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At least 721 records · Page 40

Rotorcraft application of advanced computational aerodynamics

The objective was to develop the capability to compute the unsteady viscous flow around rotor-body combinations. In the interest of tractability, the problem was divided into subprograms for: (1) computing the flow around a rotor blade in isolation; (2) computing the flow around a fuselage in isolation, and (3) integrating the pieces. Considerable progress has already been made by others toward computing the rotor in isolation (Srinivasen) and this work focused on the remaining tasks. These tasks required formulating a multi-block strategy for combining rotating blades and nonrotating components (i.e., a fuselage). Then an appropriate configuration was chosen for which suitable rotor body interference test data exists. Next, surface and volume grids were generated and state-of-the-art CFD codes were modified and applied to the problem.

Stanaway, Sharon↗

An improved three-dimensional aerodynamics model for helicopter airloads prediction

The importance of unsteady aerodynamic effects due to rotor blade motion is demonstrated for a helicopter in high-speed forward flight. These unsteady effects are modeled as surface boundary conditions to a three-dimensional, unsteady Computational Fluid Dynamics (CFD) code called the Full-Potential Rotor Code (FPR). These boundary conditions cause significant changes in the computed lift and pitching moment at the front and rear of the rotor disk. Airloads from the modified FPR code are then iteratively coupled with the helicopter comprehensive code, CAMRAD/JA. Computed airloads show good agreement with flight-test data when lift values from the FPR code are used in the coupled calculation. However, the computed airloads from CAMRAD/JA along also show good agreement with the experimental data. Thus for this case one cannot demonstrate a significant improvement in computed airloads with the hybrid coupled scheme. The addition of the pitching moment values from the FPR code into the CAMRAD/JA calculation slows down the overall iterative convergence and does not yield any improvement in the final results.

Strawn, Roger C.↗

The 1991 version of the plume impingement computer program. Volume 2: User's input guide

The Plume Impingement Program (PLIMP) is a computer code used to predict impact pressures, forces, moments, heating rates, and contamination on surfaces due to direct impingement flowfields. Typically, it has been used to analyze the effects of rocket exhaust plumes on nearby structures from ground level to the vacuum of space. The program normally uses flowfields generated by the MOC, RAMP2, SPF/2, or SFPGEN computer programs. It is capable of analyzing gaseous and gas/particle flows. A number of simple subshapes are available to model the surfaces of any structure. The original PLIMP program has been modified many times of the last 20 years. The theoretical bases for the referenced major changes, and additional undocumented changes and enhancements since 1988 are summarized in volume 1 of this report. This volume is the User's Input Guide and should be substituted for all previous guides when running the latest version of the program. This version can operate on VAX and UNIX machines with NCAR graphics ability.

Bender, Robert L.↗

Numerical Modeling of Liquid-Vapor Phase Change

We implemented a two- and three-dimensional finite difference/front tracking technique to solve liquid-vapor phase change problems. The mathematical and the numerical features of the method were explained in great detail in our previous reports, Briefly, we used a single formula representation which incorporated jump conditions into the governing equations. The interfacial terms were distributed as singular terms using delta functions so that the governing equations would be the same as conventional conservation equations away from the interface and in the vicinity of the interface they would provide correct jump conditions. We used a fixed staggered grid to discretize these equations and an unstructured grid to explicitly track the front. While in two dimensions the front was simply a connection of small line segments, in three dimensions it was represented by a connection of small triangular elements. The equations were written in conservative forms and during the course of computations we used regriding to control the size of the elements of the unstructured grid. Moreover, we implemented a coalescence in two dimensions which allowed the merging of different fronts or two segments of the same front when they were sufficiently close. We used our code to study thermocapillary migration of bubbles, burst of bubbles at a free surface, buoyancy-driven interactions of bubbles, evaporation of drops, rapid evaporation of an interface, planar solidification of an undercooled melt, dendritic solidification, and a host of other problems cited in the reference.

