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185 records · Page 11

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NASA NTRS2018

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries.

Venkatachari, Balaji Shankar↗

NASA NTRS2010

TPSAS-NF1676L-10658-DND

The systematic methodology for constructing fourth-order finite domain Energy Stable WENO schemes is developed. We prove that for hyperbolic systems, the finite domain ESWENO scheme is stable in the energy norm for both continuous and discontinuous solutions. The eigenvalues of the finite domain ESWENO dissipation operator are located in the left-half plane. Based on the rigorous truncation error analysis, the new weight functions are developed, which drastically improve the accuracy of the ESWENO scheme and provide excellent shock-capturing capabilities. Numerical experiments show that the new finite domain ESWENO scheme with the new weights outperform the conventional WENO schemes in terms of accuracy.

Travis Fisher↗

NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testingon the CobraMRV Mars Entry Vehicle Concept

The CFD solver OVERFLOW was used to simulate the CobraMRV undergoing supersonic retropropulsion (SRP) in the Langley Unitary Plan Wind Tunnel as part of a pre-test study. Aerodynamics of the CobraMRV are summarized and the sensitivity of vehicle loads to CFD parameters at a subset of operating conditions are investigated. Specific numerical methods, boundary conditions, and turbulence modeling options have been selected after considering the complex phenomena in SRP flows. Proper shock-capturing methods and dynamic grid adaption are necessary to correctly capture vehicle loads and dynamics. Present data indicates that at particular conditions, upstream asymmetries originating from the tunnel inflow plane contribute to measurable asymmetries on the CobraMRV heatshield.

OVERFLOW↗

NASA NTRSDate not supplied

An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks

The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.

HECC↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