Unsteady Regime Research Articles

Numerical investigations of the wake behind a confined flat plate

The two-dimensional flow around a confined flat plate is simulated with the spectral element code, Nek5000. Direct numerical simulations were carried out at low Reynolds numbers Re (between 10⩽Re⩽200) and various blockage ratios β (between 0.1⩽β⩽0.9) and compared with the confined two-dimensional circular cylinder flow previously reported by Sahin and Owens (2004). Four distinct flow regimes are observed for the flow over a confined flat plate. The first is a steady symmetric wake where the vortices are evenly distributed along the centerline of the channel. The second is an unsteady symmetric regime which upon time-averaging the instantaneous flow field, the wake profile is symmetric. The third is an asymmetric steady wake where the flow is steady but the vortices in the wake are skewed towards one of the channel walls. The first three have been reported for the confined flow over a circular cylinder. However, a fourth flow regime defined as unsteady asymmetric wake is found for a flat plate at β = 0.8. This flow regime was not reported in prior studies on the confined flow over a confined cylinder. Analysis using linear stability analysis is also reported in this paper which confirms the trends reported in this paper. Effects of the confinement on the wake of a flat plate on the hydrodynamic forces such as the mean drag coefficient and Strouhal number have also been documented for the same range of Re and β and compared with the flow over a confined cylinder.

A versatile friction model for Newtonian liquids flowing under unsteady regimes in pipes

A versatile friction model for Newtonian liquids flowing under unsteady regimes in pipes

Effects of viscoelasticity on the onset of vortex shedding and forces applied on a cylinder in unsteady flow regime

The present paper aims to investigate the effect of viscoelasticity on the onset of vortex shedding of a high concentration polymer solution over a cylinder using the finite volume method for the first time. To describe the behavior of the viscoelastic fluid, mathematically, the Phan–Thien–Tanner (PTT) model is employed. The convergence problems are resolved using the rheoFoam solver developed by previous researchers based on the log-conformation method. The exact critical Reynolds number (Recr), which corresponds to the onset of vortex shedding, is estimated by implementing numerous unsteady simulations at each elasticity number (El). The Recr is also calculated at every retardation ratio (β) and elongational viscosity. The results revealed a significant impact of viscoelasticity on Recr so that the flow of a high viscosity ratio PTT becomes unstable at higher Re (at very low El) or lower Re (at higher El), compared to a Newtonian fluid. In addition, Recr decreases linearly with β according to Recr=−34.5β+46.525 and increases with extensional viscosity. It is also found that β plays a vital role in the effect of viscoelasticity on the flow parameters. The averaged drag coefficient (CD¯) and the amplitude of lift coefficient (CLmax) do not have similar behaviors for low and high β. Moreover, viscoelasticity enlarges the vortices and increases the shedding frequency. A comprehensive physical analysis of flow structures is carried out using the distribution of time-averaged stress components and pressure over the cylinder. The numerical results demonstrated the three regimes of drag reduction at El < 0.015, drag enhancement at 0.015 < E1 < 1, and a Newtonian behavior at El > 1 that is an opposite trend compared to a steady regime. The variations of CLmax with El are also similar to CD¯, but at different critical elasticity numbers (El = 0.005 and 2). It is found that the normal stress changes the drag force by the variation of pressure distribution over the cylinder, while the shear stress directly affects the drag and lift forces. In addition, the viscoelasticity decreases the size of the vortices behind the cylinder and increases their vorticity, and changes the position of maximum normal stress, which leads to drag variations. It was also concluded that the higher the elongational viscosities, the lower the shedding frequency.

ГЕОЭКОЛОГИЧЕСКИЕ АСПЕКТЫ ТРАНСПОРТА НАНОСОВ В ВОДНЫХ ОБЪЕКТАХ: НОВЫЕ ПОДХОДЫ И ФОРМУЛЫ

Calculations of the solid flow of water bodies in various geoecological applications are often complicated by irregular and poor-quality observational data. With the existing multitude of formulas for sediment flow, the results of calculations using them often show unsatisfactory quality, especially under conditions of an irregular, unsteady regime of river flow. The situation is aggravated by additional factors of solid matter inflow into the stream and the influence of hydraulic engineering measures and structures. In this case, the relevance of reliable calculations of solid flow (sediment load, turbidity and transporting capacity of the flow) is undoubtedly due to many areas of water management activities. It is quite obvious that calculations of solid flow should have a theoretical basis, unambiguously coupled with the processes of two-phase mass transfer in the river flow, as well as be based on standard hydrometric observation data. The conclusion of new and a review of previously developed methods for calculating solid runoff presented in this paper allows us to give a sufficiently reliable assessment of hydraulic variables of the state of two-phase mass transfer in a water body.

