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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Gas density structure of supersonic flows impinged on by thin blades for laser-plasma accelerator targets

Density transition injection is an effective technique for controllably loading electrons into a trapped phase for laser plasma accelerators. One common technique to achieve the required fluid structure is to impinge a thin blade on the plume of a supersonic nozzle. Density transitions induced in this way are often assumed to be bow shocks and therefore sharp, but simulations and fluorescence measurements presented in this work show that in many cases of interest, the density transition accessible to a laser propagating transverse to the shock is an intercepting shock, and therefore, shock thickness and density vary with pressure, laser height, and blade position. The fluid dynamics of a supersonic nozzle impinged on by a thin, flat object are explored through simulations and relevant features are verified via planar laser-induced fluorescence measurements. Overall, the implications of the results for tuning electron beam injectors in laser plasma accelerators are discussed.

42 ENGINEERING↗

Atomic kinetics of laboratory photoionized plasmas relevant to astrophysics. Final report

The major goal of this project was to study the atomic and radiation physics of photoionized plasmas driven by a broadband x-ray flux and its impact on plasma x-ray heating and ionization, emissivity and opacity, and radiation-hydrodynamics. This problem is relevant to the physics of accretion disks surrounding black holes, x-ray binaries, and active galactic nuclei in astrophysics. In addition, it is also important for understanding non-equilibrium laboratory plasmas driven by a distribution of photons. To this end, and motivated by previous and ongoing gas-cell experiments performed by the PI at the Z facility of Sandia National Laboratories, we developed a new experimental platform at the 1MA Zebra pulsed power accelerator of the University of Nevada, Reno based on using a gas jet produced by a supersonic nozzle. The gas jet is turned into a photoionized plasma driven by the x- ray flux from a wire-array z-pinch. Establishing this new experimental platform at Zebra was a major goal of this project. In addition, we have also dedicated effort to continue complementary experiments at the Z facility using the gas-cell photoionized plasma set up with support from the Fundamental Science Program at Z as well as to perform data processing and analysis, and theory and modeling simulations, including electron kinetics and radiation-hydrodynamics. Since we seek to test and establish what physics models are needed to describe photoionized plasma guided by experimental observation, these complementary experimental efforts were central to achieving the goals of this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cooperative Research and Development Agreement between National Energy Technology Laboratory and Princeton University (Abstract)

The National Energy Technology Laboratory (NETL) and Princeton University will collaborate in the development of microwave-plasma technology to convert methane into hydrogen and valuable solid carbon materials. The effort will combine NETL’s vast resources for microwave-enhanced process development, characterization, and design with Princeton University’s extensive expertise in the study of non-equilibrium plasmas employing supersonic nozzles. Lab-scale experiments will be conducted for different conditions to convert and compare their respective performance in hydrogen production. Computational modeling will be performed to verify results from experimental studies conducted in both labs.

08 HYDROGEN↗

Validation of predictive performance models for supersonic gas-jet nozzles at the Laboratory for Laser Energetics

We present results characterizing the neutral-density distributions produced by the supersonic nozzles used in experiments on the OMEGA-60 and OMEGA-EP laser systems at the University of Rochester’s Laboratory for Laser Energetics (LLE). Axisymmetric Fluent® simulations using LLE nozzle specifications capture the viscous effects, gas expansion, and shock waves that complicate flow predictions for offsets above the nozzle exit. Here, these simulations show good agreement with neutral-density measurements obtained using a four-wave shearing interferometer. An analytical form is given for the plateau length. Fits to simulation data for boundary layer thickness, mean plateau density, and density ramps are given as functions of nozzle offset and nozzle backing pressure for a number of nozzles and gases.

