Dimensionless Time Research Articles

Sustainability assessment of hydropower water wheels with downstream migrating fish and blade strike modelling

Water wheels are low head hydropower converters considered fish friendly, although their ecological behavior has not been scientifically assessed. The results presented in the available reports are not generalized (thus hardly applicable in engineering applications), and they have not been performed at different hydraulic conditions or wheel characteristics. This work reviews available information on the ecological performance of water wheels to define the state of the art. To generalize and interpret results, a blade-strike theoretical model is developed and calibrated on field tests conducted in Germany on ten water wheels, that represent the most systematic and comprehensive series of tests. The dimensionless time T* (ratio between time needed for a fish of a certain size to access the bucket and the time for filling the bucket) and the geometric-hydraulic parameter α were identified as key parameters to estimate the ecological behavior of horizontal axis water wheels. The average injury likelihood induced by the blade strike on fish was 0.34% and 3.56% for T* < 1 and T* > 1, respectively, while the average mortality likelihood is 29% of the injury likelihood for T* < 1, and 26% for T* > 1, corresponding to a fish mortality rate of 0.10% and 0.94%, respectively. The concept of T* was applied to a dataset of water wheels in operation to estimate their compatibility with fish passage.

Adsorption Desorption Operations of Multilayer Desiccant Packed Bed for Dehumidification Applications (Dept.M)

In this work, the effect of design and operating parameters on the performance of a multilayer desiccant packed bed was theoretically and experimentally studied. In the experimental work, a silica gel packed bed of eight layers has been studied. The transient value of the mass of adsorbed water and desorbed water were measured for different values of the bed length. The theoretical model shows the dependence of the dimensionless value of water content in the bed on the dimensionless time. Also the model shows that the dimensionless temperature depends on the bed characteristics and bed water content. The effect of inlet air humidity and velocity on the adsorption process for each bed layer was studied at different inlet velocity and at different air humidity. The effect of inlet temperature on desorption process for each packed bed layer was also studied at different inlet temperatures. The theoretical model also introduces an equation which can be used to predict the optimum bed length. Good agreement between experimental and theoretical results was found.

Electrohydrodynamic instability of confined viscoelastic liquid jets

Linear stability analysis is performed to study the electrohydrodynamic instability of viscoelastic jets subjected to axisymmetric (m=0) and first non-axisymmetric (m=1) perturbations in the creeping-flow limit. The viscoelastic liquid jet is under the influence of a radially applied electric field induced by a concentrically placed electrode located at a finite gap width from the jet. The leaky dielectric model is used to account for the finite conductivity of the fluid. The gap between the liquid jet and the electrode is assumed to be occupied by a hydrodynamically passive gas. The influence of the applied electric potential, electrode width, electrical properties, fluid elasticity, and solvent viscosity on the stability of the jet is analyzed comprehensively. For m=0 mode, the electric field has a dual effect on the stability of a Newtonian jet above a critical electrode width to jet radius ratio (Rcr). Here, the dual effect means that the electric field has a stabilizing effect for low wavenumbers (k) and a destabilizing effect for higher k. However, for R<Rcr, the electric field has a uniformly destabilizing effect, and the dual nature disappears. In the limit of perfectly conducting Newtonian jet, Rcr = 2.7. The maximum growth rate increases with an increase in Deborah number (De), which is a dimensionless relaxation time of the fluid, but the range of unstable wavenumbers remains unaffected due to an increase in De. For m=0 mode, there exists a critical Deborah number (Decr), for given values of other physical parameters, above which the growth rate diverges. This behavior is similar to the previous results for the planar geometry and is caused due to the neglect of inertia. As the conductivity of the liquid increases, the Decr decreases and reaches an asymptotic value in the limit of a perfect conductor. The inclusion of elasticity has no effect on the Rcr value, thus suggesting that the dual nature of the electric field is independent of fluid elasticity. The singularity in the growth rate is shown to be mitigated by introducing solvent viscous stresses into the model. Thus, the present study shows that finite electrode distance and elasticity have important consequences on the stability of the liquid jet for the axisymmetric mode. For m=1 mode, the growth rate is singular at low wavenumbers which is due to the neglect of inertia of the system. For the Newtonian case, the range of wavenumbers where the growth rates are singular increases with either increasing the electric potential or decreasing the electrode width. Inclusion of elasticity increases the range of wavenumbers where the growth rates are singular, whereas the range of unstable wavenumbers remains unchanged. Therefore, the neglect of inertia gives rise to non-physical growth rates even in the Newtonian flow limit for m=1 mode, compared to m=0 mode where the singularity of growth rate was observed for the Maxwell fluid above Decr.

