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DOE OSTI2022

Implicit shock tracking for unsteady flows by the method of lines

Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Farassat, F.↗

NASA NTRS1992

Continuation of tailored composite structures of ordered staple thermoplastic material

The search for the cost effective composite structure has motivated the investigation of several approaches to develop composite structure from innovative material forms. Among the promising approaches is the conversion of a planar sheet to components of complex curvature through sheet forming or stretch forming. In both cases, the potential for material stretch in the fiber direction appears to offer a clear advantage in formability over continuous fiber systems. A framework was established which allows the simulation of the anisotropic mechanisms of deformation of long discontinuous fiber laminates wherein the matrix phase is a viscous fluid. Predictions for the effective viscosities of a hyper-anisotropic medium consisting of collimated, discontinuous fibers suspended in viscous matrix were extended to capture the characteristics of typical polymers including non-Newtonian behavior and temperature dependence. In addition, the influence of fiber misorientation was also modeled by compliance averaging to determine ensemble properties for a given orientation distribution. A design tool is presented for predicting the effect of material heterogeneity on the performance of curved composite beams such as those used in aircraft fuselage structures. Material heterogeneity can be induced during manufacturing processes such as sheet forming and stretch forming of thermoplastic composites. This heterogeneity can be introduced in the form of fiber realignment and spreading during the manufacturing process causing radial and tangential gradients in material properties. Two analysis procedures are used to solve the beam problems. The first method uses separate two-dimensional elasticity solutions for the stresses in the flange and web sections of the beam. The separate solutions are coupled by requiring that forces and displacements match section boundaries. The second method uses an approximate Rayleigh-Ritz technique to find the solutions for more complex beams. Analyses are performed for curved beams of various cross-sections loaded in pure bending and with a uniform distributed load. Preliminary results show that the geometry of the beam dictates the effect of heterogeneity on performance. The role of heterogeneity is larger in beams with a small average radius-to-depth ration, R/t, where R is the average radius of the beam and t is the difference between the inside and outside radii. Results of the anlysis are in the form of stresses and displacements and are compared to both mechanics of materials and numerical solutions obtained using finite element analysis.

Santare, Michael H.↗

DOE OSTI2022

Peridynamics and surrogate modeling of pressure-driven well stimulation

In this work we use the peridynamics theory of solid mechanics to simulate fracture in an annular rock domain subject to an in-situ stress and create surrogate models that predict the area of the resulting cracks. Peridynamics is a non-local formulation of continuum mechanics that naturally accommodates material discontinuities. Furthermore, unlike other fracture modeling techniques there is no need to provide information about the crack path. We utilize the peridynamics code Peridigm and take a two-stage approach to fracture modeling. First an implicit solve is performed to compute the in-situ stress state. We then execute an explicit solve where a pressure loading designed to emulate fluid-driven hydraulic fracture is applied at the borehole and transmitted to the pre-stressed rock. We present results from polynomial and single and multi-level Gaussian process surrogate models constructed from a sampling study of the peridynamics model. The surrogates predict crack area given a measure of the in-situ stress anisotropy and rise time and amplitude of the pressure loading. These surrogates take a minuscule fraction of peridynamics model's running time to evaluate and are a step towards enabling advanced optimization and uncertainty quantification workflows that require many model evaluations.

42 ENGINEERING↗

NASA NTRS1979

Bond graph for modeling valves and switches

Digital graph element represents two-state devices. It can be used in modeling mechanical stops, backlash, and other discontinuities that occur whenever subsystems are connected or disconnected.

Gebben, V. D.↗

NASA NTRS2011

Transition Analysis for the HIFiRE-1 Flight Experiment

Li, Fei↗

NASA NTRS2012

Hypersonic Transition Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis.

