Analytical and Semi-empirical Models of Tornadoes and Downbursts

2021 ◽  
Author(s):  
Djordje Romanic ◽  
Horia Hangan
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Empirical Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Simplifying Assumptions ◽  
The Individual ◽  
Semi Empirical

Analytical and semi-empirical models are inexpensive to run and can complement experimental and numerical simulations for risk analysis-related applications. Some models are developed by employing simplifying assumptions in the Navier-Stokes equations and searching for exact, but many times inviscid solutions occasionally complemented by boundary layer equations to take surface effects into account. Other use simple superposition of generic, canonical flows for which the individual solutions are known. These solutions are then ensembled together by empirical or semi-empirical fitting procedures. Few models address turbulent or fluctuating flow fields, and all models have a series of constants that are fitted against experiments or numerical simulations. This chapter presents the main models used to provide primarily mean flow solutions for tornadoes and downbursts. The models are organized based on the adopted solution techniques, with an emphasis on their assumptions and validity.

scholarly journals THE INFLUENCE OF THE TURBULENCE CLOSURE MODEL ON WAVE-CURRENT INTERACTION MODELING AT A LOCAL SCALE AT A LOCAL SCALE

2012 ◽  
Vol 1 (33) ◽  
pp. 64
Author(s):  
Maria João Teles ◽  
António Pires-Silva ◽  
Michel Benoit
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Local Scale ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Interaction Modeling ◽  
Flow Components

An advanced CFD solver based on the RANS (Reynolds Averaged Navier-Stokes) equations is used to evaluate wave-current interactions through numerical simulations of combined wave-current free surface turbulent flows. The repercussions of various schemes for modeling turbulence effects is addressed with a special attention to the exchanges and fluxes of momentum and energy between the mean flow components and the wave (oscillatory) component. Numerical simulations are compared with experimental data from Klopman (1994).

Natural convection flow far from a horizontal plate

1999 ◽  
Vol 387 ◽  
pp. 227-254 ◽  
Author(s):  
VALOD NOSHADI ◽  
WILHELM SCHNEIDER
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
The Self ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Self Similar ◽  
Similar Solutions

Plane and axisymmetric (radial), horizontal laminar jet flows, produced by natural convection on a horizontal finite plate acting as a heat dipole, are considered at large distances from the plate. It is shown that physically acceptable self-similar solutions of the boundary-layer equations, which include buoyancy effects, exist in certain Prandtl-number regimes, i.e. 0.5<Pr[les ]1.470588 for plane, and Pr>1 for axisymmetric flow. In the plane flow case, the eigenvalues of the self-similar solutions are independent of the Prandtl number and can be determined from a momentum balance, whereas in the axisymmetric case the eigenvalues depend on the Prandtl number and are to be determined as part of the solution of the eigenvalue problem. For Prandtl numbers equal to, or smaller than, the lower limiting values of 0.5 and 1 for plane and axisymmetric flow, respectively, the far flow field is a non-buoyant jet, for which self-similar solutions of the boundary-layer equations are also provided. Furthermore it is shown that self-similar solutions of the full Navier–Stokes equations for axisymmetric flow, with the velocity varying as 1/r, exist for arbitrary values of the Prandtl number.Comparisons with finite-element solutions of the full Navier–Stokes equations show that the self-similar boundary-layer solutions are asymptotically approached as the plate Grashof number tends to infinity, whereas the self-similar solution to the full Navier–Stokes equations is applicable, for a given value of the Prandtl number, only to one particular, finite value of the Grashof number.In the Appendices second-order boundary-layer solutions are given, and uniformly valid composite expansions are constructed; asymptotic expansions for large values of the lateral coordinate are performed to study the decay of the self-similar boundary-layer flows; and the stability of the jets is investigated using transient numerical solutions of the Navier–Stokes equations.