47 OTHER INSTRUMENTATION↗

Effect of Nozzle Curvature on Supersonic Gas Jets Used in Laser-Plasma Acceleration

Supersonic gas jets produced by converging-diverging (C-D) nozzles are commonly used as targets for laser-plasma acceleration (LPA) experiments. A major point of interest for these targets is the gas density at the region of interaction where the laser ionizes the gas plume to create a plasma, providing the acceleration structure. Tuning the density profiles at this interaction region is crucial to LPA optimization. A "flat-top" density profile is desired at this line of interaction to control laser propagation and high energy electron acceleration, while a short high-density profile is often preferred for acceleration of lower-energy tightly-focused laser-plasma interactions. A particular design parameter of interest is the curvature of the nozzle's diverging section. We examine three nozzle designs with different curvatures: the concave "bell", straight conical and convex "trumpet" nozzles. We demonstrate that, at mm-scale distances from the nozzle exit, the trumpet and straight nozzles, if optimized, produce "flat-top" density profiles whereas the bell nozzle creates focused regions of gas with higher densities. An optimization procedure for the trumpet nozzle is derived and compared to the straight nozzle optimization process. We find that the trumpet nozzle, by providing an extra parameter of control through its curvature, is more versatile for creating flat-top profiles and its optimization procedure is more refined compared to the straight nozzle and the straight nozzle optimization process. Furthermore, we present results for different nozzle designs from computational fluid dynamics (CFD) simulations performed with the program ANSYS Fluent and verify them experimentally using neutral density interferometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Air resonance enhanced multiphoton ionization tagging velocimetry

Air resonance enhanced multiphoton ionization (REMPI) tagging velocimetry (ART) was demonstrated in quiescent and supersonic flows. The ART velocimetry method utilizes a wavelength tunable laser beam to resonantly ionize molecular oxygen in air and generate additional avalanche-type ionization of molecular nitrogen. The fluorescence emissions from the first negative and first positive bands of molecular nitrogen are, thus, produced and used for flow tagging. Detailed characterization of ART was conducted, including the effects of oxygen resonance to fluoresce nitrogen, nitrogen fluorescence spectrum, laser energy deposition into quiescent flow showing minimal perturbations in flow, fluorescence lifetime study at various pressures, and line tagging without breakdown. Pointwise velocity measurements within a supersonic flow from a nominal Mach 1.5 nozzle have been conducted and characterized.

Clark, Aleksander↗

Comparative analysis of characteristics of a supersonic cw chemical HF laser on molecular fluorine and nitrogen trifluoride

We have experimentally studied the characteristics of a supersonic cw chemical HF laser with a flat nozzle array based on a nozzle – nozzle reagent mixing scheme operating with the use of F{sub 2} – D{sub 2} – He and NF{sub 3} – D{sub 2} – He fuel compositions in an atomic fluorine generator. The active medium flow field pattern, its gas-dynamic characteristics, and the laser radiation spectrum are considered. The comparison of these characteristics has made it possible to establish a strong impact on the flow field (lasing zone length) of the chemical composition of the combustion products from the atomic fluorine generator. The gas-dynamic parameters of the active medium formed by using a NF{sub 3} – D{sub 2} – He fuel have turned out to be less acceptable in terms of the gas flow pressure recovery than in the case of F{sub 2} – D{sub 2} – He fuel, while the radiation spectrum was more preferable from the viewpoint of passing through the atmosphere. (paper)

36 MATERIALS SCIENCE↗

Multidimensional Modeling of Mixture Formation in a Hydrogen-Fueled Heavy-Duty Optical Engine With Direct Injection

