Viscous Flow Separation Research Articles

Performance assessment of a Triple Coaxial-Cylinder Wave-Energy Converter (TCWEC)

We propose a novel Triple Coaxial-cylinder Wave-Energy Converter (TCWEC) system, as an evolution of the commonly deployed dual-coaxial cylinder WEC (DCWEC). TCWEC consists of one inner cylinder and two concentric outer cylinders, characterized by two coupled resonant frequencies, improving wave power absorption. A semi-analytical model, based on potential flow theory and matched eigenfunction expansions, is developed to analyze the 3-Degrees of Freedom (DOF) system. The viscous drag coefficients are determined by Computational Fluid Dynamics (CFD) simulations and employed as equivalent linear damping. Analysis of impact of the viscous flow-separation factor fvis on the capture width indicates that the higher energy-absorption capability of TCWEC is not merely attributed to a smaller fvis value, but rather a planned split of the outer cylinder in DCWEC design into two cylinders in TCWEC, so as to produce an effectively broader resonance property. Under identical sea conditions, it is found that, compared to DCWEC, the optimal capture width of TCWEC is increased by as much as 77% in regular waves. In irregular waves, the optimal capture width is increased up to 40% across the entire frequency range. These findings suggest that the energy absorption efficiency of TCWEC is promising and its potential for real-world applications.

Aerodynamic Performance of a Finite-Span Wing in a Time-Varying Freestream

The current study analyzes the dynamic response of a NACA 0015 finite-span wing to a time-varying freestream in an unsteady wind tunnel at a mean Reynolds number of 1.0×105. The aerodynamic response of the wing can be categorized based on the angle of attack and the degree of flow separation on the suction side of the wing. When the suction side is dominated by separated flow, either at low angles of attack with long laminar separation bubbles or at high, poststall, angles of attack, the lift is enhanced by the favorable pressure gradient during freestream acceleration and decremented by the adverse pressure gradient during freestream deceleration. In these cases, the sectional lift coefficient is shown to oscillate by as much as ±0.1 due to the unsteady pressure gradient. Comparatively, regions of attached flow on the wing surface remain largely unaffected by the time-varying conditions, regardless of the reduced frequency. Discrepancies between the measured lift and the estimated response from Isaacs’s theory demonstrate that the coupling between the viscous flow separation and the unsteady conditions dominates the unsteady aerodynamic response.

Ludwig Edward Fraenkel. 28 May 1927—27 April 2019

Edward Fraenkel’s professional career began as an experimentalist at the Royal Aircraft Establishment, Farnborough, but his preoccupation with the theoretical and mathematical aspects of aerodynamics led him into academia, working initially in aerodynamics and classical applied mathematics, but later in the modern theory of nonlinear partial differential equations and its applications to fluid mechanics. He made outstanding contributions to the mathematical theories of viscous flow separation, steady vortex rings and surface waves on water.

Editorial: Biographical Memoirs, Volume 69

Editorial: Biographical Memoirs, Volume 69

Viscous flow separation caused by the Marangoni effect in competition with capillary flow

This letter provides an analytical model that describes the viscous flow separation in a drying thin polymer solution film. While conventional flow separation occurs due to an adverse pressure gradient opposing fluid inertia, here we show that flow separation can also be caused by the Marangoni effect in an evaporation-driven creeping flow. The flow separation behavior strongly depends on the surface tension distribution and the interface profile. Viscous flow separation adds to the current understanding of flow physics during the drying of thin films, in addition to the well-known capillary transport and the Marangoni effect.

Viscous and inviscid interactions of an oblique shock with a flexible panel

The complex self-sustained oscillations arising from the interaction of an oblique shock with a flexible panel in both the inviscid and viscous regimes have been investigated numerically. The aeroelastic interactions are simulated using either the Euler or the full compressible Navier–Stokes equations coupled to the nonlinear von Karman plate equations. Results demonstrate that for a sufficiently strong shock limit-cycle oscillations emerge from either subcritical or supercritical bifurcations even in the absence of viscous separated flow effects. The critical dynamic pressure diminishes with increasing shock strength and can be much lower than that corresponding to standard panel flutter. Significant changes in panel dynamics were also found as a function of the shock impingement point and cavity pressure. For viscous laminar flow above the panel without a shock, high-frequency periodic oscillations appear due to the coupling of boundary-layer instabilities with high-mode flexural deflections. For a separated shock laminar boundary layer interaction, non-periodic self-excited oscillations arise which can result in a significant reduction in the extent of the time-averaged separation region. This finding suggests the potential use of an aeroelastically tailored flexible panel as a means of passive flow control. Forced panel oscillations, induced by a specified variable cavity pressure underneath the panel, were also found to be effective in reducing separation. For both inviscid and viscous interactions, the significant unsteadiness generated by the fluttering panel propagates along the complex reflected expansion/recompression wave system.

