Simulation of Turbulent Flows in Channel with Obstructions. Golovnya B. P. ISMEL, Cherkassy, Ukraine

Briefly about model of turbulence. It is supposed, then energy stream from mean flow to turbulence is separated on infinite series of parts by turbulence own. So full turbulent energy is separated on infinite series of parts also. Two major parts were named as "primary" and "secondary" turbulence or "big" and "middle" eddies. Primary turbulence provides interactions with mean flow, secondary is in coincidence with data by coherent structures. In mathematical sense it is need to introduce adjusting function in a new way.

(1) (2) Secondary turbulence. Primary turbulence. (3) (4)

Properties of model. It can be demonstrated, that this model nothing loses and nothing adds to exact Reynolds equations On the base of this model simulations of all main shear turbulent flows were provided. They are - boundary layer, mixing layer, jet and far wake, pipe and channel flows. The models for simulation of full tensors of turbulent stresses and heat fluxes were designed and the numerical simulations of mixed convection from forced flow till natural convection were performed. The numerical simulations of bypass laminar-turbulent transition on cold plate under high free-stream turbulence were performed also. It must be said, that simulations were started from the blade of а plate, i.e. with alone physically valid initial conditions. Calculations of turbulent energy spectra were performed. Results corresponds to "-5/3" law. Dissipative scales in channel flow, which were found by this model are in wonderful accord with Comte Bellot experimental data. And it is not complete list of problems, which can be solved on the base of this approach.

Problem for simulation. Model equations. In given work series of flow in channel with canopies type obstructions were simulated. Presence of obstructions in channel was modeled by additional term introduction into Navier-Stockes equations Here coefficient C depends on obstructions form and concentration, h – obstructions height. Turbulence production by obstructions presence was accounted by introduction of additional system for turbulence in wake for obstructions. This system completely coincides with mentioned above turbulence model by form.

First problem. Obstructions have a cylindrical form. Fig.1. Comparison of U calculations in three channel sections with experiments. H channel=320 mm, h obstr.=74 mm, D obstr.=9 mm, Re=10000, C=1.4

Second problem. Obstructions have a tree form – crown of triangle form is placed on a stem. 2H chan=1.68 m, h obstr.=h crown+h stem=( )m, D crown=0.08 m, D stem=0.009 m, Re=10000, C stem=1, C crown=10C stem. Fig.2. Results of U calculations

Fig.3. Results of velocity fluctuations calculations.

Fig.4. Components of turbulent energy.

Fig.5. Dependence of all parameters of obstructions resistance at X/h=40.

Fig.6. Development of all main turbulent parameters in flow with and without obstructions.

Fig.7. Development of channel hydraulic resistance, friction on the wall and velocity fluctuations on the way from channel inlet till stabilization point. Here - channel hydraulic resistance.

Fig.8. Comparison of stable state of flows with and without obstructions.