Radial Mass Flow Research Articles

Gas accretion onto Jupiter mass planets in discs with laminar accretion flows

Context. Numerous studies have shown that a gap-forming Jovian mass planet embedded in a protoplanetary disc, in which a turbulent viscosity operates, can accrete gas efficiently through the gap, and for typical parameters it doubles its mass in ~0.1 Myr. The planet also migrates inwards on a timescale that is closely related to the local viscous evolution timescale, which is also typically 0.1 Myr. These timescales are short compared to protoplanetary disc lifetimes, and raise questions about the origins of the cold gas giant exoplanets that have been discovered in abundance. It is understood that protoplanetary discs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. Aims. The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered protoplanetary discs, and to compare the results with those obtained for viscous models. Methods. We use 3D hydrodynamical simulations of planets embedded in protoplanetary discs, in which a constant radial mass flux towards the star of ṁ = 10−8 M⊙ yr−1 is sustained. We consider a classical viscous α disc model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers have a variety of depths, as parameterised by their column densities ΣA, and we consider values of ΣA in the range 0.1−10 g cm−2. Results. The viscous disc model gives results in agreement with previous studies. In accord with our recent work that examines the migration of Jovian mass planets in layered models, we find the accretion rate onto the planet in the layered models crucially depends on the ability of the planet to block the wind-induced mass flow towards the star. For ΣA = 10 g cm−2, the planet torque can block the mass flow in disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For ΣA = 0.1 g cm−2, the flow is not blocked, accretion is fast, and the mass doubling time is 0.2 Myr. Conclusions. Our results show that although the radial mass flow through the layered disc models is always 10−8 M⊙ yr−1, adopting different values of ΣA leads to very different gas accretion rates onto embedded gas giant planets.

Validation of inhomogeneous chamber states in rotary positive displacement vacuum pumps

Chamber model simulation is a common approach to simulate rotary positive displacement vacuum pumps. Therefore the pump is abstracted into working chambers and connecting clearances, whereby the clearance leakages can be identified as the major loss mechanism in such machines. The clearance mass flow rates are calculated with respect to the thermodynamic states in the adjacent chambers, which are inhomogeneous for rarefied gases due to the movement of the rotors which causes a pressure gradient within the chamber. This effect increases with higher Knudsen numbers, because of the increasingly dominant friction. These inhomogeneous chamber states are assumed to be quasi-static in case that the chamber volume is constant with time. Therefore the chamber must not have a connection to the suction or discharge port. This can be modelled with a one-dimensional approach for geometrically abstracted chambers. In order to validate the one-dimensional characteristics in circumferential direction three-dimensional steady state simulations of a working chamber are performed using a Computational Fluid Dynamics (CFD) solver. To improve the accuracy for rarefied gases Maxwell velocity slip boundary conditions are applied. It is shown, that the inhomogeneous chamber states can be approximated by a regression analysis of a dimensionless number. Furthermore the housing clearance and the radial clearance mass flow rates for given boundary conditions are geometrically abstracted and calculated using a one-dimensional model. The new clearance models and the inhomogeneous chamber states are implemented in a chamber model simulation software and results of a test machine are compared to measurements and to previous simulations.

Radial Motions and Radial Gas Flows in Local Spiral Galaxies

Abstract We determine radial velocities and mass flow rates in a sample of 54 local spiral galaxies by modeling high-resolution and high-sensitivity data of the atomic hydrogen emission line. We found that, although radial inflow motions seem to be slightly preferred over outflow motions, their magnitude is generally small. Most galaxies show radial flows of only a few km s−1 throughout their H i disks, either inward or outward, without any clear increase in magnitude in the outermost regions, as we would expect for continuous radial accretion. Gas mass flow rates for most galaxies are less than 1 M ⊙ yr−1. Over the entire sample, we estimated an average inflow rate of 0.3 M ⊙ yr−1 outside the optical disk and of 0.1 M ⊙ yr−1 in the outskirts of the H i disks. These inflow rates are about 5–10 times smaller than the average star formation rate of 1.4 M ⊙ yr−1. Our study suggests that there is no clear evidence for systematic radial accretion inflows that alone could feed and sustain the star formation process in the inner regions of local spiral galaxies at its current rate.

