Averaged Velocity Profiles Research Articles

Assessment of gamified mixed reality environments for upper limb robotic rehabilitation: pilot study on healthy adults

Exoskeletons for rehabilitation have the potential to aid movement and promote intensive, task-oriented, and personalized motor training. However, robotic-assisted training and user experience could be further improve by including Mixed Reality Environments (MREs) and using a gamification approach. This paper presents the design and evaluation of a MR solution based on Microsoft Hololens 2 for robot-assisted bilateral shoulder training. It is based on gamified MREs designed to guide and encourage bilateral synchronous and asynchronous movements of the upper extremities while a 6 Degrees of Freedom (DOF) exoskeleton (FLOAT) provides motor assistance only to the impared limb. The robotic-assisted bimanual tasks involve the use of rehabilitative tools (such as a dowel rod), as a means to interact with the virtual world and to enable the intact limb guide and control the motions of the disable limb. The gamified MR training solution generates meaningful performance metrics from the kinematic analysis of hands movement, captured by Hololens. The subjective evaluation of the gamified MR solution focused on usability, cognitive load, and user experience. Meanwhile, the objective evaluation encompassed the analysis of the robot-assisted movements with and without gamified MREs, a comparative analysis between metrics obtained from Hololens and Vicon data, and the collection of reference data and trajectories. There were twenty-one healthy adults involved in the evaluation of the system. The results with the gamified MREs highlight excellent system usability, low cognitive load, and high user experience. Additionally, integrating gamified MREs into robot-assisted movements enhances shoulder movements. Data collection with Hololens demonstrated to be reliable and consistent. Furthermore, the normal reference values, paths, and velocity profiles obtained from healthy individuals offer a foundation for assessing the performance of individuals with disabilities. In summary, the introduction of gamified MREs for robot-assisted bilateral shoulder movements marks a significant and promising advancement in rehabilitation technology.

Significance of mixed convection and heat transfer flow past a vertical Riga plate in the presence of alumina nanoparticles: Analysis of streamlines for oblique stagnation point

AbstractThe aim of the current study to inspect the magnetic flow properties and heat transport features near an oblique stagnation point of a nanofluid with mixed convection through a vertical Riga plate are examined. The Riga plate is a familiar actuator made out of permanently fixed electrodes and magnets that moved away from the plate due to an exponential decline in the Lorentz force. Nanofluid is taken into consideration due to its peculiar properties, such as remarkable thermal conductivity is the significance of the study. These properties are important in heat exchangers, electronics, advanced nanotechnology, and material sciences. Using usual similarity transformations, the group of leading partial differential equations is distorted into a group of nonlinear ordinary differential equations. Then, a very proficient procedure namely bvp4c is utilized to discover the solution. For particular values of the different influential fluid parameters, the characteristics of the dimensionless temperature and velocity along with drag force and heat transfer are investigated graphically. In addition, the symmetrical results were initiated for both cases of the slip and without slip parameters. It is demonstrated that for greater influence of the volume fraction of nanoparticles, the normal and tangential velocity profile drops down for the instances of aiding and opposing flows due to fluctuations in the presence of slip factor, and absence of slip factor. In contrast, the temperature profile intensifies in both the cases of slip parameters and without the slip parameter owing to the phenomenon of assisting flow and opposing flow subject to superior impressions of the nanoparticle volume fractions. It is also observed that depending on the equilibrium between buoyancy effects, obliqueness, velocity slip parameters, and straining motion, the location of the point of zero shear stress (friction factor on the surface of the wall) is displaced to the right or the left of the origin.

