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Buoyancy-opposed wall jet

Application Challenge 3-01 © copyright ERCOFTAC 2004

Concluding Remarks

The objectives of this study have been to determine how reliably isothermal and non-isothermal opposed wall jet flows can be computed using steady RANS simulations and what turbulence modelling practices would need to be adopted.

1. An experimental study, carried out at Manchester University, under the direction of Professor J. D. Jackson has produced suitable validation data for a range of isothermal and non-isothermal conditions.

2. A computational study, carried out at UMIST, under the direction of Professor B. E. Launder, Dr H. Iacovides and Dr T. J. Craft, has produced a series of RANS computations using different models of turbulence, ranging from the “industry-standard” k-ε model to advanced second-moment closures and also employing different approaches to the modelling of near-wall turbulence that include the conventional wall function, a low-Reynolds number transport model and a recently developed advanced wall function that uses analytical solutions of the near-wall form of the mean flow equations.

3. An LES study, carried out at UMIST under the direction of Professor D. Laurence, produced additional validation data for isothermal flows.

In the RANS studies, a number of steps have been taken to ensure that the resulting predictions are not affected either by numerical error, or by the locations of the inflow and outflow boundaries. Detailed comparisons have been carried out between the RANS predictions and data from the experimental and the LES studies. These have led to the following conclusions.

1. The predictions of isothermal and non-isothermal cases are surprisingly sensitive to the practices followed for the modelling of near-wall turbulence.

2. Conventional wall functions are found to be inappropriate, resulting in excessive penetration lengths and insufficient mixing across the channel.

3. The recently developed analytical wall-function produces predictions similar to those obtained with a low-Reynolds-number model, which are in closer agreement with the measurements, both in terms of the penetration length and also the jet mixing.

4. In the more extensive comparisons carried out for isothermal flows, it has been shown that one needs to resolve the anisotropy of the stress field to accurately resolve the mean velocity field satisfactorily. Satisfactory flow predictions are only obtained when an advanced second-moment closure is used, in combination with the analytical wall-function.

5. In non-isothermal flows, the Launder-Sharma low-Re k-ε and the high-Re k-ε with the advanced wall function treatment are able to return the correct penetration length. The EVM models tested so far under-predict the jet mixing.

Further Work

Further numerical work is still in progress, focussing on non-isothermal flows. The aims are to provide an LES simulation of a non-isothermal case and also to extend use of the second-moment closures to the two cases already computed with effective-viscosity models. These computations will enable us to develop a better understanding of the non-isothermal cases and will also result in a more comprehensive evaluation of the capabilities of second-moment closures.

References

Addad Y., Laurence D. and Benhamadouche S., “The negatively buoyant wall-jet. Part 1 : LES database”, Paper to be presented at 4th Turbulence, Heat and Mass Transfer Conference, Antalya, Turkey, Sept. 2003.

Craft, T. J., Gerasimov, A. V., Iacovides, H., and Launder, B. E., 2002, “Progress in the Generalization of Wall Function Treatments”, Int. J. Heat and Fluid Flow, 23, No. 2, pp. 148-160.

Craft T.J., Ince N.Z and Launder B.E., 1996, “Recent Developments in Second-Moment Closure for Buoyancy-Affected Flows.”, Dynamics of Atmospheres and Oceans, 23, pp 99-114.

Craft T.J., Launder B.E., 1992, “New Wall-Reflection Model Applied to the Turbulent Impinging Jet”, AIAA Journal, 30, pp 2970-2972.

Craft T.J., Launder B.E., 2001, “On the Spreading Mechanism of the three-dimensional Wall Jet.”, Journal of Fluid Mechanics, 435, pp 305-326.

Craft T.J., Launder B.E., 2002, Application of TCL Modelling to Stratified Flows.”,Closure Strategies for Turbulent and Transitional Flows, Ed B. E. Launder and N. Sandham, pp 407-423.

Daly B.J., Harlow F.H., 1970, “Transport Equations in Turbulence”, Physics of Fluids, 13, pp 2634-2649.

Gibson M.M., Launder B. E., 1978, “Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer”, J. Fluid Mechanics, 86, pp 491-511.

Huang P.G., Leschziner M.A., 1983, “An Introduction and Guide to the Computer Code TEAM”, Report TFD/83/9/(R) Thermofluids Division, Department of Mechanical Engineering, UMIST.

Ince N Z and Launder B E, 1989, “On the Computation of Buoyancy-driven Turbulent Flows in Rectangular Cavities”, International Journal of Heat and Fluid Flow, 10, No 2, pp 110-117.

Jackson J.D. et al, 2000, “CFD Quality and Trust - Generic Studies of Thermal Convection”,Nuclear Engineering Research Group, University of Manchester CONTRACT BB/G/40329, IMC REF: HTH/GNSR/5029.

Kidger J.W., 2000, “Progress in the Study of the Buoyancy-Opposed Wall Jet Flow”, Department of Mechanical Engineering, UMIST, CONTRACT REF BB/E/40536, IMC REF: HTH/GNSR/5032.

Launder B.E., Reece G.J., Rodi W., 1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure”, J. Fluid Mechanics, 68, pp537-566.

Launder B. E. and Rodi W, 1983, “The Turbulent Wall Jet-Measurements and Modelling.”, Annual Review of Fluid Mechanics, 15, 429-459.

Launder B.E., Sharma B.I., 1974, “Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc”, Letters in Heat and Mass Transfer, 1, pp131-138.

Leonard B.P., 1979, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation”, Comp. Meth. Appl. Mech. Eng., 98, p.59.

Patankar S.V., 1980, “Numerical Heat Transfer and Fluid Flow”, Hemisphere Publishing Corporation, Taylor and Francis Group, New York.

Patankar S.V., Spalding D.B., 1972, “A Calculation Procedure of Heat, Mass and Momentum transfer in Three-Dimensional Parabolic Flows”, Int J. Heat and Mass Transfer, 15, p1787.

ACKNOWLEDGEMENT

This work was funded under the HSE Generic Nuclear Safety Research programme and is published with the permission of the UK Nuclear Industry Management Committee (IMC). The authors gratefully acknowledge the financial assistance provided for this investigation. The Manchester University experiments were carried out under the terms of the research Contract entitled ‘CFD Quality and Trust – Generic Studies of Thermal Convection’. The UMIST computational studies were carried out under the terms of the research Contract entitled ‘CFD Quality and Trust – Model Evaluation, Refinement and Application Advice’.

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