Study on the Rheology of Foam Fracturing Fluid with Mixture Model

2012 ◽  
Vol 512-515 ◽  
pp. 1747-1752 ◽  
Author(s):  
Xiao Sun ◽  
Shu Zhong Wang ◽  
You Lian Lu
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Mixture Model ◽  
Turbulent Viscosity ◽  
Bubble Diameter ◽  
Fracturing Fluid ◽  
Viscosity Increase ◽  
Change Trend ◽  
Simulation Results

Numerical simulation study on the rheology or foam fluid was carried through by treating inner phase as granular fluid with mixture model. The simulation results show that the gas phase is well distributed on cross-section. Besides, the higher the foam quality, the higher the velocity gradient near the wall. For turbulent properties, the turbulent kinetic energy and viscosity increase as the foam quality increases. With the same foam quality, the bigger the bubble diameter, the higher the turbulent viscosity and turbulent kinetic energy. What’s more, the foam quality 63% is a catastrophe point at which the rheology of foam fracturing fluid changes sharply. The change trend of turbulent viscosity along radial direction is different between the regions where the foam quality is below and over catastrophe point, and in the latter the change trend is flatter. From the simulation results it can be seen that the mixture model is more applicable and effective to the region where foam quality is over 63%.

scholarly journals A New Method to Determine the Impact of Individual Field Quantities on Cycle-to-Cycle Variations in a Spark-Ignited Gas Engine

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4136
Author(s):  
Clemens Gößnitzer ◽  
Shawn Givler
Keyword(s):  
Kinetic Energy ◽  
Flow Field ◽  
Turbulent Kinetic Energy ◽  
Negative Impact ◽  
Operating Conditions ◽  
Engine Operation ◽  
Gas Engine ◽  
Cycle Simulation ◽  
Simulation Results ◽  
The Impact

Cycle-to-cycle variations (CCV) in spark-ignited (SI) engines impose performance limitations and in the extreme limit can lead to very strong, potentially damaging cycles. Thus, CCV force sub-optimal engine operating conditions. A deeper understanding of CCV is key to enabling control strategies, improving engine design and reducing the negative impact of CCV on engine operation. This paper presents a new simulation strategy which allows investigation of the impact of individual physical quantities (e.g., flow field or turbulence quantities) on CCV separately. As a first step, multi-cycle unsteady Reynolds-averaged Navier–Stokes (uRANS) computational fluid dynamics (CFD) simulations of a spark-ignited natural gas engine are performed. For each cycle, simulation results just prior to each spark timing are taken. Next, simulation results from different cycles are combined: one quantity, e.g., the flow field, is extracted from a snapshot of one given cycle, and all other quantities are taken from a snapshot from a different cycle. Such a combination yields a new snapshot. With the combined snapshot, the simulation is continued until the end of combustion. The results obtained with combined snapshots show that the velocity field seems to have the highest impact on CCV. Turbulence intensity, quantified by the turbulent kinetic energy and turbulent kinetic energy dissipation rate, has a similar value for all snapshots. Thus, their impact on CCV is small compared to the flow field. This novel methodology is very flexible and allows investigation of the sources of CCV which have been difficult to investigate in the past.

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

2015 ◽  
Vol 770 ◽  
pp. 210-246 ◽  
Author(s):  
M. Mehrabadi ◽  
S. Tenneti ◽  
R. Garg ◽  
S. Subramaniam
Keyword(s):  
Kinetic Energy ◽  
Phase Velocity ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Reynolds Stress ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

scholarly journals Architecture of Open Source Program for Numerical Modeling of Flows on Mountain Slopes

2020 ◽  
Vol 32 (6) ◽  
pp. 183-200
Author(s):  
Daria Igorevna Romanova
Keyword(s):  
Mathematical Model ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Velocity Model ◽  
Three Dimensional Modeling ◽  
Averaged Equations

