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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1959

Stability of a Horizontal Fluid Layer with Unsteady Heating from Below and Time-Dependent Body Force

The stability of a horizontal layer of fluid in an accelerated container heated unsteadily from below was investigated theoretically, assuming an incompressible fluid with small density changes resulting from heating. The critical Rayleigh numbers based on the over-all density differential are much higher than for the static case, are dependent only on the density distribution, and instantaneous value of the acceleration, and are independent of Prandtl number and rate of change of temperature and body force field. The initial motion corresponds to approximately the same cell shape as for the static case. Rate of transition of temperature perturbations from a stable to an unstable condition is proportional to the rate of increase of the temperature gradient in the region well removed from the walls; rate of transition of the slow motion is proportional to the Prandtl number and rate of increase of the body force field.

Goldstein, Arthur W.↗
NASA NTRS2016

Fluid Shifts: Otoacoustical Emission Changes in Response to Posture and Lower Body Negative Pressure

INTRODUCTION: The purpose of the NASA Fluid Shifts Study is to characterize fluid distribution and compartmentalization associated with long-duration spaceflight and to correlate these findings with vision changes and other elements of the visual impairment and intracranial pressure (VIIP) syndrome. VIIP signs and symptoms, as well as postflight lumbar puncture data, suggest that elevated intracranial pressure (ICP) may be associated with spaceflight-induced cephalad fluid shifts, but this hypothesis has not been tested. Due to the invasive nature of direct measures of ICP, a noninvasive technique of monitoring ICP is desired for use during spaceflight. The phase angle and amplitude of otoacoustic emissions (OAEs) have been shown to be sensitive to posture change and ICP (1, 2), therefore use of OAEs is an attractive option. OAEs are low-level sounds produced by the sensory cells of the cochlea in response to auditory stimulation. These sounds travel peripherally from the cochlea, through the oval window, to the ear canal where they can be recorded. OAE transmission is sensitive to changes in the stiffness of the oval window, occurring as a result of changes in cochlear pressure. Increased stiffness of the oval window largely affects the transmission of sound from the cochlea at frequencies between 800 Hz and 1600 Hz. OAEs can be self-recorded in the laboratory or on the ISS using a handheld device. Our primary objectives regarding OAE measures in this experiment were to 1) validate this method during preflight testing of each crewmember (while sitting, supine and in head-down tilt position), and 2) determine if OAE measures (and presumably ICP) are responsive to lower body negative pressure and to spaceflight. METHODS: Distortion-product otoacoustic emissions (DPOAEs) and transient evoked otoacoustic emissions (TEOAEs) were recorded preflight using the Otoport Advance OAE system (Otodynamics Ltd., Hatfield, UK). Data were collected in four conditions (seated, supine, 15 degrees head down tilt (HDT), and 15 degrees HDT with lower body negative pressure (LBNP)) to produce a range of ICP in each subject and test the susceptibility of OAEs to LBNP. LBNP was induced using the Russian Chibis suit to produce the same fit and pressures that would be experienced inflight during Chibis LBNP trials. Similar trials have occurred inflight on the ISS. A comparative analysis of preflight and inflight phase measurements and magnitudes was completed in both broad and narrow band frequency ranges. RESULTS: TEOAE data demonstrated notable phase shifts from 859-1640 Hz when the seated baseline condition is compared to supine, HDT, and HDT plus Chibis conditions. Changes were particularly pronounced at low frequencies and were consistent with the expected ICP changes. Preflight DPOAE magnitude data revealed changes consistent with increased ICP in two conditions at 1414 Hz, where a magnitude change (relative to the seated condition) was seen in the HDT position and in HDT plus Chibis. DISCUSSION: OAEs revealed systematic changes in phase and magnitude throughout all test conditions (including use of Chibis LBNP) that were consistent with ICP changes. Results indicate that OAEs may provide a rapid noninvasive means of monitoring ICP changes. The first two subjects are projected to complete inflight testing on the ISS in early 2016, with the full complement of 10 subjects scheduled to be complete in 2018.

