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NASA NTRS1989

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.↗

NASA NTRS1990

Interaction of minor ions with fast and slow shocks

The coronal slow shock was predicted to exist embedded in large coronal holes at 4 to 10 solar radii. A three-fluid model was used to study the jumps in minor ions propertes across the coronal slow shock. The jump conditions were formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. A simularity solution was also obtained for heavy ions. The results show that on the downstream side of the coronal slow shock the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.

Whang, Y. C.↗

NASA NTRS1990

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

Van Dommelen, Leon L.↗

NASA NTRS1990

Heating of minor ions by the coronal slow shock

The coronal slow shock has been predicted to exist embedded in large coronal holes at 4-10 solar radii. In this paper, a three-fluid model is used to study the jumps in minor ion properties across a slow shock such as the coronal slow shock. The jump conditions are formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. Also obtained is a similarity solution for heavy ions. The results show that, on the downstream side of the slow shock, the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe, in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.

Whang, Y. C.↗

NASA NTRS1993

Heat Transfer from Radiatively Heated Material in a Low Reynolds Number Microgravity Environment

A mathematical model of the transient three-dimensional heat transfer between a slowly moving ambient gas stream and a thermally thick or thin flat surface heated by external radiation in a microgravity environment is presented. The problem is motivated in part by fire safety issues in spacecraft. The gas phase is represented by variable property convection-diffusion energy and mass conservation equations valid at low Reynolds numbers. The absence of gravity and low Reynolds number together permit the flow to be represented by a self-consistent velocity potential determined by the ambient velocity and the thermal expansion in the gas. The solid exchanges energy with the gas by conduction/convection and with the surroundings by surface absorption and re-emission of radiation. Heat conduction in the solid is assumed to be one dimensional at each point on the surface as a consequence of the limited times (of order of 10 seconds) of interest in these simulations. Despite the apparent simplicity of the model, the results show a complex thermally induced flow near the heated surface. The thermal exchange between the gas and solid produces an outward sourcelike flow upstream of the center of the irradiated area and a sinklike flow downstream. The responses of the temperature fields and the associated flows to changes in the intensity of the external radiation and the ambient velocity are discussed.

Yamashita, H.↗

NASA NTRS1994

Effect of magnetic field geometry on the wave signature of the pickup of interstellar neutrals

By using the technique of Johnstone et al. (1991), the asymptotic wave spectrum induced by the pickup of interstellar ions in the heliosphere is derived. This approach is independent of quasi-linear theory. The asymptotic wave spectrum is calculated from the standard resonance condition by assuming that the asymptotic ion distribution is bispherical and by using conservation of energy. The calculation places no restriction on either the ratio of Alfven speed to solar wind flow speed or the particle pitch angle. Spectra for various geometries (relative orientations of the magnetic field and solar wind velocity) are calculated. Absolute upper limits to the expected wave enhancements are calculated. These upper limits are compared to the background fluctuation spectrum extrapolated from 0.87 AU, assuming a spectral index of -5/3 and radial dependences of -2 and -3. The heliocentric radial distances at which the peaks in the various geometry-dependent wave spectra are expected to be observable above the background are identified. Peaks due to pickup hydrogen at the proton gyrofrequency are found to be always stronger relative to the background in parallel than in perpendicular geometries. The parallel-geometry excitations consist only of sunward propagating waves. In perpendicular geometries a peak also occurs, this time near 0.1 of the proton gyrofrequency (corresponding to the peak calculated by Lee and Ip (1987)). However, the steep spectral dependence of the ambient wave field makes it unlikely that this peak will be observed inside 20 AU. A similar result holds for the case of pickup-helium induced excitation at the helium gyrofrequency. Inside 10 AU, peaks at these lower frequencies tend to be obscured by the steep frequency dependence (proportional to -5/3) of the ambient spectrum and then are only observable in parallel geometries.

Williams, L. L.↗

NASA NTRS2004

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

NASA NTRS2020

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier–Stokes Equations

In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, we utilize a computationally simple and efficient approach based upon using decoupled interpolation operators. The resulting scheme is entropy conservative/stable and elementwise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation con firm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence), which are comparable to those of the original conforming scheme. Simulations of the Taylor{Green vortex at R(e) = 1,600 and turbulent flow past a sphere at R(e(infinity)) = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h=p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.

Nonconforming interfaces↗

DOE OSTI2020

Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.

42 ENGINEERING↗

NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

DOE OSTI2023

Protecting Customer Privacy Through Distributed Energy Resource Anonymization

Due to their stochastic nature, the increase of Renewable Energy Resources (RERs) as a primary source of energy for power grids creates challenges regarding the reliability and resilience of the system. In order to combat these obstacles, expansion of Distributed Energy Resources (DERs) and their participation in Demand Response (DR) programs is necessary. Widespread participation requires prioritizing customer privacy and addressing concerns that may arise regarding communication between DERs and the Grid Service Provider (GSP). This paper discusses the use of flow reservation resources to split the operating cycles of DER load profiles into unique phases. The splitting of phases increases anonymization of the DERs by making it more difficult to determine the individual characteristics of the device. We discuss an example of this using simulated DER load profile data and examine the resulting effectiveness by using a machine learning algorithm for classification, called Support Vector Machine (SVM).