A multistate first-order Markov model for modeling time distribution of extreme rainfall events

The time distribution of extreme rainfall events is a significant property that governs the design of urban stormwater management structures. Accuracy in characterizing this behavior can significantly influence the design of hydraulic structures. Current methods used for this purpose either tend to be generic and hence sacrifice on accuracy or need a lot of model parameters and input data. In this study, a computationally efficient multistate first-order Markov model is proposed for use in characterizing the inherently stochastic nature of the dimensionless time distribution of extreme rainfall. The model was applied to bivariate extremes at 10 stations in India and 205 stations in the United States (US). A comprehensive performance evaluation was carried out with one-hundred stochastically generated extremes for each historically observed extreme rainfall event. The comparisons included: 1-h (15-min); 2-h (30-min); and, 3-h (45-min) peak rainfall intensities for India and (US) stations, respectively; number of first, second, third, and fourth-quartile storms; the dependence of peak rainfall intensity on total depth and duration; and, return levels and return periods of peak discharge when these extremes were applied on a hypothetical urban catchment. Results show that the model efficiently characterizes the time distribution of extremes with: Nash–Sutcliffe-Efficiency > 0.85 for peak rainfall intensity and peak discharge; < 20% error in reproducing different quartile storms; and, < 0.15 error in correlation analysis at all study locations. Hence the model can be used to effectively reproduce the time distribution of extreme rainfall events, thus increasing the confidence of design of urban stormwater management structures.

Particle acceleration and pressure gradient in a solitary wave traveling over a horizontal bed

This study presents experimental data on the hydrodynamic features of a nonlinear solitary wave of height H0 = 2.9 cm propagating over a horizontal bed in otherwise still water depth h0 = 8.0 cm. High-speed particle image velocimetry is used to quantify the local and convective particle accelerations and pressure gradients under the solitary wave. It is found that the magnitudes of the horizontal and vertical particle local accelerations are invariably larger than their convective counterparts, highlighting the important contribution of local acceleration to the pressure gradient in a solitary wave. The dimensionless pressure gradient in the horizontal direction is favorable, zero, and adverse for time before, at, and after the wave crest passes the section of interest. The dimensionless adverse pressure gradient exhibits a maximum for the dimensionless time T[=t(g/h0)1/2, where g is the gravitational acceleration and t is the time with respect to the crest passing the section] = 1.39, at which the dimensionless local acceleration has a negative maximum. Subsequently, flow reversal takes place above the bed surface. The relationship is elucidated between flow reversal at the bed surface and the evolution of the adverse pressure gradient in the near-bed zone, where uniform horizontal/free stream velocity exists.

Numerical investigation on the melting characteristics of wax for the safe and energy-efficiency transportation of crude oil pipelines

Wax precipitation affects the normal transportation of crude oil pipeline. Wax is generally removed by hot washing. Reducing energy of hot washing is the key to the security and energy-saving operation. It is necessary to reveal the heat transfer characteristics of the process. The melting characteristics of paraffin in the gathering and transportation pipeline are studied by numerical simulation in this paper. Mathematical model is established. Melting and flow characteristics of paraffin in gathering pipelines are researched. The effects of water temperature, size of spherical paraffin, and initial temperature on the central temperature and liquid phase ratio of the ball are analyzed. The melting stage is divided into informal melting stage and formal melting stage. The correlations between the dimensionless time Fo number, Ste number, Ra number, and subcooling degree Ci are proposed based on the dimensionless analysis. The correlation can be used to predict the complete melting time of paraffin in natural convection flow field. It is of guiding significance for hot washing.