In this paper, we compare two approaches to describe the dynamics of flows on mountain slopes using the depth-averaged equations of continuum mechanics and using the complete, not depth-averaged, equations of continuum mechanics for three-dimensional modeling. Using these two approaches, a simulation of an experimental slush flow in the tank and the interaction of the flow with dam barrier protection was carried out. Numerical solutions are compared with experimental data. Also, both approaches are applied to the calculation of an avalanche in the 22nd avalanche cite of Mount Yukspor (Khibiny). Avalanche run-out distance and the shape of the avalanche deposits are compared with field data obtained from the measurement of a real avalanche. In the course of a numerical experiment, distributions of such quantities as flow velocity, depth, density, molecular and turbulent viscosity, values of the density of turbulent kinetic energy, dissipation of turbulent kinetic energy, and shear stress at the bottom of the flow were obtained. Using the obtained data a mathematical model is developed to describe the entrainment of the underlying material by the flow during slope erosion and the deposition of the flow material on the slope. To implement the obtained mathematical model, the architecture of the multiphaseEulerChangeFoam solver was developed, which implements a three-phase multi-velocity model with phase exchange between the material of the underlying surface and the material of the flow. The classic solver multiphaseEulerFoam from the OpenFOAM package is taken as a basis for the developed solver.

Effects of surface roughness on self-excited cavitating water jet intensity in the organ-pipe nozzle: Numerical simulations and experimental results

2019 ◽  
Vol 33 (27) ◽  
pp. 1950324
Author(s):  
Xiangdong Han ◽  
Yong Kang ◽  
Deng Li ◽  
Weiguo Zhao
Keyword(s):  
Numerical Simulation ◽  
Surface Roughness ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Intensity ◽  
Volume Fraction ◽  
Water Jet ◽  
The Self ◽  
Simulation Results ◽  
Organ Pipe

This study was conducted to investigate effects of surface roughness on self-excited cavitating water jet intensity in an organ-pipe nozzle. Roughness average (Ra) values are 0.8, 1.6, 3.2, 6.3, 12.5, and 25 [Formula: see text]m, respectively. Numerical simulation results indicate that at inlet pressure of 10 MPa, the maximum, minimum, and real-time pressures in the self-excited oscillation chamber reach their respective peak values. The turbulent kinetic energy intensity in the external flow region is also most intense at this point, the vapor volume fraction in orifice is the highest, the vortex distribution scope in the orifice is the largest under [Formula: see text], and the self-excited cavitating water jet intensity is the strongest. The opposite variations emerge at [Formula: see text] compared to those of [Formula: see text], where the intensity is weakest. Pressure varies only slightly as Ra varies from 0.8 [Formula: see text]m to 6.3 [Formula: see text]m. Turbulent kinetic energy intensity behaves similarly as Ra increases from 0.8 [Formula: see text]m to 3.2 [Formula: see text]m. At [Formula: see text], it was weaker than at Ra = 0.8–3.2 [Formula: see text]m. Similarly, there are only slight differences in vapor volume fraction and vortex distribution scope with Ra from 0.8 [Formula: see text]m to 6.3 [Formula: see text]m. The intensities at Ra = 0.8–3.2 [Formula: see text]m are similar, and weaker at Ra = 6.3 [Formula: see text]m. Pressure values are maximal at inlet pressure of 20 MPa, turbulent kinetic energy intensity is most intense, vapor volume fraction is highest, vortex distribution scope is largest under [Formula: see text] [Formula: see text]m, and intensity is strongest. Distinctions among pressure, turbulent kinetic energy intensity, vapor volume fraction, and vortex distribution scope values with Ra from 0.8 [Formula: see text]m to 3.2 [Formula: see text]m are slight. Differences in the corresponding intensities are also slight; all decrease with Ra from 12.5 [Formula: see text]m to 25 [Formula: see text]m as the intensity gradually weakens. Numerical simulation results were validated by comparison against corresponding experimental phenomena.

Investigating Multiphase Turbulence Statistics of Large-Scale Two-Way Coupled Gravity-Driven Flows

2014 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Kinetic Theory ◽  
Turbulent Kinetic Energy ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Granular Temperature ◽  
Particle Phase ◽  
Simulation Results ◽  
Filtering Approach

Starting from the kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-average (RA) equations were recently derived for the particle phase in a collisional gas-particle flow by Fox [1]. The turbulence model solves for the RA particle volume fraction, the phase-average (PA) particle velocity, the PA granular temperature, and the PA particle turbulent kinetic energy (TKE). A clear distinction is made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. Mesoscale direct numerical simulation (DNS) can be used to assess the validity of the closures proposed for the unclosed terms that arise due to nonlinearities in the hydrodynamic model. In order to extract meaningful statistics from simulation results, a separation of length scales must be established to distinguish between the PA particle TKE and the PA granular temperature. In this work, we introduce an adaptive spatial filter with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The filtering approach is applied to fully-developed cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. Simulation results show a strong correlation between the local volume fraction and granular temperature, with maximum values located just upstream of clusters (i.e., where maximum compressibility of the particle velocity field exists), and negligible particle agitation is observed within clusters.

