Three-dimensional Compressible Viscous Flows Research Articles

Application of a New Hybrid Immersed Boundary Method for the Simulation of Viscous Compressible Flows

In this paper, we present a hybrid immersed boundary method (HIBM) for the simulation of two- and three-dimensional compressible viscous flows around stationary and moving obstacles. The proposed approach combines the compressible boundary condition-enforced IBM proposed by Qiu et al. and the Brinkman penalization methods. The boundary condition-enforced IBM uses a fractional step approach alongside a Dirac delta function to satisfy the boundary conditions on the body surface. Although this method works properly in subsonic regimes, it cannot correctly simulate the wake region for a supersonic flow. On the other hand, the penalization method considers the body as a porous media with a low permeability that forces the velocity and energy inside the body to converge to the body velocity and energy. However, unlike the boundary condition-enforced IBM, the streamlines penetrate the body. In the present approach, the positive features of the above-mentioned methods were included and their drawbacks were excluded. The proposed approach was applied using the finite volume method and an E-CUSP scheme. The performance of the proposed method was numerically evaluated in simulating compressible fluid flow around both stationary and moving boundaries, showing a close agreement with other numerical and experimental data available in the literature. Further, the effects of geometry, Reynolds, and Mach numbers were investigated on the supersonic flow field around elliptical cylinders of various aspect ratios. The results revealed that increasing the aspect ratio led to an increase in the shock standoff distance, recirculation zone, and drag coefficient.

Local existence of the generalized solution for three-dimensional compressible viscous flow of micropolar fluid with cylindrical symmetry

In this work, the three-dimensional model for the compressible micropolar fluid flow is considered, whereby it is assumed that the fluid is viscous, perfect, and heat conducting. The flow between two coaxial thermoinsulated cylinders, which leads to a cylindrically symmetric model with homogeneous boundary data for velocity, microrotation, and heat flux, is analyzed.The corresponding PDE system is formulated in the Lagrangian setting, and it is proven that this system has a generalized solution locally in time.

Discontinuous Galerkin and Petrov Galerkin methods for compressible viscous flows

In this paper, high-order finite-element discretizations consisting of discontinuous Galerkin (DG) and streamline upwind/Petrov Galerkin (SUPG) methods are investigated and developed for solutions of two- and three-dimensional compressible viscous flows. Both approaches treat the discretized system fully implicitly to obtain steady state solutions or to drive unsteady problems at each time step. A modified Spalart and Allmaras (SA) turbulence model is implemented and is discretized to an order of accuracy consistent with the main Reynolds Averaged Navier–Stokes (RANS) equations using the present high-order finite-element methods. To accurately represent the real geometry configurations for viscous flows, high-order curved boundary meshes are generated via a Computational Analysis PRogramming Interface (CAPRI), while the interior meshes are deformed subsequently through a linear elasticity solver. The mesh movement procedure effectively avoids the generation of invalid elements that can occur due to the projection of curved physical boundaries and thus allows high-aspect-ratio curved elements in viscous boundary layers. Several numerical examples, including large-eddy simulations of viscous flow over a three-dimensional circular cylinder and turbulent flows over a NACA 4412 airfoil and a high-lift multi-element airfoil at high angles of attack, are considered to show the capability of the present high-order finite-element schemes in capturing typical viscous effects such as flow separation and to compare the accuracy between the high-order DG and SUPG discretization methods.

Global Helically Symmetric Solutions for the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows

Global Helically Symmetric Solutions for the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows

Applications of unstructured hybrid grid method to high-Reynolds number viscous flows

An unstructured hybrid grid method is discussed for its capability to compute three-dimensional compressible viscous flows of complex geometry. A hybrid of prismatic and tetrahedral grids is used to accurately resolve the wall boundary layers for high-Reynolds number viscous flows. The Navier-Stokes equations for compressible flows are solved by a finite volume, cell-vertex scheme. The LU-SGS implicit time integration method is used to reduce the computational time for very fine grids in boundary layer regions. Two kinds of one-equation turbulence models are evaluated here for their accuracy. The method is applied to computations of transonic flows around the ONERA M5 airplane and ONERA M6 wing, and supersonic shock/boundary layer interacting flows inside a scramjet inlet to validate the accuracy and efficiency of the method

