Objective Discus Turbulence

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Presentation transcript:

Objective Discus Turbulence Introduce Reynolds Navier Stokes Equations (RANS)

Conservation Equations y z x

Turbulence Forced convection on flat plate http://www.math.rug.nl/~veldman/cfd-gallery.html

Turbulence

Size of eddies hurricane nozzle 2 in Eddy ~ 1/100 in ~200 miles

Transition from laminar to turbulent flow

Turbulence in the vicinity of human body PT-Teknik.dk

Example The figure below shows a turbulent boundary layer due to forced convection above the flat plate. The airflow above the plate is steady-state. Consider the points A and B above the plate and line l parallel to the plate. Point A y Flow direction Point A Point B line l For the given time step presented on the figure above plot the velocity Vx and Vy along the line l. b) Is the stress component txy lager at point A or point B? Why? c) For point B plot the velocity Vy as function of time.

3-D

Indoor airflow jet jet The question is: What we are interested in: exhaust supply jet The question is: What we are interested in: main flow or turbulence? turbulent

Energy Cascade Concept in Turbulence Kinetic energy is continually being transferred from the mean flow to the turbulent motion by large-scale eddies The process of vortex stretching leads to a successive reduction in eddy size and to a steepening of velocity gradients between adjacent eddies. Eventually the eddies become so small that viscous dissipation leads to the conversion of kinetic energy into heat.

Method for solving of Navier Stokes (conservation) equations Analytical Define boundary and initial conditions. Solve the partial deferential equations. Solution exist for very limited number of simple cases. Numerical - Split the considered domain into finite number of volumes (nodes). Solve the conservation equation for each volume (node). Infinitely small difference finite “small” difference

Numerical method Simulation domain for indoor air and pollutants flow in buildings 3D space Solve p, u, v, w, T, C Split or “Discretize” into smaller volumes

Capturing the flow properties 2” nozzle Eddy ~ 1/100 in Mesh (volume) should be smaller than eddies ! (approximately order of value)

Mesh size for direct Numerical Simulations (DNS) ~1000 ~2000 cells For 2D wee need ~ 2 million cells Also, Turbulence is 3-D phenomenon !

Mesh size For 3D simulation domain 2.5 m Mesh size 0.1m → 50,000 nodes 3D space (room)

We need to model turbulence! Reynolds Averaged Navier Stokes equations

First Methods on Analyzing Turbulent Flow - Reynolds (1895) decomposed the velocity field into a time average motion and a turbulent fluctuation vx’ Vx - Likewise f stands for any scalar: vx, vy, , vz, T, p, where: From this class We are going to make a difference between large and small letters Time averaged component

Time Averaging Operations

Averaging Navier Stokes equations Substitute into Navier Stokes equations Instantaneous velocity fluctuation around average velocity Average velocity Continuity equation: time Average whole equation: Average Average of average = average Average of fluctuation = 0