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NASA NTRS1971

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

Moss, J. N.↗

NASA NTRS1974

Reacting viscous-shock-layer solutions with multicomponent diffusion and mass injection

Numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented. Also the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered. The flow is treated as a mixture of five inert and thermally perfect species. The viscous-shock-layer equations are solved by using an implicit-difference scheme. All calculations are for hyperboloids with included angles of 20 and 45. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented to show the effects of the chemical models; diffusion models; surface catalysis; and mass injection of air on heat transfer; skin friction; shock standoff distance; wall pressure distribution; and tangential velocity, temperature, and species profiles. The results show that an equilibrium analysis can substantially overpredict the heat-transfer rates for flow conditions experienced by earth-orbital entry vehicles. Moreover, at such conditions surface catalysis significantly influences heat-transfer and flow-field properties. If a binary rather than a multicomponent diffusion model is assumed, negligible errors in most flow properties result. Quantitative results are presented that show the effect of mass injection on flow properties within and downstream of the injection region.

Moss, J. N.↗

NASA NTRS1995

Excitable dynamics in high-Lewis number premixed gas combustion at normal and microgravity

Freely-propagating, premixed gas flames in high-Lewis (Le) number, quiescent mixtures are studied experimentally in tubes of various diameter at normal (lg) and microgravity (mu g). A premixture of lean butane and oxygen diluted with helium, argon, neon, nitrogen or a mixture of multiple diluents is examined such that the thermal diffusivity of the mixture (and to a lesser extent, the mass diffusivity of the rate-limiting component) is systematically varied. In effect, different diluents allow variation of the Le without changing the chemistry. The flames are recorded with high speed cinematography and their stability is visually assessed. Different modes of propagation were observed depending on the diameter of the tubes (different conductive heat loss), the composition of the mixture and the g-level. At 1g, four modes of propagation were observed in small and intermediate diameter tubes (large conductive heat loss): (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, (3) 'wavering' flames, and (4) rotating spiral flames. As the diameter of the tube increases, the radial modes become more pronounced while the longitudinal modes systematically disappear. Also, multiple, simultaneous, spatially-separated 'pacemaker' sites are observed in intermediate and large diameter tubes. Each site starts as a small region of high luminosity and develops into a flamelet which assumes the form of one of the fore mentioned modes. These flamelets eventually interact, annihilate each other in their regions of intersection and merge at their newly created free-ends. For very large tubes, radially-propagating wave-trains (believed to be 'trigger waves') are observed. These are analogous to the radial pulsations observed in the smaller diameter tubes. At mu g, three modes of propagation have been observed: (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, and (3) multi-armed, rotating flames. Since the pulsating mode exists at mu g and 1g, buoyant flicker is not the mechanism which drives the pulsations. Moreover, all of the instabilities at 1g and mu g have characteristic frequencies on the O(100Hz). This value is lower than the fundamental, longitudinal acoustic frequencies of the tubes which suggests that the instabilities are not acoustically driven. The patterns formed by this reaction bear remarkable similarities with the patterns formed in most excitable media when the behavior of the system is driven by couplings between chemical reaction and diffusion (e.g., Belousov-Zhabotinsky reaction, Patterns in slime molds, spiral waves in the retina of a bird's eye). While it is recognized that the chemical mechanism associated with this premixed gas reaction is exponentially sensitive to temperature and undoubtedly different from those which govern previously observed excitable media (most are isothermal, or weakly exothermic, liquid phase reactions), similar spatial and temporal patterns should not come as a complete surprise considering heat and mass diffusion are self similar. It is concluded that this premixed gas system is a definitive example of a diffusive-thermal, gas-phase oscillator based on these experimental results and their favorable comparison with theory.

