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At least 235 records · Page 13

Theory and computation of optimal low- and medium-thrust transfers

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

Chuang, C.-H.↗

Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila

Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.

HEAT TRANSFER↗

Stagnation Region Heat Transfer: The Influence of Turbulence Parameters, Reynolds Number and Body Shape

The effect of velocity gradient on stagnation region heat transfer augmentation by free stream turbulence was investigated. Heat transfer was measured in the stagnation region of four models with elliptical leading edges with ratios of major to minor axes of 1:1, 1.5:1, 2.25:1, and 3:1. Four geometrically similar, square bar, square mesh, biplane grids were used to generate free stream turbulence with different intensities and length. Heat transfer measurements were made for the following ranges of parameters: Reynolds number, based on leading edge diameter, 37,000 to 228,000; dimensionless leading edge velocity gradient, 1.20 to 1.80; turbulence intensity, 1.1 to 15.9%; and length scale to leading edge diameter ratio, 0.05 to 0.30. Stagnation point heat transfer augmentation by free stream turbulence can be predicted using a modified version of a previously developed correlation for a circular leading edge. Heat transfer augmentation was independent of body shape at the stagnation point. The heat transfer distribution down-stream from the stagnation point can be predicted using the normalized laminar heat transfer distribution.

Vanfossen, G. James↗

Experimental determination of stator endwall heat transfer

Local Stanton numbers were experimentally determined for the endwall surface of a turbine vane passage. A six vane linear cascade having vanes with an axial chord of 13.81 cm was used. Results were obtained for Reynolds numbers based on inlet velocity and axial chord between 73,000 and 495,000. The test section was connected to a low pressure exhaust system. Ambient air was drawn into the test section, inlet velocity was controlled up to a maximum of 59.4 m/sec. The effect of the inlet boundary layer thickness on the endwall heat transfer was determined for a range of test section flow rates. The liquid crystal measurement technique was used to measure heat transfer. Endwall heat transfer was determined by applying electrical power to a foil heater attached to the cascade endwall. The temperature at which the liquid crystal exhibited a specific color was known from a calibration test. Lines showing this specific color were isotherms, and because of uniform heat generation they were also lines of nearly constant heat transfer. Endwall static pressures were measured, along with surveys of total pressure and flow angles at the inlet and exit of the cascade.

Boyle, Robert J.↗

Experimental determination of stator endwall heat transfer

Local Stanton numbers were experimentally determined for the endwall surface of a turbine vane possage. A six vane linear cascade having vanes with an axial chord of 13.81 cm was used. Resutls were obtained for Reynolds numbers based on inlet velocity and axial chord between 75,000 and 495,000. The test section was connected to a low pressure exhaust system. Ambient air was drawn into the test section, inlet velocity was controlled up to a maximum of 59.4 m/sec. The effect of the inlet boundary layer thickness on the endwall heat transfer was determined for a range of test section flow rates. The liquid crystal measurement technique was used to measure heat transfer. Endwall heat transfer was determined by applying electrical power to a foil heater attached to the cascade endwall. The temperature at which the liquid crystal exhibited a specific color was known from a calibration test. Lines showing this specific color were isotherms, and because of uniform heat generation they were also lines of nearly constant heat transfer. Endwall static pressures were measured, along with surveys of total pressure and flow angles at the inlet and exit of the cascade.

Boyle, Robert J.↗

Effects of Yaw on the Heat Transfer to a Blunt Cone-Cylinder Configuration at a Mach Number of 1.98

A heat-transfer investigation has been made on a blunt cone-cylinder model at a Mach number of 1.98 at yaw angles from 0 deg to 9 deg. The results indicate that, except for the hemispherical nose, the heat-transfer coefficient increased on the windward side and decreased on the leeward side as yaw angle was increased. In general, the increase in heat transfer on the windward side was higher than the corresponding decrease on the leeward side. A comparison with theory (NACA Technical Note 4208) yielded agreement which was, in general, within 10 percent on the cone at all test conditions and on the cylinder at an angle of yaw of 0 deg.

English, Roland D.↗

Neural Network Based Optimal Control: Resilience to Missed Thrust Events for Long Duration Transfers

A growing number of spacecraft are continuing to adopt new and more efficient forms of in-space propulsion. One shared characteristic of these high-efficiency propulsion techniques is their limited thrust capabilities. This requires them to thrust continuously for long periods of time, making the spacecraft susceptible to potential missed thrust events. This work demonstrates how neural networks can autonomously correct for missed thrust events during a low-thrust long-duration transfer trajectory. The research applies and tests the developed method to au- tonomously correct a Mars return trajectory. Additionally, methods for improving the response of neural networks to missed thrust events are presented and further investigated.

