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NASA NTRS2000

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

NASA NTRS2016

Prebiotic Chemistry and Atmospheric Warming of Early Earth by an Active Young Sun

Nitrogen is a critical ingredient of complex biological molecules. Molecular nitrogen, however, which was outgassed Into the Earth's early atmosphere, is relatively chemically inert and nitrogen fixation into more chemically reactive compounds requires high temperatures. Possible mechanisms of nitrogen fixation include lightning, atmospheric shock heating by meteorites, and solar ultraviolet radiation. Here we show that nitrogen fixation in the early terrestrial atmosphere can be explained by frequent and powerful coronal mass ejection events from the young Sun -- so-called superflares. Using magnetohydrodynamic simulations constrained by Kepler Space Telescope observations, we find that successive superflare ejections produce shocks that accelerate energetic particles, which would have compressed the early Earth's magnetosphere. The resulting extended polar cap openings provide pathways for energetic particles to penetrate into the atmosphere and, according to our atmospheric chemistry simulations, initiate reactions converting molecular nitrogen, carbon dioxide and methane to the potent greenhouse gas nitrous oxide as well as hydrogen cyanide, an essential compound for life. Furthermore, the destruction of N2, C02 and CH, suggests that these greenhouse gases cannot explain the stability of liquid water on the early Earth. Instead, we propose that the efficient formation of nitrous oxide could explain a warm early Earth.

Airapetian, V. S.↗

DOE OSTI2023

Investigating Combinations of Alkali Metal Oxides and Hydrogenation Catalysts for Reactive Capture of CO2 to Useful C1 Products

As the world endures environmental crises associated with climate change and the rise of atmospheric CO2 concentrations from anthropogenic CO2 emission, carbon capture and utilization (CCU) technologies are increasingly necessary. Reactive carbon capture (RCC) technologies, in which capture and conversion of CO2 occur in a single reactor, are more energetically and economically attractive by avoiding the need to purify, compress, and transport the captured CO2. To this end, dual function materials (DFMs) - composed of sorbents and catalysts co-dispersed on the same high surface area carrier - have been developed. The sorbent component allows for selective capture of CO2 from a gas stream and the catalyst component subsequently performs the in-situ conversion of the adsorbed CO2 upon introduction of a reactive gas (typically H2). The end product of the most established DFM, comprised of Ru and/or Ni with an alkaline sorbent, is methane via the CO2 methanation reaction. While renewable methane would be an excellent transition fuel, fossil methane is inexpensive (averaging $2.57/MMBTU in pre-pandemic 2019) and the economics of renewable methane utilization are noncompetitive. This requires the design and investigation of DFMs that enable CO2 capture and conversion to more valuable and more useful C1 products like CO or methanol (average price of methanol was $20.61/MMBTU in pre-pandemic 2019). These products can then be further upgraded to high energy density synthetic fuels, and related carbonaceous products, for more sustainable alternatives in industries that are difficult to decarbonize, specifically heavy duty vehicles and aviation. Herein, we report various sorbent + catalyst combinations to achieve the production of useful C1 products through reactive capture of CO2.

carbon capture↗

DOE OSTI2025

Investigation of the Mechanical Degradation of Zinc-Based Cold Spray Coatings for Steel Pipelines

Internal corrosion in wet natural gas is a big challenge in the oil and gas industry due to corrosive constituents such as carbon dioxide (CO2), hydrogen sulfide (H2S), other forms of sulfur, and water in the gas stream. To mitigate internal corrosion, zinc-based cold spray coatings were designed for use in natural gas pipelines to increase the lifespan of the pipeline network. However, one of the requirements in designing internal coatings is the resistance of the coatings to mechanical forces applied on the pipeline's internal wall during pigging operations. These forces are primarily compressive and shear/friction forces. This study examines material properties that must be considered when evaluating mechanical considerations. To determine the viability of the developed coatings with respect to the shear/friction forces, the shear adhesion and wear resistance of the materials have been evaluated. Shear adhesion testing was performed with modified clevises to determine the shear stress required to cause adhesion failure at the coating/substrate interface. Scanning electron microscopy was utilized to characterize the interfaces after failure. Wear testing was performed on coatings and pipeline materials utilizing pin-on-drum testing. These tests display the stress limitations and wear that the coatings can tolerate from pigging.

