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At least 1,405 records · Page 78

Kinetic Analysis of Competitive Electrocatalytic Pathways: New Insights into Hydrogen Production with Nickel Electrocatalysts

The hydrogen production electrocatalyst Ni(PPh2NPh2)22+ (1) is capable of traversing multiple electrocatalytic pathways. When using dimethylformamidium, DMF(H)+, the mechanism of formation of H2 catalyzed by 1 changes from an ECEC to an EECC mechanism as the potential approaches the Ni(I/0) couple. Two recent electrochemical methods, current-potential analysis and foot-of-the-wave analysis (FOWA), were performed on 1 to measure the detailed chemical kinetics of the competing ECEC and EECC pathways. A sensitivity analysis was performed on the electrochemical methods using digital simulations to gain a better understanding of their strengths and limitations. Notably, chemical rate constants were significantly underestimated when not accounting for electron transfer kinetics, even when electron transfer was fast enough to afford a reversible non-catalytic wave. The EECC pathway of 1 was found to be faster than the ECEC pathway under all conditions studied. Using buffered DMF: DMF(H)+ mixtures led to an increase in the catalytic rate constant (kobs) of the EECC pathway, but kobs for the ECEC pathway did not change when using buffered acid. Further kinetic analysis of the ECEC path revealed that added base increases the rate of isomerization of the exo-protonated Ni(0) isomers to the catalytically active endo-isomers, but decreases the net rate of protonation of Ni(I). FOWA on 1 did not provide accurate rate constants due to incomplete reduction of the exo-protonated Ni(I) intermediate at the foot of the wave, but FOWA could be used to estimate the reduction potential of this previously undetected intermediate. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy.

electrocatalysis↗

A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in parabolic problems with variable diffusion coefficients. This includes variable coefficient parabolic equations that might give rise to skew symmetric terms. The RKC1 and RKC2 schemes do not share this convex monotonicity preserving property. One-dimensional and two-dimensional von Neumann stability analyses of RKC1, RKC2, RKL1 and RKL2 are also presented, showing that the latter two have some advantages. The paper includes several details to facilitate implementation. A detailed accuracy analysis is presented to show that the methods reach their design accuracies. A stringent set of test problems is also presented. To demonstrate the robustness and versatility of our methods, we show their successful operation on problems involving linear and non-linear heat conduction and viscosity, resistive magnetohydrodynamics, ambipolar diffusion dominated magnetohydrodynamics, level set methods and flux limited radiation diffusion. In a prior paper (Meyer, Balsara and Aslam 2012 [36]) we have also presented an extensive test-suite showing that the RKL2 method works robustly in the presence of shocks in an anisotropically conducting, magnetized plasma.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Warfarin traps human vitamin K epoxide reductase in an intermediate state during electron transfer

Although warfarin is the most widely used anticoagulant worldwide, the mechanism by which warfarin inhibits its target, human vitamin K epoxide reductase (hVKOR), remains unclear. We show that warfarin blocks a dynamic electron-transfer process in hVKOR. A major fraction of cellular hVKOR is at an intermediate redox state of this process containing a Cys51-Cys132 disulfide, a characteristic accommodated by a four-transmembrane-helix structure of hVKOR. Warfarin selectively inhibits this major cellular form of hVKOR, whereas disruption of the Cys51-Cys132 disulfide impairs warfarin binding and causes warfarin resistance. Relying on binding interactions identified by cysteine alkylation footprinting and mass spectrometry coupled with mutagenesis analysis, we are able to conduct structure simulations to reveal a closed warfarin-binding pocket stabilized by the Cys51-Cys132 linkage. Understanding the selective warfarin inhibition of a specific redox state of hVKOR should enable the rational design of drugs that exploit the redox chemistry and associated conformational changes in hVKOR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Operando structural and chemical evolutions of TiS 2 in Na-ion batteries

