ALBERT

Description: Previous studies have demonstrated that the use of counterflowing jets can greatly reduce the drag and heat loads on blunt-body geometries, especially when the long penetration mode jet condition can be established. Previously, the authors had done some preliminary numerical studies to determine the ability to establish long penetration mode jets on a typical Mach 1.6 slender configuration, and study its impact on the boom signature. The results indicated that a jet with a longer penetration length was required to achieve any impact on the boom signature of a typical Mach 1.6 slender configuration. This paper focuses on an in-depth parametric study, done using the space-time conservation element solution element Navier-Stokes flow solver, for investigating the effect of various counterflowing jet conditions/configurations on two supersonic slender-body models (cone-cylinder and quartic body of revolution). The study is aimed at gaining a better understanding of the relationship between the shock penetration length and reduction of drag and boom signature for these two supersonic slender-body configurations. Different jet flow rates, Mach numbers, nozzle jet exit diameters and jet-to-base diameter ratios were examined. The results show the characteristics of a short-to-long-to-short penetration-mode pattern with the increase of jet mass flow rates, observed across various counterflowing jet nozzle configurations. Though the optimal shock penetration length for potential boom-signature mitigation is tied to the long penetration mode, it often results in a very unsteady flow and leads to large oscillations of surface pressure and drag. Furthermore, depending on the geometry of the slender body, longer jet penetration did not always result in maximum drag reduction. For the quartic geometry, the maximum drag reduction corresponds well to the longest shock penetration length, while this was not the case for the cone-cylinder-as the geometry was already optimized for drag. Numerical results and assessments obtained from this parametric study along with the recommendation for future implementation of counterflowing jets as a means for drag and noise reduction are detailed in this paper.

Description: A novel approach of using counterflowing jets positioned strategically on the aircraft and exploiting its long penetration mode (LPM) of interaction towards sonic-boom mitigation forms the motivation for this study. Given that most previous studies on the counterflowing LPM jet have all been on blunt bodies and at high supersonic or hypersonic flow conditions, exploring the feasibility to obtain a LPM jet issuing from a slender body against low supersonic freestream conditions is the main focus of this study. Computational fluid dynamics computations of axisymmetric models (cone-cylinder and quartic geometry), of relevance to NASA's High Speed project, are carried out using the space-time conservation element solution element viscous flow solver with unstructured meshes. A systematic parametric study is conducted to determine the optimum combination of counterflowing jet size, mass flow rate, and nozzle geometry for obtaining LPM jets. Details from these computations will be used to assess the potential of the LPM counterflowing supersonic jet as a means of active flow control for enabling supersonic flight over land and to establish the knowledge base for possible future implementation of such technologies.

Description: Use of counterflowing jets ejected into supersonic freestreams as a flow control concept to modify the external flowfield has gained renewed interest with regards to potential retropropulsion applications pertinent to entry, descent, and landing investigations. This study describes numerical computations of such a concept for a scaled wind-tunnel capsule model by employing the space-time conservation element solution element viscous flow solver with unstructured meshes. Both steady-state and time-accurate computations are performed for several configurations with different counterflowing jet Mach numbers. Axisymmetric computations exploring the effect of the jet flow rate and jet Mach number on the flow stability, jet interaction with the bow shock and its subsequent impact on the aerodynamic and aerothermal loads on the capsule body are carried out. Similar to previous experimental findings, both long and short penetration modes exist at a windtunnel Mach number of 3.48. It was found that both modes exhibit non-stationary behavior and the former is much more unstable than the latter. It was also found that the unstable long penetration mode only exists in a relatively small range of the jet mass flow rate. Solution-based mesh refinement procedures are used to improve solution accuracy and provide guidelines for a more effective mesh generation procedure for parametric studies. Details of the computed flowfields also serve as a means to broaden the knowledge base for future retropropulsion design studies.

Description: Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

Description: Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

Description: 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.

Description: Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Description: Recent NASA initiatives for space exploration have reinvigorated research on Apollo-like capsule vehicles. Aerothermodynamic characteristics of these capsule configurations during reentry play a crucial role in the performance and safety of the planetary entry probes and the crew exploration vehicles. At issue are the forebody thermal shield protection and afterbody aeroheating predictions. Due to the lack of flight or wind tunnel measurements at hypersonic speed, design decisions on such vehicles would rely heavily on computational results. Validation of current computational tools against experimental measurement thus becomes one of the most important tasks for general hypersonic research. This paper is focused on time-accurate numerical computations of hypersonic flows over a set of capsule configurations, which employ a counterflow jet to offset the detached bow shock. The accompanying increased shock stand-off distance and modified heat transfer characteristics associated with the counterflow jet may provide guidance for future design of hypersonic reentry capsules. The newly emerged space-time conservation element solution element (CESE) method is used to perform time-accurate, unstructured mesh Navier-Stokes computations for all cases investigated. The results show good agreement between experimental and numerical Schlieren pictures. Surface heat flux and aerodynamic force predictions of the capsule configurations are discussed in detail.