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This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundam...
Citations
... If a mesh were to be used directly, extra work is needed at the intersecting regions. On the other hand, if only the nodes are being used, the union of the nodes of each mesh can be taken directly as the point cloud [4,132,161]. This method has also been referred to as chimera cloud of points [3]. ...
Meshfree methods are becoming an increasingly popular alternative to mesh-based methods of numerical simulation. The biggest stated advantage of meshfree methods is the avoidance of generating a mesh on the computational domain. However, even today a surprisingly large amount of meshfree literature ironically uses the nodes of a mesh as the point set that discretizes the domain. On the other hand, already existing efficient meshfree methods to generate point clouds are apparently not very well known among meshfree communities, which has led to recent work redeveloping existing algorithms. In this paper, we present a brief overview of point cloud generation methods for domains and surfaces and discuss their features and challenges, in particular in the context of applicability to industry-relevant complex geometries.
... The Upwind Least Squares Finite Difference method christened as LSFD -U [3] is one such method which has been successfully used for solving problems of industrial relevance [5]. These methods [6,7] are known to work well on isotropic distribution of points typically needed for inviscid computations. However, on highly anisotrpoic distribution of points as encountered in the viscous padding region of hybrid-unstructured or hybrid-Cartesian point distribution needed for RANS computations, (i.e. ...
... high aspect ratio volumes in finite volumes parlance) these methods tend to fail because of the illconditioning of the associated geometric matrix. This necessitates the use of rotated cordinates for update in this region [6,7]. Yet another difficulty associated with such point distributions is the sharp turning the grid lines experience at certain locations (for example, at the trailing edge of airfoil). ...
... The flow solver employs LSFD -U methodology [3,4] which is basically upwind generalized finite difference procedure involving method of least squares. While an upwind discretization is used for inviscid flux derivatives calculation, a robust viscous discretization procedure is selected based on positivity analysis [6]. Linear solution reconstruction procedure is employed for higher order accuracy along with Venkatakrishnan limiter [8] in order to preserve solution monotonicity. ...
Upwind—Least Square Finite Difference (LSFD-U) is a generalized finite difference method capable of operating on an arbitrary distribution of points. The method is known to work well on an isotropic distribution of points typically needed for inviscid computations. However, on highly anisotrpoic distribution of points as encountered in the viscous padding region associated with the RANS computations, (i.e. high aspect ratio volumes in finite volumes parlance) these methods tend to fail because of the ill-conditioning of the associated geometric matrix. This necessitates the use of rotated coordinates for update in this region. Yet another difficulty associated with such point distributions is the sharp turning the grid lines experience at certain locations (for example, near the trailing edge of airfoil). These are identified as regions of grid folding. The work proposes two different ways for mitigating this difficulty. In the first approach points are added around points identified with grid folding and the second approach simply involves placing the fictitious interface close to these points, in contrast with the earlier convention of placing these fictitious interfaces mid-way along a ray connecting two points under consideration. Both these methods attempt to recover an isotropic distribution of points in the region of grid folding. The method is successfully demonstrated for simulating 2D high lift flows.
... The basic methodology to evaluate the gradients is elaborated in this section. A detailed review of discretization procedure for viscous fluxes is given in [76]. A brief description of popular procedures available is presented here for completeness. ...
... k and ∆S k are the unit normal and length of the k th edge. The accuracy of this class of procedures is discussed in [4]. The gradients at the centroid of a cell are then obtained by taking the volume weighted average of the gradients computed for the covolumes built around the faces forming that cell as shown in Figure 2.6a. ...
Towards a Staggered Update Procedure (SUP) for
Higher order Cell-centre Finite Volume Method : I
... Viscous fluxes are evaluated using conventional second order accurate least square based scheme 6 . For computing viscous flux components the derivatives of u, v and T are to be evaluated. ...
Analysis of plasma flows at hypersonic velocity over blunt bodies is quite complex and challenging as it involves complex flow physics and carries several uncertainties. Simultaneous simulation of all the parameters as existing in re-entry flight puts constraints on most of the ground based experiments. Numerical simulations, on the other hand, require modelling of ionisation and real gas effects and prove to be computationally costly. This paper highlights the development of unstructured, cell centred second order accurate parallel version of in-house computational fluid dynamics (CFD) solver where high temperature equivalent properties used from Hansen's 7 species model and establishment of a simplified procedure for estimation of heat flux over wedge models tested in Plasma Wind Tunnel facility, Vikram Sarabhai Space Centre. Numerical simulations were carried out for Plasma tunnel initially to get the flow properties inside the tunnel when operated without any model. A simplified CFD based approach is established for computing the heat flux over the bodies tested inside the tunnel and compared with the measured data. The comparison of numerical and measured values shows that the proposed methodology captures the flow physics and various parameters with acceptable levels of accuracy.
... Due to the complex nature of the flow, residual oscillations are observed for the SBLI case, the simulations are declared converged when the density residue falls to 10 −4 . For the computational fluid dynamics (CFD) results presented, the Harten-Lax-van Leer-Contact (HLLC) (Toro, Spruce & Speares 1994) flux formula has been used for the computation of inviscid fluxes and a diamond path reconstruction-based (Munikrishna 2007) procedure has been used for the computation of viscous fluxes. Venkatakrishnan limiter (Venkatakrishnan 1995) is used to limit the gradients of flow variables for preserving monotonicity. ...
