Nonlinear Drag Effects Research Articles

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

The effect of nonlinear drag on the rise velocity of bubbles in turbulence

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Transport of inertial particles in high-Reynolds-number turbulent boundary layers

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A unified grayscale lattice Boltzmann model for multiphase fluid flow in vuggy carbonates

In addition to intrinsic matrix pores, ranging in size from submicrons to microns, vuggy carbonates often contain significantly larger vug spaces. Immiscible multiphase fluids flowing through this type of microporous systems exhibit complicated flow mechanisms that are involved in the interactions between multiphase fluids and different types of pore spaces. Modeling multiphase fluid flows requires using the appropriate governing equations for different porosity systems. More specifically, while multiphase Darcy's equations might hold for a matrix system, they are not applicable for a vug system. To improve understanding this difficult multiphase flow problem in vuggy carbonates, we developed a unified grayscale lattice Boltzmann (LB) model for multiphase flows. The proposed model combines the generalized LB model in porous media with the pseudo-potential multiphase approach by adding the fluid-fluid interaction force, the fluid-solid interaction force, and the linear and nonlinear drag forces induced by the porous matrix. The model is still within the framework of the generalized LB model, and it switches freely from the Darcy's regime to the free-flow regime via rock property (i.e., porosity). It can also extend to a wide range of porosity systems because we incorporated both the linear and nonlinear drag effects. A continuous flow interface between the porous matrix and the vug region is captured by simulation without incorporating complex interface boundary conditions between the two porosity systems. The current model is validated and calibrated with theory, and then it is applied to a number of test cases. The test cases include the simulations of two-phase displacement in non-vuggy porous media, isolated vuggy porous media, and connected vuggy (fractured) porous media. Moreover, the effect of vug spaces on the interface-front speed and the breakthrough time is investigated. In addition, we simulated water displacing oil in two real vuggy carbonate cores imaged using low-resolution and high-resolution X-ray computed microtomography, and we investigated the effects of matrix heterogeneity, vug connectivity, and matrix wetting preference.

Non-linear drag induced entropy generation analysis in a microporous channel: The effect of conjugate heat transfer

The entropy generation analysis in a viscous dissipative flow of a Newtonian fluid through a hyper-porous microchannel formed between two heated parallel plates is conferred. Employing an analytical method, which is consistent with the perturbation analysis, the transport equations governing the thermo-hydrodynamics are studied. The effects of nonlinear Forchheimer drag and conjugate heat transfer on the thermal transport characteristics of heat are considered, while the thermal boundary conditions of third kind have been employed at the outer boundaries of channel for the conjugate heat transfer analysis. The explicit alterations are made in the thermal transport of heat in the system as attributable to the effect of dissipative heat generated due to the non-linear effect Forchheimer drag, Darcy frictional effect and the viscous shearing stress in the flow field. To account these effects, the explicit variation of Forchhiemer constant, Darcy number, porosity, thickness and conductivity of upper wall and Biot number of upper wall are carried out to shows the changes in the available energy of the system. Also, it is shown that the effect of non-linear drag mainly stemming from the presence of complex porous structure in the flow field and its interaction with the conjugate transport of heat alters the heat transfer rate in the system non-trivially, which, in turn, gives rise to the entropy generation in the system. The individual contribution of two different effects viz., the heat transfer and viscous dissipation on the system entropy generation rate for different cases are studied. It is believed that the implications of the present analysis may have direct bearing on the design of micro devices/systems typically used in electronic cooling, micro-heat pipes.

Settling regimes of inertial particles in isotropic turbulence

AbstractWe investigate the settling speeds and root mean square (r.m.s.) velocities of inertial particles in isotropic turbulence with gravity using experiments with water droplets in air turbulence from 32 loudspeaker jets and direct numerical simulations (DNS). The dependence on particle inertia, gravity and the scales of both the smallest and largest turbulent eddies is investigated. We isolate the mechanisms of turbulence settling modification and find that the reduced settling speeds of large particles in experiments are due to nonlinear drag effects. We demonstrate using DNS that reduced settling speeds with linear drag (e.g. see Nielsen, J. Sedim. Petrol., vol. 63, 1993, pp. 835–838) only arise in artificial flows that, by design, eliminate preferential sweeping by the eddies. Gravity and inertia both reduce the particle r.m.s. velocities and falling particles are more responsive to vertical than to horizontal fluctuations. The model by Wang & Stock (J. Atmos. Sci., vol. 50, 1993, pp. 1897–1913) captures these trends.

Lattice Boltzmann model for the volume-averaged Navier-Stokes equations

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.

A numerical study of open atmospheric balloon dynamics

The dynamics of open balloons in an atmosphere may be studied with a body-fluid coupled model. A numerical approach is required to solve the corresponding equation set. Solutions under different conditions are obtained here for the vertical and one horizontal direction. Relevant dynamical features during ascent, flotation, and descent depend on balloon thermodynamics, wind, air small-scale turbulence, and perturbations to the background atmosphere. After analysis of the results it is found that approximate analytical solutions may be found in certain cases. The effect of nonlinear drag on balloon oscillation period and damping near flotation is evaluated.