Distributed Energy Resource, Anonymization, Renewa↗

DOE OSTI2020

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Howard, Amanda A.↗

NASA NTRS1974

Thermoacoustic convection of fluids in low gravity

The heat flow in a confined perfect gas in low gravity is investigated, including the effects of conduction and thermal convection. Buoyancy-driven flow is neglected, due to the low-gravity environment, but the effect of thermoacoustic motion due to fluid compressibility is included. One-dimensional mathematical models are constructed from the conservation equations for a compressible, viscous, heat-conducting fluid. A conservative, time-dependent finite-difference method is used to generate numerical solutions on a digital computer. Problems for flat plates and cylindrical segments are solved for specified thermal boundary conditions. Numerical results are given which indicate that thermoacoustic convection can significantly increase the transient heat flow over conduction model predictions for cases where a confined gas is rapidly heated.

Spradley, L. W.↗

DOE OSTI2025

High-current-density electrosynthesis of formate from captured CO 2 solution by MOF-derived bismuth nanosheets

Greenhouse gas emissions present a significant challenge to humanity, and utilizing renewable electricity to convert emitted CO 2 into value-added products offers a promising solution; however, traditional CO 2 capture and regeneration processes remain energy-intensive, restricting the overall system efficiency and decarbonization efficacy. In this study, an advanced direct reduction of captured CO 2 with large current densities for formate electrosynthesis was demonstrated without the need for CO 2 regeneration or compression. The bismuth nanosheet (DRM-BiNS) was synthesized by direct reduction of a Bi-based MOF, representing a new class of catalytic materials with a large surface area and interconnected pores, suitable for the direct reduction of captured CO 2 . By seamlessly combining experimentation and simulation, insights into the structure-parameter-performance relation were acquired in a flow cell setting, including critical membrane-electrode distance, cell orientation, and pumping flow rate. Important flow-cell components, such as catholyte volume, electrode substrate, membrane choice, and ionomer type, were also carefully examined to enhance the cell performance. In sharp contrast to prior studies limited to current densities below 20 mA/cm 2 in bicarbonate-based captured CO 2 solutions, this work demonstrates a remarkable current density of 300 mA/cm 2 with an FE to formate comparable to the case with gas-fed CO 2 reduction. Moreover, the process sustained an FE above 50% at a high current density of 500 mA/cm 2 . The DRM-BiNS catalyst exhibited outstanding selectivity, activity, and stability, significantly outperforming oxide-derived bismuth nanosheets (OD-BiNS) in captured CO 2 reduction. Furthermore, these findings offer critical insights into the development of sustainable and scalable CO 2 utilization technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1993

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

NASA NTRS1994

Numerical Simulation of Shock-Induced Combustion Past Blunt Bodies Using Shock-Fitting Technique

Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one dimensional wave-interaction model than before.

Ahuja, J. K.↗

NASA NTRS1980

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

Dulikravich, D. S.↗

DOE OSTI2026

Ecological connectivity and habitat loss shape patterns of genetic diversity in a threatened salamander

Context The maintenance of genetic diversity is essential for preserving adaptive potential in populations, yet it is increasingly threatened by landscape alteration. The field of landscape genetics offers a framework for assessing how patch-level landscape conditions, modeled at multiple scales, influence genetic diversity. Objectives We sought to assess how local environmental features and connectivity influence genetic diversity across 74 four-toed salamander (Hemidactylium scutatum) breeding wetlands in the southeastern United States. Methods Using next-generation sequencing data and hierarchical Bayesian models, we examined genome-wide heterozygosity in relation to local landscape features and ecological connectivity. We also assessed the scale of effect of landscape features and tested for temporal lag effects. Results Genetic diversity was lower in wetlands with higher levels of historic deforestation and lower connectivity. An interaction between deforestation and connectivity indicated that deforestation had stronger negative effects in isolated wetlands but weaker effects in well-connected wetlands. Accounting for scale of effect and temporal lags was critical for detecting these relationships. Conclusions Our analyses highlight the importance of assessing the spatial scale (scale of effect) and temporal lag of landscape features to detect key drivers of genetic diversity. In line with population genetic theory, our results indicate that the genetic consequences of habitat loss do not affect populations uniformly and are most severe in isolated populations where gene flow cannot buffer against loss of diversity. Altogether, we highlight the importance of considering the interaction of habitat loss and connectivity in conservation genetic management.

Hemidactylium scutatum↗