Li, Fei↗

NASA NTRS2012

Stability Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13.5. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis. The transition behavior during this re-entry segment of HIFiRE-1 flight shares some common features with the predicted transition front along the elliptic cone shaped HIFiRE-5 flight article, which was designed to provide hypersonic transition data for a fully 3D geometric configuration. To compare and contrast the crossflow dominated transition over the HIFiRE-1 and HIFiRE-5 configurations, this paper also analyzes boundary layer instabilities over a subscale model of the HIFiRE-5 flight configuration that was tested in the Mach 6 quiet tunnel facility at Purdue University.

Li, Fei↗

NASA NTRS1994

Impact of land-surface moisture variability on local shallow convective cumulus and precipitation in large-scale models

Numerical experiments using state-of-the-art high-resolution mesoscale cloud model showed that land-surface moisture significantly affects the timing of onset of clouds and the intensity and distribution of precipitation. In general, landscape discontinuity enhances shallow convective precipitation. Two mechanisms that are strongly modulated by land-surface moisture-namely, random turbulent thermal cells and organized sea-breeze-like mesoscale circulations-also determine the horizontal distribution of maximum precipitation. However, interactions between shallow cumulus and land-surface moisture are highly nonlinear and complicated by different factors, such as atmospheric thermodynamic structure and large-scale background wind. This analysis also showed that land-surface moisture discontinuities seem to play a more important role in a relatively dry atmsophere, and that the strongest precipitation is produced by a wavelength of land-surface forcing equivalent to the local Rossby radius of deformation. A general trend between the maximum precipitation and the normalized maximum latent heat flux was identified. In general, large values of mesoscale latent heat flux imply strongly developed mesoscale circulations and intense cloud activity, accompanied by large surface latent heat fluxes that transport more water vapor into the atmosphere.

Chen, Fei↗

NASA NTRS1975

Optimization of duct acoustic liners of finite length

Lining design procedures generally ignore the effects of discontinuous impedance changes on reflection and modal redistribution of incident energy. The present study involves identification of the mechanisms of optimal suppression by segmented liners, including impedance discontinuity effects. The mathematical model involves rectangular ducts in the absence of mean flow. Segmented acoustic fields are represented by duct eigenfunction expansions, and mode matching is used to ensure continuity of the total field. Extensive parameter studies were used to identify attenuation mechanisms and to define preliminary liner configurations. These are used as starting values in conjugate-gradient optimization studies. Optimal segmented liners are presented and it is shown that, if the sound source is sufficiently well-defined, conventional infinite duct optimum attenuation rates can be improved upon by taking advantage of wall impedance discontinuities. Finally, follow-on work which will involve experimental verification and extension to the case with mean flow in the duct is described.

Beckemeyer, R. J.↗

NASA NTRS1982

Pioneer and Voyager observations of Forbush decreases between 6 and 24 AU

A detailed phenomenological description of deep space Forbush decreases is given, using Voyager and Pioneer data. The transient reduction in cosmic ray intensity can be produced by (1) reflection at the shock front; (2) increased modulation associated with the disturbed region behind the shock; (3) a barrier mechanism involving large-scale tangential discontinuities; or (4) particle drifts in the enhanced magnetic field by the post-shock region. The presence of a well-defined precursor peak clearly indicates that particle reflection is important. Forbush decreases appear to be an important component in the long-term modulation.

Mcdonald, F. B.↗

NASA NTRS1992

Flight test results from a supercritical mission adaptive wing with smooth variable camber

The mission adaptive wing (MAW) consisted of leading- and trailing-edge variable-camber surfaces that could be deflected in flight to provide a near-ideal wing camber shape for any flight condition. These surfaces featured smooth, flexible upper surfaces and fully enclosed lower surfaces, distinguishing them from conventional flaps that have discontinuous surfaces and exposed or semiexposed mechanisms. Camber shape was controlled by either a manual or automatic flight control system. The wing and aircraft were extensively instrumented to evaluate the local flow characteristics and the total aircraft performance. This paper discusses the interrelationships between the wing pressure, buffet, boundary-layer and flight deflection measurement system analyses and describes the flight maneuvers used to obtain the data. The results are for a wing sweep of 26 deg, a Mach number of 0.85, leading and trailing-edge cambers (delta(sub LE/TE)) of 0/2 and 5/10, and angles of attack from 3.0 deg to 14.0 deg. For the well-behaved flow of the delta(sub LE/TE) = 0/2 camber, a typical cruise camber shape, the local and global data are in good agreement with respect to the flow properties of the wing. For the delta(sub LE/TE) = 5/10 camber, a maneuvering camber shape, the local and global data have similar trends and conclusions, but not the clear-cut agreement observed for cruise camber.