The interaction of a hypersonic boundary layer on a flat plate with an impinging shock – an order of magnitude stronger than that required for incipient separation of the boundary layer – near sharp and blunt leading edges (with different bluntness radii from 2 to 6 mm) is investigated experimentally, complemented by numerical computations. The resultant separation bubble is of length comparable to the distance of shock impingement from the leading edge, rather than the boundary layer thickness at separation; it is termed large separation bubble. Experiments are performed in the IISc hypersonic shock tunnel HST-2 at nominal Mach numbers 5.88 and 8.54, with total enthalpies 1.26 and $1.85~\text{MJ}~\text{kg}^{-1}$ respectively. Schlieren flow visualization using a high-speed camera and surface pressure measurements using fast response sensors are the diagnostics. For the sharp leading edge case, the separation length was found to follow an inviscid scaling law according to which the scaled separation length $(L_{sep}/x_{r})M_{er}^{3}$ is found to be linearly related to the reattachment pressure ratio $p_{r}/p_{er}$ ; where $L_{sep}$ is the measured separation length, $x_{r}$ the distance of reattachment from the leading edge, $M$ the Mach number, $p$ the static pressure and the subscripts $r$ and $e$ denote the conditions at the reattachment location and at the edge of the boundary layer at the shock impingement location respectively. However, for all the blunt leading edges $(L_{sep}/x_{r})M_{er}^{3}$ was found to be a constant irrespective of Mach number and much smaller than the sharp leading edge cases. The possible contributions of viscous and non-viscous mechanisms towards the observed phenomena are explored.
... The solver has been validated for different geometries and flow regimes. § The convective and viscous fluxes were computed using Roe's flux difference splitting scheme [15] and the modified Green-Gauss procedure [16], respectively. The Green-Gauss procedure was also used for computing the gradients required for solution reconstruction. ...
Four different length annular cluster truncated plug nozzle flowfields have been analyzed, using both experimental and computational tools, for pressure ratios ranging from 5 to 85, which includes the transition of an open base wake to a closed base wake. The flow expansion on the plug surface has been discussed with respect to streamwise and azimuthal directions. The presence of λ shock structure and vortical pattern of the streamlines downstream of the splitter plate are discussed. For the base pressure analysis, the cluster truncated plug nozzle results have been compared with the corresponding length plug nozzle in which the primary nozzle is not a clustered one. The average base pressure and wake transition pressure ratio of these nozzles have been presented, and the limitations of the present-day computational and empirical tools in predicting the same have been discussed. In addition, the performance of the nozzle with regard to the contribution of each component toward thrust has been brought out.
... The van Leer's flux vector splitting scheme [25] and Roe's flux difference splitting scheme [26] were used for inviscid and turbulent simulations , respectively. A modified Green–Gauss procedure [27] was used for computing the gradients required for solution reconstruction and computation of viscous fluxes. The Venkatakrishnan limiter [28] has been used for limiting the gradients. ...
Computational and experimental tools have been used to understand the linear cluster plug nozzle flowfield for a range of pressure ratios. The experimental cluster configuration is arrived at from a linear plug nozzle by introducing splitter plates in the primary nozzle, and computational analysis of corresponding geometry is also carried out. The flow development on the plug surface has been analyzed for two different cluster module spacings. The interactions between the cluster module jets is a complex one with a three-dimensional shock structure because of the differential end condition the shock experiences on the plug wall and freejet boundary. A prominent streamwise vorticity resulting from curvature of the shock is also seen along the length of the plug downstream of the module junctions. The out-of-phase wave interactions occurring along the module centerline and the splitter plate centerline, resulting in a wavy surface-limiting streamline pattern, particularly at lower pressure ratios, is explained.
... The HiFUN solver is a general purpose CFD solver suited for Aerospace and Automotive applications. It employs an unstructured data based finite volume strategy in conjunction with a linear reconstruction procedure [9,10] for higher order accuracy. The solution monotonicity is preserved using Venkatakrishnan limiter [11]. ...
... The computations for the present study have been made using the Roe flux formula [9]. A diamond path based Green Gauss procedure [10,11] has been used for both linear solution reconstruction and viscous flux computations. Solution monotonicity is preserved using the limiter proposed by Venkatakrishnan [12]. ...
... Solution monotonicity is preserved using the limiter proposed by Venkatakrishnan [12]. Convergence acceleration to steady state is obtained using a matrix free implicit procedure based on Symmetric Gauss Seidel iterations [11,13]. The effect of turbulence is modeled using the standard Spalart-Allmaras one equation turbulence model (SA model) [14] and most of the results presented in this paper (unless otherwise stated) are generated using SA model. ...
... Typically in HiFUN execution, the CFL number is made proportional to the iteration number and convergence is declared after at least 8 decades of fall in relative residue and the change in force coefficients (referred to as Delta CL and Delta CD in Fig. 4) over 100 iterations is less than one count. 11 The residual and the iterative convergence in lift/drag coefficients for a critical case pertaining to fine grid FG1 having around 63 million volumes and high angle of attack (33°) are presented in Fig. 4. This level of solution convergence is representative for all the solutions presented in this work. ...
A summary of the results obtained using the flow solver HiFUN for the 3D High lift NASA Trapezoidal wing are presented. Hybrid unstructured grids have been used for the computations. Grid converged solution obtained for the clean wing and the wing with support brackets, are compared with experimental data. The ability of the solver to predict critical design parameters associated with the high lift flow, such as α
max
and \(C_{L_{max}}\) is demonstrated. The utility of the CFD tools, in predicting change in aerodynamic parameters in response to perturbational changes in the configuration is brought out. The solutions obtained for the high lift configuration from two variants of the Spalart-Almaras turbulence model are compared. Inferences from the study on useful design practices pertaining to the 3D high lift flow simulations are summarized.