Heat transfer characterization under radial jet and falling film induced rewetting

Abstract Empirical correlations are developed for rewetting velocity and maximum heat transfer coefficient during rewetting phase of single hot vertical Fuel Pin Simulator (FPS) by using radial jet impingement and falling film. Emergency Core Cooling System (ECCS) has been designed for Advance Heavy water Reactor (AHWR) to rewet the hot fuel pin under the loss of coolant accident. Coolant injection takes place from a water rod which is located at the center of the fuel bundle in form of jets to rewet hot surface of fuel pin under loss of coolant accident. This kind of design to reflood the fuel bundle is different than bottom and top spray reflooding practiced in PWR and BWR type of nuclear reactors. There are two different kinds of rewetting found during radial jet induced cooling. The first one is due to radial jet impingement and the second one is due to falling film which is below the jet impingement point. Rewetting velocity has been predicted along the length of fuel pin due to radial jet impingement cooling. Temperature of FPS has been varied from 400°C to 700°C with help of different powers supply, simulating decay heat of reactor. A variation of coolant radial jet mass flow rate is from 0.5 lpm to 1.8 lpm. It is considered during ECCS injection. It has been observed from the experiments that rewetting velocity decreases with increasing the clad surface temperature and increases with increasing the coolant mass flow rate. The rewetting velocity in falling film is found to be nearly 1.8 times higher than rewetting velocity predicted in circumferential direction. Further, it is found that maximum heat transfer coefficient increases with increasing the radial jet coolant mass flow rate. The maximum heat transfer coefficient in case of radial jet impingement is found to be nearly 1.5 times the falling film rewetting. Developed correlation predicts the maximum heat transfer coefficient with experimental data well within the error band of ±10%.

Mass flow extrapolation model for automotive turbine and confrontation to experiments

The turbochargers performance maps given by the manufacturer present a narrow range for the turbine mass flow rate which requires extrapolation models. This paper presents a new partly empirical model for radial turbine mass flow rate performance map extrapolation. An experimental measurement of a complete mass flow map is presented. An existing model is used to show the need for a better fitting because the results do not correspond to the values in all the experimental range. The proposed model is done in two steps. The first step is the calculation of the isentropic expansion across an ideal nozzle with four fitting coefficients to take into consideration the effect of the rotational speed, the two stages expansion across a turbine, the friction and the choking. The second step is the calculation of a reversed flow to represent the effect of the centrifugal forces pushing the fluid to the outer radius direction: in this part there are three constants and one variable, the blade speed. No fitting coefficients are used in this part. The final model is the difference between the two parts. The results present a good correlation of the experiment inside and outside the manufacturer’s data map range.

Development and validation of a radial turbine efficiency and mass flow model at design and off-design conditions

Turbine performance at extreme off-design conditions is growing in importance for properly computing turbocharged reciprocating internal combustion engines behaviour during urban driving conditions at current and future homologation cycles. In these cases, the turbine operates at very low flow rates and power outputs and at very high blade to jet speed ratios during transitory periods due to turbocharger wheel inertia and the high pulsation level of engine exhaust flow. This paper presents a physically based method that is able to extrapolate radial turbines reduced mass flow and adiabatic efficiency in blade speed ratio, turbine rotational speed and stator vanes position. The model uses a very narrow range of experimental data from turbine maps to fit the necessary coefficients. By using a special experimental turbocharger gas stand, experimental data have been obtained for extremely low turbine power outputs for the sake of model validation. Even if the data used for fitting only covers the turbine normal operation zone, the extrapolation model provides very good agreement with the experiments at very high blade speed ratio points; producing also good results when extrapolating in rotational speed and stator vanes position.

N-body simulations of collective effects in spiral and barred galaxies

We present gravitational N-body simulations of the secular morphological evolution of disk galaxies induced by density wave modes. In particular, we address the demands collective effects place on the choice of simulation parameters, and show that the common practice of the use of a large gravity softening parameter was responsible for the failure of past simulations to correctly model the secular evolution process in galaxies, even for those simulations where the choice of basic state allows an unstable mode to emerge, a prerequisite for obtaining the coordinated radial mass flow pattern needed for secular evolution of galaxies along the Hubble sequence. We also demonstrate that the secular evolution rates measured in our improved simulations agree to an impressive degree with the corresponding rates predicted by the recently-advanced theories of dynamically-driven secular evolution of galaxies. The results of the current work, besides having direct implications on the cosmological evolution of galaxies, also shed light on the general question of how irreversibility emerges from a nominally reversible physical system.

