Mass Velocity Profiles Research Articles

The results of a magnetic field on flow past an inclined isothermal vertical plate with heat and varying mass diffusion

This work describes the influence of a magnetic environment on the circulation of matter and thermal energy over an accelerating advanced inclined isothermal sectional surface. The temperature is elevated to . The proximity intensity is increased to . The Laplace-transform approach is applied to solve the dimensionless analytical equation. In this research work different physical variables including thermal grashof number (Tg), mass grashof number (Tm), Schmidt number (Sc), Prandtl number(Pr), time(t), velocity profile ( ), temperature ( ), and intensity ( ) are investigated. The output of the graph produced by the Matlab software commands an energy equation, momentum equation, and concentration equation. The values are shown in an aligned pattern for a variety of flow variables. Diagrammatic representations of the fluid velocity profiles are provided. The velocity rises corresponding to different Tg and the velocity rises corresponding to different Tm. As the angle is decreased, the velocity increases differently. , As the different magnetic environment values lower, the velocity rises. Elevated values of angle ( ), Sc, Pr, and contribute to an enhancement in local skin friction, and an upsurge in Gr, Gc, and t leads to a reduction. A tabulated presentation of Nusselt quantities reveals a positive correlation with increasing Pr. Similarly, Sherwood quantities, as tabulated for various parameters, demonstrate a proportional increase with rising Sc.

Combination of two-fluid model and delayed equilibrium model for the critical flow in a slit

Accurately predicting the mass flux, pressure profile, and velocity profile of the critical flow in a slit is essential for analyzing the breaking process of the liquid phase and calculating the aerosol source term for leak-before-break (LBB) monitoring and Loss of Coolant Accident (LOCA) risk analysis. A new critical flow model combining Two-fluid Model (TFM) and Delayed Equilibrium Model (DEM) is built to get accurate profiles while avoiding the same phase velocity in DEM and the arbitrary critical flow criterion in TFM. The new model is verified using past experiments of the critical flow in a slit. It proves to be accurate in mass flux but not in critical pressure, with maximum relative errors of around 25% in mass flux and around 80% in critical pressure. The new model is optimized for higher accuracy in critical pressure. The empirical equation of saturated phase mass flow rate fraction gradient is optimized by conducting approximate pressure profile calculation and regression analysis. The maximum relative error decreases little while the ratio of critical pressure relative errors lying in the range of ±40% increases after optimization. In contrast, the difference in the average abstract relative error of pressure between original TFM-DEM and DEM is much larger, for the maximum relative error of mass flux and critical pressure are around 25% and 110%. The comparison between the original and optimized TFM-DEM proves that the new critical flow model is accurate in mass flux and can be optimized to raise pressure calculation accuracy. The comparison between the original TFM-DEM and DEM proves that the phase velocity difference is the major source of accuracy improvement in the pressure profile.

Mass Velocity Profiles for Non-Ideal Detonation of Mixtures of Nitromethane and Ammonium Perchlorate Overloaded with Aluminum. Measurements and Calculation

Earlier, by comparing the results of mathematical modeling with experimental data on the non-ideal detonation velocities of triple mixtures of nitromethane and ammonium perchlorate with aluminum excess, the rates of exothermic reactions and the consumption degree of components within the detonation wave reaction zone were determined. A quasi-one-dimensional model of steady detonation was used for calculations, in which all components have a common pressure and move with a common mass velocity, and exothermic conversion is carried out in three stages, which include decomposition of nitromethane and ammonium perchlorate and diffusion combustion of aluminum. To confirm the obtained results and the applicability of the relatively simple theoretical model, calculations of the mass velocity profile during detonation of one of the triple mixtures with 17% nitromethane have been carried out. The calculation results are in agreement with the measured mass velocity profile, concerning the shape of the profile, the amplitude and the rate of decrease of the mass velocity along the detonation reaction zone. A possible explanation of a “leaning” of the beginning portion of the mass velocity profile observed in experiments has been proposed, and an estimate of the rise time of the sensor signal is given, taking into account the calculated curvature of the shock front of the detonation wave.

