Important Dimensionless Parameters Research Articles

A numerical study on the wave loading on offshore structures of different cross-sectional geometries under the action of regular waves

Coastal engineering and maritime hydraulics have experienced significant development over the years with the construction of bridges, oil exploration platforms, and ports, highlighting the importance of studying and quantifying the efforts resulting from wave loads on these structures. The present work aims to identify how a variation in the geometry of the cross-section, along the wave climate, can modify the magnitude of the wave loadings experienced by the structure. The open-source computational code OpenFOAM v. 4.1 was applied in the considered cases, along with the OlaFlow extension, considering the application of a structured mesh, the VOF (Volume of Fluid) methodology for representing the free surface, and the turbulence modeling according to Reynolds averaged equations (RANS). The results demonstrated that the shape of the cross-section plays an important role in the efforts experienced by the structure, and this influence is directly related to a characteristic length, whose intensification causes an increase in the magnitude of the experienced horizontal force. Likewise, by defining important dimensionless parameters, it was possible to obtain approximate expressions to determine the maximum wave force on the structures. The results and analyses carried out demonstrated that the force value calculated according to this approximation methodology is quite adequate, presenting relative errors smaller than 11,00%, corresponding to a relevant simplified approach for the determination of the maximum wave loads experienced by the structures, which can be important for proper design and analysis.

An analytical study on transient thermal behavior of a packed-bed molten salt thermocline thermal storage

A volume averaged set of the governing equations for local thermal non-equilibrium fluid saturated porous media was applied to study transient thermal behavior of convection and conduction within a packed-bed thermocline thermal storage tank. General analytical expressions, which agree well with numerical results, were derived for the prediction of transient temperature fields of molten salt and granulated material. Three important dimensionless parameters, namely, the solid fluid heat capacity ratio, interstitial Stanton number and Peclet number based on the effective thermal diffusivity, are identified to investigate their effects on the thermal response of the packed-bed thermocline thermal storage tank. An explicit analytical expression for the effective discharging efficiency has been derived as a function of the three important dimensionless parameters. The expression may serve as a powerful tool to design a packed-bed thermocline thermal storage tank according to required operational conditions.

Exploring the parameter space of MagLIF implosions using similarity scaling. I. Theoretical framework

Magneto-inertial fusion concepts, such as the magnetized liner inertial fusion (MagLIF) platform [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)], constitute an alternative path for achieving ignition and significant fusion yields in the laboratory. The space of experimental input parameters defining a MagLIF load is highly multi-dimensional, and the implosion itself is a complex event involving many physical processes. In the first paper of this series, we develop a simplified analytical model that identifies the main physical processes at play during a MagLIF implosion. Using non-dimensional analysis, we determine the most important dimensionless parameters characterizing MagLIF implosions and provide estimates of such parameters using typical fielded or experimentally observed quantities for MagLIF. We then show that MagLIF loads can be “incompletely” similarity scaled, meaning that the experimental input parameters of MagLIF can be varied such that many (but not all) of the dimensionless quantities are conserved. Based on similarity-scaling arguments, we can explore the parameter space of MagLIF loads and estimate the performance of the scaled loads. In the follow-up papers of this series, we test the similarity-scaling theory for MagLIF loads against simulations for two different scaling “vectors,” which include current scaling and rise-time scaling.

Mathematical Study of unsteady micropolar fluid flow due to non-linear stretched sheet in the presence of magnetic field

The goal of this research is to check irregularity in heat generation, chemical reaction and thermal radiation effect an unsteady micropolar fluid flow. With the help of suitable similarity variables, the group of governing system of PDE and their associative boundary conditions are converted into the family of ODE and then solved using the HAM. The effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms. It is observed that buoyancy force parameter, mixed convection parameter and permeability parameter enhance the velocity distribution while micropolar reduces the velocity profile. The temperature profiles are boosted for time and space dependent heat generation and absorption parameter respectively but reverse trend is observed for Prandtl number and unsteadiness parameter. Skin-friction factor, mass transfer rate and heat transfer rate have been listed and displayed in tables.

