Low Mach number performance of three-dimensional compressible Navier-Stokes codes

1995 ◽  
Author(s):  
William Milholen, am E, I ◽  
Ndaona IChokani
Keyword(s):  
Mach Number ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Low Mach Number

scholarly journals A 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation

2009 ◽  
pp. 607-625
Author(s):  
Ouafa Bouloumou ◽  
Eric Serre ◽  
Jochen Fröhlich
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Time Discretization ◽  
Navier Stokes ◽  
Working Fluid ◽  
Uzawa Algorithm ◽  
Low Mach Number ◽  
Preconditioned Iterative

A three-dimensional spectral method based on Chebyshev-Chebyshev-Fourier discretizations is presented in the framework of the low Mach number approximation of Navier-Stokes equations. The working fluid is assumed to be a perfect gas with constant thermodynamic properties. The generalized Stokes problem, which arises from the time discretization by a second-order semi-implicit scheme, is solved by a preconditioned iterative Uzawa algorithm. Several validation results are presented in the case of steady and unsteady flows. This model is also evaluated for natural convection flows with large density variations in the case of a tall differentially heated cavity of aspect ratio 8. It is found that on contrary to convection at small temperature differences (Boussinesq), the 2D unsteady solution at Ra = 3.4 x 105 is unstable to 3D perturbations.

Assessment of the Academic CFD Code Galatea-I With the DLR-F11 Model in High Lift Configuration

2016 ◽  
Author(s):  
Sotirios S. Sarakinos ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Mach Number ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Test Case ◽  
High Lift ◽  
Low Mach Number ◽  
Flow Phenomena ◽  
Number Flow

In this study the development and assessment of an academic CFD (Computational Fluid Dynamics) code, named Galatea-I, is reported. The proposed solver employs the RANS (Reynolds-Averaged Navier-Stokes) approach, modified by the artificial compressibility method, along with the SST (Shear Stress Transport) turbulence model to predict steady or unsteady turbulent incompressible flow phenomena on three-dimensional unstructured hybrid grids, composed of prismatic, tetrahedral and pyramidal elements. Parallel processing and an agglomeration multigrid method have been included for the acceleration of the solver’s methodologies. Galatea-I is evaluated against a test case of the HiLiftPW-2 (Second High Lift Prediction Workshop). In particular, the low Mach number flow at 7° incidence angle over the DLR-F11 aircraft configuration of Case 1 of the aforementioned workshop was examined; it considers a three-element wing with a leading edge slat and a trailing edge flap attached on a body pod, without including though any of the support brackets used in the wind tunnel experiments. The obtained results are close to the available experimental data, as well as the numerical results of other reference solvers, indicating the proposed methodology’s potential to predict accurately such low Mach number flows over complex geometries.

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

Experimental investigation of aerofoil tonal noise at low Mach number

2021 ◽  
Vol 932 ◽  
Author(s):  
Prateek Jaiswal ◽  
Yann Pasco ◽  
Gyuzel Yakhina ◽  
Stéphane Moreau
Keyword(s):  
Experimental Investigation ◽  
Mach Number ◽  
Three Dimensional ◽  
Normal Modes ◽  
Wall Pressure ◽  
Far Field ◽  
Tonal Noise ◽  
Trailing Edge ◽  
Modal Shape ◽  
Low Mach Number

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ( $0.05$ ), moderate Reynolds number based on the chord length ( $1.4 \times 10^{5}$ ) and moderate incidence ( $5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

scholarly journals On the Low Mach Number Limit for Quantum Navier--Stokes Equations

2020 ◽  
Vol 52 (6) ◽  
pp. 6105-6139
Author(s):  
Paolo Antonelli ◽  
Lars Eric Hientzsch ◽  
Pierangelo Marcati
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Low Mach Number Limit

Numerical Simulation on Aerodynamics of Ramjet Projectiles

2011 ◽  
Vol 201-203 ◽  
pp. 89-92 ◽  
Author(s):  
Jia Xian Zhang ◽  
Yan Na Wang ◽  
Rui Min Liu
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Pressure Center ◽  
Complex Wave ◽  
Center Increase

Three-dimensional Reynolds-averaged Navier-Stokes simulations have been performed to explore the aerodynamic characteristics of ramjet projectiles. The turbulence model used is the RNG k-ε model. The numerical algorithms termed total variational diminishing (TVD) was adopted. The complex wave structures of ramjet projectiles with different architecture at different inflow Mach number were achieved by numerical simulation. The influence of inflow Mach number on aerodynamic characteristics and pressure center of ramjet projectiles were analyzed. Results show that lift coefficient and pressure center increase with the argument of inflow Mach number. Ramjet projectiles with different architecture have different drag coefficient trend.

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