Variable Density Fluid Research Articles

A 3D unstructured triangular numerical algorithm for simultaneous effects of fluid density variation and water table gradient in saturated porous media

A fully three dimensional hydrodynamic implicit numerical algorithm has been proposed for simultaneous simulation of fluid density variation and water table gradient in saturated porous media. Unlike the most of the performed researches that primarily restricted to solute transport simulation in confined or unconfined aquifers without proceeding to forecast water table transient situation, the proposed model can truly handle corresponding problems in an unconfined aquifer having sharp water table gradient. The algorithm is based upon a staggered finite volume scheme on an unstructured triangular mesh in the plane and structured grid in vertical that solves the most general form of Darcy equation without limiting assumptions, not expressed as a function of the groundwater potential but presented in term of the water pressure. Avoiding the excessive computational efforts, an efficient and simple algorithm has been proposed to discretize flow equations, track the water table position and determine salinity distribution. A line iterative method has been utilized efficiently, in a way that, resultant linear equations system splits into a series of tri-diagonal square matrix systems whereby the direct together with iterative procedure employed simultaneously to achieve problem unknowns. Prediction of passive scalar salinity quantity has been achieved efficiently by employing the advantageous time splitting algorithm. This has allowed designing and applying different numerical schemes more compatible with the mathematical and physical properties of the corresponding phenomena. Performance of the 3D model has been validated against a range of problems. Comparison between numerical results, analytical solutions, and experimental data demonstrates that the model represents well the simultaneous effects of fluid density variation and water table gradient processes.

Fully iterative ILU preconditioning of the unsteady Navier–Stokes equations for GPGPU

In this work we investigate the numerical difficulties that arise in optimizing the efficiency of Newtonian fluids simulations on a massively parallel computing hardware like a GPU. In particular, we will concentrate on the resulting algebraic problem. We will present an approximate, fully-iterative, ILU preconditioner and we will show that this solution is very efficient on a GPU if compared with an intrinsic massively parallel preconditioner like the diagonal preconditioner, which indeed goes faster than more robust techniques, like ILU, despite their strong decrease in the number of iterations. We refer to GMRES as the iterative scheme used to solve the linear system. In particular, we will deal with the solution of incompressible flows with variable density and we will investigate the interplay between Reynolds and Atwood numbers. We will show that the numerical simulation at medium–high Reynolds numbers produces linear systems whose matrices can be reasonably preconditioned with the diagonal preconditioner, while at low Reynolds numbers the higher viscosity of the fluid makes the diagonal preconditioner ineffective in the solution time requested from GMRES and, decreasing the Reynolds number, unable to let GMRES converge at all. In this situation, we will show how an adequate iterative approach to the parallel solution of the triangular systems that result from the ILU preconditioning, turns out to be robust and efficient. We will show numerical results for variable-density fluids, discretized with the scheme described in Calgaro et al. (2008), in classical benchmarks and, in particular, in the well-known Rayleigh–Taylor instability.

Dynamic analysis of a cantilevered pipe conveying fluid with density variation

The fluid flow conveyed by a cantilevered pipe might be a multi-phase flow, the density of which can fluctuate with time and space. In this paper, variable density fluid is simulated by a new mathematical model that satisfies the continuity of the fluid flow. The fluid forces acting on the pipe are derived from Newton’s second law. Combined with a Bernoulli–Euler beam model, a new dynamic model for a cantilevered pipe conveying a variable density fluid is established. The numerical results of the present model can be obtained by utilizing finite difference methods and agree with the classical theoretical results. The influences of the fluctuating amplitude, wave number and initial phase angle of the fluid density on the stability and dynamics of the cantilevered pipe system are analysed in detail. It can be found that when the fluid density varies with a large amplitude, the cantilevered pipe system is prone to losing its stability, which consequently leads to flutter. A small wave number of the fluid density has a notable influence on the system’s stability. Moreover, the stability of this system is seldom affected by the initial phase angle of the fluid density. Based on the current research work, an improved stability criterion is proposed with which the stability of the present system can be more precisely determined.

