Search results for "Stokes equations"
showing 9 items of 49 documents
A dynamic subgrid-scale tensorial eddy viscosity model
1999
In the Navier-Stokes equations the removal of the turbulent fluctuating velocities with a frequency above a certain fixed threshold, employed in the Large Eddy Simulation (LES), causes the appearance of a turbulent stress tensor that requires a number of closure assumptions. In this paper insufficiencies are demonstrated for those closure models which are based on a scalar eddy viscosity coefficient. A new model, based on a tensorial eddy viscosity, is therefore proposed; it employs the Germano identity [1] and allows dynamical evaluation of the single required input coefficient. The tensorial expression for the eddy viscosity is deduced by removing the widely used scalar assumption of the …
Transition to turbulence and Singularity in Boundary Layer Theory
2007
We compute the solutions of Prandtl’s and Navier- Stokes equations for the two dimensional flow induced by an array of periodic rectilinear vortices interacting with a boundary in the halfplane. This initial datum develops, in a finite time, a separation singularity for Prandtl’s equation. We investigate the different stages of unsteady separation in Navier-Stokes solutions for various Reynolds numbers. We show the presence of a large- scale interaction between viscous boundary layer and inviscid outer flow in all Re regimes, while the presence of a small-scale interaction is visible only for moderate-high Re numbers. We also investigate the asymptotic validity of boundary layer theory in t…
Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver
2017
Due to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, non- hydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractional- time-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydro…
Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions
2010
In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…
Implementation and application of the actuator line model by OpenFOAM for a vertical axis wind turbine
2017
University of Stavanger has started The Smart Sustainable Campus & Energy Lab project, to gain knowledge and facilitate project based education in the field of renewable and sustainable energy and increase the research effort in the same area. This project includes the future installation of a vertical axis wind turbine on the campus roof. A newly developed Computational Fluid Dynamics (CFD) model by OpenFOAM have been implemented to study the wind behavior over the building and the turbine performance. The online available wind turbine model case from Bachant, Goude and Wosnik from 2016 is used as the starting point. This is a Reynolds-Averaged Navier-Stokes equations (RANS) case set up th…
Numerical and experimental investigation of a cross-flow water turbine
2016
ABSTRACTA numerical and experimental study was carried out for validation of a previously proposed design criterion for a cross-flow turbine and a new semi-empirical formula linking inlet velocity to inlet pressure. An experimental test stand was designed to conduct a series of experiments and to measure the efficiency of the turbine designed based on the proposed criterion. The experimental efficiency was compared to that from numerical simulations performed using a RANS model with a shear stress transport (SST) turbulence closure. The proposed semi-empirical velocity formula was also validated against the numerical solutions for cross-flow turbines with different geometries and boundary c…
Well-posedness of Prandtl equations with non-compatible data
2013
In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.
Mathematical modelling of alternating electromagnetic and hydrodynamic fields, induced by bar type conductors in a cylinder
2009
The heating of buildings by ecologically clean and compact local devices is an interesting and actual problem. One of the modern areas of applications developed during last ten years is an effective usage of electrical energy by alternating current to produce heat energy. This work presents the mathematical model of one of such devices. It is a finite cylinder with viscous incompressible liquid and with metal electrodes of the form of bars placed parallel to the cylinder axis in the liquid. These conductors are connected to the alternating current. First published online: 14 Oct 2010
Effect of the junction angle on turbulent flow at a hydraulic confluence
2018
Despite the existing knowledge concerning the hydrodynamic processes at river junctions, there is still a lack of information regarding the particular case of low width and discharge ratios, which are the typical conditions of mountain river confluences. Aiming at filling this gap, laboratory and numerical experiments were conducted, comparing the results with literature findings. Ten different confluences from 45 ∘ to 90 ∘ were simulated to study the effects of the junction angle on the flow structure, using a numerical code that solves the 3D Reynolds Averaged Navier-Stokes (RANS) equations with the k- ϵ turbulence closure model. The results showed that the higher the junction angle, the …