Powers, Sheryll Goecke↗

NASA NTRS1992

Flight Test Results From a Supercritical Mission Adaptive Wing With Smooth Variable Camber

The mission adaptive wing (MAW) consisted of leading- and trailing-edge variable-camber surfaces that could be deflected in flight to provide a near-ideal wing camber shape for any flight condition. These surfaces featured smooth, flexible upper surfaces and fully enclosed lower surfaces, distinguishing them from conventional flaps that have discontinuous surfaces and exposed or semiexposed mechanisms. Camber shape was controlled by either a manual or automatic flight control system. The wing and aircraft were extensively instrumented to evaluate the local flow characteristics and the total aircraft performance. This paper discusses the interrelationships between the wing pressure, buffet, boundary-layer and flight deflection measurement system analyses and describes the flight maneuvers used to obtain the data. The results are for a wing sweep of 26°, a Mach number of 0.85, leading and trailing-edge cambers ( δ LE/TE ) of 0/2 and 5/10, and angles of attack from 3.0° to 14.0°. For the well-behaved flow of the δ LE/TE = 0/2 camber, a typical cruise camber shape, the local and global data are in good agreement with respect to the flow properties of the wing. For the δ LE/TE = 5/10 camber, a maneuvering camber shape, the local and global data have similar trends and conclusions, but not the clear-cut agreement observed for cruise camber.

Flight Testing↗

DOE OSTI2023

Natural Fracture Pattern Development Using 3D Coupled Numerical Model: Mechanics and Diagenesis

In the earth's crust, while tectonic processes can mechanically create natural fractures, cementation can simultaneously grow on the surfaces of the fractures. This crystallization can affect the growth of the fractures. To more accurately address the modeling of natural fracture development, both mechanical deformation and chemical diagenesis should be carried out in an integrated manner. Here, we achieve this with a three-dimensional (3D) simulator that couples mechanical and chemical processes for natural fracture pattern development in layer confined situations. Tectonic loading over geologic time is mimicked by displacement driven boundary conditions in a 3D displacement discontinuity method (DDM) scheme. Quartz diagenesis competes with mechanical fracture opening, resulting in three different cementation conditions - open, bridging or fully infilled – which define fracture element stiffness that is used as feedback within the 3D-DDM code during propagation. An important milestone of this work is that this coupled structural diagenetic model can reproduce power-law aperture population statistics which cannot be generated using mechanics alone. More accurately estimated mechanical fracture apertures and their cementation condition is a critical step toward better permeability estimation and fluid path analysis for subsurface reservoirs.

58 GEOSCIENCES↗

DOE OSTI2023

Rapid grain refinement and compositional homogenization in a cast binary Cu50Ni alloy achieved by friction stir processing

