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NASA NTRS2022

Stability Analysis of Streaks Induced by Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗

NASA NTRS2022

Stability Analysis of Streaks Induced By Optimized Vortex Generators

Boundary layer transition↗

NASA NTRS1979

Stability of sequences generated by nonlinear differential systems

A local stability analysis is presented for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. It is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and the one-leg k-step numerical solution can be approximated. Attention is given to the example of the two-dimensional problem involving the stability of the longitudinal equations of motion of a gliding jet aircraft.

Brown, R. L.↗

DOE OSTI2014

The multifacet graphically contracted function method. II. A general procedure for the parameterization of orthogonal matrices and its application to arc factors

Practical algorithms are presented for the parameterization of orthogonal matrices Q ∈ R {sup m×n} in terms of the minimal number of essential parameters (φ). Both square n = m and rectangular n < m situations are examined. Two separate kinds of parameterizations are considered, one in which the individual columns of Q are distinct, and the other in which only Span(Q) is significant. The latter is relevant to chemical applications such as the representation of the arc factors in the multifacet graphically contracted function method and the representation of orbital coefficients in SCF and DFT methods. The parameterizations are represented formally using products of elementary Householder reflector matrices. Standard mathematical libraries, such as LAPACK, may be used to perform the basic low-level factorization, reduction, and other algebraic operations. Some care must be taken with the choice of phase factors in order to ensure stability and continuity. The transformation of gradient arrays between the Q and (φ) parameterizations is also considered. Operation counts for all factorizations and transformations are determined. Numerical results are presented which demonstrate the robustness, stability, and accuracy of these algorithms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Uniform Pt/Pd Bimetallic Nanocrystals Demonstrate Platinum Effect on Palladium Methane Combustion Activity and Stability

Bimetallic catalytic materials are in widespread use for numerous reactions, as the properties of a monometallic catalyst are often improved upon addition of a second metal. In studies with bimetallic catalysts, it remains challenging to establish clear structure–property relationships using traditional impregnation techniques, due to the presence of multiple coexisting active phases of different sizes, shapes, and compositions. Here, a convenient approach to prepare small and uniform Pt/Pd bimetallic nanocrystals with tailorable composition is demonstrated, despite the metals being immiscible in the bulk. By depositing this set of controlled nanocrystals onto a high-surface-area alumina support, we systematically investigate the effect of adding platinum to palladium catalysts for methane combustion. At low temperatures and in the absence of steam, all bimetallic catalysts show activity nearly identical with that of Pt/Al 2 O 3 , with much lower rates in comparison to that of the Pd/Al 2 O 3 sample. BUt, unlike Pd/Al 2 O 3 , which experiences severe low-temperature steam poisoning, all Pt/Pd bimetallic catalysts maintain combustion activity on exposure to excess steam. These features are due to the influence of Pt on the Pd oxidation state, which prevents the formation of a bulk-type PdO phase. Despite lower initial combustion rates, hydrothermal aging of the Pd-rich bimetallic catalyst induces segregation of a PdO phase in close contact to a Pd/Pt alloy phase, forming more active and highly stable sites for methane combustion. Altogether, this work unambiguously clarifies the activity and stability attributes of Pt/Pd phases which often coexist in traditionally synthesized bimetallic catalysts and demonstrates how well-controlled bimetallic catalysts elucidate structure–property relationships.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1981

