MECH 523 Applied CFD Sagar Kapadia
description
Transcript of MECH 523 Applied CFD Sagar Kapadia
Numerical study of the blade cooling effect generated by multiple jets issuing
at different angles and speed into a compressible horizontal cross flow.
MECH 523Applied 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
Design Variables(1) Blowing Ratio(R) =
where, 'h' stands for the hole,and 's' for the source. Three different values of R (1, 2, 2.5) has been used.
(2) Angle of Att
h h
s s
uu
o oack ( )
Two different values of (20 , 35 ) has been used
Grid Information Grid has been created using Gridgen-
14.03 preprocessor. Grid information:
Unstructured Grid Number of nodes = 121316 Number of elements = 651499 Element Type – Tetrahedran Quality of the grid = 99.78 %
(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 1000000.
^ ^ ^ ^ ^ ^ ^ ^( ). ( ).
v
QdV f i g j h k n d r i g j t k n dt
uQ v
we
2
( )
uu p
f uvuw
u e p
2
( )
vuv
g v pvw
v e p
2
( )
wuw
h vww p
w e p
0 0 0
xx xy xz
xy yy yz
xz yz zz
r s t
a b c
, , ;xx xy xz x xy yy yz y xz yz zz zHere a u v w k b u v w k and c u v w k
Governing equation for this case is unsteady, compressible Navier-Stokesequation. In integral form, it can be written as following:
where, is the fluid element volume; is the fluid element surface area; i, j,k are the Cartesian
unit vectors and is the unit normal to .
Governing Equation
. . . .
. . . .
. . . .. . . ..
w x
y z
i,j
i,j-1/2
i,j+1/2
i+1/2,j i-1/2,j
Finite Volume Method
x
y
2-D Problem : 0
Integrating theequation over the volume 'wxyz ',
0 0
where, ( )( )(1)
Applying Green'sTheorem,
(1) . 0
wxyz
wxyz wxy
U F Gt x y
U F Gd
t x yd dx dy
U dxdy H ndSt
where,n is the unit normal to thesurfaceSof the finite volumeand H can beexpressed
in Cartesian coordinates as
For the 2-D geometry,. ( )(1)
z
i jH F G
H ndS Edy Fdx
i+1/2,j.
w x
y z
i,j
i,j-1/2
i,j+1/2
i-1/2,j
Discretization
Discretization
1, ,
, 1/ 2 1/ 2, , 1/ 2 1/ 2,
, 1/ 2 1/ 2, , 1
( ) 0
which can be written as,
( )
(
wxyz wxyz
n ni j i j
wxyz i j ab i j bc i j cd i j da
i j ab i j bc i j
Udxdy Fdy Gdxt
U US F y F y F y F y
t
G x G x G
/ 2 1/ 2,
12 1 2
,
) 0
Area of thecell
Average valueof Uin thecell
, Flux Vectors,calculated either explicitly(n) or implicitly(n+1) , depends on thealgorithm
cd i j da
wxyz
i j
x G x
x x xS
U
F G
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 Cellw
InputsTypeBoundary Condition
Static Pressure = 101325 PaPressure Outlet
Outlet
Symmetric Wall (Gradient of all physical quantity is zero).
SymmetrySymmetry
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= 3000K, 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
w
w
S-A - One equation RANS model. Switch between RANS and LES model :
DES length scale, l = min(d , ) d - Distance to the closest wall, which is the turbulence length scale for S-A model.
desC
des
w
w
C - Adjustable model constant - max(dx,dy,dz)
For the regions, where d , Turbulence model will work as RANS (S-A) model. Length scale = d E.g. - Inside the Boundary La
desC
w
des
yer
For the regions, where d , Turbulence model will work as subgrid scale (LES) model. Length scale = C Length scale becomes grid dependent. E.g. - Separated Regions.
desC
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 = 20o combination.
Minimum cooling is obtained with R = 1 and = 35o combination.
Solution is unsteady after 400 time steps. Cooling effect is the combined function of
blowing ratio and .