Hydrogen (H 2 ), as a carbon-free fuel, is considered as one of the most promising solutions to reduce the carbon footprint of hard-to-decarbonize energy and transportation sectors. As such, hydrogen-fueled internal combustion engines (H 2 ICEs) have recently been receiving increasing attention, particularly in applications such as on-road/off-road heavy-duty transport and combined heat and power. The direct injection (DI) of gaseous hydrogen into the combustion chamber offers great potential for achieving high power density and high engine efficiency, while mitigating the risk of backfire and reducing pre-ignition. However, the numerical simulation of H 2 DI system remains a formidable challenge associated with the high computational cost of reproducing compressible supersonic flow and shocks in narrow injector passages and in near-nozzle regions. In general, there is a lack of well-established and validated practices for the modeling of high-pressure H 2 DI in large-bore engines. Here, to this end, this study focuses on computational fluid dynamics (CFD) modeling of the mixture formation process in a heavy-duty optical engine employing a medium-pressure H 2 DI system. Both large eddy simulations (LES) and Reynolds Averaged Navier–Stokes (RANS) simulations are performed and evaluated against optical data. Gaseous hydrogen is injected into the combustion chamber via a centrally located outward opening hollow-cone injector at a pressure of 40 bar. Simulations are carried out for two injection timings, namely, −120 and −60 °CA. The numerical predictions for H 2 distribution in different horizontal and vertical planes during the compression stroke are systematically compared against optical data obtained through planar laser-induced fluorescence (PLIF) measurements. Overall, the LES approach using the Dynamic Structure model is found to have good predictive capabilities for the early jet penetration in terms of length and shape, as well as the later H 2 distributions. However, the unsteady RANS approach with the renormalization group $k - ϵ$ model, which is widely used by industry to model heavy-duty ICEs, significantly underpredicts the H 2 mixing, even at similar mesh resolution to that used in LES. These results indicate that there is a need for the improvement of mixing submodels within the RANS approach when applied to H 2 DI simulations.

LES↗

High-resolution rovibrational spectroscopy of trans -formic acid in the v 1 OH stretching fundamental: Dark state coupling and evidence for charge delocalization dynamics

High-resolution infrared (IR) reduced-Doppler absorption spectra of jet-cooled gas phase trans-formic acid in the v 1 OH stretching fundamental region are reported for the first time, obtained by supersonically expanding trans- formic acid/Ar mixtures through a slit jet nozzle source and rotationally cooling to T rot ≈ 10.9(5) K, with ab- sorption signals recorded by high-resolution difference-frequency IR absorption spectroscopy. Two a/b-type rovibrational bands of comparable intensity, one ~10-fold weaker b-type band, and one ~6-fold weaker a-type band are observed, with vibrational band origins at 3570.493(5), 3566.793(5), 3560.032(9), and 3534.6869(2) cm –1 , respectively. Based on previous Raman jet spectroscopic work by Nejad and Sibert [A. Nejad, E.L. Sibert III, The Raman jet spectrum of trans-formic acid and its deuterated isotopologs: Combining theory and experi- ment to extend the vibrational database, J. Chem. Phys. 154(6) (2021) 064301.], these four rovibrational bands have been assigned to v 1 , (v 2 + v 7 ), (v 6 + 2v 7 + 2v 9 ), and 2v 3 , respectively. Specifically, two of the three upper dark states (2 1 7 1 (a') and 6 1 7 2 9 2 (a')) are close enough to the “bright” 1 1 (a') state to facilitate strong anharmonic resonance interactions, which results in intensity mixing into the two zero-order bands that would otherwise be “dark”. Furthermore, our high-resolution spectral analysis reveals that there are local rotational crossings be- tween these zero-order 1 1 and 2 1 7 1 states resulting in extra lines (i.e., some upper levels in the nominally v 1 band have majority zero-order 2 1 7 1 state character). This motivates development of a 3 coupled state (1 1 , 2 1 7 1 , and 6 1 7 2 9 2 ) picture to aid in the spectral analysis, which is able to match all 3 observed band origins and relative band intensities, as well as indicate the necessity of multistate (> 2) coupling. Though limited by range of J and Ka levels (J’ ≤ 9 and K a ’ ≤ 3) populated at supersonic jet temperatures, this work offers first precision spec- troscopic analysis of trans-formic acid in the v 1 OH stretch region, which should aid in assignment of the more complete yet highly congested room temperature FTIR spectra. Lastly, and in sharp contrast to the spectral complexity in the three predominantly b-type bands, the lone a-type 2v 3 rovibrational band at 3534.6869(2) cm –1 is well described by a simple, rigid asymmetric top Hamiltonian.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficiency of using nitrogen trifluoride as an oxidiser in a supersonic continuous-wave chemical HF laser