A moving-boundary based dynamic model for predicting the transient free convection and thermal stratification in liquefied gas storage tank

Thermal stratification occurs frequently in liquefied gas storage tank due to inevitable heat leak or unexpected thermal attack, and has vital influence on equipment safety. For predicting the thermal stratification of liquefied gas, a comprehensive dynamic model of the thermodynamic process in liquefied gas storage tank is proposed in this paper. In the model, the transient free convection in the vicinity of tank walls is simulated by a set of integral equations using the moving boundary method; the thermal stratification is predicted based on the coupling effects of the free convection and interfacial heat-mass transfer; the pressure build-up in storage tank is calculated according to the thermal non-equilibrium response of the liquefied gas. Comparisons of model predictions and experimental results show consistent trends of the thermal stratification and pressure response under different heat fluxes and liquid fill levels. The results indicate that the free convection is enhanced by the development of boundary layer at the initial phase of tank heat-up, and subsequently impeded by the thermal stratification development; the penetration time for thermal stratification will be shortened with the increase of external heat fluxes, while the dimensionless penetration time expressed by the equivalent thermal diffusivity maintains almost constant under various external heat fluxes.

Micro-segregation Study of Directional Solidified Fe–Mn–C–Al TWIP Steels

Chemical variation occurring during the solidification process can cause undesirable effects on the material property, especially for alloys with high solute content. The current study investigated the distributions of solute elements in directional solidified Fe–Mn–C–Al TWIP steels and compared the micro-segregation with various pulling rates and C contents using the phase field model and the grid analysis based on the data performed by EPMA, which could provide advice for mitigating micro-segregation in high Mn steel. The results indicated that C and Mn preferentially segregated toward the liquid phase, while Al entered the solid phase. The occurrence of solid-state diffusion was observed, which led to a homogenization effect in the solid phase during solidification. The pulling speed increase made a more severe micro-segregation because the change of pulling speeds had more effect on the SDAS than on the local solidification time; thus, the dimensionless diffusion time decreased with increasing pulling rates, representing a more serious micro-segregation. For a C content increasing from 0.06 to 0.68 wt pct, the micro-segregation level of C and Al reduced first and then increased, which was caused by the change in the solidification mode. The continuous accumulation of solute elements and the slower solute element diffusion in austenite in combination led to the presence of more severe micro-segregation in the case of one-phase solidification. Besides, a C content increase could attract Mn, resulting in more serious Mn micro-segregation.

Dynamic spreading characteristics of droplet on the hydrophobic surface with microstructures

The behaviors of droplet impact on the two different microstructures (regular micro-grooved structure and irregular microstructure) exhibiting hydrophobic features are investigated experimentally in this study. Images captured by the high-speed cameras are used to examine the differences between regular and irregular microstructures on the droplet impact process. Dimensionless parameters including dimensionless spreading factor, height and time are introduced to quantitatively analyze the spreading process. The results show that two microstructure accelerate the droplet to reach the maximum dimensionless spreading factor and height, compared with flat surface. It should be also noticed that the droplet breaks up while bouncing on the irregular microstructure surface, which is because that the sum of kinetic and surface energy is slightly higher than the initial total energy during receding process. This study further shows that the beating phenomenon of the dimensionless height of the droplet impact is developed on the regular micro-grooved structure surface.

Deformation and regimes of liquid column during water exit of a partially submerged sphere using the front-tracking lattice Boltzmann method

When a solid sphere exits water at a given velocity, the liquid column is pulled out of a liquid reservoir. The present study focuses on the dynamic deformation of the liquid column and on the identification of the liquid column regime on the Weber number and dimensionless time (We-t*) map. The three-dimensional model of water exit has been established on the basis of the lattice Boltzmann method. A mass tracking algorithm was incorporated to capture the free surface, where the liquid–gas​ two-phase flow is simplified to a single-phase free surface flow. The surface tension is included by adding a perturbation term and the gravity as a body force is introduced in form of calculating the equilibrium distribution with an altered velocity. The contact angle condition in numerical simulation is not considered. The accuracy of the numerical results is demonstrated through the comparisons with the prior numerical and the experimental results in the literature. A parametric study has been conducted numerically on the radius and volume and of liquid column. Besides, the relationship between the pinch-off time of a liquid column and the Froude number has been obtained. Moreover, the evolution of the liquid column shape with a wide range of the Weber number and time scales are discussed based on the number of ligaments and droplets. The liquid column exhibits different characteristics and has been divided into three regimes. The transition between different regimes has been analyzed and the critical Weber number is given.

