# Gold:UFR3-05 instruct

## Instructions for transonic axisymmetric bump flow calculation

### Grid

A Fortran program for generating a single-block two-dimensional grid, together with sufficient documentation, can be found in files gridaxibump.f and gridaxibump For an axisymmetric calculation the 2D plane should be rotated as mentioned at the top of gridaxibump.f

### Boundary Conditions

Boundary conditions for the variables are as follows:

X=XMIN: inflow - Uniform inlet Mach Number of 0.875 for axial component and zero value for others

X=XMAX: outflow - zero longitudinal gradient

Y=YMIN: no-slip wall

Y=YMAX: Euler wall

Notes about the dimension of the computational domain:

• XMAX set at x/c=3.5 from bump trailing edge. This is sufficiently far from the zone of interest; here c is the bump chord length.
• YMAX set at 4.5*c ensures that there is no shock reflection. There is, however, a fluctuation of ~1% of free-stream Mach No. on the top boundary. This is found to have negligible effect on the critical flow features such as CP.
• XMIN set at 4.0*c upstream from the bump leading edge. After several trials, we found that if we specify a plug velocity profile at this location, the corresponding profile at x/c=-0.25 matches with experiment reasonably well. However, other inlet profiles with different XMIN location may be possible.
• All of above observations are based on high-Re k – ε calculations.

### Experimental Data

The experimental data at different axial locations are given in files Experiment-CP.dat and Experiment-UV.dat.

Wall static Pressure (CP) is calculated as

CP = (p - p0)/0.5ρ0u02

p0, ρ0 and u0 are the free-stream quantities

X: Normalised distance along the flow. (= x/c, where c is the bump chord length. X=1.0 corresponds to the bump trailing edge.

Y: Vertical distance from the bottom solid wall (= y/c)

U: Normalised streamwise velocity (= u/u0)

V: Normalised transverse velocity (= v/u0)

UU: Normalised streamwise component of normal stress (= u′u′/u02)

VV: Normalised transverse component of normal stress (= v′v′/u02)

MUV: Normalised Reynolds shear stress (= -u′v′/u02)

TKE: Turbulent Kinetic Energy (= k/u02) where, k = 0.5(u′2+v′2+w′2)

Since only u ′ and v ′ were measured, the third component was calculated from :

${w^{\prime }}^{2}=0.5({u^{\prime }}^{2}+{v^{\prime }}^{2})$ NOTE: Please note that at some locations, data for all the above variables were not always available. This may be recognized in the data sets below by the appearance of a '999' which does not represent a real value.

### CFD Calculations

The data derived from CFD calculations using a number of different turbulence models can be found in:

The interpretation of the tabulated data is the same as that above for the experimental data with the following additions.

CF = (wall shear stress)/(0.5ρ0u02)

NUT = (Turbulent Viscosity)/(ρu0c)

The final column of data is the normalised second scale determining variable (e.g e or w etc.)