mechanical degradation↗

NASA NTRS2016

Modeling and Simulation of Radiative Compressible Flows in Aerodynamic Heating Arc-Jet Facility

Numerical simulations of an arc heated flow inside NASA's 20 [MW] Aerodynamics heating facility (AHF) are performed in order to investigate the three-dimensional swirling flow and the current distribution inside the wind tunnel. The plasma is considered in Local Thermodynamics Equilibrium(LTE) and is composed of Air-Argon gas mixture. The governing equations are the Navier-Stokes equations that include source terms corresponding to Joule heating and radiative cooling. The former is obtained by solving an electric potential equation, while the latter is calculated using an innovative massively parallel ray-tracing algorithm. The fully coupled system is closed by the thermodynamics relations and transport properties which are obtained from Chapman-Enskog method. A novel strategy was developed in order to enable the flow solver and the radiation calculation to be preformed independently and simultaneously using a different number of processors. Drastic reduction in the computational cost was achieved using this strategy. Details on the numerical methods used for space discretization, time integration and ray-tracing algorithm will be presented. The effect of the radiative cooling on the dynamics of the flow will be investigated. The complete set of equations were implemented within the COOLFluiD Framework. Fig. 1 shows the geometry of the Anode and part of the constrictor of the Aerodynamics heating facility (AHF). Fig. 2 shows the velocity field distribution along (x-y) plane and the streamline in (z-y) plane.

Pasma flows↗

DOE OSTI2022

Leaf structural and chemical traits, and BNL field campaign sample details, San Lorenzo, Panama, 2020

This data package includes leaf traits, canopy traits and sample details for leaves from 71 species sampled from the San Lorenzo forest canopy crane site, Panama (PA-SLZ) during the BNL field campaign in January to March 2020. Each leaf sample is described with species, phenological stage and location within vertical canopy profiles. Leaf area index (LAI) and height is presented for each canopy profile location. Leaf mass per area (LMA), leaf water content (LWC) and leaf carbon and nitrogen content are included for a subset of the samples. This data package includes sample details, processed data for leaf traits and LAI (*.csv), LAI raw data (compressed as *.zip) and digital camera images (*.jpg, compressed as *.zip) of the leaf samples. Metadata files include data descriptions (_dd.csv) for tabular data, a list of all species sampled during the campaign (*.csv) and a detailed description of the field campaign protocol and methods (*.pdf). See related datasets for leaf gas exchange, leaf water potential and leaf spectral measurements made on the samples described here.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

The nonlinear breakup of the sun's toroidal field

There are good reasons for believing that the sun has a strong toroidal magnetic field in the stably stratified region of convective overshoot sandwiched between the radiative zone and convective zone proper. The magnetic field in this region is modeled by studying the behavior of a layer of uniform field embedded in a subadiabatic atmosphere. Since the field can support extra mass, such a configuration is top-heavy, and instabilities of the Rayleigh-Taylor type can occur. Numerical integration of the two-dimensional compressible MHD equations makes it possible to follow the evolution of this instability into the nonlinear regime. The initial buoyancy-driven instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The somewhat surprising subsequent motions are determined primarily by the strong interactions between vortices.

