Numerical study of the blade cooling effect generated by multiple jets issuing at different angles and speed into a compressible horizontal cross flow. MECH 523 Applied CFD Sagar Kapadia

Content Industrial Applications Geometry, Grid and Design Parameters Governing Equations (N-S) And Solver – Cobalt Finite Volume Method Turbulence Model (DES) Results And Discussion Conclusion and Future Scope

Industrial Applications Take off and landing engineering Film cooling of Turbine blades Jets into combustors

0.2m 0.9m 0.2m Geometry Hot Crossflow Cool Jet

Design Variables

Grid Information Grid has been created using Gridgen preprocessor. Grid information:  Unstructured Grid  Number of nodes =  Number of elements =  Element Type – Tetrahedran  Quality of the grid = % (Blacksmith)

Solver:Cobalt A parallel, implicit, unstructured Euler/Navier-Stokes Flow solver. It was developed in the computational science branch of the Air-Force. This code is used to solve the high speed, highly separated flow problems. Six different turbulence models are available in this code for different kind of simulation. (1) S-A model. (2) DES/S-A model. (3) Menter Baseline (BSL). (4) Menter Baseline + Shear Stress Transport (SST). (5) DES/M-SST. (6) Wilcox k- . Spatial Accuracy : Second Order. Temporal Accuracy : Second Order. CFL can be as large as

Governing Equation

w x yz i,j i,j-1/2 i,j+1/2 i+1/2,j i-1/2,j Finite Volume Method x y

i+1/2,j. w x yz i,j i,j-1/2 i,j+1/2 i-1/2,j Discretization

Boundary Implementation of Boundary Condition in Finite Volume P1=P2, u1 = -u2 (No-Slip Condition) v1 = -v2 T1=T2 (Adiabatic) i,j+1/2. x y z 1 w1 y1. x1 z1 2 Mirror Cell w

InputsTypeBoundary Condition Static Pressure = PaPressure OutletOutlet Symmetric Wall (Gradient of all physical quantity is zero). Symmetry P, T, Mach Number, Turbulent Viscosity(Ref. Condition) FarfieldOpen Faces No-Slip ConditionAdiabatic WallBlade Density,Velocity profile (depends on R), P, Turbulence Viscosity User-DefinedHole P, T= K, Mach Number=0.3, Turbulence Viscosity SourceInlet Model Boundary Conditions

Turbulence Model : Detached Eddy Simulation (DES) Purpose of DES – To overcome the disadvantages of LES and RANS Hybrid Turbulence Model of, (1) RANS and (2) LES Used for High Speed, Massively separated flows. RANS - Attached Boundary Layers LES - Separated Regions. Presently available definition of DES is not related with any particular turbulence model. DEFINITION : DES is a 3-D unsteady numerical solution using single turbulence model which functions as a sub-grid scale model in the regions where grid density is fine enough for LES and as a RANS where it is not. “fine enough” – when maximum spatial step,is much smaller than the flow turbulence length scale,

Overview of Spalart-Allmaras(S-A) Based DES Model

Flow Visualization- Temperature Distribution (400 time steps)

Flow Visualization- Vortex Formation

Temperature Contours for R =1 and  = 35 o x =

x = Temperature Contours for R =2.50 and  = 20 o

x = Temperature Contours for R = 2 and  = 20 o

Cooling Effect Obtained by the recirculation of the cold air

Conclusion Three different combinations of R (blowing ratio) and  (angle of attack) has been used to measure the cooling effect after 400 time steps. Maximum cooling is obtained with R = 2 and  = 20 o combination. Minimum cooling is obtained with R = 1 and  = 35 o combination. Solution is unsteady after 400 time steps. Cooling effect is the combined function of blowing ratio and .

Future Scope To solve the problem with more combinations of R and . To get the steady state solution for the cases described in the presentation and compare the cooling. To find out the optimum combination of Blowing Ratio and Angle of attack of the jet for maximum cooling.