**Published at : ** 25 Apr 2019

**Volume :** **IJtech**
Vol 10, No 2 (2019)

**DOI :** https://doi.org/10.14716/ijtech.v10i2.800

Darmawan, S., & Tanujaya, H. 2019. CFD Investigation of Flow Over a Backward-facing Step using an RNG k-? Turbulence Model.

1,095

Steven Darmawan | Faculty of Engineering, Universitas Tarumanagara,, Jl. Letjen S. Parman No. 1, Jakarta 11440, Indonesia |

Harto Tanujaya | Faculty of Engineering, Universitas Tarumanagara,, Jl. Letjen S. Parman No. 1, Jakarta 11440, Indonesia |

Abstract

Backward-facing step (BFS) is a benchmarked
geometry for visualizing recirculation flow and validating turbulence models.
Nowadays, numerical analysis with the CFD method has became more popular and
has stimulated research involving CFD without avoiding the experimental method.
In this paper, flow over a BFS was numerically investigated with an RNG *k-?* turbulence model to predict
recirculating flow. BFS geometry refers to the geometry proposed by Kasagi
& Matsunaga; it is three-dimensional, with inlet Re = 5.540. The paper aims
to investigate the performance of the RNG *k-?*
turbulence model over a BFS. Two important parameters were analayzed: the
performance of the RNG *k-?* on the
recirculation zone and on the reattachment length. Recirculation flow is
presented by the x-velocity for Y = 17.4 mm and Y = 34.9 mm. In these Y-section,
the RNG *k-? *is compared to the STD *k-?* and both models show the
recirculation flow occurred from X = 0 mm to about X = 200 mm. The following
results were obtained. The RNG *k-?*
predicted a slightly higher x-velocity component than that predicted by the STD
*k-?*. This result shows that the RNG *k-?* turbulence model is suitable for
predicting recirculation flow on the BFS. The reattachment length was measured
by non-dimensional X/h to the x-velocity component with the RNG *k-?* turbulence model. The analyzed data
were taken from X/h = 4.5 to X/h = 10, on the x-velocity component from Y =
17.4 mm. The reattachment point was achieved at X/h = 7.22, close to that
achieved by Kasagi & Matsunaga of X/h = 6.51.

Backward-facing step; CFD; Reattachment point; Recirculation flow; RNG k-? turbulence model

Introduction

Backward-facing step (BFS) is the one of the most powerful geometries for visualizing flow, validating the performance of turbulence model on recirculating flow (Thangam & Speziale, 1991; Thangam, 1991). Generally, there are two main specific flows in a BFS considered as a benchmarking geometry: the recirculating flow after the expansion zone and the reattachment point reaching near to the outlet zone. The recirculated and swirling flow occurs in many engineering applications well-presented by BFS geometry. This type of flow can be useful or harmful, depending on the application; examples include recirculation flow in electronic devices; recirculation flow in aerodynamics fields; flow around buildings in architectural applications; flow in combustion chambers; and the disadvantage of swirling flow at pipe bends (Mouza et al., 2005; Rouizi et al., 2009; Gautier & Aider, 2014; Ramšak, 2015; Saha & Nandi, 2017; Selimefendigil & Öztop 2017). There remain many turbulent flow phenomena over a BFS which are yet to be explored (Kasagi & Matsunaga 1995; Avancha, 2002).

There are several geometrical
aspects to BFS, most of which are non-dimensional parameters, such as step
height (*h*), upstream height (*H*), the expansion ratio and total length
(*L*). Several papers have investigated
turbulent flow over a BFS, with specific cases examined experimentally and/or
numerically. A review of these geometry parameters was previously made by (Darmawan, 2016). Experimental method of flow over BFS
geometry as done by (Kasagi &
Matsunaga, 1995; Gautier & Aider, 2013) and many others
involving advanced measurement techniques and recording facilities, which are
very costly (Gautier & Aider
2014; Kasagi & Matsunaga
1995). Moreover, flexibility in varying the
geometry design, lower cost, and faster and better visualization have made the
CFD method more popular over the years, two dimensionally and three dimensionally
(Thangam, 1991; Avancha & Pletcher, 2002; Nie & Armaly, 2002; Kanna &
Das, 2006; Rouizi et al., 2009; Ramšak, 2015). The growth of commercial CFD
codes in the market is also increasing the number of CFD applications, with
choices of characteristics, acuration. Turbulence model choice plays an
important role in producing the acceptable results, needing a physical flow and
mathematical knowledge to perform CFD simulation (Ramdlan et al., 2016). An appropriate
turbulence model is needed in order to represent the flow with commercial CFD
codes. For example, in 2007 Anwar-ul-Haque et al. assessed the performance of
turbulence models on backward-facing step applications (Haque et al., 2007).