Predicting Lateral Resistance of Piles in Cohesive Soils

The ultimate lateral resistance of free- and fixed-headed piles in cohesive soil is examined in this paper using the three-dimensional finite element limit analysis with upper and lower bound theorems. A special concern, and that is the novelty of this study, is devoted to the combined effect of the three important dimensionless parameters; namely, the overburden stress factor (n), the pile length-diameter ratio (L/D), and the ratio of eccentric length to diameter (e/D). Numerical results are expressed by using Broms’s horizontal load factor, and comparisons are made with several published solutions. In addition, the associated failure mechanisms are investigated with respect to the three parametric effects. The adopted new technique has been successfully used to study a number of different geo-stability problems. It is thus the aim of this paper to produce accurate and practical results with design equations and charts that can be used by practitioners to predict the undrained lateral capacity of fixed- and free-headed piles.

A force explosion condition for spherically symmetric core-collapse supernovae

ABSTRACT Understanding which stars explode leaving behind neutron stars and which stars collapse forming black holes remains a fundamental astrophysical problem. We derive an analytic explosion condition for spherically symmetric core-collapse supernovae. The derivation starts with the exact governing equations, considers the balance of integral forces, includes the important dimensionless parameters, and includes an explicit set of self-consistent approximations. The force explosion condition is $\tilde{L}_\nu \tau _g - 0.06 \tilde{\kappa } \gt 0.38$, and only depends upon two dimensionless parameters. The first compares the neutrino power deposited in the gain region with the accretion power, $\tilde{L}_\nu \tau _g = L_{\nu } \tau _g R_{\rm NS}/ (G \dot{M} M_{\rm NS})$. The second, $\tilde{\kappa } = \kappa \dot{M} / \sqrt{G M_{\rm NS} R_{\rm NS}}$, parametrizes the neutrino optical depth in the accreted matter near the neutron star surface. Over the years, many have proposed approximate explosion conditions: the critical neutrino-luminosity, ante-sonic, and time-scale conditions. We are able to derive these other conditions from the force explosion condition, which unifies them all. Using numerical, steady-state and fully hydrodynamic solutions, we test the explosion condition. The success of these tests is promising in two ways. One, the force explosion condition helps to illuminate the underlying physics of explosions. Two, this condition may be a useful explosion diagnostic for more realistic, three-dimensional radiation hydrodynamic core-collapse simulations.

Applying Bayesian Markov chain Monte Carlo (MCMC) modeling to predict the melting behavior of phase change materials

A key practical application of PCM-based spherical containers is in packed bed thermal energy storage (TES) devices utilized for air conditioning in large buildings. Proposing high-precision models for the melting characteristics in spherical containers can provide deep insights into the design of TES systems. Herein, a methodology based on Bayesian inference was adopted to provide reliable models that predict the melting rate (f) and surface-averaged Nusselt number (Nu) as two significant factors in PCM melting process in spherical heat storage units. Five proposed models for f and Nu prediction were applied to available datasets. The input of Bayesian-based predictive models included three important dimensionless parameters of the melting problem, namely Ste, Gr, and Fo. Ste (Stefan number) describes the driving force of melting, Gr (Grashof number) reflects the natural convection intensity, and Fo (Fourier number) represents the dimensionless time. For accurate inference of model parameters using the Bayesian Markov chain Monte Carlo (MCMC) technique, an analysis was performed by coding in the WinBUGS language. Several statistical performance criteria (R2, RMSE, and MSE) were utilized to evaluate the efficiency of Bayesian-based predictive models. The results showed that model #4 recorded R2 = 0.980 in the prediction of melting rate. Furthermore, model #5 with R2 = 0.966, had the best performance in predicting the values of surface-averaged Nusselt number. The models recommended in this research yield superior results compared to the previous study, which suggested R2 = 0.975 and R2 = 0. 925 for f and Nu, respectively.

Prediction of discharge coefficients for broad-crested weirs using expert systems

ABSTRACT Broad crested weirs can be used to make discharge measurements in irrigation canals; the entrance of stepped weirs or chutes are sometimes designed as a broad crested weir structure. These structures are also sometimes used for the dam body. In this study, the Artificial Neural Network (ANN) and M5 model tree methods are used to predict discharge coefficients (Cd ) for broad crested weirs. The results from these two models are compared with nonlinear regression equations. Four series of data obtained from different rectangular broad crested weirs have been used and important dimensionless parameters have been defined. Results show that the ANN procedure is superior to the M5 model and regression approaches. The accuracy for ANN is quantified by R = 0.966 and RMSE = 0.038. All the three methods are able to provide a reasonable prediction for Cd ; the M5 model tree provides four linear equations that can be used to estimate Cd . The shape of the Cd contours shows that the effect of weir height (P) exceeds that of the weir length (L).