Measurements of the Low-acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories

Low-acceleration gravitational anomaly is investigated with a new method of exploiting the normalized velocity profile v˜≡vp/vc of wide binary stars as a function of the normalized sky-projected radius s/r M, where v p is the sky-projected relative velocity between the pair, v c is the Newtonian circular velocity at the sky-projected separation s, and r M is the MOND radius. With a Monte Carlo method, Gaia observed binaries and their virtual Newtonian counterparts are probabilistically distributed on the s/r M versus v˜ plane, and a logarithmic velocity ratio parameter Γ is measured in the bins of s/r M. With three samples of binaries covering a broad range in size, data quality, and implied fraction of hierarchical systems including a new sample of 6389 binaries selected with accurate distances and radial velocities, I find a unanimous systematic variation from the Newtonian flat line. With Γ = 0 at s/r M ≲ 0.15 or s ≲ 1 kau, I get Γ = 0.068 ± 0.015 (stat) −0.015+0.024 (syst) for s/r M ≳ 0.7 or s ≳ 5 kau. The gravitational anomaly (i.e., acceleration boost) factor given by γ g = 102Γ is measured to be γg=1.37−0.09+0.10 (stat) −0.09+0.16 (syst). With a reduced χ 2 test of Newtonian and Milgromian nonrelativistic theories, I find that Newtonian gravity is ruled out at 5.8σ ( χν2=9.4 ) by the new sample (and 9.2σ by the largest sample used). The Milgromian AQUAL theory is acceptable with 0.7≲χν2≲3.1 . These results agree well with earlier results with the “acceleration-plane analysis” for a variety of samples and the “stacked velocity profile analysis” for a pure binary sample.

A Numerical Approach to Analyzing Shallow Flows over Rough Surfaces

The hydraulic characteristics (such as velocity profiles, near-bed velocity profile, bed shear stress, and resistance coefficients) of shallow flows over rough surfaces were investigated using numerical simulations. A novel method is presented to simulate shallow flows over rough surfaces in a two-dimensional (2D) numerical domain, where the physical numerical domain represents bed topography. Results reveal that the model can accurately predict spatially averaged velocity profiles, turbulence characteristics, shear stresses, and uniform flow depths. The analysis identified two distinct flow regions based on mean and turbulent flow profiles. Results show that the turbulent shear stress profiles provide a more accurate estimation of the bed shear stresses. Resistance coefficients (friction factor or Manning’s roughness coefficient) vary with Froude number and submergence ratio (depth divided by roughness height).

Numerical investigation of MHD mixed convection in an octagonal heat exchanger containing hybrid nanofluid

Nowadays, the advancement of heat transmission for the heat exchanger device is an important field of research for many researchers. In this work, a numerical study has been conducted to investigate the thermal performance of a mixed convective flow through the octagonal heat exchanger covered by hybrid nanofluid (Cu-TiO2-H2O). A magnetic field has been introduced inside the cavity to investigate the mixed convective hydrodynamics heat flow characteristics. The nanofluid cores absorb/release energy to manage heat transmission by increasing or decreasing inside the cavity domain as the host fluid and dispersed hybrid nanofluid circulate within the cavity. After transforming the governing equations into a generalized, non-dimensional formulation, the finite element approach is utilized to solve the associated equations. Additionally, response surface methodology is also applied to test the responses of the associated factors. Heat transport was examined in relation to the effects of nanofluids fusion temperature, boundary wall properties, Reynolds number, Hartmann number and nanoparticle volume fractions. The outcomes of this study are analysed by measuring streamline profiles, isotherms, average Nusselt number, velocity profile, and 2D and 3D response surfaces of the computational domain. The underlying flow controlling parameters for instance Reynolds number (10 ≤ Re ≤ 200), Hartmann number (0 ≤ Ha ≤100), and nanoparticle volume fractions (0 ≤ ϕ ≤ 0.1), the influences have been considered. The findings also reveal that the thermal performance is being boosted due to augmentation of Re and ϕ, but reverse behavior is noticed for Ha. Furthermore, the response surfaces obtained from response surfaces methodology express that the Re and ϕ have shown positive influence, and Ha has shown negative influence on Nuav. Utilizing a hybrid nanofluid of Cu-TiO2-H2O increases the heat transfer capacity of water to 25.75 %. Moreover, the findings could guide to design of a mixed convective heat exchanger for industrial purposes.