Melgoza, R.↗
NASA NTRS1996

Magnetothermal Convection in Nonconducting Diamagnetic and Paramagnetic Fluids

Nonuniform magnetic fields exert a magnetic body force on electrically nonconducting classical fluids. These include paramagnetic fluids such as gaseous and liquid oxygen and diamagnetic fluids such as helium. Recent experiments show that this force can overwhelm the force of gravity even at the surface of the earth; it can levitate liquids and gases, quench candle flames, block gas flows, and suppress heat transport. Thermal gradients render the magnetic force nonuniform through the temperature-dependent magnetic susceptibility. These thermal gradients can therefore drive magnetic convection analogous to buoyancy-driven convection. This magnetothermal convection can overwhelm convection driven by gravitational buoyancy in terrestrial experiments. The objectives of the proposed ground-based theoretical study are (a) to supply the magnetothermohydrodynamic theory necessary to understand these recent experiments and (b) to explore the consequences of nonuniform magnetic fields in microgravity. Even the linear theory for the onset of magnetothermal convection is lacking in the literature. We intend to supply the linear and nonlinear theory based on the thermohydrodynamic equations supplemented by the magnetic body force. We intend to investigate the effect of magnetic fields on gas blockage and heat transport in microgravity. Since magnetic fields provide a means of creating arbitrary, controllable body force distributions, we intend to investigate the possibility of using magnetic fields to position and control fluids in microgravity. We also intend to investigate the possibility of creating stationary terrestrial microgravity environments by using the magnetic force to effectively cancel gravity. These investigations may aid in the design of space-based heat-transfer, combustion, and human-life-support equipment.

Edwards, Boyd F.↗
NASA NTRS1993

Conceptual design of a device to measure hand swelling in a micro-gravity environment

In the design of pressurized suits for use by astronauts in space, proper fit is an important consideration. One particularly difficult aspect of the suit design is the design of the gloves. If the gloves of the suit do not fit properly, the grip strength of the astronaut can be decreased by as much as fifty percent. These gloves are designed using an iterative process and can cost over 1.5 million dollars. Glove design is further complicated by the way the body behaves in a micro-gravity environment. In a micro-gravity setting, fluid from the lower body tends to move into the upper body. Some of this fluid collects in the hands and causes the hands to swell. Therefore, a pair of gloves that fit well on earth may not fit well when they are used in space. The conceptual design process for a device which can measure the swelling that occurs in the hands in a micro-gravity environment is described. This process involves developing a specifications list and function structure for the device and generating solution variants for each of the sub functions. The solution variants are then filtered, with the variants that violate any of the specifications being discarded. After acceptable solution variants are obtained, they are combined to form design concepts. These design concepts are evaluated against a set of criteria and the design concepts are ranked in order of preference. Through this process, the two most plausible design concepts were an ultrasonic imaging technique and a laser mapping technique. Both of these methods create a three dimensional model of the hand, from which the amount of swelling can be determined. In order to determine which of the two solutions will actually work best, a further analysis will need to be performed.

Hysinger, Christopher L.↗
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 NTRS1986

Fluid dynamics of unsteady separated flow. I - Bodies of revolution

An analytic method is described that uses static experimental data to predict the separated flow effect on rigid and elastic aerospace-vehicle dynamics. Spike-induced flow separation, nose-induced flow separation, shock-induced flow separation, and base flow effects are studied. It is observed that the time lag occurring before a change of flow conditions causes a statically stabilizing load to produce negative aerodynanamic damping and an unstabilizing load causes a positive aerodynamic damping. The time-lagged quasi-steady theory predictions are compared with dynamic experimental results and good correlation exists for a large variety of vehicle geometries and types of flow separation.

Ericsson, L. E.↗
NASA NTRS1990

Effect of a central redistribution of fluid volume on response to lower-body negative pressure

Cardiovascular responses to lower-body negative pressure (LBNP) were studied following 1 hour of 6-deg head-down tilt to determine whether a redistribution of blood volume toward the central circulation modifies the subsequent response to orthostatic stress. Responses of 12 men, ages 30-39 years, were evaluated by electrocardiography, impedance cardiography, sphygmomanometry, and measurement of calf circumference. During the LBNP that followed head-down tilt, as compared with control LBNP (no preceding head-down tilt) subjects, had smaller stroke volume and cardiac output, greater total peripheral resistance, and less calf enlargement. These differences reflect differences in the variables immediately preceding LBNP. Magnitudes of the responses from pre-LBNP to each pressure stage of the LBNP procedure did not differ between protocols. Mean and diastolic arterial pressures were slightly elevated after LBNP-control, but they fell slightly during LBNP post-tilt.