Hughes, D. W.↗

NASA NTRSDate not supplied

Scroll Pump Dust Tolerance Test for Martian Atomospheric Acquisition

The ability to generate oxygen on the Martian surface will be essential to establishing a human presence on Mars. Flow generating devices such as pumps, compressors, and blowers will be essential components in Martian atmospheric acquisition and processing systems that need to work reliably during the mission duration. A concern with the reliability of the system is its ability to continue to perform nominally when Martian dust, if it bypasses the inlet filter, enters into the system. A series of tests were conducted to simulate the ingesting of Martian dust on a small scroll pump, similar to the one used on the MOXIE payload, during its pumping operation. The inlet of the pump was connected to a large volume closed-loop pipe system, known as the Mars Atmospheric Flow Loop, containing pure CO2 gas at a Martian pressure of 7 Torr. A length of stainless steel tubing was extended from the inlet port of scroll pump, which was mounted outside the flow loop, to the inside volume of the flow loop using a feed-through compression fitting. A steady low-speed flow was generated inside the flow loop to continuously disperse and transport the dust toward the inlet tubing. JSC-Mars 1 Martian simulant was used to challenge the pump. The pump performance parameters such as flow rate, pump speed, pressures and temperature were monitored during these tests. Samples of the dust entering the pump inlet were taken prior to exposure tests, using an inline filter element to determine the rate of dust ingestion into the internal components of the pump. After two tests with exposure times of the order of 60 minutes, the data indicated that small changes in pump performance took place under high rates of dust exposure.

scroll pump↗

NASA NTRSDate not supplied

Scroll Pump Dust Tolerance Test for Martian Atmospheric Acquisition

The ability to generate oxygen on the Martian surface will be essential to establishing a human presence on Mars. Flow generating devices such as pumps, compressors, and blowers will be crucial components in Martian atmospheric acquisition and processing systems that need to work reliably during the mission duration. A concern with the reliability of the system is its ability to continue to perform nominally when Martian dust, if it bypasses the inlet filter, enters into the system. A series of tests were conducted to simulate the ingestion of Martian dust on a small scroll pump, similar to the one used on the MOXIE payload. The inlet of the pump was connected to a large volume closed-loop pipe system, known as the Mars Atmospheric Flow Loop, containing pure CO2 gas at a Martian pressure of 7 Torr. A length of stainless steel tubing was extended from the inlet port of scroll pump, which was mounted outside the flow loop, to the inside volume of the flow loop using a feed-through compression fitting. A steady low-speed flow was generated inside the flow loop to continuously disperse and transport the dust toward the inlet tubing. JSC-Mars 1 Martian simulant was used to challenge the pump. Pump performance parameters such as flow rate, pump speed, pressure and temperature were monitored during these tests. Samples of the dust entering the pump inlet were taken prior to the exposure tests, using an inline filter element to determine the rate of dust ingestion into the internal components of the pump. After two tests with exposure times of one hour, the data indicated that small changes in pump performance took place under high rates of dust exposure.

Martian Atmospheric↗

DOE OSTI2025

Examining astrophysical gas cloud collapse using an optical depth-scaled, x-ray-irradiated, carbon-foam sphere

When stellar radiation interacts with a molecular cloud, the cloud's fate depends on the strength of the incident radiation and the radiation's mean-free-path within the cloud [F. Bertoldi, Astrophys. J. 346, 735–755 (1989)]. Under the right conditions, the radiation compresses the cloud and a star formation may occur. Where and when the stellar formation occurs in the cloud's collapse are open questions. Direct observation of the complete star–cloud lifecycle is nearly impossible due to the immense timescales and distances over which the interaction occurs. Laboratory astrophysics offers a way to investigate such a system by scaling the important astrophysical parameters to the laboratory. This work describes laboratory experiments to study the radiation-driven implosion of clouds, using x rays from a laser-irradiated, thin, gold foil as a surrogate star and a carbon-foam sphere as a surrogate cloud. An optically thick system, theoretically corresponding to a star-forming regime, was selected by choice of the foam density. Gold foil and sphere motions were imaged by x-ray radiography. Radiographic images show the formation of an interface between rarefied gold and carbon plasmas, a shock moving into the sphere, and a blunting of the initial sphere's shape. Measurements show that the shock moved linearly around 64 μm/ns into the sphere, and the gold–carbon interface formed by 2 ns at the sphere edge remained stationary. The deformation of the sphere was driven by the incident radiation and not by mechanical pressures applied by gold plasma. The blunting of the sphere was likely due to the geometric reduction of flux near the sphere's poles. Higher x-ray flux near the sphere's equator caused high compression and a faster shock, which flattened the sphere. We will discuss the results and implications of our observations.