Prediction of mean wave overtopping at simple sloped breakwaters using kernel-based methods

Abstract The accurate prediction of the mean wave overtopping rate at breakwaters is vital for a safe design. Hence, providing a robust tool as a preliminary estimator can be useful for practitioners. Recently, soft computing tools such as artificial neural networks (ANN) have been developed as alternatives to traditional overtopping formulae. The goal of this paper is to assess the capabilities of two kernel-based methods, namely Gaussian process regression (GPR) and support vector regression for the prediction of mean wave overtopping rate at sloped breakwaters. An extensive dataset taken from the EurOtop database, including rubble mound structures with permeable core, straight slopes, without berm, and crown wall, was employed to develop the models. Different combinations of the important dimensionless parameters representing structural features and wave conditions were tested based on the sensitivity analysis for developing the models. The obtained results were compared with those of the ANN model and the existing empirical formulae. The modified Taylor diagram was used to compare the models graphically. The results showed the superiority of kernel-based models, especially the GPR model over the ANN model and empirical formulae. In addition, the optimal input combination was introduced based on accuracy and the number of input parameters criteria. Finally, the physical consistencies of developed models were investigated, the results of which demonstrated the reliability of kernel-based models in terms of delivering physics of overtopping phenomenon.

An Efficient Numerical Simulation of 2D Natural Convection in an Inclined Cavity with Internal Heat Generation Using Differential Quadrature Method

Natural laminar convective fluid flow has been simulated inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles. The most important basic dimensionless parameters for this problem are the external Rayleigh number (RaE) and the internal Rayleigh number (RaI), where RaE refers to the effects of the differential heating of the side walls and RaI refers to the amount of heat produced internally. Results were obtained for 4 cases with 192 tests: case (1), RaI = 0 without internal source generation, and cases (2, 3, and 4) with internal source generation for RaI = RaE, 10 RaE, and 100 RaE, respectively. In all cases, the parameters of study changed as 103 ≤ RaE ≤106, 0 ≤ RaI ≤ 107, inclination angle from 0 to 60 deg., and aspect ratios of the enclosure from 0.5 to 2. Results were represented graphically for flow and thermal fields as a streamline, isothermal contours, and Nusselt number. The computed results show that the strength of convection currents is measured by the internal energy. Finally, it is illustrated that by using a few grid points and a shorter CPU time for calculation, the present method can produce accurate numerical results. Also, increase in RaI leads to increasing heat transfer rate and its direction out from the cavity at both hot and cold walls. For lower values of RaI, heat transfer diffusion is more prominent, while for higher values of RaI, convection outweighs diffusion.
 HIGHLIGHTS
 
 Natural laminar convective fluid flow inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles has been simulated
 The most important basic dimensionless parameters, the external Rayleigh number (RaE) and the internal Rayleigh number (RaI) are studied
 DQ method performance was excellent
 The obtained computational results indicate that the strength of the convection currents depends on the internal energy
 Accurate numerical results can be obtained by the present method using a few grid points and shorter CPU time for calculation
 
 GRAPHICAL ABSTRACT

A review of flow and heat transfer in cavities and their applications

The study of fluid flows in a cavity and their effect on thermal performance in heat transporting and entropy generation are found in many heating and cooling engineering applications such as energy storage geothermal reservoirs, boilers, solar collectors, underground water flow, lakes, nuclear reactors. This paper presents a comprehensive review of the recent numerical and experimental studies on both heat transfer and entropy generation and their applications in cavities. The effect of the fluid thermal properties, the cavity configuration, the boundary, and initial conditions, the magnetic field, the thermal source discretion, and other geometrical and physical parameters on heat transfer and entropy generation are discussed. This study also presents the effect of several important dimensionless parameters such as the Reynolds, Richardson, Grashof, Rayleigh, Darcy, Hartmann, and Prandtl numbers on both natural and combined convection heat transfer mechanisms in cavities.