Numerical analysis on non-uniform flow and heat transfer of supercritical cryogenic methane in a heated horizontal circular tube

This paper numerically studied non-uniform flow and heat transfer of supercritical cryogenic methane in a heated horizontal circular tube. Numerical results indicated that the peak value of heat transfer coefficient appeared near the vicinity of pseudo-critical point. The Reynold number monotonically increased with the augment of bulk fluid temperature, however, the Prandtl number exhibited both peak and trough values. Compared with mass fluxes, operating pressures had less influence on the heat transfer performances. Moreover, the flow stratification phenomenon and lateral secondary flows were developed as a result of the combined interaction of buoyancy and gravity. The “flow acceleration” caused by the variation of bulk fluid density had important effect on the decrease of heat transfer capacity. Further analysis demonstrated that the Blasius and Han models were suggested to predict the pressure drop and heat transfer of supercritical cryogenic methane.

A numerical study on the non-Boussinesq effect in the natural convection in horizontal annulus

In the present study, the non-Boussinesq effect in the thermal convection in an air-filled horizontal concentric annulus is studied numerically by using the variable property-based lattice Boltzmann flux solver (VPLBFS), with the radial temperature difference ratio of 1.0, the radius ratio of 2.0, and the Rayleigh number in the range 104 ≤ Ra ≤ 106. Several solutions are obtained by using the standard form or simplified versions of the VPLBFS, including the real solution with the total variation in fluid properties considered, named as the variable property solution (VPS), the constant property solution (CPS) based on the Boussinesq approximation, the solution with variable dynamic viscosity (VVS), the solution based on the partial Boussinesq approximation (PBAS), the solution with variable thermal conductivity (VCS) and the solution with variable fluid density (VDS). The discrepancy between these solutions is analyzed to illuminate the influence of the non-Boussinesq effects induced by partial or total variation in fluid properties on flow instability behaviors and heat transfer characteristics. The present study reveals the complicated flow instability behavior under non-Boussinesq conditions and its tight association with heat transfer characteristics. Also, it demonstrates the necessity of considering the integral effect of the total variation in fluid properties and highlights the essential role of the fluid density variation.

IB2d Reloaded: A more powerful Python and MATLAB implementation of the immersed boundary method

The immersed boundary (IB) method is an elegant way to fully couple the motion of a fluid and deformations of an immersed elastic structure. In that vein, the IB2d software allows for expedited explorations of fluid‐structure interaction for beginners and veterans to the field of computational fluid dynamics. While most open‐source computational fluid dynamics codes are written in low‐level programming environments, IB2d was specifically written in high‐level programming environments to make its accessibility extend beyond scientists with vast programming experience. Although previously introduced by Battista et al. 2006 many improvements and additions have been made to the software to allow for even more robust models of material properties for the elastic structures, including a data analysis package for both the fluid and immersed structure data, an improved time‐stepping scheme for higher accuracy solutions, and functionality for modeling slight fluid density variations as given by the Boussinesq approximation.

Static and dynamic properties of smoothed dissipative particle dynamics

In this paper, static and dynamic properties of the smoothed dissipative particle dynamics (SDPD) method are investigated. We study the effect of method parameters on SDPD fluid properties, such as structure, speed of sound, and transport coefficients, and show that a proper choice of parameters leads to a well-behaved and accurate fluid model. In particular, the speed of sound, the radial distribution function (RDF), shear-thinning of viscosity, the mean-squared displacement (〈R2〉∝t), and the Schmidt number (Sc∼O(103)−O(104)) can be controlled, such that the model exhibits a fluid-like behavior for a wide range of temperatures in simulations. Furthermore, in addition to the consideration of fluid density variations for fluid compressibility, a more challenging test of incompressibility is performed by considering the Poisson ratio and divergence of velocity field in an elongational flow. Finally, as an example of complex-fluid flow, we present the applicability and validity of the SDPD method with an appropriate choice of parameters for the simulation of cellular blood flow in irregular geometries. In conclusion, the results demonstrate that the SDPD method is able to approximate well a nearly incompressible fluid behavior, which includes hydrodynamic interactions and consistent thermal fluctuations, thereby providing, a powerful approach for simulations of complex mesoscopic systems.