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

Fowlis, W. W.↗

DOE OSTI2017

Double Arc Instability in the Solar Corona

The stability of the magnetic field in the solar corona is important for understanding the causes of solar eruptions. Although various scenarios have been suggested to date, the tether-cutting reconnection scenario proposed by Moore et al. is one of the widely accepted models to explain the onset process of solar eruptions. Although the tether-cutting reconnection scenario proposes that the sigmoidal field formed by internal reconnection is the magnetic field in the pre-eruptive state, the stability of the sigmoidal field has not yet been investigated quantitatively. In this paper, in order to elucidate the stability problem of the pre-eruptive state, we developed a simple numerical analysis in which the sigmoidal field is modeled by a double arc electric current loop and its stability is analyzed. As a result, we found that the double arc loop is more easily destabilized than the axisymmetric torus, and it becomes unstable even if the external field does not decay with altitude, which is in contrast to the axisymmetric torus instability. This suggests that tether-cutting reconnection may well work as the onset mechanism of solar eruptions, and if so, the critical condition for eruption under a certain geometry may be determined by a new type of instability rather than by the torus instability. Based on them, we propose a new type of instability called double arc instability (DAI). We discuss the critical conditions for DAI and derive a new parameter κ , defined as the product of the magnetic twist and the normalized flux of the tether-cutting reconnection.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Airflow Bypass in Centrifugal Compressor and Operational Stability

The influence of the airflow bypass at the impeller input on the operational stability of a compressor is considered. The bypass structure is discussed, and a new chamber design is proposed for a compressor with diffuser blades. Numerical analysis of the flow structure is conducted. The compressor’s margin of operational stability is assessed experimentally for bypass chambers of different geometry.

42 ENGINEERING↗

DOE OSTI2023

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the errorcorrecting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Stability of PT and anti- PT -symmetric Hamiltonians with multiple harmonics

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time periodicity offers avenues to engineer the landscape of Floquet quasienergies across the complex plane. We investigate two-level non-Hermitian PT and anti- PT -symmetric Hamiltonians with coefficients that have multiple harmonics using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasienergies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany these cyclic changes with the biorthogonality approach. Our results demonstrate that these time-periodic Hamiltonians generate a rich landscape of stable (real) and unstable (complex) regions. Published by the American Physical Society 2024

Cen, Julia (ORCID:0000000299353943)↗

DOE OSTI2016

Radial stability of anisotropic strange quark stars

The influence of the anisotropy in the equilibrium and stability of strange stars is investigated through the numerical solution of the hydrostatic equilibrium equation and the radial oscillation equation, both modified from their original version to include this effect. The strange matter inside the quark stars is described by the MIT bag model equation of state. For the anisotropy two different kinds of local anisotropic σ = p {sub t} − p {sub r} are considered, where p {sub t} and p {sub r} are respectively the tangential and the radial pressure: one that is null at the star's surface defined by p {sub r} ( R ) = 0, and one that is nonnull at the surface, namely, σ {sub s} = 0 and σ {sub s} {sub ≠} {sub 0}. In the case σ {sub s} = 0, the maximum mass value and the zero frequency of oscillation are found at the same central energy density, indicating that the maximum mass marks the onset of the instability. For the case σ {sub s} {sub ≠} {sub 0}, we show that the maximum mass point and the zero frequency of oscillation coincide in the same central energy density value only in a sequence of equilibrium configurations with the same value of σ {sub s} . Thus, the stability star regions are determined always by the condition dM / d ρ {sub c} {sub >} {sub 0} only when the tangential pressure is maintained fixed at the star surface's p {sub t} ( R ). These results are also quite important to analyze the stability of other anisotropic compact objects such as neutron stars, boson stars and gravastars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Demonstration of Plume Stability for Carbon Storage Projects

Conference paper presented at 17th International Conference on Greenhouse Gas Control Technologies (GHGT-17), Calgary, Alberta, Canada, October 20–24, 2024. A technical approach has been developed to demonstrate CO 2 plume stabilization: 1) construct a geologic model, 2) perform numerical simulations, and 3) estimate the rate of change in circumferential area of the CO 2 plume with respect to time (dA/dt). Demonstration of the technical approach for plume stabilization is presented using a North Dakota case study.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗

NASA NTRS1973

Preliminary study of a wall stabilized constructed arc

An iterative, implicit, finite-difference numerical technique is described which is suitable for obtaining solutions to the governing equations for a gas flowing in an axially symmetric constricted-arc heater. The method is shown to provide adequate solutions for three cases of simple pipe flows found in the literature, and for flow in a constricted-arc heater by direct comparison with experimental data. The comparison with arc-heater data includes static pressure, arc voltage, and wall heat flux, all as a function of axial location, and a radial temperature profile at one axial station. The arc-heater data were taken with air as the test gas at a heater inlet pressure approximately 0.40 atm and two flow rates of 2.2 and 4.8 g/sec. The arc currents investigated were between 377 and 584 amperes.

