Gary C. Cheng

Effect of Counterflow Jet on a Supersonic Reentry Capsule

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.

Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows

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.

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Minimum drag and heating 0.3-caliber projectile nose geometry

Understanding the performance of penetrators and aerodynamic bodies of revolution (missiles, rockets, aircraft noses, etc.) requires a close look at the drag and the heat transfer characteristics at a wide range of supersonic flight conditions. This research utilizes computational study and compares the aerothermal loads of supersonic flows around a new penetrator geometry, derived based on the optimization of the nose factor, to those of other common projectile shapes: conical, tangent-ogive, and power series nose geometries. The abundance of research on 0.3-caliber projectile made the choice for this research simple in order to maximize our ability to compare to the existing data. The comparison of our 0.3 caliber cylindrical projectile with other geometries shows that within the range of 500–1500 m/s flight speed the new geometry has the lowest aerodynamic drag, lowest body temperature, and least amount of heating.

Thermal Hydraulics Design and Analysis Methodology for a Solid-Core Nuclear Thermal Rocket Engine Thrust Chamber

Nuclear thermal propulsion is a leading candidate for in-space propulsion for human Mars missions. This chapter describes a thermal hydraulics design and analysis methodology developed at the NASA Marshall Space Flight Center, in support of the nuclear thermal propulsion development effort. The objective of this campaign is to bridge the design methods in the Rover/NERVA era, with a modern computational fluid dynamics and heat transfer methodology, to predict thermal, fluid, and hydrogen environments of a hypothetical solid-core, nuclear thermal engine the Small Engine, designed in the 1960s. The computational methodology is based on an unstructured-grid, pressure-based, all speeds, chemically reacting, computational fluid dynamics and heat transfer platform, while formulations of flow and heat transfer through porous and solid media were implemented to describe those of hydrogen flow channels inside the solid24 core. Design analyses of a single flow element and the entire solid-core thrust chamber of the Small Engine were performed and the results are presented herein

Development of a Higher Order CESE scheme for Transient Viscous Flows

In this paper, we attempt to develop a higher-order version of the novel space-time CESE framework (originally 2 nd order accurate in both space and time) that is suitable for modeling transient viscous flows. Although higher-order versions of the CESE framework have been proposed in recent times, all of them are non-dissipative (neutrally stable) in nature, making them difficult to apply to both inviscid and viscous problems. In this regard, concepts like space-time inversion invariance, that determine the non-dissipative nature of the numerical framework, and the procedure to break the space-time inversion invariance of the original scheme- a necessary step to develop a viscous flow solver from the neutrally stable CESE framework- are explained here.

Validation and Verification of CE/SE Method based Courant Number Insensitive Transient Viscous Flow Solver

In this paper, we rigorously validate and verify the recently developed Space-Time Conservation Element/Solution Element (CE/SE) based Courant Number Insensitive transient viscous flow solver. Although, the CE/SE framework in two spatial dimension was originally designed for triangular meshes, in recent times it has been extended to utilize polygon shaped meshes also. However the effect of use of quadrilateral meshes on the Courant Number Insensitive scheme (CNIS) has not been well documented and tested. Therefore, in this paper we propose to verify and compare the effect of using triangular and quadrilateral meshes on the numerical accuracy through use of benchmark test cases such as laminar flow over a flat plate, laminar flow over a thin flat plate (splitter plate) and laminar flow over a square cylinder. The numerical results and their comparison with analytical and experimental results are also presented. Possible future work is also discussed.