Image of local energy anomaly during a heavy rainfall event**Project supported by the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology, China (Grant Nos. GYHY201406003 and GYHY201406001), the Opening Foundation of the State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences (Grant Nos. 2015LASW-B01 and 2015LASW-A02), and the National Natural

A clear and interesting image of local total energy anomaly (EA) is depicted for a heavy rainfall event in this study. Before the convection development, it exhibits a positive local EA, implying local total energy (TE) experiences heaping up to prepare for the future system development. As the convection grows, it transforms into an opposite spatial modality with negative EA dominant, which means that the local TE is consumed to feed the convection growth in the middle and lower levels. The local total EA has consistent variation regular in intensity with severe weather system evolution. By utilizing the local TE budget equation in variable density fluid, the flux divergence of energy and its components are investigated, which could account for the local TE variation better. To relax the restriction and complexity introduced by identifying sporadic and alternative positive/negative signals of EA, the method taking the absolute-value operator on energy flux divergence is used to further simplify analyses. The derived characteristic signal of absolute EA is clearer and cleaner than before. Thus, the EA could be illustrated based on the active degree of energy supply/consumption in a generalized sense whatever positive or negative anomaly should be it, which could be used easily to identify and even predict the system development for operational application. Note that, although two sets of methodologies are used to define EA herein, they play absolutely different roles in nature throughout the whole context. For example, the taking-perturbation method provides a diagnostic tool to portray a preliminary sketch and to give sufficient necessity of this research, while tendency equation of local TE illuminates more predictive sense and accounts for future local EA related to following system evolution. Therefore, the latter could be a more effective tool to routine usage.

A unified phase equilibrium model for hydrogen solubility and solution density

For the transition to a clean and sustainable energy production from renewable sources like solar or wind power, large and secure storage of energy is required to compensate for the intermittent nature of these sources. Hydrogen could be a suitable energy carrier and hydrogen geological storage could provide the large capacities required. During storage hydrogen will be brought in contact with the formation fluids present, resulting in dissolution and possibly inducing geochemical reactions. Therefore in this work an accurate, consistent and reliable hydrogen solubility model is established, which allows to calculate the hydrogen solubility in the formation fluid and the corresponding variation of fluid density. The model accounts for system pressure, temperature and formation fluid salinity as well as the molar fraction, fugacity coefficient, Henry's constant, Poynting factor and activity coefficient of hydrogen. In the range of typical hydrogen geological storage conditions of 273–373 K, 1–50 MPa and 0–5 mol/kg NaCl this model can reproduce all available experimental data and predict hydrogen solubility in the formation fluid and the formation fluid density accurately. The model can predict hydrogen solubility within a maximum relative error of 5% for pure water and 15% for brines within the salinity range considered, which is in the range of uncertainty of measurement data. For realistic hydrogen gas geological storage, the model is extended to represent also H2-N2 or H2-CH4 mixed gas systems as well as mixed electrolyte solutions containing Na, K, Ca, Mg, Cl or SO4 and combinations of those. Model derivation, model calculations and implementation as well as an application example are presented to demonstrate the applicability of the developed methods and the model.

On modification of pressure gradient operator in integrated ISPH for multifluid and porous media flow with free-surface

In Incompressible Smoothed Particle Hydrodynamics (ISPH) simulation, choice of pressure gradient operator plays an important role. Variations in effective porosity, fluid density, and free-surface conditions dictate the nature of the formulation. This study proposes an integrated ISPH framework with an implicit free-surface treatment. Pressure variation at the multi-fluid interface is maintained using a modified density-weighted pressure gradient with linear momentum conservation. Different pressure gradients with diffused interfaces for a porous domain as well as multifluid interface have been compared with the proposed operator. A unified form of Brinkman and Navier-Stokes equations are utilized to describe the flow-physics inside and outside the porous domain. Density variation in fluids is modelled by solving the scalar-transport equation. Effect of the porous domain is incorporated in terms of varying representative volume of the fluid particles. Porous media interface conditions are implicitly implemented using Darcy velocity and by introducing porosity into Pressure Poisson Equation (PPE). The present model is capable of minimizing error in velocity-divergence due to implicit free-surface treatment combined with linear momentum conservation. Proposed framework is validated by using existing experimental data of density-dependent flow with very low-density ratio and flow through porous blocks. A result of density-current passing through porous domain demonstrates the capability of the developed model for complex scenarios.