Graves, R. A.↗

DOE OSTI2013

Modeling of the rotational stabilization of tokamak plasmas with account of skin effect in the resistive wall

The influence of the Resistive Wall Mode (RWM) rotation on its stability in tokamaks is analyzed. Recently developed analytical theory [V. D. Pustovitov, Phys. Plasmas 19, 062503 (2012)] predicts that, when the skin depth s becomes much smaller than the wall thickness d{sub w}, the resistive dissipation in the wall in combination with the mode rotation stabilizes the mode up to complete suppression of instability. Here this effect is studied without the restriction on the ratio s/d{sub w}. Thereby the applicability of analytical predictions and accuracy of asymptotic expressions relating the growth rate to the rotation frequency of RWM is clarified. The dispersion relation for the rotating modes is derived in the single-mode cylindrical approximation and solved numerically. It is shown that the rotational stabilization of the plasma, the same as found earlier, is possible even at s/d{sub w} of the order unity if the mode rotation frequency is above a critical level. The dependences of the growth rate on the mode frequency are calculated for different plasma parameters. It is shown that, at a given plasma state with a linear response to external perturbations, the growth rate of the mode is maximal at the mode locking (when the rotation is lost). The relation of the mode minimal rotation frequency at the stability boundary with the growth rate at the mode locking is found. The analysis demonstrates strong influence of dissipation in the wall on the dynamics of rotating and locked RWMs and confirms the necessity to incorporate the skin effect into their description. The obtained estimates allow one to compare these predictions with experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Triple flame structure and diffusion flame stabilization

The stabilization of diffusion flames is studied using asymptotic techniques and numerical tools. The configuration studied corresponds to parallel streams of cold oxidizer and fuel initially separated by a splitter plate. It is shown that stabilization of a diffusion flame may only occur in this situation by two processes. First, the flame may be stabilized behind the flame holder in the wake of the splitter plate. For this case, numerical simulations confirm scalings previously predicted by asymptotic analysis. Second, the flame may be lifted. In this case a triple flame is found at longer distances downstream of the flame holder. The structure and propagation speed of this flame are studied by using an actively controlled numerical technique in which the triple flame is tracked in its own reference frame. It is then possible to investigate the triple flame structure and velocity. It is shown, as suggested from asymptotic analysis, that heat release may induce displacement speeds of the triple flame larger than the laminar flame speed corresponding to the stoichiometric conditions prevailing in the mixture approaching the triple flame. In addition to studying the characteristics of triple flames in a uniform flow, their resistance to turbulence is investigated by subjecting triple flames to different vortical configurations.

Veynante, D.↗

NASA NTRS1991

Effect of gravity on the stability and structure of lean hydrogen-air flames

Detailed, time-dependent, 2D numerical simulations with full hydrogen-oxygen chemistry are used to investigate the effects of gravity on the stability and structure of laminar flames in lean, premixed hydrogen-air mixtures. The calculations show that the effects of gravity becomes more important as the lean flammability limit is approached. In a 12 percent hydrogen-air mixture, gravity plays only a secondary role in determining the multidimensional structure of the flame with the stability and structure of the flame controlled primarily by the thermo-diffusive instability mechanism. However, in leaner hydrogen-air mixtures gravity becomes more important. Upward-propagating flames are highly curved and evolve into a bubble rising upwards in the tube. Downward-propagating flames are flat or even oscillate between structures with concave and convex curvatures. The zero-gravity flame shows only cellular structures. Cellular structures which are present in zero gravity can be suppressed by the effect of buoyancy for mixtures leaner than 11 percent hydrogen. These observations are explained on the basis of an interaction between the processes leading to buoyancy-induced Rayleigh-Taylor instability and the thermo-diffusive instability.

Patnaik, G.↗

NASA NTRS1987

Reynolds stress closure in jet flows using wave models

Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.

Morris, P. J.↗