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Probabalistic Risk Analysis and Thermal Margin Process for an Inflatable Aeroshell

Uncertainties always exist in atmospheric entry aeroheating environments and the thermal response of thermal protection system (TPS) material. These uncertainties are mitigated in the design by ap-plying margin and factors of safety to the TPS. Entry vehicle TPS is often conservatively over-sized for the heat loads that are experienced along the entry trajectory by stacking worst-case scenarios together. Additionally, the current TPS design and margin process used by NASA offers very little insight into the risk of over-temperature during flight and the reliability of the heat shield performance [1,3]. A probabilistic margin process can be used to calculate the amount of TPS margin necessary to survive a given entry heat load at a specified level of risk [2,3,4]. The vehicle’s initial entry state (entry velocity, flight path angle, and entry mass) determines the expected atmospheric entry environmental conditions and resulting heat load that the entry vehicle will experience. If there is flexibility in the entry state, then this process can be used to select an appropriate combination of entry state parameters and TPS size to target a desired reentry reliability. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory design, and TPS performance risk trades while preventing excessive TPS margin from being applied. The probabilistic TPS margin process has been performed to determine TPS thickness and entry heating constraints given an acceptable risk level for the Low Earth Orbit Flight Experiment of an Inflatable Decelerator (LOFTID) flight project. The process is used in a manner to size the entry heat load for a given flexible TPS (FTPS) thickness so that it meets project reliability standards while allowing the FTPS and the underlying inflatable structure (IS) to be pushed to adequately high temperatures. Since the LOFTID project is an experimental flight demonstration, it is de-sired to drive the FTPS and IS to temperatures that cover a large range of their thermal response models’ applicability. This will allow the thermal response models to be better improved and validated post-flight using LOFTID’s extensive instrumentation embedded within the aeroshell. The presentation demonstrates how uncertainty analysis is carried out using an end-to-end Monte Carlo process where three separate Monte Carlo simulations are run in sequence. The first Monte Carlo simulation operates on the entry trajectory model to generate trajectory parameter dispersions that are fed into the second Monte Carlo simulation. The second Monte Carlo simulation operates on the aerothermodynamics model to generate aeroheating parameter dispersions that are fed into the third Monte Carlo simulation. The third Monte Carlo simulation operates on the FTPS material thermal response model to generate the final FTPS/IS thermal response dispersions. The end-to-end Monte Carlo simulation propagates the uncertainties of each model into the next to quantify the resulting uncertainty of the FTPS/IS thermal response. The fractional contributions of the uncertain parameters in the trajectory, aerothermal, and thermal response models to the variance in the FTPS/IS thermal response is determined as a byproduct of the Monte Carlo analysis. The structural uncertainty of the FTPS thermal response model is evaluated by flight relevant ground testing and model error analysis using test measurements. This probabilistic TPS margin process had never been applied to an entry vehicle and it is one of the LOFTID project’s goals to demonstrate its merits.

Steven A. Tobin↗

NASA NTRS1992

Microencapsulated PCM slurries for heat transfer and energy storage in spacecraft systems

The technical feasibility for providing significantly enhanced heat transport and storage as well as improved thermal control has been investigated during several Small Business Innovative Research (SBIR) programs for NASA, the United States Air Force (USAF), and the Strategic Defense Initiative Organization (SDIO) using microencapsulated phase change materials (PCMs) in both aqueous and nonaqueous two-component slurries. In the program for SDIO, novel two-component coolant fluids were prepared and successfully tested at both low (300 K) and intermediate temperatures (460 to 700 K). The two-component fluid slurries of microencapsulated PCMs included organic particles in aqueous and nonaqueous liquids, as well as microencapsulated metals that potentially could be carried by liquid metals or used as powdered heat sinks. Simulation and experimental studies showed that such active cooling systems could be designed and operated with enhancements of heat capacity that exceeded 10 times or 1000 percent that for the base fluid along with significant enhancement in the fluid's heat capacity. Furthermore, this enhancement provided essentially isothermal conditions throughout the pumped primary coolant fluid loop. The results suggest that together with much higher fluid thermal capacity, greater uniformity of temperature is achievable with such fluids, and that significant reductions in pumping power, system size, and system mass are also possible.

Colvin, David P.↗

NASA NTRS1991

Thermal and solutal conditions at the tips of a directional dendritic growth front

The line-of-sight averaged, time-dependent dendrite tip concentrations for the diffusion dominated vertical directional solidification of a metal model (ammonium chloride and water) were obtained by extrapolating exponentially fit diffusion layer profiles measured using a laser interferometer. The tip concentrations were shown to increase linearly with time throughout the diffusion dominated growth process for an initially stagnant dendritic array. The process was terminated for the cases chosen by convective breakdown suffered when the conditionally stable diffusion layer exceeded the critical Rayleigh criteria. The transient tip concentrations were determined to significantly exceed the values predicted for steady state, thus producing much larger constitutional undercoolings. This has ramifications for growth speeds, arm spacings and the dendritic structure itself.