scholarly journals Numerical Thermodynamic Analysis of Two-Phase Solid-Liquid Abrasive Flow Polishing in U-Type Tube

2014 ◽  
Vol 6 ◽  
pp. 921831 ◽  
Author(s):  
Junye Li ◽  
Zhaojun Yang ◽  
Weina Liu ◽  
Weihua Cai ◽  
Zemin Qiao
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dynamic Pressure ◽  
Turbulent Viscosity ◽  
Internal Surface ◽  
Two Phase ◽  
Solid Liquid ◽  
Abrasive Flow Polishing ◽  
Type Tube

U-type tubes are widely used in military and civilian fields and the quality of the internal surface of their channel often determines the merits and performance of a machine in which they are incorporated. Abrasive flow polishing is an effective method for improving the channel surface quality of a U-type tube. Using the results of a numerical analysis of the thermodynamic energy balance equation of a two-phase solid-liquid flow, we carried out numerical simulations of the heat transfer and surface processing characteristics of a two-phase solid-liquid abrasive flow polishing of a U-type tube. The distribution cloud of the changes in the inlet turbulent kinetic energy, turbulence intensity, turbulent viscosity, and dynamic pressure near the wall of the tube were obtained. The relationships between the temperature and the turbulent kinetic energy, between the turbulent kinetic energy and the velocity, and between the temperature and the processing velocity were also determined to develop a theoretical basis for controlling the quality of abrasive flow polishing.

Swirling, Particle-Laden Flows Through a Pipe Expansion

1992 ◽  
Vol 114 (4) ◽  
pp. 648-656 ◽  
Author(s):  
M. Sommerfeld ◽  
A. Ando ◽  
D. Wennerberg
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Gas Phase ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Particle Dispersion ◽  
Recirculation Bubble ◽  
Numerical Predictions ◽  
Pipe Expansion

The present study concerns a particle-laden, swirling flow through a pipe expansion. A gas-particle flow enters the test section through a center tube, and a swirling air stream enters through a coaxial annulus. The swirl number based on the total inflow is 0.47. Numerical predictions of the gas flow were performed using a finite-volume approach for solving the time-averaged Navier-Stokes equations. The predicted mean velocity profiles showed good agreement with experimental results when using the standard k-ε turbulence model. The turbulent kinetic energy of the gas phase, however, is considerably underpredicted by this turbulence model, especially in the initial mixing region of the two jets. The particle dispersion characteristics in this complex flow were studied by using the Lagrangian method for particle tracking and considering the particle size distribution. The influence of the particle phase onto the fluid flow was neglected in the present stage, since only low particle loadings were considered. The particle mean velocities were again predicted reasonably well and differences between experiment and simulation were only found in the velocity fluctuations, which is partly the result of the underpredicted turbulent kinetic energy of the gas phase. The most sensitive parameter for validating the quality of numerical simulations for particle dispersion is the development of the particle mean number diameter which showed reasonable agreement with the experiments, except for the core region of the central recirculation bubble. This, however, is attributed again to the predicted low turbulent kinetic energy of the gas phase.

Numerical modeling of the influence of bubbles on flow and heat transfer in the descending gas-liquid flow in a pipe

2012 ◽  
Vol 9 (1) ◽  
pp. 131-135
Author(s):  
M.A. Pakhomov
Keyword(s):  
Heat Transfer ◽  
Gas Phase ◽  
Liquid Flow ◽  
Bubble Diameter ◽  
Gas Content ◽  
Two Phase ◽  
Eulerian Description ◽  
Flow And Heat Transfer ◽  
Gas Liquid Flow ◽  
The Mathematical Model

The paper presents the results of modeling the dynamics of flow, friction and heat transfer in a descending gas-liquid flow in the pipe. The mathematical model is based on the use of the Eulerian description for both phases. The effect of a change in the degree of dispersion of the gas phase at the input, flow rate, initial liquid temperature and its friction and heat transfer rate in a two-phase flow. Addition of the gas phase causes an increase in heat transfer and friction on the wall, and these effects become more noticeable with increasing gas content and bubble diameter.

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