We report the results of an experimental study of possible ways to increase the efficiency of using NF{sub 3} nitrogen trifluoride as an oxidiser in an atomic fluorine generator of a supersonic continuous-wave chemical HF laser with a flat nozzle block corresponding to the nozzle – nozzle reagent mixing scheme. As such ways, we consider increasing the residence time of reagents in the combustion chamber and rising temperature in the chemical reaction zone. Comparison of specific energy characteristics of an HF laser operating with the use of the studied (NF{sub 3}) and ‘basic’ (F{sub 2}) oxidisers shows that the replacement of molecular fluorine with nitrogen trifluoride during the burning with deuterium in the combustion chamber of an atomic fluorine generator with allowance for the proposed measures leads to a reduction in the specific laser energy output by no more than 23 % – 24 % at high burning completeness. (paper)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Broadband Rotational Spectroscopy in Uniform Supersonic Flows: Chirped Pulse/Uniform Flow for Reaction Dynamics and Low Temperature Kinetics

ConspectusThe study of gas-phase chemical reactions at very low temperatures first became possible with the development and implementation of the CRESU (French acronym for Reaction Kinetics in Uniform Supersonic Flows) technique. CRESU relies on a uniform supersonic flow produced by expansion of a gas through a Laval (convergent-divergent) nozzle to produce a wall-less reactor at temperatures from 10 to 200 K and densities of 1016-1018 cm-3 for the study of low temperature kinetics, with particular application to astrochemistry. In recent years, we have combined uniform flows with revolutionary advances in broadband rotational spectroscopy to yield an instrument that affords near-universal detection for novel applications in photodissociation, reaction dynamics, and kinetics. This combination of uniform supersonic flows with chirped-pulse Fourier-transform microwave spectroscopy (Chirped-Pulse/Uniform Flow, CPUF) permits detection of any species with a modest dipole moment, thermalized to the uniform temperature of the gas flow, with isomer, conformer, and vibrational state specificity. In addition, the use of broadband, high-resolution, and time-dependent (microsecond time scale) micro- and mm-wave spectroscopy makes it an ideal tool for characterizing both transient and stable molecules, as well as studying their spectroscopy and dynamics.In this Account, we review recent advances made using the CPUF technique, including studies of photodissociation, radical-radical reaction dynamics, and low temperature kinetics. These studies highlight both the strength of universal and multiplexed detection and the challenges of coupling it to a high-density collisional environment. Product branching and product evolution as a function of time have been measured for astrochemically relevant systems, relying on the detailed characterization of these flow conditions via experiments and fluid dynamics simulations. In the photodissociation of isoxazole, an unusual heterocyclic molecule with a very low-energy conical intersection, we have identified 7 products in 5 reaction channels and determined the product branching, pointing to both direct and indirect pathways. We have also approached the same system from separated NO and C3H3 reactants to explore a broader range of the potential energy surface, demonstrating the power of multichannel branching measurements for complex radical-radical reactions. We determined the product branching in the C3H2 isomers in the photodissociation of the propargyl radical and identified the importance of a hydrogen atom catalyzed isomerization to the lowest energy cyclic form. This then motivated a study of direct D-H exchange reaction in radicals, in which we demonstrate that it is an important and overlooked pathway for deuterium fractionation in astrochemical environments. Recently, we have shown the measurement of low temperature kinetics inside an extended Laval nozzle, after which a shock-free secondary expansion to low temperature and density affords an ideal environment for detection by rotational spectroscopy. These results highlight the power and potential of the CPUF approach, and future prospects will also be discussed in light of these developments.

