Current Research Work

My most substantial work in the computational field is my current research work. Presently, I am working as a project officer with Prof. Santanu Ghosh in his CFD research group at IIT Madras. My research focus is on studying flow over a porous medium which can serve as a potential passive flow control technique with overall drag reduction and suppression of flow separation over an airfoil. Based on my present work, an extended abstract titled "Numerical Investigation of Transonic Flow over Porous Medium Using Immersed Boundary Method" has been accepted for 2018 Applied Aerodynamics Conference, AIAA Aviation and Aeronautics Forum and Exposition going to be held on June 2018 in Atlanta, Georgia, USA. I have spelled out the crux of my research work below.

Brief Description

• Investigating flow characteristics over a porous medium in high subsonic to transonic regime.
• Employed in-house finite volume flow solver 'REACTMB' to solve RANS equations and Immersed boundary method to render the porous medium.
• Used Menter’s SST (k-ω/k-𝝴) turbulence model.
• Observed a finite slip velocity and lower velocity gradient at the interface of the porous medium in the preliminary results which has the potential to suppress flow separation even in the presence of adverse pressure gradients.
• Submitted the present research work as an extended abstract to AIAA Aviation Forum 2018 going to be held on June 2018 in Atalanta, Georgia, USA.

Introduction

Flow over a porous surface is encountered in a variety of natural and engineering systems and has been studied extensively in a number of fields such as hydrology, soil mechanics, bio-medical engineering, thermal engineering, and petroleum engineering etc. In aerospace industry, porous surface can potentially be used as a passive flow control technique which can suppress the boundary layer separation and minimize the drag over an airfoil. Interaction of shock waves with developing boundary layer over an airfoil surface in the transonic flow regime can cause detrimental effects like boundary layer thickening and possibly flow separation, increased viscous dissipation, large scale unsteadiness, and buffet. This interaction between shock waves and boundary layer is termed as Shock wave-boundary-layer-interaction (SBLI). Even in the absence of shock wave, adverse pressure gradient on the decelerating flow on the upper surface of the airfoil can make the flow prone to separation. Flow separation is harmful for the airfoil performance as it leads to higher drag and lower lift to drag (L/D) ratio. So, a lot of research has been performed in the past to develop active (energy required) or passive flow control techniques to mitigate these detrimental effects.

Out of these two techniques, passive flow control techniques are widely popular because of its simplicity and cost effectiveness. Some examples of passive flow control techniques are vortex generators, shock-control bumps, and porous surface etc. The porous surface can be of two types : 1) Perforated wall : a cavity (plenum chamber) covered by perforated plate, and 2) Porous wall : a cavity constituted by a metal-foam-like material. The schematic of these flow control techniques are showed in the Fig. 1 and 2. Flow over a perforated wall has been studied extensively in the past. A schematic presented in the Fig. 3 shows the weakening of normal shock near its foot, forming a weaker lambda shock due to the re-circulation of flow inside the plenum chamber. The weakening of normal shock results in the reduction of wave drag on the airfoil. In the case of porous medium, a lot of research has been done to analyze the flow characteristics at lower speeds but not much research has gone into investigating its potential as a flow control mechanism. In the recent work by Roy et. al. (2017) [1], normal SBLI at transonic speeds over a porous medium presented in the Fig. 4 shows similar results that of Fig. 3. This configuration also shows a considerable overall drag reduction.

Objective

In the work done by Roy et. al. (2017) [1], it was established that presence of re-circulation inside the porous cavity helps in weakening the normal shock near its foot, thereby smearing the pressure gradient across the shock and resulting in the formation of a weaker lambda shock. Reduction in the loss of total pressure across the lambda shock resulted in overall drag reduction. The present study is intended to extend this work, to investigate the flow behaviour at the interface of flat-plate/porous-medium in the absence of shock or any externally imposed pressure gradients. The study focuses on the determination of the slip velocity and shear stress (or velocity gradient) at the free-porous interface and the boundary layer properties of the flow leaving the porous region for at least three different Mach numbers (0.4 to 1.3) and different configurations (length, depth, porosity) of the porous medium.