Effects of Nonlinear Drag and Negative Loop Correlations on Heavy Particle Motion in Isotropic Stationary Turbulence Using a New Lagrangian Stochastic Model

A new model for the prediction of particle dispersion in homogeneous isotropic stationary turbulence, based on an autoregressive moving average (ARMA) process, is presented in order to predict the fluctuating component of the fluid velocity along a heavy particle path. This model accounts for the crossing trajectory effect in that the transverse fluid velocity correlation is perfectly consistent with the negative loop correlation derived by Wang and Stock (1993). The particle turbulent intensity is shown to be increased compared to predictions based on exponential correlations. Possible consequences of the finite particle Reynolds number are also investigated, showing that the anisotropy of the motion of heavy particles is increased by nonlinear drag effects. In case of zero mean drift velocity, significant effects of nonlinear drag may also appear.

Temperature fluctuations of discrete particles in a homogeneous turbulent flow: a Lagrangian model

Within the frame of Lagrangian approaches for the prediction of heat transfer in dispersed two-phase flows, a new dispersion model is proposed which involves correlated stochastic processes to predict the velocity and temperature of a discrete particle along its path in terms of the instantaneous velocity and temperature of the surrounding fluid element. The dispersion problem is carefully addressed in taking into account the anisotropy of the flow and the turbulent heat flux resulting from velocity–temperature correlations. The model is used to simulate the behavior of particles suspended in a homogeneous turbulent shear flow. The numerically predicted correlations between the fluctuating quantities are in perfect agreement with the results of an analytical study by Zaichik (Phys. Fluids 11 (1999) 1521–1534). A supplementary investigation of the associated effects of non-linear drag and heat transfer is then proposed.

Modelling turbulent collision of bidisperse inertial particles

We study finite-inertia effects on the collision rate of bidisperse heavy particles in a turbulent gas, using direct numerical simulations and kinematic descriptions. As shown previously for a monodisperse system (Sundaram & Collins 1997; Wang, Wexler & Zhou 2000), a statistical mechanical description of the average collision kernel consists of two parts, namely a description of the relative velocity between two colliding particles (the turbulent transport effect) and of the non-uniform particle distribution due to dynamic interaction of particles with coherent vortex structures (the accumulation effect). We first show that this description remains valid and accurate for a bidisperse system involving two groups of particles of inertial response time τp1 and τp2, respectively. Numerical results for the turbulent transport effect and the accumulation effect have been obtained as a function of τp1 and τp2. Interestingly, the accumulation effect in a bidisperse system is bounded above by that of a monodisperse system. An explanation for this observation is given, in terms of the correlation between concentration fields of the two size groups. Simulations show that particles from two size groups were found in different regions of a vortex, thus reducing the net accumulation effect in a bidisperse system. The turbulent transport effect, on the other hand, is bounded below by the level in a monodisperse system, due to a differential inertia effect. The above observations imply that the size polydispersity enhances the turbulent transport effect but weakens the accumulation effect, relative to a monodisperse system.A simple eddy–particle interaction (EPI) model was developed and shown to give a reasonable prediction of the collision kernel, except for a small parametric region where both τp1 and τp2 are on the order of the ow Kolmogorov time τk and thus the accumulation effect must be included. A more accurate model incorporating both the turbulent transport effect and the accumulation effect has also been developed. The model would provide an upper bound on the collision rates for a non-dilute bidisperse system, since turbulence modulation and particle-particle interactions are not considered in this model.Finally, some consideration is given to the effect of nonlinear drag on the collision kernel. The results show that the drag nonlinearity can increase the collision kernel slightly (less than 10%) at large particle inertia.

Effect of nonlinear drag on the settling velocity of particles in homogeneous isotropic turbulence

We study the average settling velocity of small spherical particles under gravity through a Gaussian random velocity field generated by Fourier modes with a von Kárman energy spectrum. The particles are subjected to the effects of a linear (Stokes) or nonlinear drag force, inertia and gravity. It is shown that the effect of drag nonlinearity is a function of the particle to fluid density ratio ρp/ρf and a function of the ratio τp/τk of the particle time constant to the Kolmogorov timescale of the fluid. Simulations show that as ρp/ρf decreases from 877 to 2.65 or as τp/τk increases from 1 to 2.74, the drag nonlinearity increases as a result of the increase in particle Reynolds numbers. Hence the settling velocity changes from larger to smaller as compared with the still fluid settling velocity, showing that one of the major mechanisms governing the fall velocity reduction in a turbulent flow is the drag nonlinearity. The maximum increase in settling rate occurs at VT/υk ≈ 2 for ρp/ρf ≥ 87 (where VT is the terminal velocity of the particle and υk is the Kolmogorov velocity); this is consistent with the results of Wang and Maxey [1993]. The maximum decrease in settling rate occurs at VT/VK ≈ 1 for ρp/ρf ≈ 2.65, consistent with the results of Fung [1993]. In addition, the role of the spatial and temporal variations of the flow field on the settling rate is investigated. Finally, the Gaussian velocity field is also simulated with an exponential energy spectrum, and similar results are observed.