About Height of the Surface Air Layer by Sodar Data

Average empirical estimations of the surface air layer height in Moscow have been received by the data of long-term acoustic remote sensing of the atmosphere using MODOS Doppler sodar of METEK (Germany) production. Based on the assumption that the average conditions are close to neutral stratification, this height, as the top of the quasi-linear section of the average long-term wind velocity profile in semi-logarithmic coordinates, is 40–60 m. The wind rotation height, i. e. the height of intersection of day and night wind profiles is on average 95 meters per year. The roughness length in conditions of loose but high urban development in vicinity of Moscow State University in Moscow is 5 m. According to the criterion of the constant wind direction in the surface air layer, its height appears in the average monthly wind direction profiles over the “dead zone” of the sodar (40 m) in approximately one case out of three and usually amounts to 60 m, less often 80 or 100 m. In the rest cases, it is apparently masked by “dead zone”. The average height of the surface layer according to this approach is probably a little less than 50 m, which is close to the estimate obtained from the logarithmic distribution of wind velocity with height in this layer. The daily course of the surface air layer height is noted by the largest values in the afternoon (80–100 m in summer under conditions of prevailing unstable stratification and 60–80 m in winter) and the smallest ones (less than 40 m) in the late evening and at night in summer and from evening to noon in winter.

Experimental study on the interaction between particles and coherent structures in dilute liquid–solid two-phase turbulent boundary layer

In order to reveal the modulation of particles on turbulent coherent structures and particle concentration variations induced by turbulence, particle image velocimetry experiments were performed in a dilute liquid–solid two-phase turbulent boundary layer. Large-scale coherent structures, including streaks and hairpin vortices, were extracted in the liquid–solid two-phase turbulent boundary layer by using multiple methods, such as proper orthogonal decomposition and finite-time Lyapunov exponent. The results showed that the addition of particles thickened the buffer layer of the average velocity profile, weakened the streamwise turbulence intensity at y+ > 10, strengthened the wall-normal turbulence in the near wall region (y+ < 52), and weakened the Reynolds stress in the logarithmic law region. A more thorough study of the turbulent structure revealed that the particles caused the mean spacing of the near-wall streak structure to increase, hairpin vortex migration to slow down, the uplift of hairpin vortex to be suppressed, and the overall size of the hairpin vortex packet to be compressed. This demonstrated that particles could modulate turbulence by inhibiting the development of hairpin vortices.

Onset of absolute instability on a pitching aerofoil

A global transient linear stability analysis of the three-dimensional time-dependent flow around an aerofoil undergoing small-amplitude pitching motion is performed using the optimally time-dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its spatial and temporal evolution, including the formation of a laminar separation bubble and its gradual spanwise modulation via primary global instability, leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of spanwise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted, which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself.

The multi-scale coupled model: a new framework capturing wind farm–atmosphere interaction and global blockage effects

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13 % to 20 % for the modeled regimes.

The splashback radius and the radial velocity profile of galaxy clusters in IllustrisTNG

We used 1697 clusters of galaxies from the TNG300-1 simulation (mass M200c > 1014 M⊙ and redshift range 0.01 ≤ z ≤ 1.04) to explore the physics of the cluster infall region. We used the average radial velocity profile derived from simulated galaxies, vrad(r), and the average velocity dispersion of galaxies at each redshift, σv(r), to explore cluster-centric dynamical radii that characterize the cluster infall region. We revisited the turnaround radius, the limiting outer radius of the infall region, and the radius where the infall velocity has a well-defined minimum. We also explored two new characteristic radii: (i) the point of inflection of vrad(r) that lies within the velocity minimum, and (ii) the smallest radius where σv(r) = |vrad(r)|. These two, nearly coincident, radii mark the inner boundary of the infall region where radial infall ceases to dominate the cluster dynamics. Both of these galaxy velocity based radii lie within 1σ of the observable splashback radius. The minimum in the logarithmic slope of the galaxy number density is an observable proxy for the apocentric radius of the most recently accreted galaxies, the physical splashback radius. The two new dynamically derived radii relate the splashback radius to the inner boundary of the cluster infall region.