Mass Velocity Profiles for Nonideal Detonation of Mixtures of Nitromethane and Ammonium Perchlorate Overloaded with Aluminum: Measurements and Calculation

Mass Velocity Profiles for Nonideal Detonation of Mixtures of Nitromethane and Ammonium Perchlorate Overloaded with Aluminum: Measurements and Calculation

Impact of Arrhenius activation energy on MHD nanofluid flow past a stretching sheet with exponential heat source: A modified Buongiorno’s model approach

Nanofluids have a wide range of applications in biological research. They are employed in targeted medication administration, hyperthermia (for cancer treatment) and differential diagnostics like magnetic resonance image (MRI). In light of these medical applications, the impact of an external magnetic field and an exponential heat source on the dynamics of [Formula: see text]–[Formula: see text] over a nonlinearly stretched surface has been investigated. A realistic modified Buongiorno model has been used which includes the effects of reaction rate, Biot number and activation energy. The boundary value problem governing the model is solved on MATLAB R2022a using the solver, BVP5C. Further, the consequences of different parameters on rate of heat transfer coefficient (Nusselt number), rate of mass transfer coefficient (Sherwood number), drag coefficient, velocity, temperature and volume fraction profile are observed graphically. It is noted that volume fraction and uniform heat source intensity have a positive effect on the Nusselt number and negative effect on Sherwood number. The effects of thermal radiation and magnetic field on volume fraction profile are, respectively, positive and negative. The current physics of flow across a vertical stretching surface is expected to serve as the foundation for various medical science, engineering and technology applications.

Natural convection compound heat transfer enhancement by discrete rings and the chimney effect in a vertical cylinder

Natural convection is an indispensable heat transfer process considered in the design of advanced autonomous nuclear reactors. The renaissance of inherently safe micro nuclear reactors calls for increased post shut down heat rejection rates by passive means. This study numerically investigated heat transfer enhancement in a heated cylinder by discrete rings and the chimney effect. Five equally spaced rings of varying thicknesses and heights were fitted in the heated channel to effect enhancement by flow interruption. The chimney effect was studied by appending adiabatic chimney extensions of different heights, giving rise to extension ratios of 1.5, 1.6, 1.65, and 1.75. Compound enhancement was achieved by attaching chimney extensions to a ringed channel. Nusselt number ratios, mass flow rates, temperature, and velocity profiles were presented. The results showed that compound heat transfer enhancement could increase Nusselt numbers by between 44 and 54% and lower temperatures by over 30% depending on the chimney height. Furthermore, very short chimney heights would be required in the compound setup in comparison to the tall chimneys in the chimney-only cases, for the same target heat transfer rates. The resulting compactness could greatly influence the design of very small reactors and contribute to improvements of other air-cooled passive systems.

Bose–Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials

We consider the effects of an uncorrelated random potential on the properties of Bose–Einstein Condensate (BEC) dark matter halos, which acts as a source of disorder, and which is added as a new term in the Gross–Pitaevskii equation, describing the properties of the halo. By using the hydrodynamic representation we derive the basic equation describing the density distribution of the galactic dark matter halo, by also taking into account the effects of the baryonic matter, and of the rotation. The density, mass and tangential velocity profiles are obtained exactly in spherical symmetry by considering a simple exponential density profile for the baryonic matter, and a Gaussian type disorder potential. To test the theoretical model we compare its predictions with a set of 39 galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. We obtain estimates of the relevant astrophysical parameters of the dark matter dominated galaxies, including the baryonic matter properties, and the parameters of the random potential. The BEC model in the presence of baryonic matter and a random confining potential gives a good statistical description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core/cusp problem.

