scholarly journals EULER EQUATIONS WITH SEVERAL INDEPENDENT PRESSURE LAWS AND ENTROPY SATISFYING EXPLICIT PROJECTION SCHEMES

2006 ◽  
Vol 16 (09) ◽  
pp. 1469-1504 ◽  
Author(s):  
CHRISTOPHE CHALONS ◽  
FRÉDÉRIC COQUEL
Keyword(s):  
Stokes Equations ◽  
Scale Effects ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Small Scale ◽  
Stability Estimates ◽  
Jump Conditions ◽  
Riemann Solutions ◽  
Navier Stokes Equations

This work aims at numerically approximating the entropy weak solutions of Euler-like systems asymptotically recovered from the multi-pressure Navier–Stokes equations in the regime of an infinite Reynolds number. The nonconservation form of the limit PDE model makes the shock solutions to be sensitive with respect to the underlying small scales. Here we propose to model these small scale effects via a set of generalized jump conditions expressed in terms of the independent internal energies. The interest in considering internal energies stems from the presence of solely first-order nonconservative products by contrast to other variables. These nonconservative products are defined in the now classical sense proposed by Dal Maso, LeFloch and Murat. We show how to enforce the generalized jump conditions at the discrete level with a fairly simple numerical procedure. This method is proved to satisfy a full set of stability estimates and to produce approximate solutions in good agreement with exact Riemann solutions.

scholarly journals Numerical simulation of complex 3D compressible viscous flows through rotating blade passage

2003 ◽  
pp. 55-82
Author(s):  
M. Despotovic ◽  
Milun Babic ◽  
D. Milovanovic ◽  
Vanja Sustersic
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Convergence Acceleration ◽  
Design Tool ◽  
Navier Stokes ◽  
Internal Flows ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Compressible Viscous Flows

This paper describes a three-dimensional compressible Navier-Stokes code, which has been developed for analysis of turbocompressor blade rows and other internal flows. Despite numerous numerical techniques and statement that Computational Fluid Dynamics has reached state of the art, issues related to successful simulations represent valuable database of how particular tech?nique behave for a specifie problem. This paper deals with rapid numerical method accurate enough to be used as a design tool. The mathematical model is based on System of Favre averaged Navier-Stokes equations that are written in relative frame of reference, which rotates with constant angular velocity around axis of rotation. The governing equations are solved using finite vol?ume method applied on structured grids. The numerical procedure is based on the explicit multistage Runge-Kutta scheme that is coupled with modem numerical procedures for convergence acceleration. To demonstrate the accuracy of the described numer?ical method developed software is applied to numerical analysis of flow through impeller of axial turbocompressor, and obtained results are compared with available experimental data.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

scholarly journals Aerodynamic Dissipation

1958 ◽  
Vol 8 ◽  
pp. 966-974
Author(s):  
H. E. Petschek
Keyword(s):  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Mean Free Path ◽  
Navier Stokes ◽  
Small Scale ◽  
Minimum Length ◽  
Ionized Gas ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Rate Of Dissipation

Analyses of aerodynamic dissipation in ordinary un-ionized gases are all based upon the Navier-Stokes equations. These equations relate the rate of dissipation to the local gradients in velocity and temperature through the viscosity and heat conduction coefficients. Although it is true that in many flow situations the magnitude of the total dissipation in the gas does not depend on the magnitude of the viscosity coefficient, this coefficient does determine the minimum scale of variations observed in the gas and the form of the Navier-Stokes equations determines the type of phenomena which are observed on a small scale. In order to discuss dissipation in an ionized gas in the presence of a magnetic field, it is therefore necessary to re-examine the derivation of the basic flow equations. This paper attempts to do this for a case of a completely ionized gas and demonstrates that the basic microscopic dissipation mechanism is appreciably different. For example, it is shown that the minimum length in which the properties of the flow field can change noticeably is appreciably less than one mean free path.