Improved Treatment of External Boundary Conditions for Three-Dimensional Flow Computations

An innovative numerical approach is presented for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous flows over finite bodies. The approach is based on application of the special boundary operators analogous to Calderon's projections (Calderon, A. P.) and the difference potentials method by Ryaben'kii; it extends the previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations

Improvements to a tightly coupled viscous–inviscid procedure for three-dimensional unsteady transonic flow

A tightly coupled procedure for solving three-dimensional compressible viscous flows has been developed. In this approach, the flow field is divided into two domains, a viscous domain surrounding viscous wakes and solid surfaces such as wings or rotor blades, and an outer domain where the inviscid, unsteady compressible potential flow equations hold. These two zones are tightly coupled to each other, allowing conservation of mass, momentum and energy at the interface, and permitting the propagation of non-linear acoustic waves from one zone to another in a seamless fashion. The location of the interface dividing the two zones is allowed to adjust its position relative to blade based on an investigation of the instantaneous flow physics. The effects of rotor trim, aeroelasticity, and far wake induced inflow are included in the analysis through a coupling with a comprehensive rotor analysis. The methodology has been applied to two cases which represent the flow physics typically encountered by modern helicopter rotors. A cruise condition for a UH-60 is analyzed and the results compared with both experimental data and full Navier–Stokes results. Computer time savings realized by the zonal method over the full Navier–Stokes analysis are given. A non-lifting high speed case is also investigated to assess the accuracy of unsteady shock motion. The shock structure is examined to determine whether inaccuracies are introduced by the presence of the interface.

Diagonally inverted lower-upper factored implicit multigrid scheme for the three-dimensional Navier-Stokes equations

An approximately factored, implicit multigrid algorithm is developed to calculate three-dimensional compressible viscous flows. This scheme solves the full Reynolds-averaged Navier-Stokes equations with a k-e model of turbulence. The flow equations are solved within the framework of the multigrid method using a four grid level W-cycle, while the k-e equations are solved only on the finest grid and uncoupled from the flow calculations

Parabolic Procedure for Flows in Ducts with Arbitrary Cross Sections

A computer program has been developed to predict three-dimensional compressible viscous flows in ducts with arbitrary cross-sectional shapes. A curvilinear boundary-fitted coordinate system is used to simplify boundary conditions. The parabolized Navier-Stokes equations are transformed, and the solution is marched down the duct using an iterative ADI procedure. Computed results are compared with test data for laminar test cases in square and round ducts. A two-equation turbulence model is demonstrated for a developing turbulent pipe flow. A comparison between predicted results and test data is presented for a turbulent diffuser flow with a rectanguiar-to-round transition in cross-sectional geometry.

On the asymptotic expansion in three-dimensional compressible viscous flow

An exact solution of the set of equations (of motion, energy, continuity, and state) of a three-dimensional flow of a compressible viscous fluid (in which pressure, density, coefficients of viscosity and heat conductivity are functions of position) represents insurmountable difficulties and cannot be achieved. Consequently, only approximation methods may be considered. Goldstein (1, 2) 2 proposed an asymptotic expansion for the two-dimensional steady flow of an incompressible viscous fluid behind a solid body by means of exponential functions.That type of expansion was applied by the author to a few cases of a two-dimensional steady flow of a compressible viscous flow ( 3, 4, 5). In the present paper the author extends this method to a case of a three dimensional flow of a compressible fluid.Not to obscure the problem by many items of a simple algebraic nature, the paper presents only a general outline of the method of attack, applied to the simplest possible case, that is, to a flow along a yawed flat plate whose plane is parallel to the direction of the undisturbed flow.From two requirements: ( a) to solve exactly or approximately the equations, ( b) to satisfy exactly or approximately the boundary conditions, in a case of a compressible viscous fluid (when no use is made of velocity potential—or stream—functions) it is possible to satisfy the requirement ( a) approximately and ( b) exactly. This was shown by the author in the present as well as in previous papers.The presented method may be easily adjusted to three-dimensional wakes and jets similarly as it was done in plane flows.