VanDervort, R. W. [University of Michigan 1 , Ann ↗

NASA NTRS1996

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗

DOE OSTI2020

Investigation of Mixing Law Efficacy for Gaseous Hydrodynamic Simulations

A computational simulation of various mixing laws for gaseous equations of state using planar traveling shocks for multiple mixtures in three dimensions is analyzed against nominal experimental data. Numerical simulations utilize the Sandia National Laboratories shock hydrodynamic code CTH and other codes including the thermochemical equilibrium code TIGER and the uncertainty qualification and sensitivity analysis code DAKOTA. The mixtures are a 1:1 and a 1:3 molar mixture of helium and sulfur hexafluoride. The mixing laws to be analyzed are the ideal gas law, Amagat's Law, Dalton's Law, the BKW EOS, the EXP6 EOS, and the JCZ3 EOS. Examination of the experimental data with TIGER revealed that the shock strength should not be strong enough to turn the mixture non-ideal as the compressibility factor z was essentially unity (z ≈ 1.02). Experimental results show that none of the equations of state are able to accurately predict the properties of the shocked mixture; similar discrepancies have been observed in previous works. Kinetic molecular theory appears to introduce a parameter which offers an explanation regarding the discrepancies. Implementation of the KMT pararneter into the EOS is left for future work.

42 ENGINEERING↗

NASA NTRS1994

The interstellar medium in the starburst regions of NGC 253 and NGC 3256

We discuss observations of the (C II) 158 micrometers, (O I) 63 micrometers, (Si II) 35 micrometers, (O III) 52,88 micrometers, and (S III) 33 micrometers fine-structure transitions toward the central 45 seconds of the starburst galaxies NGC 253 and NGC 3256. The (C II) and (O I) emission probably originates in photodissociated gas at the surfaces of molecular clouds, although a small (less than or approximately 30%) contribution to the (C II) flux from H II regions cannot be ruled out. The (O III) and (S III) lines originate in H II regions and the (Si II) flux is best explained as originating in H II regions with some contribution from photodissociation regions (PDRs). The gas phase silicon abundance is nearly solar in NGC 253, which we interpret as evidence for grain destruction in the starburst region. We find that the photodissociated atomic gas has densities approximately 10(exp 4)/cu cm and temperature 200-300 K. About 2% of the gas is in this phase. The thermal gas pressure in the PDRs, P(PDR)/k approximately 1-3 x 10(exp 6) K/cu cm, might represent the 'typical' interstellar gas pressure in starburst systems. The Far Ultraviolet (FUV) radiation fields illuminating the clouds are 10(exp 3)-10(exp 4) stronger than the local Galactic FUV field and come from the contribution of many closely packed O and B stars. For the central 250 pc of NGC 253, we find that the H II gas has an average density n(sub e) is approximately 400/cu cm. This corresponds to a thermal pressure P(H II)/k approximately 7 x 10(exp 6) K/cu cm which is approximately P(PDR)/k, suggesting that the ionized gas is in pressure equilibrium with the photodissociated gas at the surfaces of molecular clouds. The H II gas fills a significant fraction, approximately 0.01-0.3, of the volume between the clouds. The effective temperature of the ionizing stars in NGC 253 is greater than or approximately 34,500 K; 2 x 10(exp 5) O7.5 stars would produce the observed Lyman countinuum photon luminosity. The average separation between the stars is approximately 3 pc. Applying the simple model for the interstellar medium in galactic nuclei of Wolfire, Tielens, & Hollenbach (1990), we find the molecular gas in the central regions of NGC 253 and NGC 3256 to be distributed in a large number (5 x 10(exp 3) to 5 x 10(exp 5)) of small (0.5-2 pc), dense (approximately 10(exp 4)/cu cm) clouds (or alternatively 'thin-flattened' structures) with volume filling factors 10(exp -3) to 10(exp -2), very different from the local Interstellar Medium (ISM) of the Galaxy. We suggest a self-consistent scenario for the ISM in NGC 253 in which clouds and H II gas are in pressure balance with a supernova-shocked, hot 1-3 x 10(exp 6) K, low-density (approximately 10(exp 4)/cu cm), all pervasive medium. A feedback mechanism may be indicated in which the pressure generated by the supernovae compresses the molecular clouds and triggers further massive star formation. The similarity of ISM parameters deduced for NGC 253, NGC 3256, and M82 (Lord et al. 1993) suggests that the ISM properties are independent of the luminosity of the starburst or the triggering mechanism, but are rather endemic to starburst systems. The starburst in NGC 3256 appears to be a scaled-up version of the NGC 253 and M82 starbursts.

