Part I: Some experiences on simple panel methods applied to attached and separated flows

1987 ◽  
Vol 91 (908) ◽  
pp. 350-359 ◽  
Author(s):  
H. B. Tou ◽  
G. J. Hancock
Keyword(s):  
Piecewise Linear ◽  
Separated Flows ◽  
Surface Singularity ◽  
List Type ◽  
Trailing Edge ◽  
Kutta Condition ◽  
First Order ◽  
Panel Methods ◽  
Total Head ◽  
Order Surface

Summary Simple first order surface singularity methods based on: (i) Smith and Hess uniform source panels plus a uniform vorticity around aerofoil profile, (ii) piecewise linear vorticity around aerofoil profile, with different assumption for Kutta condition, have been applied to attached flows and separated flows past an aerofoil/spoiler configuration, assuming an inviscid model. For separated flows, piecewise linear vorticity methods give reasonable results as long as small panel elements are taken in the region of the separations at the spoiler tip and aerofoil trailing edge. The Smith and Hess method gives results which do not agree too closely with the vorticity methods. There is doubt concerning uniqueness. Results have been compared using two different wake models; in one, the total head inside the wake is taken to be uniform, in the second, the static pressures along the separation streamlines are taken to be uniform. There appears to be a difference of about 5% in CL. It is not known why.

Part II: Steady aerofoil-spoiler characteristics

1987 ◽  
Vol 91 (908) ◽  
pp. 359-366
Keyword(s):  
Separated Flow ◽  
Experimental Results ◽  
Surface Singularity ◽  
Separation Region ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Singularity Method ◽  
Total Head ◽  
Low Speeds ◽  
Theoretical Results

Summary A surface singularity method has been formulated to predict two-dimensional spoiler characteristics at low speeds. Vorticity singularities are placed on the aerofoil surface, on the spoiler surface, on the upper separation streamline from the spoiler tip and on the lower separation streamline from the aerofoil trailing edge. The separation region is closed downstream by two discrete vortices. The flow inside the separation region is assumed to have uniform total head. The downstream extent of the separated wake is an empirical input. The flows both external and internal to the separated regions are solved. Theoretical results have been obtained for a range of spoiler-aerofoil configurations which compare reasonably with experimental results. The model is deficient in that it predicts a higher compression ahead of the spoiler than obtained in practice. Furthermore, there is a minimum spoiler angle below which a solution is not possible; it is thought that this feature is related to the physical observation that at small spoiler angles, the separated flow from the spoiler reattaches on the aerofoil upper surface ahead of the trailing edge.

scholarly journals On the Kutta Condition in Potential Flow over Airfoil

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Farzad Mohebbi ◽  
Mathieu Sellier
Keyword(s):  
Potential Flow ◽  
Trailing Edge ◽  
Airfoil Surface ◽  
Kutta Condition ◽  
Edge Angle ◽  
Panel Methods ◽  
Flow Potential ◽  
Novel Method ◽  
Elliptic Grid Generation ◽  
Fast Procedure

This paper proposes a novel method to implement the Kutta condition in irrotational, inviscid, incompressible flow (potential flow) over an airfoil. In contrast to common practice, this method is not based on the panel method. It is based on a finite difference scheme formulated on a boundary-fitted grid using an O-type elliptic grid generation technique. The proposed algorithm uses a novel and fast procedure to implement the Kutta condition by calculating the stream function over the airfoil surface through the derived expression for the airfoils with both finite trailing edge angle and cusped trailing edge. The results obtained show the excellent agreement with the results from analytical and panel methods thereby confirming the accuracy and correctness of the proposed method.

scholarly journals Note on the Physical Basis of the Kutta Condition in Unsteady Two-Dimensional Panel Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
M. La Mantia ◽  
P. Dabnichki
Keyword(s):  
Pressure Difference ◽  
Energy Requirements ◽  
Aquatic Species ◽  
Biological Applications ◽  
Velocity Difference ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Wing Motion ◽  
Panel Methods ◽  
New Formulation