Effect of constriction height on flow separation in a two-dimensional channel

We studied numerically the effect of the constriction height on viscous flow separation past a two-dimensional channel with locally symmetric constrictions. A numerically stable scheme in primitive variables (velocity and pressure) for the solution of two-dimensional incompressible time-dependent Navier–Stokes equations is employed using finite-difference approximation in staggered grid. The wall shear stresses at different heights of the constriction are computed and presented graphically. It is noticed that the maximum stress and the length of the recirculating region associated with two shear layers of the constriction increase with the increase of the area reduction of the constriction. The critical Reynolds number for symmetry breaking bifurcation for the 50%, 60% and 70% area reduction are obtained numerically. The flow field separates after the symmetry breaking bifurcation and the symmetry of the flow depends on the Reynolds number and the height of the constriction.

Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically. It is found that the flow separates downstream of the constriction. With increase in the magnetic field, the flow separation zone diminishes in size and for large magnetic field, the separation zone disappears completely. Wall shear stress increases with increase in the magnetic field strength. It is also found that for symmetrically situated constrictions on the channel walls, the critical Reynolds number for the flow bifurcation (i.e., flow asymmetry) increases with increase in the magnetic field.

Reduced-Order Modeling of Unsteady Viscous Flow in a Compressor Cascade

A simultaneously coupled viscous-inviscid interaction (VII) analysis is used to model the unsteady viscous separated flow through a subsonic compressor. The inner viscous flow around the airfoil and in the wake is modeled using a finite difference discretization of the boundary-layer equations and a one-equation turbulence transport model. The outer inviscid flow is modeled using a variational finite element discretization of the compressible full potential equation. The viscous and inviscid regions are simultaneously coupled using a injection type boundary condition along the airfoil and wake. The resulting nonlinear unsteady equations are linearized about the nonlinear steady flow to obtain a set of linear equations that describe the unsteady small-disturbance behavior of the viscous flow through the cascade. The discretized small-disturbance VII equations are used to form a generalized, quadratic, non-Hermitian eigenvalue problem that describes the eigenmodes (natural modes) and eigenvalues (natural frequencies) of fluid motion about the cascade. Using a Lanczos algorithm, the eigeninformation is computed efficiently for various steady flow inflow angles and unsteady interblade phase angles

Numerical prediction of transonic viscous separated flow past an airfoil

A method for the numerical treatment of transonic viscous flows past an airfoil has been developed allowing for calculation of both attached flows and flows with large separation regions including shock-induced separation. The method accounts for the entropy correction and the presence of vorticity behind the shock. The method is based on a zonal approach. The computation of the separated-flow regimes is provided by a quasi-simultaneous method of viscous—inviscid interaction. A computer code, called “VISTRAN,” is developed on the basis of this method and extensive comparisons of computed results with experimental data are made.

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios of U-m to U-0 are of O(10(-1)), O(10) and O(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re = 10(2), 10(3) and 3 x 10(3) are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Karman vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method.

Comparison of inviscid and viscous separated flows

INVISCID compressible flow separation on simple two-dimensional configurations has been investigated by solving the Euler equations numerically, using different computational schemes. The results were compared with numerical solutions of the Navier-Stokes equations. The computational schemes used in this study included a lambda scheme with shock fitting, a flux-vector splitting scheme for the Euler equations, and a flux-vector splitting scheme for the Navier-Stockes equations

Numerical modeling of viscous separated flow in the near wake

The present paper studies laminar flow in the near wake behind a short blunt body. We have obtained the dependence on the Mach number and Reynolds number of the incident stream of a number of geometrical characteristics of the wake, the relative base pressure, and its contribution to the total body drag. Examples are given of the influence of body shape and its surface thermal regime on the base pressure. It has been observed that for some incident stream parameters fine-scale vortices form near the separation point (an analogous phenomenon has been mentioned earlier in individual experimental studies), and a local supersonic zone can occur on the axis of symmetry in the reverse flow. i. Formulation of the Problem and Method of Solution. We consider flow about an axisymmetric body with a vertical base truncation. A uniform supersonic stream of viscous compressible heat-conducting gas flows over the body at zero angle of attack. In accordance with theoretical ideas and on the basis of the available test data (see, e.g., [i, 3]) we can give the following scheme for the separated flow in the near wake. Under the influence of inertia forces, which predominate over the viscous forces, the boundary layer leaving the body separates from the body corner at the point G (Fig. i), located somewhat below the corner point F. The separated viscous layer entrains part of the gas occupying the wake region, thereby lowering the pressure there, and together with the external stream it is deviated toward the axis, where at some distance from the base rim it merges with the symmetric viscous layer, forming the wake throat. In the merge zone the base pressure increases, the flow is turned again (almost parallel to the axis), and a tail shock forms. The internal part of the viscous layer, close to the axis, losing speed due to interaction with the gas from the separated region, cannot overcome the increased pressure in the wake throat, and turns back toward the base of the body, and in the established near wake there forms a closed region of recirculating flow, separated from the rest of the flow by the dividing streamline GH. In the external inviscid flow there is flow expansion in the vicinity of the corner point F; immediately beyond the fan of expansion waves there is a stern shock wave, due to re-expansion of the wall viscous layer at the corner point. (Figure 1 also shows stream lines and pressure profiles obtained in one of the computations, and in these one can see the location of the tail shock.)

