A full-field simulation methodology for sonic boom modeling on adaptive Cartesian cut-cell meshes

Abstract This paper develops a full-field direct numerical simulation methodology of sonic boom in a stratified atmosphere. The entire flow field, ranging from the near field around a supersonic body to the far field extending to the ground, is modeled by the three-dimensional Euler equations with a gravitational source term. Thus far, it has been solved using a structured grid, and an application of previous simulation to complex geometries has been limited. In this study, we realize a full-field simulation by employing the following four numerical approaches: (i) a hierarchical structured adaptive mesh refinement (AMR) method, (ii) a Cartesian cut cell method, (iii) a well-balanced finite volume method, and (iv) a segmentation method of the computational domain. A new well-balanced, MUSCL-Hancock scheme applied over Cartesian AMR and cut cell grids for a stratified atmosphere is formulated. The computational results of an oblique shock wave in a stratified atmosphere agree well with the exact solution. A full-field simulation successfully reproduces the Drop test for Simplified Evaluation of Non-symmetrically Distributed sonic boom (D-SEND) #1, conducted by the Japan Aerospace Exploration Agency (JAXA). The results of this simulation are in good agreement with those of the previous computational study, the waveform parameter method, and flight test measurements. The grid convergence study shows that the mesh size is fine enough to assess pressure signatures over the entire flow field. These results demonstrate that a full-field simulation with AMR and cut cell grids is a powerful tool for extensively analyzing three-dimensional shock wave propagation in a stratified atmosphere.

[1]  Kojiro Suzuki,et al.  Full-Field Simulation for Sonic Boom Cutoff Phenomena , 2015 .

[2]  Boris Diskin,et al.  Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology , 2012 .

[3]  Richard L. Campbell,et al.  Summary of the 2008 NASA Fundamental Aeronautics Program Sonic Boom Prediction Workshop , 2014 .

[4]  C. L. Thomas.  Extrapolation of sonic boom pressure signatures by the waveform parameter method , 1972 .

[5]  Frédéric Alauzet,et al.  High-order sonic boom modeling based on adaptive methods , 2010, J. Comput. Phys..

[6]  Nikos Nikiforakis,et al.  A dimensionally split Cartesian cut cell method for hyperbolic conservation laws , 2017, J. Comput. Phys..

[7]  Anthony R. Pilon.  Spectrally Accurate Prediction of Sonic Boom Signals , 2007 .

[8]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[9]  Kenneth J Plotkin,et al.  State of the art of sonic boom modeling. , 1998, The Journal of the Acoustical Society of America.

[10]  Mathias Wintzer,et al.  Adjoint-based adaptive mesh refinement for sonic boom prediction , 2008 .

[11]  David S. Miller,et al.  Sonic-Boom Wind-Tunnel Testing Techniques at High Mach Numbers , 1972 .

[12]  Michael A. Park,et al.  Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom Prediction Workshop , 2017, Journal of Aircraft.

[13]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[14]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[15]  Juan J. Alonso,et al.  Multidisciplinary Optimization with Applications to Sonic-Boom Minimization , 2012 .

[16]  Yusuke Naka,et al.  Numerical Evauation of Effect of Atmospheric Turbulence on Sonic Boom Observed in D-SEND#2 Flight Test , 2017 .

[17]  Michael J. Aftosmis,et al.  Cart3D Simulations for the Second AIAA Sonic Boom Prediction Workshop , 2017, Journal of Aircraft.

[18]  F. Coulouvrat,et al.  Numerical Simulation of Sonic Boom Focusing , 2002 .

[19]  M Sullivan Brenda,et al.  A Loudness Calculation Procedure Applied to Shaped Sonic Booms , 2003 .

[20]  Kojiro Suzuki,et al.  Full-Field Sonic Boom Simulation in Stratified Atmosphere , 2016 .

[21]  Shigeru Obayashi,et al.  Global Sonic Boom Overpressure Variation from Seasonal Temperature, Pressure, and Density Gradients , 2013 .

[22]  S. Mishra,et al.  Well-balanced schemes for the Euler equations with gravitation , 2014, J. Comput. Phys..

[23]  Kojiro Suzuki,et al.  Sonic Boom Analysis for Hypersonic Vehicle by Global Direct Simulation , 2014 .

[24]  Shigeru Obayashi,et al.  Sonic Boom Variability Due to Homogeneous Atmospheric Turbulence , 2009 .

[25]  Sriram K. Rallabhandi,et al.  Advanced Sonic Boom Prediction Using the Augmented Burgers Equation , 2011 .

[26]  Larry J. Cliatt,et al.  Lateral Cutoff Analysis and Results from NASA's Farfield Investigation of No-Boom Thresholds , 2016 .

[27]  Kojiro Suzuki,et al.  Rise Time Prediction of Sonic Boom by Full-Field Simulation , 2018 .

[28]  Scott D. Thomas,et al.  Euler/experiment correlations of sonic boom pressure signatures , 1991 .

[29]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[30]  Kojiro Suzuki,et al.  Lateral cutoff analysis of sonic boom using full-field simulation , 2019, Aerospace Science and Technology.

[31]  Yusuke Naka,et al.  Comparison of Simulated Sonic Boom in Stratified Atmosphere with Flight Test Measurements , 2018, AIAA Journal.

[32]  S. S. Stevens.  Perceived Level of Noise by Mark VII and Decibels (E) , 1972 .

[33]  Peter G. Coen,et al.  Sonic Boom: Six Decades of Research , 2014 .

[34]  Michael A. Park,et al.  Summary and Statistical Analysis of the First AIAA Sonic Boom Prediction Workshop , 2016 .

[35]  Bram van Leer,et al.  On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe , 1984 .

[36]  Raymond Brun,et al.  Elements of Gas Dynamics , 2009 .

[37]  Rupert Klein,et al.  Well balanced finite volume methods for nearly hydrostatic flows , 2004 .

[38]  Adrien Loseille,et al.  Anisotropic Adaptive Simulations in Aerodynamics , 2010 .

[39]  N. Nikiforakis,et al.  Well-balanced compressible cut-cell simulation of atmospheric flow , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[40]  C. M. Darden,et al.  Sonic-boom minimization with nose-bluntness relaxation , 1979 .

[41]  Alexandra Loubeau,et al.  Summary of Propagation Cases of the Second AIAA Sonic Boom Prediction Workshop , 2019, Journal of Aircraft.

[42]  Peter G. Coen,et al.  Origins and Overview of the Shaped Sonic Boom Demonstration Program , 2005 .

[43]  Victor W. Sparrow,et al.  Solution of the Lossy Nonlinear Tricomi Equation Applied to Sonic Boom Focusing , 2013 .

[44]  B. Edward McDonald,et al.  High-angle formulation for the nonlinear progressive-wave equation model , 2000 .