Unsteady Regimes of Hydrogen Ignition and Flame Stabilization in a Channel

Unsteady Regimes of Hydrogen Ignition and Flame Stabilization in a Channel

DERIVATION OF THE EQUATION OF UNSTEADY-STATE MOISTURE BEHAVIOUR IN THE ENCLOSING STRUCTURES OF BUILDINGS USING A DISCRETE-CONTINUOUS APPROACH

Two differential equations of moisture transfer based on the theory of moisture potential have been considered. The first equation includes the record of moisture transfer mechanisms of vapor and liquid phases and their relationship. The second equation is a simplified form of the first equation which makes it possible to apply a discrete-continuous approach. The peculiar properties of the boundary conditions setting of the outside air for temperature and humidity fields have been presented. It is proved that the use of the discrete-continuous method provides high accuracy of calculations and can be used in engineering practice to assess the unsteady humidity regime of enclosing structures.

Screening analysis and unconstrained optimization of a small-scale vertical axis wind turbine

The demand for alternative and renewable energy sources has been substantially growing in recent years, mainly steered by economic and environmental inconveniences of conventional energy sources, such as oil and its derivatives. In this context, wind energy has emerged as an attractive renewable source, envisioning possibilities of developing more efficient equipment to meet the ever-growing energy demand. In this work, we coupled Computational Fluid Dynamics (CFD) with an optimization based on response surface (RS) methodologies to find an optimal design for a small-scale NACA 0021 Darrieus vertical axis wind turbine (VAWT) operating at a tip speed ratio of 2.63. For that, we investigated four geometric parameters: number of blades (N), rotor diameter (D), chord length (c), and pitch angle (β). For the numerical model, we considered a two-dimensional, incompressible, turbulent, and unsteady flow regime. A sensitivity analysis (SA) via Morris’ method was performed to identify the influence of the four geometric parameters on the turbine aerodynamic performance. Our results reveal that the pitch angle (β) contributes the most (58%) to the turbine performance. The resulting optimized turbine design increased the conversion efficiency by 40%. Additionally, we also present a detailed discussion on the flow phenomenology considering the impact of each one of the four geometric parameters on the power coefficient. Finally, the strategy adopted here, in which a qualitative sensitivity analysis combined to the response surface and unconstrained optimization, was shown to be robust and can be applied to high-dimensional and computational-expensive CFD models to reduce costs with adequate results regarding fluid flow phenomena.

Numerical and physical study of transitions to unsteady modes of melt flow with the Prandtl number 16 in the Czochralski method

The evolution of the flow structure and heat transfer with an increase in the characteristic temperature drop in the ranges of Grashof and Marangoni numbers 3558 ≤ Gr ≤ 7116 and 2970 ≤ Ma ≤ 5939 are investigated numerically. The boundary of the transition to unsteady flow and heat transfer regimes has been determined.

Statistical analysis of vapor distribution in a cavitation flow based on an ensemble of instantaneous liquid velocity fields

A new method was developed for statistical analysis of ensembles of instantaneous velocity fields measured by PIV in liquid (continuous phase) to determine the distribution of the vapor phase in cavitating flow. The method is based on two main principles: the absence of tracers used for PIV measurements in vapor, and the statistical independence of individual measurements. This allowed establishing an exponential dependence of repeatability of the vapor phase at a certain point of a cavitating flow. Compliance with this theoretical law was verified using the Pearson chi-square test. All theoretical distributions were divided into several groups depending on the time-averaged local vapor content calculated over the entire ensemble of realizations and the probability of a single event. As a result, dimensions of the stationary part of an attached cavity and the place of detachments of cloud cavities from the hydrofoil surface were determined using the new method of statistical analysis for an unsteady cloud cavitation regime.

Numerical simulations of MHD flows around a 180-degree sharp bend under a strong transverse magnetic field