Numerical Prediction of Impact-Related Wave Loads on Ships

2006 ◽  
Vol 129 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Thomas E. Schellin ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Ship Motions ◽  
Normal Velocity ◽  
Wave Loads ◽  
Navier Stokes Equations ◽  
Critical Areas ◽  
Strip Theory ◽  
A Chain

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Ship speed, wave frequency, and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the nonlinear pressure distribution up to the wave contour and the frequency dependence of the radiation forces (memory effect). Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier–Stokes equations code that was used to obtain slamming loads. Favorable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

Navier–Stokes solutions of unsteady separation induced by a vortex

2002 ◽  
Vol 465 ◽  
pp. 99-130 ◽  
Author(s):  
A. V. OBABKO ◽  
K. W. CASSEL
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Scale Interaction

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

scholarly journals Dynamic Behaviour of the Loads of Podded Propellers in Waves: Experimental and Numerical Simulations

2014 ◽  
Author(s):  
Patrick Queutey ◽  
Jeroen Wackers ◽  
Alban Leroyer ◽  
GanBo Deng ◽  
Emmanuel Guilmineau ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Scale Effects ◽  
Computational Study ◽  
Essential Feature ◽  
Flow Distribution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Wave Basin

The paper focuses on the hydrodynamic flow around a ship with pods in waves and compares the results of an experimental campaign with numerical simulations conducted during the EU-funded STREAMLINE project. It was the first project for which the effect of waves on cavitation and ventilation was explored in both experimental and numerical ways for a ship with pods. The measurements were carried out in MARIN’s Depressurized Wave Basin (DWB) with a fully instrumented podded ship model, in sailing condition, in waves and depressurised conditions. In this way, the correct representation of cavitation and possible ventilation bubbles and vortices is ensured, resulting in a correct physical behaviour. The discretisation of the Reynolds-Averaged Navier-Stokes Equations (RANSE) is based on the unstructured finite-volume flow solver ISIS-CFD developed by ECN-CNRS. An essential feature for full RANSE simulations with this code is the use of a sliding grid technique to simulate the real propeller rotating behind a ship hull. The computational study in operational service conditions considered here has been conducted to evaluate the instantaneous flow distribution around the podded propellers and to analyse and to compare the unsteady behaviour of the forces induced by the rotating propeller in waves with the measurements from omnidirectional propeller loads as well as the blade forces and moments. The computational study has been done in model and full scale to evaluate the scale effects.

Prediction of Wall-Jet and Wall-Wake Flows

1970 ◽  
Vol 12 (6) ◽  
pp. 404-420 ◽  
Author(s):  
S. C. Kacker ◽  
J. H. Whitelaw
Keyword(s):  
Film Cooling ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Wall Jet ◽  
Two Dimensional ◽  
Constant Property ◽  
Navier Stokes Equations ◽  
Wake Flows ◽  
Wide Range

An existing numerical procedure for solving the steady, two-dimensional, constant property form of the Navier–Stokes equations, has been used to obtain predictions of mean and fluctuating properties downstream of a two-dimensional wall jet. The Prandtl–Kolmogorov model of turbulence, with a simple empirical expression for the length scale, is shown to permit satisfactory predictions over a wide range of flow situations. These flow situations are relevant to the design of film-cooling slots.

Heat Transfer Generated by the Interaction of Single and Multiple Tandem Jets in Crossflow

2010 ◽  
Author(s):  
Amina Radhouane ◽  
Nejla Mahjoub ◽  
Hatem Mhiri ◽  
George Lepalec ◽  
Philippe Bournot
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Cooling Power ◽  
Small Scale ◽  
Fluid Composition ◽  
Navier Stokes Equations ◽  
The Impact

“Twin jets in Crossflow” is a common configuration that finds application in several large and/or small scale industrial fields. The interest in such a configuration is further enhanced by its dependence in several parameters, that may be geometric, dynamic, thermal, or relative to the handled fluid composition. We propose to focus in the present work on the effect of the number of the emitted jets on the generated heat transfer, in presence of an unchanged uniform crossflow. To reach this goal, single, double and triple jet configurations were simulated, based upon the resolution of the Navier Stokes equations by means of the RSM (Reynolds Stress Model) second order turbulent closure model, together with a non uniform grid system particularly tightened near the emitting nozzles. After validation, we tried to find out the impact of the number of the handled jets on their cooling “power” by tracking the temperature distribution of the resulting flowfield. Since in practically all applications we are in need of higher efficiencies and then of higher operating temperatures, we are constantly concerned about not going beyond the shielding material melting temperature. If the use of cooling jets proves to be efficient, this may bring a significant progress in the technological field.

Sign in / Sign up

Export Citation Format

Share Document