Laipert, Frank E.↗

High Reynolds number and turbulence effects on aerodynamics and heat transfer in a turbine cascade

Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 million and a range of turbulence intensities from 1.8 to about 15 percent. Fundamental heat transfer and pressure distribution data are obtained over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the SSME turbopump turbines. The results obtained indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a 2D Navier-Stokes code.

Yeh, Frederick C.↗

Surface Pressures and Heat Transfer on Unswept Blunt Plates in Helium at High Mach Numbers

Pressure distributions and local convective heat-transfer coefficients on a flat plate at zero angle of attack were measured in helium. Data were obtained with various amounts of leading-edge bluntness at Mach numbers of 12.5 and 14.7. The pressures on a sharp leading-edged plate were not influenced by the leading edge and were predicted by the first-order, hypersonic, weak-interaction theory. Pressures on blunt plates were correlated by introducing the leading-edge Reynolds number as a parameter. Measured heat-transfer coefficients on the sharp plate agreed with predictions obtained form existing exact solutions for hear transfer across the laminar boundary layer. For the blunt plates a comparison of theory with experiment indicated that more knowledge of the flow field between the sock wave and plate surface is necessary before an adequate prediction of convective heat transfer can be made. Shock-wave shapes for the blun plates at a Mach number 12.5 and zero angle of attack were measured. At distances between 2 and 60 leading-edge thicknesses from the shock vertex, the shock-wave shapes were found to be represented by a modified form of the blast-wave analogy.

Marvin, Joseph G.↗

Analysis of Turbulent Flow and Heat Transfer on a Flat Plate at High Mach Numbers with Variable Fluid Properties

A previous analysis of turbulent heat transfer and flow with variable fluid properties in smooth passages is extended to flow over a flat plate at high Mach numbers, and the results are compared with experimental data. Velocity and temperature distributions are calculated for a boundary layer with appreciative effects of frictional heating and external heat transfer. Viscosity and thermal conductivity are assumed to vary as a power or the temperature, while Prandtl number and specific heat are taken as constant. Skin-friction and heat-transfer coefficients are calculated and compared with the incompressible values. The rate of boundary-layer growth is obtained for various Mach numbers.

Deissler, R. G.↗

Superfluid helium on orbit transfer (SHOOT)

A number of space flight experiments and entire facilities require superfluid helium as a coolant. Among these are the Space Infrared Telescope Facility (SIRTF), the Large Deployable Reflector (LDR), the Advanced X-ray Astrophysics Facility (AXAF), the Particle Astrophysics Magnet Facility (PAMF or Astromag), and perhaps even a future Hubble Space Telescope (HST) instrument. Because these systems are required to have long operational lifetimes, a means to replenish the liquid helium, which is exhausted in the cooling process, is required. The most efficient method of replenishment is to refill the helium dewars on orbit with superfluid helium (liquid helium below 2.17 Kelvin). To develop and prove the technology required for this liquid helium refill, a program of ground and flight testing was begun. The flight demonstration is baselined as a two flight program. The first, described in this paper, will prove the concepts involved at both the component and system level. The second flight will demonstrate active astronaut involvement and semi-automated operation. The current target date for the first launch is early 1991.