Titanium disulfide (TiS 2 ) with high electric conductivity, fast rate capability, and good cycling performance is a promising candidate for electrode material in sodium (Na)-ion batteries. Despite the well-studied electrochemical behaviors of TiS 2 in Li-ion batteries, the detailed reaction mechanism of TiS 2 in Na-ion batteries is not yet fully understood due to a more complex multi-phase conversion process. In this work, reactions of TiS 2 in Na-ion batteries are investigated via a multi-modal synchrotron approach: operando X-ray Absorption Spectroscopy (XAS) – including X-ray Absorption Near-Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) – and ex situ X-ray Powder Diffraction (XPD), coupled with computational modeling. Operando XANES spectra indicate that the redox reactions occur in both Ti and S during the electrochemically driven phase transformation. Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis of XAS suggests that different numbers of components are involved in the lithiation and sodiation of TiS 2 , with the sodiation including at least one intermediate phase in addition to the starting material and the final sodiation product. Ex situ XPD and Rietveld refinement further determined and quantified the unknown phases, showing that three phases, TiS 2 , Na 0.55 TiS 2 , and NaTiS 2 , participate in the sodiation of TiS 2 . Operando EXAFS results show the changes in the Ti–Ti coordination number and interatomic distance. This explains the coulombic efficiency decay due to the incomplete recovery of the coordination number of Ti after cycling. Overall, this work reveals the reaction mechanism occurring in Na–TiS 2 batteries with a greater quantitative understanding of the structural evolution. By combining the multi-modal synchrotron approach and computational work, this study provides a framework for studying a broader range of electrochemically driven phase-transformation systems towards advanced energy storage and conversion applications.

25 ENERGY STORAGE↗

The triaxial particle plus rotor model and wobbling mode: A semiclassical view

A systematic analysis of the triaxial particle rotor model with single-j shell configuration is carried out to explain the prominent features of observed wobbling excitations in odd A nuclei. The equations of motion for the angular momentum vectors I-vector and j-vector generate two types of equilibrium (i.e., (i) the axes aligned and (ii) the planar) states. The planar equilibrium states involve mainly the orientation degree of freedom {gamma} and their Jacobian matrix J gives purely imaginary eigenvalues in conjugate pairs. Also, our dynamical results show a substantial projection of angular momentum vectors on all the three principal axes, which implies that the resultant angular momentum lies outside the planes of three axes. Both these signatures confirm the spontaneous breakdown of time reversal (T) plus rotation by 180 deg. (R{sub {pi}}) i.e., R{sub {pi}T} symmetry and as a result nearly two identical bands consisting of even and odd spins emerge. We have tested our dynamical formalism for the wobbling mode observed in {sup 163}Lu.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A new TriBeam system for three-dimensional multimodal materials analysis

The unique capabilities of ultrashort pulse femtosecond lasers have been integrated with a focused ion beam (FIB) platform to create a new system for rapid 3D materials analysis. The femtosecond laser allows for in situ layer-by-layer material ablation with high material removal rates. The high pulse frequency (1 kHz) of ultrashort (150 fs) laser pulses can induce material ablation with virtually no thermal damage to the surrounding area, permitting high resolution imaging, as well as crystallographic and elemental analysis, without intermediate surface preparation or removal of the sample from the chamber. The TriBeam system combines the high resolution and broad detector capabilities of the DualBeam{sup TM} microscope with the high material removal rates of the femtosecond laser, allowing 3D datasets to be acquired at rates 4-6 orders of magnitude faster than 3D FIB datasets. Design features that permit coupling of laser and electron optics systems and positioning of a stage in the multiple analysis positions are discussed. Initial in situ multilayer data are presented.

36 MATERIALS SCIENCE↗

Experimental and modeling study of chemical-based strategies for mitigating dust formation in fusion reactors [Plasma Flow Reactor Chemical Kinetics: A Method Toward Optimizing Nano-Manufacturing and Laser Inertial Fusion Energy Strategies]

We studied carbon/hydrogen/oxygen chemical kinetics at time scales and thermal conditions relevant to fusion energy applications using a custom-built plasma flow reactor to investigate chemical-based strategies for eliminating carbon dust formation in fusion reactors. Acetylene and oxygen gases under varying conditions of initial concentrations are injected into an inductively coupled argon plasma where complete molecular dissociation occurs. The evolution of chemical species is investigated along the plasma flow reactor as a function of temperature and residence time. Atomized species of C, H, and O cool from 5000 K to 1000 K within 30 ms at atmospheric pressures. We employed optical emission and infrared absorption spectroscopy to measure the reaction intermediates (e.g. C 2 ) and products (e.g. C 2 H 2 ). Chemical equilibrium models are inadequate to describe the evolution of carbon molecular products, and thus a chemical kinetics model is developed. In both experiments and kinetic modelling, we find that the addition of oxygen in 1:1 proportion to carbon strongly favors the formation of CO, preventing the formation of acetylene (an important soot precursor) in less than 10 milliseconds. The kinetics model is also used to perform a reaction sensitivity and a rate of production analyses to identify the rate determining steps and the major chemical pathways that control the acetylene production/consumption. The results demonstrate the feasibility of chemical-based strategies for eliminating the formation of carbonaceous particles in fusion energy reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Positronium formation for positron scattering from hydrogen: Maximum positions and scaling law