Flow structure evolution for laminar vortex rings impinging onto a fixed solid wall

Laser Induced Fluorescence (LIF) and Particle Image Velocimetry (PIV) techniques are used to investigate the synthetic jet actuated laminar vortex rings impinging onto a solid wall. Four cases with different stroke lengths (19mm⩽L0⩽50mm) are adopted to generate laminar vortex rings with Reynolds number (ReV0≈151) and orifice-to-wall distance (H=40mm) unchanged. It is found that the dimensionless stroke length normalized by the orifice-to-wall distance (L0/H) has a significant influence on the evolution of near wall flow structure of the impinging synthetic jet. Specifically, as the stroke length is relatively small (L0/H=0.475 and 0.775), the impinging vortex ring could only induce a weak secondary vorticity near the wall, which cannot roll up into a coherent structure. It is illustrated with LIF visualization and Finite Time Lyapunov Exponents (FTLEs) that a large-scale spiral vortex ring is generated in the near wall region for these two cases, which is explored for the first time. However, as the stroke length becomes larger (L0/H=0.95 and 1.25), the strong secondary vorticity rolls up and pairs with the impinging vortex ring to form a vortex dipole. As a result, the impinging vortex rings are prevented to merge with the vorticity clustering near the wall causing a rapid reduction of the near wall vortex strength. The analysis of the radial wall jet shows that the induced large-scale spiral vortex ring at the case of the smaller stroke length could slow down both the decay rates of radial mass flow rate and momentum flux, and this might be of benefit for the mass and heat transfer of wall surface when applying the impinging synthetic jet.

Parametric study of turbine NGV blade lean and vortex design

The effects of blade lean and vortex design on the aerodynamics of a turbine entry nozzle guide vane (NGV) are considered using computational fluid dynamics. The aim of the work is to address some of the uncertainties which have arisen from previous studies where conflicting results have been reported for the effect on the NGV. The configuration was initially based on the energy efficient engine turbine which also served as the validation case for the computational method. A total of 17 NGV configurations were evaluated to study the effects of lean and vortex design on row efficiency and secondary kinetic energy. The distribution of mass flow ratio is introduced as an additional factor in the assessment of blade lean effects. The results show that in the turbine entry NGV, the secondary flow strength is not a dominant factor that determines NGV losses and therefore the changes of loading distribution due to blade lean and the associated loss mechanisms should be regarded as a key factor. Radial mass flow redistribution under different NGV lean and twist is demonstrated as an addition key factor influencing row efficiency.

Shorten the Intermediate Turbine Duct Length by Applying an Integrated Concept

The demand of further increased bypass ratio of aero engines will lead to low pressure turbines with larger diameters, which rotate at lower speed. Therefore, it is necessary to guide the flow leaving the high pressure turbine to the low pressure turbine at larger diameters minimizing the losses and providing an adequate flow at the low pressure (LP)-turbine inlet. Due to costs and weight, this intermediate turbine duct has to be as short as possible. This would lead to an aggressive (high diffusion) s-shaped duct geometry. It is possible to shorten the duct simply by reducing the length but the risk of separation is rising and losses increase. Another approach to shorten the duct and thus the engine length is to apply a so called integrated concept. These are novel concepts where the struts, mounted in the transition duct, replace the usually following LP-vane row. This configuration should replace the first LP-vane row from a front bearing engine architecture where the vane needs a big area to hold bearing services. That means the rotor is located directly downstream of the strut. This means that the struts have to provide the downstream blade row with undisturbed inflow with suitable flow angle and Mach number. Therefore, the (lifting) strut has a distinct three-dimensional design in the more downstream part, while in the more upstream part, it has to be cylindrical to be able to lead through supply lines. In spite of the longer chord compared with the base design, this struts have a thickness to chord ratio of 18%. To apply this concept, a compromise must be found between the number of struts (weight), vibration, noise, and occurring flow disturbances due to the secondary flows and losses. The struts and the outer duct wall have been designed by Industria de Turbopropulsores. The inner duct was kept the same as for the base line configuration (designed by Motoren und Turbinen Union). The aim of the design was to have similar duct outflow conditions (exit flow angle and radial mass flow distribution) as the base design with which it is compared in this paper. This base design consists of a single transonic high pressure (HP)-turbine stage, an aggressive s-shaped intermediate turbine duct, and a LP-vane row. Both designs used the same HP-turbine and were run in the continuously operating Transonic Test Turbine Facility at Graz University of Technology under the same engine representative inlet conditions. The flow field upstream and downstream the LP-vane and the strut, respectively, has been investigated by means of five hole probes. A rough estimation of the overall duct loss is given as well as the upper and lower weight reduction limit for the integrated concept.