Dipirro, Michael J.↗

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

Xiao, X.↗

The 2023 Gold Run in the Injectors

RHIC Run 23 used Gold beam from Tandem with an AGS extraction energy of 9.8 GeV. The same basic setup, 8 single bunch transfers from the Booster and a 12-6 merge in the AGS to provide 4 bunches at extraction, had been used before to deliver Tandem Au to RHIC. But in those cases, it was used for low energy runs (3.85 GeV in 2021 and 5.75 GeV in 2020) where extraction was below transition energy (7.9 GeV). Tandem beam was used for this run because the intensity and stability of EBIS Au did not meet the requirements for RHIC. Physics was first declared in RHIC on May 22 nd and on August 1 st the run was cut short by about 2 months due to a major failure in RHIC. Prior to the advent of EBIS as the preinjector in 2012, 9.8 GeV Tandem Au was regularly delivered to RHIC but the setup in the Booster and AGS was quite different: Four Booster transfers of 6 bunches each were merged into 4 bunches using a 24-12-4 merge scheme. The supercycle length was 6.0 sec before June 29 th when it was extended to 6.6 sec to accommodate EBIS commissioning. The Tandem, Booster, and AGS were on user 1 for the 9.8 GeV setup. Some work with EBIS Au 32+ took place on EBIS, Booster, and AGS user 5 using the standard 9.8 GeV injector setup with a 4 to 1 merge in Booster and a 6-3-1 type merge in AGS. The Siemens motor generator was used for the entire run. An intensity limit of 8.0e9 Au 77+ ions in the AGS was in effect during the run to protect the J7 plunging stripping foil and the Copper absorber of the AGS beam dump. This corresponds to a merged bunch intensity limit of 2.0e9 Au 77+ ions for 4 equal intensity bunches. The per bunch intensity limit can be increased to 2.67e9 by reducing the number of BtA transfers from 8 to 6. There was also a Booster Late intensity limit of 16e9 Au ions in effect to protect the BtA stripping foil from damage due to overheating. Lowering the number of transfers also makes this limit less of a constraint. BtA foil 5, which was installed in 2020 and had not been used regularly prior to this run was used all run and showed no obvious signs of deterioration. In May, a Tandem Au 3.85 GeV setup from 2021 was also re-established on AGS user 2. It was used for APEX on May 24 and July 26. Initial work with 3.85 GeV beam was on May 19. Proton beam was also set up during the run and extracted to W dump on July 10. It was used for APEX on July 12. Although the OPPIS source was used the AGS setup was without snakes.

43 PARTICLE ACCELERATORS↗

Experimental Investigation of Free-Convection Heat Transfer in Vertical Tube at Large Grashof Numbers

Report presents the results of an investigation conducted to study free-convection heat transfer in a stationary vertical tube closed at the bottom. The walls of the tube were heated, and heated air in the tube was continuously replaced by fresh cool air at the top. The tube was designed to provide a gravitational field with Grashof numbers of a magnitude comparable with those generated by the centrifugal field in rotating-blade coolant passages (10(8) to 10(13)). Local heat-transfer coefficients in the turbulent-flow range and the temperature field within the fluid were obtained.

Eckert, E R G↗

Chemical and thermal nonequilibrium heat transfer analysis for hypervelocity, low Reynolds number flow

Chemical and thermal nonequilibrium phenomena are studied in the stagnation region of a hypervelocity blunt body. This investigation is motivated by the need to predict the heat transfer rate to the leading edge of Aeromaneuvering Orbital Transfer Vehicles. Flight speeds of approximately 10 km/s at altitudes of approximately 80 km are considered for body radii of 1 to 50 cm. The analysis is based on continuum theory and is applicable to the viscous-layer and incipient-merged-layer rarefied-flow regimes. A two-species, two-temperature gas model is assumed. Comparisons are made with previous theories, experimental data, and results based on the thermodynamic equilibrium assumption. The equation accounting for vibrational nonequilibrium is presented and its effects on flow properties are discussed. Parameters which require further investigation are identified. Preliminary results indicate that the inclusion of vibrational relaxation has little effect on heat transfer rate for a catalytic surface. However, vibrational nonequilibrium may increase the heat transfer rate to a noncatalytic surface, depending on the degree of nonequilibrium.

Brown, K. G.↗

Heat transfer on a flat plate in continuum to rarefied hypersonic flows at Mach numbers of 19.2 and 25.4

Local heat transfer rates were measured on a flat steel plate (10 in. wide and 16 in. long) with sharp and blunt leading edges (0.001 and 0.010 in.) in the transition from the strong interaction boundary layer regime with no slip at the surface to the free molecule regime. The tests were conducted in a combustion driven hypersonic shock tunnel, with the nominal free stream Mach numbers of 19.2 and 25.4, and a reflected stagnation temperature of approximately 2340 R. The twelve heat transfer gages were made of platinum sputtered on a Pyrex backing to a thickness of approximately 350 A, insulated by a silicone dioxide film. For both Mach numbers the heat transfer data agreed reasonably well with the strong interaction prediction of Li and Nagamatsu (1953, 1955) for unit Reynolds numbers greater than approximately 100,000 and leading edge Knudsen numbers less than approximately 4. At lower density conditions the rarefied flow effects began to dominate the flow phenomena near the leading edge region of the sharp flat plate. A systematic reduction in the heat transfer rate close to the leading edge was observed for both Mach number tests as the leading edge density was reduced and the mean free path was increased.

Nagamatsu, H. T.↗