Bayesian Inference of Globular Cluster Properties Using Distribution Functions

Abstract We present a Bayesian inference approach to estimating the cumulative mass profile and mean-squared velocity profile of a globular cluster (GC) given the spatial and kinematic information of its stars. Mock GCs with a range of sizes and concentrations are generated from lowered-isothermal dynamical models, from which we test the reliability of the Bayesian method to estimate model parameters through repeated statistical simulation. We find that given unbiased star samples, we are able to reconstruct the cluster parameters used to generate the mock cluster and the cluster’s cumulative mass and mean-squared velocity profiles with good accuracy. We further explore how strongly biased sampling, which could be the result of observing constraints, might affect this approach. Our tests indicate that if we instead have biased samples, then our estimates can be off in certain ways that are dependent on cluster morphology. Overall, our findings motivate obtaining samples of stars that are as unbiased as possible. This may be achieved by combining information from multiple telescopes (e.g., Hubble and Gaia), but will require careful modeling of the measurement uncertainties through a hierarchical model, which we plan to pursue in future work.

Using kinematics to re-define the pull test as a quantitative biomarker of the postural response in normal pressure hydrocephalus patients.

Quantitative biomarkers are needed for the diagnosis, monitoring and therapeutic assessment of postural instability in movement disorder patients. The goal of this study was to create a practical, objective measure of postural instability using kinematic measurements of the pull test. Twenty-one patients with normal pressure hydrocephalus and 20 age-matched control subjects were fitted with inertial measurement units and underwent 10-20 pull tests of varying intensities performed by a trained clinician. Kinematic data were extracted for each pull test and aggregated. Patients participated in 103 sessions for a total of 1555 trials while controls participated in 20 sessions for a total of 299 trials. Patients were separated into groups by MDS-Unified Parkinson's Disease Rating Scale (MDS-UPDRS) pull test score. The center of mass velocity profile easily distinguished between patient groups such that score increases correlated with decreases in peak velocity and later peak velocity onset. All patients except those scored as "3" demonstrated an increase in step length and decrease in reaction time with increasing pull intensity. Groups were distinguished by differences in the relationship of step length to pull intensity (slope) and their overall step length or reaction time regardless of pull intensity (y-intercept). NPH patients scored as "normal" on the MDS-UPDRS scale were kinematically indistinguishable from age-matched control subjects during a standardized perturbation, but could be distinguished from controls by their response to a range of pull intensities. An instrumented, purposefully varied pull test produces kinematic metrics useful for distinguishing clinically meaningful differences within hydrocephalus patients as well as distinguishing these patients from healthy, control subjects.

Analytical solution to the problem of diffusion of the light component of the binary gas mixture in a plane channel

Within the framework of the kinetic approach, an analytical solution to the problem of diffusion of the light component of a binary mixture in a flat channel with infinite parallel walls is constructed. It is assumed that the mass of light component molecules and their concentration is much less than the mass of molecules and the concentration of heavy components. The flow rate of the heavy component is assumed to be zero. The change in the state of a light gas component is described on the basis of the BGK (Bhatnagar, Gross, Kruk) model of the Boltzmann kinetic equation. The diffuse reflection model is used as a boundary condition on the channel walls. The mass velocity profile of the light gas component is constructed. The flow rate of the light gas component per unit channel width is calculated. A comparison with similar results presented in open sources was done.

Effect of Compressibility on Velocity Profile and Friction Factor of Gaseous Laminar Flows in a Microtube

