Navier-Stokes Equations based Flow Simulations of Low Reynolds Number Propeller for Unmanned Aerial Vehicle

2017 ◽  
Author(s):  
Jun Liu ◽  
ShiBin Luo
Keyword(s):  
Reynolds Number ◽  
Unmanned Aerial Vehicle ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Aerial Vehicle ◽  
Low Reynolds

An Implicit Multigrid Scheme for the Compressible Navier-Stokes Equations With Low-Reynolds-Number Turbulence Closure

1998 ◽  
Vol 120 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Peter Gerlinger ◽  
Dieter Bru¨ggemann
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Convergence Acceleration ◽  
Iterative Solvers ◽  
Turbulence Closure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds ◽  
Turbulence Transport

A multigrid method for convergence acceleration is used for solving coupled fluid and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed, which requires very fine grids in the near wall regions. Due to the use of fine grids, convergence of most iterative solvers slows down, making the use of multigrid techniques especially attractive. However, special care has to be taken on the strong nonlinear turbulent source terms during restriction from fine to coarse grids. Due to the hyperbolic character of the governing equations in supersonic flows and the occurrence of shock waves, modifications to standard multigrid techniques are necessary. A simple and effective method is presented that enables the multigrid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mack 2 flow over a backward facing step.

Drag Force on a Sphere Moving in Low-Reynolds-Number Pipe Flows

2007 ◽  
Vol 23 (4) ◽  
pp. 423-432 ◽  
Author(s):  
S.-H. Lee ◽  
Tzuyin Wu
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Time Derivative ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Sphere Diameter ◽  
Navier Stokes Equations ◽  
Low Reynolds

AbstractIn this paper, the drag force on a sphere moving constantly along the centerline of a circular pipe filled with viscous fluid (the falling-sphere problem) under low Reynolds number condition is investigated via numerical calculation. The incompressible Navier-Stokes equations are formulated in a pseudocompressibility form. The numerical scheme makes use of finite-volume method and the numerical flux terms are evaluated using the Total-Variation Diminishing (TVD) strategy commonly applied to the compressible flow. Steady solution is obtained by marching (iterating) in time until the artificial time derivative of pressure term in the continuity equation drops to zero.In the calculation, six different Reynolds number (Re) ranging from 0.1 to 1 and seven different pipe-to-sphere diameter ratios (D/d) ranging from 5 to 40 are selected to study the pipe-wall effect. In each case, the drag force on the sphere is evaluated and the results are compared with the existing approximate theoretical values derived from correcting the Stokes' formula. Both results agree in trend, but with noticeable deviation in values, particularly for cases with large pipe-to-sphere diameter ratios. The deviation is due to the fact that theoretical values were based on the solution to the linearized Navier-Stokes equations (Stokes' creeping-flow equations), while the fully nonlinear form of the Navier-Stokes equations are adopted in the present calculations. Finally, a least-square regression technique is applied to collapse the calculated results into a single expression exhibiting the functional relationship between the drag force, Reynolds number (Re), and the pipe-to-sphere diameter ratio (D/d).

Numerical Simulation of a Low Reynolds Number Airfoil

2013 ◽  
Vol 390 ◽  
pp. 141-146
Author(s):  
Yu Fu Wang ◽  
Guo Quan Tao ◽  
Ze Hai Wang ◽  
Zhe Wu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Lift Coefficient ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Low Reynolds ◽  
Low Reynolds Number Airfoil

In this paper, a low Reynolds number airfoil (S1223) is the objective of the study. The Navier-Stokes equations were established to simulate the complex flow around a low Reynolds number airfoil, in which the turbulence model was used. The complex flow around the airfoil was simulated at 2x105 Reynolds number and its aerodynamic characteristics were analyzed. The relationship among lift coefficient, drag coefficient and angle of attack was studied.

Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem

2019 ◽  
Vol 868 ◽  
pp. 141-175 ◽  
Author(s):  
Haithem Taha ◽  
Amir S. Rezaei
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
High Frequencies ◽  
Kutta Condition ◽  
Low Reynolds

The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers.

scholarly journals Supersonic turbulent flow simulation using a scalable parallel modal discontinuous Galerkin numerical method

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tomas Houba ◽  
Arnob Dasgupta ◽  
Shivasubramanian Gopalakrishnan ◽  
Ryan Gosse ◽  
Subrata Roy
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Performance Study ◽  
Navier Stokes Equations ◽  
Flow Simulations

Abstract The scalability and efficiency of numerical methods on parallel computer architectures is of prime importance as we march towards exascale computing. Classical methods like finite difference schemes and finite volume methods have inherent roadblocks in their mathematical construction to achieve good scalability. These methods are popularly used to solve the Navier-Stokes equations for fluid flow simulations. The discontinuous Galerkin family of methods for solving continuum partial differential equations has shown promise in realizing parallel efficiency and scalability when approaching petascale computations. In this paper an explicit modal discontinuous Galerkin (DG) method utilizing Implicit Large Eddy Simulation (ILES) is proposed for unsteady turbulent flow simulations involving the three-dimensional Navier-Stokes equations. A study of the method was performed for the Taylor-Green vortex case at a Reynolds number ranging from 100 to 1600. The polynomial order P = 2 (third order accurate) was found to closely match the Direct Navier-Stokes (DNS) results for all Reynolds numbers tested outside of Re = 1600, which had a normalized RMS error of 3.43 × 10−4 in the dissipation rate for a 603 element mesh. The scalability and performance study of the method was then conducted for a Reynolds number of 1600 for polynomials orders from P = 2 to P = 6. The highest order polynomial that was tested (P = 6) was found to have the most efficient scalability using both the MPI and OpenMP implementations.

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