Cavitation bubble collapse between parallel rigid walls with the three-dimensional multi-relaxation time pseudopotential lattice Boltzmann method

Studying the flow characteristics of bubbles in a narrow gap is an important problem related to bearing cavitation and gas–liquid two-phase flow. In this paper, we present a modified three-dimensional multi-relaxation-time pseudo-potential model for large density ratio multiphase phenomena. The accuracy of the model is verified by the Maxwell construction, Laplace law, and Rayleigh–Plesset equation. The influence of the force scheme parameter and the dimensionless relaxation time on the thermodynamic consistency of the model is analyzed. The results show that the three-dimensional lattice Boltzmann pseudo-potential model proposed in this paper has good numerical stability in simulating multiphase phenomena. Furthermore, the cavitation bubble collapse process between parallel rigid walls is simulated by the proposed model. The collapse process obtained by the present method agrees well with the experimental result. The different orientations for the bubble to the wall exert a significant influence on the variation of the pressure field, velocity field, and evolution of maximum pressure and micro-jet velocity. During the cavitation bubble collapse process, the pressure and the velocity at the collapse point will increase instantaneously, and the orientation for the bubble to the wall is a key factor to determine the collapsed form of the cavitation bubble. The results verified the practicability of the addressed model to study the collapse of three-dimensional cavitation bubbles in the presence of parallel rigid walls.

To seal or not to seal: The closure dynamics of a splash curtain

When an object impacts the free surface of a liquid, it ejects a splash curtain upwards and creates an air cavity below the free surface. As the object descends into the liquid, the air cavity eventually closes under the action of hydrostatic pressure (deep seal). In contrast, the surface curtain may splash outwards or dome over and close, creating a surface seal. In this paper we experimentally investigate how the splash curtain dynamics are governed by the interplay of cavity pressure difference, gravity, and surface tension and how they control the occurrence, or not, of surface seal. Based on the experimental observations and measurements, we develop an analytical model to describe the trajectory and dynamics of the splash curtain. The model enables us to reveal the scaling relationship for the dimensionless surface seal time and discover the existence of a critical dimensionless number that predicts the occurrence of surface seal. This scaling indicates that the most significant parameter governing the occurrence of surface seal is the velocity of the airflow rushing into the cavity. This is in contrast to the current understanding which considers the impact velocity as the determinant parameter.

Analytical Study of Nonstationary Modes in Recuperative Heat Exchangers

Recuperative heat exchanger transient operation modes during the start-up were considered in order to identify the time for establishing the stationary mode. This is important in carrying out technological processes that require constancy in values of certain parameters ensuring both product quality and process safety. The research was carried out using the analytical method for direct-flow and counter-flow heat exchangers. It was demonstrated that stationary state establishment in the direct-flow heat exchangers occurs immediately after the heat carrier gets into the apparatus. It should be noted that the entire apparatus reaches the stationary mode, when the slower heat carrier arrives at the apparatus output section. In case of a heat exchanger with the heat carrier counter-flow, it was found out that at the moment of the less heated heat carrier appearing at the apparatus output section, it was having the highest temperature. Then the temperature was decreasing, and after passing its minimum was beginning to oscillate along a curve with the damping amplitude. In the case under consideration, the stationary process started, when the dimensionless time value was ϕ ≥ 0.5. The indicated solution was obtained under assumption that thermal and physical characteristics were constant in time and space. It was assumed that total heat capacity of the heat exchanger heat transferring wall was infinitesimal. This assumption is valid with an error of up to 1 % at Fo ≥ 100, which is the case in most practical cases. For apparatuses under study, a formula was also obtained for the time required to reach the stationary state

Application of level-set method in simulation of normal and cancer cells deformability within a microfluidic device

