux-removal mechanisms involved in this cancelling process are retraction and reconnection. Aims. We seek to find distinct observational signatures characterising retraction and reconnection. Methods. We carried out three-dimensional non-grey radiative magnetohydrodynamic (MHD) simulations of convection near the solar surface and the solar photosphere using the STAGGER code, and employing different initial conditions: (1) mixed-polarity simulations with alternating horizontal stripes of opposite vertical magnetic field and separated by a zero field stripe, and (2) flux emergence simulations with continuous injection of magnetic flux from the lower boundary. These initial conditions are meant to represent two different situations in the solar photosphere, namely magnetic flux cancelling in the absence or presence of magnetic flux emergence, respectively. Results. We analyse the observational signatures of magnetic flux-removal processes for flux emergence as well as for mixed-polarity MHD simulations. In the flux emergence simulation, we are able to identify ubiquitous reconnection events anywhere from the solar surface to the upper photosphere. For a few of those reconnection events, we can identify supersonic upflow velocities in the upper photosphere as well as strong temperature enhancements. We also see strong electric currents very close to the locations where reconnection takes place, as well as supersonic horizontal velocities leading to sideways plasma compression. In the mixed-polarity simulations, we only detect observational signatures of magnetic field retraction related to large downflow velocities that appear in between regions where opposing horizontal velocities converge. These horizontal velocities are often supersonic, leading to heating due to shock dissipation. We do not see clear signatures of magnetic reconnection in these mixed-polarity simulations. Conclusions. We suggest that, in the emerging flux regions of the quiet Sun, the main flux-removal process is reconnection, while in regions without flux emergence, retraction is the dominant flux-removal process.

Effects of resistivity and viscosity on dynamic evolution and radial position change of m/n = 3/1 double tearing mode

The effects of the plasma resistivity and viscosity on the dynamic evolution of the m/n = 3/1 double tearing mode (DTM) are studied and analyzed quantitatively using the CLT (Ci-Liu-Ti, which means magnetohydrodynamics in Chinese) code. In this work, we mainly focus on the change in the radial positions and the oscillatory dynamics of the magnetic islands grown on the two rational surfaces. We conduct a systematic investigation on the effect of viscosity on the DTM dynamics, which has rarely been studied before. From the results of the study, it is observed that the time required for entering the explosive phase decreases with decreasing viscosity. In the nonlinear phase, the kinetic energy exhibits an oscillatory behavior due to the magnetic flux injection and magnetic reconnection, and the oscillation amplitude is suppressed for a large viscosity due to dissipation. The effects of the plasma resistivity and viscosity on the change in the radial positions of magnetic islands are systematically explained. The change in the radial positions of magnetic islands occurs in an abrupt growth phase before the kinetic energy reaches its maximum value. Multiple position changes take place with a relatively higher reconnection rate and magnetic flux injection at low viscosity damping. A large range of radial vortices formed as a result of the change in the positions may have a positive effect on the transport.

Reconfiguration of nondestructively readable superconductor memory by direct injection of magnetic flux to storage loop

In this study, we demonstrate a novel method for the reconfiguration of a nondestructively readable memory cell for superconductor integrated circuits. The proposed reconfiguration method involves the direct injection of flux quantum to the storage loop of the memory cell, which has been achieved using interface circuits in previous studies. By applying this method, the footprint of the superconductor memory cell can be reduced by half. We experimentally demonstrate the proof-of-concept of the investigated reconfiguration method. We expect that the memory cell reconfigured using the proposed method will be suitable for building large-scale lookup tables using superconductor circuits.

Mathematical modeling of injection of negative ion flux into the wall plasma

Mathematical modeling of injection of negative ion flux into the wall plasma

EFFERVESCENT SUSPENSION SPRAY IN A GASEOUS CROSSFLOW

A spray of suspension, forms mainly solid particles in a liquid phase from the atomization of two or multiphase flow, mainly solid particles in a liquid phase, and its transport phenomena by a gaseous crossflow have many natural and industrial applications. For example, injection of suspension jet in a high-speed flow is used in the emerging surface engineering process called suspension plasma spray. Typically, submicron ceramic oxide particles are mixed with water or ethanol to form a suspension that is injected in a plasma plume using different types of injectors. Injection parameters such as the type of injector and momentum flux influence the size, velocity, and trajectory of suspension droplets in the plasma and the microstructure of the deposited coatings. Using an effervescent atomizer, due to its capability in transporting flows with various rheological properties is promising for injection of suspension into the gaseous crossflow. In this study, an effervescent atomizer was employed to introduce a suspension radially into the flow of gas at room temperature. The spray of suspensions with different concentrations of glass particles in water was investigated in the crossflow by phase Doppler particle analyzer. The results were validated and supported by studying the spray by shadowgraph and light diffraction techniques. The results of this study provide a better understanding of the suspension spray generated by an effervescent atomizer in a crossflow configuration. It was found that the solid concentration of the suspension (up 10 wt.%) causes a slight decrease in size and brings the penetration of the suspension droplets in the gas flow.

