Gold:UFR3-05 instruct

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Instructions for transonic axisymmetric bump flow calculation

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Grid

====

A Fortran program for generating a single-block two-dimensional grid,

together with sufficient documentation, can be found in files

[../C/gridaxibump.f.txt gridaxibump.f] and [../C/gridaxibump.htm 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:

1. 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.

2. 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.

3. 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.

4. All of above observations are based on high-Re k-e calculations.

Experimental Data

=================

The experimental data at different axial locations are given in files

Experiment-CP.txt and Experiment-UV.txt

Wall static Pressure (CP) is calculated as

CP = (p-p0)/0.5*rho0*u0**2

p0, rho0 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'/u0**2)

VV: Normalised transverse component of normal stress (= v'v’/u0**2)

MUV: Normalised Reynolds shear stress (= -u'v'/uo**2)

TKE: Turbulent Kinetic Energy (=k/u0**2)

where, k = 0.5*(u'**2+v'**2+w'**2)

Since only u' and v' were measured, the third component was

calculated from :

w'**2=0.5*(u'**2+v'**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:

[../U3-05des.htm#CFD_Data CFD Files]

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

CF = (wall shear stress)/(0.5*rho0*u0**2)

NUT = (Turbulent Viscosity)/(rho*u0*c)

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

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