Methodology :

An in-house finite volume flow solver 'REACTMB' (Roy and Edwards (2000) [4]) developed by Prof. Jack Edwards of North Carolina State University (NCSU) is used for the present numerical study. The above solver is capable of solving high-speed turbulent flows on structured grid. It is also capable of performing parallel processing. The solver uses central difference scheme for viscous flux calculation and Low-Diffusion Flux Splitting Scheme (LDFSS) (Edwards (1997) [5]) for inviscid flux calculation at the cell interfaces. Higher order spatial reconstruction of the primitive variables at the interfaces is done using the piece-wise parabolic method due to Colella and Woodward (1984) [6]. Euler implicit scheme is used with local time-stepping for steady state simulations. Menter’s SST (k-ω/k-𝝴) turbulence model (Menter (1984) [7]) is used for the Reynolds (Favre) averaged Navier-Stokes (RANS) computations. An immersed boundary (IB) method suitable for compressible turbulent flows (Ghosh et. al. (2010) [8]) is used to render the porous medium.

Immersed Boundary (IB) methods comprise a technique of CFD in which flow past objects can be simulated without the need for the grid to conform to the surface of the object. This method decouples grid generation from the geometry of the body to a considerable extent. The advantage of using an IB method is that the simulations can be run on the same grid, while changing the IB surfaces as required. This expends much less computation resources and time. Also, complex geometries, like circles used in the present study, can be negotiated with ease, as opposed to a body-conforming grid.

The IB method consists of rendering the boundary of the body (outline profile for present 2-D case) as a collection of points. The IB module of the solver uses the coordinates of these points and the outward normal at each point to classify the computational domain as follows: field cells (cell centers outside the immersed object and far from the IB), interior cells (cell centers inside the IB), and band cells (field cell with a neighbouring interior cell). Fig. 6 shows the classification of cells for IB method. A discrete forcing approach is used, wherein the solution is reconstructed in the band cells, with the underlying assumption that flow in the immediate vicinity of the immersed surface is a function of the wall normal co-ordinate. A power law function is used to determine the tangential velocity at the band cell relative to the IB. It offers flexibility to account for energizing effects of laminar or turbulent boundary layer, by suitably modifying the power law index. Walz’s distribution for temperature in compressible boundary layers, and law-of-the-wall type closure for turbulence variables, are used to reconstruct temperature and turbulence variables respectively. Density is integrated in the band cells to achieve improved mass-conservation.

The computational domain is shown in the Fig. 5. The porous medium comprises of multiple circles (projection of cylinder in 2-D) located at a fixed distance from each other. The porosity of a porous material is defined by the ratio of volume of void to total volume of sample. Here a Representative Elemental Volume (REV) convention used by Nair and Sameen (2015) [2] have been followed. The rectangular-type array of circular cylinders (circles in the present case) has 2-D porosity defined as: Porosity, (φ)= ( (S1∗S2)-(4∗0.25∗π∗D^2/4 ) ) / ( (S1∗S2 ) ) where D is the diameter of the immersed circles and S1, S2 are the distances between the centers of the circles in horizontal and vertical direction. Fig. 7 shows the REV and Fig. 8 shows the grid and IB cavity for a particular configuration. The outer most line represents the boundary of the grid cavity while the inner line represents the boundary of the IB cavity. The left surface of the IB cavity is in flush with the grid cavity.

Preliminary results :

Some preliminary results of the ongoing research work is presented here. The plots shown in the following section corresponds to a transonic flow of Mach 1.3 over a porous medium which is embedded in a cavity underneath a flat surface. Contour plots of Z-vorticity for the flat plate and porous medium in flush with flat plate are presented in the Figs. 9 and 10 for qualitative assessment. The regions of high negative vorticity in the plots give an estimation of boundary layer thickness, which is slightly higher for the porous medium case. High gradients of vorticity are seen within the porous medium, resulting from the interaction of the shear-induced flow with the IB circles constituting the porous medium.

