Gustavo C. R. Bodstein

The three-dimensional interaction of a streamwise vortex with a large-chord lifting surface : theory and experiment

The three-dimensional vortex flow that develops around a close-coupled canard-wing configuration is characterized by a strong interaction between the vortex generated at the canard and the aircraft wing. In this paper, a theoretical potential flow model is devised to uncover the basic structure of the pressure and velocity distributions on the wing surface. The wing is modelled as a semi-infinite lifting-surface set at zero angle of attack. It is assumed that the vortex is a straight vortex filament, with constant strength, and lying in the freestream direction. The vortex filament is considered to be orthogonal to the leading-edge, passing a certain height over the surface. An incompressible and steady potential flow formulation is created based on the three-dimensional Laplaces equation for the velocity potential. The boundary-value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed-form solution for the velocity potential is determined, from which the velocity and pressure distributions on the surface and a vortex path correction are obtained. The model predicts an anti-symmetric pressure distribution along the span in region near the leading-edge, and a symmetric pressure distribution downstream from it. The theory also predicts no vertical displacement of the vortex, but a significant lateral displacement. A set of experiments is carried out to study the main features of the flow and to test the theoretical model above. The experimental results include helium-soap bubble and oil-surface flow pattern visualization, as well as pressure measurements. The comparison shows good agreement only for a weak interaction case, whereas for the case where the interaction is strong, secondary boundary-layer separation and vortex breakdown are observed to occur, mainly owing to the strong vortex-boundary layer interaction. In such a case the model does not agree well with the experiments.

DISCRETE VORTEX METHOD SIMULATION OF THE FLOW AROUND A CIRCULAR CYLINDER WITH AND WITHOUT ROTATION

In this paper we simulate the two-dimensional, incompressible, unsteady flow around a circular cylinder. Two cylinder configurations are considered: with and without rotation. We use a lagrangian meshfree vortex method to calculate global as well as local quantities in a high Reynolds number flow. In our novel algorithm vortices with a Lamb core are generated along the cylinder surface, whose strengths are determined to ensure that the no-slip condition is satisfied and that circulation is conserved. The impermeability condition is imposed through the application of the circle theorem. The dynamics of the body wake is computed using the convection-diffusion splitting algorithm, where the convection process is carried out with a lagrangian firstorder time-marching scheme, and the diffusion process is simulated using the random walk method. The aerodynamic forces are calculated from the unsteady Blasius equation, and the pressure distribution is also computed. Our results for the lift and drag coefficients, Strouhal number and pressure coefficient are found to be in good agreement when compared to numerical and experimental results available in the literature.

Subgrid-Scale Modeling of Turbulent Flow Around Circular Cylinder by Mesh-Free Vortex Method

Abstract: This paper proposes a numerical model for the two-dimensional, incompressible, unsteady, turbulent flow applied to an impulsively started flow around a circular cylinder in the Reynolds number range from 1×104 to 6×105. A Lagrangian mesh-free vortex method blended with the Large Eddy Simulation theory is employed to simulate the large-scale motion, whereas the turbulent subgrid-scale motion is modeled with an eddy viscosity coefficient, expressed in terms of the Second-Order Velocity Structure Function. The filtered vorticity field is calculated by a superposition of Lamb vortices that are generated near the body surface such that circulation is conserved and the no-slip boundary condition is explicitly imposed at a finite number of points on the cylinder. The no-penetration boundary condition is satisfied exactly on the entire cylinder surface through the application of the circle theorem. The vorticity transport equation is solved using the convective-diffusive operator-splitting algorithm, where vorticity diffusion is simulated with the random walk method and the convective motion of the vortices is integrated in time using the second-order Adams-Bashforth scheme. Numerous simulations for high Reynolds numbers are carried out to determine the numerical parameters of the model. Results for the drag coefficient and the Strouhal number as a function of the Reynolds number present satisfactory agreement with other results from the literature.

A Modified Logarithmic Law for Neutrally Stratified Flow over Low-Sloped Hills

The study of the atmospheric boundary layer flow over two-dimensional low-sloped hills under a neutral atmosphere finds numerous applications in meteorology and engineering, such as the development of large-scale atmospheric models, the siting of wind turbines, and the estimation of wind loads on transmission towers and antennas. In this paper, the intermediate variable technique is applied to the momentum equations in streamline coordinates to divide the flow into regions, with each characterized by the dominance of different terms. Using a simple mixing-length turbulence closure, a simplified form of the x momentum equation is solved for the fully turbulent region, resulting in a modified logarithmic law. The solution is expressed as a power series correction to the classical logarithmic law that is valid for flat terrain. A new parameter appears: the effective radius of curvature of the hill. The modified logarithmic law is used to obtain new equations for the speedup, the relative speedup, the maximum speedup, and the height at which it occurs. A new speedup ratio is proposed to calculate the relative speedup at specific heights. The results are in very good agreement with the Askervein and Black Mountain field data.