Abstract Laminar flow of nitrogen gas in a microtube was simulated numerically to obtain velocity profile and Fanning friction factor in a quasi-fully developed region. The numerical procedure based on Arbitrary-Lagrangian-Eulerian method solved two-dimensional compressible momentum and energy equations. The computations were performed for a wide range of Reynolds number in laminar flow regime with adiabatic wall condition. It was found that the velocity profile deviates from the parabola as Mach number increases, and the product of Fanning friction factor and Reynolds number is not a constant but a function of only Mach number. To explain the compressibility effect, a new theoretical flow model which gives the velocity profile of gaseous laminar flows in a microtube was proposed under the assumption of purely axial flow. The theoretical velocity profile is taking radial-direction density change into account, and coincides with the numerically obtained velocity profile. The proposed flow model also shows that the Fanning friction factor of a compressible flow in a microtube is expressed by a quadratic function of Mach number. The coefficient of the Mach squared term is 40% of the numerically obtained correlation. The compressibility effect on friction factor of gaseous laminar flows in a microtube partly results from velocity profile change which must occur to keep the mass velocity profile when density changes in radial direction. The remainder of the compressibility effect can be considered to result from actual mass transfer in the radial direction whose existence was demonstrated by the numerical results.

Assisted Spatial Sit-to-Stand Prediction—Part 2: Virtual Injured Elderly Individuals

Abstract Sit-to-stand (STS) is a challenging task, especially for injured elderly in their daily life. This paper presents Part 2 of the assisted spatial STS computational motion prediction to investigate the effect of a unilateral grab-rail bar placed on the right-hand side on STS motion performance for injured virtual individuals (computational digital human model-DHM) with either right or left knee injury. The motion prediction formulation was constructed as a nonlinear optimization and validated in Part 1 of the assisted spatial STS motion prediction (Yang, J., and Ozsoy, B., 2021, “Assisted Spatial Sit-to-Stand Prediction—Part 1: VirtualHealthy Elderly Individuals,” ASME J. Comput. Inf. Sci. Eng., 21(4), p. 041002). Injuries are implemented into the formulation with reduction rates of 75% in a single knee‘s extension torque limits. Two different objective functions are tested: The first one is just minimizing the dynamic effort where the second one is minimizing the difference between right and left side support reaction forces in addition to the dynamic effort. Computational simulations resulted in that systematic changes are seen in the joint coordination better with the first objective function for the elderly group with either right or left knee injury. Since only one of the knees is modeled to experience a strength loss, virtual-individuals tend to flex their trunk to the intact side whilst rotating the upper-body to the right side with both objective functions due to holding the grab-rail bar, which was placed to the right side of the biomechanical model. Based on the peak values of the center of mass velocity and displacement profiles in both the medial-lateral axis, virtual-individuals prefer to use lateral plane motions less and transverse plane motions more to minimize the difference between right and left side-vertical support reaction forces with the second objective function.

H2 mass–velocity relationship from 3D numerical simulations of jet-driven molecular outflows

Context. Previous numerical studies have shown that in protostellar outflows, the outflowing gas mass per unit velocity, or mass–velocity distribution m(v), can be well described by a broken power law ∝ v−γ. On the other hand, recent observations of a sample of outflows at various stages of evolution show that the CO intensity–velocity distribution, closely related to m(v), follows an exponential law ∝ exp(−v∕v0). Aims. In the present work, we revisit the physical origin of the mass–velocity relationship m(v) in jet-driven protostellar outflows. We investigate the respective contributions of the different regions of the outflow, from the swept-up ambient gas to the jet. Methods. We performed 3D numerical simulations of a protostellar jet propagating into a molecular cloud using the hydrodynamical code Yguazú-a. The code takes into account the most abundant atomic and ionic species and was modified to include the H2 gas heating and cooling. Results. We find that by excluding the jet contribution, m(v) is satisfyingly fitted with a single exponential law, with v0 well in the range of observational values. The jet contribution results in additional components in the mass–velocity relationship. This empirical mass–velocity relationship is found to be valid locally in the outflow. The exponent v0 is almost constant in time and for a given level of mixing between the ambient medium and the jet material. In general, v0 displays only a weak spatial dependence. A simple modeling of the L1157 outflow successfully reproduces the various components of the observed CO intensity–velocity relationship. Our simulations indicate that these components trace the outflow cavity of swept-up gas and the material entrained along the jet, respectively. Conclusions. The CO intensity–velocity exponential law is naturally explained by the jet-driven outflow model. The entrained material plays an important role in shaping the mass–velocity profile.

