Fluid-Structure Interaction for Flutter Predictions in Transonic and Supersonic Flows

2011 ◽  
Author(s):  
Zhi Yang ◽  
Xiang Zhao ◽  
Sijun Zhang ◽  
Chien-Pin Chen
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Structural Response ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Solver ◽  
Compressible Turbulent Flow ◽  
Transonic And Supersonic Flows

This paper describes a numerical methodology coupling Euler/Navier-Stokes equations and structural modal equations for predicting flutter in transonic and supersonic flows. This coupling between Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) is achieved through a Multi-Disciplinary Computing Environment (MDICE), which allows several computer codes or ‘modules’ to communicate in a highly efficient fashion. The present approach offers the advantage of utilizing well-established single-disciplinary codes in a multi-disciplinary framework. The flow solver is density-based for modeling compressible, turbulent flow problems using structured and/or unstructured grids. A modal approach is employed for the structural response. Two benchmark cases are employed to validate the present method. Flutter predictions in subsonic flows for an AGARD 445.6 wing at different Mach numbers (0.499 to 1.141) are presented and compared with experimental data. Supersonic plate flutter with Mach number range between 1.8 and 3.2 is studied and the critical Mach number is computed, our results are in a good agreement with the analytical solutions.

Direct simulation of turbulent supersonic boundary layers by an extended temporal approach

2001 ◽  
Vol 429 ◽  
pp. 187-216 ◽  
Author(s):  
THIERRY MAEDER ◽  
NIKOLAUS A. ADAMS ◽  
LEONHARD KLEISER
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Mach Numbers

The present paper addresses the direct numerical simulation of turbulent zero-pressure-gradient boundary layers on a flat plate at Mach numbers 3, 4.5 and 6 with momentum-thickness Reynolds numbers of about 3000. Simulations are performed with an extended temporal direct numerical simulation (ETDNS) method. Assuming that the slow streamwise variation of the mean boundary layer is governed by parabolized Navier–Stokes equations, the equations solved locally in time with a temporal DNS are modified by a distributed forcing term so that the parabolized Navier–Stokes equations are recovered for the spatial average. The correct mean flow is obtained without a priori knowledge, the streamwise mean-flow evolution being approximated from its upstream history. ETDNS reduces the computational effort by up to two orders of magnitude compared to a fully spatial simulation.We present results for a constant wall temperature Tw chosen to be equal to its laminar adiabatic value, which is about 2.5 T∞, 4.4 T∞ and 7 T∞, respectively, where T∞ is the free-stream temperature for the three Mach numbers considered. The simulations are initialized with transition-simulation data or with re-scaled turbulent data at different parameters. We find that the ETDNS results closely match experimental mean-flow data. The van Driest transformed velocity profiles follow the incompressible law of the wall with small logarithmic regions.Of particular interest is the significance of compressibility effects in a Mach number range around the limit of M∞ ≃ 5, up to which Morkovin's hypothesis is believed to be valid. The results show that pressure dilatation and dilatational dissipation correlations are small throughout the considered Mach number range. On the other hand, correlations derived from Morkovin's hypothesis are not necessarily valid, as is shown for the strong Reynolds analogy.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

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.

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

Influences of lateral jet location and its number on the drag reduction of a blunted body in supersonic flows

2020 ◽  
Vol 124 (1277) ◽  
pp. 1055-1069 ◽  
Author(s):  
M. Dong ◽  
J. Liao ◽  
Z. Du ◽  
W. Huang
Keyword(s):  
Drag Reduction ◽  
Drag Force ◽  
Blunt Body ◽  
Stokes Equations ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduction Strategies ◽  
Promising Application ◽  
Force Reduction

ABSTRACTThe analysis of the aerodynamic environment of the re-entry vehicle attaches great importance to the design of the novel drag reduction strategies, and the combinational spike and jet concept has shown promising application for the drag reduction in supersonic flows. In this paper, the drag force reduction mechanism induced by the combinational spike and lateral jet concept with the freestream Mach number being 5.9332 has been investigated numerically by means of the two-dimensional axisymmetric Navier-Stokes equations coupled with the shear stress transport (SST) k-ω turbulence model, and the effects of the lateral jet location and its number on the drag reduction of the blunt body have been evaluated. The obtained results show that the drag force of the blunt body can be reduced more profoundly when employing the dual lateral jets, and its maximum percentage is 38.81%, with the locations of the first and second lateral jets arranged suitably. The interaction between the leading shock wave and the first lateral jet has a great impact on the drag force reduction. The drag force reduction is more evident when the interaction is stronger. Due to the inclusion of the lateral jet, the pressure intensity at the reattachment point of the blunt body decreases sharply, as well as the temperature near the walls of the spike and the blunt body, and this implies that the multi-lateral jet is beneficial for the drag reduction.

scholarly journals A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

2015 ◽  
Vol 771 ◽  
pp. 520-546 ◽  
Author(s):  
Nicola De Tullio ◽  
Anatoly I. Ruban
Keyword(s):  
Mach Number ◽  
Boundary Layers ◽  
Asymptotic Theory ◽  
Stokes Equations ◽  
Roughness Element ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Compressible Boundary Layers ◽  
Tollmien Schlichting ◽  
Low Amplitude

The capabilities of the triple-deck theory of receptivity for subsonic compressible boundary layers have been thoroughly investigated through comparisons with numerical simulations of the compressible Navier–Stokes equations. The analysis focused on the two Tollmien–Schlichting wave linear receptivity problems arising due to the interaction between a low-amplitude acoustic wave and a small isolated roughness element, and the low-amplitude time-periodic vibrations of a ribbon placed on the wall of a flat plate. A parametric study was carried out to look at the effects of roughness element and vibrating ribbon longitudinal dimensions, Reynolds number, Mach number and Tollmien–Schlichting wave frequency. The flat plate is considered isothermal, with a temperature equal to the laminar adiabatic-wall temperature. Numerical simulations of the full and the linearised compressible Navier–Stokes equations have been carried out using high-order finite differences to obtain, respectively, the steady basic flows and the unsteady disturbance fields for the different flow configurations analysed. The results show that the asymptotic theory and the Navier–Stokes simulations are in good agreement. The initial Tollmien–Schlichting wave amplitudes and, in particular, the trends indicated by the theory across the whole parameter space are in excellent agreement with the numerical results. An important finding of the present study is that the behaviour of the theoretical solutions obtained for $\mathit{Re}\rightarrow \infty$ holds at finite Reynolds numbers and the only conditions needed for the theoretical predictions to be accurate are that the receptivity process be linear and the free-stream Mach number be subsonic.

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