Mccay, T. D.↗

NASA NTRS1989

Study of the atmospheric general circulation as an initial value problem with the NCAR Community Climate Model

The essential elements of the transition of a model atmosphere to the equilibrium state from two extreme rest states, a cold (240 K) state and a warm (310 K) state, were examined using the NCAR Community Climate Model. It is shown that the same equilibrium state was reached in the two spinup conditions, which was also the same that was reported for this model by Williamson and Williamson (1984), who started from still a different initial condition. The spinup from the cold initial condition was faster than that from the warm condition, although the final stages of the approach to equilibrium were very simular in both cases. It was also found that the spinup of the barotropic flow lagged behind that of the baroclinic flow and the thermal field, and the model tropics spinup was faster than that of the mid-latitudes.

Chen, Tsing-Chang↗

NASA NTRS2000

Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.↗

NASA NTRS2015

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗

NASA NTRS2001

Validation of NASA Thermal Ice Protection Computer Codes: The Validation of Antice - Part 3

An experimental program was generated by the Icing Technology Branch at NASA Glenn Research Center to validate two ice protection simulation codes: (1) LEWICE/Thermal for transient electrothermal de-icing and anti-icing simulations, and (2) ANTICE for steady state hot gas and electrothermal anti-icing simulations. An electrothermal ice protection system was designed and constructed integral to a 36 inch chord NACA0012 airfoil. The model was fully instrumented with thermo-couples, RTD'S, and heat flux gages. Tests were conducted at several icing environmental conditions during a two week period at the NASA Glenn Icing Research Tunnel. Experimental results of running-wet and evaporative cases were compared to the ANTICE computer code predictions and are presented in this paper.

Al-Khalil, Kamel M.↗

NASA NTRS1988

Fatigue life prediction modeling for turbine hot section materials

This paper presents a summary of the life prediction methods developed under the NASA Lewis Research Center's Hot Section Technology (HOST) program. A major objective of the fatigue and fracture efforts under the HOST program was to significantly improve the analytic life prediction tools used by the aeronautical gas turbine engine industry. This has been achieved in the areas of high-temperature thermal and mechanical fatigue of bare and coated high-temperature superalloys. Such technical improvements will eventually reduce life cycle costs. The cyclic crack initiation and propagation resistance of nominally isotropic polycrystalline alloys and highly anisotropic single crystal alloys has been addressed. A sizeable data base has been generated for three alloys [cast PWA 1455 (B-1900 + Hf), wrought Inconel 718, and cast single crystal PWA 1480] in bare and coated conditions. Two coatings systems, diffusion aluminide (PWA 273) and plasma sprayed MCrAIY overlay (PWA 286) were employed. Life prediction modeling efforts were devoted to creep-fatigue interaction, oxidation, coatings interactions, multiaxiality of stress-strain states, mean stress effects, cumulative damage, and thermomechanical fatigue. The fatigue crack initiation life models developed to date include the Cyclic Damage Accumulation (CDA) Model of Pratt & Whitney and the Total Strain Version of Strainrange Partitioning (TS-SRP) of NASA Lewis for nominally isotropic materials, and the Tensile Hysteretic Energy Model of Pratt & Whitney for anisotropic superalloys. The fatigue model being developed by the General Electric Company is based upon the concepts of Path-lndependent Integrals (PII) for describing cyclic crack growth under complex nonlinear response at the crack tip due to thermomechanical loading conditions. A micromechanistic oxidation crack extension model has been derived by researchers at Syracuse University. The models are described and discussed in the paper. Only limited verification has been achieved to-date as several of the technical programs are still in progress and the verification tasks are scheduled, quite naturally, near the conclusion of the program. To-date, efforts have concentrated on development of independent models for cyclic constitutive behavior, cyclic crack initiation, and cyclic crack propagation. The transition between crack initiation and crack propagation has not been thoroughly researched as yet, and the integration of these models into a unified life prediction method has not been addressed.

Metal fatigue↗

NASA NTRS1991

Electromagnetic finite elements based on a four-potential variational principle

Electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as a primary variable are derived. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are that the number of degrees of freedom per node remains modest as the problem dimensionally increases, that jump discontinuities on interfaces are naturally accommodated, and that statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady state forcing conditions. The results are in excellent agreement with analytical solutions.