Linear Stability Analysis of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion

Abstract We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheetlike cloud or disk. Our results show that there is always a preferred length scale and associated minimum timescale for gravitational instability. We investigate their dependence on important dimensionless free parameters of the problem: the initial normalized mass-to-flux ratio μ 0, the rotational Toomre parameter Q, the dimensionless ohmic diffusivity η ˜ OD , 0 , and the dimensionless neutral–ion collision time τ ˜ ni , 0 , which is a measure of the ambipolar diffusivity. One consequence of η ˜ OD , 0 is that there is a maximum preferred length scale of instability that occurs in the transcritical (μ 0 ≳ 1) regime, qualitatively similar to the effect of τ ˜ ni , 0 , but with quantitative differences. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified length scales and timescales for collapse. When nonideal MHD effects are also included, the Toomre criterion reverts back to the hydrodynamic value. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be ∼10–90 M Jup.

Regimes of wettability-dependent and wettability-independent bouncing of a drop on a solid surface

Abstract

Numerical study of natural convection in an enclosure with discrete heat sources on one of its vertical walls

In this study, natural convection in a fluid-filled rectangular enclosure is analyzed using COMSOL? commercial software. The fluid in which natural convection takes place is a dielectric liquid called FC-75. Attached to one of the vertical walls of the enclosure is an array of rectangular protrusions, each representing computer chips mounted on a printed circuit board. The nominal power consumed by each chip is assumed to be 0.35, 1.07, 1.65, and 2.35 W. This corresponds exactly to the values used in the experiments, which were performed once by the author of this study. The results of the experiment and the numerical study are shown as Nusselt numbers vs. Rayleigh numbers, both being the most important dimensionless parameters of natural convection. A comparison of the results has shown that COM-SOL? can achieve reliable results in similar problems, eliminating the need to build expensive experimental set-ups and spending time conducting experiments. The simulation results are aimed to be used in similar designs of electronic circuits in confined spaces.

Dominated flow parameters applied in a recirculation microbial fuel cell

Scaling up of microbial fuel cells is a challenge for practical applications in wastewater treatment. In addition, the flow control is an important aspect for the electrochemical reactions occurring at the electrodes are influenced by fluid motions. By using dimensionless parameter analysis fluid regimes can be investigated in different scales of reactors. In this study, four important dimensionless flow parameters such as Reynolds number, Péclet number, Schmidt number, and Sherwood number were used for systematic analysis of hydrodynamic effects and power performance of recirculation mode microbial fuel cells together with computational fluid dynamics method. Results showed that the higher value of Reynolds number enhanced the convective flow of anolyte due to the dominant inertial forces in the flow field. Therefore, Reynolds number of 1.6 × 101 were obtained high mass transfer coefficient of 4.76 × 10−7 m s-1 and thin diffusion layer thickness of 2.52 × 10-3 m. Maximum power density and limited current density of 2422.8 mW m-2 and 4736.4 mA m-2 were obtained respectively which were higher than Reynolds number of 0 by 1.61 and 1.69 times. These findings shall be useful for effective recirculation flow mode MFCs power production and have a great possibility for large scale applications.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

Analysis of unsteady non-axisymmetric Homann stagnation point flow of nanofluid and possible existence of multiple solutions

This study examines the unsteady 3D non-axisymmetric Homann flow of an electrically conducting nanofluid in the presence of buoyancy forces. We consider the uniform external magnetic field B0, by neglecting induced magnetic field and examine the three possible directions of magnetic field which coincides with the direction of axes. A similarity solution is derived which involves the important physical dimensionless parameters like the nanoparticles volume fraction φ, the unsteadiness parameter ω, the buoyancy parameter λ,Hartmann numberMandshear to strain ratioγ. We have treated the case for forced convection when λ=0 which arise from the singularity γ=∓1. We found that, for large γ and λ, the leading terms of the solutions are independent of M and ω, and the effects of φ in that solutions are negligible. Numerical results are found for illustrative values of all the flow parameters by using bvp4c scheme in MATLAB. The critical values λc of λ are seen in opposing flow for small rate of deceleration parameter ω while it changes to assisting flow for large value of ω.