Pearlman, Howard↗

NASA NTRS1995

Analysis of Aerothermal Heating Over Reusable Single-Stage to Orbit Vehicles

Using the General Aerodynamic Simulation Program (GASP) with finite-rate surface catalysis and radiative equilibrium surface temperature conditions, a computational study has been conducted to predict three-dimensional aero-convective heating over the proposed reusable single-stage to orbit vehicles. The solutions for three basic classes of usable single-stage-to-orbit vehicles, including wing body, lifting body and vertical lander, are presented and compared to provide information for vehicle design. The free stream conditions used in this study occur at an altitude of 57.5 km, ambient density of 4.129e-4 kg/cubic m, and velocity of 4,849 m/s. The convective heating over the vehicle surface in both laminar and turbulent flow regimes were computed. The Baldwin-Lomax algebraic model with a modified van Driest damping factor was applied in the turbulent flow calculations. A bifurcation model which guarantees the conservation of mass diffusive fluxes was adopted to account for the multi-species mass diffusion. The effects of turbulence and surface catalysis on the surface heating are discussed in detail The solutions indicate the degree of oxygen dissociation over the leeward side is sensitive to the shape of vehicle body. Predicted convective heating over the entire surface of lifting body is strongly affected by the presence of surface catalysis. For wing body and vertical lander, the surface catalysis effect does not appear to be important in the far downstream region, and turbulence is the dominant effect on the heating prediction in this region.

Chen, Y. K.↗

NASA NTRS1979

Performance of a vortex-controlled diffuser in an annular swirl-can combustor at inlet Mach numbers up to 0.53

A short, annular dump diffuser with suction stabilized vortices in the region of abrupt area change was tested with a full scale, annular swirl can combustor. The prediffuser area ratio was 1.4. Performance data were obtained for both isothermal and burning conditions at inlet temperatures of 589 to 895 K and pressures of 0.5 to 1.0 MPa for a range of diffuser inlet Mach numbers from 0.25 to 0.53. Suction rates were 0 to 20 percent of the total diffuser mass flow rate. Diffuser effectiveness increased from 47 percent without suction to approximately 80 percent for a total suction rate of 14 percent. Combustor total pressure loss for the same total suction rate was reduced from 6.8 percent without suction to 4.0 percent at an inlet Mach number of 0.40.

Smith, J. M.↗

NASA NTRS2010

Ocean Turbulence, III: New GISS Vertical Mixing Scheme

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.

Canuto, V. M.↗

NASA NTRS2000

Stereo Imaging Velocimetry of Mixing Driven by Buoyancy Induced Flow Fields

Mixing of two fluids generated by steady and particularly g-jitter acceleration is fundamental towards the understanding of transport phenomena in a microgravity environment. We propose to carry out flight and ground-based experiments to quantify flow fields due to g-jitter type of accelerations using Stereo Imaging Velocimetry (SIV), and measure the concentration field using laser fluorescence. The understanding of the effects of g-jitter on transport phenomena is of great practical interest to the microgravity community and impacts the design of experiments for the Space Shuttle as well as the International Space Station. The aim of our proposed research is to provide quantitative data to the community on the effects of g-jitter on flow fields due to mixing induced by buoyancy forces. The fundamental phenomenon of mixing occurs in a broad range of materials processing encompassing the growth of opto-electronic materials and semiconductors, (by directional freezing and physical vapor transport), to solution and protein crystal growth. In materials processing of these systems, crystal homogeneity, which is affected by the solutal field distribution, is one of the major issues. The understanding of fluid mixing driven by buoyancy forces, besides its importance as a topic in fundamental science, can contribute towards the understanding of how solutal fields behave under various body forces. The body forces of interest are steady acceleration and g-jitter acceleration as in a Space Shuttle environment or the International Space Station. Since control of the body force is important, the flight experiment will be carried out on a tunable microgravity vibration isolation mount, which will permit us to precisely input the desired forcing function to simulate a range of body forces. To that end, we propose to design a flight experiment that can only be carried out under microgravity conditions to fully exploit the effects of various body forces on fluid mixing. Recent flight experiments, by the P.I. through collaboration with the Canadian Space Agency (STS-85, August 1997), aimed at determining the stability of the interface between two miscible liquids inside an enclosure show that a long liquid column (5 cm) under microgravity isolation conditions can be stable, i.e. the interface remains sharp and vertical over a short time scale; thus transport occurs by molecular mass diffusion. On the other hand, when the two liquids were excited from a controlled vibration source (Microgravity Vibration Isolation Mount) two to four mode large amplitude quasi-stationary waves were observed. The data was limited to CCD recording of the dynamics of the interface between the two fluids. We propose to carry out flight experiments to quantify the dynamics of the flow field using Stereo Imaging Velocimetry and measure the concentration field using laser fluorescence. The results will serve as a basis to understand effects of g-jitter on transport phenomena, in this case mass diffusion. As the measurement of the kinematics of the flow field will shed light on the instability mechanism. The research will allow measurement of the flow field in microgravity environment to prove two hypotheses: (1) Maxwell's hypothesis: finite convection always exists in diffusing systems, and (2) Quasi-stationary waves inside a bounded enclosure in a microgravity environment is generated by Kelvin-Helmholtz instability; resonance of the interface which produces incipient mixing is due to Rayleigh-Taylor instability. The first hypothesis can be used as a benchmark experiment to illustrate diffusive mixing. The second hypothesis will lead to the understanding of g-jitter effects on buoyancy driven flow fields which occur in many situations involving materials processing, and other basic fluid physics phenomena. In addition, the second hypothesis will also provide insight in how Rayleigh-Taylor and Kelvin-Helmholtz instabilities propagate concentration fronts during mixing. Measurement of the flow field using SIV is important because it is the flow field which causes instability at the interface between the two fluids. Mixing driven by buoyancy induced flow fields will be addressed both experimentally and computationally. The experimental effort will address the kinematics of mixing: stretching, transport and chaos. Quantification of the mechanisms of mixing will consists of measuring the flow field using the SIV system at Glenn and capturing the dynamics of the interface, to measure mass transport, using a CCD camera. These experiments will be carried out within the framework of Earth's gravity and g-jitter microgravity acceleration as in a Space Shuttle environment or the International Space Station. The g-jitter will be induced and controlled using a tunable vibration isolation platform to isolate against vibration as well as input periodic and random vibration to the system. The parametric range of the microgravity experiment will be extended from the experiments on STS-85 to investigate higher mode quasi-stationary waves (8 to 12), as well as resonance regions which leads to chaos and turbulence. Ground-based experiments will focus on effects of vibration on stably stratified fluid layers in order to scale for possible scenarios in a microgravity environment. These vibrations will be subjected perpendicular to the concentration field on the ground since the parallel case can only be carried out in a microgravity environment. The concept of dynamical similarity will be applied to tune the experiments as closely as possible to a Space Shuttle environment or the International Space Station. The computational effort will take advantage of the Computational Laboratory at Glenn to corroborate the experimental findings with predictions of the dynamics of the flow field using the codes FLUENT (finite difference based) and FIDAP (finite element based). We will investigate two important cases, single-fluid model to address dilute systems with negligible jump in viscosity and the more general two-fluid model which accounts for finite jump in viscosity. Apart from its microgravity relevance, this experiment is well suited to study dynamics in nonlinear systems.