Esmaeeli, Asghar↗

Structural and Acoustic Numerical Modeling of a Curved Composite Honeycomb Panel

The finite and boundary element modeling of the curved section of a composite honeycomb aircraft fuselage sidewall was validated for both structural response and acoustic radiation. The curved panel was modeled in the pre-processor MSC/PATRAN. Geometry models of the curved panel were constructed based on the physical dimensions of the test article. Material properties were obtained from the panel manufacturer. Finite element models were developed to predict the modal parameters for free and supported panel boundary conditions up to a frequency of 600 Hz. Free boundary conditions were simulated by providing soft foam support under the four comers of the panel or by suspending the panel from elastic bands. Supported boundary conditions were obtained by clamping the panel between plastic tubing seated in grooves along the perimeter of a stiff and heavy frame. The frame was installed in the transmission loss window of the Structural Acoustic Loads and Transmission (SALT) facility at NASA Langley Research Center. The structural response of the curved panel due to point force excitation was predicted using MSC/NASTRAN and the radiated sound was computed with COMET/Acoustics. The predictions were compared with the results from experimental modal surveys and forced response tests on the fuselage panel. The finite element models were refined and updated to provide optimum comparison with the measured modal data. Excellent agreement was obtained between the numerical and experimental modal data for the free as well as for the supported boundary conditions. Frequency response functions (FRF) were computed relating the input force excitation at one panel location to the surface acceleration response at five panel locations. Frequency response functions were measured at the same locations on the test specimen and were compared with the calculated FRF values. Good agreement was obtained for the real and imaginary parts of the transfer functions when modal participation was allowed up to 3000 Hz. The validated finite element model was used to predict the surface velocities due to the point force excitation. Good agreement was obtained between the spatial characteristics of the predicted and measured surface velocities. The measured velocity data were input into the acoustic boundary element code to compute the sound radiated by the panel. The predicted sound pressure levels in the far-field of the panel agreed well with the sound pressure levels measured at the same location.

Grosveld, Ferdinand W.↗

Meteoroid Risk Assessment of Lunar Habitat Concepts

Preliminary analyses have been performed of meteoroid impacts on lunar surface structures built with elements made from in situ materials. The SPHC hydrodynamic code was used to simulate impacts, and was validated against hypervelocity impact test results. Impact risk will affect necessary wall thicknesses, depth of burial, and placement of lunar base structures.

Evans, Steven W.↗

Lunar Solar Origins Exploration (LunaSOX)

The Moon offers a unique vantage point from which to investigate the Sun and its interaction via the solar wind magnetic fields, plasma, and energetic particles with the geospace system including the Moon itself. The lunar surface and exosphere provide in part a record of solar coronal plasma material input and resultant space weathering over billions of years. The structure and dynamics of solar wind interactions with the Moon provide an accessible near-Earth laboratory environment for study of general solar wind interactions with the vast multitude of airless asteroidal bodies of the inner solar system. Spacecraft in lunar orbit have the often simultaneous opportunity, except when in the Earth's magnetosphere, to make in-situ compositional measurements of the solar wind plasma and to carry out remote observations from the Moon of the solar corona, potentially enabled by lunar limb occultation of the solar disk. The LunaSOX project at NASA Goddard Space Flight Center is addressing these heliophysical science objectives from and of the Moon with support from NASA's Lunar Advanced Science and Exploration Research (LASER) program: (1) specify history of solar wind parameters at and sunward of the Moon through enhanced access (http://lunasox.gsfc.nasa.gov/) to legacy and operational mission data products from the Apollo era to the present, (2) model field and plasma interactions with the lunar surface, exosphere, and wake, as constrained by the available data, through hybrid kinetic code simulations, and (3) advance mission concepts for heliophysics from and of the Moon.

Cooper, John F.↗

Radiant Heating Tests on Meteoritic Material

A new effort geared toward modeling the physics of meteor entry and break-up is underway at NASA Ames Research Center. This is part of a broader interdisciplinary effort on providing physics-based risk assessment models for potentially hazardous objects. As part of the entry modeling task we are seeking to improve our understanding of, among other things, the ablation of meteoric material during high speed entry into earths atmosphere. Meteoroid entry differs greatly in some key respects from spacecraft entry modeling. First, the aerothermal environment at these high velocities (18 km/s) is dominated by radiation. Second, meteoroids less than, say, 50m in size, will likely lose a significant portion of their mass during the high-speed atmospheric entry process due to vaporization as well as melting and spallation. The mass of the object, in turn, directly affects the amount of energy deposited in the atmosphere, and therefore the amount of damage done. Thus it is important for us to understand and be able to model this process in greater detail in order to assess the hazard posed by these objects.In this presentation, we first give an overview of the simple ablation models that are typically used in meteor entry calculations. Additionally, we will present a new model which utilizes a similar approach to what is typically done for spacecraft TPS response modeling. This uses an equilibrium assumption near the surface to compute the ablation rate, as is done in heritage material response codes. Next we describe the radiant heating experiment which uses a high-powered laser to emulate the radiation dominated heating environment experienced by meteoroids during atmospheric entry. The facility the Laser Hardened Material Evaluation Laboratory (LHMEL) permits us to expose samples of meteoritic material to heating rates in excess of 100kW/sq.cm. An overview of the experimental set-up and test plan for the initial exploratory campaign at this facility will be given. Then we present both qualitative and quantitative results from this initial test series. Comparisons between predicted and measured ablation rates suggest that there may be significant blockage of the incident beam by the ablation plume. Furthermore, melt is shown to be a significant ablation mechanics, even at high heating rates (16 kW/sq.cm). Finally, comparisons between the phenomenology of the ablation of terrestrial rocks namely, basalt -- to that of meteorites show very different behavior. This is shown to likely be due in part to the effect of composition on the melt viscosity.