Tomaselli, Clare M.↗
NASA NTRS1944

The "limiting line" in mixed subsonic and supersonic flow of compressible fluids

It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small viscosity, its effect will be limited in the boundary layer over the solid body and the body will have a drag due to the skin friction. This type of essentially isentropic irrotational flow is generally observed for a streamlined body placed in a uniform stream, if the velocity of the stream is kept below the so-called "critical speed." At the critical speed or rather at a certain value of the ratio of the velocity of the undisturbed flow and the corresponding velocity of sound, shock waves appear. This phenomenon is called the "compressibility bubble." Along a shock wave, the change of state of the fluid is no longer isentropic, although still adiabatic. This results in an increase in entropy of the fluid and generally introduces vorticity in an originally irrotational flow. The increase in entropy of the fluid is, of course, the consequence of changing part of the mechanical energy into heat energy. In other words, the part of fluid affected by the shock wave has a reduced mechanical energy. Therefore, with the appearance of shock waves, the wake of the streamline body is very much widened, and the drag increases drastically. Furthermore, the accompanying change in the pressure distribution over the body changes the aerodynamic moment acting on it and in the case of an airfoil decreases the lift force. All these consequences of the breakdown of isentropic irrotational flow are generally undesirable in applied aerodynamics. Its occurrence should be delayed as much as possible by modifying the shape or contour of the body. However, such endeavor will be very much facilitated if the cause or the criterion for the breakdown can be found first.

MACH NUMBER↗
NASA NTRS2013

High Speed Gear Sized and Configured to Reduce Windage Loss

A gear and drive system utilizing the gear include teeth. Each of the teeth has a first side and a second side opposite the first side that extends from a body of the gear. For each tooth of the gear, a first extended portion is attached to the first side of the tooth to divert flow of fluid adjacent to the body of the gear to reduce windage losses that occur when the gear rotates. The gear may be utilized in drive systems that may have high rotational speeds, such as speeds where the tip velocities are greater than or equal to about 68 m/s. Some embodiments of the gear may also utilize teeth that also have second extended portions attached to the second sides of the teeth to divert flow of fluid adjacent to the body of the gear to reduce windage losses that occur when the gear rotates.

Kunz, Robert F.↗
NASA NTRS2014

Physics-Based Fragment Acceleration Modeling for Pressurized Tank Burst Risk Assessments

As part of comprehensive efforts to develop physics-based risk assessment techniques for space systems at NASA, coupled computational fluid and rigid body dynamic simulations were carried out to investigate the flow mechanisms that accelerate tank fragments in bursting pressurized vessels. Simulations of several configurations were compared to analyses based on the industry-standard Baker explosion model, and were used to formulate an improved version of the model. The standard model, which neglects an external fluid, was found to agree best with simulation results only in configurations where the internal-to-external pressure ratio is very high and fragment curvature is small. The improved model introduces terms that accommodate an external fluid and better account for variations based on circumferential fragment count. Physics-based analysis was critical in increasing the model's range of applicability. The improved tank burst model can be used to produce more accurate risk assessments of space vehicle failure modes that involve high-speed debris, such as exploding propellant tanks and bursting rocket engines.