Duval, W. M. B.↗

NASA NTRS1985

Transport-induced shifts in condensate dew-point and composition in multicomponent systems with chemical reaction

Partial heterogeneous condensation phenomena in multicomponent reacting systems are analyzed taking into consideration the chemical element transport phenomena. It is demonstrated that the dew-point surface temperature in chemically reactive systems is not a purely thermodynamic quantity, but is influenced by the multicomponent diffusion and Soret-mass diffusion phenomena. Several distinct dew-points are shown to exist in such systems and, as a result of transport constraints, the 'sharp' locus between two chemically distinct condensates is systematically moved to a difference mainstream composition.

Rosner, D. E.↗

NASA NTRS1999

Reflight of the Solid Surface Combustion Experiment: Flame Radiation Near Extinction

In flame spreading in quiescent and low-velocity opposing flows, effects of surface reradiation and flame radiation are important in establishing the spread rate and whether the flame, once ignited, survives to steady spread or extinguishes after a time long compared to the ignition event. A reflight of the Solid Surface Combustion Experiment (SSCE), supported by modelling, demonstrates that for thick, flat fuels, the ultimate fate of the flame is extinction rather than steady spread. A mismatch between the thermal scale in the gas, driven by radiation, and the species diffusion scale, driven by mass diffusion, develops such that the high temperature regions of the flame are ultimately located in a region to which oxygen cannot be supplied at a sufficient rate to sustain reaction, and extinction occurs. Results of the experiment conducted on Space Shuttle mission STS 85 on 9 August 1997 are reviewed. For the flat surface geometry, while the hydrodynamic phenomena associated with opposed-flow flame spread may be treated two dimensionally, the radiative effects are three dimensional, and so modelling the radiative processes, with the mismatch in dimensionality, is difficult. The cylindrical geometry at least one long compared to the radius, provides a configuration in which the radiative processes for spread in the axial direction are two dimensional, thus simplifying the modelling. The cylindrical geometry allows for the development of more sophisticated radiative models without the complication of dimensionality concerns, e.g., discrete transfer, which is discussed in detail by Bundy (1998). Additionally, the cylindrical geometry results in a "focussing" of the heat transfer to the surface and may allow for steady spread for radii that for thick fuels of the same half-thickness there is no steady spread.