The stream-wise velocity contour plot is shown in Fig. 11. The velocity is normalized using the free-stream velocity. Node data from the simulation is used for this plot. In addition to this, the velocity vectors, and streamlines inside the cavity, are shown. The vectors clearly show the velocity profile to be continuous across the free-porous interface in the wall-normal direction with a non-zero (slip) velocity at the interface. A presence of boundary layer in the porous medium beneath the free-porous interface can be observed. The streamlines indicate re-circulation in the porous medium. The velocity gradient at the free-porous interface is observed to be smaller compared to the velocity gradient near the no-slip wall.

The presence of a slip velocity or higher kinetic energy of the flow at the free-porous interface can potentially suppress boundary layer separation even in the presence of adverse pressure gradient. Based on this observation, if a portion of the wing upper surface, where the flow is decelerating (with or without a shock) and can separate, is replaced with a porous material (like metal foam), it can mitigate flow separation. This will be investigated in the present work.

Ongoing Work :

• Simulations for flow over the porous medium for a set of free-stream Mach numbers between 0.4 and 1.3 has been performed to see the influence of porous medium on flows with varying Reynolds number.
• Length and depth of the porous cavity, diameter of the circles, and the porosity of the medium are varied to study their effects on the magnitude of slip velocity and the reduction of viscous drag.
• The effectiveness of porous medium in suppressing and/or delaying boundary layer separation over an airfoil is currently being be explored.

References

[1] Roy, S., Subramaniam, K., and Ghosh, S., “Passive Control of Normal-shock-wave/Boundary-layer Interaction Using Porous Medium : Computational Study,” 35th AIAA Appl. Aerodyn. Conf., American Institute of Aeronautics and Astronautics, Reston, Virginia, 2017, pp. 1–21. doi:10.2514/6.2017-3912.

[2] Nair, K. A., and Sameen, A., “Experimental Study of Slip Flow at the Fluid-porous Interface in a Boundary Layer Flow,” Procedia IUTAM, Vol. 15, 2015, pp. 293–299. doi:10.1016/j.piutam.2015.04.041.

[3] Bharadwaj S, A., Ghosh, S., and Joseph, C., “Interpolation Techniques for Data Reconstruction at Surface in Immersed Boundary Method,” 55th AIAA Aerosp. Sci. Meet., American Institute of Aeronautics and Astronautics, Reston, Virginia, 2017. doi:10.2514/6.2017-1427.

[4] Roy, C. J., and Edwards, J. R., “Numerical Simulation of a Three-Dimensional Flame/Shock Wave Interaction,” AIAA J., Vol. 38, No. 5, 2000, pp. 745–754. doi:10.2514/2.1035.

[5] Edwards, J. R., “A low-diffusion flux-splitting scheme for Navier-Stokes calculations,” Comput. Fluids, Vol. 26, No. 6, 1997, pp. 635–659. doi:10.1016/S0045-7930(97)00014-5.

[6] Colella, P., and Woodward, P. R., “The Piecewise Parabolic Method (PPM) for gas-dynamical simulations,” J. Comput. Phys., Vol. 54, No. 1, 1984, pp. 174–201. doi:10.1016/0021-9991(84)90143-8.

[7] Menter, F. R., “Two-equation eddy-viscosity turbulence models for engineering applications,” AIAA J., Vol. 32, No. 8, 1994, pp. 1598–1605. doi:10.2514/3.12149.

[8] Ghosh, S., Choi, J.-I., and Edwards, J. R., “Numerical Simulations of Effects of Micro Vortex Generators Using Immersed-Boundary Methods,” AIAA J., Vol. 48, No. 1, 2010, pp. 92–103. doi:10.2514/1.40049.