Ground- and excited-state positronium (Ps) formation from the hydrogen atom by positron impact at low and intermediate energies have been studied within the framework of two-center two-channel eikonal final state-continuum initial distorted wave model. A general method for obtaining Ps formation into arbitrary final states has been derived. The present results of Ps (1s), Ps (n=2), and total Ps formation cross sections agree very well with previous close-coupling calculations and experimental measurements. The maximum positions of Ps(n) formation cross sections are found to be in good agreement with the prediction of wave vector matching model introduced by Charlton [J. Phys. B: At. Mol. Opt. Phys. 39, 4575 (2006)]. We also present a scaling law for Ps (n) formation cross sections that is valid for all n in the entire energy range.

74 ATOMIC AND MOLECULAR PHYSICS↗

Linkages between terrestrial ecosystems and the atmosphere

The primary research issue in understanding the role of terrestrial ecosystems in global change is analyzing the coupling between processes with vastly differing rates of change, from photosynthesis to community change. Representing this coupling in models is the central challenge to modeling the terrestrial biosphere as part of the earth system. Terrestrial ecosystems participate in climate and in the biogeochemical cycles on several temporal scales. Some of the carbon fixed by photosynthesis is incorporated into plant tissue and is delayed from returning to the atmosphere until it is oxidized by decomposition or fire. This slower (i.e., days to months) carbon loop through the terrestrial component of the carbon cycle, which is matched by cycles of nutrients required by plants and decomposers, affects the increasing trend in atmospheric CO2 concentration and imposes a seasonal cycle on that trend. Moreover, this cycle includes key controls over biogenic trace gas production. The structure of terrestrial ecosystems, which responds on even longer time scales (annual to century), is the integrated response to the biogeochemical and environmental constraints that develop over the intermediate time scale. The loop is closed back to the climate system since it is the structure of ecosystems, including species composition, that sets the terrestrial boundary condition in the climate system through modification of surface roughness, albedo, and, to a great extent, latent heat exchange. These separate temporal scales contain explicit feedback loops which may modify ecosystem dynamics and linkages between ecosystems and the atmosphere. The long-term change in climate, resulting from increased atmospheric concentrations of greenhouse gases (e.g., CO2, CH4, and nitrous oxide (N2O)) will further modify the global environment and potentially induce further ecosystem change. Modeling these interactions requires coupling successional models to biogeochemical models to physiological models that describe the exchange of water, energy, and biogenic trace gases between the vegetation and the atmosphere at fine time scales. There does not appear to be any obvious way to allow direct reciprocal coupling of atmospheric general circulation models (GCM's), which inherently run with fine time steps, to ecosystem or successional models, which have coarse temporal resolution, without the interposition of physiological canopy models. This is equally true for biogeochemical models of the exchange of carbon dioxide and trace gases. This coupling across time scales is nontrivial and sets the focus for the modeling strategy.

Bretherton, Francis↗

H-cluster Intermediates and Catalytic Properties of Clostridium pasteurianum [FeFe]-Hydrogenase III

[FeFe]-Hydrogenases are structurally diverse enzymes that catalyze reversible H2 activation at a catalytic cofactor or H-cluster. The H-cluster is a [4Fe-4S] cubane linked by a cysteine thiolate to a diiron subsite containing unique CO, CN-, and dithiomethylamine ligands. The established H-cluster resting state of [4Fe-4S]2+-[FeII-FeI], or Hox, functions in H2 binding and oxidation, or by proton-coupled reduction initiates H2 evolution. In contrast, in Clostridium pasteurianum [FeFe]-hydrogenase III (CpIII) the resting state of the H-cluster is fully oxidized, [4Fe-4S]2+-[FeII-FeII], or Hox+1. To begin to understand if Hox+1 has a role in the mechanism of CpIII, we determined the spectroscopic and redox properties of CpIII H-cluster states under catalytic conditions. CpIII poised in Hox+1 and either equilibrated under 1 atm of H2 or reduced with sodium dithionite, resulted in a mixture of reduced states including Hox (Em8 = -407 mV), Htrans-like [4Fe-4S]+-[FeII-FeII] (Em8 = -418 mV), Hred [4Fe-4S]+-[FeII-FeI], and HredH+ [4Fe-4S]2+-[FeI-FeI] (Em8 = -455-480 mV). Under H2 the population of the Htrans-like state was >20-fold higher than Hox, implicating a role in CpIII catalysis. Unlike other enzymes, there was no spectral evidence of fully reduced states, such as HsredH+ ([4Fe-4S]+-[FeI-FeI]) or Hhyd ([4Fe-4S]+-[FeII-FeII]-H-). Thus, while the H-cluster states of CpIII encompass most of the catalytic intermediates, it is either unable to form HsredH+ and Hhyd, or these states are highly destabilized in CpIII. Thus, these results demonstrate that catalytic intermediates of reduced CpIII differ from the typical intermediates of other catalytic [FeFe]-hydrogenases and may explain the catalytic preference for H2 production.