Schuler, James J.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process-I: Thermal

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra, ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non- uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗

NASA NTRS2008

Thermal Expansion Studies of Selected High Temperature Thermoelectric Materials

Radioisotope thermoelectric generators (RTGs) generate electrical power by converting the heat released from the nuclear decay of radioactive isotopes (typically plutonium-238) into electricity using a thermoelectric converter. RTGs have been successfully used to power a number of space missions and have demonstrated their reliability over an extended period of time (tens of years) and are compact, rugged, radiation resistant, scalable, and produce no noise, vibration or torque during operation. System conversion efficiency for state-of-practice RTGs is about 6% and specific power less than or equal to 5.1 W/kg. Higher specific power would result in more on-board power for the same RTG mass, or less RTG mass for the same on-board power. The Jet Propulsion Laboratory has been leading, under the advanced thermoelectric converter (ATEC) project, the development of new high-temperature thermoelectric materials and components for integration into advanced, more efficient RTGs. Thermoelectric materials investigated to date include skutterudites, the Yb14MnSb11 compound, and SiGe alloys. The development of long-lived thermoelectric couples based on some of these materials has been initiated and is assisted by a thermo-mechanical stress analysis to ensure that all stresses under both fabrication and operation conditions will be within yield limits for those materials. Several physical parameters are needed as input to this analysis. Among those parameters, the coefficient of thermal expansion (CTE) is critically important. Thermal expansion coefficient measurements of several thermoelectric materials under consideration for ATEC are described in this paper. The stress response at the interfaces in material stacks subjected to changes in temperature is discussed, drawing on work from the literature and project-specific tools developed here. The degree of CTE mismatch and the associated effect on the formation of stress is highlighted.

silicon germanium↗

NASA NTRS2013

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used.

Smith, T. E. R.↗

NASA NTRS1977

Inclusion of explicit thermal requirements in optimum structural design

A finite-element based procedure is described for obtaining minimum mass designs of structures subjected to combined thermal and mechanical loading and both strength and thermal constraints. The procedure is based on a mathematical programming method using the Sequence of Unconstrained Minimizations Technique (SUMT) in which design requirements are incorporated by an exterior penalty function. The procedure is limited to steady-state temperatures which are controlled by structural sizing only. The optimization procedure is demonstrated by the design of a structural wing box with both mechanical loading and external heating, subject to design constraints on stress, minimum gage, and temperature. The final design for these conditions is compared with a corresponding design in which temperature constraints are omitted.

Adelman, H. M.↗

NASA NTRS1990

Electromagnetic finite elements based on a four-potential variational principle

Electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as primary variable are derived. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are: (1) the number of degrees of freedom per node remains modest as the problem dimensionality increases, (2) jump discontinuities on interfaces are naturally accommodated, and (3) statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady-state forcing conditions. The results are in excellent agreement with analytical solutions.

Schuler, James↗

NASA NTRS1981

Transient catalytic combustor model

A quasi-steady gas phase and thermally thin substrate model is used to analyze the transient behavior of catalytic monolith combustors in fuel lean operation. The combustor response delay is due to the substrate thermal inertia. Fast response is favored by thin substrate, short catalytic bed length, high combustor inlet and final temperatures, and small gas channel diameters. The calculated gas and substrate temperature time history at different axial positions provides an understanding of how the catalytic combustor responds to an upstream condition change. The computed results also suggest that the gas residence times in the catalytic bed in the after bed space are correlatable with the nondimensional combustor response time. The model also performs steady state combustion calculations; and the computed steady state emission characteristics show agreement with available experimental data in the range of parameters covered. A catalytic combustor design for automotive gas turbine engine which has reasonably fast response ( 1 second) and can satisfy the emission goals in an acceptable total combustor length is possible.

Tien, J. S.↗

NASA NTRS1985

Acetylene terminated matrix resins

The synthesis of resins with terminal acetylene groups has provided a promising technology to yield high performance structural materials. Because these resins cure through an addition reaction, no volatile by-products are produced during the processing. The cured products have high thermal stability and good properties retention after exposure to humidity. Resins with a wide variety of different chemical structures between the terminal acetylene groups are synthesized and their mechanical properties studied. The ability of the acetylene cured polymers to give good mechanical properties is demonstrated by the resins with quinoxaline structures. Processibility of these resins can be manipulated by varying the chain length between the acetylene groups or by blending in different amounts of reactive deluents. Processing conditions similar to the state-of-the-art epoxy can be attained by using backbone structures like ether-sulfone or bis-phenol-A. The wide range of mechanical properties and processing conditions attainable by this class of resins should allow them to be used in a wide variety of applications.

Goldfarb, I. J.↗

NASA NTRS1995

Validation of the SINDA/FLUINT code using several analytical solutions

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

Keller, John R.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process: Thermal - 1

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra(sub tau) ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non-uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