Stern, Eric↗

Magnetohydrodynamics (MHD) Aerocapture System for Enabling Faster-Larger Planetary Science & Human Exploration Missions

Since our completing the NIAC Phase I NIAC on this Advanced Aerocapture System, NASA Langley Research Center has funded or supported a number of studies and code enhancements through its Center Innovation Fund (CIF) and NASA’s NSTGRO and Internship Programs to mature the analysis capabilities and quantify the merits of the MHD Aerocapture System technology. These efforts have resulted in a plug and play analysis capability for assessing MHD aerocapture system performance for arrival at many planetary bodies of interest. Our efforts have especially focused on the potential mass savings for improving the capacity for science observations at Neptune and Triton. A re-cent Forbes article published “‘Orbital mechanics is probably going to decide for us whether we go to Uranus or Neptune because we need to flyby Jupiter,’ said Kunio Sayanagi at Hampton University, Virginia, who also worked on the Neptune Odyssey proposal…. Exactly when a mission can be sent to Uranus, or Neptune, depends on the relative position of Jupiter, which can help give a spacecraft a gravitational slingshot. That drastically shortens the cruise phase.” [1] Since shortening the cruise phase is important for these science missions, any mass savings enabled by the MHD Aerocapture System could be reallocated to increasing Thermal Protection System mass to allow faster arrival speeds and/or for onboarding additional payloads such as science instruments, batteries, or propellant for conducting more science for longer durations in the desired orbits. The analysis steps and codes for conducting trades and sizing vehicles for aerocapture are as follows: Step 1 is to conduct aeroheating analysis using LAURA of the selected entry vehicle shape to identify locations on the forebody where ionization and flow velocity are sufficient for producing Lo-rentz forces. LAURA is a multiblock structured grid finite-volume CFD solver developed at the NASA Langley Research Center. [2] LAURA has been used for aerothermal analysis support of the entry, de-scent and landing (EDL) phase of interplanetary missions over the last three decades [3-7]. Step 2 is to port the LAURA results into CFDWARP to calcu-late electrical and thermal conductivities of ionized flow for sizing MHD patch system and calculating Lorentz forces needed for controls analysis. CFDWARP is a CFD code that uses advanced nu-merical methods that enable the simulation of the full coupling between the aerodynamics, the magne-tohydrodynamics, and the non-neutral plasma sheaths. CFDWARP has the unique capability to simulate efficiently the non-neutral sheaths (near the electrodes) in coupled form with the quasi-neutral bulk MHD flow [8-11]. Step 3 is to link re-sults from LAURA and CFDWARP into POST2 for calculating entry trajectories and comparing MHD control results with other aerodynamic control strategies. The Program to Optimize Simulated Tra-jectories II (POST2) is a generalized point mass, discrete parameter targeting and optimization pro-gram. POST2 provides the capability to target and optimize point mass trajectories for multiple pow-ered or un-powered vehicles near an arbitrary rotat-ing, oblate planet [12]. Step 4: TPS sizing was per-formed using the Fully Implicit Ablation and Ther-mal-response code (FIAT) tool which computes the transient one-dimensional thermal response and surface thermochemistry of a multilayer stackup of thermal protection, bonding, and structural materi-als subject to aeroheating on one surface [13]. The sizing and margining methodology used was based on the approach documented by Mahzari and Milos [14] for the dual-layered heatshield for extreme entry environment technology (DL-HEEET) TPS concept. TPS analysis utilizes trajectory information from POST2. Using this step-wise plug and play MHD Aerocapture performance assessment process, our analysis targets a Neptune aerocapture trajectory that will place the spacecraft in an observation orbit for Triton. [15]. Magnetohydrodynamic (MHD) control of a 4.5-meter diameter MSL-style capsule resulted in TPS mass savings of nearly 2000 kg when using an MHD system mass of under 200 kg. The flight path for a vehicle using the MHD control strategy has a much lower heat rate and heat load compared to the conventional aerodynamic aerocapture strategies known as bank angle con-trolled (BAC) and direct force controlled (DFC). Both BAC and DFC have heat rates significantly greater than 1500 W/cm2 typically used as an upper limit for PICA. Thus, DL-HEEET TPS concept was required for the BAC and DFC control strategies. However, considering the more benign environ-ments for the MHD case, additional TPS concepts with improved mass efficiency were also assessed. PICA was considered for the MHD controlled strat-egy since the maximum heat rate was well within the limits (<1500 W/cm2) of PICA. TPS sizing re-sulted in a significant mass reduction. The PICA layer for this sizing case was about 7.8 cm. As a point of reference, the Mars 2020 mission, which used this same PICA concept, had a PICA thickness of 3.18 cm [16]. The trajectories used for the TPS sizing originat-ed from the POST2 simulations. The current, I, to an electromagnet configuration can be manipulated to allow for active control of the vehicle. Manipula-tion of the current, I, changes the magnetic field, B, which affects the Lorentz force and therefore the MHD drag force on the vehicle. Our analysis in-cluded both open-loop and close-loop control. Closed-loop control will enable improved overall performance when taking into account mission level uncertainties, such as interplanetary delivery errors and atmospheric modeling uncertainties. The open-loop and closed-loop MHD control cases do not dip as deep into the atmosphere as the aerodynamic cases. Three types of aerodynamic-only approach-es are investigated: bank angle modulation (BAM), director force control (DFC), and Drag Modulated. BAM and DFC make use of vehicle aerodynamic angles to steer the vehicle. Thus, changing the aer-odynamic forces acting on the vehicle for control, aerodynamic drag modulated case requires a vary-ing drag area to modulate the drag force. The MHD drag modulated case modulates MHD generated drag force that adds to the aerodynamic drag. This higher atmospheric activation of drag forces by the MHD patch results in significantly less heat flux on the vehicle. The MHD technology will enable shorter cruise times and deceleration of larger payloads for increasing the capacity for science at the Ice Giants or for returning astronauts to Earth from cislunar space or from Mars. The purpose of this presentation is to provide more details about this work and to highlight plans for further research and development including a flight demonstration.

