Critical Dimensionless Number Research Articles

A Novel Approach to Visualize Liquid Aluminum Flow to Advance Casting Science.

Turbulent filling of molten metal in sand-casting leads to bi-films, porosity and oxide inclusions which results in poor mechanical properties and high scrap rate of sand castings. Hence, it is critical to understand the metal flow in sand-molds, i.e., casting hydrodynamics to eliminate casting defects. While multiple numerical methods have been applied to simulate this phenomenon for decades, harsh foundry environments and expensive x-ray equipment have limited experimental approaches to accurately visualize metal flow in sand molds. In this paper, a novel approach to solve this challenge is proposed using Succinonitrile (SCN) as a more accurate metal analog in place of water. SCN has a long history in solidification research due to its BCC (Body-Centered-Cubic) crystal structure and dendrite-like solidification (melting temperature ~60 °C) like molten aluminum. However, this is the first reported study on applying SCN through novel casting hydrodynamics to accurately visualize melt flow for casting studies. This paper used numerical simulations and experiments using both water and SCN to identify the critical dimensionless numbers to perform accurate metal flow analog testing. Froude's number and wall roughness were identified as critical variables. Experimental results show that SCN flow testing was more accurate in recreating the flow profile of molten aluminum, thus validating its utility as a metal analog for metal flow research. Findings from this study can be used in future metal flow analysis such as: runner, in-gate and integrated filling-feeding-solidification studies.

Enhancing ϕ-sensitivity of ignition delay times through dilution of fuel-air mixture

The high ϕ-sensitivity (η) of ignition delay time (τIDT) is one of the desirable fuel properties for the high-load extension of advanced compression ignition engine. Recent studies revealed the effectiveness of a high dilution rate (xD) for enhancing η at the engine-relevant conditions. This study aims to quantify the effect of dilution on the η of isooctane using a combined experiment-simulation approach. The ignition delay of the isooctane/air mixture was measured with an Advanced Fuel Ignition Delay Analyzer (AFIDA) over the temperature range of 623 – 923 K at 10 bar pressure with global ϕ = 0.3 – 0.6, with and without 28.6% of additional N2 dilution. For precise evaluation of experimental η, the facility effect of the AFIDA experiment was characterized with three-dimensional computational fluid dynamics (3-D CFD) simulation. The temperature in the combustion chamber from 3-D CFD indicated a substantial temporal dependency, varying up to ∼52 K by charge-cooling of fuel injection and heat transfer from the wall. We introduced the dimensionless number θ(t) for characterizing the temporal profile of chamber temperature. Consideration of the facility effect using θ(t) resulted in better agreement between the experimental η and zero-dimensional (0-D) kinetics simulation. The refined η were then further utilized to quantify the effectiveness of dilution to η. The extent of η enhancement with dilution strategy was maximized at the low-temperature chemistry regime, increasing η by 77% with a 28.6% dilution rate. Further analysis on the dilution effect was carried out using 0-D kinetics simulation, revealing the critical dimensionless numbers relevant to the effectiveness of dilution to η enhancement. This study is the first experiment-simulation combined research to quantify the effect of dilution on η, facilitating the kinetics model refinement for better reproduction of ϕ-sensitivity.

S-PAL: A stabilized finite element formulation for computing viscoplastic flows

• Stabilized finite element method for viscoplastic flows using equal order polynomials. • Computational cost is considerably reduced. • Increased numerical stability in critical flow conditions, i.e., bubble entrapment • Numerical results in quantitative agreement with other popular methods Ideal viscoplastic models present an inherent discontinuity at the yielded/unyielded interface, which poses great numerical difficulties. In this work, the recently proposed method for the solution of viscoplastic flows, the Penalized Augmented Lagrangian (PAL) method (Dimakopoulos et al. (2018)) is coupled with a new projection-based finite element formulation that allows for equal order interpolants in all variables. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: (a) the buoyancy-driven bubble rise through a viscoplastic medium, (b) the steady-state lid-driven cavity and its transient counterpart, and (c) the transient gas-assisted displacement of a viscoplastic material in straight and corrugated tubes. The method presents increased numerical stability and reduced computational cost without hindering the accuracy of the solution. By changing the solution procedure, we are able to obtain solutions that are as accurate as those obtained with the Augmented Lagrangian (AL) method. In addition, we show that the optimal value of the penalty parameter is correlated with the mesh and the critical dimensionless numbers that correspond in each problem.

A molecular dynamics study of evaporation mode transition of hydrocarbon fuels under supercritical conditions

The mode transition of evaporation for single- and multi-component hydrocarbon fuels is investigated at the molecular level. This study scrutinizes first the subcritical and supercritical evaporation of n-hexadecane droplets and liquid films by molecular dynamics (MD) simulations. The mode regime map of n-hexadecane droplets is obtained. Then the mode transition of evaporation of a three-component droplet and a six-component droplet is studied. A critical dimensionless number τ0.9P of 0.5 based on the average displacement increment (ADI) of fuel atoms is used to identify the evaporation mode transition of fuels with any type and number of components. It is found that in the diffusion mode of evaporation, the entropy becomes the dominant factor in the evaporation of fuels, and the disorder of the fuel molecules increases significantly compared with that in the classic evaporation mode. Compared with the case of the quiescent droplet, with increasing relative velocity between the droplet and the ambient gas, the mode transition becomes easier, although this is a non-linear process. Fuel droplets and liquid films with different initial sizes are investigated to understand the size effect. In addition, for the same ambient temperature and pressure, the smaller the normalized specific heat transfer surface area of the fuel is, the easier the mode transition of evaporation is. A correlation was proposed to compare the possibility of mode transition of evaporation for single- and multi-component fuels.