Force generation in avian and aquatic species is of considerable interest for possible engineering applications. The aim of this work is to highlight the theoretical and physical foundations of a new formulation of the unsteady Kutta condition, which postulates a finite pressure difference at the trailing edge of the foil. The condition, necessary to obtain a unique solution and derived from the unsteady Bernoulli equation, implies that the energy supplied for the wing motion generates trailing-edge vortices and their overall effect, which depends on the motion initial parameters, is a jet of fluid that propels the wing. The postulated pressure difference (the value of which should be experimentally obtained) models the trailing-edge velocity difference that generates the thrust-producing jet. Although the average thrust values computed by the proposed method are comparable to those calculated by assuming null pressure difference at the trailing edge, the latter (commonly used) approach is less physically meaningful than the present one, as there is a singularity at the foil trailing edge. Additionally, in biological applications, that is, for autonomous flapping, the differences ought to be more significant, as the corresponding energy requirements should be substantially altered, compared to the studied oscillatory motions.

Biodegradation rates of aromatic contaminants in biofilm reactors

1995 ◽  
Vol 31 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Jean-Pierre Arcangeli ◽  
Erik Arvin
Keyword(s):  
Aromatic Hydrocarbons ◽  
Competitive Inhibition ◽  
Removal Rate ◽  
First Order ◽  
Biofilm Reactors ◽  
First Order Kinetics ◽  
Reducing Conditions ◽  
Low Concentrations ◽  
Degradation Rates ◽  
Order Surface

This study has shown that microorganisms can adapt to degrade mixtures of aromatic pollutants at relatively high rates in the μg/l concentration range. The biodegradation rates of the following compounds were investigated in biofilm systems: aromatic hydrocarbons, phenol, methylphenols, chlorophenols, nitrophenol, chlorobenzenes and aromatic nitrogen-, sulphur- or oxygen-containing heterocyclic compounds (NSO-compounds). Furthermore, a comparison with degradation rates observed for easily degradable organics is also presented. At concentrations below 20-100 μg/l the degradation of the aromatic compounds was typically controlled by first order kinetics. The first-order surface removal rate constants were surprisingly similar, ranging from 2 to 4 m/d. It appears that NSO-compounds inhibit the degradation of aromatic hydrocarbons, even at very low concentrations of NSO-compounds. Under nitrate-reducing conditions, toluene was easily biodegraded. The xylenes and ethylbenzene were degraded cometabolically if toluene was used as a primary carbon source; their removal was influenced by competitive inhibition with toluene. These interaction phenomena are discussed in this paper and a kinetic model taking into account cometabolism and competitive inhibition is proposed.

Heat/mass transport in shear flow over a heterogeneous surface with first-order surface-reactive domains

2015 ◽  
Vol 782 ◽  
pp. 260-299 ◽  
Author(s):  
Preyas N. Shah ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Mass Transfer ◽  
Shear Rate ◽  
Shear Flow ◽  
Reaction Rate ◽  
Patch Size ◽  
Patch Area ◽  
First Order ◽  
Effective Boundary ◽  
Order Surface ◽  
Slip Distance

Surfaces that include heterogeneous mass transfer at the microscale are ubiquitous in nature and engineering. Many such media are modelled via an effective surface reaction rate or mass transfer coefficient employing the conventional ansatz of kinetically limited transport at the microscale. However, this assumption is not always valid, particularly when there is strong flow. We are interested in modelling reactive and/or porous surfaces that occur in systems where the effective Damköhler number at the microscale can be $O(1)$ and the local Péclet number may be large. In order to expand the range of the effective mass transfer surface coefficient, we study transport from a uniform bath of species in an unbounded shear flow over a flat surface. This surface has a heterogeneous distribution of first-order surface-reactive circular patches (or pores). To understand the physics at the length scale of the patch size, we first analyse the flux to a single reactive patch. We use both analytic and boundary element simulations for this purpose. The shear flow induces a 3-D concentration wake structure downstream of the patch. When two patches are aligned in the shear direction, the wakes interact to reduce the per patch flux compared with the single-patch case. Having determined the length scale of the interaction between two patches, we study the transport to a periodic and disordered distribution of patches again using analytic and boundary integral techniques. We obtain, up to non-dilute patch area fraction, an effective boundary condition for the transport to the patches that depends on the local mass transfer coefficient (or reaction rate) and shear rate. We demonstrate that this boundary condition replaces the details of the heterogeneous surfaces at a wall-normal effective slip distance also determined for non-dilute patch area fractions. The slip distance again depends on the shear rate, and weakly on the reaction rate, and scales with the patch size. These effective boundary conditions can be used directly in large-scale physics simulations as long as the local shear rate, reaction rate and patch area fraction are known.