R. W. Moses↗

Radiation protection using Martian surface materials in human exploration of Mars

To develop materials for shielding astronauts from the hazards of GCR, natural Martian surface materials are considered for their potential as radiation shielding for manned Mars missions. The modified radiation fluences behind various kinds of Martian rocks and regolith are determined by solving the Boltzmann equation using NASA Langley's HZETRN code along with the 1977 Solar Minimum galactic cosmic ray environmental model. To develop structural shielding composite materials for Martian surface habitats, theoretical predictions of the shielding properties of Martian regolith/polyimide composites has been computed to assess their shielding effectiveness. Adding high-performance polymer binders to Martian regolith to enhance structural properties also enhances the shielding properties of these composites because of the added hydrogenous constituents. Heavy ion beam testing of regolith simulant/polyimide composites is planned to validate this prediction. Characterization and proton beam tests are performed to measure structural properties and to compare the shielding effects on microelectronic devices, respectively.

NASA Center LaRC↗

Parametric Studies of the Ejector Process within a Turbine-Based Combined-Cycle Propulsion System

Performance characteristics of the ejector process within a turbine-based combined-cycle (TBCC) propulsion system are investigated using the NPARC Navier-Stokes code. The TBCC concept integrates a turbine engine with a ramjet into a single propulsion system that may efficiently operate from takeoff to high Mach number cruise. At the operating point considered, corresponding to a flight Mach number of 2.0, an ejector serves to mix flow from the ramjet duct with flow from the turbine engine. The combined flow then passes through a diffuser where it is mixed with hydrogen fuel and burned. Three sets of fully turbulent Navier-Stokes calculations are compared with predictions from a cycle code developed specifically for the TBCC propulsion system. A baseline ejector system is investigated first. The Navier-Stokes calculations indicate that the flow leaving the ejector is not completely mixed, which may adversely affect the overall system performance. Two additional sets of calculations are presented; one set that investigated a longer ejector region (to enhance mixing) and a second set which also utilized the longer ejector but replaced the no-slip surfaces of the ejector with slip (inviscid) walls in order to resolve discrepancies with the cycle code. The three sets of Navier-Stokes calculations and the TBCC cycle code predictions are compared to determine the validity of each of the modeling approaches.