Many
turbulence models are available, with very wide range characteristics, from
zero equation to DNS (Direct Numerical Simulation). The two-equation turbulence
models (RANS-based) are often used in research regarding acuration and
computational resources compared to more complicated models (Thangam, 1991).
The STD *k-?* turbulence model is the
most used model despite its weakness in presenting swirl-dominated flow (Launder & Spalding,
1974; Lakshminarayana, 1996; Marshall & Bakker,
2003). Another turbulence model based on the two-equation model is the RNG *k-?*, with improvement in swirling and
recirculating flow by renormalizing small scale eddies compared to the STD *k-?* (Yakhot & Orszag,
1986; Thangam & Speziale,
1991; Versteeg &
Malalasekera, 2007; Budiarso et al., 2013; Darmawan et al., 2013), Therefore, the RNG *k-?* may be appropriate for predicting the recirculation flow and
reattachment point of the flow on the BFS geometry.

However,
the performance of the RNG *k-?*
turbulence model needs to be compared with the STD *k-?* model, as the most used one, with faster computation and lower
computational resources. The results then compared with the experimental
results obtained by (Kasagi & Matsunaga
1995). The BFS geometry used here also refers to
the geometry proposed by Kasagi and Matsunaga, but the effects of the boundary
layer are not considered here. Therefore, this paper aims to investigate the
performance of RNG *k-?* turbulence
model over a BFS. The results may might be used as a reference and may be
applied in future research involving flow in BFS geometry.

Conclusion

A
numerical study of the flow over a backward-facing step was conducted with Re =
5.540 with STD *k?* and RNG *k-?* turbulence models. The conclusions
are as follows: (1) The recirculation flow predicted by the RNG *k-?* turbulence model is higher than that
predicted by STD *k-?* turbulence model
in qualitative terms. This was measured by the x-velocity component along the
x-direction, which shows that the RNG *k-?*
is better for use in such a flow; and (2) With the RNG *k-?* turbulence model, at Y = 17.4 mm the reattachment point was
achieved at *X*/*h* = 7.22.

Acknowledgement

The authors would like to thank LPPI (*Lembaga
Penelitian dan Publikasi Ilmiah* – Centre of Research and Publication)
Universitas Tarumanagara for funding this research through the Hibah Riset
Internal – Periode 2, 2016 scheme.

Supplementary Material

References

Avancha, R.V.R., Pletcher, R.H.,
2002. Large Eddy Simulation of the Turbulent Flow Past a Backward-facing Step
with Heat Transfer and Property Variations. *International Journal of Heat
and Fluid Flow*, Volume 23(5), pp. 601–614

Blazek, J., 2005. *Computational Fluid Dynamics:
Principles and Applications.* 2^{nd} ed. Amsterdam: Elsevier

Budiarso, Siswantara, A.I., Darmawan, S., 2013. *Secondary Flow pada Pipa Keluar Kompresor
Turbin Gas Mikro Bioenergi Proto X-2 : Analisis dengan Model Turbulen STD k-?
dan RNG k-? *(Secondary
Flow on Compressor Discharge Pipe of Proto X-2 Bioenergy Micro Gas Turbine:
Analysis with STD k- ? and RNG k- ? Turbulence Model) *In: *Seminar Nasional Tahunan Teknik Mesin.
Volume XII, pp. 23–24

Darmawan, S., 2017. Experimental Study of Smoke over a Backward-facing
Step Geometry. *In:* The 3^{rd} International Conference
on Engineering of Tarumanagara, Jakarta: Faculty of Engineering,
Universitas Tarumanagara

Darmawan, S., 2016. Backward Facing-step Geometry for
Flow Analysis: A Review of Non-dimensional Parameters. *Journal of Academic
Faculty Development*, Volume
1(1), pp. 1–11

Darmawan, S., Budiarso, Siswantara, A.I., 2013. CFD
Investigation of Standard *k-?* and RNG *k-?* Turbulence Model in Compressor Discharge of Proto X-2
Bioenergy Micro Gas Turbine. *In*: The 8^{th} International Conference in
Fluid Thermal and Energy Conversion. Semarang

Darmawan, S., Siswantara, A.I., Budiarso, 2013.
Comparison of Turbulence Models on Reynolds Number of a Proto X-2 Bioenergy
Micro Gas Turbine’s Compressor Discharge. *In*:
International Conference on
Engineering of Tarumanagara, pp. 978–979. Faculty of Engineering,
Universitas Tarumanagara

Gautier, N., Aider, J.L., 2013. Control of the
Separated Flow Downstream of a Backward-facing Step using Visual Feedback. *Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences*,
Volume 469(2160), pp. 1–13

Gautier, N., Aider, J.L., 2014. Upstream Open Loop
Control of the Recirculation Area Downstream of a Backward-facing Step. *Comptes
Rendus - Mecanique*, Volume 342(6–7), pp. 382–388