Parametric study of the Crossing elongation effect on the mixing performances using short Two-Layer Crossing Channels Micromixer (TLCCM) geometry

In this study we investigate the mixing performances of a modified micromixer which achieves a very good mixing quality that can be compared to other micromixers proposed recently, our idea proposes a modification of the crossing zone to reduce the unit number. The numerical simulations have been carried out at low Reynolds numbers using the CFD Fluent code to solve the 3D momentum equations, continuity equation, and the species transport equations. The elongation of the crossing zone is defined by a parameter called aspect ratio (l/W). A parametric study was realized using five values of aspect ratio (l/W) from 0 to 1 in a wide range of Reynolds numbers: from 0.2 to 80. To analyze the obtained results through the numerical simulations, the mass fraction contours, velocity vectors, velocity profiles, and pressure losses were presented in different cross-sectional planes and positions. The selected geometry (with l/W = 1) has excellent mixing performances where the obtained mixing index exceeds 85.67% for Re = 0.2 and reaches 99.22% for Re = 50, it also has a lower pressure drop compared to other geometries studied recently. Therefore, the selected micromixer shows high mixing performances at low Reynolds numbers, so it can be employed to improve fluid mixing in various microfluidic systems.

Study of the discharge behavior of Rosin-Rammler particle-size distributions from hopper by discrete element method: A systematic analysis of mass flow rate, segregation and velocity profiles

In the present work, the discrete element method (DEM) is used to investigate the behaviour of Rosin-Rammler (R-R) particle size distribution (PSD) during hopper discharge. The study attempts to identify mass flow rate (MFR) and segregation as a function of spread parameter (PSD width) and location parameter, which includes detailed analysis of bulk density, segregation and velocity profile of particles. The applicability of the widely used Beverloo correlation for prediction of MFR for studied R-R PSDs is also investigated. The results show that, (1) MFR increases as PSD width (at fixed location parameter) increases, whereas MFR decreases with increase in location parameter at fixed PSD width; (2) the studied R-R PSDs exhibit a monotonic trend of flow bulk density and MFR with respect to PSD width and location parameter; (3) the effect of PSD width on overall segregation is found to be more than the location parameter; (4) the velocity profiles for considered R-R PSDs vary along the height of hopper, but remain uniform in shape and follow a pure parabolic increase from the hopper wall; (5) DEM flow rate prediction shows a good agreement with the Beverloo correlation by applying the concept of flow bulk density.

Application of the analytical discrete velocities method for calculating mass and heat fluxes of rarefied gas in the problem of the Poiseuille flow

Analytical version of the discrete ordinates method is used to for calculating the gas macroparameters in a plane channel in the problem of Poiseuille flow. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables is written in a matrix form. Householder algorithm is used for reducing the coefficient matrix to a tridiagonal one. QL algorithm with implicit shifts is applied for searching eigenvalues. The Gauss method with a permutation of the rows is used to determine the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls. The software implementation of the algorithm is developed using the C ++ programming language. The mass velocity profile and the heat flow profile of the gas, the flow rate and heat flow through the cross section of the channel are calculated for a wide range of the Knudsen number. The comparison with similar results presented in the open press is performed.

Software Implementation of the discrete ordinates method in the problem of the Poiseuille flow in a plane channel with infinite parallel walls

The algorithm for calculating the gas macroparameters in a channel using the discrete ordinates method was considered. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables was written in a matrix form. The coefficient matrix in the resulting system of equations was reduced to a symmetric one and then to a tridiagonal matrix using the Householder algorithm. The search for the eigenvalues of the tridiagonal matrix was performed using a QL algorithm with implicit shifts. The determination of the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls was reduced to a system of linear algebraic equations. The Gauss method with a permutation of the rows was used to solve it. The software implementation of the algorithm was carried out using the C++ programming language. The mass velocity profile of the gas and the flow rate through the cross section of the channel in the Poiseuille flow problem were calculated as an application. The comparison with similar results presented in the open press was performed.