Estimation of the diameter–charge distribution in polydisperse electrically charged sprays of electrically insulating liquids

The majority of scientific and industrial electrical spray applications make use of sprays that contain a range of drop diameters. Indirect evidence suggests the mean drop diameter and the mean drop charge level are usually correlated. In addition, within each drop diameter class there is every reason to suspect a distribution of charge levels exist for a particular drop diameter class. This paper presents an experimental method that uses the joint PDF of drop velocity and diameter, obtained from phase Doppler anemometry measurements, and directly obtained spatially resolved distributions of the mass and charge flux to obtain a drop diameter and charge frequency distribution. The method is demonstrated using several data-sets obtained from experimental measurements of steady poly-disperse sprays of an electrically insulating liquid produced with the charge injection technique. The space charge repulsion in the spray plume produces a hollow cone spray structure. In addition an approximate self-similarity is observed, with the maximum radial mass and charge flow occurring at r/d ~ 200. The charge flux profile is slightly offset from the mass flux profile, and this gives direct evidence that the spray specific charge increases from approximately 20% of the bulk mean spray specific charge on the spray axis to approximately 200% of the bulk mean specific charge in the periphery of the spray. The results from the drop charge estimation model suggest a complex picture of the correlation between drop charge and drop diameter, with spray specific charge, injection velocity and orifice diameter all contributing to the shape of the drop diameter–charge distribution. Mean drop charge as a function of the Rayleigh limit is approximately 0.2, and is invariant with drop diameter and also across the spray cases tested.

SPRAY CHARACTERISTICS OF CHARGE INJECTION ELECTROSTATIC ATOMIZERS WITH SMALL-ORIFICE DIAMETERS

Here the characteristics of charged sprays of insulating liquids generated by an improved charge injection (electrostatic) atomizer design are described, and the experimental database previously available in the literature is extended to a smaller range of orifice diameters and to more viscous liquids. Previously identified “subcritical” and “supercritical” electrohydrodynamic (EHD) regimes for the atomizer are confirmed to be present for the viscosity and orifice diameter ranges studied here, showing that these EHD regimes appear to be generic to the atomization method. The jet breakup dynamics and length are qualitatively and quantitatively studied using imaging and phase Doppler anemometry (PDA), and the general spray plume characteristics are quantitatively described in terms of droplet velocity and diameter probability density functions (PDFs). Radial spray charge and mass flow rates are quantified as using a purpose-built collecting system. By appropriately normalizing the data, the degree of self-similarity between different spray data sets is clearly evident and proves that the near-axis droplets are poorly charged and that the mean specific charge increases with radial displacement, again in a self-similar manner.

New evidence for a role of vessel‐associated cells and phloem in the rapid xylem refilling of cavitated stems of Laurus nobilis L.

ABSTRACTXylem recovery from embolism was studied in Laurus nobilis L. stems that were induced to cavitate by combining negative xylem pressure potentials (PX = −1.1 MPa) with positive air pressures (PC) applied using a pressure collar. Xylem refilling was measured by recording the percentage loss of hydraulic conductance (PLC) with respect to the maximum 2 min, 20 min and 15 h after pressure release. Sodium orthovanadate (an inhibitor of many ATP‐ases) strongly inhibited xylem refilling while fusicoccin (a stimulator of the plasma membrane H+‐ATPase) promoted complete embolism reversal. So, the refilling process was interpreted to result from energy‐dependent mechanisms. Stem girdling induced progressively larger inhibition to refilling the nearer to the embolized stem segment phloem was removed. The starch content of wood parenchyma was estimated as percentages of ray and vasicentric cells with high starch content with respect to the total, before and after stem embolism was induced. A closely linear positive relationship was found to exist between recovery from PLC and starch hydrolysis. This, was especially evident in vasicentric cells. A mechanism for xylem refilling based upon starch to sugar conversion and transport into embolized conduits, assisted by phloem pressure‐driven radial mass flow is proposed.

The Structure and Appearance of Protostellar Accretion Disks: Limits on Disk Flaring

Vertical structure models are used to investigate the structure of protostellar, α-law, accretion disks. Conditions investigated cover a range of mass fluxes (10-9 to 10-5 M☉ yr-1), viscous efficiencies (α = 10-2 and 10-4), and stellar masses (0.5-3 M☉). Analytic formulae for midplane temperatures, optical depths, and volume and surface densities are derived and are shown to agree well with numerical results. The temperature dependence of the opacity is shown to be the crucial factor in determining radial trends. We also consider the effect on disk structure of illumination from a uniform field of radiation such as might be expected of a system immersed in a molecular cloud core or other star-forming environment: Tamb = 10, 20, and 100 K. Model results are compared to Hubble Space Telescope observations of HH30 and the Orion proplyds. Disk shape is derived in both the Rosseland mean approximation and as viewed at particular wavelengths (λλ = 0.66, 2.2, 60, 100, 350, and 1000 μm). In regions where the opacity is an increasing function of temperature (as in the molecular regions where κ ∝ T2), the disk does not flare, but decreases in relative thickness with radius under both Rosseland mean and single wavelength approximations. The radius at which the disk becomes shadowed from central object illumination depends on radial mass flow and varies from a few tenths to about 5 au over the range of mass fluxes tested. This suggests that most planet formation occurred in environments unheated by stellar radiation. Viewing the system at any single wavelength increases the apparent flaring of the disk but leaves the shadow radius essentially unchanged. External heating further enhances flaring at large radii, but, except under extreme illumination (100 K), the inner disk will shield the planet-forming regions of all but the lowest mass flux disks from radiation originating near the origin such as from the star or from an FU Orionis outburst.