Carral, P.↗

NASA NTRS1961

Some Nuclear Calculations of U-235-D2O Gaseous-Core Cavity Reactors

The results of a multigroup, diffusion theory study of spherical gaseous-core cavity reactors are presented in this report. The reactor cavity of gaseous U235 is enclosed by a region of hydrogen gas and is separated from an external D2O moderator-reflector by a zirconium structural shell. Some cylindrical reactors are also investigated. A parametric study of spherical reactors indicates that, for the range of variables studied, critical mass increases as: (1) Fuel region is compressed within the reactor cavity, (2) moderator thickness is decreased, (3) structural shell thickness is increased, and (4) moderator temperature is increased. A buckling analogy is used to estimate the critical mass of fully reflected cylindrical reactors from spherical results without fuel compression. For a reactor cavity of a 120-centimeter radius uniformly filled with fuel, no structural shell, a moderator temperature of 70 F, and a moderator thickness of 100 centimeters, the critical mass of a spherical reactor is 3.1 kilograms while that of a cylinder with a length-to-diameter ratio of 1.0 (L/D = 1) is approximately 3.8 kilograms and, with L/D = 2, 5.9 kilograms. For the range of variables considered for U235-D2O gaseous-core cavity reactors, the systems are characterized by 95 to 99 percent thermal absorptions, with the flux reaching a maximum in the moderator about 10 to 15 centimeters from the reactor cavity.

Ragsdale, Robert G.↗

NASA NTRS1967

Direct measurement of compressible, turbulent boundary layer skin friction on a porous flat plate with mass injection.

Skin friction under mass injection on porous flat plate in supersonic turbulent flow

SUPERSONIC FLOW↗

DOE OSTI2020

Femtosecond X-ray Diffraction of Laser-shocked Forsterite (Mg 2 SiO 4 ) to 122 GPa

The response of forsterite, Mg 2 SiO 4 , under dynamic compression is of fundamental importance for understanding its phase transformations and high-pressure behavior. Here, we have carried out an in situ X-ray diffraction study of laser-shocked polycrystalline and single-crystal forsterite from 19 to 122 GPa using the Matter in Extreme Conditions end-station of the Linac Coherent Light Source. Under laser-based shock loading, forsterite does not transform to the high-pressure equilibrium assemblage of MgSiO 3 bridgmanite and MgO periclase, as has been suggested previously. Instead, we observe forsterite and forsterite III, a metastable polymorph of Mg 2 SiO 4 , coexisting in a mixed-phase region from 33 to 75 GPa for both polycrystalline and single-crystal samples. Densities inferred from X-ray diffraction are consistent with earlier gas-gun shock data. At higher stress, the response is sample-dependent. Polycrystalline samples undergo amorphization above 79 GPa. For [010]- and [001]-oriented crystals, a mixture of crystalline and amorphous material is observed to 108 GPa, whereas the [100]-oriented forsterite adopts an unknown phase at 122 GPa. The first two sharp diffraction peaks of amorphous Mg 2 SiO 4 show a similar trend with compression as those observed for MgSiO 3 in both recent static- and laser-driven shock experiments. This study provides new insight into the transformation of forsterite under nanosecond-duration shock loading. This work emphasizes the importance of formation of metastable phases along the Hugoniot and adds to evidence that the 300-K single-crystal diamond anvil cell experiments have relevance for understanding structures formed under shock compression. In particular, the metastable phase forsterite III has now been shown to form under dynamic compression from 10s to 100s of nanoseconds as well as under 300-K static compression. Upon compression to higher pressures, Mg 2 SiO 4 transforms to an amorphous phase. These results have broad relevance for understanding the behavior of silicates under dynamic compression.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Phase Transitions in (Mg,Fe) 2 SiO 4 Olivine under Shock Compression

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effect of slip on vortex shedding from a circular cylinder in a gas flow

Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60–100 at a Mach number of 0.3. Finally, conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

42 ENGINEERING↗