**Published at : ** 25 Apr 2019

**IJtech :** 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.

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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

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