scholarly journals Convergence Analysis of a Fully Discrete Family of Iterated Deconvolution Methods for Turbulence Modeling with Time Relaxation

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
R. Ingram ◽  
C. C. Manica ◽  
N. Mays ◽  
I. Stanculescu
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Convergence Theory ◽  
Existence Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fully Discrete ◽  
Mathematical Properties ◽  
The Family ◽  
Special Operator

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified) Tikhonov-Lavrentiev and (modified) Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.

Steady Flow in the Transition Length of a Straight Tube

1942 ◽  
Vol 9 (2) ◽  
pp. A55-A58 ◽  
Author(s):  
Henry L. Langhaar
Keyword(s):  
Velocity Field ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Straight Tube ◽  
Pressure Function ◽  
Navier Stokes Equations ◽  
Dimensionless Constant ◽  
The Family ◽  
Transition Length

Abstract By means of a linearizing approximation, the Navier-Stokes equations are solved for the case of steady flow in the transition length of a straight tube. The family of velocity profiles is defined by Bessel functions, and the parameter of this family is tabulated against the axial co-ordinate in a dimensionless form. Hence, the length of transition is obtained. The curves give a comparison of the author’s calculations of the velocity field with those of other investigators, and with the experimental data of Nikuradse. The pressure function is derived from the computed velocity field by means of the energy equation, and the pressure drop in the transition length is defined by a dimensionless constant m, which is computed to be 2.28. A discussion of this constant is given in the conclusions.

A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

2014 ◽  
Vol 6 (5) ◽  
pp. 615-636 ◽  
Author(s):  
Zhendong Luo
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Stokes Equations ◽  
Volume Element ◽  
Navier Stokes ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Fully Discrete ◽  
Finite Volume Element ◽  
Stationary Navier Stokes Equations

AbstractA semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.

scholarly journals Turbulence Modeling a Review for Different Used Methods

2021 ◽  
Vol 39 (1) ◽  
pp. 227-234
Author(s):  
Khelifa Hami
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Simulation Models ◽  
Navier Stokes ◽  
Future Research ◽  
Detached Eddy Simulation ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Complicated Geometries

This contribution represents a critical view of the advantages and limits of the set of mathematical models of the physical phenomena of turbulence. Turbulence models can be grouped into two categories, depending on how turbulent quantities are calculated: direct numerical simulations (DNS) and RANS (Reynolds Averaged Navier-Stokes Equations) models. The disadvantage of these models is that they require enormous computing power, inaccessible, especially for large and complicated geometries. For this reason, hybrid models (combinations between DNS and RANS methods) have been developed, for example, the LES (“Large Eddy Simulation”) or DES (“Detached Eddy Simulation”) models. They represent a compromise - are less precise than DNS, but more precise than RANS models. The results presented in this contribution will allow and facilitate future research in the field the choice of the model approach necessary for the case studies whatever their difficulty factor.

Calculation of Debris Trajectories During High-Speed Snowplowing

2002 ◽  
Author(s):  
H. K. Nakhla ◽  
B. E. Thompson
Keyword(s):  
Particle Tracking ◽  
High Speed ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Cutting Edge ◽  
Navier Stokes ◽  
Engineering Model ◽  
Navier Stokes Equations ◽  
Snow Plowing ◽  
Reynolds Averaged Navier Stokes

An engineering model is presented to calculate the trajectory of airborne debris that adversely affects visibility during high-speed snow plowing. Reynolds-averaged Navier-Stokes equations are solved numerically with turbulence-modeling, particle-tracking, and cutting-edge approximations. Results suggest snow can be divided into splash and snow-cloud when designing treatments to improve visibility for snowplow drivers and following traffic. Calculated results confirm the findings of windtunnel and road tests, specifically that the trap angle of overplow deflectors should be less than 50 degrees to eliminate snow debris blowing over top of the plow onto the windscreen.

Film Cooling of Compound Angle Upstream Sister Holes

2019 ◽  
Author(s):  
Sana Abd Alsalam ◽  
Bassam Jubran
Keyword(s):  
Film Cooling ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cooling Performance ◽  
Film Cooling Effectiveness ◽  
Simple Strategy ◽  
Compound Angle

Abstract This study introduces a novel and simple strategy; compound angle upstream sister holes (CAUSH) to increase film cooling performance of the cylindrical hole by combining two techniques: Sister holes; (two small round holes placed upstream the primary hole) and compound angle hole. Whereas the upstream sister holes were injected at several compound angles β = 0°, 45°, 75°, and 90°, while the main hole was injected to the streamwise direction at 35° on a flat plate. FLUENT-ANSYS code was used to perform the simulation by solving the 3D Reynolds Averaged Navier-Stokes Equations. The capability of three types of k-ε turbulence modeling combined with the enhanced wall treatment is investigated to predict the film cooling performance of sister holes. A detailed computational analysis of the cooling performance of the (CAUSH) and the flow field was done at a density ratio equal to two (D.R = 2) and four blowing ratios M = 0.25, 0.5, 1.0 and 1.5 to predict the centerline and laterally averaged film cooling performance. The centerline effectiveness results showed that the highest cooling performance from the examined (CAUSH) was obtained at β = 0°, 45°, and 90° for low and high blowing ratio, the highest laterally averaged film cooling performance was captured at β = 0° and 90° for all tested blowing ratios. Also, the results indicated that the upstream sister hole with 90° compound angle holes has the best overall film cooling effectiveness while the worst performance is attained at β = 75°.

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