Flow resistance over heterogeneous roughness made of spanwise-alternating sandpaper strips

The Reynolds number dependent flow resistance of heterogeneous rough surfaces is largely unknown at present. The present work provides novel reference data for spanwise-alternating sandpaper strips as one idealised case of a heterogeneous rough surface. Experimental data are presented and analysed in direct comparison with drag measurements of homogeneous sandpaper surfaces and numerical simulations. Based on the homogeneous roughness data, the related challenges and sensitivities for the evaluation of roughness functions from experiments and simulations are discussed. A hydraulic channel height is suggested as an alternative measure for the drag impact of rough surfaces in internal flows. For the investigated heterogeneous roughness, it is found that turbulent flow does not exhibit a fully rough flow behaviour, indicating that the assignment of an equivalent sand grain height as commonly applied for homogeneous roughness is not possible. A prediction of the drag behaviour of rough strips based on an average between rough and smooth drag curves appears promising, but requires further refinement to capture the impact of turbulent secondary flows and spatial transients linking smooth and rough surface parts. While turbulent secondary flow induced by the roughness strips yield significant spanwise variation of the mean velocity profile for the investigated rough strips, we show that the spanwise averaged velocity profiles collapse reasonably well with a smooth or homogeneous rough wall flow. This allows to extract a global roughness function from the spanwise averaged flow field in good agreement with the one deduced from global pressure drop measurements.

Analysis of particle dispersion and cavity formation during bulk particle water entry using fully coupled CFD-DEM-VOF approach

This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid (CFD-DEM-VOF) model to simulate the complex behavior of particle-laden flows with free surfaces. The coupling between the fluid and particle phases is established through the implemented continuity, momentum, and alpha transport equation. The coupled particle forces such as drag, pressure gradient, dense virtual mass, viscous, and interface forces are also integrated, with drag and dense virtual mass forces being dependent on local porosity. The integrated conservative alpha transport equation ensures phase volume conservation during interactions between particles and water. Additionally, we have implemented a trilinear interpolation method designed to operate on unstructured hexahedral meshes. This method has been tested for its ability to properly resolve the coupling effects in the numerical simulations, particularly in cases with a relatively low cell-size ratio. The model is validated through three distinct test cases: single particle water entry, dam break with particles, and water entry of a group of particles case. The experimental setup is built to study the dynamics of the water entry of a group of particles, where three key flow features are analyzed: the evolution of average particle velocity, cavity shape, and particle dispersion cloud profiles in water. The tests involve four different scenarios, including two different water levels (16.1 and 20.1 cm) and two different particle densities (2650 and 4000 kg/m3). High-speed videometry and particle tracking velocimetry (using ImageJ/TrackMate) methods are employed for experimental data acquisition. It is demonstrated that numerical results are in excellent agreement with theoretical predictions and experimental data. The study highlights the significance of vortices in cavity shaping and particle dispersion. The validated CFD-DEM-VOF model constitutes a robust tool for simulating particle-laden flows, contributing valuable insights into the complex interplay between particles and fluids.

Direct numerical simulation of laminar, transitional and turbulent radially inward flow between closely spaced corotating disks

This study describes direct numerical simulation (DNS) of radially inward spiralling corotating disk flow with a narrow disk spacing, using the open source solver Nek5000 and the supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. Knowledge about laminar and turbulent regime boundaries in this flow scenario is important for modelling and performance prediction of friction turbines. Simulations are performed in differently sized sections of the flat annulus that is formed by two opposing corotating disk surfaces. Three sets of operating conditions are covered, from the laminar, transitional and turbulent region of a previously determined stability chart respectively. Directly downstream of the inlet boundary, the flow is artificially perturbed with a random body force acting normal to the disk surfaces. Fourier analysis of the DNS flow field reveals that the artificial perturbation is dampened across all wavenumbers for the laminar conditions, while at the transitional conditions a small range of modes is weakly amplified towards the outlet. The identified unstable modes were previously correctly predicted by linear stability analysis. Comparison to experimental velocity profile measurements from a previous study at the same transitional operating conditions suggests strongly perturbed flow during the experiment. For inflow conditions leading to turbulent flow, average velocity profiles from DNS coincide with those from experiment and from commercial fluid simulation software with turbulence modelling (ANSYS CFX). Close to the walls, turbulent dissipation and turbulent kinetic energy distributions do not agree with the ANSYS CFX results. Friction Reynolds number settles at about 118 after turbulent flow has developed from the initial perturbation. Two point correlations and corresponding energy spectra are presented.

