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NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗
NASA NTRS1995

Mars Sample Return mission utilizing in-situ propellant production

This report presents the results of a study examining the potential of in-situ propellant production (ISPP) on Mars to aid in achieving a low cost Mars Sample Return (MSR) mission. Two versions of such a mission were examined: a baseline version employing a dual string spacecraft, and a light weight version employing single string architecture with selective redundancy. Both systems employed light weight avionics currently being developed by Lockheed Martin, Jet Propulsion Lab and elsewhere in the aerospace community, both used a new concept for a simple, light weight parachuteless sample return capsule, both used a slightly modified version of the Mars Surveyor lander currently under development at Lockheed Martin for flight in 1998, and both used a combination of the Sabatier-electrolysis and reverse water gas shift ISPP systems to produce methane/oxygen propellant on Mars by combining a small quantity of imported hydrogen with the Martian CO2 atmosphere. It was found that the baseline mission could be launched on a Delta 7925 and return a 0.5 kg sample with 82 percent mission launch margin;over and beyond subsystem allocated contingency masses . The lightweight version could be launched on a Mid-Lite vehicle and return a 0.25 kg sample with 11 percent launch margin, over and above subsystem contingency mass allocations.

Zubrin, Robert↗
NASA NTRS1995

Advanced Methodology for Simulation of Complex Flows Using Structured Grid Systems

Detailed simulations of viscous flows in complicated geometries pose a significant challenge to current capabilities of Computational Fluid Dynamics (CFD). To enable routine application of CFD to this class of problems, advanced methodologies are required that employ (a) automated grid generation, (b) adaptivity, (c) accurate discretizations and efficient solvers, and (d) advanced software techniques. Each of these ingredients contributes to increased accuracy, efficiency (in terms of human effort and computer time), and/or reliability of CFD software. In the long run, methodologies employing structured grid systems will remain a viable choice for routine simulation of flows in complex geometries only if genuinely automatic grid generation techniques for structured grids can be developed and if adaptivity is employed more routinely. More research in both these areas is urgently needed.

Steinthorsson, Erlendur↗
NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Park, K. C.↗
NASA NTRS1994

A simulation of the intracluster medium with feedback from cluster galaxies

We detail method and report first results from a three-dimensional hydrodynamical and N-body simulation of the formation and evolution of a Coma-sized cluster of galaxies, with the intent of studying the history of the hot, X-ray emitting intracluster medium. Cluster gas, galaxies, and dark matter are included in the model. The galaxies and dark matter fell gravitational forces; the cluster gas also undergoes hydrodynamical effects such as shock heating and PdV work. For the first time in three dimensions, we include modeling of ejection of processed gas from the simulated galaxies by winds, including heating and heavy element enrichment. For comparison, we employ a `pure infall' simulation using the same initial conditions but with no galaxies or winds. We employ an extreme ejection history for galactic feedback in order to define the boundary of likely models. As expected, feedback raises the entropy of the intracluster gas, preventing it from collapsing to densities as high as those attained in the infall model. The effect is more pronounced in subclusters formed at high redshift. The cluster with feedback is always less X-ray luminous, but experiences more rapid luminosity evolution, than the pure infall cluster. Even employing an extreme ejection model, the final gas temperature is only approximately 15% larger than in the infall model. The radial temperature profile is very nearly isothermal within 1.5 Mpc. The cluster galaxies in the feedback model have a velocity dispersion approximately 15% lower than the dark matter. This results in the true ratio of specific energies in galaxies to gas being less than one, beta(sub spec) approximately 0.7. The infall model predicts beta(sub spec) approximately 1.2. Large excursions in these values occur over time, following the complex dynamical history of the cluster. The morphology of the X-ray emission is little affected by feedback. The emission profiles of both clusters are well described by the standard beta-model with beta(sub fit) approximately equal to 0.7 - 0.9. X-ray mass estimates based on the assumptions of hydrostatic equilibrium and the applicability of the beta-model are quite accurate in both cases. A strong, radial iron abundance gradient is present, which develops as a consequence of the steepening of the galaxy density profile over time. Spectroscopic observations using nonimaging detectors with wide (approximately 45 min) fields of view dramatically smear the gradient. Observations with arcminute resolution, made available with the ASCA satellite, would readily resolve the gradient.