Measurement of Pressure Distribution on a Conventional and a Highly Skewed Propeller Model

Recently many researchers have performed the pressure measurement on propeller models to obtain reliable data for validating propeller theories. This paper describes the new experimental techniques and the results of the measurement of pressure distribution on the blade of propeller models. In the present measurement, two kinds of propeller models were used ; a conventional propeller and a highly skewed propeller. In order to measure the pressure not only under the non-cavitating condition but also the cavitating condition accurately, “Helmholtz chamber-type waterproof pressure transducers with high sensitivity” were employed.In earlier measurements, the measured pressure in some locations on the blades were greatly affected by the tortional or bending deformation of propeller blades. To remove such a detrimental effect, a special care has been taken of the attachment of pressure transducers to the propeller blades. In this paper, the pressure measurement performed by the improved procedure are described on two large propeller models working not only in uniform flow but in non-uniform flow. The present technique has the major advantage of the ability to measure unsteady pressure with high accuracy and no disruption to the measuring surface. The disadvantage is that the pressure transducers are very costly and specially fine techniques to install each pressure gauge in a chamber are demanded.Finally this paper discusses the comparison of pressure distribution between the measured results and computational results given by the existing propeller lifting surface theory on two types of propellers, both in uniform flow and in non-uniform flow produced by the wire mesh screen, respectively. On the conventional propeller, good agreements between the computation and the measurement in the pressure distribution on the back side were observed, while the theory presented higher pressure values on the face side at any advance ratios in the present measurement. On the other hand, in the case of the highly skewed propeller, wavy profiles of the pressure distribution on the back side were obtained under the respective advance ratios probably due to viscous effects. The discrepancy between the theory and the measurements for the highly skewed propeller is the same as that for the conventsonal propeller, except near the tip region of propeller blades.These discrpancies between the ewperiment and the theory should be attributed to the incomplete ness of the ewisting propeller lifting surface theory, that is, the two dimensional treatmdnt for thickness effects, the deformation of propeller blades and the neglect of viscous flow separation around the propeller blades.

Advances in the study of separated flows

This paper consists of three parts. The first deals with the separation conditions for three dimensional steady viscous separated flows, in which the behaviour of separated flow described by Navier-Stokes equations and boundary layer equations is studied. The second part involves an application of differential topology to qualitative analysis of flow fields. Here the distribution rule of singular points on the separation line is studied. The last part discusses the numerical method solving Navier-Stokes equations for separated flows. The obtained computational results are analysed by the above mentioned theories and methods.

A mixed explicit-implicit antidiffusive method of navier-stokes equations for supersonic and hypersonic separated flows

The supersonic and hypersonic, laminar and turbulent viscous separated flows over two and three-dimensional compression corners are solved by the antidissipative explicit-implicit difference scheme presented in this paper. The results obtained show that a high accuracy has been achieved by this method and the time needed for computation is greatly reduced.

Lift on a Rotating Porous Cylinder

Abstract Two-dimensional flow past a rotating circular cylinder with uniform suction at the surface is considered. The method of solution follows closely that used by Glauert [1] and the problem is solved for the case in which there is no viscous flow separation from the cylinder surface. Expressions in terms of the ratio of the cylinder peripheral velocity and a suction parameter are obtained for the lift and torque. The results show that uniform suction has a limited effect on the lift; however, the torque increases with suction. Possible application of these results to wind power generation is briefly discussed.

On the curvature of compressible boundary layer flows near separation

Oswatitsch's analytical expression for the slope of a viscous flow separation or reattachment streamline is shown to be consistent with detailed experimental data on a supersonic boundary layer flow past a compression corner. An extension of his analysis is then given which yields a comparable new relation for the streamlinecurvature just above separation in either laminar or turbulent two-dimensional compressible boundary layer flows. This result is applied to examine the possible occurrence of Gortler streamwise vortices due to such curvature.