Dias, Nureshan↗

Near-field acoustical holography and acoustic power analysis of a simulated, highly heated supersonic jet

Although near-field acoustical holography (NAH) and acoustic intensity analysis have previously been used to investigate the apparent jet noise sources produced by military aircraft, explicit connections to supersonic jet characteristics cannot be made due to a lack of information about the exhaust plume. Here, to begin to bridge this gap and better understand the source information yielded by NAH, the current study instead applies NAH to a virtual measurement of the near-field pressures of a highly heated laboratory-scale supersonic jet generated by large-eddy simulation (LES). The holographic reconstructions of the pressure, particle velocity, and acoustic intensity are found to match the LES-generated acoustic field well and are used to calculate the acoustic power of the jet. The jet's calculated overall acoustic power is compared to the free-stream mechanical power, resulting in an acoustic efficiency of 1.5%. Ray-tracing of the acoustic intensity to the jet centerline generates an axial distribution of the acoustic power origin, showing that almost all the power originates from the supersonic portion of the flow and with the distribution peak upstream of the potential core tip. Holographic reconstruction of the pressures along the nozzle lipline captures the general spectral shape of the LES-generated pressures, though it underestimates the amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exploration of Water Jets in Supersonic Crossflow Using X-Ray Diagnostics

Here, near-field structures of pure- and aerated-liquid jets injected into Mach 2 crossflow environments were experimentally investigated at the 7-BM beamline of the Advanced Photon Source at Argonne National Laboratory using high-speed shadowgraph imaging, high-speed x-ray imaging, and pathlength-integrated x-ray fluorescence. Liquid was flush injected into a blowdown supersonic wind tunnel. Test section top and side windows were fitted with a polycarbonate plate for high x-ray transmittance. An axisymmetric aerated-liquid injector was fitted with an exchangeable nozzle adaptor to generate a liquid jet. Water and nitrogen, the gas used for aerated-liquid jets, were doped with specially selected dopants to facilitate x-ray measurements. Liquid column structures for a pure-liquid jet, typically masked by dense droplet clouds in a supersonic crossflow environment, were visualized with the present x-ray imaging setup. Surface-wave formation, movement, and transformation on the column windward surface of the pure-liquid jet, along with column deformation and breakup processes, were qualitatively characterized. We measured time-averaged line-of-sight (LOS) liquid mass distributions within the liquid jet near fields. Cross-sectional liquid column contours of pure-liquid jets at various deformation stages were reconstructed from LOS liquid mass distributions. The pure-liquid jet deformed liquid column reached a maximum width of 1.47 times the orifice diameter before exhibiting rapid mass removal. We also observed the plume-crossing phenomenon in the aerated-liquid jet.

47 OTHER INSTRUMENTATION↗

Particle Image Velocimetry and Total Temperature Characterization of Arc-Heated Mach 4.5 Free Jet

Particle image velocimetry (PIV) measurements were conducted in the Arc-Heated Combustion Tunnel (ACT-II) on a high-enthalpy Mach 4.5 nozzle flow. The primary motivation for the current work is to establish the feasibility of PIV as a high-quality flow diagnostic technique in hypersonic arc-heated flows and produce a high-resolution hypersonic nozzle flow characterization, including nozzle free jet shear layer velocity profiles. Due to the uncertain nature of the gas composition in the flowfield of interest, PIV measurements of a supersonic wedge flow were used to couple the flow velocities to the oblique shock relations. This enabled a PIV-derived total temperature calculation that does not require a priori assumptions of the exact gas composition. A PIV expansion module was developed for this study, and proper seed sizing and material were selected for the present flow. An analysis of the seed particle response from the PIV measurements provided an initial validation of the seed performance while revealing potential issues with consistent seed sizing. These measurements and derived conditions represent a means of acquiring high-resolution velocimetry and temperature datasets that consider uncertainties in the experimental generation of hypersonic high-enthalpy flows.