Altenkirch, R. A.↗

NASA NTRS1966

On mass transfer between two parallel streams

Convective and diffusive mass transfer between two parallel gas streams

CONVECTION↗

NASA NTRS1992

Flow effects in a vertical CVD reactor

A model is presented to simulate the non-Boussinesq flow in a vertical, two-dimensional, chemical vapor deposition reactor under atmospheric pressure. Temperature-dependent conductivity, mass diffusivity, viscosity models, and reactive species mass transfer to the substrate are incorporated. In the limits of small Mach number and small aspect ratio, asymptotic expressions for the flow, temperature, and species fields are developed. Soret diffusion effects are also investigated. Analytical solutions predict an inverse relationship between temperature field and concentration field due to Soret effects. This finding is consistent with numerical simulations, assisting in the understanding of the complex interactions amongst the flow, thermal, and species fields in a chemically reacting system.

Young, G. W.↗

NASA NTRS2003

Flame Oscillations In Non-Premixed Systems Diffusion Flames and Edge-Flames

Diffusive-thermal instabilities are well known features of premixed and diffusion flames. In one of its form the instability appears as spontaneous oscillations. In premixed systems oscillations are predicted to occur when the effective Lewis number, defined as the ratio of the thermal diffusivity of the mixture to the mass diffusivity of the deficient component, is sufficiently larger than one. Oscillations would therefore occur in mixtures that are deficient in the less mobile reactant, namely in lean hydrocarbon-air or rich hydrogen-air mixtures. The theoretical predictions summarized above are in general agreement with experimental results; see for example [5] where a jet configuration was used and experiments were conducted for various inert-diluted propane and methane flames burning in inert-diluted oxygen. Nitrogen, argon and SF6 were used as inert in order to produce conditions of substantially different Lewis numbers and mixture strength. In accord with the predicted trend, it was found that oscillations arise at near extinction conditions, that for oscillations to occur it suffices that one of the two Lewis numbers be sufficiently large, and that oscillations are more likely to be observed when is relatively large.

Matalon, Moshe↗

NASA NTRS1991

Response of a confined gas to volumetric heating in the absence of gravity. I - Slow transients

A one-dimensional model for bulk motion induced by a transient volumetric heat source in a confined gas at zero gravity is considered. Rational approximation methods are used to derive a quantitative theory for the gas response to a spatiallly distributed, time-dependent internal power deposition. The resulting low Mach number compressible flow equations are solved by using perturbation methods. Solutions are given for a conduction-free core and thin conductive boundary layers adjacent to the end walls. It is found that may any spatially nonuniform power deposition will cause fluid motion. Net mass transport in the closed container will occur for certain spatially distributed heating. The model mimics the thermal effects of an exothermic gas phase reaction in vapor transport experiments conducted in space. The solutions demonstrate that thermally induced mass transport can be as large as diffusive mass transport in a typical experiment.

Herczynski, A.↗

NASA NTRS1997

Premixed Gas Combustion: An Excitable System

Rotating spiral and target patterns have been observed experimentally on freely-propagating premixed gas flames in large diameter tubes at normal gravity (1-g). These modes of propagation occur in near-limit mixtures which have a Lewis number (Le, defined as the ratio of the thermal diffusivity of the cold mixture to the mass diffusivity of the scarce component into the mixture) sufficiently greater than one. However, at 1-g, buoyant flows strongly distort the flame curvature, hydrodynamics (thus stretch) and convective transport of species and heat. In turn, these alter the critical Le required for onset of instability. To isolate and better understand the mechanisms which drive the observed patterns and their dynamics, 1-g and microgravity (micro-g) experiments are being conducted to determine: (1) the structure and dynamics of the patterns, (2) a map of the critical Le and heat loss for their occurrence, (3) the relative significance of the chemical kinetics, and (4) the effect of curvature (local wave and global flame front) on wave propagation. With this in hand, we will be better prepared to discuss an additional mode, a state of 'chemical turbulence,' which seems to be the ultimate fate of many of these near-limit flames prior to extinction.