Metzler, Christopher A.↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗
NASA NTRS1994

New multigrid approach for three-dimensional unstructured, adaptive grids

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

Parthasarathy, Vijayan↗
NASA NTRS1994

Computation of axisymmetric and ionized hypersonic flows using particle and continuum methods

Comparisons between particle and continuum simulations of hypersonic near-continuum flows are presented. The particle approach employs the direct simulation Monte Carlo (DSMC) method, and the continuum approach solves the appropriate equations of fluid flow. Both simulations have thermochemistry models for air implemented including ionization. A new axisymmetric DSMC code that is efficiently vectorized is developed for this study. In this DSMC code, particular attention is paid to matching the relaxation rates employed in the continuum approach. This investigation represents a continuum of a previous study that considered thermochemical relaxation in one-dimensional shock waves of nitrogen. Comparison of the particle and continuum methods is first made for an axisymmetric blunt-body flow of air at 7 km/s. Very good agreement is obtained for the two solutions. The two techniques also compare well for a one-dimensional shock wave in air at 10 km/s. In both applications, the results are found to be sensitive to various aspects of the chemistry model employed.

Boyd, Iain D.↗
NASA NTRS1995

High temperature superconductors applications in telecommunications

The purpose of this paper is twofold: (1) to discuss high temperature superconductors with specific reference to their employment in telecommunications applications; and (2) to discuss a few of the limitations of the normally employed two-fluid model. While the debate on the actual usage of high temperature superconductors in the design of electronic and telecommunications devices - obvious advantages versus practical difficulties - needs to be settled in the near future, it is of great interest to investigate the parameters and the assumptions that will be employed in such designs. This paper deals with the issue of providing the microwave design engineer with performance data for such superconducting waveguides. The values of conductivity and surface resistance, which are the primary determining factors of a waveguide performance, are computed based on the two-fluid model. A comparison between two models - a theoretical one in terms of microscopic parameters (termed Model A) and an experimental fit in terms of macroscopic parameters (termed Model B) - shows the limitations and the resulting ambiguities of the two-fluid model at high frequencies and at temperatures close to the transition temperature. The validity of the two-fluid model is then discussed. Our preliminary results show that the electrical transport description in the normal and superconducting phases as they are formulated in the two-fluid model needs to be modified to incorporate the new and special features of high temperature superconductors. Parameters describing the waveguide performance - conductivity, surface resistance and attenuation constant - will be computed. Potential applications in communications networks and large scale integrated circuits will be discussed. Some of the ongoing work will be reported. In particular, a brief proposal is made to investigate of the effects of electromagnetic interference and the concomitant notion of electromagnetic compatibility (EMI/EMC) of high T(sub c) superconductors.

Kumar, A. Anil↗
NASA NTRS1996

Low Frequency Vibration Characteristics of the Space Acceleration Measurement System 2 Tape Drive Assembly

This report summarizes results of force and moment measurements of the Space Acceleration Measurement System 2 (SAMS 2) Tape Drive Assembly (TDA) over the frequency range from 0.35 Hz to 256 Hz for steady state operations including write, read, rewind, and fast forward. Time domain force results are presented for transient TDA operations that include software eject, manual eject, and manual load. Three different mounting configurations were employed for attaching the inner box with the tape drive unit to the outer box. Two configurations employed grommet sets with spring rates of 42 and 62 pounds per inch respectively. The third configuration employed a set of metallic washers. For all four steady state operations the largest average forces were on the Y axis with the metallic washers and were less than 0.005 pounds. The largest average moments were on the X axes with the washers and were less than 0.030 pound inches. At the third octave centerband frequency of 31.5 Hz, the 42 pound per inch grommets showed the greatest forces and moments for read and write operations. At the third octave centerband frequency of 49.6 Hz, the 62 pound per inch grommets showed the greatest forces and moments for rewind operation. Transient operation forces ranged from 0.75 pounds for the software eject to greater than 1 pound for manual load and eject.