Viscous tails in Hele-Shaw flow

1971 ◽  
Vol 46 (3) ◽  
pp. 569-576
Author(s):  
C. J. Wood
Keyword(s):  
Reynolds Number ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Quantitative Discrepancy ◽  
Edge Flow ◽  
Hele Shaw Cell

An experiment has been performed, using pulsed dye injection on an aerofoil in a Hele-Shaw cell. The purpose was to observe the form of the trailing-edge flow when the Reynolds number was high enough to permit separation and the initiation of a Kutta condition. The experiment provides a successful confirmation of the existence of a ‘viscous tail’ as predicted by Buckmaster (1970) although there is an unexplained quantitative discrepancy.

scholarly journals Imaging of first-order surface-related multiples by reverse-time migration

2016 ◽  
Vol 208 (2) ◽  
pp. 1077-1087 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Hao Hu ◽  
Peng Li ◽  
Majid Khan
Keyword(s):  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Order Surface

A B-Spline Higher-Order Panel Method Applied to Two-Dimensional Lifting Problem

2003 ◽  
Vol 47 (04) ◽  
pp. 290-298
Author(s):  
Chang-Sup Lee ◽  
Justin E. Kerwin
Keyword(s):  
Present Method ◽  
Gaussian Quadrature ◽  
Solution Process ◽  
Higher Order ◽  
Panel Method ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Kutta Condition ◽  
B Spline ◽  
Panel Methods

A higher-order panel method based on B-spline representation for both the geometry and the solution is developed for the solution of the flow around two-dimensional lifting bodies. The influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts; then the former is integrated analytically, whereas the latter is integrated using Gaussian quadrature. Through a desingularization process, the accuracy of the present method can be increased without limit to any order by selecting a proper numerical quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with far fewer panels than existing low-order panel methods.

scholarly journals On a Propositional Calculus Whose Decision Problem is Recursively Unsolvable

1970 ◽  
Vol 38 ◽  
pp. 145-152
Author(s):  
Akira Nakamura
Keyword(s):  
Decision Problem ◽  
Propositional Calculus ◽  
Predicate Calculus ◽  
Reduction Theorem ◽  
List Type ◽  
First Order ◽  
Order Predicate Calculus

The purpose of this paper is to present a propositional calculus whose decision problem is recursively unsolvable. The paper is based on the following ideas: (1) Using Löwenheim-Skolem’s Theorem and Surányi’s Reduction Theorem, we will construct an infinitely many-valued propositional calculus corresponding to the first-order predicate calculus.(2) It is well known that the decision problem of the first-order predicate calculus is recursively unsolvable.(3) Thus it will be shown that the decision problem of the infinitely many-valued propositional calculus is recursively unsolvable.

HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT

2004 ◽  
Vol 14 (01) ◽  
pp. 221-243 ◽  
Author(s):  
K. THAMILMARAN ◽  
M. LAKSHMANAN ◽  
A. VENKATESAN
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laboratory Experiments ◽  
System Parameter ◽  
Piecewise Linear ◽  
Electrical Circuit ◽  
First Order ◽  
Regular Behavior ◽  
Linear Elements

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis.

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