# UFR 4-04 Test Case

# Flow in a curved rectangular duct - non rotating

Underlying Flow Regime 4-04 © copyright ERCOFTAC 2004

# Test Case

## Brief description of the study test case

Briefly, the experimental set-up was as follows (refer to Fig. 1):

- The geometry is a rectangular-section duct, with an aspect ratio of 6.

- The width is 20.3 cm, and the height is 121.9 cm.

- A 1.52 metre straight upstream section leads to a 90-degree bend, which is followed by a 5.18 metre straight downstream section.

- The bend has an inner radius of 61.0 cm, and an outer radius of 81.3 cm.

- The working fluid is air, with a freestream velocity of 16 m/s at inlet, giving a Reynolds Number of 224,000.

- Data were collected at two upstream locations (designated U1 and U2), three locations around the bend (15, 45 and 75 degrees) and two downstream locations (designated D1 and D2).

- A comprehensive set of data was collected at each location.

- The assessment quantities by which the success or failure of the CFD calculations was judged included fluid velocity, turbulence kinetic energy and friction coefficient, C
_{f}.

## Test Case Experiments

Full details of the experimental set-up, together with test data in electronic format, can be found in the ERCOFTAC “Classic Collection” database, Case C62

An alternative source is the Journal of Fluids Engineering database at:

http://scholar.lib.vt.edu/ejournals/JFE/data/JFE/DB94-045/wjkim/

Detailed 2-D flow data at location ‘U1’ are available, and these should be used as the inlet parameters for the CFD calculations.

## CFD Methods

Five selected test cases from the ERCOFTAC database (one of which was the present UFR study) were offered to the CFD community, to calculate them and submit results to be presented at an ERCOFTAC workshop. This workshop entitled “Data Bases and Testing of Calculation Methods for Turbulent Flows” took place in Karlsruhe from April 3 to 7, 1995, and was the fourth in a series of ERCOFTAC/IAHR Workshops on Refined Flow Modelling.

Five computer groups submitted altogether 7 results for test case 5 (the present UFR). Several errors and inconsistencies were detected during this workshop, and the contributors were invited to send corrected and updated results afterwards, to be included in the final workshop proceedings (Rodi et al 1995).

Test case 5 on the curved duct flow was issued again for the 5th ERCOFTAC/IAHR Workshop, which took place in Chatou (near Paris) during April 25-26, 1996. At this workshop, 10 groups (all different from those who submitted results for the Karlsruhe Workshop) submitted altogether 25 different results for this case. The figures from the published proceedings of the Chatou workshop are available at the following link:

A summary of the updated and corrected results submitted for the Karlsruhe Workshop, and also for the subsequent workshop hosted by EDF-LNH in Paris, is provided in an EDF report (Rodi et al 1998). This report discusses and interprets the results, and draws conclusions as far as is possible. Fuller details of the results can be found in the workshop proceedings (Rodi et al 1995, Dauthieu et al 1996) where they are, however, compiled without any discussion. Full details of the numerous codes employed, numerical methods used and computational grids are provided in these workshop proceedings.

For the Karlsruhe workshop, 5 groups submitted 7 results for this case obtained with various versions of the k-ε model, including non-linear and algebraic stress (ASM) variants and with the Gibson-Launder RSM. All models employed wall functions. For the Paris workshop, 10 (different) groups submitted altogether 25 results for this case. The turbulence models used include the standard k-ε model with wall functions, various low-Re k-ε models, two-layer k-ε models, various non-linear k-ε models, the k-ω model, and a variety of Reynolds-stress models, mostly using wall functions, but also low-Re versions. Mostly 200,000 to 300,000 grid points were used, but with typically 50 - 60 grid points in the cross-flow directions, the resolution may not be high enough when low-Re versions of turbulence models are employed.

© copyright ERCOFTAC 2004

Contributors: Lewis Davenport - Rolls-Royce Marine Power, Engineering & Technology Division