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

Comparative predictions of turbulent non-isothermal flow of a viscoplastic fluid with yield stress

RANS simulation of turbulent non-isothermal flow in a pipe by transition of Newtonian fluid into a viscoplastic non-Newtonian fluid is carried out. Carrier phase turbulence was modeled using two-equation isotropic k‒ε˜ – model and Reynolds stress transport model. Results of calculations of Newtonian and non-Newtonian power-law fluids were compared with data of DNS calculations of other authors. Comparisons with data from other works for isothermal Schwedoff-Bingham fluid were performed in this work using k‒ε˜ – model. Satisfactory agreement was obtained with data from other studies for the axial averaged velocity and turbulent kinetic energy radial profiles (the difference is up to 15 %). Reynolds stress transport model showed significant anisotropy between streamwise and transverse velocity fluctuations (up to several times) and good agreement with DNS results of other authors. Averaged and pulsation profiles express the indicated transformation of the non-isothermal turbulent flow.

Particle Image Velocimetry in a Centrifugal Pump: Influence of Walls on the Flow at Different Axial Positions

Abstract For almost a century, humans have relied on centrifugal pumps for the transport of low-viscous fluids in commercial, agricultural, and industrial activities. Details of the fluid flow in impellers often influence the overall performance of the centrifugal pump and may explain unstable and inefficient operations taking place sometimes. However, most studies in the literature were devoted to understanding the flow in the midaxial position of the impeller, only with a few focusing their analysis on regions closer to solid walls. This paper aims to study the water flow in the vicinity of the front and rear covers (shroud and hub) of a radial impeller to address the influence of these walls on the fluid dynamics. For that, experiments using particle image velocimetry (PIV) were conducted in a transparent pump at three different axial planes, and the PIV images were processed to obtain the average velocity fields and profiles, as well as turbulence levels. Our results suggest that: (i) significant angular deviations are observed when the velocity vectors on the peripheral planes are compared with those on the central plane; (ii) the velocity profiles close to the border are similar to those in the middle, but the magnitudes are lower close to the hub than to the shroud; (iii) the turbulent kinetic energy on the periphery is up to eight times greater than that measured at the center. Our results bring new insights that can help propose mathematical models and improve the design of new impellers. A database and technical drawings of the centrifugal pump are also available in this paper so that other researchers can perform numerical simulations and validate them against experimental data.

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

Entrainment and bulk flow characteristics of heated and unheated transient plumes using direct numerical simulations

An off-source volumetrically heated turbulent transient plume, known as transient diabatic plume (TDP), is compared with an unheated transient plume (TP). Both the TDP and TP are simulated using direct numerical simulations at a source Reynolds number (Re) of 2000. The flow is sufficiently resolved till the Kolmogorov (η) scale. The radius of the TP shows a self-similar behavior of linear increase with height after about five diameters from the source hot-patch. However, the velocity does not show a self-similar behavior. The addition of off-source buoyancy in the TDP triples the vertical velocity and also causes an order of magnitude increase in the vorticity magnitude (ω) due to the effect of the baroclinic torque. Compared to the TP, the entrainment coefficient and radius of the TDP increase and this shows enhanced entrainment due to heating. The transient flows fields are analyzed using local scales based on integral quantities of volume, momentum, and buoyancy. Normalizing the vorticity with these integral scales results in a more uniform scaled ωl for both flows. Hence, for both TP and TDP, we use the same values of ωl to quantify the inner and outer boundaries of the turbulent non-turbulent layer (TNTL). The width of the TNTL (δTNTL) decreases by ∼25% due to heating. The conditionally averaged velocity profiles suggest that very close to the outer irrotational boundary (IB) of the TNTL, the TDP exhibits stronger updrafts and downdrafts in comparison to the TP. Entrainment is studied using the mean relative velocity (⟨vn⟩) defined at the IB. The analysis of the components of ⟨vn⟩ reveal that the viscous diffusion component, which is of the order of the Kolmogorov velocity (uη), is balanced by the baroclinic and viscous dissipation components, while the inviscid term is negligible in comparison.