Parametric Study and Sensitivity Analysis of Latent Heat Thermal Energy Storage System in Concentrated Solar Power Plants

Compared to solar photovoltaics, concentrated solar power (CSP) can store excessive solar thermal energy, extend the power generation, and levelize the mismatch between the demand and supply. Thermal energy storage (TES) system filled with phase change material (PCM) is a key to make CSP competitive, and it is also a promising indirect energy storage technique. It is of great interests to the solar thermal engineering community to apply the latent heat thermal energy storage (LHTES) system for large-scale CSP application, because PCMs can store more energy due to the latent heat during the melting/freezing process. Therefore, a comprehensive parametric analysis of LHTES system is necessary in order to identify the most sensitive ranges of various parameters to design the LHTES system with better systematic performances. In this study, unlike the existing parametric study based on dimensional parameters, we aimed to provide a more general analysis using dimensionless parameters; therefore, an 11-dimensionless-parameter space of LHTES system was developed, by considering the technical constraints (material properties and operation parameters), without economic constraints. The parametric study and sensitivity analysis were then performed based on a 1D enthalpy-based transient model, and the energy storage efficiency was used as the objective function to minimize the number of variables in the parameter space. It was found that Stanton number (St), dimensionless PCM radius (r/D), and void fraction (ε) are the three most important dimensionless parameters. It is expected that the discovery of this study can bring more discussions in the solar thermal engineering community about the implementation of LHTES system in CSP plant, to further explore the significances of these three dimensionless parameters to the operation of the LHTES system.

New Analytical Study of the Effects Thermo-Diffusion, Diffusion-Thermo and Chemical Reaction of Viscous Fluid on Magneto Hydrodynamics Flow in Divergent and Convergent Channels

In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.

COMPUTATION OF TRANSIENT RADIATIVE REACTIVE THERMOSOLUTAL MAGNETOHYDRODYNAMIC CONVECTION IN INCLINED MHD HALL GENERATOR FLOW WITH DISSIPATION AND CROSS DIFFUSION

The present article investigates the collective influence of chemical reaction, viscous dissipation and Hall current magnetic effects on timedependent radiative magnetohydrodynamic flow, heat and mass transfer from an inclined wall embedded in a homogenous, isotropic highpermeability porous medium. The model developed is relevant to near wall magnetohydrodynamic energy generator transport phenomena in which chemical corrosion effects may arise during operations. The governing non-linear partial differential equations for mass, momentum, energy and species conservation are transformed into a system of coupled non-linear dimensionless partial differential equations with appropriate similarity variables. The normalized conservation equations are then solved with a robust finite element method (MATLABFEM) subject to corresponding initial and boundary conditions. Important dimensionless parameters emerging are Eckert number, thermal Grashof number, solutal Grashof number, magnetic body force parameter, Hall parameter, permeability parameter, Dufour number, Soret number, time, radiation-conduction parameter, chemical reaction parameter, heat absorption parameter, Prandtl number, Schmidt number and wall angle. Primary velocity is enhanced with Eckert number, thermal Grashof number, solutal Grashof number, Hall parameter, permeability parameter, Dufour number, Soret number, radiation-conduction parameter and time whereas it is reduced with first order chemical reaction parameter, heat absorption, magnetic body force parameter, Prandtl number, Schmidt number and wall inclination. Secondary velocity is elevated with Eckert number, solutal Grashof number, thermal Grashof number, magnetic body force parameter, Hall parameter, radiation-conduction parameter, Dufour number, Soret number and time whereas it is suppressed with reaction parameter, heat absorption, Prandtl number, Schmidt number and wall inclination. Temperature is enhanced with Eckert number, Dufour number, heat absorption, radiation-conduction parameter and time whereas it is depressed with Prandtl number. Species concentration is reduced with increasing chemical reaction parameter (destructive homogenous reaction) and Schmidt number whereas it is elevated with Soret number and time. Extensive discussion of the finite element formulation, convergence and validation is provided Skin friction, Nusselt number and Sherwood number distributions are also provided for selected parameter variation. Validation of solutions with published literature is also included for several special cases, namely non-reactive, non-dissipative flow in the absence of heat generation or absorption. Further validation is included using a multi-step differential transform method (MS-DTM). The present simulations provide an interesting insight into complex fluid/thermal/species diffusion characteristics in the boundary layer region of relevance to working MHD generator systems.