Acceleration↗
NASA NTRS2015

Development of Long-Lifetime Pulsed Gas Valves for Pulsed Electric Thrusters

It is advantageous for gas-fed pulsed electric thrusters to employ pulsed valves so propellant is only flowing to the device during operation. The propellant utilization of the thruster will be maximized when all the gas injected into the thruster is acted upon by the fields produced by the electrical pulse. Gas that is injected too early will diffuse away from the thruster before the electrical pulse can act to accelerate the propellant. Gas that is injected too late will miss being accelerated by the already-completed electrical pulse. As a consequence, the valve must open quickly and close equally quickly, only remaining open for a short duration. In addition, the valve must have only a small amount of volume between the sealing body and the thruster so the front and back ends of the pulse are as coincident as possible with the valve cycling, with very little latent propellant remaining in the feed lines after the valve is closed. For a real mission of interest, a pulsed thruster can be expected to pulse at least 10(exp 10) - 10(exp 11) times, setting the range for the number of times a valve must open and close. The valves described in this paper have been fabricated and tested for operation in an inductive pulsed plasma thruster (IPPT) for in-space propulsion. In general, an IPPT is an electrodeless space propulsion device where a capacitor is charged to an initial voltage and then discharged, producing a high-current pulse through a coil. The field produced by this pulse ionizes propellant, inductively driving current in a plasma located near the face of the coil. Once the plasma is formed, it can be accelerated and expelled at a high exhaust velocity by the electromagnetic Lorentz body force arising from the interaction of the induced plasma current and the magnetic field produced by the current in the coil. The valve characteristics needed for the IPPT application require a fast-acting valve capable of a minimum of 10(exp 10) valve actuation cycles. Since even 10(exp 9) cycles is well above anything demonstrated, this lower value was selected as the design point for the present work. The valve seal must remain leak-tight throughout operation, and the body must maintain a low internal leakage at relatively high operating temperatures. The full set of design requirements used for this program are summarized in Table 1. In this work, we describe two pulsed gas valves that have been fabricated to have long lifetime and demonstrate the characteristics listed above. The first is a miniaturized, conventional electromagnet-based valve while the second is a piezoelectric-based valve design. The conventional valve, shown in Fig. 1, is opened by use of a solenoid electromagnetic actuator. When current is applied to the solenoid coil, magnetic forces pull the plunger away from the valve seat, allowing fluid to flow through the valve. Removal of electrical current permits the spring and fluid pressure to seat the plunger, halting the flow of fluid. The valve body is fabricated from 304L corrosion resistant steel (CRES) and while the parts that form the magnetic circuit are fabricated from 430 CRES. This material does not have optimum magnetic properties, but its corrosion resistance permits incorporation into a design without requiring an additional plating process. A viton O-ring compound (Parker V0884-75), selected for its mechanical strength at elevated temperatures, was used for the valve seat seal. The design was based solely on the use of analytical sizing calculations, as opposed to a more rigorous finite element analysis. While this valve is small and relatively lightweight, it does not represent a design that is optimized for mass and/or a given volume envelope. The piezoelectric valve is a "puller" valve design. Applying a voltage to the piezo crystal causes it to elongate and pull a pintle off the seat, opening the valve. The valve seal consists of the pintle with an external, spherically-formed tip fabricated from Inconel 625 and the seat fabricated from Inconel 718 and possessing a spherical surface that permits the pintle to align with the valve body centerline after each cycle, maintaining the circumferential metal-on-metal seal. The contact stress on the valve pintle is expected in the worst case to be 96.5 MPa (14 ksi), which is well below the work hardening value of 413.7 MPa (60 ksi) for Inconel 615. Results presented in this work will compare the performance of each valve, both to each other and to the valve design requirements given in Table 1. In general, both valves meet all the performance envelope requirements, but the piezoelectric valve consumes considerably less power and has a faster response time over the conventional solenoid-driven valves.

Burkhardt, Wendel M.↗
NASA NTRS2012

Long Duration Head-Down Tilt Bed Rest Studies: Safety Considerations Regarding Vision Health

Visual symptoms reported in astronauts returning from long duration missions in low Earth orbit, including hyperopic shift, choroidal folds, globe flattening and papilledema, are thought to be related to fluid shifts within the body due to microgravity exposure. Because of this possible relation to fluid shifts, safety considerations have been raised regarding the ocular health of head-down tilt (HDT) bed rest subjects. HDT is a widely used ground ]based analog that simulates physiological changes of spaceflight, including fluid shifts. Thus, vision monitoring has been performed in bed rest subjects in order to evaluate the safety of HDT with respect to vision health. Here we report ocular outcomes in 9 healthy subjects (age range: 27-48 years; Male/Female ratio: 8/1) completing bed rest Campaign 11, an integrated, multidisciplinary 70-day 6 degrees HDT bed rest study. Vision examinations were performed on a weekly basis, and consisted of office-based (2 pre- and 2 post-bed rest) and in-bed testing. The experimental design was a repeated measures design, with measurements for both eyes taken for each subject at each planned time point. Findings for the following tests were all reported as normal in each testing session for every subject: modified Amsler grid, red dot test, confrontational visual fields, color vision and fundus photography. Overall, no statistically significant differences were observed for any of the measures, except for both near and far visual acuity, which increased during the course of the study. This difference is not considered clinically relevant as may result from the effect of learning. Intraocular pressure results suggest a small increase at the beginning of the bed rest phase (p=0.059) and lesser increase at post-bed rest with respect to baseline (p=0.046). These preliminary results provide the basis for further analyses that will include correlations between intraocular pressure change pre- and post-bed rest, and optical coherence tomography measurements of the retina.