Application of microfluidic systems for the study of cellular behaviors has been a flourishing area of research in the past decade. In the process of probing cell biomechanics the passage of a cell through a narrow microchannel or a small pore has attracted much attention during the recent years. And the study of cellular deformability and transportability using these systems with enhanced resolution and accuracy has opened a new paradigm for high-throughput characterization of both healthy and diseased cell populations.Here we use the level-set method to explore the relationship between the transit time and mechanical properties of normal white blood cells (WBCs) and breast cancer epithelial cells (MCF7) under different microenvironmental parameters (i.e., pressure difference, cell size, effective cell surface tension, constriction size and taper angle) in a 2-D computational domain by considering the cell as a viscous drop. The novel biomechanical relations are obtained for each cell type by the Response Surface Method (RSM), relating microenvironmental parameters to the dimensionless entry time of the normal and cancer cells. Our results revealed that MCF7 cells show asignificantly different behavior (a bifurcating behavior when the pressure difference of inlet/outlet increases) in regards to the dimensionless entry time as a function of microchannel taper angle in comparison with the WBC. These results suggest that the microenvironmental parameters have a significant effect on the transportability of the cells and different cells have different behaviors in response to a specific microenvironmental parameter. Finally, it can be claimed that this method can be also utilized to distinguish between benign and cancerous cells or even to probe tumor heterogeneity toward high throughput cell cytometry.

A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation

We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method for the assimilation window from 2004.50 to 2014.25 confirms that the linear approximation holds for 10-year assimilation window with our iterative ensemble renewal method. We demonstrate that the forecast performance of our data assimilation and forecast scheme is comparable with that of IGRF-12 by comparing data misfits 4.5 years after the release epoch. For estimation of our IGRF-13SV candidate model, we set assimilation window from 2009.50 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.

On the diffusion reaction of fourth-grade hydromagnetic fluid flow and thermal criticality in a plane Couette medium

This study investigates hydromagnetic fourth-grade reactive diffusion, exothermic temperature distribution of the fluid flow and ignition criticality in a channel. This is important to improve the optimal efficiency of engineering devices and industrial machines. The fully exothermic combustible reaction occurs in a Couette medium with molecular diffusion. Ignoring material reacting consumption, the heat exchange in the system is greater than the ambient heat exchange, and the viscoelastic liquid is propelled by pre-exponential reaction rate and upper wall motion of the device. The resulted highly nonlinear dimensionless time variation, boundary value equations are solved by finite semi-discretization difference method. The obtained solutions for various parameters dependent flow characteristic are plotted and discussed. It is seen that activation energy increases the system thermal criticality while chemical kinetics decreases thermal ignition. Also, it is noticed from the study that the terms that raises the heat generation must be managed in order to prevent solution explosion and enhances optimal performance of engineering devices. The results from this study will assist in understanding the safe and unsafe regime of a system which can help in the chemical synthesis industries and thermal engineering operations.

Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated With Uniform Heat Flux: Scrutiny of New Critical Fourier Numbers

Abstract The alternate infinite series at “small time” have been used to analyze the time variation of surface temperatures (ϕs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for ϕs in a plate, cylinder, and sphere in the “small time” sub-domain extending from 0 to the critical dimensionless time or critical Fourier number. For the “large time” sub-domain, the exact solution is approximated in two ways: with the “one-term” series and with the simple asymptotes corresponding to extreme “large time” conditions. Maximum relative errors of 1.23%, 6.24%, and 0.96% in ϕs for the plate, cylinder, and sphere are τcr obtained, respectively, with the “small time”—“large time” approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr is proposed to minimize the maximum relative error of the approximated solutions so that values of 1.19%, 3.93%, and 0.16% are then obtained for the plate, cylinder, and sphere, respectively, with the “small time”—“large time” approximation. For the “small time”—“one-term” approximation maximum relative errors of 0.024%, 1.33%, and 0.004% for the plate, cylinder, and sphere are obtained, respectively, with this approach.

Microstructural Capture of Living Ultrathin Polymer Brush Evolution via Kinetic Simulation Studies.