An Accretion Disk Model for the Innermost 200PC of the Galaxy

AbstractWe demonstrate that it is possible to understand observed radial velocities of molecular clouds close to the Galactic Center as being due to motion of this material in an accretion disk. Our models indicate a stationary disk with a radial mass flow rate of 10-1.8 Mʘ/yr with a viscosity of 1.9 · 103 pc km/s at 100 pc from the Galactic Center and a radial dependence of it, that goes approximately like the square root of the radius from the Galactic Center.

Similarity vortices in a stratified atmosphere

Similarity equations relating to steady and unsteady vortices in a stratified atmosphere are shown to possess more general solutions than hitherto reported. Solutions with n cells, where n = 1,2,3, ..., are possible such that the axial and radial velocities tend to zero far from the axis of the vortex. For solutions with a finite number of cells, far from the axis the radial mass flow is directed towards the axis, with the exception of a subclass of solutions relating to one-cell and two-cell vortices associated with the unsteady configuration where the radial velocity is directed outwards.

Premixed combustion in a vortex

An asymptotic analysis for large Peclet numbers has been performed in order to describe the roll-up of a premixed flame by a single vortex. In this limit the process consists of two steps: o 1) The fast-time inviscid roll-up of the flame surface as a passive surface into a spiral around the vortex. 2) The slow-time flame propagation between the spirals. Since the spirals are closer to each other towards the center of the vortex, the latter process leads to the development of a reacted core, similar to that found by Marble for diffusion flames. The growth rate of the reacted core is derived first in terms of a more global order-of-magnitude estimate, then a detailed mathematical analysis is performed to test the estimate. Its essential parts are a transformation to Lagrangian coordinates and an asymptotic analysis of the resulting equation. The flame propagation between the spirals is assumed to be quasi-stationary. The flames are stretched by the convective motion and may extinguish for Lewis numbers larger than unity. Finally, under an approximation of radial symmetry, the radial mass flow rate produced by gas expansion is calculated.

Radial mass flow in electrohydrodynamically-enhanced forced heat transfer in tubes

Experimental results of an electrohydrodynamically-enhanced oil heater of annular cross-section are presented. When a high d.c. voltage (typically 30 kV) was applied across the annular gap, it induced a very strong radial motion of the fluid resulting in a heat transfer increase of more than 20 fold over the fully-developed laminar flow, yet the pressure drop only increased 3 fold. The electrohydrodynamically-enhanced Nusselt number correlates well with electrical current passed, which is typically a few millionths of an ampere per metre of tube.

Numerical Simulation of Band Propagation in Nonlinear Chromatography

Abstract A model for the propagation of a finite concentration zone in a chroma-tographic column is discussed for the case of a single component sample. This model is based on the modern theory of nonlinear hyperbolic systems of partial differential equations. It accounts for the nonlinear effects due 1) to the thermodynamics of solute-stationary phase equilibrium (i.e., the nonlinearity of the equilibrium isotherm), 2) to the interaction between radial mass transfer and flow velocity (the sorption effect in gas chromatography), and 3) to the pressure gradient along the column (in gas chromatography). Numerical results are obtained by using the Godunov method. The column is divided into a large

Analysis of Confined Magnetohydrodynamic Vortex Flows

The vortex flow of a viscous, incompressible, and electrically conducting fluid confined between two finite flat plates (with a net radial mass flow) in the presence of an applied axial magnetic field is considered. The details of the velocity field including boundary‐layer thickness and redistribution of radial mass flow are of primary concern. The analysis is limited to the case of the separation distance between the two end plates being small compared with the radius of the plates; this allows the momentum equations to be uncoupled from the electromagnetic equations. The momentum equations are linearized and solved for the velocities and the pressure as Fourier series. It is found that magnetic effects tend to decrease the boundary‐layer thickness by a small percentage and tend to decrease substantially the mass flow drawn into the boundary layers.