Separated laminar boundary layers

Classical boundary layer theory is inadequate to deal with the problem of flow separation owing to its underlying assumption that the boundary layer has an insignificant effect on the external stream. This difficulty is resolved by a theory which includes interaction with the external flow. This theory is described from the viewpoint of the asymptotic triple deck structure. Several triple deck studies are reviewed with emphasis on results of interest in aeronautical applications

Analysis of large bending deformations of a filamentary tubular shell typical for pressure constraint components of space suits

Analysis of large bending deformations of filamentary tubular shell typical for pressure constraint components of space suit

Interacting boundary-layer solutions for laminar separated flow past airfoils

Numerical solutions of the interacting laminar boundary layer equations are presented for two symmetric airfoils at zero incidence: the NACA 0012 and the NACA 66 sub 3-108 airfoils. The potential flow was computed using Carlson's code, and viscous interaction was treated following a Hilbert integral scheme due to Veldman. Effects of various grid parameters are studied, and pressure and skin friction distributions are compared at several Reynolds numbers. For the NACA 0012 airfoil, Reynolds number is varied from a value just below separation (R sub N = 3000) to a value for which extensive separation occurs (R sub N = 100,000). For the 66 sub 3-018 airfoil, results are given at intermediate values (R sub N - 10,000 and 40,000). The method fails to converge for greater values of Reynolds number, corresponding to the development of very thin well separated shear layers where transition to turbulence would occur naturally

Axisymmetric filamentary structures

Axisymmetric filamentary structure

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

Hysteresis and precession of a swirling jet normal to a wall

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.V. Shtern, J. M

Charge Delocalization in Self-Assembled Mixed-Valence Aromatic Cation Radicals

The spontaneous assembly of aromatic cation radicals (D+•) with their neutral counterpart (D) affords dimer cation radicals (D2+•). The intermolecular dimeric cation radicals are readily characterized by the appearance of an intervalence charge-resonance transition in the NIR region of their electronic spectra and by ESR spectroscopy. The X-ray crystal structure analysis and DFT calculations of a representative dimer cation radical (i.e., the octamethylbiphenylene dimer cation radical) have established that a hole (or single positive charge) is completely delocalized over both aromatic moieties. The energetics and the geometrical considerations for the formation of dimer cation radicals is deliberated with the aid of a series of cyclophane-like bichromophoric donors with drastically varied interplanar angles between the cofacially arranged aryl moieties. X-ray crystallography of a number of mixed-valence cation radicals derived from monochromophoric benzenoid donors established that they generally assemble in 1D stacks in the solid state. However, the use of polychromophoric intervalence cation radicals, where a single charge is effectively delocalized among all of the chromophores, can lead to higher-order assemblies with potential applications in long-range charge transport. As a proof of concept, we show that a single charge in the cation radical of a triptycene derivative is evenly distributed on all three benzenoid rings and this triptycene cation radical forms a 2D electronically coupled assembly, as established by X-ray crystallography

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies