Stability analysis of cross buoyancy ﬂow past a circular cylinder using OpenFOAM Sartaj Tanweer, Anupam Dewan ⇑ , Sanjeev Sanghi, Anuj Kumar Shukla Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India article info Article history: Received 11 December 2019 Received in revised form 14 February 2020 Accepted 19 February 2020 Available online xxxx Keywords: Instability Buoyancy Circular cylinder OpenFOAM Selective frequency damping abstract A global instability analysis has been performed to study the inﬂuence of buoyancy on ﬂow past a circular cylinder placed near a moving wall for 1  Ri  1 at a ﬁxed value of G/D = 0.3 and a constant Re = 105. An open source ﬁnite-volume code OpenFOAM has been used. Selective frequency damping (SFD) method is implemented and used for calculations of the base ﬂow. For the solution of the perturbation quantities linearized Navier-Stokes equations have been implemented in OpenFOAM. The growth rate and frequency have been obtained using the power iteration method. It has been observed that the ﬂow is steady for Ri = 0 while it becomes unsteady for both positive and negative buoyancies. The most unsta- ble modes appear as the traveling modes. These modes are similar to the Kelvin-Helmholtz (KH) modes with some distortion due to the presence of the moving wall. Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientiﬁc committee of the 2nd International Conference on Advances in Mechanical Engineering and Nanotechnology. 1. Introduction Flow past a circular cylinder is a fundamental problem of ﬂuid mechanics and has various practical applications [1,2]. It involves ﬂow separation and interactions of the free-shear layers and the wake, which makes the ﬂow quite complex. The ﬂow undergoes various transitions ranging from a steady state for Re < 40, to Hopf bifurcation to 3-dimensional Mode A to Mode B and becomes tur- bulent at high values of Reynolds number Re ¼ UD=m ð Þ [3]. The presence of an obstacle, such as, a wall or an external force, such as, buoyancy, alters the ﬂow signiﬁcantly [4]. In this paper the inﬂuence of buoyancy on ﬂow transition from a steady state to unsteady state is examined. The inﬂuence of buoyancy can be quantiﬁed in terms of a non-dimensional parameter, Richardsn number (Ri). It represents the ratio of buoyancy force to inertia force. The inﬂuence of buoyancy differs in the case of a free- stream ﬂow and in the case of an obstructed ﬂow [5]. Therefore, the ﬂow is examined in the presence of a wall. In the present study the wall moves with the free-stream velocity in order to avoid the formation of a conventional wall boundary-layer so that the inﬂu- ence of buoyancy can be observed clearly. The ﬂow is examined using the global instability analysis. Flow past a circular cylinder near a moving wall has been stud- ied by many researchers. Nishino et al. [6] performed experiments and reported the suppression of vortex shedding for G/D  0.3. Huang and Sung [7] reported that the vortex shedding suppression occurs at a low value of G/D with an increase in Re. Zhen and Wu [8] observed different streamwise velocity proﬁles in the gap- region for steady and unsteady ﬂows. Rao et al. [9] studied the ﬂow using linear stability analysis and examined variation of the critical Re with the gap-ratio. Jiang et al. [10] numerically studied the ﬂow using direct numerical simulations. From the above discussion it can be observed that no study has been reported to assess the inﬂuence of buoyancy on ﬂow past a circular cylinder placed near a moving wall. In the present study the inﬂuence of buoyancy is examined for 1  Ri  1 through a global instability analysis using the power iteration method. For this purpose an open source library OpenFOAM is used. For the cal- culation of the base ﬂow the selective frequency damping (SFD) method and for the simulation of perturbed ﬁelds, linearized Navier-Stokes equations have been implemented in OpenFOAM. The problem statement and formulation are presented in Section 2. Results and discussion are presented in Section 3 with conclusions in Section 4. https://doi.org/10.1016/j.matpr.2020.02.724 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientiﬁc committee of the 2nd International Conference on Advances in Mechanical Engineering and Nanotechnology. ⇑ Corresponding author. E-mail address: adewan@am.iitd.ac.in (A. Dewan). Materials Today: Proceedings xxx (xxxx) xxx Contents lists available at ScienceDirect Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr Please cite this article as: S. Tanweer, A. Dewan, S. Sanghi et al., Stability analysis of cross buoyancy ﬂow past a circular cylinder using OpenFOAM, Materi- als Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.02.724