06Aug01

Research Summary for August 6, 2001

1. Determination of the Modeling and Simulation Phases for which the Aerodynamic Simulation Errors are considered

1. Conceptual Modeling
2. Mathematical Modeling
3. Programming Activities
4. Discreatization and Algorithm Selection
5. Numerical Solution
6. Solution Presentation

Hongman's work included errors associated with phases 4 and 5. For the current study, we may consider the same phases and maybe phase 2 for the investigation of the CFD simulation errors . (Or we can choose one specific phase)

2. Simulation Parameters:

a. Parameters associated with the program: This may include the modeling of the viscous terms (Thin-Layer N-S, Full N-S, or Euler for no viscous terms), inviscid flux schemes (Roe, Van-Leer, AUSM+), limiters, turbulence models (k-w, k-epsilon, Spalart-Allmaras). The number of cycles for the convergence of the solution is influenced by these parameters.

b. Parameters used in the description of the geometry

c. Parameters associated with the grid (discreatization of the flow field): These will effect the discreatization error.

d. Flow parameters: Mach number M, Reynolds number Re , and other flow conditions.

(b) and (c) are used in the description of the boundary conditions.

3. Review of the Validation Cases for GASP version 4:

All the validation cases except the last two ( turbulent wake of a flat plate and mixing-layer problem) are taken from NPARC alliance validation archive. The grid files and the experimental results of these cases are given in the same location.

3.1. Blasius Flat Plate:
Problem Description: 2-D, steady, laminar, uniform flow on a flat plate. The Blasius similarity solution is the exact solution to this problem.

Flow Parameters: M, Re, static temperature T, density rho, velocity v, and static pressure p of the inflow (freestream conditions)

Grid: 2-D, single zone grid (21x41x2)

Simple case with analytical solution
Computationally inexpensive (less grid points)
Used to demonstrate the viscous capabilities of GASP v4.
As the output, velocity profiles and/or the skin-friction cf distribution can be monitored.

3.2. Turbulent Flat Plate:
Problem Description: 2-D, steady, turbulent flow on a flat plate.

Flow Parameters: M, Re, static temperature T, density rho, velocity v, and static pressure p of the inflow (freestream conditions)

Grid: 2-D, single zone grid (21x41x2)

This validation case is used to test different turbulence models on wall-bounded flows
As the output, velocity profiles and/or the skin-friction cf distribution can be monitored. The velocity profiles can be compared with the analytical law of the wall profiles and experimental results.
Simple grid geometry

3.3. Transonic Diffuser:
Problem Description: Computation of a 2-D, turbulent flow field in a converging-diverging duct. Flow enters the duct at a subsonic M, accelerates to a supersonic flow, decelerates due to a shock in the diverging portion of the duct.

Flow Parameters: P0 (total pressure at the inlet), T0 (total temperature at the inlet), M0 (inlet Mach number), Pb (back pressure).

The selection of the Pb sets the strength of the shock. (In the validation process two different Pb has been used in order to compute a weak shock and a strong shock case)

Parameters Defining the Geometry: l (length of the duct), h0 (height of the duct at inflow), he (height of the duct et the exit), ht (throat height). In the validation case,
h0=1.4 ht and he=1.5 ht.

Grid: 2-D, single zone grid (81 x 51 x 2)

Figure 1. Single zone grid used in the transonic diffuser computation

Numerical oscillations due to the shock effect the number of cycles required for convergence.
In the strong shock case, a separated flow region is observed on the top wall just after the shock .
For our study, the shock location , the pressure distribution, and the cf distribution can be calculated over a range of flow parameters or geometries.

3.4. Transonic Airfoil:
Problem Description: Computation of the 2-D, transonic, turbulent flow around RAE 2822 airfoil. In the validation case, M=0.729 and angle of attack (AoA) is 2.31 degrees.

Flow Parameters: Freestream M, T, rho and Re, angle of attack.

Grid: 2-D, single zone C-grid (369 x 65 x 2)

Figure 2. Close-up view of the RAE 2822 airfoil grid

For our study, cp and cf distributions can be obtained for different freestream M and angle of attack.
cp and cf distributions can be computed for different grids
It may be computationally expensive to run multiple cases.

3.5. Rearward-facing Step:
Problem Description: Computation of incompressible, 2-D, turbulent flow over rearward-facing step.

Flow Parameters: Vi (inlet velocity), T, rho, Re (based on unit length) and Re_h (based on step height)

Parameters Defining the Geometry: lu ( length in the freestream direction upstream of the step), ld (length in the freestream direction downstream of the step), h step height

Grid: 2-D, two zone grid. 1st zone upstream of the step (51 x 66 x 2)
2nd zone downstream of the step (138 x 93 x 2)

Figure 3. Close-up view of the grid in the step region

Recirculation region downstream of the step
Multiple runs can be computationally expensive

3.6. Symmetric Turbulent Wake of a Flat Plate:
Problem Description: Computation of incompressible 2-D, turbulent flow over a flat plate and its wake. The flow is symmetric (AoA=0 degrees) so that the flow is identical on the top and bottom of the plate, thus resulting in a symmetric wake. Only the top half of the plate and the wake region can be considered for the computations.

Flow Parameters: The freestream M, T, rho and Re (based on unit length)

Grid: 2-D, two zone grid. 1st zone models the flat plate (51 x 151 x 2)
2nd zone models the wake region (71 x 151 x 2)

This validation case is used to test different turbulence models for the wake region.
The velocity defect profiles of the wake region are compared with the asymptotic wake profile.

3.7. The Two-Dimensional Mixing Layer:
Problem Description: Computation of the shear layer that results from mixing two streams of flow. The flow is two-dimensional. The flow designated as stream 1 mixes with a second flow, stream 2.

Figure 4. Schematic of the Mixing Layer problem

In the validation, two cases were studied: Compressible shear layer involving supersonic flow and incompressible mixing layer.

Flow Parameters: For the compressible case: The freestream conditions of the stream 2 (U2, T, rho, and AoA) are held constant. U1 is changed for obtaining different convection Mach number Mc=(U1-U2)/(a1-a2). The rest of the flow conditions of stream 2 are held constant.
For the incompressible case: T and rho for both streams are held constant. U1 and U2 are different.

Grid: 2-D, single zone grid. For the compressible case: (201 x 52 x 2)
For the incompressible case: (201 x 101 x 2)

Figure 5. The grid used in the compressible shear layer computations

This validation case is used to test different turbulence models for the mixing-layer problems.
The growth rate of a compressible shear layer behaves different than that of an incompressible flow, which posses a problem for most turbulent models.
Physical models used for compressible and and incompressible cases are different.
The variation of the growth rate of the compressible shear layer can be calculated as a function of Mc.

Table 1. Total number of grid points for each validation case:

Validation Case	Total number of grid points
Blasius Flat Plate	1722
Turbulent Flat Plate	1722
Transonic Diffuser	8262
RAE 2822 Transonic Airfoil	47970
Rearward-facing Step	32400
Symmetric Turbulent Wake of a Flat Plate	36844
Two-Dimensional Mixing Layer (Compressible)	20904
Two-Dimensional Mixing Layer (Incompressible)	40602