Georgiadis, Nicholas J.↗

Particle-In-Cell Simulations of the Solar Wind Interaction with Lunar Crustal Magnetic Anomalies: Magnetic Cusp Regions

As the solar wind is incident upon the lunar surface, it will occasionally encounter lunar crustal remanent magnetic fields. These magnetic fields are small-scale, highly non-dipolar, have strengths up to hundreds of nanotesla, and typically interact with the solar wind in a kinetic fashion. Simulations, theoretical analyses, and spacecraft observations have shown that crustal fields can reflect solar wind protons via a combination of magnetic and electrostatic reflection; however, analyses of surface properties have suggested that protons may still access the lunar surface in the cusp regions of crustal magnetic fields. In this first report from a planned series of studies, we use a 1 1/2-dimensional, electrostatic particle-in-cell code to model the self-consistent interaction between the solar wind, the cusp regions of lunar crustal remanent magnetic fields, and the lunar surface. We describe the self-consistent electrostatic environment within crustal cusp regions and discuss the implications of this work for the role that crustal fields may play regulating space weathering of the lunar surface via proton bombardment.

Solar↗

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Navier↗

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.↗

Some recent applications of Navier-Stokes codes to rotorcraft

Many operational limitations of helicopters and other rotary-wing aircraft are due to nonlinear aerodynamic phenomena incuding unsteady, three-dimensional transonic and separated flow near the surfaces and highly vortical flow in the wakes of rotating blades. Modern computational fluid dynamics (CFD) technology offers new tools to study and simulate these complex flows. However, existing Euler and Navier-Stokes codes have to be modified significantly for rotorcraft applications, and the enormous computational requirements presently limit their use in routine design applications. Nevertheless, the Euler/Navier-Stokes technology is progressing in anticipation of future supercomputers that will enable meaningful calculations to be made for complete rotorcraft configurations.

Mccroskey, W. J.↗

Unsteady Aerodynamic Force Sensing from Measured Strain

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing built and tested at the NASA Langley Research Center (Hampton, Virginia, USA) in 1959 is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics (CFD) code and an MSC/NASTRAN code (MSC Software Corporation, Newport Beach, California, USA), and these CFL3D-based results are assumed as measured quantities. Based on the measured strains, wing deflections, velocities, accelerations, and aerodynamic forces are computed using the proposed approach. These computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. In general, computed aerodynamic forces based on the lifting surface theory in subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. Excellent aeroelastic responses are obtained even with unsteady strain data under the signal to noise ratio of -9.8dB. The deflections, velocities, and accelerations at each sensor location are independent of structural and aerodynamic models. Therefore, the distributed strain data together with the current proposed approaches can be used as distributed deflection, velocity, and acceleration sensors. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data. An active induced drag control system thus can be designed using the two computed aerodynamic forces, induced drag and lift, to improve the fuel efficiency of an aircraft. Interpolation elements between structural finite element grids and the CFD grids and centroids are successfully incorporated with the unsteady aeroelastic computation scheme. The most critical technology for the success of the proposed approach is the robust on-line parameter estimator, since the least-squares curve fitting method depends heavily on aeroelastic system frequencies and damping factors.

shape sensing↗

Recent Results in the Study of Static Ground Effect Using an Inviscid Unstructured Grid Code

The TetrUSS (Tetrahedral Unstructured Software System), developed at NASA LaRC, enables one to take a vehicle from its surface definition to its analyzed solution. The important parts are the shape definition, accomplished in GRIDTOOL; the initial front and volume grid generation in VGRID; the flow solver USM3D, and the various ways used to post-process the computational results.

Yaros, Steven F.↗

Program Computes Dendrite-Settling Velocities

DENDRIFT computer code calculates settling velocities of metal-alloy crystals of various shapes. Also calculates number of other parameters of interest such as volume and surface area of dendrite. Exploits concept of envelope around dendrite to enable calculation of effective sphericity. Program also used to estimate settling velocities of spheres and cylinders with hemispherical ends. Code useful as subprogram in comprehensive solidification/casting code. Concepts widely applicable in chemical-processing industry, helping describe settling or floating of precipitates and flocs. Written in FORTRAN 77.

De Groh, Henry, III↗