Friction stir processing (FSP) has been increasingly adopted for joining and processing materials in automotive, aerospace and industrial construction. During FSP a dynamic competition between high-speed shear deformation and deformation-induced heating brings about a complex competition between multiple dynamic microstructural evolution mechanisms making it difficult to predict the microstructural evolution pathway. Hence, improved understanding of microstructural evolution mechanisms during FSP can be beneficial for continued growth in the adoption of FSP for demanding applications of future. Towards this goal, this study uses a model binary Cu – 50 at.% Ni alloy to clarify the effect of single and double pass FSP on the microstructural evolution of a coarse grained and compositionally heterogeneous cast microstructure. High energy synchrotron X-ray diffraction, electron backscatter diffraction, and nanoindentation are used to clarify the microstructural evolution due to FSP. The process of compositional homogenization of as-cast segregations is studied by energy dispersive spectroscopy and atom probe tomography. Our results show that a single fast FSP pass at 30 mm.s -1 produces a 100 µm deep layer of submicrometric and hall-petch hardened CuNi grains. The initial cast compositional heterogeneities in a micrometric scale is rapidly transformed to nano-sized domains, mainly confined at grain boundaries. Double pass FSP increases the penetration depth of the processed layer and leads to a 2.9 times grain growth relative to single pass FSP. Grain fragmentation, discontinuous dynamic recrystallization, grain growth, and twinning mechanisms are discussed. In conclusion, these results highlight the value of FSP for ultrafast grain refinement and compositional homogenization of cast alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A numerical extension of the spatially-filtered Euler equations for contact discontinuities

Solving the spatially-filtered Euler equations with a kinetic energy-preserving centered discretization is an efficient framework for simulating shock-dominated flows. Here, the present work describes a numerical treatment of the spatially-filtered Euler equations to minimize oscillations when simulating contact discontinuities. To counteract dispersive errors inherent to centered schemes, a WENO-like correction term is applied to the enthalpy transport in the energy equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Development and performance of INCONEL® alloy 740H® seam-welded piping

INCONEL® alloy 740H® is an age-hardenable nickel-based alloy approved for pressure vessels and piping within ASME Section I, VIII, and B31.1. Currently, the code applies a weld strength reduction factor (WSRF) of 0.7 to the allowable stresses for longitudinal seam welds in the time dependent creep regime. In this work, a full-scale seam weld was successfully produced using typical industrial practices. The component was solution heat-treated and aged after fabrication to improve the performance of the weldment. Tensile, bend, impact, and low-cycle fatigue tests showed the component met all the specification requirements and elevated temperature properties were within base metal expectations with failures predominately in the weld metal. Long-term creep tests, including large samples more representative of the entire weldment, were fabricated and tested to times in excess of 10,000 h at multiple temperatures. Analysis of the creep data supports a WSRF of 0.9 for the solution annealed + aged weldments in contrast to the WSRF of 0.7 currently applied to welded + aged weldments. Metallurgical analysis shows that the solution annealing causes recrystallization of the weld metal and reduces the chemical compositional and microstructural gradients in the weldments resulting in acceptable short-term performance. In long-term creep, evidence for coarsened zones in the weldments due to discontinuous coarsening reactions were identified as the mechanism leading to accelerated creep damage formation in the weld metal and sample failure.

14 SOLAR ENERGY↗

NASA NTRS1992

Measurement of mechanical and thermophysical properties of dimensionally stable materials for space applications

Mechanical, thermal, and physical property test data was generated for as-fabricated advanced composite materials at room temperature (RT), -150 and 250 F. The results are documented of mechanical and thermophysical property tests of IM7/PEEK and discontinuous SiC/Al (particulate (p) and whisker (w) reinforced) composites which were tested at three different temperatures to determine the effect of temperature on material properties. The specific material systems tested were IM7/PEEK (0)8, (0, + or - 45, 90)s, (+ or - 30, 04)s, 25 vol. pct. (v/o) SiCp/Al, and 25 v/o SiCw/Al. RT material property results of IM7/PEEK were in good agreement with the predicted values, providing a measure of consolidation integrity attained during fabrication. Results of mechanical property tests indicated that modulus values at each test temperature were identical, whereas the strength (e.g., tensile, compressive, flexural, and shear) values were the same at -150 F, and RT, and gradually decreased as the test temperature was increased to 250 F. Similar trends in the strength values was also observed in discontinuous SiC/Al composites. These results indicate that the effect of temperature was more pronounced on the strength values than modulus values.

Rawal, Suraj P.↗