Engineering↗

Dynamic separation of gases using microsieves

Separation of light weight molecules, such as nitrogen, argon, and oxygen, from heavier compounds can have significant impacts on energy capture, environmental monitoring, or isotopic applications. Large-scale gas separation techniques, like gas centrifugation and membrane mitigation, can be problematic as they impart tremendous energy and induce high mechanical stress onto the instrumentation. Microsieves, also known as micronozzles or microfunnels, are developed to create physical barriers to separate specific isotopes and gases. Separation is achieved using a converging and diverging micronozzle to impose supersonic gas flow around a curved wall, and it has been used for the separation of heavy actinide isotopes in low weight gas as well as separation of low weight gas compositions of nitrogen and argon back in 1900s. However, systematic reviews of this unique technology are lacking. The application of the Laval style nozzle, which has a converging/diverging entrance fundamental to the micronozzle, is included in this review due to its importance in industrial applications in uranium (U) isotope refinement. Using advanced computational fluid dynamic (CFD) simulations, the extent of gas separation can be modelled. Herein, we first examine the literature and survey recent advances on fabrication techniques for creating curved micronozzles, methods and separation principles used to design devices. Furthermore, we then follow with highlights of CFD simulations applied to evaluate the separation effects using microsieves. Finally, identification of the gap and recommendation for future development and applications are suggested for using intrinsic molecular features and fluidic dynamics in formulating separation strategies.

30 Microfluidics↗

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen–Air Rotating Detonation Combustor-Stator Integrated System

In the present work, a first-of-its-kind three-dimensional (3D) large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale nonpremixed hydrogen–air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen–air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the rotating detonation engine-nozzle guide vanes (RDE-NGV) configuration exhibits higher total pressure loss compared to rotating detonation engine (RDE) without stator across both the mass flux conditions. In conclusion, this study extends the state-of-the-art in numerical modeling of pressure gain combustion (PGC) systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems relevant to RDE-turbine integration for stationary power generation.

Combustion↗

Magic Numbers and Stabilities of Photoionized Water Clusters: Computational and Experimental Characterization of the Nanosolvated Hydronium Ion

The stability and distributions of small water clusters generated in a supersonic beam expansion are interrogated by tunable vacuum ultraviolet (VUV) radiation generated at a synchrotron. Time-of-flight mass spectrometry reveals enhanced population of various protonated water clusters (H + (H 2 O) $n$ ) based upon ionization energy and photoionization distance from source, suggesting there are "magic" numbers below the traditional $n$ = 21 that predominates in the literature. These intensity distributions suggest that VUV threshold photoionization (11.0-11.5 eV) of neutral water clusters close to the nozzle exit leads to a different nonequilibrium state compared to a skimmed molecular beam. This results in the appearance of a new magic number at 14. Metadynamics conformer searches coupled with modern density functional calculations are used to identify the global minimum energy structures of protonated water clusters between $n$ = 2 and 21, as well as the manifold of low-lying metastable minima. New lowest energy structures are reported for the cases of $n$ = 5, 6, 11, 12, 16, and 18, and special stability is identified by several measures. These theoretical results are in agreement with the experiments performed in this work in that $n$ = 14 is shown to exhibit additional stability, based on the computed second-order stabilization energy relative to most cluster sizes, though not to the extent of the well-known $n$ = 21 cluster. Other cluster sizes that show some additional energetic stability are $n$ = 7, 9, 12, 17, and 19. To gain insight into the balance between ion-water and water-water interactions as a function of the cluster size, an analysis of the effective two-body interactions (which sum exactly to the total interaction energy) was performed. In conclusion, this analysis reveals a crossover as a function of cluster size between a water-hydronium-dominated regime for small clusters and a water-water-dominated regime for larger clusters around $n$ = 17.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