A simple description of some inertia effects in the behaviour of heavy particles in a turbulent gas flow

The effects of some inertia parameters and the influence of non-linear drag in the behaviour of heavy particles in a turbulent gas flow are investigated by examining th properties of their streamwise fluctuating motion. The particles are suspended in a stationary homogeneous turbulent gas flow, under the influence of an external body force field, which implies a non-zero mean slip velocity between the two phases. Two kinds of methods, the results of which are compared, are used. The first method is based on a simplified kinematic simulation of the fluid velocity fluctuation in the streamwise direction, according to a known turbulence spectrum. The second method is a classical Lagrangian tracking technique. The presence of an external body force field makes the particle turbulent response depend on three dimensionless parameters, among them the conventional Stokes number St and the particle Reynolds number Re p , based on the mean relative velocity between the fluid and the particle, are found to be the most influential ones for heavy particles. A particle response diagram is built, leading to an approximate expression for the particle-to-fluid turbulent intensity ratio in terms of a modified Stokes number which embodies the effects of both St and Re p . Numerical predictions are provided in the case of an upward vertical flow, in a large range of particle mean Reynolds numbers exceeding unity. A significant influence of the drag non-linearity can be observed. The main conclusion is that the effect of non-linear drag may surpass the well-known crossing-trajectory effect, in causing the particle mean-square velocity to increase with increasing mean relative velocity, contrary to what is generally expected for small inertia particles.

The Effect of Nonlinear Drag on the Motion and Settling Velocity of Heavy Particles

Abstract The effects of nonlinear drag on the motion and settling velocity of heavy particles in a turbulent atmosphere are investigated. The authors approach the problem rather systematically by first considering the response of particles to much simpler fluid motions that are subprocesses of the more complex turbulent field. The authors first consider the motion and time response of particles falling under gravity in still fluid. Then the effects of a sudden gust or step change in relative velocity between a falling particle and its surrounding fluid are investigated. The authors demonstrate that horizontal relative motion produced by a sudden gust tends to reduce the settling velocity of a panicle. In simple oscillating fluids it is shown that the reduction of settling velocity increases with increasing amplitude of fluid oscillation. The authors also explore the effects of oscillation frequency on the settling velocity and show that if the period of fluid oscillation is less than the particle response...

Response of articulated tower platforms to random wind and wave forces

The displacement response of an articulated tower is mainly governed by its rigid body mode of vibration which has a very low frequency. Since the wind velocity spectrum of the fluctuating component has a low frequency energy content, the wind-induced vibration of an articulated tower may be significant. The combined wind-, wave- and current-induced vibration of the tower is an important phenomenon to study because of the complex hydrodynamic interactions. In this paper, the response of a model articulated tower to random wind force alone and to the combined effect of wind, wave and current forces is investigated. Only the first-order forces due to the waves have been considered. The response of the tower is determined by a frequency domain iterative method and is evaluated for a parametric study. Both wind velocity and random sea are characterized by Power Spectral Density Functions. A Monte-Carlo simulation procedure is used to obtain sample records of time histories of both the wind velocity and water particle kinematics. The response analysis considers the nonlinearities due to writing the equilibrium equation based on the instantaneous position of the tower and relative-velocity squared drag force. Using this method of analysis a parametric study is conducted to investigate the behaviour of the tower under different important factors which include the pressure drag effect, the effect of nonlinear drag on both wind and wave forces, the mean wind velocity at the reference height, the current velocity and different combinations of wind, wave and current forces.

Linearization Technique for Probabilistic Riser Frequency Domain Analysis

This paper presents a rigorous derivation of equations for the minimization of the mean-squared error and defines the describing function for different input components. The technique has a direct application to analyze the dynamic response of marine risers. The describing function method will be used to determine the linearization coefficients for the nonlinear drag effects, taking into account a steady current and the random sea waves. The method will have significant impact on other problems such as fixed offshore platforms and tension leg platforms.

Stochastic seismic analysis of offshore towers

After a brief review of the main problems and the most common analysis methods for offshore structures, a method of analysis for offshore towers submerged in water and subjected to strong earthquake motions is proposed. Nonlinear drag effects as well as random non-stationary seismic excitations are considered by means of a linearization technique based on a particular step-by-step procedure. Using a discrete lumped-mass model, the standard deviations of nodal displacements and velocities are evaluated. The probability of not exceeding a defined threshold of nodal displacements is also computed.