Cromwell, Ronita L.↗
NASA NTRS2013

Association Between Cardiovascular and Intraocular Pressure Changes in a 14-Day 6 deg Head Down Tilt (HDT) Bed Rest Study: Possible Implications in Retinal Anatomy

Visual symptoms and intracranial pressure increase reported in astronauts returning from long duration missions in low Earth-orbit are thought to be related to fluid shifts within the body due to microgravity exposure. Because of this possible relation to fluid shifts, studies conducted in head-down tilt (HDT) bed rest are being monitored for potential changes in ocular health. These measures will also serve to determine whether HDT is a suitable ground-based analog to model subclinical cardiovascular and ocular changes that could shed light on the etiology of the VIIP syndrome observed in spaceflight. Sixteen healthy normotensive (12M, 4F, age range 29-54 years), non-smoker and normal weight subjects, volunteered to participate in a 14 day 6 deg head HDT study conducted at the NASA Flight Analogs Research Unit (FARU). This facility provides standard bed rest conditions (diet, wake/sleep time, time allowed in sunlight) during the time that the subjects stay at the FARU. Cardiovascular parameters were obtained in supine posture at BR-5, BR+0, and BR+3 and ocular monitoring was performed weekly. Intraocular pressure (IOP) increased from pre-bed rest BR-3) to the third day into bed rest (BR+3). Values reached a plateau towards the end of the bed rest phase (BR10) and decreased within the first three days of recovery (BR+2) returning to levels comparable to baseline at BR-3. As expected, most cardiovascular parameters were affected by 14 days of HDT bed rest. Plasma volume decreased as a result of bed rest but recovered to baseline levels by BR+3. Indications of cardiovascular deconditioning included increase in both systolic and diastolic blood pressure and heart rate, and a decrease in stroke volume and cardiac output between BR-5 and BR+3. Due to the experimental design of this study, we were not able to test the hypothesis that fluid shifts might be involved in the IOP increase during the bed rest phase, since cardiovascular measures were not available for those time points. There was no correlation between the largest change in IOP (BR-3 versus BR3) and cardiovascular measure changes between baseline (BR-5) and post bed rest (BR+2). While no clinically relevant visual changes were observed during the study, measurement of various retinal parameters was performed with optical coherence tomography (OCT). A decrease in central subfield retinal thickness was observed between BR+2 and baseline at BR-10, but no association was observed with IOP changes. This work investigates the time course of changes in IOP during 14-day HDT bed rest in an attempt to characterize HDT bed rest as a model of the VIIP syndrome and delve into its etiology.

Cromwell, Ronita↗
NASA NTRS1992

Three-dimensional simulation of slender delta wing rock and divergence

Computational simulation of three-dimensional flows around a delta wing undergoing rock and roll-divergence motions is presented. The problem is a multidisciplinary one where fluid-dynamics equations and rigid-body-dynamics equations are sequentially solved. For the fluid-dynamics part, the unsteady Euler equations, which are written relative to a moving frame of reference, are solved using an implicit, approximately-factored, central-difference, finite-volume scheme. For the rigid-body dynamics part, the Euler equation of rigid-body rolling motion is solved using a four-stage Runge-Kutta scheme. Since the applications do not include deforming wings or relative-rigid-body motions, the computational-fluid-dynamics grid, which is fixed in the moving frame of reference, does not need to be updated once it is generated.

Kandil, Osama A.↗