The quasi-two-dimensional flow of a liquid metal subjected to a strong transverse magnetic field around a 180-degree sharp bend is investigated by means of parametric numerical simulations where the Reynolds number Re, Hartmann number Ha and the gap ratio β (defined as the ratio of the gap thickness to the inlet width) vary in the respective ranges [100–50 000], [100–2000] and [0.04–1]. Both steady-state flow solutions and the evolution of unsteady flow regimes can be captured within this parameter space. The critical Reynolds number for transition from steady to unsteady flow increases as Ha increases for all β. It is shown, for 0.04 ⩽ β ⩽ 0.25, the critical Reynolds number remains almost linear relationship with the parameter Re/Ha0.9, whereas for β = 1, the key parameter is dominated by Re/Ha0.6. The present simulations aim to investigate the physical mechanism of this phenomenon and characterizing the position where the vortices are shed from the free shear layer. We discover that the vortices shedding is originated in the outlet region for 0.04 ⩽ β ⩽ 0.25 other than the turning part in bend region for β = 1. Additionally, the free shear layer separates the recirculation bubble from mainstream and its instability is proposed to interpret the transition, commonly known as Kelvin–Helmholtz instability. The effect of a strong transverse magnetic field on flow characteristics is considered such as the length of recirculation bubbles and the pressure drop between inlet and outlet. A further frequency analysis reveals that at the end of vortices shedding, the oblique waves resonance exists, or a new vortex street consisting of the vortices detached from the boundary layer and upstream fluctuations appears. Finally, according to the influence of β on the transition, we present a modified map of fluid regimes for prediction, which provides useful information for improved mixing and heat transport.

Effect of Wave Instabilities in Thermal and Solutal Mixing of Double-Diffusive Opposed Jets Impinging in a Passive-Mixer

Abstract Two-dimensional (2D) numerical experiments are performed to investigate the flow instabilities and mixing of different nonisothermal counterflowing jets in a passive-mixer. The fluid is modeled as a binary mixture with thermal and solutal buoyancy effects considered through the Boussinesq approximation. The streams are arranged in a thermal and solutal buoyancy aiding configuration. Computations are carried out for three different ratios of the upper jet bulk velocity to the lower jet bulk velocity (VR), namely, VR = 0.5, 1.0, and 2. Within the parametric domain of RiT and RiC defined by region (RiT + RiC) ≤ 3, the instability causing transition from steady to unsteady flow regime is observed for VR = 1 and 2, while no transition is found to occur at VR = 0.5. Using Landau theory, it is established that the transition from steady to unsteady flow regime is a supercritical Hopf bifurcation. A complete regime map identifying the steady and unsteady flow regimes, within the parametric space of this study, is obtained by plotting the neutral curves of RiC and RiT (obtained using Landau theory) for different values of VR. Proper orthogonal decomposition (POD) analysis of the unsteady flows at VR = 1 establishes the presence of standing waves. However, for VR = 2, the presence of degenerate pairs in the POD eigenspectrum ascertains the presence of traveling waves in the unsteady flows. The standing wave unsteady flow mode is found to yield the highest rate of mixing.

Physicochemical mechanisms of the growth of oxide crystals on the surface of tungsten conductors heated by electric current

Physical and mathematical modeling of stationary thermal modes of heating and oxidation of tungsten conductors heated by electric current in air has been carried out. The dependences of the stationary temperature of the conductor on the strength of the heating current are obtained. The critical values of the current strength are found, which determine the transitions to the unsteady oxidation regime. The results of calculating the temperature regimes describe well the experimental data obtained by us using the electrothermographic method.
 As a result of experimental studies, the features of the appearance and growth of crystalline oxide structures on the surface of an oxidizing tungsten conductor have been studied. The temperatures at which filamentous crystals appear on the tungsten surface are determined, and the regularities of their growth are investigated. A physicochemical mechanism of the formation and growth of crystalline oxide structures on the surface of a tungsten conductor is proposed. It was found that carbon particles, which are part of the impurity, are the reason for the formation of nitrate crystals of tungsten trioxide on the basic oxide. With an increase in the temperature of the sample, the filaments grow, branch out and transform into dendritic structures of a complex bush-like shape. It has been proven that the rapid growth of crystal structures occurs due to the deposition of clusters and microgranules of WO3 oxide from the gas phase on the crystallization centers on the surface of the conductor. At the initial stage, these are impurity particles or mechanical inhomogeneities of the basic oxide, then a growing crystal. Clusters arise due to large temperature gradients at the surface of the conductor. It has been established that carbon atoms can migrate along the branches of oxide crystal structures.
 It was found that at the initial stage the crystals grow more intensively in the longitudinal direction. However, upon reaching a certain height, they begin to expand intensively in the transverse direction. The growth rates of crystal structures in the longitudinal and transverse directions are found.

Flow regimes and mixing performance in T-T jet reactor

T-T jet reactor, obtained from the classical T jet reactor by duplicating two identical inlet channels below the original inlet channels, is considered to be the study object herein. The T and T-T jet reactors have been chosen for comparison since they show significantly various flow topologies and mixing performances at 50 ≤ Re ≤ 600. In this work, both the particle image velocimetry (PIV) experiment and three-dimensional numerical simulations are employed to clarify the mixing behaviors of the T-T jet reactor. The results show that the mixing performance of the T-T jet reactor is dramatically improved due to the secondary impinging, especially for the segregated flow and vortex flow regimes at low Reynolds number, and the unsteady symmetric flow regime at high Reynolds number. The impingement plane of the segregated flow and vortex flow regimes are increased due to the secondary impinging of the T-T geometry, for which the mixing effect is improved. The secondary impinging influences flow dynamics in the unsteady symmetric flow regime and has a significant impact on mixing.