08 HYDROGEN↗

Consequences of Different Air-Sea Feedbacks on Ocean Using MITgcm and MERRA-2 Forcing: Implications for Coupled Data Assimilation Systems

Ocean surface flux estimates from atmospheric and oceanic reanalyses contain errors that compensate for inaccuracies in the respective atmosphere and ocean models used to generate these reanalyses. A conundrum for climate studies is the discrepancy between surface fluxes that minimize model-data differences for an atmosphere-only model vs surface fluxes that minimize model-data differences for an ocean model. As a first step towards a consistent coupled ocean-atmosphere data-assimilation (DA) system, we compare surface net heat flux from a state-of-the-art atmospheric reanalysis, the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), to net heat flux from a state-of-the-art ocean state estimate, the Estimating the Circulation and Climate of the Ocean Version 4 (ECCO-v4). The possible impacts of the MERRA-2 and ECCO-v4 air-sea net heat flux difference in a coupled DA system were assessed using a set of experiments designed to imitate different “flavors” of a coupled DA system in an ocean-only setup. This was done by forcing the ECCO-v4 underlying ocean model - the Massachusetts Institute of Technology general circulation model (MITgcm) - with different sets of MERRA-2 fields and utilizing different forcing methods. By doing so we were able to turn off different air-sea feedbacks which, in a coupled DA setup, are partially muted by the constraining observations. The set of experiments, therefore, represents a range of active feedbacks in different “flavors” of coupled data-assimilation systems. For the period 1992–2011, MERRA-2 net heat flux has a global mean difference of -4.9 Wm(exp -2) relative to ECCO-v4. When MERRA-2 surface fields are used to force MITgcm, imbalances in the energy and the hydrological cycles of MERRA-2, which are directly related to the fact that MERRA-2 was created without an interactive ocean, propagate to the ocean. The experiment in which MITgcm is forced with MERRA-2 fluxes (MERRA-2-flux experiment) results in a 2.5°C global mean Sea Surface Temperature (SST) cooling, a 1m reduction in global mean sea level, and other drastic changes in the large scale ocean circulation relative to those resulting when the MITgcm is forced with the optimized ECCO-v4 net heat flux (the ECCO-v4 experiment itself). When MITgcm is forced with MERRA-2 state variables (MERRA-2-state experiment), the SST is somewhat restored to the observed SST, but the errors are shifted to the water cycle, resulting in a global mean sea level increase of 2.7 m. To further explore the pros and cons of these two approaches, we introduce a new intermediate forcing method in which the ocean is forced with turbulent fluxes but has a long wave feedback. This method, unlike MERRA-2 state, preserves the MERRA-2 water and salinity cycles, and it reduces the SST error compared to the MERRA-2-flux experiment, but the SST is not as good as that in the MERRA-2-state experiment. Our results have implications for ocean-model forcing recipes and clearly reveal the undesirable consequences of limiting the feedbacks in either these types of experiments or in coupled DA.

Ehud Strobach↗

Phase diagram of the lattice G{sub 2} Higgs model

We study the phases and phase transition lines of the finite temperature G{sub 2} Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms, and susceptibilities. On smaller lattices we calculate the phase diagram in terms of the inverse gauge coupling {beta} and the hopping parameter {kappa}. For {kappa}{yields}0 the model reduces to G{sub 2} gluodynamics and for {kappa}{yields}{infinity} to SU(3) gluodynamics. In both limits the system shows a first order confinement-deconfinement transition. We show that the first order transitions at asymptotic values of the hopping parameter are almost joined by a line of first order transitions. A careful analysis reveals that there exists a small gap in the line where the first order transitions turn into continuous transitions or a crossover region. For {beta}{yields}{infinity} the gauge degrees of freedom are frozen and one finds a nonlinear O(7) sigma model which exhibits a second order transition from a massive O(7) symmetric to a massless O(6) symmetric phase. The corresponding second order line for large {beta} remains second order for intermediate {beta} until it comes close to the gap between the two first order lines. Besides this second order line and the first order confinement-deconfinement transitions we find a line of monopole-driven bulk transitions which do not interfere with the confinement-deconfinment transitions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Targeted Metabolomics of the Phenylpropanoid Pathway in Arabidopsis thaliana using Reversed Phase Liquid Chromatography Coupled with Tandem Mass Spectrometry: Measuring Lignin Precursors by LC-MS