Haque, A.U., Ahmad. F., Yamada, S., Chaudhry. S.R.,
2007. Assessment of Turbulence Models for Turbulent Flow over Backward Facing
Step. *The World Congress on Engineering 2007, *Volume* *II, pp. 1–6

Kanna, P.R., Das, M.K., 2006. Conjugate Heat Transfer
Study of Backward-facing Step Flow - A Benchmark Problem. *International
Journal of Heat and Mass Transfer, *Volume
49(21-22), pp. 3929–3941

Kasagi, N., Matsunaga, A., 1995. 3-D Particle-tracking
Velocimetry Measurement of Turbulence Statistics and Energy Budget in a
Backward-facing Step Flow. *International
Journal of Heat and Fluid Flow, *Volume 16(6), pp. 477–478

Lakshminarayana, B., 1996. *Fluid Dynamics and Heat
Transfer of Turbomachinery*. New Jersey: John Wiley & Sons, Inc.

Launder, B., Spalding, D.B., 1974. The Numerical Computation
of Turbulent Flows. *Computer Methods in Applied Mechanics and Engineering*,
Volume 3(2), pp. 269–289

Marshall, E.M., Bakker, A., 2003. *Computational
Fluid Mixing*. Lebanon, NH: Fluent, Inc.

Mouza, A.A., Pantzali, M.N., Paras, S.V., Tihon, J.,
2005. Experimental and Numerical Study of Backward-facing Step Flow *In:* The 5^{th} National Chemical Engineering Conference, Thessaloniki,
Greece

Munson, B.R., Okiishi, T.H., Huebsch, W.W., 2009. *Fundamentals
of Fluid Mechanics*. 6^{th} Edition: John Wiley & Sons, Inc.

Nie, J.H.,
Armaly, B.F., 2002. Three-dimensional Convective Flow Adjacent to
Backward-facing Step - Effects of Step Height. *International Journal of Heat
and Mass Transfer*, Volume 45(12), pp. 2431–2438

Ramdlan., G.G., Siswantara, A.I., Budiarso, Daryus, A.,
Pujowidodo, H., 2016. Turbulence Model and Validation of Air Flow in Wind
Tunnel. *International Journal of Technology*,
Volume 7(8), pp. 1362–1372

Ramšak, M., 2015. Conjugate Heat Transfer of Backward-facing
Step Flow: A Benchmark Problem Revisited. *International Journal of Heat and
Mass Transfer*, Volume 84, pp. 791–799

Rao, D.C., Kalavathy, N., Mohammad, H.S., Hariprasad,
A., Kumar, C.R., 2015. Evaluation of the Surface Roughness of Three Heat ? Cured Acrylic Denture Base Resins
with Different Conventional Lathe Polishing Techniques?: A Comparative Study. *The Journal of Indian Prosthodontic Society,
*Volume 15(4), pp. 374–380

Rouizi, Y., Favennec, Y., Ventura, J., Petit, D., 2009.
Numerical Model Reduction of 2D Steady Incompressible Laminar Flows:
Application on the Flow over a Backward-facing Step. *Journal of
Computational Physics, *Volume
228(6), pp. 2239–2255

Saha, S., Nandi, N., 2017. Kinetic Model Development
for Biogas Production from Lignocellulosic Biomass. *International Journal of Technology*, Volume 8(4), pp. 681–689

Selimefendigil, F., Öztop, H.F., 2017. Forced
Convection and Thermal Predictions of Pulsating Nanofluid Flow over a Backward
Facing Step with a Corrugated Bottom Wall. *International Journal of Heat and
Mass Transfer,* Volume 110, pp. 231–247

Tennekes, H., Lumley, J.L., 1972. *A First Course in
Turbulence*. Massachusetts: MIT Press, Cambridge, Massachusetts, and London,
England

Thangam, S., 1991. *Analysis
of Two-equation Turbulence Models for Recirculating Flows*. Report 91-61,
Institute for Computer Applications in Science and Engineering, NASA, Langley
Research Center, Hampton, Virginia

Thangam, S., Speziale, C.G., 1991. Turbulent Separated
Flow Past a Backward-facing Step: A Critical Evaluation of Two-equation
Turbulence Models. *American Institute of
Aeronautics and Astronautics Journal, *Volume 30(10),* *pp. 2576–2576

TM-107. 1993. *Introduction
to the Renormalization Group Method and Turbulence Modeling*. Lebanon, NH:
Fluent, Inc.

Versteeg, H.K., Malalasekera, W., 2007. *Introduction
to Computational Fluid: The Finite Volume Method*. 2^{nd} edition Essex:
Pearson Education Limited, London, England

Yakhot, V., Orszag, S.A., 1986. Renormalization Group
Analysis of Turbulence. I. Basic Theory. *Journal of Scientific Computing*,
Volume 1(1), pp. 3–51