A finite volume shock‐capturing solver of the fully coupled shallow water‐sediment equations

SummaryThis paper describes a numerical solver of well‐balanced, 2D depth‐averaged shallow water‐sediment equations. The equations permit variable horizontal fluid density and are designed to model water‐sediment flow over a mobile bed. A Godunov‐type, Harten–Lax–van Leer contact (HLLC) finite volume scheme is used to solve the fully coupled system of hyperbolic conservation laws that describe flow hydrodynamics, suspended sediment transport, bedload transport and bed morphological change. Dependent variables are specially selected to handle the presence of the variable density property in the mathematical formulation. The model is verified against analytical and semi‐analytical solutions for bedload transport and suspended sediment transport, respectively. The well‐balanced property of the equations is verified for a variable‐density dam break flow over discontinuous bathymetry. Simulations of an idealised dam‐break flow over an erodible bed are in excellent agreement with previously published results, validating the ability of the model to capture the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure of the system of variable‐density governing equations. Flow hydrodynamics and final bed topography of a laboratory‐based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical model. Comparison of the final bed topographies, computed for two distinct sediment transport methods, highlights the sensitivity of shallow water‐sediment models to the choice of closure relationships. Copyright © 2016 John Wiley & Sons, Ltd.

Spectral analysis of energy transfer in turbulent flows laden with heated particles

In this study we consider particle-laden turbulent flows with significant heat transfer between the two phases due to sustained heating of the particle phase. The sustained heat source can be due to particle heating via an external radiation source as in the particle-based solar receivers or an exothermic reaction in the particles. Our objective is to investigate the effects of fluid heating by a dispersed phase on the turbulence evolution. An important feature in such settings is the preferential clustering phenomenon which is responsible for non-uniform distribution of particles in the fluid medium. Particularly, when the ratio of particle inertial relaxation time to the turbulence time scale, namely the Stokes number, is of order unity, particle clustering is maximized, leading to thin regions of heat source similar to the flames in turbulent combustion. However, unlike turbulent combustion, a particle-laden system involves a wide range of clustering scales that is mainly controlled by particle Stokes number. To study these effects, we considered a decaying homogeneous isotropic turbulence laden with heated particles over a wide range of Stokes numbers. Using a low-Mach-number formulation for the fluid energy equation and a Lagrangian framework for particle tracking, we performed numerical simulations of this coupled system. We then applied a high-fidelity framework to perform spectral analysis of kinetic energy in a variable-density fluid. Our results indicate that particle heating can considerably influence the turbulence cascade. We show that the pressure-dilatation term introduces turbulent kinetic energy at a range of scales consistent with the scales observed in particle clusters. This energy is then transferred to high wavenumbers via the energy transfer term. For low and moderate levels of particle heating intensity, quantified by a parameter $\unicode[STIX]{x1D6FC}$ defined as the ratio of eddy time to mean temperature increase time, turbulence modification occurs primarily in the dilatational modes of the velocity field. However, as the heating intensity is increased, the energy transfer term converts energy from dilatational modes to divergence-free modes. Interestingly, as the heating intensity is increased, the net modification of turbulence by heating is observed dominantly in divergence-free modes; the portion of turbulence modification in dilatational modes diminishes with higher heating. Moreover, we show that modification of divergence-free modes is more pronounced at intermediate Stokes numbers corresponding to the maximum particle clustering. We also present the influence of heating intensity on the energy transfer term itself. This term crosses over from negative to positive values beyond a threshold wavenumber, showing the cascade of energy from large scales to small scales. The threshold is shown to shift to higher wavenumbers with increasing heating, indicating a growth in the total energy transfer from large scales to small scales. The fundamental energy transfer analysis presented in this paper provides insightful guidelines for subgrid-scale modelling and large-eddy simulation of heated particle-laden turbulence.