Numerical simulation of inviscid incompressible two-dimensional airfoil-vortex interaction in ground effect

A numerical inviscid vortex method is employed to study the unsteady, two-dimensional, incompressible flow that occurs during an airfoil-vortex interaction in the vicinity of a ground plane. The airfoil bound vorticity is modeled using a panel method with linear piecewise-continuous vorticity distribution. The vortex is considered to be a point vortex, and the ground effect is obtained using the method of images. Point vortices are also generated at the airfoil trailing edge to ensure that circulation is conserved and that the Kutta condition is satisfied. All vortices are convected using a first-order Lagrangian time-marching scheme. After code validation, numerical results for the airfoil-vortex interaction in ground effect reveal that the loading on the airfoil is affected by the thickness, angle of attack, and height of the airfoil above the ground, as well as the vortex strength, direction of rotation, and distance to the airfoil. The wake evolution is nonlinear and strongly influenced by the interaction, whereas the pressure distribution on the ground presents steep adverse gradients

Comprehensive Solution for Transient Flow in Heterogeneous Porous Media

Solutions of the hydraulic diffusivity equation are of utmost importance for many reservoir engineering problems. Despite all the efforts, there is still a need for the development of rigorous and comprehensive solutions for transient flow problems in heterogeneous oil reservoirs. This study demonstrates the use of an integral transform approach to obtain such a rigorous and comprehensive solution for the hydraulic diffusivity equation in heterogeneous porous domain. The reservoir heterogeneities can be approximated by any continuous differentiable function. The presented general solution and its derivation are valid for multi-dimensional problems in any orthogonal coordinate system. It has the advantage of rigorously solving the hydraulic diffusivity equation for transient, late-transient and steady-state (or pseudo-steady-state) flow regimes in a single formulation that allows the consideration of variable flowrates. In this work, applications of the general solution for one-dimensional problems in the Cartesian and radial coordinate systems are presented, showing comparisons of the results obtained with a finite difference numerical scheme. The solution presented can be used to analyze buildup, drawdown and interference test data, making it a useful tool for pressure transient analysis applied to reservoir engineering problems.

Transient Solution for the Energy Balance in Porous Media Considering Viscous Dissipation and Expansion/Compression Effects Using Integral Transforms

Monitoring of downhole flowing temperatures in oil wells is gaining attention in the recent years due to the possibility of exploring these data for reservoir characterization and determination of inflow profiles along the well completions, leading to an increased interest in the development of solutions for the equations governing the thermal behavior of a reservoir. In this work, it is proposed to use the generalized integral transform technique (GITT) to provide solutions for the energy balance equation, considering the thermal effects related to fluid flow. A formal and general solution for the energy balance in the porous media is presented and validated. It is presented the application of the proposed solution to one-dimensional and two-dimensional problems in the Cartesian coordinate system. The two-dimensional problem, which considers heat transfer to the surrounding impermeable formations, is tackled by a single domain formulation. The mathematical approach taken in these solutions is rigorous, valid for all flow regimes (transient, late-transient and pseudo-steady-state/steady-state) and for any orthogonal coordinate system, presenting the possibility of achieving differentiable and stable solutions with controlled accuracy. The solution comprises an important contribution to support the application of temperature data to reservoir engineering problems.

Numerical Simulation of Non-Isothermal Two-Phase Flow in a Pipeline Using the Flux-Corrected Transport Method

Two phase flows occur in many engineering problems, especially in the nuclear, gas and petroleum industries. In oil and gas applications, specifically, a mixture of oil and natural gas is transported in pipelines from offshore platforms to the continent. The prediction of how the flow behaves in time as it moves along the pipe is extremely important, mainly during the pipeline design stage or regular operation. This paper presents simulations for stratified gas-liquid two-phase flow in a horizontal pipeline that is subject to the temperature gradients that exist in the bottom of the ocean, and the resulting heat transfer process that may lead to wax formation and deposition. A one-dimensional two-fluid mathematical model was employed that includes conservation equations of mass and momentum for each fluid and one energy equation for the mixture of liquid and gas. The problem was formulated as an initial-boundary value problem of the hyperbolic type and it was solved using the Flux Corrected Transport (FCT) numerical method, which is second-order accurate in space, coupled with an explicit discretization in time that is first-order accurate. The FCT method is appropriate to solve problems characterized by hyperbolic equations that may contain discontinuities and shock waves, and it presents small dispersive effects. The results showed excellent accuracy results when compared to commercial software widely used in the oil and gas industry.Copyright

Hyperbolicity Analysis of a One-Dimensional Two-Fluid Two-Phase Flow Model for Stratified-Flow Pattern

Two-phase flows in pipelines occur in a variety of processes in the nuclear, petroleum and gas industries. Because of the practical importance of accurately predicting steady and unsteady flows along the line, one-dimensional two-fluid flow models have been extensively employed in numerical simulations. These models are usually written as a system of non-linear hyperbolic partial-differential equations, but some of the available formulations are physically inconsistent due to a loss of the hyperbolicity property. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of a one-dimensional single-pressure four-equation two-fluid model for an isothermal stratified flow that occurs in a horizontal pipeline. The diameter, pressure and volume fraction are kept constant, whereas the liquid and gas velocities are varied to cover the entire range of superficial velocities in the stratified region. For each point, the eigenvalues are numerically computed to verify whether they are real numbers and to assess their signs. The results show that hyperbolicity is lost near the boundaries of the stratified pattern and in a vast area of the region itself. Moreover, the eigenvalue signs alternate, which has implications on the prescription of numerical boundary conditions.Copyright

Numerical Simulation of Stratified Two-Phase Flow in a Nearly Horizontal Gas-Liquid Pipeline With a Leak

The capability of producing accurate numerical simulations of transient gas-liquid flows in gas pipelines has long been a serious concern in the oil industry. In this paper we are particularly interested in simulating this type of flow during the occurrence of a leak in the pipe. We use the flux-corrected transport (FCT) finite-difference method, which is second-order in space, to solve a one-dimensional single-pressure four-equation two-fluid model. We consider this two-phase flow to occur in a nearly horizontal pipeline characterized by the stratified-flow pattern, and we assume that the flow is isothermal with a compressible gas phase and an incompressible liquid phase. We model the leak as a source term in the mass conservation equations. The results of the numerical simulations allow the model sensitivity to be studied by changing the leak diameter and the leak location. From this analysis, we may observe how these parameters affect the pressure gradients along the pipeline that develop upstream and downstream of the leak.© 2014 ASME