# 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 - p _{0})/0.5ρ_{0}u_{0}^{2}*

*p _{0}*,

*ρ*and

_{0}*u*are the free-stream quantities

_{0}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/u _{0}*)

V: Normalised transverse velocity (= *v/u _{0}*)

UU: Normalised streamwise component of normal stress (= *u′u′/u _{0}^{2}*)

VV: Normalised transverse component of normal stress (= *v′v′/u _{0}^{2}*)

MUV: Normalised Reynolds shear stress (= *-u′v′/u _{0}^{2}*)

TKE: Turbulent Kinetic Energy (= *k/u _{0}^{2}*)
where,

*k = 0.5(u′*

^{2}+v′^{2}+w′^{2})Since only *u ′* and *v ′* were measured, the third component was
calculated from :

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)/*(0.5ρ _{0}u_{0}^{2})*

NUT = (Turbulent Viscosity)/(*ρu _{0}c*)

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