i.z. naqavi 1, e. savory 1 & r.j. martinuzzi 2 1 advanced fluid mechanics research group...

I.Z. Naqavi1, E. Savory1 & R.J. Martinuzzi2

1Advanced Fluid Mechanics Research GroupDepartment of Mechanical and Materials Engineering

The University of Western Ontario

2Mechanical and Manufacturing EngineeringUniversity of Calgary

Flow Characterization of Inclined Jet in Cross Flow for Thin Film Cooling via Large Eddy

Simulation

Overview:

Jets in Cross Flow

Thin Film Cooling

Background

Current Work

Large Eddy Simulation

Results

Conclusions

Jets in Cross Flow:

A flow configuration representing a variety of industrial and environmental flows.

A jet is introduced from the wall at a certain angle to the main stream.

Used in VTOL, thin film cooling, pollutant dispersion etc.

Thin film cooling (Durbin, 2000)

Cold fluid

Holes for film cooling on turbine blade.

Thin Film Cooling:

Separation of a hot fluid from a wall by a cold fluid, in form of a thin layer ejecting from wall, is called thin film cooling.

Hot fluid

Cooling film

Background:

Four major structures have been identified i.e. horse shoe vortex, jet shear-layer vortex, counter rotating vortex pair and wake vortices.

Horseshoe vortices

Jet shear-layer vortices

Counter rotating vortex pair

Wake vortices

Wall

Current Work:

In this work LES is performed for inclined jet in cross flow.

Effort is being made to introduce a cross flow with true turbulence.

Previous LES simulations lack effective turbulence specification at the inlet. In this work a real turbulent field is specified at the inlet.

This will enhance the understanding of the effect of background turbulence on the jet in cross flow.

Large Eddy Simulation:

massx

U

i

i 0

momentumxx

U

x

p

x

UU

t

U

j

ij

j

i

Dij

jii Re

12

2

pressureFilteredp

velocityFilteredU i

)(

Re Re

sgstensorstressscaleSubgrid

numberynolds

ij

D

In LES spatially filtered unsteady Navier Stokes equation are solved numerically.

A fractional step scheme (Moin, 1982) is used to solve Navier Stokes equations.

A semi implicit time advancement scheme is used where convection terms are discretized explicitly with 3rd order Runge-Kutta scheme and diffusion terms are discretized implicitly with Crank-Nicolson scheme.

Resulting set of linear system is approximately factorized and solved using Tri-diagonal matrix algorithm.

To solve pressure poisson equation fourier decomposition is applied in span-wise direction and resulting system of equation is solved using cyclic reduction method.

Large Eddy Simulation (cont.):

Large Eddy Simulation (cont.):

ReD =3500

Domain size ]3,3[]5.7,0[]12,5[ DDDDD

Grid size

At inlet a true turbulent velocity field is specified for that purpose a separate channel flow code is run and velocities are saved at a plane for some 150 flow through time.

6471171

Results

Average Vorticity Field:

Average stream-wise vorticity at different y-z planes

Streamlines overlaid on average stream-wise vorticity on a y-z plane at x=5D showing counter rotating vortex pair.

Average wall normal vorticity at the bottom x-z plane

Average span-wise vorticity at the central x-y plane

Instantaneous Vorticity Field:

Instantneous stream-wise vorticity at different y-z planes

Instantaneous wall normal vorticity at the bottom x-z plane

Instantaneous span-wise vorticity at the central x-y plane

Coherent Structure:

ijij

iiii SSp

2,

TensorStrainVelocityS

Vorticity

Poissonessurep

ij

i

ii

Pr ,

Coherent structures can be represented by iso-surfaces of pressure poisson.

Coherent structures for inclined jet in cross flow (Laminar)

Coherent structures for inclined jet in cross flow (Turbulent)

Hairpin structures

Stream-wise structure

Conclusions:

Instantaneous flow picture is presenting a very strong interaction of cross flow with jet.

Vortical structures coming from upstream interact with the jet.

Such interactions can have strong influence on heat transfer.

http://www.eng.uwo.ca/research/afm/default.htm

Thank you