An experimental study of steam turbulent jet condensation & upward propagation of thermal plume into sub-cooled water pool

Supersonic steam’s axial injection into water in a cylindrical vessel (1 m high and 24 cm in diameter) was achieved through a nozzle of 6 mm diameter, located at the center of the vessel. Optical examinations were determined through a steam jet to find out condensation rate, which was allied with the steam mass flux (295–672 kg/m2/s) while leaving the nozzle’s exit. The Reynolds number (i.e., 41,000–73,610) has been estimated based on most swollen section of the steam’s jet. Further beyond the condensation zone, the steam, that has been condensed, progresses into a condensed steam plume, which is surrounded by the sub-cooled water. Particle Image Velocimetry (PIV) has been applied to focus region through the mid axis of the heated water plume along a vertical plane of 100 mm × 100 mm cross sections till 400 mm from the nozzle. Central upward averaged velocity profile of the condensed water thermal plume has been evaluated at 295 and 672 kg/m2s, both have hinted the exponential decrease of mean axial velocity when the plume travels vertically upward. The radial velocity distribution of the mean axial velocity across the radial dispersal of the jet, has been obtained as self-preservable and the mean axial velocity attained the Gaussian profile by incorporating appropriate grading of axial distance and mean velocity. Other significant aspect of the current work is to apply the buoyant scaling evolved from the single-phase non-condensing upward thermal plumes to the condensed upward plume through the relations of volume flow, momentum and buoyant being computed from the steam jet operating conditions. The source values of physical dimensionless parameters such as Reynolds number (Reo), Plume Richardson number (Ripo), entrainment coefficient (αo), buoyant vertical scale (Bo) have been evaluated. Based on the radial spread of the velocity profiles along the vertical distance from the condensation region, the dynamics of the thermal and the jet propagation has been highlighted through the evaluation of the dimensionless buoyant parameters along the downstream of the plume. The present experimental measurements obtained for condensed single-phase plume are compared with the experimental results of the non-condensed single-phase thermal plume to signify the vitality of the dimensionless parameters derived from non-condensed plumes.

Entropy analysis of unsteady MHD nanofluid flow over a stretching surface with effects of variable viscosity and nonuniform heat generation

An unsteady two-dimensional nanofluid flow across a permeable stretched sheet is examined in terms of thermodynamic analysis. Water is utilized as the basic fluid, together with four distinct types of nanoparticles: copper (Cu), copper oxide (CuO), aluminum oxide (Al2O3), and titanium dioxide (TiO2). An external source is used to describe the heat transfer phenomena. The effects of heat generation and absorption are also taken into account. The nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via a similarity transformation. The spectral quasi-linearization approach is then used to numerically integrate the altered equations. Except when otherwise noted, the findings are provided for copper nanoparticle situations. A visual and detailed explanation of the effects of several physical factors on the profiles of dimensionless velocity, temperature, average entropy generation function, skin friction, and the Nusselt number are discussed. As exceptional circumstances of the current findings, there is a strong agreement between the current conclusion and the findings of the other researchers. The average entropy generation number, temperature, and velocity profiles are shown to be strongly influenced by regulating factors. It is concluded that the average entropy generation decreased in the presence of a temperature- and space-dependent heat source/sink, but it improves with enhanced viscosity parameter. The significance of the present study has frequent applications in the major area of heat transfer enhancement in renewable energy systems, industrial thermal management, and also materials processing.