Design Considerations for the Implementation of a High-Field-Side Transient CHI System on QUEST

Transient coaxial helicity injection (T-CHI), a method first developed on the small helicity injected torus (HIT-II) experiment and then validated on the much larger National Spherical Torus Experiment (NSTX) device, is a method to initiate an inductive-like tokamak plasma discharge without reliance on the central solenoid. A CHI discharge is initiated by driving current along magnetic flux that connects the inner and outer divertor plates on one end of the tokamak. To permit this, on both HIT-II and NSTX, toroidal ceramic insulators were used to electrically separate the inner and outer vessel components. The use of such large toroidal vacuum insulators may not be easy to implement in reactors. To address this issue, the Q-shu University experiments with steady-state spherical tokamak (ST) (QUEST) is developing a reactor-relevant CHI configuration in which one of the divertor plates is electrically insulated from the rest of the vessel. The first application of T-CHI on QUEST biased the CHI electrode to the outer vessel. While the CHI discharges could be easily generated, it was found that as the discharge filled the vessel, the separation distance between the injector magnetic flux footprints widened, a condition that is not favorable for the generation of closed flux surfaces. Biasing the electrode to the inner wall is a configuration similar to that used on NSTX and HIT-II, but initial testing in this configuration has proved to be challenging. The design described here overcomes the present limitation by locating the CHI electrode much closer to the CHI injector flux coil and using an NSTX-like gas injection manifold to enable high-field-side T-CHI startup on QUEST. The concepts described in this article should also benefit the future implementation of T-CHI systems in other tokamaks and spherical tokamaks.

A Volumetric Study of Flux Transfer Events at the Dayside Magnetopause

Localized magnetic reconnection at the dayside magnetopause leads to the production of Flux Transfer Events (FTEs). The magnetic fields within the FTEs exhibit complex helical flux-rope topologies. Leveraging the adaptive mesh refinement strategy, we perform a three-dimensional magnetohydrodynamic simulation of the magnetosphere of an Earth-like planet and study the evolution of these FTEs. For the first time, we detect and track the FTE structures in 3D and present a complete volumetric picture of FTE evolution. The temporal evolutions of thermodynamic quantities within the FTE volumes confirm that continuous reconnection is indeed the dominant cause of active FTE growth, as indicated by the deviation of the pressure–volume curves from an adiabatic profile. An investigation into the magnetic properties of the FTEs shows a rapid decrease in the perpendicular currents within the FTE volume, exhibiting the tendency of internal currents toward being field-aligned. An assessment of the validity of the linear force-free flux-rope model for such FTEs shows that the structures drift toward a constant-α state but continuous reconnection inhibits the attainment of a purely linear force-free configuration. Additionally, the fluxes enclosed by the selected FTEs are computed to range between 0.3 and 1.5 MWb. The FTE with the highest flux content constitutes ∼1% of the net dayside open flux. These flux values are further compared against the estimates provided by the linear force-free flux-rope model. For the selected FTEs, the linear force-free model underestimated the flux content by up to 40%, owing to the continuous reconnected flux injection.

A two-dimensional semi-analytical model for tracer gas injection and transport in a landfill system

Identifying the location of a leakage is the very first basic step for preventing the escape of landfill gas and leachate from defects. A two-dimensional semi-analytical model is presented for the transport of tracer gas injection in landfills. Tracer gas transport in the landfill cover, liner and waste body is considered. Constant concentration and flux boundary conditions for the injection well are adopted. The proposed approach can be used for leakage detection of the barrier systems in landfills. It is shown that the air-filled porosities of the waste body and the upper cover have a great influence on the tracer gas emission flux on the cover system while the effect of air-filled porosity of the bottom liner can be neglected. The transport mechanism of the tracer gas in the waste body can have a significant impact on the behaviour of the tracer gas in the upper cover and the bottom liner. SF6 emission flux increases with decreasing of the thickness of the upper cover and increasing thickness of the waste body. It is proposed that a constant flux injection boundary should be adopted in the field for leakage detection. The analytical model presented here is a relatively simplified model, which can be used for the validation and guidance of field tracer test.