Javeed, Mehzad↗
NASA NTRS1996

Methods of Measuring Vapor Pressures of Lubricants With Their Additives Using TGA and/or Microbalances

The life of a space system may be critically dependent on the lubrication of some of its moving parts. The vapor pressure, the quantity of the available lubricant, the temperature and the exhaust venting conductance passage are important considerations in the selection and application of a lubricant. In addition, the oil additives employed to provide certain properties of low friction, surface tension, antioxidant and load bearing characteristics, are also very important and need to be known with regard to their amounts and vapor pressures. This paper reports on the measurements and analyses carried out to obtain those parameters for two often employed lubricants, the Apiezon(TM)-C and the Krytox(TM) AB. The measurements were made employing an electronic microbalance and a thermogravimetric analyzer (TGA) modified to operate in a vacuum. The results have been compared to other data on these oils when available. The identification of the mass fractions of the additives in the oil and their vapor pressures as a function of the temperature were carried out. These may be used to estimate the lubricant life given its quantity and the system vent exhaust conductance. It was found that the Apiezon(TM)-C has three main components with different rates of evaporation while the Krytox(TM) did not indicate any measurable additive.

Scialdone, John J.↗
NASA NTRS1995

The OEOP Duties of Reasonable Accommodation

I was fortunate enough to be assigned two assignments during my ten weeks here at NASA's Langley Research Center, in the Office of Equal Opportunity Programs (OEOP). One of my projects gave me the chance to gain experience in developing calculation formulas for the EXCEL computer system, while my second project gave me the chance to put my research skills and legal knowledge to use. The function of the OEOP is to ensure the adherence to personnel policy and practices in the employment, development, advancement and treatment of Federal employees and applicants for employment. This includes veterans and disabled as well. My initial project involved the research of hiring and promotion among the different minorities and females employed here at Langley. The objective of my first project was to develop graphs that showed the number of promotions during the past five years for each minority group here on the Center. I also had to show the average number of years it took for each promotion. The objective of my second and main research project was to find and research cases regarding the reasonable accommodation of disabled workers. The research of these cases is to ensure that individuals with disabilities are provided the necessary accommodations that are essential to the function of their job.

Coppedge, Angela↗
NASA NTRS1996

Calcium Balance in Mature Rats Exposed to a Space Flight Model

Negative calcium balances are seen in humans during spaceflight and bed rest, an analog of space flight. Due to the infrequency and costliness of space flight and the difficulties, cost, and restraints in using invasive procedures in bed rest studies, several ground based animal models of space flight have been employed. The most useful and well developed of these models is hind limb unloading in the rat. In this model the hind limbs are non-weight bearing (unloaded) but still mobile; there is a cephalad fluid shift similar to that seen in astronauts in flight; the animals are able to feed, groom and locomote using their front limbs; the procedure is reversible; and, importantly, the model has been validated by comparison to space flight. Several laboratories have studied calcium balance using rats in hind limb unweighting. Roer and Dillaman used young male rats to study calcium balance in this model for 25 days. They found no differences in dietary calcium intake, percent calcium absorption, urinary and fecal excretion, hence indicating no differences in calcium balance between control and unloaded rats. In another study, employing 120 day old females, rats' hind limbs were unloaded for 28 days. While negative calcium balances were observed during a 25 day recovery period no balance measurements were possible during unweighting since the researchers did not employ appropriate metabolic cages. In a recent study from this laboratory, using 200 g rats in the space flight model for two weeks, we found depressed intestinal calcium absorption and increased fecal calcium excretion (indicating less positive calcium balances) and lower circulating 1,25-dihydroxyvitamin D. The above studies indicate that there remains a dearth of information on calcium balance during the hind limb unloading rat space flight model, especially in mature rats, whose use is a better model for planned manned space flight than juvenile or growing animals. With the aid of a newly designed metabolic cage developed in our laboratory it is now possible to accurately measure urinary and fecal calcium excretions in this space flight model. The purpose of this study, then, was to extend and enlarge our previous findings viz: to measure calcium balances in mature rats exposed to a space flight model.