Mixed Convection Heat Transfer and Entropy Generation in a Water-filled Square Cavity Partially Heated from Below: The Effects of Richardson and Prandtl Numbers

In the present study, fluid flow, heat transfer, and entropy generation for mixed convection inside a water-filled square cavity were investigated numerically. The sidewalls of the cavity, which move upwards, are kept at low-temperature Tc while only a part in the center of the bottom wall is kept at high-temperature Th and the remaining parts are kept adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Particular attention was paid to the influence of the Prandtl numbers of 5.534, 3.045 and 2, corresponding respectively to the water temperatures of 303.15 K, 333.15 K and 363.15 K. The numerical results are presented in the form of streamlines, isotherms, and entropy generation contours for different values of the Richardson numbers at an arbitrary Reynolds number Re=102. Besides this, the evolution of the average Nusselt number and the average entropy generation is also reported. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve stable symmetric and non-symmetric steady-state solutions, as well as unsteady regimes, depending on specific values of the Richardson and Prandtl numbers. It is additionally observed that the average Nusselt number increases and the average entropy generation decreases when both the Richardson and Prandtl numbers increase.

Application of projection methods to simulating mass transport in reverse osmosis systems

Reverse Osmosis has important applications to seawater desalination and advanced water treatment. Its efficiency depends, however, on unsteady fluid flow and solute transport that are challenging to simulate. The challenges arise due to interactions between solute boundary layers and unsteady vortical flow structures generated by complicated geometries. These flow structures also interact with semi-permeable membranes through which the permeate flow depends on the local pressure. We show that this additional pressure coupling causes the temporal accuracy of traditional projection methods to drop to first-order. We track the source of this accuracy drop to the treatment of viscous terms in the derivation of the Poisson equation used to update the velocity and pressure fields. This allows us to propose a modified projection method that recovers second-order temporal accuracy. Finally, we show that the modified projection method can be coupled to convective outlet conditions and immersed boundary conditions to simulate reverse osmosis in steady and unsteady flow regimes.

Dynamic thermal behaviour characterization of integrated insulation clay hollow blocks for buildings energy simulations applications

A method is proposed to obtain the thermal properties of hollow clay blocks with integrated insulation for use in building energy simulation tools. Then, we show the significant impact of the interior coating on the dynamic thermal behaviour of these blocks. This method is composed of two numerical and two experimental phases. First, a numerical model in an unsteady regime has been created and calibrated by experimental studies on a wall sample tested in a guarded hot box. Finally, a validation phase is carried out by comparing TRNSYS simulations with in situ test data from a residential building. Finally, we provide reliable values for the thermal properties to be used in energy simulation software (equivalent thermal conductivity of 0.08 W.m−1.K−1, equivalent density of 630 kg.m−3 and equivalent heat capacity of 430 J.kg−1.K−1).

Numerical Analysis of Mixed Convective Heat Transfer from a Square Cylinder Utilizing Nanofluids with Multi-Phase Modelling Approach

The present study deals with the numerical simulation of mixed convective heat transfer from an unconfined heated square cylinder using nanofluids (Al2O3-water) for Reynolds number (Re) 10–150, Richardson number (Ri) 0–1, and nanoparticles volume fractions (φ) 0–5%. Two-phase modelling approach (i.e., Eulerian-mixture model) is adopted to analyze the flow and heat transfer characteristics of nanofluids. A square cylinder with a constant temperature higher than that of the ambient is exposed to a uniform flow. The governing equations are discretized and solved by using a finite volume method employing the SIMPLE algorithm for pressure–velocity coupling. The thermo-physical properties of nanofluids are calculated from the theoretical models using a single-phase approach. The flow and heat transfer characteristics of nanofluids are studied for considered parameters and compared with those of the base fluid. The temperature field and flow structure around the square cylinder are visualized and compared for single and multi-phase approaches. The thermal performance under thermal buoyancy conditions for both steady and unsteady flow regimes is presented. Minor variations in flow and thermal characteristics are observed between the two approaches for the range of nanoparticle volume fractions considered. Variation in φ affects CD when Reynolds number is varied from 10 to 50. Beyond Reynolds number 50, no significant change in CD is observed with change in φ. The local and mean Nusselt numbers increase with Reynolds number, Richardson number, and nanoparticle volume fraction. For instance, the mean Nusselt number of nanofluids at Re = 100, φ = 5%, and Ri = 1 is approximately 12.4% higher than that of the base fluid. Overall, the thermal enhancement ratio increases with φ and decreases with Re regardless of Ri variation.