scholarly journals Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

2017 ◽  
Vol 826 ◽  
pp. 396-420 ◽  
Author(s):  
M. Bouyges ◽  
F. Chedevergne ◽  
G. Casalis ◽  
J. Majdalani
Keyword(s):  
Cross Section ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Internal Flow ◽  
Navier Stokes ◽  
Solid Rocket Motor ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Radial Deviation

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Low-Frequency Fluctuations In The Flow Over Confined Cylinder In A Narrow Rectangular Duct At Re = 3 750

2017 ◽  
Vol 12 (1) ◽  
pp. 43-49
Author(s):  
Egor Palkin ◽  
Rustam Mullyadzhanov
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Horseshoe Vortex ◽  
Navier Stokes ◽  
Infinite Cylinder ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Frequency Modulations ◽  
Bounding Surfaces

Flows between two closely spaced bounding surfaces are frequently appear in engineering applications and natural flows. In current paper the flow over a cylinder in a narrow rectangular duct was investigated by numerical computations of Navier-Stokes equations using Large eddy simulations (LES) at ReD = 3 750 based on cylinder diameter and the bulk velocity at inflow boundary. The influence of the bounding walls was demonstrated by comparing mean flow streamlines with the flow over an infinite cylinder at close Reynolds numbers. A comparison between the time-averaged velocity field in front and past the cylinder with experimental from the literature data showed good agreement although the characteristic horseshoe vortex structures are highly sensitive to Reynolds number and turbulence level at inflow boundary. Most energetic modes in recirculating region were revealed by spectral analysis. These low-frequency modulations were characterized by the pair of dominating vortices which are expected to have high influence on the heat transfer in near wake of the cylinder.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

Numerical Simulations of Nonlinear Post-Critical Vibrations of an Airfoil After Flutter Instability

2011 ◽  
Author(s):  
Jaromi´r Hora´cˇek ◽  
Miloslav Feistauer ◽  
Petr Sva´cˇek
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Mass Matrix ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Classical Flutter

The contribution deals with the numerical simulation of the flutter of an airfoil with three degrees of freedom (3-DOF) for rotation around an elastic axis, oscillation in the vertical direction and rotation of a flap. The finite element (FE) solution of two-dimensional (2-D) incompressible Navier-Stokes equations is coupled with a system of nonlinear ordinary differential equations describing the airfoil vibrations with large amplitudes taking into account the nonlinear mass matrix. The time-dependent computational domain and a moving grid are treated by the Arbitrary Lagrangian-Eulerian (ALE) method and a suitable stabilization of the FE discretization is applied. The developed method was successfully tested by the classical flutter computation of the critical flutter velocity using NASTRAN program considering the linear model of vibrations and the double-lattice aerodynamic theory. The method was applied to the numerical simulations of the post flutter regime in time domain showing Limit Cycle Oscillations (LCO) due to nonlinearities of the flow model and vibrations with large amplitudes. Numerical experiments were performed for the airfoil NACA 0012 respecting the effect of the air space between the flap and the main airfoil.

Unsteady Multicellular Natural Convection in a Narrow Horizontal Cylindrical Annulus

1990 ◽  
Vol 112 (2) ◽  
pp. 379-387 ◽  
Author(s):  
D. B. Fant ◽  
J. Prusa ◽  
A. P. Rothmayer
Keyword(s):  
Chaotic Systems ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Cylindrical Annulus ◽  
Gap Spacing ◽  
Limiting Case

Numerical and analytical solutions are presented for multicellular flow instability and the subsequent nonlinear development in a horizontal cylindrical annulus. The Boussinesq approximated Navier–Stokes equations are simplified to Cartesian-like boundary layer equations by means of a high Rayleigh number small gap asymptotic expansion. The full numerical problem is explored for the limiting case of zero Prandtl number. At a finite scaled gap spacing, an instability sets in, which results in periodic multicellular flow. The numerical solutions are found to progress through an increasingly complex sequence of periodic solutions, culminating in a very complex unsteady solution that has features normally associated with chaotic systems.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

Sign in / Sign up

Export Citation Format

Share Document