Wolinsky, Ira↗
NASA NTRS1994

High-Performance X-ray Detection in a New Analytical Electron Microscope

X-ray detection by energy-dispersive spectrometry in the analytical electron microscope (AEM) is often limited by low collected X-ray intensity (P), modest peak-to-background (P/B) ratios, and limitations on total counting time (tau) due to specimen drift and contamination. A new AFM has been designed with maximization of P. P/B, and tau as the primary considerations. Maximization of P has been accomplished by employing a field-emission electron gun, X-ray detectors with high collection angles, high-speed beam blanking to allow only one photon into the detector at a time, and simultaneous collection from two detectors. P/B has been maximized by reducing extraneous background signals generated at the specimen holder, the polepieces and the detector collimator. The maximum practical tau has been increased by reducing specimen contamination and employing electronic drift correction. Performance improvments have been measured using the NIST standard Cr thin film. The 0-3 steradian solid angle of X-ray collection is the highest value available. The beam blanking scheme for X-ray detection provides 3-4 times greater throughput of X-rays at high count rates into a recorded spectrum than normal systems employing pulse-pileup rejection circuits. Simultaneous X-ray collection from two detectors allows the highest X-ray intensity yet recorded to be collected from the NIST Cr thin film. The measured P/B of 6300 is the highest level recorded for an AEM. In addition to collected X-ray intensity (cps/nA) and P/B measured on the standard Cr film, the product of these can be used as a figure-of-merit to evaluate instruments. Estimated minimum mass fraction (MMF) for Cr measured on the standard NIST Cr thin film is also proposed as a figure-of-merit for comparing X-ray detection in AEMs. Determinations here of the MMF of Cr detectable show at least a threefold improvement over previous instruments.

Lyman, C. E.↗
NASA NTRS1997

Kinetics and Thermochemistry of the Br((sup 2)P3/2) + NO2 Association Reaction

A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the Br((sup 2)P3/2) + NO2 association reaction as a function of temperature (259-432 K) pressure (12.5 - 700 Torr), and buffer gas identity (He, Ar, H2, N2, CO2, CF4, SF6). The reaction is found to be in the falloff regime between third and second order over the entire range of conditions investigated. At temperatures below 350 K, the association reaction is found to be irreversible on the time scale of the experiment (approximately 30 ms). At higher temperatures reversible addition is observed, allowing equilibrium constants for BrNO2 formation and dissociation to be determined. Second- and third-law analyses of the equilibrium data are in only fair agreement and lead to the following thermochemical parameters for the association reaction: Delta-H(298) = 19.6 +/- 1.7 kcal/mol, Delta-H(0) = -18.6 +/- 2.0 kcal/mol, Delta-S(298) = 29.3 +/- 4.2 cal/mol/K, Delta-H(sub f)(sub 298)(BrNO2) = 17.0 +/-1.8 kcal/mol(uncertainties are 2 sigma estimates of absolute accuracy). The value for Delta-H(0) determined in this study has been employed to calculate k(sub 0)(sup SC), the low-pressure third-order rate coefficient in the strong collision limit, by using the method of Troe; calculated values of k(sub 0)(sup SC) are inconsistent with experimental results unless Delta-H(0) is assigned a value near the lower limit derived from analysis of the high-temperature approach to equilibrium data, i.e. delta-H(0) approximately equals -16.6 kcal/mol. A potential source of systematic error in the calculation of both k(sub 0)(sup SC) and the absolute entropy of BrNO2 results from the complete lack of knowledge of the energies and degeneracies of the electronic states of BrNO3. The procedure developed by Troe and co-workers has been employed to extrapolate experimental falloff curves to the low- and high-pressure limits. Derived values for k(sub 0)(M,298K) in units of 10(exp -31) cm(exp 6)/sq molecule/s range from 2.75 for M = He to 6.54 for M = CO2; 2 sigma uncertainties are estimated to be +/- 20%. Values for k(sub 0)(N2,T) in units of 10(exp -31) cm(exp 6)/sq molecule/s are 5.73 at 259 K, 4.61 at 298 K, and 3.21 at 346 K; the observed temperature dependence for k(sub 0)(N2,T) is consistent with the theoretical temperature dependence for Beta(sub c)k(sub 0)(sup SC). Values for k(sub infinity)(T) in units of 10(exp -11) cu cm/molecule/s are 2.86 at 259 K, 3.22 at 298 K, and 3.73 at 346 K; 2 sigma uncertainties are estimated to be a factor of 2. Approximate falloff parameters in a convenient format for atmospheric modeling are also derived.