Simulation Methodology of the Screw-Centrifugal Pump for Liquid Hydrogen

The article describes the basic modeling methods of hydrodynamic processes in screw centrifugal hydrogen pumps using software ANSYS CFD; the variable fluid density is taken into account. Three methods of modeling fluid flow with variable density were proposed in ANSYS CFD. Regression models of variable density were obtained. Regression models characteristics are of the second and fourth order, the pressure range is from 0.09 to 30 MPa and the temperature range is from 18 to 34 K. Regression models were implemented in the method by reference variable density of liquid hydrogen in the form of functional dependence.

A New Calculation Method of Dynamic Kill Fluid Density Variation during Deep Water Drilling

There are plenty of uncertainties and enormous challenges in deep water drilling due to complicated shallow flow and deep strata of high temperature and pressure. This paper investigates density of dynamic kill fluid and optimum density during the kill operation process in which dynamic kill process can be divided into two stages, that is, dynamic stable stage and static stable stage. The dynamic kill fluid consists of a single liquid phase and different solid phases. In addition, liquid phase is a mixture of water and oil. Therefore, a new method in calculating the temperature and pressure field of deep water wellbore is proposed. The paper calculates the changing trend of kill fluid density under different temperature and pressure by means of superposition method, nonlinear regression, and segment processing technique. By employing the improved model of kill fluid density, deep water kill operation in a well is investigated. By comparison, the calculated density results are in line with the field data. The model proposed in this paper proves to be satisfactory in optimizing dynamic kill operations to ensure the safety in deep water.

An improved lattice Boltzmann method for simulating advective–diffusive processes in fluids

Lattice Boltzmann methods are widely used to simulate advective–diffusive processes in fluids. Lattice Bhatnagar–Gross–Krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared. Formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations. We present and demonstrate here a formulation that produces no such second order errors. This formulation suggests that a subtle, but important, adjustment is all it takes to improve the accuracy of the method. The key to the improved accuracy of this new model is the non-standard definition of the concentration that relates to the distribution function describing the advection–diffusion in lattice Boltzmann. The main advantage of the algorithm comes to view when simulating situations where fluid density variations appear. The present formulation of the advection–diffusion algorithm will, by taking into account these fluid density variations, drastically reduce the errors produced compared to the standard formulations. We also show how a source term is included in this new formulation without it losing its second order spatial accuracy.

Effect of salinity on mass and energy transport by hydrothermal fluids based on the physical and thermodynamic properties of H2O‐NaCl

AbstractVarious thermodynamic properties of H2O that are defined as pressure or temperature derivatives of some other variable, such as isothermal compressibility (β, pressure derivative of density), isobaric thermal expansion (α, temperature derivative of density), and specific isobaric heat capacity (cf, temperature derivative of enthalpy), all show large magnitudes near the critical point, reflecting large variations in fluid density and specific enthalpy with small changes in temperature and pressure. As a result, mass (related to fluid density) and energy (related to fluid enthalpy) transport in this PT region are sensitive to changing PT conditions. Addition of NaCl to H2O causes the region of anomalous behavior, here defined as the critical region, to migrate to higher temperatures and pressures. The critical region is defined as that region of PT space in which the dimensionless reduced susceptibility ≥ 0.5. When NaCl is added to H2O, the critical region migrates to higher temperature and pressure. However, the absolute magnitudes of thermodynamic properties that are defined as temperature and/or pressure derivatives (α, β, and cf) all decrease with increasing salinity. Thus, the mass and energy transporting capacities of hydrothermal fluids in the critical region become less sensitive to changing PT conditions as the salinity increases. For example, quartz solubility can be described as a function of fluid density, and because density becomes less sensitive to changing PT conditions as salinity increases, quartz solubility also becomes less sensitive to changing PT conditions as fluid salinity increases. Similarly, fluxibility describes the ability of a fluid to transport heat by buoyancy‐driven convection, and fluxibility decreases with increasing salinity. Results of this study show that the mass and energy transport capacity of fluids in the Earth's crust are maximized in the critical region and that the sensitivity to changing PT conditions decreases with increasing salinity.

Coupling between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces.

Recent investigations have revealed that ion transport from aqueous electrolytes to ion-selective surfaces is subject to electroconvective instability that stems from coupling of hydrodynamics with electrostatic forces. These systems inherently involve fluid density variation set by salinity gradients. However, the coupling between the buoyancy effects and electroconvective instability has not yet been investigated although a wide range of electrochemical systems are naturally prone to these interplaying effects. In this study we thoroughly examine the interplay of gravitational convection and chaotic electroconvection. Our results reveal that buoyant forces can significantly influence the transport rates, otherwise set by electroconvection, when the Rayleigh number Ra of the system exceeds a value Ra∼1000. We show that buoyancy forces can significantly alter the flow patterns in these systems. When the buoyancy acts in the stabilizing direction, it limits the extent of penetration of electroconvection, but without eliminating it. When the buoyancy destabilizes the flow, it alters the electroconvective patterns by introducing upward and downward fingers of respectively light and heavy fluids.

Influences of fluid properties on the hydrothermal fluid flow and alteration halos at the Dajishan tungsten deposit, China

The Nanling Range located in South China is a world-class tungsten province. Those tungsten deposits are spatially and temporally associated with the granitic magmatism during the Late Mesozoic (J2-K2). It is common that alteration halos decrease with increasing depth at the vein-type tungsten deposits. However, the mechanisms forming the alteration characteristics are still enigmatic. In this contribution, we investigate the influences of variable fluid density and viscosity on the fluid flow and species diffusion from fractures to adjacent wallrock at the Dajishan tungsten deposit using finite element based numerical experiments. Fluid density has a negative influence on the transient pressure-driven fluid flow at Dajishan. Large-density fluids slow fluid flow and heat transfer. High-viscosity fluids flow slowly. Variations of fluid viscosity at Dajishan are large and influence hydrothermal fluid flow and species diffusion from fractures to surrounding wallrock. Depth-dependent porosity and permeability of wallrock are effective mechanisms forming the alteration halos at Dajishan. Hydraulic and geometric characteristics of joint zones influence diffusion of chemical species at the initial stages of hydrothermal fluids injected into fractures. High-permeability narrow joint zones favor formation of thick alteration halos at shallower levels. Depth-dependent wallrock porosity also impedes diffusion of metals from fractures to adjacent wallrock increasing ore formation efficiency at Dajishan.

Methods of modeling the work process of hydrogen screw-centrifugal pumps using ANSYS CFD

Basic methods of modeling hydrodynamic processes in hydrogen screw-centrifugal pumps using the ANSYS CFD software are described in the paper, including those that take into account variable density of the fluid. Compressibility of liquid hydrogen caused by temperature and pressure changes, despite the alowances of average density, requires taking into account variable density for improved accuracy of modeling the workflow of hydrogen pumps. A technique of CFD-modeling of hydrogen pumps using special software tools to build the geometry and grid models of interblade channels is presented. Three methods for modeling variable-density fluid flows in ANSYS CFD are proposed. Regression models of the second and fourth orders have been obtained in the pressure range from 0.09 to 30 MPa and in the temperature range from 18 to 34 K to implement the method of setting variable density of liquid hydrogen in the form of functional relation.

Lattice Boltzmann Simulation of Particle Motion in Binary Immiscible Fluids

AbstractWe combine the Shan-Chen multicomponent lattice Boltzmann model and the link-based bounce-back particle suspension model to simulate particle motion in binary immiscible fluids. The impact of the slightly mixing nature of the Shan-Chen model and the fluid density variations near the solid surface caused by the fluid-solid interaction, on the particle motion in binary fluids is comprehensively studied. Our simulations show that existing models suffer significant fluid mass drift as the particle moves across nodes, and the obtained particle trajectories deviate away from the correct ones. A modified wetting model is then proposed to reduce the non-physical effects, and its effectiveness is validated by comparison with existing wetting models. Furthermore, the first-order refill method for the newly created lattice node combined with the new wetting model significantly improves mass conservation and accuracy.