Performing dynamic off-lattice multicanonical Monte Carlo simulations, we study the statics, dynamics, and scission-recombination kinetics of a self-assembled in situ-polymerized polydisperse living polymer brush (LPB), designed by surface-initiated living polymerization. The living brush is initially grown from a two-dimensional substrate by end-monomer polymerization-depolymerization reactions through seeding of initiator arrays on the grafting plane which come in contact with a solution of nonbonded monomers under good solvent conditions. The polydispersity is shown to significantly deviate from the Flory-Schulz type for low temperatures because of pronounced diffusion limitation effects on the rate of the equilibration reaction. The self-avoiding chains take up fairly compact structures of typical size Rg(N) ∼ Nν in rigorously two-dimensional (d = 2) melt, with ν being the inverse fractal dimension (ν = 1/d). The Kratky description of the intramolecular structure factor F(q), in keeping with the concept of generalized Porod scattering from compact particles with fractal contour, discloses a robust nonmonotonic fashion with qdF(q) ∼ (qRg)-3/4 in the intermediate-q regime. It is found that the kinetics of LPB growth, given by the variation of the mean chain length, follows a power law ⟨N(t)⟩ ∝ t1/3 with elapsed time after the onset of polymerization, whereby the instantaneous molecular weight distribution (MWD) of the chains c(N) retains its functional form. The variation of ⟨N(t)⟩ during quenches of the LPB to different temperatures T can be described by a single master curve in units of dimensionless time t/τ∞, where τ∞ is the typical (final temperature T∞-dependent) relaxation time which is found to scale as τ∞ ∝ ⟨N(t = ∞)⟩5 with the ultimate average length of the chains. The equilibrium monomer density profile ϕ(z) of the LPB varies as ϕ(z) ∝ ϕ-α with the concentration of segments ϕ in the system and the probability distribution c(N) of chain lengths N in the brush layer scales as c(N) ∝ N-τ. The computed exponents α ≈ 0.64 and τ ≈ 1.70 are in good agreement with those predicted within the context of the Diffusion-Limited Aggregation theory, α = 2/3 and τ = 7/4.

Diastolic Vortex Alterations With Reducing Left Ventricular Volume: An In Vitro Study.

Despite the large number of studies of intraventricular filling dynamics for potential clinical applications, little is known as to how the diastolic vortex ring properties are altered with reduction in internal volume of the cardiac left ventricle (LV). The latter is of particular importance in LV diastolic dysfunction (LVDD) and in congenital diseases such as hypertrophic cardiomyopathy (HCM), where LV hypertrophy (LVH) can reduce LV internal volume. We hypothesized that peak circulation and the rate of decay of circulation of the diastolic vortex would be altered with reducing end diastolic volume (EDV) due to increasing confinement. We tested this hypothesis on physical models of normal LV and HCM geometries, under identical prescribed inflow profiles and for multiple EDVs, using time-resolved particle image velocimetry (TR-PIV) measurements on a left heart simulator. Formation and pinch-off of the vortex ring were nearly unaffected with changes to geometry and EDV. Pinch-off occurred before the end of early filling (E-wave) in all test conditions. Peak circulation of the vortex core near the LV outflow tract (LVOT) increased with lowering EDV and was lowest for the HCM model. The rate of decay of normalized circulation in dimensionless formation time (T*) increased with decreasing EDV. When using a modified version of T* that included average LV cross-sectional area and EDV, normalized circulation of all tested EDVs collapsed closely in the normal LV model (10% maximum difference between EDVs). Collectively, our results show that LV shape and internal volume play a critical role in diastolic vortex ring dynamics.

The effects of double-diffusion and viscous dissipation on the oscillatory convection in a viscoelastic fluid saturated porous layer

The effects of the double-diffusion and viscous dissipation on the convective instability in a horizontal porous layer are investigated. The porous medium is saturated with a binary viscoelastic fluid. The Oldroyd-B model of viscoelastic fluid is considered. Constant temperature and concentration differences are maintained between the boundaries. A basic flow is present in the horizontal direction. The governing parameters are the thermal Rayleigh number (RaT), solutal Rayleigh number (RaS), Gebhart number (Ge), Lewis number (Le), Péclet number (Pe), dimensionless relaxation time (λ1), and dimensionless retardation time (λ2). A small perturbation to the basic flow is assumed, and a linear stability analysis is performed. A detailed discussion is carried out considering RaT as the eigenvalue. The critical wave number and frequency are also derived for a wide range of Lewis numbers and solutal Rayleigh numbers. The oscillatory modes are analyzed. It is found that transverse rolls are the preferred mode for the onset of oscillatory convection, except for some special cases. Moreover, a negative solutal Rayleigh number stabilizes the flow. An opposite effect is seen in the presence of a positive solutal Rayleigh number.