Pressure-dependent transport characteristic of methane gas in slit nanopores

The transport mechanism of methane gas through the nanopores is a fundamental concern in the shale gas extraction. Shale gas is mainly stored in nanopores of shale formations over a wide range of pressure which is a fundamental thermodynamic variable dominating the properties of substances, rendering that it is important to understand the pressure-dependent transport characteristic of gas molecules in nanopores. Toward this end, we performed molecular dynamics (MD) simulations to investigate the transport characteristic and its mechanism of methane gas in slit nanopores under different pressures. A modified bin method considering local gas density was proposed to reveal the mass velocity profile of methane gas in nanopores. Combining the trajectories of representative molecules, we found that the underlying mechanism of methane gas transport characteristic behaves as the competition between gas intermolecular collisions and gas-wall interactions. The transport characteristic of methane gas in slit nanopores is dependent on the pressure. Meanwhile, the pore width can significantly influence the mass flux contributions of different transport mechanisms. Under the high pressure, viscous flow is the primary transport mechanism due to the frequent gas intermolecular collisions. Under lower pressure and in larger nanopores, Knudsen diffusion becomes the dominating transport mechanism due to the enhancement of gas-wall interactions (collisions). Narrower nanopores can significantly increase the mass flux contribution of surface diffusion due to the increased proportion of absorbed gas molecules. In particular, we proposed a theoretical model coupling multiple transport mechanisms, which can accurately predict the apparent permeability of methane gas in slit nanopores. Under lower pressure and in narrower nanopores, the enhancement of surface diffusion and Knudsen diffusion can increase the apparent permeability of methane gas by as much as 50 times or more, demonstrating the sensitivity of pressure and pore size for methane gas transport.

Heat and mass fluxes upon incomplete accommodation of rarefied gas molecules by the walls of an elliptic channel

The free-molecular rarefied-gas flow in a long channel of elliptic cross-section is considered. The Maxwellian mirror-diffuse reflection model is used as the boundary condition on the channel walls. Under the assumption that a longitudinal temperature gradient is maintained in the channel the mass and heat fluxes are determined as functions of the accommodation coefficient and the ellipse semi-axis ratio. The gas mass velocity profile is obtained. It is shown that for the channels with the same ellipse semi-axis ratios a decrease in the accommodation coefficient leads generally to an increase in the gas mass velocity. The results obtained are compared with those for the case of full gas accommodation on the channel surface.

Development of a compressible multiphase cavitation approach for diesel spray modelling

The influence of in-nozzle phenomena including cavitation on the morphology of the spray from a diesel injector with a sharp nozzle inlet is investigated numerically. A compressible, multi-phase Volume of Fluid Large Eddy Simulation is implemented in the OpenFOAM environment. The volume fraction transport equations for liquid and gas phases are reformulated to include mass transfer source terms. These source terms are modelled with two cavitation models by Schnerr and Kunz, which are extended to eliminate non-physical mass transfer rates. Validation is carried out only for the Schnerr cavitation model due to its independence of empirical parameters. The numerical method is validated by comparing the simulated mass flow rates, pressure and velocity profiles at different cavitation conditions against published experimental data obtained using a slightly converging square channel. Favourable comparison between simulations and experiments is achieved with minor discrepancies attributable to uncertainties in fuel properties, experimental artefacts and assumptions made in numerical models. Application of the method to calculation of in-nozzle phenomena and primary breakup of a diesel spray reveals that in-nozzle flow separation, wall shear and cavitation contribute greatly to the fragmentation of the jet. Comparison of the two cavitation models shows that after the onset of complete flow detachment, the Kunz implementation predicts higher air inflow at the nozzle outlet than the Schnerr model.