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.

Comprehensive study of the interactions between the critical dimensionless numbers associated with multiphase flow in 3D porous media

Multiphase flow in porous media is of great interest in many engineering applications, such as geologic carbon sequestration, enhanced oil recovery, and groundwater contamination and remediation. In order to advance the fundamental understanding of multiphase flow in complex three-dimensional (3D) porous media, the interactions between the critical dimensionless numbers, including the contact angle, viscosity ratio, and capillary (Ca) number, were investigated using X-ray micro-computed tomography (micro-CT) scanning and lattice Boltzmann (LB) modeling. In this study, the 3D pore structure information was extracted from micro-CT images and then used as interior boundary conditions of flow modeling in a pore-scale LB simulator to simulate multiphase flow within the pore space. A Berea sandstone sample was scanned and then two-phase flow LB simulations were performed based on the micro-CT images. The LB-simulated water/CO2 distributions agreed well with the micro-CT scanned images. Simulation results showed that a decreasing contact angle causes a decrease in wetting-fluid relative permeability and an increase in non-wetting fluid relative permeability. A rising Ca number increases both wetting and non-wetting fluid relative permeabilities. An increasing viscosity ratio (the ratio of non-wetting fluid viscosity to wetting fluid viscosity) facilitates the increase of non-wetting fluid relative permeability and mitigates the reduction of wetting fluid relative permeability, when the contact angle decreases continuously. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. To the best of our knowledge, it is the first time that comprehensive interactions between these dimensionless numbers are demonstrated in a sandstone sample based on real 3D structures. We also investigated the role of the changes of flow direction and sample location on relative permeability curves. Simulation results showed that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid.

A nonlinear analysis of the effect of heat transfer on capillary jet instability

Breakup of slender liquid jets under isothermal conditions has been studied extensively. In this work, we investigate the breakup of a viscous jet emanating from an orifice in the presence of convective heat transfer. We study the case where heat is transferred from the jet to the ambient fluid. The temperature varies axially and both viscosity and surface tension are taken to be temperature dependent. Marangoni stresses caused by a thermally induced surface tension gradient are included here. A numerical model based on a one-dimensional slender jet approximation of the equations of motion and heat transfer is used. This results in three coupled nonlinear partial differential equations, which are solved using the method of lines. The advantages of using this approximation lie in (i) its computational elegance and (ii) the physical insight that it provides. We compare the model predictions of both spatial and temporal stability analysis with experiments of a jet of molten Woods metal in water. Molten Woods metal emanating from various orifice diameters (1-10 mm) into water under the action of gravity is analysed for drop sizes and these are compared with the numerical predictions. The presence of heat transfer is found to shorten the breakup length of the jet. This is attributed to the increase in surface tension induced by the heat loss from jet to the ambient. It is found that including the effect of temperature dependence of viscosity and surface tension, however, does not affect the drop size. A critical dimensionless number (Π1 ∼ 10) is found to exist beyond which the breakup is dominated by Marangoni stresses. Below this critical number, the jet breaks up due to the combined effects of the capillary force and the Marangoni stresses. It is shown that including the effect of gravity is necessary to predict the drop size accurately. The results of this work have implications in evaluating safety strategies in the event of a core disruptive accident in a nuclear reactor. A wider application of this analysis is in improving the efficiency of thermally modulated inkjet printing.

Critical droplet volume for spontaneous capillary wrapping

In this work, we show that an elastic thin sheet can be folded up by the surface tensions at the contact line when it is in contact with a droplet of sufficient volume. The critical volumes of different droplets for the wrapping of square and triangular polydimethylsiloxane sheets are measured. A dimensionless number involving the droplet volume is proposed and it is found that the critical dimensionless number, for which spontaneous capillary wrapping takes place, scales with the characteristic length of the sheet exponentially.

Magnetic tower outflows from a radial wire array Z-pinch

We present the first results of high energy density laboratory astrophysics experiments which explore the evolution of collimated outflows and jets driven by a toroidal magnetic field. The experiments are scalable to astrophysical flows in that critical dimensionless numbers such as the Mach number, the plasma β and the magnetic Reynolds number are all in the astrophysically appropriate ranges. Our experiments use the MAGPIE pulsed power machine and allow us to explore the role of magnetic pressure in creating and collimating the outflow as well as showing the creation of a central jet within the broader outflow cavity. We show that currents flow along this jet and we observe its collimation to be enhanced by the additional hoop stresses associated with the generated toroidal field. Although at later times the jet column is observed to go unstable, the jet retains its collimation. We also present simulations of the magnetic jet evolution using our two-dimensional resistive magnetohydrodynamic laboratory code. We conclude with a discussion of the astrophysical relevance of the experiments and of the stability properties of the jet.

The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media

Abstract This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media.