The Hyper-inflation Stage in the Coronal Mass Ejection Formation: A Missing Link That Connects Flares, Coronal Mass Ejections, and Shocks in the Low Corona

We analyze the formation and three-dimensional (3D) evolution of two coronal mass ejections (CMEs) and their associated waves in the low corona via a detailed multi-viewpoint analysis of extreme-ultraviolet observations. We analyze the kinematics in the radial and lateral directions and identify three stages in the early evolution of the CME: (1) a hyper-inflation stage, when the CME laterally expands at speeds of ∼1000 km s−1, followed by (2) a shorter and slower expansion stage of a few minutes and ending with (3) a self-similar phase that carries the CME into the middle corona. The first two stages coincide with the impulsive phase of the accompanying flare, the formation and separation of an EUV wave from the CME, and the start of the metric type II radio burst. Our 3D analysis suggests that the hyper-inflation phase may be a crucial stage in the CME formation with wide-ranging implications for solar eruption research. It likely represents the formation stage of the magnetic structure that is eventually ejected into the corona, as the white-light CME. It appears to be driven by the injection of poloidal flux into the ejecting magnetic structure, which leads to the lateral (primarily) growth of the magnetic flux rope. The rapid growth results in the creation of EUV waves and eventually shocks at the CME flanks that are detected as metric type II radio bursts. In other words, the hyper-inflation stage in the early CME evolution may be the “missing” link between CMEs, flares, and coronal shocks.

The merging process of chromospheric fibrils into a filament

Context. Although solar filaments have been intensively studied, detailed observations that show an entire process of filament maintenance are rare. Aims. The aim of this paper is to study the whole process of the material supply and the magnetic flux injection from chromospheric fibrils to a nearby filament. Methods. Based on multiwavelength observations from the New Vacuum Solar Telescope and the Solar Dynamics Observatory (SDO), we tracked the evolution of the chromospheric fibrils involved in the process of filament maintenance and estimated the relevant kinetic parameters. The possible reconnection process was further analyzed in detail by using the SDO magnetic field and extreme ultraviolet observations. Results. In the southeast of the filament, two sets of chromospheric fibrils approach and interact with each other, accompanied by weak brightening at the interacting region. Subsequently, a long fibril is formed, keeps moving toward the filament, and finally merges into it. The mergence results in a disturbance in the filament, for example, some of the original filament fibrils move northward. Ten minutes later, a similar process occurs again. By checking the photospheric magnetograms, we find that the two sets of chromospheric fibrils are rooted in a pair of opposite-polarity magnetic patches, and magnetic cancellation takes place between them. We propose that magnetic reconnection could occur between chromospheric fibrils and that it plays an important role in the formation of the new longer fibrils. Conclusions. Magnetic reconnections between chromospheric fibrils produce new fibrils, which then merge into a nearby filament. Such observations imply that filament material and magnetic flux can be supplied from surrounding chromospheric fibrils.

Computation of magnetohydrodynamic electro-osmotic modulated rotating squeezing flow with zeta potential effects

Motivated by exploring novel intelligent functional materials deployed in electromagnetic squeezing flows such systems, a comprehensive mathematical model is developed to investigate the squeezing flow of a smart viscous ionic magneto-tribological fluid with zeta potential effects, intercalated between two parallel plates rotating in unison, under the simultaneous application of electric and magnetic fields. The lower disk permits lateral mass flux (suction or injection). Continuity and momentum equations are represented in the proposed three-dimensional mathematical model by a set of partial differential equations. The electro-viscous effects resulting from distorted electric double-capacity flow fields are comprehensively examined for various intensities of applied plate motion. The formulation features a more robust approach to the traditional Poisson-Boltzmann equation model. A similarity transformation is used to translate the governing equations into ordinary differential equations, which are then numerically solved with appropriate boundary conditions at the disks using MATLAB software. Via graphical visualization of velocity profiles, pressure gradients and the upper wall coefficient of skin friction, several characteristics of squeezing flow are analysed. The computations show that there is a rise in pressure near the plate walls and a fall in pressure in the centre with increment in rotational, electroosmosis, electric field, and magnetic parameters. However, by selecting the appropriate squeezing velocity, the viscous drag on the lower plate can be effectively reduced. It is also observed that as the disk (wall) suction parameter increases, both radial and transverse velocities are damped. The current study generalizes previous investigations with the novelty of rotation and also pressure gradient computations. Furthermore, it provides a useful benchmark for alternative numerical simulations.