Pearlman, Howard↗

NASA NTRS1997

Premixed Atmosphere and Convection Influences on Flame Inhibition and Combustion (Pacific)

Flame spread over flat solid fuel beds is a useful paradigm for studying the behavior of more complex two-phase nonpremixed flames. For practical applications, two of the most important elements of flame spreading are the effects of (1) the ambient atmosphere (e.g. pressure and composition) and (2) the flow environment on the spread rate and extinction conditions. Concerning (1), studies of flame spread in vitiated air and non-standard atmospheres such as those found in undersea vessels and spacecraft are particularly important for the assessment of fire hazards in these environments as well as determination of the effectiveness of fire suppressants. Concerning (2), the flow environment may vary widely even when no forced flow is present because of buoyancy effects. Consequently, the goal of this work is to employ microgravity (micro g) experiments to extend previous studies of the effects of ambient atmosphere and the flow environment on flame spread through the use of microgravity (micro g) experiments. Because of the considerable differences between upward (concurrent-flow) and downward (opposed-flow) flame spread at 1g (Williams, 1976, Fernandez-Pello, 1984), in this work both upward and downward 1g spread are tested. Two types of changes to the oxidizing atmosphere are considered in this work. One is the addition of sub-flammability-limit concentrations of a gaseous fuel ('partially premixed' atmospheres). This is of interest because in fires in enclosures, combustion may occur under poorly ventilated conditions, so that oxygen is partially depleted from the air and is replaced by combustible gases such as fuel vapors, H2 or CO. Subsequent fire spread over the solid fuel could occur under conditions of varying oxygen and gaseous fuel content. The potential significance of flame spread under vitiated or partially premixed conditions has been noted previously (Beyler, 1984). The second change is the diluent type, which affects the radiative properties of the mixture as well as the Lewis number (Le) of the reactants in the atmosphere, which for oxygen is defined as the thermal diffusivity of the bulk mixture divided by the mass diffusivity of oxygen into the bulk mixture. Understanding the effect of diluent type is desirable because in some undersea and spaceborne habitations, it is desirable to use diluent gases other than nitrogen. Prior experiments have shown that both radiation (Bhattacharjee and Altenkirch, 1993) and Lewis number (Zhang et al, 1992) effects are important in flame spreading problems.

Honda, Linton K.↗

NASA NTRS2000

Structure of Laminar Permanently Blue, Opposed-Jet Ethylene-Fueled Diffusion Flames

The structure and state relationships of laminar soot-free (permanently blue) ethylene-fueled diffusion flames at various strain rates were studied both experimentally and computationally using an opposed-jet configuration. Measurements of gas velocities, temperatures, and compositions were carried out along the stagnation stream line. Corresponding predictions of flame structure were obtained, based on numerical simulations using several contemporary reaction mechanisms for methane oxidation. Flame conditions studied included ethylene-fueled opposed-jet diffusion flames having stoichiometric mixture fractions of 0.7 with measurements involving strain rates of 60-240/s and predictions involving strain rates of 0-1140/s at normal temperature and pressure. It was found that measured major gas species concentrations and temperature distributions were in reasonably good agreement with predictions using mechanisms due to GRI-Mech and Peters and that effects of preferential diffusion significantly influence flame structure even when reactant mass diffusivities are similar. Oxygen leakage to fuel-rich conditions and carbon monoxide leakage to fuel-lean conditions both increased as strain rates increased. Furthermore, increased strain rates caused increased fuel concentrations near the flame sheet, decreased peak gas temperatures, and decreased concentrations of carbon dioxide and water vapor throughout the flames. State relationships for major gas species and gas temperatures were found to exist over a broad range of strain rates, providing potential for significant computational simplifications for modeling purposes in some instances.

Lin, K.-C.↗

NASA NTRS2000

Structure of Laminar Permanently Blue, Opposed-Jet Ethylene-Fueled Diffusion Flames

Lin, K.-C.↗

NASA NTRS1992

Stratification of chemical elements in the atmosphere of the Ap star 53 Camelopardalis

A detailed abundance analysis of Cr, Fe, Mn, Ca, and Ti in the Ap star 53 Cam from IUE high-resolution spectra has been performed. It is found that UV lines give significantly lower abundance than visible lines for Cr and Fe. Theoretical spectra of Cr II line calculated with the stratified chromium abundance distributions predicted a priori by the diffusion-mass loss model match well both visible and UV lines. The spectral shape of the Ca II K line and its variation are well accounted for by the diffusion model with mass loss. A spectrum synthesis with a stratified abundance well reproduces the observations. These findings provide convincing evidence for stratification in the photosphere of 53 Cam.

Babel, J.↗