• Vol 10, No 2 (2019)
  • Mechanical Engineering

CFD Investigation of Flow Over a Backward-facing Step using an RNG k-? Turbulence Model

Steven Darmawan, Harto Tanujaya

Corresponding email: stevend@ft.untar.ac.id

Published at : 25 Apr 2019
IJtech : IJtech Vol 10, No 2 (2019)
DOI : https://doi.org/10.14716/ijtech.v10i2.800

Cite this article as:
Darmawan, S., & Tanujaya, H. 2019. CFD Investigation of Flow Over a Backward-facing Step using an RNG k-? Turbulence Model. International Journal of Technology. Volume 10(2), pp. 280-289
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
Email to Corresponding Author


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


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.


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.


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.


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