Case 8.2: Flow through an asymmetric plane diffuser


Description of the flow field

An asymmetric two-dimensional diffuser flow is considered. This flow includes three important features: First, the well defined inlet conditions. The inlet channel flow is turbulent and fully-developed with a Re=20,000 based on the centreline velocity and the channel height. Second, a smooth-wall separation due to an adverse pressure gradient is involved. The prediction of the separation point and the extent of the recirculation region is particularly challenging for computational models. Finally, this flow includes reattachment and redevelopment of the downstream boundary layer. The physics of reattachment and recovery are still not well understood and continue to pose a challenge to fluid mechanicians.

Diffuser geometry:

The x- and y-axes are taken in the streamwise and straight-wall normal directions, respectively. The origin of the x-axis is located at the intersection of the tangents to the straight and inclined walls. The y-axis originates from the bottom wall of the downstream channel. Figure 1 illustrates the configuration.

Eaton_kuva3.jpg (43150 bytes)

Fig. 1. The geometrical description of the diffuser, from Buice and Eaton.

Instructions for Computers

Boundary Conditions:

On the upstream boundary (x/H <-5.87), the flow is fully developed two-dimensional channel flow of Re=20,000 based on the centreline velocity and channel height. It is recommended that each contributor first separately computes the fully developed channel flow using the same turbulence model as he or she will use for the diffuser flow itself. This way, one obtains a consistent set of inflow boundary conditions for the actual flow problem. Another way is to compose a computational model of the diffuser that includes a sufficiently long inlet channel. If this method is employed, one should use sufficiently long inlet channel (110H in experiments) in order to ensure fully developed flow at the diffuser inlet.

On the outflow boundary (x/H > 74) one may specify zero-gradient conditions.

Data for Comparison:

We plan to compare the profiles of mean velocity U / Ub, as well as the Reynolds stresses: uu / Ub2,
vv / Ub2,
and uv / Ub2 at certain locations in the diffuser channel. These locations are given in Table 1 and the naming of the data files indicate the location as well as the variable in question.

Naming of the data files follows the practice of the previous workshops. As an example the file name may look like:

f_uu%.x-6

The first letter of the file name indicates the class of the variable: "g" indicates a global parameter such as pressure coefficient, "m" indicates the mean velocity components and, "f" second moments. The next three characters represent the variable name: "__U", "_uu", "_uv", and "_vv". These should be self explanatory. The next character is either "_", "%", or "+" and it indicates the way of non-dimensionalising. Underbar "_" means a dimensional quantity, "%" indicates scaling by a reference quantity such as Ub, and "+" means that this variable is non-dimensionalised like y+ and u+ using the friction velocity . In this case all the data is scaled using the inlet bulk velocity Ub. After the dot the direction of the section (either x or y) is given and finally follows the two-number section code. The section codes and the corresponding x/H coordinates are given in Table 1.


Table 1. The section codes and the corresponding x / H coordinates. The variables given in each section are marked by x.

Section code x/H U / Ub uu / Ub2 uv / Ub2 vv / Ub2
-6 -5.87 x x x x
03 2.59 x x x x
06 5.98 x x x x
13 12.75     x x
14 13.56 x x    
16 16.14     x x
17 16.93 x x    
19 19.53     x x
20 20.32 x x    
23 22.91     x x
24 23.71 x x    
26 26.3     x x
27 27.09 x x    
29 29.69     x x
30 30.48 x x    
33 33.07     x x
34 33.87 x x    
40 39.85 x x x x
47 46.62 x x x x
53 53.39 x x x x
60 60.17 x x x x
67 66.94 x x x x
74 73.71 x x x x


The following experimental results are available:


Please, note that the stresses uv and vv are not always measured in the same locations as the mean velocity component U and the uu - stresses. The existence of each variable in each section is given in the Table 1. Also note, that the stresses uv and vv are not available inside the recirculation zone.

As clearly expressed above, the scaling is based on the inlet bulk velocity Ub defined as

Ub = mfr / (rho H W)

where mfr is the mass flow rate and H is the inlet channel height and W is the width. Density rho is assumed to be constant. The definition of the non-dimensional coefficients Cp and cf are already given above. The other variables given are scaled as follows:

U* = U / Ub uu* = uu / Ub2 uv* = uv / Ub2 vv* = vv / Ub2

where the variables marked by asterisk (*) are non-dimensional. Here from, the asterisk is omitted for convenience and all variables are non-dimensional unless otherwise stated. The coordinates x and y are always scaled with the inlet channel height H.

Available Data:

Reference

  1. Buice, C. U. and Eaton, J. K., "Experimental investigation of flow through an asymmetric plane diffuser". Report No. TSD-107. Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, USA. August, 1997.