The phenylpropanoid pathway is a source of a diverse group of compounds derived from phenylalanine, many of which are involved in lignin biosynthesis and serve as precursors for the production of valuable compounds, such as coumarins, flavonoids, and lignans. Consequently, recent efforts have been invested in mechanistically understanding monolignol biosynthesis, making the quantification of these metabolites vital. To develop an improved and comprehensive analytical method for (i) extensively profiling, and (ii) accurately quantifiying intermediates of the monolignol biosynthetic network, using Arabidopsis thaliana as a model system. A liquid chromatography-tandem mass spectrometry with electrospray ionization was developed to quantify phenylpropanoid metabolites in Arabidopsis wildtype and cinnamoyl CoA reductase1 (CCR1) deficient lines (ccr1). Vortexing at high temperatures (65°C) enhanced release of phenylpropanoids, specifically the more hydrophobic compounds. A pH of 5.3 and ammonium acetate buffer concentration of 2.5 mM resulted in an optimal analyte response across standards. Ion suppression was estimated using standard spike recovery studies for accurate quantitation. The optimized method was used to profile Arabidopsis wildtype and ccr1 stems. An increase in hydroxycinnamic acid derivatives and a decrease in the hydroxycinnamyl aldehydes and alcohols in ccr1 lines, supports a shift of flux from lignin synthesis to other secondary metabolites and phenylpropanoid derivatives. Compared to existing targeted profiling techniques, our method is capable of quantifying a wider range of intermediates (15 out of 22 in WT Arabidopsis stems) at low in vivo concentrations (~50 pmol/g-FW for certain compounds), while requiring minimal sample preparation.

09 BIOMASS FUELS↗

Pressure-Induced Diels-Alder Reactions in C 6 H 6 -C 6 F 6 Cocrystal towards Graphane Structure

Pressure-induced polymerization (PIP) of aromatics is a novel method to construct sp 3 -carbon frameworks, and nanothreads with diamond-like structures were synthesized by compressing benzene and its derivatives. Here, by compressing benzene-hexafluorobenzene cocrystal (CHCF), we identified H-F-substituted graphane with a layered structure in the PIP product. Based on the crystal structure determined from the in situ neutron diffraction and the intermediate products identified by the gas chromatography-mass spectrum, we found that at 20 GPa CHCF forms tilted columns with benzene and hexafluorobenzene stacked alternatively, which leads to a [4+2] polymer, and then transfers to short-range ordered hydrogenated-fluorinated graphane. The reaction process contains [4+2] Diels-Alder, retro-Diels-Alder, and 1-1' coupling, and the former is the key reaction in the PIP. In conclusion, our studies confirmed the elemental reactions of the CHCF for the first time, which provides a novel insight into the PIP of aromatics.

36 MATERIALS SCIENCE↗

Multiple Reaction Pathways for the Oxygen Evolution Reaction May Contribute to IrO 2 (110)’s High Activity

Density functional theory calculations in conjunction with statistical mechanical arguments are performed on the rutile IrO 2 (110) facet in order to characterize multiple reaction pathways on the surface at the highest active limit (the stoichiometric surface with all metal sites available) and at the lowest active limit (the oxygen-terminated surface). Alternative pathways to the oxygen evolution reaction (OER) are found, with multiple pathways determined at each step of the four proton-coupled electron transfer reaction. Of particular interest is the detailed characterization of a co-adsorption pathway utilizing neighboring, adsorbed O, OH species in order to evolve oxygen; activation energies of this pathway are <0.5 eV and therefore easily surmountable at the high operating potentials of OER. We also determined that surface Ir atoms can potentially participate in deprotonating an OOH* intermediate; the activation energy to this is 0.67 eV on the oxygen-terminated surface. These theoretical findings explain in part the high activity present in iridium oxide catalysts and also provide insight into the mechanistic pathways available on metal oxide catalysts, which may require the concerted interaction of nearest neighbor co-adsorbates to produce chemicals of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Korte, John J.↗