Kreutter, K. D.↗
NASA NTRS1998

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

Movriplis, Dimitri J.↗
NASA NTRS1998

Noncontact Acousto-Ultrasonics for Material Characterization

A NdYAG 1064 nm, laser pulse was employed to produce ultrasonic waves in specimens of SiC/SiC and SiC/Ti 6-4 composites which are high temperature materials of interest for aerospace applications. Air coupled transducers were used to detect and collect the signals used for acousto-ultrasonic analysis. Conditions for detecting ultrasonic decay signals were examined. The results were compared to those determined on the same specimens with contact coupling. Some non-contact measurements were made employing conventional air focused detectors. Others were performed with a more novel micromachined capacitance transducer. Concerns of the laser-in technology include potential destructiveness of the laser pulse. Repeated laser pulsing at the same location does lead to deterioration of the ultrasonic signal in some materials, but seems to recover with time. Also, unlike contact AU, the frequency regime employed is a function of laser-material interaction rather than the choice of transducers. Concerns of the air coupled-out technology include the effect of air attenuation. This imposes a practical upper limit to frequency of detection. In the case of the experimental specimens studied ultrasonic decay signals could be imaged satisfactorily.

Kautz, Harold E.↗
NASA NTRS1998

Locations of Halide Ions in Tetragonal Lysozyme Crystals

Anions play an important role in the crystallization of lysozyme, and are known to bind to the crystalline protein. Previous studies employing X-ray crystallography had found one chloride ion binding site in the tetragonal crystal form of the protein and four nitrate ion binding sites in the monoclinic form. Studies using other approaches have reported more chloride ion binding sites, but their locations were not known. Knowing the precise location of these anions is also useful in determining the correct electrostatic fields surrounding the protein. In the first part of this study the anion positions in the tetragonal form were determined from the difference Fourier map obtained from the lysozyme crystals grown in bromide and chloride solutions under identical conditions. The anion locations were then obtained from standard crystallographic methods and five possible anion binding sites were found in this manner. The sole chloride ion binding site found in previous studies was confirmed. The remaining four sites were new ones for tetragonal lysozyme crystals. However, three of these new sites and the previously found one corresponded to the four unique binding sites found for nitrate ions in monoclinic crystals. This suggests that most of the anion binding sites in lysozyme remain unchanged, even when different anions and different crystal forms of lysozyme are employed. It is unlikely that there are many more anions in the tetragonal lysozyme crystal structure. Assuming osmotic equilibrium it can be shown that there are at most three more anions in the crystal channels. Some of the new anion binding sites found in this study were, as expected, in pockets containing basic residues. However, some of them were near neutral, but polar, residues. Thus, the study also showed the importance of uncharged, but polar groups, on the protein surface in determining its electrostatic field. This was important for the second part of this study where the electrostatic field surrounding the protein was accurately determined. This was achieved by solving the linearized version of the Poisson-Boltzmann equation for the protein in solution. The solution was computed employing the commercial code Delphi which uses a finite difference technique. This has recently become available as a module in the general protein visualization code Insight II. Partial charges were assigned to the polar groups of lysozyme for the calculations done here. The calculations showed the complexity of the electrostatic field surrounding the protein. Although most of the region near the protein surface had a positive field strength, the active site cleft was negatively charged and this was projected a considerable distance. This might explain the occurrence of "head-to-side" interactions in the formation of lysozyme aggregates in solution. Pockets of high positive field strength were also found in the vicinity of the anion locations obtained from the crystallographic part of this study, confirming the validity of these calculations. This study clearly shows not only the importance of determining the counterion locations in protein crystals and the electrostatic fields surrounding the protein, but also the advantage of performing them together.

Lim, Kap↗