Time-dependent homogeneous states of binary granular suspensions

The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag force plus a stochastic Langevin-like term. It is found first that, regardless of the initial conditions, the system reaches (after a transient period lasting a few collisions per particle) a universal unsteady hydrodynamic regime where the distribution function of each species not only depends on the dimensionless velocity (as in the homogeneous cooling state) but also on the instantaneous temperature scaled with respect to the background temperature. To confirm this result, theoretical predictions for the time-dependent partial temperatures are compared against direct simulation Monte Carlo (DSMC) results; the comparison shows an excellent agreement confirming the applicability of hydrodynamics in granular suspensions. Also, in the transient regime, the so-called Mpemba-like effect (namely, when an initially hotter sample cools sooner than the colder one) is analyzed for inelastic collisions. The theoretical analysis of the Mpemba effect is performed for initial states close to and far away from the asymptotic steady state. In both cases, good agreement is found again between theory and DSMC results. As a complement to the previous studies, we determine in this paper the dependence of the steady values of the dynamic properties of the suspension on the parameter space of the system. More specifically, we focus our attention on the temperature ratio T1/T2 and the fourth degree cumulants c1 and c2 (measuring the departure of the velocity distributions f1 and f2 from their Maxwellian forms). While our approximate theoretical expression for T1/T2 agrees very well with computer simulations, some discrepancies are found for the cumulants. Finally, a linear stability analysis of the steady state solution is also carried out showing that the steady state is always linearly stable.

Analytical temperature profiles for laser-irradiated gold nanorod immersed in an optically non-absorbing medium

Laser heating of gold nanorods immersed in an optically non-absorbing medium is important in both therapeutic and diagnostic medical procedures. For both continuous wave and pulsed lasers, we derive analytical temperature solutions by modeling a nanorod as a prolate spheroid. For the continuous wave laser irradiation, an exact analytical solution for the steady state heat transfer case using integer-degree Legendre function expansions in prolate spheroidal coordinates is presented. The steady state solution reveals that for the case of gold nanorod immersed in water, there is insignificant temperature variations on any single spheroidal surface that is coincident or confocal to the prolate spheroid surface, and the temperature only changes across spheroidal surfaces within the immediate surrounding water. This is found to be due to the very high thermal conductivity of gold which is more than a hundred-fold higher than that of water. The insight that the temperature rise is nearly invariant on any single spheroidal surface, along with a dimensional analysis, helps reduce the complexity of the heat equation in the unsteady regime of a pulsed laser illumination, and leads to a simple, lower dimensional model of unsteady heat equation, which takes into account the temporal dependency and spatial dependency in the direction across spheroidal surfaces. For the reduced unsteady heat equation, a simple, efficient, and insightful solution algorithm based on the Laplace transform and complex-degree Legendre functions is proposed. The maximum temperature and temperature profiles as functions of laser power, and nanorod geometries are obtained, revealing that for a fixed laser fluence and fixed nanorod mass, the more stretched nanorods yield higher temperatures in the spheroid and its immediate surroundings. In other words, more stretched nanorods are more efficient in converting the laser energy into localized, elevated temperatures. The obtained temperature solutions are useful in designing a parameter space for optimum therapeutic procedures for ablating cancer cells using high temperatures generated in the immediate vicinity of nanoparticles. The unsteady temperature solutions can also be used to obtain solutions to thermo-elastic models which are used to compute the photoacoustic signals that can, in turn, be used for cellular imaging and diagnostics.

Stereo-PIV investigation of the unsteady flow in the draft tube of a model hydro turbine

Varying the generator load of a hydro turbine results in short-term changes in the rotation frequency of the runner, leading inevitably to flow instability and strong flow swirling behind the turbine. This may lead to the formation of unsteady flow regimes featured by vortex instability of the swirling flow behind the runner, known as the precessing vortex core (PVC) Dorfler et al. (2012). This effect causes dangerous periodic pressure pulsations that propagate throughout the water column in the draft tube. The present study reports on stereo PIV measurements of the air flow field inside a transparent draft tube of a model hydro turbine for a wide range of operation conditions. The research is focused on the time-averaged flow properties (mean velocity field and the second-order moments of velocity fluctuations), pressure pulsations and coherent flow structures in the velocity field.