scholarly journals The Seepage Model Considering Liquid/Solid Interaction in Confined Nanoscale Pores

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Xiaona Cui ◽  
Erlong Yang ◽  
Kaoping Song ◽  
Yuming Wang
Keyword(s):  
Solid Wall ◽  
Pore Wall ◽  
Interaction Coefficient ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Confined Space ◽  
Navier Stokes Equation ◽  
Capillary Radius ◽  
Seepage Model ◽  
Shale Reservoirs

Different from conventional reservoirs, nanoscale pores and fractures are dominant in tight or shale reservoirs. The flow behaviors of hydrocarbons in nanopores (called “confined space”) are more complex than that of bulk spaces. The interaction between liquid hydrocarbons and solid pore wall cannot be neglected. The viscosity formula which is varied with the pore diameter and interaction coefficient of liquids and solids in confined nanopores has been introduced in this paper to describe the interaction effects of hydrocarbons and pore walls. Based on the Navier-Stokes equation, the governing equation considered liquid/solid effect in two dimensions has been established, and approximate theoretical solutions to the governing equations have been achieved after mathematic simplification. By introducing the vortex equation, the complex numerical seepage model has been discretized and solved. Numerical results show that the radial velocity distribution near the solid wall has an obvious change when considering the liquid/solid interaction. The results consist well with that approximate mathematical solution. And when the capillary radius is smaller, the liquid and solid interaction coefficient n is greater. The liquid and solid interaction obviously cannot be neglected in the seepage model if the capillary radius is small than 50 nm when n>0.1. The numerical model has also been further validated by two types of nanopore flow tests: from pore to throat and inversely from throat to pore. There is no big difference in flow regularity of throat to pore model considering when liquid/solid interaction or not, whereas the liquid/solid interaction of pore to throat model totally cannot be overlooked.

Numerical Investigation of a Transient Operation of a Heat Pipe With Experimental Validation

2004 ◽  
Author(s):  
Gustavo Gutierrez ◽  
Juan Catan˜o ◽  
Tien-Chien Jen
Keyword(s):  
Heat Flux ◽  
Heat Pipe ◽  
Stokes Equations ◽  
Solid Wall ◽  
Control Volume ◽  
Navier Stokes ◽  
Interface Temperature ◽  
Vapor Flow ◽  
Navier Stokes Equation ◽  
Wick Structure

In this paper, a full transient analysis of the performance of a heat pipe with a wick structure is performed. For the vapor flow, the conventional Navier-Stokes equations are used. For the liquid flow in the wick structure, which is modeled as a porous media, volume averaged Navier-Stokes equation are adopted. The energy equation is solved for the solid wall and wick structure of the heat pipe. The energy and momentum equations are coupled through the heat flux at the liquid-vapor interface that defines the suction and blowing velocities for the liquid and vapor flow. The evolution of the vapor-liquid interface temperature is coupled through the heat flux at this interface that defines the mass flux to the vapor and the new saturation conditions to maintain a fully saturation vapor all the time. A control volume approach is used in the development of the numerical scheme. A parametric study is conducted to study the effect of different parameters that affect the thermal performance of the heat pipe. And experimental setup is developed and numerical results are validated with experimental data. The results of this study will be useful for the heat pipe design and implementation in processes that are essentially transient and steady state conditions are not reached like for example drilling applications.

scholarly journals Numerical Investigation of Newtonian Fluid Flow around Sharp & Rounded Corner Rectangular Obstruction

2021 ◽  
Vol 10 (2) ◽  
pp. , 922-927
Keyword(s):  
Dead Zone ◽  
Rectangular Domain ◽  
Two Dimensions ◽  
Least Square ◽  
Navier Stokes ◽  
Stream Line ◽  
Circulation Rate ◽  
Navier Stokes Equation ◽  
Recirculation Flow ◽  
Flow Circulation

In the present study, very stable and converging Least Square finite element method (LSFEM) is employed to calculate the approximate solution of steady state Navier – Stokes equation, consisting continuity and momentum equations in two dimensions. The 2D rectangular domain is considered to study the behavior of linear fluid passing two parallel rectangular obstructions in an open channel. The current numerical analysis is based on two instances, in the first one two rectangular obstructions possesses sharp corners set to face the entering flow while in the other case, obstructions having round corners are analyzed concerning to examine the enhancement in the size of vortex formed due to the flow blockage, intensity of vortex and the recirculation flow rate in the dead zone for Reynolds number from 250 to 2000. The stream line patterns are also presented to monitor the changes appears in the shape of vortex for different Re. The information gather through the analysis suggests the cutoff corner obstruction is congenial in restricting the vortex length and favorable for slow down the flow circulation rate in the lower stream of the channel. The acquired results are compared with established data in past literature which turn out to be in good agreement.

An exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point flow in two dimensions

1986 ◽  
Vol 163 ◽  
pp. 141-147 ◽  
Author(s):  
J. M. Dorrepaal
Keyword(s):  
Exact Solution ◽  
Stagnation Point ◽  
Stokes Equation ◽  
Similarity Solution ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Arbitrary Angle ◽  
Navier Stokes Equation ◽  
Flat Wall

A similarity solution is found which describes the flow impinging on a flat wall at an arbitrary angle of incidence. The technique is similar to a method used by Jeffery (1915) and discussed more recently by Peregrine (1981).

Transpiration Boundary Conditions for a Steady Inverse Method

2012 ◽  
Author(s):  
Jinguang Yang ◽  
Hu Wu
Keyword(s):  
Boundary Conditions ◽  
Inverse Method ◽  
Solid Wall ◽  
Design Tool ◽  
Navier Stokes ◽  
Separation Flow ◽  
Time Cost ◽  
Navier Stokes Equation ◽  
Tangency Condition ◽  
Turbomachinery Blades

Computational fluid dynamics has been widely used in the analysis of turbomachinery blades, however, its use as a design tool is far from sophisticated. The inverse method is such a design approach, which lends it self to the latter category. One application of the inverse method is the so called “pure inverse methd”, which differs from common analysis solver mainly in the boundary conditions on the blade surfaces. For this application, the usual non-penetration boundary conditions on the blade surfaces are aborted, instead, some aerodynamic constraints are imposed, and the flow is allowed to transpire through the actual solid wall. A camber line generation equation is added to periodically re-generate the blade camber line and drive the normal velocities on the blade surfaces to zero. When converged, the inverse method should obtain the blade shapes which satisfy the specified aerodynamic performance. In the present paper, three transpiration boundary conditions for turbomachinery blades design are compared in terms of time cost, robustness, capability of coping separation flow etc. The first inverse boundary condition is based on the flow-tangency condition on the blade surfaces, the second relys on the propagating characteristics in the flow field, and the third is a hybrid version of the first and the second. The computation is validated for 2D Navier-Stokes equation. Two compressor cascades are taken as examples to compare the performance of the three transpiration boundary conditions. Finally some conclusions are drawn.

scholarly journals Numerical Solution of Three-Dimensional Turbulent Flows for Modern Gas Turbine Components

1987 ◽  
Author(s):  
C. Hah ◽  
J. H. Leylek
Keyword(s):  
Gas Turbine ◽  
Turbulent Flows ◽  
Gas Turbines ◽  
Solid Wall ◽  
Control Volume ◽  
Three Dimensional ◽  
Computer Code ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Aerodynamic Loss

This paper describes the development and assessment of a computer code for three-dimensional compressible turbulent flows in modern gas turbine components. The code is based on a high-order upwinding relaxation scheme with fully conservative control volume. A three-dimensional Reynolds-averaged Navier-Stokes equation is solved with a two-equation turbulence model that has a low Reynolds number modification near the solid wall. The code is applied to the study of compressible flow inside turbine blade rows of modern gas turbines. Measured data and calculations are carefully compared for the production and convection of aerodynamic loss to evaluate the code as an advanced design technique. The predicted aerodynamic performance is further compared with predictions based on current design techniques.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 430
Author(s):  
Changyou Ding ◽  
Hong Lei ◽  
Hong Niu ◽  
Han Zhang ◽  
Bin Yang ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Mass Concentration ◽  
Distribution Curve ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Residence Time Distribution Curve ◽  
Tracer Solution ◽  
Time Distribution Curve

The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concentration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

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